{
    "url": "http://arxiv.org/abs/2404.16926v1",
    "title": "Observational predictions for the survival of atomic hydrogen in simulated Fornax-like galaxy clusters",
    "abstract": "The presence of dense, neutral hydrogen clouds in the hot, diffuse\nintra-group and intra-cluster medium is an important clue to the physical\nprocesses controlling the survival of cold gas and sheds light on cosmological\nbaryon flows in massive halos. Advances in numerical modeling and observational\nsurveys means that theory and observational comparisons are now possible. In\nthis paper, we use the high-resolution TNG50 cosmological simulation to study\nthe HI distribution in seven halos with masses similar to the Fornax galaxy\ncluster. Adopting observational sensitivities similar to the MeerKAT Fornax\nSurvey (MFS), an ongoing HI survey that will probe to column densities of\n$10^{18}$ cm$^{-2}$, we find that Fornax-like TNG50 halos have an extended\ndistribution of neutral hydrogen clouds. Within one virial radius, we predict\nthe MFS will observe a total HI covering fraction around $\\sim$ 12\\% (mean\nvalue) for 10 kpc pixels and 6\\% for 2 kpc pixels. If we restrict this to gas\nmore than 10 half-mass radii from galaxies, the mean values only decrease\nmildly, to 10\\% (4\\%) for 10 (2) kpc pixels (albeit with significant\nhalo-to-halo spread). Although there are large amounts of HI outside of\ngalaxies, the gas seems to be associated with satellites, judging both by the\nvisual inspection of projections and by comparison of the line of sight\nvelocities of galaxies and intracluster HI.",
    "authors": "Avinash Chaturvedi, Stephanie Tonnesen, Greg L. Bryan, Gerg\u00f6 Popping, Michael Hilker, Paolo Serra, Shy Genel",
    "published": "2024-04-25",
    "updated": "2024-04-25",
    "primary_cat": "astro-ph.GA",
    "cats": [
        "astro-ph.GA"
    ],
    "label": "Original Paper",
    "paper_cat": "Diffusion AND Model",
    "gt": "1. The formation and evolution of galaxies is now under- stood to be strongly linked with the diffuse gas filling their dark matter halos. Depending on galaxy mass, this gas is called the circumgalactic medium (CGM) when the gas resides in the halos of galaxies of the Milky Way mass or lower, or the intracluster medium (ICM) for gas living in more massive cluster-sized halos (Mtot \u22731014 M\u2299). Various physical processes, such as gas accretion from the intergalactic medium, and feedback driven by stars and AGN, occur in this gaseous halo. These pro- cesses drive flows which regulate the rate at which gas cools on to the galaxy itself, controlling the amount of mass in the interstellar medium and hence the rate of star formation itself, including possibly quenching (see avi.chaturvedi@aip.de Tumlinson et al. 2017, for a review). Therefore, under- standing the physical processes in the CGM or ICM is crucial to building a comprehensive picture of galaxy evolution. We highlight here the important question of the origin and survival of cold gas in the hot ICM, by studying the phase-space distribution of cold gas in massive halos at low redshift, with a particular focus on the observability of this gas in ongoing and future HI surveys. For low-mass, star-forming galaxies, it is expected that their halo can host an abundant amount of cold gas that may be the fuel for future star formation. The halos of massive galaxies, on the other hand, may lack cold gas, resulting in the lack of any recent star for- mation activity (Gauthier & Chen 2011). In addition, current observational (Chen et al. 2018; Berg et al. 2019; Zahedy et al. 2019) and simulation studies (Dav\u00b4 e et al. 2020; Rahmati et al. 2015; Nelson et al. 2020) suggest that at intermediate redshift (0.3 \u2264z \u22640.8), massive ha- arXiv:2404.16926v1  [astro-ph.GA]  25 Apr 2024 2 los have a significant amount of cold gas. For example, Chen et al. (2018); Zahedy et al. (2019) studied lumi- nous red galaxies (LRG) at redshift z \u223c0.21-0.55 and found that these galaxies host a high column density of the cold gas tracers HI and MgII. Other similar stud- ies point toward the same conclusion that LRGs host an abundant amount of cold gas (Zhu et al. 2014; Lan & Mo 2018; Anand et al. 2021, 2022). At low-redshift, simulation studies of Milky Way-like galaxies show that their CGM also host substantial amounts of cold gas (van de Voort et al. 2019). Recently, simulations have made improved predictions for the cold gas distribution in halos that reproduce many of the observed galactic properties. For example, Nelson et al. (2020) have shown that cold gas in the ha- los of LRGs can be attributed to the thermal instability triggered by local density perturbations. They suggest that these perturbations are related to gas stripped from infalling galaxies via tidal interactions, or ram pressure stripping. Performing a comparative study between cos- mological and idealized simulations (individual galaxy halo simulations), Fielding et al. (2020) have also shown that cold gas extends to the virial radius for Milky Way- mass halos. They also suggest that non-spherical accre- tion and satellite galaxies contribute to the cold gas con- tent in the outer halos. Previously, Villaescusa-Navarro et al. (2018) performed a detailed study using the Il- lustris TNG100 simulation, investigating the HI abun- dance and clustering properties in halos for z \u22645. They showed that HI density profiles are sensitive to various processes such as AGN feedback and tidal stripping. For massive halos, they found that HI is mostly concentrated in their satellite galaxies, whereas for small halos it is concentrated in the central galaxy. In contrast to intermediate redshifts, the study of cold gas in the ICM of massive halos (M\u2217\u22651011 M\u2299) in the local Universe (z \u223c0) is limited to a few studies. Nonetheless, using the HI 21 cm emission line, radio observations have demonstrated the abundant existence of cold neutral atomic gas around early-type galaxies (E/S0) galaxies (Serra et al. 2012, 2013b; Young et al. 2014; Serra et al. 2013a). However, these observations are limited to tens of kpc around the targeted galax- ies and are typically not sensitive to HI column densi- ties below \u22641019 cm\u22122, and therefore do not provide a comprehensive picture of the cold gas in the ICM. The ongoing observations from the MeerKAT Fornax survey (hereafter MFS, Serra et al. 2019; Serra et al. 2023), a radio continuum and line survey of the Fornax cluster, provides an excellent opportunity to study the HI gas in great detail in the nearby Fornax ICM (d \u223c20 Mpc). Photometric and spectroscopic studies (Cantiello et al. 2020; Chaturvedi et al. 2022) have shown that the Fornax cluster mass assembly is still ongoing, making it an interesting target to study. MFS is dedicated to studying the HI distribution and kinematics within the Fornax environment. The HI column density sensitiv- ity of the MFS ranges from \u223c5\u00d71019 cm\u22122 at a spatial resolution of \u223c10 arcsec (\u223c1 kpc at Fornax distance) down to 1018 cm\u22122 at \u223c100 arcsec (\u223c10 kpc at For- nax distance). With a mosaic area of the 12 square degrees, MFS will detect HI in the Fornax intracluster (hereafter IC) region - which in this paper refers to the region within the massive dark matter halo and outside satellite galaxies. The high-resolution TNG50 cosmological simulations (Nelson et al. 2019; Pillepich et al. 2019) provide a me- dian spatial resolution of \u223c100 parsec and its validation of cold gas (neutral and molecular hydrogen) against observational work (Popping et al. 2019; Diemer et al. 2019) makes TNG50 an ideal framework to explore the cold gas distribution in Fornax-like halos. This also pro- vides a chance to forecast the upcoming MFS survey results and test the simulations against the MFS obser- vations. In this work, we use the TNG50 simulations (Nelson et al. 2019; Pillepich et al. 2019) and adopt the observing criteria of the MFS to study the HI content in the TNG50 halos similar to the Fornax galaxy cluster. We also study the HI distribution in these halos and their IC region. We calculate the HI covering fraction for these halos and predict the expected observed MFS HI covering fraction. In addition, both the spatial and velocity distribution of HI gas in the ICM of clusters and groups can be used to gain insight into the origin and survival of this cold gas. If the gas is correlated in both position and velocity with satellites, we can argue that the HI is likely either stripped from satellites or cooling is induced by satel- lites. However, if cold gas is not correlated with satel- lite galaxy positions or velocities, we might argue that either cold gas formation is related to the central galaxy or that cold gas survives in the ICM long enough to be- come virialized (e.g., Voit et al. 2017; Rohr et al. 2023). In this paper we take the first step of making these spa- tial and velocity maps, leaving gas particle tracking to future work. The paper is organized as follows: In section 2, we briefly introduce the TNG50 simulation and present the methodology for calculating the HI covering fraction. Section 3 presents our results about the HI distribution and its covering fraction. In section 4, we compare our results to current simulation (Section 4.1) and observa- tional (Section 4.2) studies, and discuss the likely origin of the cold gas in the intracluster medium of Fornax-like 3 halos (Section 4.3). Section 5 presents the summary of the work. 2. SIMULATION AND METHODOLOGY This section briefly introduces the TNG50 simulation that we use for our analysis as well as our criteria for selecting Fornax-like halos. In addition, we present our methodology for calculating the HI column density and HI covering fraction of the selected halos in TNG50 in order to compare to observational surveys. 2.1. The TNG simulations For our study, we use the TNG50 simulation (Nelson et al. 2019; Pillepich et al. 2019), the highest resolution simulation of the IllustrisTNG cosmological magneto- hydrodynamical (MHD) simulation suite (Nelson et al. 2018; Springel et al. 2018; Pillepich et al. 2018; Mari- nacci et al. 2018; Naiman et al. 2018). The IllustrisTNG project is a set of large cosmological simulations that include a variety of galaxy formation physics including AGN feedback. The model has been designed to match a wide range of observational constraints (Pillepich et al. 2018; Springel et al. 2018) and was carried out with the moving mesh code AREPO (Springel 2010). The AREPO code solves the coupled evolution of dark mat- ter, gas, stars, and black holes under the influence of self- gravity and ideal MHD. Developed with the key motiva- tion to study galaxy formation physics and understand the growth of cosmic structure physics, the IllustrisTNG project uses three distinct simulation box sizes. TNG50 was carried out with a box size of 51.7 Mpc per side with 21603 gas and dark matter cells, resulting in a baryon mass resolution of 8.4 \u00d7 104 M\u2299. In partic- ular, we used TNG50-1 (hereafter TNG50), the highest resolution of the three variants run, which provides a me- dian spatial resolution of \u223c100 pc. We analyze this run, although the other larger boxes (TNG100 and TNG300) contain a larger number of Fornax cluster-sized objects, because we need high spatial resolution to study the in- teraction of cold high density columns and the hot group medium. TNG50 adopts initial conditions and cosmo- logical parameters consistent with the Planck Collabo- ration et al. (2016) cosmology with h = 0.68, \u2126b = 0.05, \u2126m = 0.31, \u2126\u03bb = 0.69, and \u03c38 = 0.82 and assuming a flat universe governed by a \u039b cold dark matter (\u039bCDM) cosmology. 2.2. Fornax-like Halo selection In TNG50 a galaxy cluster and groups of galaxies are referred to as halo or FOF (hereafter referred as halo), identified through the friends-of-friends algorithm (Davis et al. 1985). Within each halo, the SUBFIND algorithm (Springel et al. 2001) identifies the subhalos including the primary (central) galaxy and other satel- lite galaxies (hereafter referred as satellite). To find ha- los similar to the Fornax cluster in TNG50 at snapshot 99 (redshift z = 0), we applied a virial mass selection criterion analogous to the Fornax cluster mass (M200 \u223c5 \u00d7 1013 M\u2299, adopted from Drinkwater et al. 2001), namely the mass range of 1013.5 \u2264M200 \u22641014 M\u2299, where M200 is defined as the mass enclosed within a virial radius R200 equal to 200 times the critical density of the Universe. With this condition, we find a total of seven halos. For these halos, we measured the stellar velocity dis- persion of their central galaxy and found that this value is quite close to that of NGC1399, the central galaxy of the Fornax cluster. Except for halo IDs 4 and 9, all other halo central galaxy stellar velocity dispersions fall within \u00b1 20 % to the stellar velocity dispersion value of 315 kms of NGC1399 (Vaughan 2019). In addition to this, the velocity dispersion of all the subhalos within these halos agrees to within 15% of the observed For- nax cluster members (giants and dwarf galaxies) mean velocity dispersion value of 374 \u00b125 km/s (Drinkwater et al. 2001). A previous study of the hot X-ray emitting medium of galaxy groups in the TNG50 cosmological simulations (Truong et al. 2020) showed a good match to observations. More recently, a new set of zoom-in cosmological simulations using the same model \u2018TNG- cluster\u2019 (Truong et al. 2023) have demonstrated good agreement on a larger sample. These successes in repro- ducing observable properties of galaxy clusters indicates that our seven halos are reasonable matches to the For- nax cluster. From here onward, we refer to these halos as Fornax-like halos. In Table 1, we list the physical properties of these halos. 2.3. Atomic HI content To determine the HI mass of gas cells in TNG50 Fornax-like halos, we use the Popping et al. (2019) molecular hydrogen fraction (H2) catalogue, previously calculated for the TNG simulations. In this work we use their fiducial recipe, which is based on the work by Gnedin & Kravtsov (2011). Gnedin & Kravtsov (2011) performed detailed simu- lations including non-equilibrium chemistry and simpli- fied 3D on-the-fly radiative transfer calculations. Based on these simulations, the authors presented fitting for- mulae for the H2 fraction of neutral gas as a function of the dust-to-gas ratio of the gas, the impinging UV radiation field, and surface density of the neutral gas. 4 Table 1. TNG50 halos similar to the Fornax galaxy cluster TNG50 Halo ID Virial Mass (M200) Virial radius (R200) Total HI mass Central galaxy vel. dispersion Halo members vel. dispersion Log M\u2299 (\u00d7 100 kpc) Log M\u2299 km/s km/s 1 13.97 9.59 10.80 384.24 446.20 2 13.81 8.46 10.37 373.80 402.12 3 13.54 6.92 11.24 306.22 321.83 4 13.50 6.71 11.07 204.56 345.08 6 13.54 6.88 10.67 279.20 320.58 7 13.52 6.80 10.38 348.00 331.76 9 13.51 6.75 10.49 254.10 325.88 Popping et al. (2019) assume that the dust-to-gas ratio scales with the metallicity of the neutral gas, that the local UV radiation field scales with the SFR of the gas cell with an additional contribution from the ionising UV background field and they calculate the gas surface density of a gas cell by multiplying its density by the Jeans length of the cell. A detailed description of the implementation of the Gnedin & Kravtsov (2011) fitting formulae within the TNG simulation suite is presented in Popping et al. 2019, (see their Section 2). 2.4. Halo HI covering fraction To understand and quantify the HI distribution in the halos, we measure their HI covering fraction in differ- ent column densities bins (hereafter denoted as NHI), adopting a range of NHI> 1018, 1019, and 1020 cm\u22122. We first measured the HI column density, by perform- ing a two-dimensional binning of all HI gas cells along the three projected axis X, Y and Z (spatial position), regardless of the velocity space and adopted a pixel size of 2 kpc, similar to the MFS spatial resolution limit. This assumes that gas particle sizes are smaller than 2 kpc, which is generally true for the TNG50 halos gas cells. We checked that larger gas cells have negligible contribution to the HI mass and hence to HI column density. In Section 3.2, we present the HI covering frac- tion results as a function of velocity. We measure the HI covering fraction in two ways, sim- ilar to Rahmati et al. (2015), as follows: Cumulative HI covering fraction, hereafter denoted as fHI(R), is defined as the fraction of surface area covered by the binned pixels having column density higher than a given NHI value within a radius R divided by the total area of pixels within radius R. fHI(R) is expressed as: fHI(R) = PN i=1 ANHI|R PN i=1 A|R (1) Here ANHI is the single pixel area with a column density equal or higher than the given NHI value and is summed over N such pixels in a given area of radius R divided by the total area of pixels in radius R. Differential HI covering fraction, hereafter denoted as fHI(\u2206R), is defined similarly to be cumulative HI cov- ering fraction, except here we consider only the covering fraction within the radial bin defined between radius Rj and Rj+1 and fHI(\u2206R) is expressed as: fHI(\u2206R) = PN i=1 ANHI|\u2206R PN i=1 A|\u2206R (2) We also separately measure the total HI covering frac- tion and the HI covering fraction in the intracluster (IC) regions of the halos, that is, the regions well away from identified galaxies. For the IC measurement, we first select the satellite galaxies within a halo with a stellar mass \u2265108.5 M\u2299and having at least 10 gas cells (vary- ing this to 1 gas particle has no effect on our results). Then, we remove the HI gas cells associated with these satellite (including the central galaxy) using the SUB- FIND algorithm of TNG50. This removal of HI gas is done out to ten times the stellar half mass radius (de- noted as R1/2\u2217) of a satellite. In TNG50, the SUBFIND algorithm identifies all the gas cells that are gravita- tionally bound to a specific satellite. After removing the gas cells of a satellite identified with the SUBFIND procedure out to 10\u00d7R1/2\u2217, we measure the HI covering fraction in the same way as defined earlier. The R1/2\u2217 radii of satellite vary from a few kpc to tens of kpc, and with our adopted radial limit (10\u00d7R1/2\u2217), we make sure that we exclude all gas cells that are within the domain of an individual galaxy. However, the IC measurement may contain the very extended tidal/stripped gas tails originating from the individual galaxies. 3. RESULTS 5 Log NHI cm-2 < Figure 1. HI distribution in the TNG50 halo 6 at redshift z=0, colour-coded with the HI column density. The maps are made using a pixel scale of 2 kpc and are shown projected along the (arbitrarily chosen) z-axis. The three pink circles indicate the viral radius of the halos marked at 0.5, 1.0 and 1.5 times Rvir. Dark blue color in the maps indicate the HI column density lower than NHI= 1016 cm\u22122. Left: Full halo HI distribution, right: HI distribution in the intracluster (IC) region (i.e. after removing HI within 10 stellar half-mass radii of all galaxies). This section presents our results showing the HI dis- tribution and covering fraction in the TNG50 halos and their IC regions. For our study, we considered gas cells gravitationally bound to a halo, including gas cells ex- tending to an average 1.5 Rvir radii of halos. Figure 1 shows the HI distribution in TNG50 halo 6 (left panel) and in its IC region (right panel). Three pink circles indicate the virial radius drawn at 0.5, 1.0 and 1.5 Rvir. These images demonstrates both the patchy nature of HI in the simulated clusters, as well as it\u2019s distributed nature. The IC image (right) emphasizes that much of the HI (at least by area) is not immediately connected to galaxies \u2013 that is, it is at least 10 stellar half-mass radii from any galaxy in the simulation. Figure 2 shows the HI distributions for all other Fornax-like halos (top two rows) and in their IC regions (bottom two rows). The first visual impression we get from these plots is that the large-scale distribution of HI extends beyond 0.5 virial radii (\u223c350 kpc) for all the halos. Otherwise, these halos demonstrate diverse HI distributions with significant variations in the amount of HI mass (Table 1). The diverse and extended HI dis- tribution in these halos could potentially be related to the merger/accretion history of these halos or the ac- tivity of supermassive black holes (Zinger et al. 2020). We can also see the streams or filamentary structures connecting the central and satellite galaxies. We notice, in addition, a large number of small HI regions with relatively high column densities, which are possibly not related to any satellite. We refer to these as clouds. We caution that, unlike Nelson et al. (2019), we have not performed Voronoi tessellation over the gas cells to identify these clouds-like structures and it merely rep- resents HI clumps around the satellite galaxies and in the intra-cluster regions of these halos. For the halos HI map, we see that the centers of the satellite are domi- nated by HI column densities NHI between 1020 to 1021 cm\u22122. Looking at these maps, it is quite clear that HI clouds extend out to the virial radius (corresponding to \u223c700 kpc) covering the IC regions. Within the inner region of each halo, around \u223c0.25 Rvir, a large fraction of the HI gas cells are associated with the central galaxy of the halo. In the IC region, the observed HI struc- tures primarily have column densities NHI< 1020 cm\u22122, whereas the structures beyond 0.5 virial radii lie mainly at 1018 < NHI/cm\u22122< 1019. We present the results of the HI covering fraction of halos and in the IC regions in subsections 3.1 and 3.2, respectively. 6 Log NHI cm-2 < Figure 2. HI maps in the Fornax-like halos (first two rows) and in their IC regions (bottom two rows) made with a pixel size of 2 kpc (projected along the arbitrarily chosen z-axis). The three pink circles indicate the viral radius of the halos marked at 0.5, 1.0 and 1.5 times Rvir. 7 Figure 3. HI cumulative (left panel) and differential (right panel) covering fraction profiles of Fornax-like halos HI maps (Figure 2, first two rows) measured along the arbitrarily chosen z-axis for a pixel size of 2 kpc. The first, middle, and bottom rows show the covering fraction for HI column densities log NHI \u226518, 19 and 20 cm\u22122 respectively. The thin lines indicate the individual halos, and the thick lines mark the average value. The vertical dashed lines indicate the average virial radii of the halos. 8 Figure 4. The same as Figure 3, but for the HI distribution in the intracluster (IC) region of Fornax-like halos HI maps (Figure 2, bottom two rows) measured along the arbitrarily chosen z-axis for a pixel size of 2 kpc. We obtain the IC HI by removing the gas cells gravitationally bound to all galaxies within 10\u00d7 their stellar half mass radii. Note the y-axis ranges differ from Figure 3. 3.1. HI covering fraction profiles We used the HI projected maps as shown in Figure 1 to measure the HI covering fraction as discussed in sec- tion 2. We measured the HI covering fractions of halos for three projections, along the X, Y, and Z directions, using a pixel scale of 2 kpc. In this section, we present the HI covering fraction for the full halo maps (top two rows in Figure 2) and in the next section, we discuss the covering fraction of IC regions. In Figure 3 we show the cumulative and dif- ferential covering fraction profiles measured along the (arbitrarily chosen) z-axis in the left and right panel, respectively. For these panels, we include all of the HI gas in the covering fraction calculation, whether or not it is within the central or a satellite galaxy. We do this because, in a blind HI survey, the satellite galaxies may not be identified, so the HI would be measured glob- ally. By definition, the innermost point of the cumu- lative and differential covering fractions are the same, then the differential covering fraction begins decreasing more steeply than the cumulative covering fraction. The first, middle, and bottom rows in both panels show the covering fraction for HI column density for NHI \u22651018, 1019 and 1020 cm\u22122 respectively. The thin lines indi- 9 cate the individual halos, and the thick lines mark the average value. We focus mainly on the NHI bins of 1018 and 1019 cm\u22122, which are the optimal range for studying the HI distribution at \u223ckpc scales for the MFS. We find that regardless of the projection axis, the average cov- ering fraction for the NHI \u22651018 cm\u22122 bin remains be- tween 10-15% at 0.5 Rvir and drops to 6-10% at 1 Rvir. With increasing column density, the covering fraction decreases, such that for the NHI \u22651019 cm\u22122 bin the covering fraction drops to 5-10% at 0.5 Rvir and to less then 5% at 1 Rvir. The differential covering fraction at 0.5 virial radius is between 5-10% and drops to less than 5% at 1 Rvir. These covering fractions quantify our visual impres- sions. Although all the halos have some HI gas within 0.5 Rvir, it is distributed non-uniformly in small struc- tures that look like filaments or clouds. In Figure 3 we verify that the covering fraction of these structures is low, even when including column densities down to 1018 cm\u22122. These structures and clouds could potentially be associated with the central galaxy and satellite galaxies, but from Figure 2 we see that the HI is clearly extended well beyond the satellite stellar radii. However, this gas might have been stripped from satellites to form part of the IC region, which we discuss in the next section and in Section 4.3. 3.2. Intra-cluster HI covering fraction The bottom two rows of Figure 2 show the HI dis- tribution in the IC regions of the halos. The majority of pixels with column density NHI\u22651018 cm\u22122 extend into the IC regions (the cumulative HI covering fraction drops by about 30% at 1 Rvir). It is primarily pixels with high column density HI, NHI > 1020 cm\u22122, which are removed when only including the IC gas cells in our column density measurement (the cumulative HI cover- ing fraction drops by about 70% at 1 Rvir). Similar to Figure 3, we show the HI covering profiles for the IC regions in Figure 4. For the NHI bins 1018 and 1019 cm\u22122, the cumulative covering fraction at 0.5 Rvir is between 5-10 % and drops to less than 5% at 1 Rvir. We checked the differences in the HI covering fraction along the different projected directions and find that, on average, the HI covering fraction remains the same and varies only by a few percent when changing the projected axis. Figure 5 shows the cumulative HI covering fraction at 0.5 Rvir (upper panel) and 1 Rvir (lower panel) be- tween the Fornax-like halo and their IC region in three different projected axes for a column density NHI \u22651018 cm\u22122. The open blue (green) star, circle and square in- Figure 5. Halo and intra-cluster cumulative HI covering fractions at 0.5 Rvir (upper panel) and 1 Rvir (lower panel) for three projected axes. Open star, circle and square in- dicate the X, Y and Z projections, respectively. The open black (red) star, circle and square indicate the average val- ues. dicate the covering fractions at 0.5 Rvir (1 Rvir) along the X, Y and Z axis projections, respectively. The open black (red) star, circle and square indicate the average values measured at 0.5 Rvir (1 Rvir). On average, the IC HI covering fraction is between 70-80% of the total HI covering fraction. This suggests that a large fraction, around \u223c75% (by covering fraction) of the low-column density HI gas that is distributed throughout these mas- sive halos is well outside the satellite galaxies. We also note that some pixels that had a high column density when including the satellite gas have lower column den- sities when only including IC gas. This can be seen as some red pixels in the top panels of Figure 2 turning into green pixels in the bottom panels. Depending on the HI column sensitivity, MFS will map the HI distribution in Fornax at different spatial resolutions, varying from 1 to 10 kpc. We created sim- ilar HI maps, as shown in Figure 2, with different pixel 10 Figure 6. Average halo and intra-cluster cumulative HI covering fractions of seven halos at 1 Rvir for three projected axes corresponding to different pixel scale size of HI maps. Numbers in the plot mark the pixel size in kpc used in cre- ating the HI maps. sizes ranging from 2 to 10 kpc. Examples of HI maps made with 10 kpc pixel scale are shown in Appendix A. In Figure 6, we show the average halo and IC cumulative HI covering fraction of the 7 halos at 1 Rvir radius for different pixel scales. As anticipated, when degrading the pixel size of HI maps, the HI covering fraction in- creases and, for NHI\u22651018 cm\u22122, reaches 12% at 10 kpc pixel scale for the full halo and is around 10% for the IC halo map. These are then our resolution-matched pre- dicted values for the NHI\u22651018 cm\u22122covering fraction that will be observed by MFS. Finally, in order to investigate whether we can see any signature of diffuse HI gas in the inter-galactic medium or cosmic filamentary structures around these mock Fornax-like halos, we made HI maps extending out to 3 Rvir, which we show in Appendix B. Visu- ally inspecting these maps, we do not find diffuse HI in the inter-galactic medium of halos. We notice that outside 1.5 Rvir, there are several infalling smaller satel- lite galaxies, particularly for Halos 1, 2 and 4, but they contribute a negligible amount in the HI covering frac- tion profile. In particular, we computed HI covering fractions for these maps and found similar results as for the maps shown in Figure 2. 3.3. HI covering fraction in velocity space We also measured the cumulative HI covering fraction in the line-of-sight velocity space, adopting a velocity bin size of \u223c100 kms\u22121 within a range of -700 to 700 kms\u22121. This allows us to connect the HI gas at different column densities in velocity space. A correlation of HI gas in velocity space with the satellite velocity distribution can give us hints about its possible stripping origin from satellite galaxies. Figure 7 shows the HI distribution in velocity space for Halo 6 (left panel) and in its IC region (right panel). Similar to Figure 1, we created these velocity space maps (Sec. 2.4) by performing two- dimensional binning in the phase space and taking the mean velocities in bins corresponding to the X, Y and Z axis, with a pixel scale of 2 kpc. In the velocity maps, we consider the halo velocity as the zero velocity point. Remaining HI velocity maps of other halos and their IC regions are shown in Figure 8. In these maps, we can see the distribution of larger satellite galaxies having different velocities then the surrounding lower density HI (first two rows in Figure 8). We used these maps to measure the HI covering fraction in velocity space for these halos which is shown in Figure 9. The top, middle, and bottom panels show cumulative HI covering fraction for NHI column densities of 1018, 1019 and 1020 cm\u22122 with a velocity bin size of 100 kms\u22121. The thin lines indicate the individual halos, and the thick continuous and dashed lines mark the average value of halo and IC region respectively. Vertical dashed gray line marks the halo velocity which is taken as the zero velocity point. We find that, for a velocity bin size of 100 kms\u22121, on average the cumulative HI covering fraction is less than 4 % (2 %) for the column density NHI \u22651018 (1019) cm\u22122 and significantly drops to less than 1% for NHI \u22651020 cm\u22122. The halo and IC HI velocity covering fraction looks bimodal for most of the halos (except halo 4 and 9), as also shown by the average HI covering fraction (continuous and dashed blue lines in Figure 10). On a halo-by-halo comparison, we have verified that the IC HI does not show a more Gaussian velocity distribution than the total HI, as would be expected by virialized, ballistic gas clouds. We can also use our HI velocity covering fraction anal- ysis to learn about the origin of the HI gas in the IC region. To do this, we looked for a possible correla- tion between the HI velocity covering fraction and the satellite velocity distribution. In Figure 10, we show the velocity distribution of all satellite galaxies (all identi- fied satellites with at least 100 cells and stellar mass \u2265108.5 M\u2299), as a function of the number of galaxies (orange leftmost y-axis of each panel) and their stellar mass (black left y-axis of each panel). The grey bars in Figure 10 indicate the summed stellar mass of galaxies binned within velocity ranges of 100 kms\u22121. The orange histogram represents the number counts of all satellite galaxies in each velocity bin. Additionally, we overlay the velocity covering fraction (right y-axis of each panel) 11 Figure 7. HI distribution in the TNG50 halo 6 at redshift z=0, colour-coded with the HI mean velocity (projected along the arbitrarily chosen Z axis) for a pixel size of 2 kpc. Left: Full halo HI distribution, right: HI distribution in the IC region. for log NHI \u226518 cm\u22122 in blue (total and IC HI in solid and dashed lines, respectively). For most of the ha- los, we find that the velocity covering fraction for both the halo and IC regions follows the velocity distribu- tion of satellite galaxies. This points towards a scenario where the IC HI gas originated from satellite galaxies. We performed a similar analysis considering only the HI-rich galaxies (satellite having HI gas cells outside 10 R1/2\u2217) and found similar correlation between the stellar mass distribution and HI velocity covering fraction, ex- cept that the stellar mass distribution is less centrally peaked (as we would expect for gas rich galaxies that have likely recently entered the cluster). We show both the number distribution and the stellar mass distribution of satellites because both could effect the total HI mass brought into the cluster. The stellar mass distribution of satellite galaxies may even be more likely to predict where HI will be found as, for example, a single 1010 M\u2299galaxy is likely to fall into the clus- ter with more HI than two 109 M\u2299galaxies. In Figure 10, we note that besides the agreement with the num- ber distribution of satellites, the HI velocity covering fraction also correlates with peaks in the velocity distri- bution of the stellar masses of all satellite galaxies (grey histogram). Indeed, in Halos 3 and 7, where the satel- lite stellar mass distribution shows multiple peaks, the HI velocity distribution seems to follow the stellar mass more closely than the number of satellites. This general agreement between the satellite and IC HI velocity dis- tributions suggests that IC HI originates from satellite galaxies, and the possibly stronger relation between the satellite stellar mass and HI velocity gives a hint that the IC HI may even originate from more massive galaxies (although we stress that this does not necessarily imply the gas is stripped from massive disks but may fall in as part of the galaxy\u2019s circumgalactic gas). Although a detailed investigation is outside the scope of this paper, we note that it is expected that some pro- cesses occurring in clusters affect the gas dynamics, and therefore some offset between the HI and satellite ve- locity distributions is unsurprising. For example, a past merger can cause long-lived motions in the ICM (Vaez- zadeh et al. 2022), or black hole activity could affect gas dynamics (Weinberger et al. 2017). 4. DISCUSSION In this section, we discuss our results and compare the HI covering fraction to available observations and other cosmological simulation studies. 4.1. Comparison to other cosmological simulations We begin by comparing our measured cumulative HI covering fraction with the available HI covering fraction 12 Figure 8. HI distribution in the TNG50 halos (top two rows) and in their IC (bottom two rows) at redshift z=0, colour-coded with the HI velocity (projected along the arbitrarily chosen Z axis) for a pixel size of 2 kpc. 13 Figure 9. HI cumulative covering fraction profiles of Fornax-like halos in the velocity space. The top, middle, and bottom panels show the covering fraction for HI column densities log NHI \u226518, 19 and 20 cm\u22122, respectively. The thin lines indicate the individual halos, and the thick lines mark the average value. The thick dashed lines mark the average IC HI cumulative covering fraction in velocity space. from the studies of Nelson et al. (2020). They measured the abundance of cold gas in TNG50 halos for massive halos with mass > 1011 M\u2299at intermediate redshift z \u223c 0.5. Although we have only 7 TNG50 halos, and apart from the evolution of the halos from redshift z\u223c0.5 to 0, the simulations and HI model we used are the same as Nelson et al. (2020); therefore, the HI covering fraction should be of the same order. Our measured HI covering fraction for NHI agrees well with the Nelson et al. (2020) measured values. For a column density of NHI> 1017 cm\u22122, we find a covering fraction around 70 \u00b1 15 % at 10 kpc, dropping to 30 \u00b1 15% at 100 kpc, and for NHI> 1020 cm\u22122, at 100 kpc, the covering fraction is roughly 10%, similar to the findings of Nelson et al. (2020). Rah- mati et al. (2015) used the EAGLE simulation to study the HI distribution around high-redshift massive galax- ies. They found a strong evolutionary trend in the HI covering fraction within the virial radius with redshift. For an averaged HI column density in between 1017.3 < NHI/cm\u22122< 1021, the HI covering fraction drops from 70 % at z = 4 to 10 % at z =1. The HI content of galaxies in the EAGLE cosmological simulations was also inves- tigated (Marasco et al. 2016; Crain et al. 2017), finding that the highest resolution simulations reproduced the HI masses of galaxies as well as their clustering. In ad- dition, in dense group and cluster environments, they found that ram pressure stripping was the primary HI mass removal process but that galaxy interactions also played a role. Studying the spatial distribution and ionisation state of cold gas in the CGM, Faerman & Werk (2023) per- formed semi-analytical modelling of cold gas in the CGM of low-redshift star-forming galaxies. Assuming that cold clouds in the CGM are in local pressure equilib- rium with the warm/hot phase, they reported that cold gas can be found out to 0.6 Rvir or beyond. Although we examine more massive halos (1013.5 \u2264M200 \u22641014 M\u2299) compared to Faerman & Werk (2023), we also find that the CGM of Fornax-like halos normally shows a spatially extended distribution of cold gas clouds out to more than 0.5 Rvir. Previously, van de Voort et al. (2019) have shown that standard mass refinement and a high spatial resolution of a few kpc scale can significantly change the inferred HI column density. Studying zoom-in simulations of a Milky-way mass galaxy within the virial radius, they found that the HI covering fraction of NHI\u22641019 cm\u22122 at 150 kpc is almost doubled from 18% to 30% when increasing the spatial resolution of the CGM. Although the simulation setup of van de Voort et al. (2019) and TNG50 is different, we compare our findings to theirs based on the similar resolutions (\u223c1 kpc). We find that the cumulative HI covering fraction within 150 kpc is around 25%, quite close to the van de Voort et al. (2019) result. 14 Figure 10. HI covering fraction profiles of Fornax-like halos in velocity space for log NHI \u226518 cm\u22122 gas over-plotted on the number counts of all satellite galaxies (orange histogram) and the stellar mass velocity distribution (grey histogram). The profiles and histograms are measured in 100 km/s bins. The leftmost y-axis (orange) of each subplot represents the number count of satellite galaxies, while the second axis (black) represents the log stellar mass of satellite galaxies. Solid and dashed blue lines indicate the velocity covering fraction of the halo and IC regions, respectively (right y-axis of each panel). In addition to the van de Voort et al. (2019) work, several papers have focused on studying CGM proper- ties using higher spatial and mass resolution simulations. For example, the FOGGIE group (Peeples et al. 2019) has used the cosmological code Enzo Bryan et al. (2014) to carry out a set of simulations with high resolution in the CGM, finding that a great deal of small-scale struc- ture emerged in the multiphase gas, producing many more small clouds. However, they found that the HI covering fractions did not change significantly. Simi- larly, Hummels et al. (2019) studied the simulated CGM with an enhanced halo resolution technique in the TEM- PEST simulation, again based on ENZO cosmological zoom simulations. They found that increasing the spa- tial resolution resulted in increasing cool gas content in the CGM. With an enhanced spatial resolution in the CGM, they found that observed HI content and column density increases in the CGM. In a similar vein Suresh et al. (2019) explored the CGM of a 1012 M\u2299mass halo with a super-Lagrangian zoom in method, reaching up to \u223c95 pc resolution in CGM. They reported that en- hanced resolution results in an increased amount of cold gas in the CGM and this increase in the cold gas also results in a small increase in the HI covering fraction. For a column density of NHI\u22651019 cm\u22122, they found a HI covering fraction value of around 10 % at one virial radius, which agrees well with our measured covering fraction of 12 % at one virial radius. More recently, Ramesh & Nelson (2024) re-simulated a sample of Milky Way galaxies at z \u223c0 from TNG50 simulation with the super Lagrangian refinement method. Going down to a scale of 75 pc, they also reported that the abundance of cold gas clouds increases with enhanced resolution but did not find a large change in the covering fraction. 4.2. Detection of HI clouds in the Intracluster (IC) region through observational work For all the TNG50 Fornax-like halos, we found that the HI clouds can be found beyond 0.5 Rvir, which cor- responds to an average physical scale of around 350 kpc. 15 Although only a few, there are observational studies showing the existence of remote HI clouds associated with galaxies. An important example is the detection of HI clouds in the inter-galactic medium of the galaxy group HCG44, where the HI clouds extend to more than \u223c300 kpc (Serra et al. 2013b). Another example is the case of NGC 4532, in the Virgo cluster, where the HI tail of the galaxy with some discrete clouds extends to 500 kpc and constitutes around 10% of the total HI mass (Koopmann 2007). A number of observational properties of the multi- phase nature of the CGM in groups and clusters have been explored through absorption lines of background quasars with the HST-Cosmic Origins Spectrograph (COS). Studying a sample of low redshift luminous red galaxies (LRG) with metal absorption lines such MgII, CIII, and SiIII, Werk et al. (2013) measured the occur- rence of cool metal enriched CGM and reported a MgII ion covering fraction (down to very low column densi- ties) of 0.5 within 160 kpc radius. Using a sample of 16 LRG at z \u223c0.4 observed with the HST/COS, (Chen et al. 2018; Zahedy et al. 2019) found a high HI covering fraction for column density NHI> 1017.2 cm\u22122of about 0.44 within 160 kpc impact parameter. In comparison to this, we measured an HI covering fraction of around 0.75 for column density NHI> 1017.2 cm\u22122at 160 kpc. Studying the CGM of a sample of 21 massive galaxies at z \u223c0.5, Berg et al. (2019) measured an HI covering fraction of column density for NHI> 1017.2 cm\u22122within the virial radius of 15 %, which closely agrees with our average measured HI covering fraction of 12 %. Finally, Emerick et al. (2015) compared HI covering fractions within the virial radius in Virgo-like clusters between simulations and observations, finding values consistent with those found here. Most recently, using the MeerKAT observations of the Fornax A subgroup, Kleiner et al. (2021) reported the detection of HI clouds at \u223c220 kpc from NGC 1316, the central galaxy of Fornax A. Another study done with the MeerkAT telescope have detected a large extended HI cloud, extending \u223c400 kpc in proximity to a large galaxy group at a redshift of z \u223c0.03 (J\u00b4 ozsa et al. 2022). Although observational detections of HI clouds in the IC regions around massive galaxies are few and rare, our and other simulation work like Rahmati et al. (2015); van de Voort et al. (2019); Nelson et al. (2020) strongly suggest the existence of dense small HI clumps within the ICM. For our work we find that within the IC region, HI tends to have a column density log NHI \u223c19 cm\u22122 or less, and current observations are mostly not that sensitive yet. A strong test of cosmological simulations will be to compare our predicted HI covering fractions Figure 11. HI intra-cluster (IC) mass as a function of num- ber of satellites for our seven Fornax-like halos. with MFS observations. If simulations overpredict the covering fraction of cold gas, some combination of i) ex- cess cold gas removal from satellites, ii) excess cold gas added to the ICM from feedback or filamentary accre- tion, and iii) suppressed heating of cold gas in the ICM are likely at play. On the other hand, if simulations un- derpredict the HI covering fraction, some combinations of these effects are leading to too little cold gas. 4.3. Possible Origin Scenario A detailed study of the origin or production of the large amount of HI gas in TNG50 Fornax-like halos is beyond the scope of this work. However, we speculate here on the possible source of the HI gas we do find. Nelson et al. (2020) studied the cold gas distribution in TNG50 massive halos at intermediate redshift z \u223c0.5. Using Lagrangian tracer analysis, they argued that cold gas in TNG50 halos is related to gas that is removed from the halos in infalling satellites. These gas clouds can later stimulate the cooling process leading to a sig- nificant amount of cold gas. Most recently, using the TNG50 simulation Ramesh & Nelson (2024) studied the cold gas clouds in the CGM of Milky-Way like galaxies. They reported that these high density gas clouds show clustering behaviour and this over-density increases around satellite galaxies, sug- gesting that a fraction of these clouds originate from ram-pressure stripping. This suggests that, not only for massive halos (like our Fornax-like halos), but even for smaller galaxies, the satellite gas stripping scenario can be important in producing HI clouds in the CGM. We however do not discount the possibility that a fraction of these clouds, whether around the satellite galaxies 16 or isolated, may originate from the in-situ condensa- tion of hot halo CGM gas in the cluster environment, or may be associated with outflows from the central galaxy (Fraternali & Binney 2006). Studying the for- mation mechanism of high velocity clouds around the Milky-Way like disk galaxies, Binney et al. (2009); Fra- ternali et al. (2015) have suggested that condensation of hot CGM gas can produce the HI clouds. It will be interesting to learn which is the effective mechanism for producing these HI clouds in the CGM. Possibly all the mechanisms: a) satellite stripping, b) thermal instabil- ity in CGM, or c) the feedback from the galaxy play roles in the formation of these clouds and could be ex- plored by characterising these cloud properties in phase space (spatial and velocity) such as was done in Ramesh & Nelson (2024). In addition to the analysis in Section 3.3, which in- dicates that the IC velocity covering fraction is associ- ated with the satellite galaxies\u2019 velocity distribution, we checked if we could see any correlation between the satel- lite galaxies\u2019 number with the total IC HI mass. Fig- ure 11 shows the halo intracluster HI mass as function of satellite galaxy number. In Figure 11, red stars denote all of the satellite galaxies and open squares mark the satellites having HI gas cells outside their 10 \u00d7 R1/2\u2217. With only 7 halos, its hard to quantify any relation, but we find that the halo IC HI mass increases with increas- ing number of satellite galaxies. The IC HI mass corre- lates more steeply with satellites having HI and shows less scatter. This further suggests that the HI mass in the IC regions of Fornax-like clusters could be associated with the stripped HI gas from satellite galaxies, similar to the findings of Nelson et al. (2020). We find a simi- lar level of correlation between the total stellar mass in satellites and the halo IC HI mass. 5. SUMMARY AND CONCLUSION In this paper, using the publicly available TNG50 sim- ulation data, we have studied the distribution of HI gas in halos similar to the Fornax galaxy cluster. Adopt- ing the MeerKAT Fornax survey (MFS) observational conditions, we have measured the HI covering fraction of the halos with a mass of 1013.5 <= M200 <= 1014 M\u2299. The following points summarise our findings and conclusions: 1. Atomic hydrogen in TNG50 Fornax-like halos shows a wide spatial distribution, appearing as clouds and filamentary structures (Figures 1 and 2). HI is non-uniformly distributed and extends in patches well beyond 0.5 virial radii of the central galaxy. On a physical scale, this corresponds to \u223c 350 kpc. 2. Using our HI covering fraction measurements, we find that individual Fornax-like halos in TNG50 show a wide scatter in the measured HI covering fraction ranging from 3% to 15% at 1 Rvir (Figure 5). We predict the upcoming MFS should observe a total HI covering fraction of \u223c25% at 0.5 virial radii and \u223c12% at 1 Rvir (Figure 6) at NHI\u22651018 cm\u22122(spatial resolution \u223c10 kpc). For intraclus- ter regions, this values drops to \u223c20% at 0.5 virial radii and \u223c9% at 1 Rvir. 3. Intracluster (IC) regions (i.e. more than 10 stellar half-mass radii from identified galaxies) in Fornax- like halos hold a substantial fraction of the HI. When using the NHI \u22651018 cm\u22122 contour, the IC HI covering fraction at 1 Rvir (spatial resolution \u223c10 kpc) corresponds to around 75% of the total HI covering fraction (Figure 5). 4. The HI velocity covering fraction for the Fornax- like halos (both in total and in the IC regions only) shows a broad velocity distribution that is not gen- erally Gaussian, indicating that HI is not virialized in the halos (Figure 9). The HI velocity covering fraction for both halo and IC largely follows the velocity distribution of satellite galaxies, suggest- ing that IC HI is associated with satellite galaxies (Figure 10). 5. We find that halo HI intracluster mass increases with increasing number of satellite galaxies and shows an even stronger correlation with the satel- lites having HI presence in their outskirts (Figure 11). This also suggests that HI in the IC regions is associated with the stripped gas of satellite galax- ies, similar to the results of Nelson et al. (2020). With this work, we have demonstrated, based on TNG50 simulation data, that HI cold gas is predicted to co-exist and survive in the hot intracluster medium for Fornax-like clusters. Based on HI maps of Fornax-likes halos in TNG50, we expect MFS to find extended HI well beyond the satellites in the halo, but should gener- ally follow the large-scale satellite distribution, both on the sky and in velocity space. This is also reflected in the asymmetry of the HI in velocity space - while the aver- age distribution of the seven halos studied is symmetric, any individual halo can show strong asymmetries. We plan to perform a future follow-up study to pinpoint the origin of these HI clouds, whether they are possibly stripped or formed in situ in the cluster environment. It will be illuminating to see what MFS will observe within the Fornax cluster. With its higher sensitivity, there re- mains a good chance that the MeerKAT telescope can 17 provide observational support and constraints for cur- rent and future simulation work on the multiphase na- ture of halo gas. 6. ACKNOWLEDGEMENTS A.C. would like to thank Abhijeet Anand and Roland Sazacks for helpful suggestions and discussions regard- ing this work. A.C. acknowledges the financial and computing support from Simons Foundation and thanks the Flatiron Institute pre-doctoral fellowship program through which this research work was carried out. GLB acknowledges support from the NSF (AST-2108470, AC- CESS), a NASA TCAN award, and the Simons Founda- tion through the Learning the Universe Collaboration. APPENDIX A. TNG50 HALOS MAPS AT 10 KPC PIXEL SIZE In our paper we use pixels that are 2 kpc on a side in order to match the MFS resolution at HI column densities of about 1019 cm\u22122. However, the resolution at HI column densities of 1018 cm\u22122 is about 10 kpc. In Figure 6 we show how the covering fraction at this column density increases with pixel size, and in this Appendix Figure 12, we show HI maps made with 10 kpc pixels so the reader can directly compare with the higher resolution maps shown in Figures 2 and 1. B. TNG50 HALOS MAPS AT OUT TO 3 RVIR For our study we considered only the gas cells gravitationally bound to a halo (Sec. 2), which generally includes cells out to an average of 1 to 1.5 Rvir. Here in this Appendix Figure 13, we show TNG50 Fornax-like halos maps out to 3 Rvir, demonstrating that there are several infalling satellite galaxies, particularly for Halos 1, 2 and 4. Their contribution to the HI covering profile are minimal. These maps also confirm that we do not detect any signature of diffuse HI (not closely associated with satellite galaxies) in the outer IGM of halos). 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    "main_content": "**[introduction]*",
    "additional_graph_info": {
        "graph": [
            [
                "Avinash Chaturvedi",
                "Michael Hilker"
            ],
            [
                "Avinash Chaturvedi",
                "Stephanie Tonnesen"
            ],
            [
                "Avinash Chaturvedi",
                "Paolo Serra"
            ],
            [
                "Michael Hilker",
                "Tom Richtler"
            ],
            [
                "Michael Hilker",
                "Holger Baumgardt"
            ],
            [
                "Michael Hilker",
                "Antonio Sollima"
            ],
            [
                "Michael Hilker",
                "Carlos Eduardo Barbosa"
            ],
            [
                "Stephanie Tonnesen",
                "Renyue Cen"
            ],
            [
                "Stephanie Tonnesen",
                "Daniel Defelippis"
            ],
            [
                "Stephanie Tonnesen",
                "Jeremiah P. Ostriker"
            ],
            [
                "Paolo Serra",
                "Tom Oosterloo"
            ],
            [
                "Paolo Serra",
                "Michele Cappellari"
            ],
            [
                "Paolo Serra",
                "Davor Krajnovic"
            ]
        ],
        "node_feat": {
            "Avinash Chaturvedi": [
                {
                    "url": "http://arxiv.org/abs/2404.16926v1",
                    "title": "Observational predictions for the survival of atomic hydrogen in simulated Fornax-like galaxy clusters",
                    "abstract": "The presence of dense, neutral hydrogen clouds in the hot, diffuse\nintra-group and intra-cluster medium is an important clue to the physical\nprocesses controlling the survival of cold gas and sheds light on cosmological\nbaryon flows in massive halos. Advances in numerical modeling and observational\nsurveys means that theory and observational comparisons are now possible. In\nthis paper, we use the high-resolution TNG50 cosmological simulation to study\nthe HI distribution in seven halos with masses similar to the Fornax galaxy\ncluster. Adopting observational sensitivities similar to the MeerKAT Fornax\nSurvey (MFS), an ongoing HI survey that will probe to column densities of\n$10^{18}$ cm$^{-2}$, we find that Fornax-like TNG50 halos have an extended\ndistribution of neutral hydrogen clouds. Within one virial radius, we predict\nthe MFS will observe a total HI covering fraction around $\\sim$ 12\\% (mean\nvalue) for 10 kpc pixels and 6\\% for 2 kpc pixels. If we restrict this to gas\nmore than 10 half-mass radii from galaxies, the mean values only decrease\nmildly, to 10\\% (4\\%) for 10 (2) kpc pixels (albeit with significant\nhalo-to-halo spread). Although there are large amounts of HI outside of\ngalaxies, the gas seems to be associated with satellites, judging both by the\nvisual inspection of projections and by comparison of the line of sight\nvelocities of galaxies and intracluster HI.",
                    "authors": "Avinash Chaturvedi, Stephanie Tonnesen, Greg L. Bryan, Gerg\u00f6 Popping, Michael Hilker, Paolo Serra, Shy Genel",
                    "published": "2024-04-25",
                    "updated": "2024-04-25",
                    "primary_cat": "astro-ph.GA",
                    "cats": [
                        "astro-ph.GA"
                    ],
                    "main_content": "**[introduction]*",
                    "introduction": "1. The formation and evolution of galaxies is now under- stood to be strongly linked with the diffuse gas filling their dark matter halos. Depending on galaxy mass, this gas is called the circumgalactic medium (CGM) when the gas resides in the halos of galaxies of the Milky Way mass or lower, or the intracluster medium (ICM) for gas living in more massive cluster-sized halos (Mtot \u22731014 M\u2299). Various physical processes, such as gas accretion from the intergalactic medium, and feedback driven by stars and AGN, occur in this gaseous halo. These pro- cesses drive flows which regulate the rate at which gas cools on to the galaxy itself, controlling the amount of mass in the interstellar medium and hence the rate of star formation itself, including possibly quenching (see avi.chaturvedi@aip.de Tumlinson et al. 2017, for a review). Therefore, under- standing the physical processes in the CGM or ICM is crucial to building a comprehensive picture of galaxy evolution. We highlight here the important question of the origin and survival of cold gas in the hot ICM, by studying the phase-space distribution of cold gas in massive halos at low redshift, with a particular focus on the observability of this gas in ongoing and future HI surveys. For low-mass, star-forming galaxies, it is expected that their halo can host an abundant amount of cold gas that may be the fuel for future star formation. The halos of massive galaxies, on the other hand, may lack cold gas, resulting in the lack of any recent star for- mation activity (Gauthier & Chen 2011). In addition, current observational (Chen et al. 2018; Berg et al. 2019; Zahedy et al. 2019) and simulation studies (Dav\u00b4 e et al. 2020; Rahmati et al. 2015; Nelson et al. 2020) suggest that at intermediate redshift (0.3 \u2264z \u22640.8), massive ha- arXiv:2404.16926v1  [astro-ph.GA]  25 Apr 2024 2 los have a significant amount of cold gas. For example, Chen et al. (2018); Zahedy et al. (2019) studied lumi- nous red galaxies (LRG) at redshift z \u223c0.21-0.55 and found that these galaxies host a high column density of the cold gas tracers HI and MgII. Other similar stud- ies point toward the same conclusion that LRGs host an abundant amount of cold gas (Zhu et al. 2014; Lan & Mo 2018; Anand et al. 2021, 2022). At low-redshift, simulation studies of Milky Way-like galaxies show that their CGM also host substantial amounts of cold gas (van de Voort et al. 2019). Recently, simulations have made improved predictions for the cold gas distribution in halos that reproduce many of the observed galactic properties. For example, Nelson et al. (2020) have shown that cold gas in the ha- los of LRGs can be attributed to the thermal instability triggered by local density perturbations. They suggest that these perturbations are related to gas stripped from infalling galaxies via tidal interactions, or ram pressure stripping. Performing a comparative study between cos- mological and idealized simulations (individual galaxy halo simulations), Fielding et al. (2020) have also shown that cold gas extends to the virial radius for Milky Way- mass halos. They also suggest that non-spherical accre- tion and satellite galaxies contribute to the cold gas con- tent in the outer halos. Previously, Villaescusa-Navarro et al. (2018) performed a detailed study using the Il- lustris TNG100 simulation, investigating the HI abun- dance and clustering properties in halos for z \u22645. They showed that HI density profiles are sensitive to various processes such as AGN feedback and tidal stripping. For massive halos, they found that HI is mostly concentrated in their satellite galaxies, whereas for small halos it is concentrated in the central galaxy. In contrast to intermediate redshifts, the study of cold gas in the ICM of massive halos (M\u2217\u22651011 M\u2299) in the local Universe (z \u223c0) is limited to a few studies. Nonetheless, using the HI 21 cm emission line, radio observations have demonstrated the abundant existence of cold neutral atomic gas around early-type galaxies (E/S0) galaxies (Serra et al. 2012, 2013b; Young et al. 2014; Serra et al. 2013a). However, these observations are limited to tens of kpc around the targeted galax- ies and are typically not sensitive to HI column densi- ties below \u22641019 cm\u22122, and therefore do not provide a comprehensive picture of the cold gas in the ICM. The ongoing observations from the MeerKAT Fornax survey (hereafter MFS, Serra et al. 2019; Serra et al. 2023), a radio continuum and line survey of the Fornax cluster, provides an excellent opportunity to study the HI gas in great detail in the nearby Fornax ICM (d \u223c20 Mpc). Photometric and spectroscopic studies (Cantiello et al. 2020; Chaturvedi et al. 2022) have shown that the Fornax cluster mass assembly is still ongoing, making it an interesting target to study. MFS is dedicated to studying the HI distribution and kinematics within the Fornax environment. The HI column density sensitiv- ity of the MFS ranges from \u223c5\u00d71019 cm\u22122 at a spatial resolution of \u223c10 arcsec (\u223c1 kpc at Fornax distance) down to 1018 cm\u22122 at \u223c100 arcsec (\u223c10 kpc at For- nax distance). With a mosaic area of the 12 square degrees, MFS will detect HI in the Fornax intracluster (hereafter IC) region - which in this paper refers to the region within the massive dark matter halo and outside satellite galaxies. The high-resolution TNG50 cosmological simulations (Nelson et al. 2019; Pillepich et al. 2019) provide a me- dian spatial resolution of \u223c100 parsec and its validation of cold gas (neutral and molecular hydrogen) against observational work (Popping et al. 2019; Diemer et al. 2019) makes TNG50 an ideal framework to explore the cold gas distribution in Fornax-like halos. This also pro- vides a chance to forecast the upcoming MFS survey results and test the simulations against the MFS obser- vations. In this work, we use the TNG50 simulations (Nelson et al. 2019; Pillepich et al. 2019) and adopt the observing criteria of the MFS to study the HI content in the TNG50 halos similar to the Fornax galaxy cluster. We also study the HI distribution in these halos and their IC region. We calculate the HI covering fraction for these halos and predict the expected observed MFS HI covering fraction. In addition, both the spatial and velocity distribution of HI gas in the ICM of clusters and groups can be used to gain insight into the origin and survival of this cold gas. If the gas is correlated in both position and velocity with satellites, we can argue that the HI is likely either stripped from satellites or cooling is induced by satel- lites. However, if cold gas is not correlated with satel- lite galaxy positions or velocities, we might argue that either cold gas formation is related to the central galaxy or that cold gas survives in the ICM long enough to be- come virialized (e.g., Voit et al. 2017; Rohr et al. 2023). In this paper we take the first step of making these spa- tial and velocity maps, leaving gas particle tracking to future work. The paper is organized as follows: In section 2, we briefly introduce the TNG50 simulation and present the methodology for calculating the HI covering fraction. Section 3 presents our results about the HI distribution and its covering fraction. In section 4, we compare our results to current simulation (Section 4.1) and observa- tional (Section 4.2) studies, and discuss the likely origin of the cold gas in the intracluster medium of Fornax-like 3 halos (Section 4.3). Section 5 presents the summary of the work. 2. SIMULATION AND METHODOLOGY This section briefly introduces the TNG50 simulation that we use for our analysis as well as our criteria for selecting Fornax-like halos. In addition, we present our methodology for calculating the HI column density and HI covering fraction of the selected halos in TNG50 in order to compare to observational surveys. 2.1. The TNG simulations For our study, we use the TNG50 simulation (Nelson et al. 2019; Pillepich et al. 2019), the highest resolution simulation of the IllustrisTNG cosmological magneto- hydrodynamical (MHD) simulation suite (Nelson et al. 2018; Springel et al. 2018; Pillepich et al. 2018; Mari- nacci et al. 2018; Naiman et al. 2018). The IllustrisTNG project is a set of large cosmological simulations that include a variety of galaxy formation physics including AGN feedback. The model has been designed to match a wide range of observational constraints (Pillepich et al. 2018; Springel et al. 2018) and was carried out with the moving mesh code AREPO (Springel 2010). The AREPO code solves the coupled evolution of dark mat- ter, gas, stars, and black holes under the influence of self- gravity and ideal MHD. Developed with the key motiva- tion to study galaxy formation physics and understand the growth of cosmic structure physics, the IllustrisTNG project uses three distinct simulation box sizes. TNG50 was carried out with a box size of 51.7 Mpc per side with 21603 gas and dark matter cells, resulting in a baryon mass resolution of 8.4 \u00d7 104 M\u2299. In partic- ular, we used TNG50-1 (hereafter TNG50), the highest resolution of the three variants run, which provides a me- dian spatial resolution of \u223c100 pc. We analyze this run, although the other larger boxes (TNG100 and TNG300) contain a larger number of Fornax cluster-sized objects, because we need high spatial resolution to study the in- teraction of cold high density columns and the hot group medium. TNG50 adopts initial conditions and cosmo- logical parameters consistent with the Planck Collabo- ration et al. (2016) cosmology with h = 0.68, \u2126b = 0.05, \u2126m = 0.31, \u2126\u03bb = 0.69, and \u03c38 = 0.82 and assuming a flat universe governed by a \u039b cold dark matter (\u039bCDM) cosmology. 2.2. Fornax-like Halo selection In TNG50 a galaxy cluster and groups of galaxies are referred to as halo or FOF (hereafter referred as halo), identified through the friends-of-friends algorithm (Davis et al. 1985). Within each halo, the SUBFIND algorithm (Springel et al. 2001) identifies the subhalos including the primary (central) galaxy and other satel- lite galaxies (hereafter referred as satellite). To find ha- los similar to the Fornax cluster in TNG50 at snapshot 99 (redshift z = 0), we applied a virial mass selection criterion analogous to the Fornax cluster mass (M200 \u223c5 \u00d7 1013 M\u2299, adopted from Drinkwater et al. 2001), namely the mass range of 1013.5 \u2264M200 \u22641014 M\u2299, where M200 is defined as the mass enclosed within a virial radius R200 equal to 200 times the critical density of the Universe. With this condition, we find a total of seven halos. For these halos, we measured the stellar velocity dis- persion of their central galaxy and found that this value is quite close to that of NGC1399, the central galaxy of the Fornax cluster. Except for halo IDs 4 and 9, all other halo central galaxy stellar velocity dispersions fall within \u00b1 20 % to the stellar velocity dispersion value of 315 kms of NGC1399 (Vaughan 2019). In addition to this, the velocity dispersion of all the subhalos within these halos agrees to within 15% of the observed For- nax cluster members (giants and dwarf galaxies) mean velocity dispersion value of 374 \u00b125 km/s (Drinkwater et al. 2001). A previous study of the hot X-ray emitting medium of galaxy groups in the TNG50 cosmological simulations (Truong et al. 2020) showed a good match to observations. More recently, a new set of zoom-in cosmological simulations using the same model \u2018TNG- cluster\u2019 (Truong et al. 2023) have demonstrated good agreement on a larger sample. These successes in repro- ducing observable properties of galaxy clusters indicates that our seven halos are reasonable matches to the For- nax cluster. From here onward, we refer to these halos as Fornax-like halos. In Table 1, we list the physical properties of these halos. 2.3. Atomic HI content To determine the HI mass of gas cells in TNG50 Fornax-like halos, we use the Popping et al. (2019) molecular hydrogen fraction (H2) catalogue, previously calculated for the TNG simulations. In this work we use their fiducial recipe, which is based on the work by Gnedin & Kravtsov (2011). Gnedin & Kravtsov (2011) performed detailed simu- lations including non-equilibrium chemistry and simpli- fied 3D on-the-fly radiative transfer calculations. Based on these simulations, the authors presented fitting for- mulae for the H2 fraction of neutral gas as a function of the dust-to-gas ratio of the gas, the impinging UV radiation field, and surface density of the neutral gas. 4 Table 1. TNG50 halos similar to the Fornax galaxy cluster TNG50 Halo ID Virial Mass (M200) Virial radius (R200) Total HI mass Central galaxy vel. dispersion Halo members vel. dispersion Log M\u2299 (\u00d7 100 kpc) Log M\u2299 km/s km/s 1 13.97 9.59 10.80 384.24 446.20 2 13.81 8.46 10.37 373.80 402.12 3 13.54 6.92 11.24 306.22 321.83 4 13.50 6.71 11.07 204.56 345.08 6 13.54 6.88 10.67 279.20 320.58 7 13.52 6.80 10.38 348.00 331.76 9 13.51 6.75 10.49 254.10 325.88 Popping et al. (2019) assume that the dust-to-gas ratio scales with the metallicity of the neutral gas, that the local UV radiation field scales with the SFR of the gas cell with an additional contribution from the ionising UV background field and they calculate the gas surface density of a gas cell by multiplying its density by the Jeans length of the cell. A detailed description of the implementation of the Gnedin & Kravtsov (2011) fitting formulae within the TNG simulation suite is presented in Popping et al. 2019, (see their Section 2). 2.4. Halo HI covering fraction To understand and quantify the HI distribution in the halos, we measure their HI covering fraction in differ- ent column densities bins (hereafter denoted as NHI), adopting a range of NHI> 1018, 1019, and 1020 cm\u22122. We first measured the HI column density, by perform- ing a two-dimensional binning of all HI gas cells along the three projected axis X, Y and Z (spatial position), regardless of the velocity space and adopted a pixel size of 2 kpc, similar to the MFS spatial resolution limit. This assumes that gas particle sizes are smaller than 2 kpc, which is generally true for the TNG50 halos gas cells. We checked that larger gas cells have negligible contribution to the HI mass and hence to HI column density. In Section 3.2, we present the HI covering frac- tion results as a function of velocity. We measure the HI covering fraction in two ways, sim- ilar to Rahmati et al. (2015), as follows: Cumulative HI covering fraction, hereafter denoted as fHI(R), is defined as the fraction of surface area covered by the binned pixels having column density higher than a given NHI value within a radius R divided by the total area of pixels within radius R. fHI(R) is expressed as: fHI(R) = PN i=1 ANHI|R PN i=1 A|R (1) Here ANHI is the single pixel area with a column density equal or higher than the given NHI value and is summed over N such pixels in a given area of radius R divided by the total area of pixels in radius R. Differential HI covering fraction, hereafter denoted as fHI(\u2206R), is defined similarly to be cumulative HI cov- ering fraction, except here we consider only the covering fraction within the radial bin defined between radius Rj and Rj+1 and fHI(\u2206R) is expressed as: fHI(\u2206R) = PN i=1 ANHI|\u2206R PN i=1 A|\u2206R (2) We also separately measure the total HI covering frac- tion and the HI covering fraction in the intracluster (IC) regions of the halos, that is, the regions well away from identified galaxies. For the IC measurement, we first select the satellite galaxies within a halo with a stellar mass \u2265108.5 M\u2299and having at least 10 gas cells (vary- ing this to 1 gas particle has no effect on our results). Then, we remove the HI gas cells associated with these satellite (including the central galaxy) using the SUB- FIND algorithm of TNG50. This removal of HI gas is done out to ten times the stellar half mass radius (de- noted as R1/2\u2217) of a satellite. In TNG50, the SUBFIND algorithm identifies all the gas cells that are gravita- tionally bound to a specific satellite. After removing the gas cells of a satellite identified with the SUBFIND procedure out to 10\u00d7R1/2\u2217, we measure the HI covering fraction in the same way as defined earlier. The R1/2\u2217 radii of satellite vary from a few kpc to tens of kpc, and with our adopted radial limit (10\u00d7R1/2\u2217), we make sure that we exclude all gas cells that are within the domain of an individual galaxy. However, the IC measurement may contain the very extended tidal/stripped gas tails originating from the individual galaxies. 3. RESULTS 5 Log NHI cm-2 < Figure 1. HI distribution in the TNG50 halo 6 at redshift z=0, colour-coded with the HI column density. The maps are made using a pixel scale of 2 kpc and are shown projected along the (arbitrarily chosen) z-axis. The three pink circles indicate the viral radius of the halos marked at 0.5, 1.0 and 1.5 times Rvir. Dark blue color in the maps indicate the HI column density lower than NHI= 1016 cm\u22122. Left: Full halo HI distribution, right: HI distribution in the intracluster (IC) region (i.e. after removing HI within 10 stellar half-mass radii of all galaxies). This section presents our results showing the HI dis- tribution and covering fraction in the TNG50 halos and their IC regions. For our study, we considered gas cells gravitationally bound to a halo, including gas cells ex- tending to an average 1.5 Rvir radii of halos. Figure 1 shows the HI distribution in TNG50 halo 6 (left panel) and in its IC region (right panel). Three pink circles indicate the virial radius drawn at 0.5, 1.0 and 1.5 Rvir. These images demonstrates both the patchy nature of HI in the simulated clusters, as well as it\u2019s distributed nature. The IC image (right) emphasizes that much of the HI (at least by area) is not immediately connected to galaxies \u2013 that is, it is at least 10 stellar half-mass radii from any galaxy in the simulation. Figure 2 shows the HI distributions for all other Fornax-like halos (top two rows) and in their IC regions (bottom two rows). The first visual impression we get from these plots is that the large-scale distribution of HI extends beyond 0.5 virial radii (\u223c350 kpc) for all the halos. Otherwise, these halos demonstrate diverse HI distributions with significant variations in the amount of HI mass (Table 1). The diverse and extended HI dis- tribution in these halos could potentially be related to the merger/accretion history of these halos or the ac- tivity of supermassive black holes (Zinger et al. 2020). We can also see the streams or filamentary structures connecting the central and satellite galaxies. We notice, in addition, a large number of small HI regions with relatively high column densities, which are possibly not related to any satellite. We refer to these as clouds. We caution that, unlike Nelson et al. (2019), we have not performed Voronoi tessellation over the gas cells to identify these clouds-like structures and it merely rep- resents HI clumps around the satellite galaxies and in the intra-cluster regions of these halos. For the halos HI map, we see that the centers of the satellite are domi- nated by HI column densities NHI between 1020 to 1021 cm\u22122. Looking at these maps, it is quite clear that HI clouds extend out to the virial radius (corresponding to \u223c700 kpc) covering the IC regions. Within the inner region of each halo, around \u223c0.25 Rvir, a large fraction of the HI gas cells are associated with the central galaxy of the halo. In the IC region, the observed HI struc- tures primarily have column densities NHI< 1020 cm\u22122, whereas the structures beyond 0.5 virial radii lie mainly at 1018 < NHI/cm\u22122< 1019. We present the results of the HI covering fraction of halos and in the IC regions in subsections 3.1 and 3.2, respectively. 6 Log NHI cm-2 < Figure 2. HI maps in the Fornax-like halos (first two rows) and in their IC regions (bottom two rows) made with a pixel size of 2 kpc (projected along the arbitrarily chosen z-axis). The three pink circles indicate the viral radius of the halos marked at 0.5, 1.0 and 1.5 times Rvir. 7 Figure 3. HI cumulative (left panel) and differential (right panel) covering fraction profiles of Fornax-like halos HI maps (Figure 2, first two rows) measured along the arbitrarily chosen z-axis for a pixel size of 2 kpc. The first, middle, and bottom rows show the covering fraction for HI column densities log NHI \u226518, 19 and 20 cm\u22122 respectively. The thin lines indicate the individual halos, and the thick lines mark the average value. The vertical dashed lines indicate the average virial radii of the halos. 8 Figure 4. The same as Figure 3, but for the HI distribution in the intracluster (IC) region of Fornax-like halos HI maps (Figure 2, bottom two rows) measured along the arbitrarily chosen z-axis for a pixel size of 2 kpc. We obtain the IC HI by removing the gas cells gravitationally bound to all galaxies within 10\u00d7 their stellar half mass radii. Note the y-axis ranges differ from Figure 3. 3.1. HI covering fraction profiles We used the HI projected maps as shown in Figure 1 to measure the HI covering fraction as discussed in sec- tion 2. We measured the HI covering fractions of halos for three projections, along the X, Y, and Z directions, using a pixel scale of 2 kpc. In this section, we present the HI covering fraction for the full halo maps (top two rows in Figure 2) and in the next section, we discuss the covering fraction of IC regions. In Figure 3 we show the cumulative and dif- ferential covering fraction profiles measured along the (arbitrarily chosen) z-axis in the left and right panel, respectively. For these panels, we include all of the HI gas in the covering fraction calculation, whether or not it is within the central or a satellite galaxy. We do this because, in a blind HI survey, the satellite galaxies may not be identified, so the HI would be measured glob- ally. By definition, the innermost point of the cumu- lative and differential covering fractions are the same, then the differential covering fraction begins decreasing more steeply than the cumulative covering fraction. The first, middle, and bottom rows in both panels show the covering fraction for HI column density for NHI \u22651018, 1019 and 1020 cm\u22122 respectively. The thin lines indi- 9 cate the individual halos, and the thick lines mark the average value. We focus mainly on the NHI bins of 1018 and 1019 cm\u22122, which are the optimal range for studying the HI distribution at \u223ckpc scales for the MFS. We find that regardless of the projection axis, the average cov- ering fraction for the NHI \u22651018 cm\u22122 bin remains be- tween 10-15% at 0.5 Rvir and drops to 6-10% at 1 Rvir. With increasing column density, the covering fraction decreases, such that for the NHI \u22651019 cm\u22122 bin the covering fraction drops to 5-10% at 0.5 Rvir and to less then 5% at 1 Rvir. The differential covering fraction at 0.5 virial radius is between 5-10% and drops to less than 5% at 1 Rvir. These covering fractions quantify our visual impres- sions. Although all the halos have some HI gas within 0.5 Rvir, it is distributed non-uniformly in small struc- tures that look like filaments or clouds. In Figure 3 we verify that the covering fraction of these structures is low, even when including column densities down to 1018 cm\u22122. These structures and clouds could potentially be associated with the central galaxy and satellite galaxies, but from Figure 2 we see that the HI is clearly extended well beyond the satellite stellar radii. However, this gas might have been stripped from satellites to form part of the IC region, which we discuss in the next section and in Section 4.3. 3.2. Intra-cluster HI covering fraction The bottom two rows of Figure 2 show the HI dis- tribution in the IC regions of the halos. The majority of pixels with column density NHI\u22651018 cm\u22122 extend into the IC regions (the cumulative HI covering fraction drops by about 30% at 1 Rvir). It is primarily pixels with high column density HI, NHI > 1020 cm\u22122, which are removed when only including the IC gas cells in our column density measurement (the cumulative HI cover- ing fraction drops by about 70% at 1 Rvir). Similar to Figure 3, we show the HI covering profiles for the IC regions in Figure 4. For the NHI bins 1018 and 1019 cm\u22122, the cumulative covering fraction at 0.5 Rvir is between 5-10 % and drops to less than 5% at 1 Rvir. We checked the differences in the HI covering fraction along the different projected directions and find that, on average, the HI covering fraction remains the same and varies only by a few percent when changing the projected axis. Figure 5 shows the cumulative HI covering fraction at 0.5 Rvir (upper panel) and 1 Rvir (lower panel) be- tween the Fornax-like halo and their IC region in three different projected axes for a column density NHI \u22651018 cm\u22122. The open blue (green) star, circle and square in- Figure 5. Halo and intra-cluster cumulative HI covering fractions at 0.5 Rvir (upper panel) and 1 Rvir (lower panel) for three projected axes. Open star, circle and square in- dicate the X, Y and Z projections, respectively. The open black (red) star, circle and square indicate the average val- ues. dicate the covering fractions at 0.5 Rvir (1 Rvir) along the X, Y and Z axis projections, respectively. The open black (red) star, circle and square indicate the average values measured at 0.5 Rvir (1 Rvir). On average, the IC HI covering fraction is between 70-80% of the total HI covering fraction. This suggests that a large fraction, around \u223c75% (by covering fraction) of the low-column density HI gas that is distributed throughout these mas- sive halos is well outside the satellite galaxies. We also note that some pixels that had a high column density when including the satellite gas have lower column den- sities when only including IC gas. This can be seen as some red pixels in the top panels of Figure 2 turning into green pixels in the bottom panels. Depending on the HI column sensitivity, MFS will map the HI distribution in Fornax at different spatial resolutions, varying from 1 to 10 kpc. We created sim- ilar HI maps, as shown in Figure 2, with different pixel 10 Figure 6. Average halo and intra-cluster cumulative HI covering fractions of seven halos at 1 Rvir for three projected axes corresponding to different pixel scale size of HI maps. Numbers in the plot mark the pixel size in kpc used in cre- ating the HI maps. sizes ranging from 2 to 10 kpc. Examples of HI maps made with 10 kpc pixel scale are shown in Appendix A. In Figure 6, we show the average halo and IC cumulative HI covering fraction of the 7 halos at 1 Rvir radius for different pixel scales. As anticipated, when degrading the pixel size of HI maps, the HI covering fraction in- creases and, for NHI\u22651018 cm\u22122, reaches 12% at 10 kpc pixel scale for the full halo and is around 10% for the IC halo map. These are then our resolution-matched pre- dicted values for the NHI\u22651018 cm\u22122covering fraction that will be observed by MFS. Finally, in order to investigate whether we can see any signature of diffuse HI gas in the inter-galactic medium or cosmic filamentary structures around these mock Fornax-like halos, we made HI maps extending out to 3 Rvir, which we show in Appendix B. Visu- ally inspecting these maps, we do not find diffuse HI in the inter-galactic medium of halos. We notice that outside 1.5 Rvir, there are several infalling smaller satel- lite galaxies, particularly for Halos 1, 2 and 4, but they contribute a negligible amount in the HI covering frac- tion profile. In particular, we computed HI covering fractions for these maps and found similar results as for the maps shown in Figure 2. 3.3. HI covering fraction in velocity space We also measured the cumulative HI covering fraction in the line-of-sight velocity space, adopting a velocity bin size of \u223c100 kms\u22121 within a range of -700 to 700 kms\u22121. This allows us to connect the HI gas at different column densities in velocity space. A correlation of HI gas in velocity space with the satellite velocity distribution can give us hints about its possible stripping origin from satellite galaxies. Figure 7 shows the HI distribution in velocity space for Halo 6 (left panel) and in its IC region (right panel). Similar to Figure 1, we created these velocity space maps (Sec. 2.4) by performing two- dimensional binning in the phase space and taking the mean velocities in bins corresponding to the X, Y and Z axis, with a pixel scale of 2 kpc. In the velocity maps, we consider the halo velocity as the zero velocity point. Remaining HI velocity maps of other halos and their IC regions are shown in Figure 8. In these maps, we can see the distribution of larger satellite galaxies having different velocities then the surrounding lower density HI (first two rows in Figure 8). We used these maps to measure the HI covering fraction in velocity space for these halos which is shown in Figure 9. The top, middle, and bottom panels show cumulative HI covering fraction for NHI column densities of 1018, 1019 and 1020 cm\u22122 with a velocity bin size of 100 kms\u22121. The thin lines indicate the individual halos, and the thick continuous and dashed lines mark the average value of halo and IC region respectively. Vertical dashed gray line marks the halo velocity which is taken as the zero velocity point. We find that, for a velocity bin size of 100 kms\u22121, on average the cumulative HI covering fraction is less than 4 % (2 %) for the column density NHI \u22651018 (1019) cm\u22122 and significantly drops to less than 1% for NHI \u22651020 cm\u22122. The halo and IC HI velocity covering fraction looks bimodal for most of the halos (except halo 4 and 9), as also shown by the average HI covering fraction (continuous and dashed blue lines in Figure 10). On a halo-by-halo comparison, we have verified that the IC HI does not show a more Gaussian velocity distribution than the total HI, as would be expected by virialized, ballistic gas clouds. We can also use our HI velocity covering fraction anal- ysis to learn about the origin of the HI gas in the IC region. To do this, we looked for a possible correla- tion between the HI velocity covering fraction and the satellite velocity distribution. In Figure 10, we show the velocity distribution of all satellite galaxies (all identi- fied satellites with at least 100 cells and stellar mass \u2265108.5 M\u2299), as a function of the number of galaxies (orange leftmost y-axis of each panel) and their stellar mass (black left y-axis of each panel). The grey bars in Figure 10 indicate the summed stellar mass of galaxies binned within velocity ranges of 100 kms\u22121. The orange histogram represents the number counts of all satellite galaxies in each velocity bin. Additionally, we overlay the velocity covering fraction (right y-axis of each panel) 11 Figure 7. HI distribution in the TNG50 halo 6 at redshift z=0, colour-coded with the HI mean velocity (projected along the arbitrarily chosen Z axis) for a pixel size of 2 kpc. Left: Full halo HI distribution, right: HI distribution in the IC region. for log NHI \u226518 cm\u22122 in blue (total and IC HI in solid and dashed lines, respectively). For most of the ha- los, we find that the velocity covering fraction for both the halo and IC regions follows the velocity distribu- tion of satellite galaxies. This points towards a scenario where the IC HI gas originated from satellite galaxies. We performed a similar analysis considering only the HI-rich galaxies (satellite having HI gas cells outside 10 R1/2\u2217) and found similar correlation between the stellar mass distribution and HI velocity covering fraction, ex- cept that the stellar mass distribution is less centrally peaked (as we would expect for gas rich galaxies that have likely recently entered the cluster). We show both the number distribution and the stellar mass distribution of satellites because both could effect the total HI mass brought into the cluster. The stellar mass distribution of satellite galaxies may even be more likely to predict where HI will be found as, for example, a single 1010 M\u2299galaxy is likely to fall into the clus- ter with more HI than two 109 M\u2299galaxies. In Figure 10, we note that besides the agreement with the num- ber distribution of satellites, the HI velocity covering fraction also correlates with peaks in the velocity distri- bution of the stellar masses of all satellite galaxies (grey histogram). Indeed, in Halos 3 and 7, where the satel- lite stellar mass distribution shows multiple peaks, the HI velocity distribution seems to follow the stellar mass more closely than the number of satellites. This general agreement between the satellite and IC HI velocity dis- tributions suggests that IC HI originates from satellite galaxies, and the possibly stronger relation between the satellite stellar mass and HI velocity gives a hint that the IC HI may even originate from more massive galaxies (although we stress that this does not necessarily imply the gas is stripped from massive disks but may fall in as part of the galaxy\u2019s circumgalactic gas). Although a detailed investigation is outside the scope of this paper, we note that it is expected that some pro- cesses occurring in clusters affect the gas dynamics, and therefore some offset between the HI and satellite ve- locity distributions is unsurprising. For example, a past merger can cause long-lived motions in the ICM (Vaez- zadeh et al. 2022), or black hole activity could affect gas dynamics (Weinberger et al. 2017). 4. DISCUSSION In this section, we discuss our results and compare the HI covering fraction to available observations and other cosmological simulation studies. 4.1. Comparison to other cosmological simulations We begin by comparing our measured cumulative HI covering fraction with the available HI covering fraction 12 Figure 8. HI distribution in the TNG50 halos (top two rows) and in their IC (bottom two rows) at redshift z=0, colour-coded with the HI velocity (projected along the arbitrarily chosen Z axis) for a pixel size of 2 kpc. 13 Figure 9. HI cumulative covering fraction profiles of Fornax-like halos in the velocity space. The top, middle, and bottom panels show the covering fraction for HI column densities log NHI \u226518, 19 and 20 cm\u22122, respectively. The thin lines indicate the individual halos, and the thick lines mark the average value. The thick dashed lines mark the average IC HI cumulative covering fraction in velocity space. from the studies of Nelson et al. (2020). They measured the abundance of cold gas in TNG50 halos for massive halos with mass > 1011 M\u2299at intermediate redshift z \u223c 0.5. Although we have only 7 TNG50 halos, and apart from the evolution of the halos from redshift z\u223c0.5 to 0, the simulations and HI model we used are the same as Nelson et al. (2020); therefore, the HI covering fraction should be of the same order. Our measured HI covering fraction for NHI agrees well with the Nelson et al. (2020) measured values. For a column density of NHI> 1017 cm\u22122, we find a covering fraction around 70 \u00b1 15 % at 10 kpc, dropping to 30 \u00b1 15% at 100 kpc, and for NHI> 1020 cm\u22122, at 100 kpc, the covering fraction is roughly 10%, similar to the findings of Nelson et al. (2020). Rah- mati et al. (2015) used the EAGLE simulation to study the HI distribution around high-redshift massive galax- ies. They found a strong evolutionary trend in the HI covering fraction within the virial radius with redshift. For an averaged HI column density in between 1017.3 < NHI/cm\u22122< 1021, the HI covering fraction drops from 70 % at z = 4 to 10 % at z =1. The HI content of galaxies in the EAGLE cosmological simulations was also inves- tigated (Marasco et al. 2016; Crain et al. 2017), finding that the highest resolution simulations reproduced the HI masses of galaxies as well as their clustering. In ad- dition, in dense group and cluster environments, they found that ram pressure stripping was the primary HI mass removal process but that galaxy interactions also played a role. Studying the spatial distribution and ionisation state of cold gas in the CGM, Faerman & Werk (2023) per- formed semi-analytical modelling of cold gas in the CGM of low-redshift star-forming galaxies. Assuming that cold clouds in the CGM are in local pressure equilib- rium with the warm/hot phase, they reported that cold gas can be found out to 0.6 Rvir or beyond. Although we examine more massive halos (1013.5 \u2264M200 \u22641014 M\u2299) compared to Faerman & Werk (2023), we also find that the CGM of Fornax-like halos normally shows a spatially extended distribution of cold gas clouds out to more than 0.5 Rvir. Previously, van de Voort et al. (2019) have shown that standard mass refinement and a high spatial resolution of a few kpc scale can significantly change the inferred HI column density. Studying zoom-in simulations of a Milky-way mass galaxy within the virial radius, they found that the HI covering fraction of NHI\u22641019 cm\u22122 at 150 kpc is almost doubled from 18% to 30% when increasing the spatial resolution of the CGM. Although the simulation setup of van de Voort et al. (2019) and TNG50 is different, we compare our findings to theirs based on the similar resolutions (\u223c1 kpc). We find that the cumulative HI covering fraction within 150 kpc is around 25%, quite close to the van de Voort et al. (2019) result. 14 Figure 10. HI covering fraction profiles of Fornax-like halos in velocity space for log NHI \u226518 cm\u22122 gas over-plotted on the number counts of all satellite galaxies (orange histogram) and the stellar mass velocity distribution (grey histogram). The profiles and histograms are measured in 100 km/s bins. The leftmost y-axis (orange) of each subplot represents the number count of satellite galaxies, while the second axis (black) represents the log stellar mass of satellite galaxies. Solid and dashed blue lines indicate the velocity covering fraction of the halo and IC regions, respectively (right y-axis of each panel). In addition to the van de Voort et al. (2019) work, several papers have focused on studying CGM proper- ties using higher spatial and mass resolution simulations. For example, the FOGGIE group (Peeples et al. 2019) has used the cosmological code Enzo Bryan et al. (2014) to carry out a set of simulations with high resolution in the CGM, finding that a great deal of small-scale struc- ture emerged in the multiphase gas, producing many more small clouds. However, they found that the HI covering fractions did not change significantly. Simi- larly, Hummels et al. (2019) studied the simulated CGM with an enhanced halo resolution technique in the TEM- PEST simulation, again based on ENZO cosmological zoom simulations. They found that increasing the spa- tial resolution resulted in increasing cool gas content in the CGM. With an enhanced spatial resolution in the CGM, they found that observed HI content and column density increases in the CGM. In a similar vein Suresh et al. (2019) explored the CGM of a 1012 M\u2299mass halo with a super-Lagrangian zoom in method, reaching up to \u223c95 pc resolution in CGM. They reported that en- hanced resolution results in an increased amount of cold gas in the CGM and this increase in the cold gas also results in a small increase in the HI covering fraction. For a column density of NHI\u22651019 cm\u22122, they found a HI covering fraction value of around 10 % at one virial radius, which agrees well with our measured covering fraction of 12 % at one virial radius. More recently, Ramesh & Nelson (2024) re-simulated a sample of Milky Way galaxies at z \u223c0 from TNG50 simulation with the super Lagrangian refinement method. Going down to a scale of 75 pc, they also reported that the abundance of cold gas clouds increases with enhanced resolution but did not find a large change in the covering fraction. 4.2. Detection of HI clouds in the Intracluster (IC) region through observational work For all the TNG50 Fornax-like halos, we found that the HI clouds can be found beyond 0.5 Rvir, which cor- responds to an average physical scale of around 350 kpc. 15 Although only a few, there are observational studies showing the existence of remote HI clouds associated with galaxies. An important example is the detection of HI clouds in the inter-galactic medium of the galaxy group HCG44, where the HI clouds extend to more than \u223c300 kpc (Serra et al. 2013b). Another example is the case of NGC 4532, in the Virgo cluster, where the HI tail of the galaxy with some discrete clouds extends to 500 kpc and constitutes around 10% of the total HI mass (Koopmann 2007). A number of observational properties of the multi- phase nature of the CGM in groups and clusters have been explored through absorption lines of background quasars with the HST-Cosmic Origins Spectrograph (COS). Studying a sample of low redshift luminous red galaxies (LRG) with metal absorption lines such MgII, CIII, and SiIII, Werk et al. (2013) measured the occur- rence of cool metal enriched CGM and reported a MgII ion covering fraction (down to very low column densi- ties) of 0.5 within 160 kpc radius. Using a sample of 16 LRG at z \u223c0.4 observed with the HST/COS, (Chen et al. 2018; Zahedy et al. 2019) found a high HI covering fraction for column density NHI> 1017.2 cm\u22122of about 0.44 within 160 kpc impact parameter. In comparison to this, we measured an HI covering fraction of around 0.75 for column density NHI> 1017.2 cm\u22122at 160 kpc. Studying the CGM of a sample of 21 massive galaxies at z \u223c0.5, Berg et al. (2019) measured an HI covering fraction of column density for NHI> 1017.2 cm\u22122within the virial radius of 15 %, which closely agrees with our average measured HI covering fraction of 12 %. Finally, Emerick et al. (2015) compared HI covering fractions within the virial radius in Virgo-like clusters between simulations and observations, finding values consistent with those found here. Most recently, using the MeerKAT observations of the Fornax A subgroup, Kleiner et al. (2021) reported the detection of HI clouds at \u223c220 kpc from NGC 1316, the central galaxy of Fornax A. Another study done with the MeerkAT telescope have detected a large extended HI cloud, extending \u223c400 kpc in proximity to a large galaxy group at a redshift of z \u223c0.03 (J\u00b4 ozsa et al. 2022). Although observational detections of HI clouds in the IC regions around massive galaxies are few and rare, our and other simulation work like Rahmati et al. (2015); van de Voort et al. (2019); Nelson et al. (2020) strongly suggest the existence of dense small HI clumps within the ICM. For our work we find that within the IC region, HI tends to have a column density log NHI \u223c19 cm\u22122 or less, and current observations are mostly not that sensitive yet. A strong test of cosmological simulations will be to compare our predicted HI covering fractions Figure 11. HI intra-cluster (IC) mass as a function of num- ber of satellites for our seven Fornax-like halos. with MFS observations. If simulations overpredict the covering fraction of cold gas, some combination of i) ex- cess cold gas removal from satellites, ii) excess cold gas added to the ICM from feedback or filamentary accre- tion, and iii) suppressed heating of cold gas in the ICM are likely at play. On the other hand, if simulations un- derpredict the HI covering fraction, some combinations of these effects are leading to too little cold gas. 4.3. Possible Origin Scenario A detailed study of the origin or production of the large amount of HI gas in TNG50 Fornax-like halos is beyond the scope of this work. However, we speculate here on the possible source of the HI gas we do find. Nelson et al. (2020) studied the cold gas distribution in TNG50 massive halos at intermediate redshift z \u223c0.5. Using Lagrangian tracer analysis, they argued that cold gas in TNG50 halos is related to gas that is removed from the halos in infalling satellites. These gas clouds can later stimulate the cooling process leading to a sig- nificant amount of cold gas. Most recently, using the TNG50 simulation Ramesh & Nelson (2024) studied the cold gas clouds in the CGM of Milky-Way like galaxies. They reported that these high density gas clouds show clustering behaviour and this over-density increases around satellite galaxies, sug- gesting that a fraction of these clouds originate from ram-pressure stripping. This suggests that, not only for massive halos (like our Fornax-like halos), but even for smaller galaxies, the satellite gas stripping scenario can be important in producing HI clouds in the CGM. We however do not discount the possibility that a fraction of these clouds, whether around the satellite galaxies 16 or isolated, may originate from the in-situ condensa- tion of hot halo CGM gas in the cluster environment, or may be associated with outflows from the central galaxy (Fraternali & Binney 2006). Studying the for- mation mechanism of high velocity clouds around the Milky-Way like disk galaxies, Binney et al. (2009); Fra- ternali et al. (2015) have suggested that condensation of hot CGM gas can produce the HI clouds. It will be interesting to learn which is the effective mechanism for producing these HI clouds in the CGM. Possibly all the mechanisms: a) satellite stripping, b) thermal instabil- ity in CGM, or c) the feedback from the galaxy play roles in the formation of these clouds and could be ex- plored by characterising these cloud properties in phase space (spatial and velocity) such as was done in Ramesh & Nelson (2024). In addition to the analysis in Section 3.3, which in- dicates that the IC velocity covering fraction is associ- ated with the satellite galaxies\u2019 velocity distribution, we checked if we could see any correlation between the satel- lite galaxies\u2019 number with the total IC HI mass. Fig- ure 11 shows the halo intracluster HI mass as function of satellite galaxy number. In Figure 11, red stars denote all of the satellite galaxies and open squares mark the satellites having HI gas cells outside their 10 \u00d7 R1/2\u2217. With only 7 halos, its hard to quantify any relation, but we find that the halo IC HI mass increases with increas- ing number of satellite galaxies. The IC HI mass corre- lates more steeply with satellites having HI and shows less scatter. This further suggests that the HI mass in the IC regions of Fornax-like clusters could be associated with the stripped HI gas from satellite galaxies, similar to the findings of Nelson et al. (2020). We find a simi- lar level of correlation between the total stellar mass in satellites and the halo IC HI mass. 5. SUMMARY AND CONCLUSION In this paper, using the publicly available TNG50 sim- ulation data, we have studied the distribution of HI gas in halos similar to the Fornax galaxy cluster. Adopt- ing the MeerKAT Fornax survey (MFS) observational conditions, we have measured the HI covering fraction of the halos with a mass of 1013.5 <= M200 <= 1014 M\u2299. The following points summarise our findings and conclusions: 1. Atomic hydrogen in TNG50 Fornax-like halos shows a wide spatial distribution, appearing as clouds and filamentary structures (Figures 1 and 2). HI is non-uniformly distributed and extends in patches well beyond 0.5 virial radii of the central galaxy. On a physical scale, this corresponds to \u223c 350 kpc. 2. Using our HI covering fraction measurements, we find that individual Fornax-like halos in TNG50 show a wide scatter in the measured HI covering fraction ranging from 3% to 15% at 1 Rvir (Figure 5). We predict the upcoming MFS should observe a total HI covering fraction of \u223c25% at 0.5 virial radii and \u223c12% at 1 Rvir (Figure 6) at NHI\u22651018 cm\u22122(spatial resolution \u223c10 kpc). For intraclus- ter regions, this values drops to \u223c20% at 0.5 virial radii and \u223c9% at 1 Rvir. 3. Intracluster (IC) regions (i.e. more than 10 stellar half-mass radii from identified galaxies) in Fornax- like halos hold a substantial fraction of the HI. When using the NHI \u22651018 cm\u22122 contour, the IC HI covering fraction at 1 Rvir (spatial resolution \u223c10 kpc) corresponds to around 75% of the total HI covering fraction (Figure 5). 4. The HI velocity covering fraction for the Fornax- like halos (both in total and in the IC regions only) shows a broad velocity distribution that is not gen- erally Gaussian, indicating that HI is not virialized in the halos (Figure 9). The HI velocity covering fraction for both halo and IC largely follows the velocity distribution of satellite galaxies, suggest- ing that IC HI is associated with satellite galaxies (Figure 10). 5. We find that halo HI intracluster mass increases with increasing number of satellite galaxies and shows an even stronger correlation with the satel- lites having HI presence in their outskirts (Figure 11). This also suggests that HI in the IC regions is associated with the stripped gas of satellite galax- ies, similar to the results of Nelson et al. (2020). With this work, we have demonstrated, based on TNG50 simulation data, that HI cold gas is predicted to co-exist and survive in the hot intracluster medium for Fornax-like clusters. Based on HI maps of Fornax-likes halos in TNG50, we expect MFS to find extended HI well beyond the satellites in the halo, but should gener- ally follow the large-scale satellite distribution, both on the sky and in velocity space. This is also reflected in the asymmetry of the HI in velocity space - while the aver- age distribution of the seven halos studied is symmetric, any individual halo can show strong asymmetries. We plan to perform a future follow-up study to pinpoint the origin of these HI clouds, whether they are possibly stripped or formed in situ in the cluster environment. It will be illuminating to see what MFS will observe within the Fornax cluster. With its higher sensitivity, there re- mains a good chance that the MeerKAT telescope can 17 provide observational support and constraints for cur- rent and future simulation work on the multiphase na- ture of halo gas. 6. ACKNOWLEDGEMENTS A.C. would like to thank Abhijeet Anand and Roland Sazacks for helpful suggestions and discussions regard- ing this work. A.C. acknowledges the financial and computing support from Simons Foundation and thanks the Flatiron Institute pre-doctoral fellowship program through which this research work was carried out. GLB acknowledges support from the NSF (AST-2108470, AC- CESS), a NASA TCAN award, and the Simons Founda- tion through the Learning the Universe Collaboration. APPENDIX A. TNG50 HALOS MAPS AT 10 KPC PIXEL SIZE In our paper we use pixels that are 2 kpc on a side in order to match the MFS resolution at HI column densities of about 1019 cm\u22122. However, the resolution at HI column densities of 1018 cm\u22122 is about 10 kpc. In Figure 6 we show how the covering fraction at this column density increases with pixel size, and in this Appendix Figure 12, we show HI maps made with 10 kpc pixels so the reader can directly compare with the higher resolution maps shown in Figures 2 and 1. B. TNG50 HALOS MAPS AT OUT TO 3 RVIR For our study we considered only the gas cells gravitationally bound to a halo (Sec. 2), which generally includes cells out to an average of 1 to 1.5 Rvir. Here in this Appendix Figure 13, we show TNG50 Fornax-like halos maps out to 3 Rvir, demonstrating that there are several infalling satellite galaxies, particularly for Halos 1, 2 and 4. Their contribution to the HI covering profile are minimal. These maps also confirm that we do not detect any signature of diffuse HI (not closely associated with satellite galaxies) in the outer IGM of halos). 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                },
                {
                    "url": "http://arxiv.org/abs/2109.08694v1",
                    "title": "The Fornax Cluster VLT Spectroscopic Survey III -- Kinematical characterisation of globular clusters across the Fornax galaxy cluster",
                    "abstract": "The Fornax cluster provides an unparalleled opportunity to investigate in\ndetail the formation and evolution of early-type galaxies in a dense\nenvironment. We aim at kinematically characterizing photometrically detected\nglobular cluster (GC) candidates in the core of the cluster. We used the\nVLT/VIMOS spectroscopic data from the FVSS survey in the Fornax cluster,\ncovering one square degree around the central massive galaxy NGC 1399. We\nconfirmed a total of 777 GCs, almost doubling the previously detected GCs,\nusing the same dataset by Pota et al. (2018). Combined with previous literature\nradial velocity measurements of GCs in Fornax, we compiled the most extensive\nspectroscopic GC sample of 2341 objects in this environment. We found that red\nGCs are mostly concentrated around major galaxies, while blue GCs are\nkinematically irregular and are widely spread throughout the core region of the\ncluster. The velocity dispersion profiles of blue and red GCs show a quite\ndistinct behaviour. Blue GCs exhibit a sharp increase in the velocity\ndispersion profile from 250 to 400km/s within 5 arcminutes (29 kpc/1 reff of\nNGC 1399) from the central galaxy. The velocity dispersion profile of red GCs\nfollows a constant value in between 200-300km/s until 8 arcminutes (46\nkpc/1.6reff), and then rises to 350km/s at 10 arcminutes (58 kpc/2 reff).\nBeyond 10 arcminutes and out to 40 arcminutes (230 kpc/8 reff), blue and red\nGCs show a constant velocity dispersion of 300+/-50km/s, indicating that both\nGC populations are tracing the cluster potential. We have kinematically\nconfirmed and characterized the previously photometrically discovered\noverdensities of intra-cluster GCs. We found that those substructured\nintra-cluster regions in Fornax are dominated mostly by blue GCs.",
                    "authors": "Avinash Chaturvedi, Michael Hilker, Michele Cantiello, Nicola R. Napolitano, Glenn van de Ven, Chiara Spiniello, Katja Fahrion, Maurizio Paolillo, Massimiliano Gatto, Thomas Puzia",
                    "published": "2021-09-17",
                    "updated": "2021-09-17",
                    "primary_cat": "astro-ph.GA",
                    "cats": [
                        "astro-ph.GA"
                    ],
                    "main_content": "This work examines the detection and kinematical characterization of GCs in the Fornax cluster core within one square degree. We have reanalyzed Fornax cluster VLT/VIMOS spectroscopic data taken in 2014/2015 via the ESO program 094.B-0687 (PI: M. Capaccioli). For a detailed description of observations preparation and target selection, we refer the reader to Pota et al. (2018). Here we briefly summarize the observations details and present the new data reduction. 2.1. Photometry and globular cluster selection The Fornax Deep Survey (FDS, Iodice et al. 2016) and Next Generation Fornax Survey (NGFS, Mu\u00f1oz et al. 2015) formed the photometric data base to select GC candidates for the VIMOS/VLT spectroscopic survey. The FDS deep multiband (u, g, r and i) imaging data from OmegaCAM cover an area of \u223c30 square degrees out to the virial radius of the Fornax cluster. NGFS is an optical and near-infrared imaging survey and covers nearly the same area as the FDS survey. GC candidates for spectroscopic observations were selected based on de-reddened g and i band magnitudes from the FDS and preliminary VISTA/VIRCAM photometry in the Ks band from the NGFS. Additionally wide-field Washington photometry (Dirsch et al. 2004; Bassino et al. 2006) was used to construct the C \u2212i vs i \u2212Ks diagram to select the bonafide GCs. Hubble Space Telescope/ACS photometry was used to find additional GCs in the central regions of NGC 1399 (Puzia et al. 2014). Finally, with a magnitude restriction of 17.0 < i < 23.0 mag, a total of 4340 unique spectroscopic targets were selected. This selection includes, on purpose, also some background galaxies and compact sources outside the selection criteria whenever there was space for additional VIMOS slits. 2.2. Observations The spectroscopic observations for this study were carried out with the Visible Multi Object Spectrograph (VIMOS, LeFevre et al. 2003) at the VLT and were acquired in ESO Period 94 between October 2014 and January 2015. A total of 25 VIMOS pointings were defined to cover the central square degree of the Fornax cluster. Each pointing consists of 4 quadrants of 7\u00d78 arcmin2. The MR grism was used together with filter GG475, which allows a multiplexing of two in spectral direction with a spectral coverage of 4750-10000\u00c5 at 12\u00c5 FWHM resolution. Three exposures of 30 minutes each were taken for each pointing. 2.3. Data Reduction The data reduction was performed with the VIMOS pipeline version 3.3.0 incorporated in the ESO Reflex workflow (Freudling et al. 2013). The reduction follows the steps as described in Pota et al. (2018). The dataset of each VIMOS pointing consisted of biases, flat fields, scientific spectral images, and arc lamp spectra. The older version of the VIMOS pipeline, used for the analysis performed in Pota et al. (2018), did not correct for flexure induced wavelength shifts in multiple science exposure before their combination. This caused an incorrect absolute wavelength calibration and line broadening in the stacked spectra. Pota et al. (2018) manually corrected for this limitation, by applying the median wavelength shift of the second science exposure to the final stacked spectra. On the other hand, the improved pipeline version we used for our work takes care of wavelength shifts before stacking the individual spectra and prevents the line broadening effects. We confirmed this by reducing the individual exposures of a few VIMOS pointings and compared them with the final stacked reduced spectra. In Figure 1 we show the CaT region of the reduced individual spectra and the stacked one for one example case. Red, green, and blue colours show the three single exposures. The black colour shows the final stacked spectrum. We repeated this test for several masks of different pointings, and no significant broadening was noticed. We checked this quantitatively by fitting a Gaussian to the CaT line at 8842 \u00c5 to the stacked and individual exposures of spectra with different signal-to-noise (S/N). The scatter among the mean positions of the CaT at 8842 \u00c5 line was found to be within the 10% spaxel resolution limit of 2.58 \u00c5 for the used Article number, page 3 of 22 A&A proofs: manuscript no. paper1_catalog VIMOS grism. In order to obtain the \ufb01nal wavelength calibration, we provided our own skylines catalogue to calculate the residual shifts from the sky emission lines and corrected them. 3. Analysis In this section, we describe our analysis of the VIMOS data to obtain the line-of-sight (LOS) velocities from the spectra. We discuss our methodology for disentangling the GCs from background and foreground objects. 3.1. Radial velocity measurements The radial velocity measurements of GCs were calculated using the python implemented penalized-PiXel \ufb01tting (pPXF) method of Cappellari & Emsellem (2004); Cappellari (2017). pPXF is a full-spectrum \ufb01tting technique which generates a model spectrum by convolving a set of weighted stellar templates, to the parametric LOS velocity distribution (LSOVD), modelled as a Gauss-Hermite series. The intrinsic velocity dispersion of GCs (usually \u223c20 km s\u22121) is well below the spectral resolution of the used VIMOS grism (\u223c88 km s\u22121). Our initial test of deriving the radial velocities shows that we obtained a velocity dispersion always lower than 20 km s\u22121 (i.e. in most cases pPXF gives a value of zero if the velocity dispersion is not resolved), which is an expected value for most of the GCs. We derive the mean velocity from pPXF and use the velocity dispersion value as a limiting criterion to select GCs. For the stellar templates, we used the single stellar population spectra from the extended medium resolution INT Library of Empirical spectra (E-MILES Vazdekis et al. 2010, 2016) covering a wavelength range of 1680 to 50000 \u00c5. We preferred this stellar library, as it provides us \ufb02exibility in obtaining the stellar spectrum on a grid of ages ranging from 8 to 14 Gyr and metallicities in the range \u22122.27 < [M/H] < +0.04 dex. We used an MW like double power law (bimodal) initial mass function with a mass slope of 1.30. With these settings, we obtain a set of 84 stellar templates from the E-MILES library at a spectral resolution of 2.51 \u00c5. We convolved the stellar library with a Gaussian \ufb01lter of standard deviation \u03c3 =12 \u00c5 to bring it to the same resolution as the VIMOS spectra. For the spectral \ufb01tting, we use a wavelength region of 48008800 \u00c5. This wavelength region covers the major absorption line features, like H\u03b2 (4862 \u00c5), Mg\u03b2 (5176 \u00c5), NaD (5895 \u00c5), H\u03b1 (6564 \u00c5), and CaT lines (at 8498, 8548, 8662 \u00c5). We masked several regions to avoid residual sky lines or telluric lines. pPXF requires starting values of the velocity moments parameter; in our case, its radial velocity and velocity dispersion. pPXF uses the given redshift of an object to make this initial guess (see section 2.3 Cappellari 2017). For the velocity dispersion, we chose a value of 0 km/s, which is expected for a GC (i.e. its internal velocity dispersion is not resolved). For the Fornax cluster redshift, the initial radial velocity was chosen to be \u223c1375 km s\u22121, close to the radial velocity of Fornax central galaxy NGC 1399, which is 1425 km s\u22121(taken from Graham et al. 1998). However, pPXF does not produce a meaningful \ufb01t with this guess in the case of foreground stars or background galaxies. Moreover, GC in the outer halo of NGC 1399 or in the intra-cluster regions of the Fornax cluster can have radial velocities di\ufb00erent from the initial guess by about \u00b1500 km s\u22121. Therefore, it is crucial to test how the pPXF initial velocity guess can a\ufb00ect the resulting radial velocities, especially for GCs lying in the intra-cluster regions. To check this, we measured the radial velocities of di\ufb00erent GCs belonging to the intra-cluster regions as a function of di\ufb00erent initial velocity guesses, as shown in \ufb01gure A.1. We found that the change in the resulting radial velocities is within 5%, and this variation is within the measured velocity error. This shows that the initial guess of pPXF does not impact our radial velocity measurements. We present this test in detail in appendix A. pPXF allows the use of additive and multiplicative Legendre polynomials to adjust the continuum shape in the spectral calibration. As a \ufb01rst guess, we have used a 3rd and 5th order for additive and multiplicative polynomials, respectively. However in cases, where we obtained a radial velocity consistent with the Fornax cluster but a velocity dispersion higher than 20 km s\u22121, we varied the polynomials such that we can obtain a velocity dispersion lower than 20 km s\u22121. We did a quantitative analysis to see how varying polynomials in pPXF can a\ufb00ect the derived mean velocities and dispersions. We did a test as follows: We de\ufb01ned a grid of additive and multiplicative polynomials in the range from 0 to 6. For each pair of polynomials, we derive the mean velocity and dispersion. First, we make sure that the velocity dispersion is lower than 20 km s\u22121 and the variation in the mean velocity is not more than 5% for di\ufb00erent pairs of polynomials. Based on these two conditions, we select the most suitable value of these polynomials. We also checked the e\ufb00ect of higher order polynomials on the derived radial velocity as well as not using multiplicative polynomials. We found that in all cases there are only subtle variations in the derived radial velocities; they are all consistent within 5%. We present more details on these tests of varying the order of polynomials in appendix A. Figure 2 shows examples of pPXF \ufb01ts for two GC spectra with di\ufb00erent S/N ratios. Masked regions are shown in the upper left panels as blue bands, and residuals from the masked regions are plotted in green in the panels below. The right panels show zoomed in views of individual absorption line features of the GC spectra. Uncertainties on the mean velocity were estimated through Monte-Carlo (MC) realizations of the GC spectrum. For each pPXF model \ufb01t, we generated 100 realizations of spectra by adding Gaussian noise equivalent to the root mean square (RMS) of the residuals of the best \ufb01t. pPXF also returns the weights of template stars used for obtaining the best \ufb01t. To save computational time, we used only template stars with non-zero weights (around \u223c7-10) for performing the MC realizations. 3.2. Selecting Fornax Cluster Members Our VIMOS dataset is contaminated by foreground stars and background galaxies. To distinguish Fornax cluster GCs from the contaminants, we used the expected radial velocity range of 450 < v < 2500 km s\u22121 from Schuberth et al. (2010) for objects belonging to the Fornax cluster. We developed a two-step test to separate the GCs from the background galaxies and stars: First, we checked for the presence of emission lines in all spectra. In the case of multiple strong emission lines in a spectrum, we classify that object as a background galaxy. Second, the remaining spectra are \ufb01tted with an initial velocity guess of zero, and if pPXF returns a velocity lower than 450 km s\u22121, we classify the object as a star. All the remaining spectra are \ufb01tted as mentioned in section 3.1. In this way we reject most of the contaminants at the very beginning, before deriving \ufb01nal radial velocity measurements. To select the \ufb01nal bona\ufb01de GCs, we visually inspected the pPXF results for all remaining spectra. For that, we created a portfolio of each object with its 1D spectrum, pPXF \ufb01t with zoomed in views of major absorption features like H\u03b2, Mg\u03b2, NaD, H\u03b1, CaT lines and a 2D image of the source, with attributes like Article number, page 4 of 22 Avinash Chaturvedi et al.: Globular cluster kinematics in the Fornax cluster Fig. 2. Examples of pPXF \ufb01ts to two GC spectra with di\ufb00erent S/N ratios. In the top left panel, red and black colours show the pPXF \ufb01t and a GC spectrum with S/N\u223c25. Masked regions are shown as blue bands. Blue and green dots in the lower sub-panel show the residuals for unmasked and masked regions, respectively. The top right panel shows a zoom-in view for the absorption features of H\u03b2, Mg\u03b2, NaD, H\u03b1, and the CaT lines. Orange bands in the sub-panels show the expected position of absorption features at the Fornax cluster redshift. The two lower panels show the same, but for a spectrum with S/N \u223c6. Fig. 3. S/N versus g-magnitude for the three classes of objects, as shown in the legend. S/N and radial velocity. One example of such a portfolio is shown in appendix B. Based on these portfolios, we further classi\ufb01ed the objects into three quality classes: Class A objects, where we can clearly see all the above-mentioned absorption features. Class B objects, where we see CaT and H\u03b1 absorption features, but MgB and H\u03b2 are rarely recognizable. Class C objects, where we get Fornax cluster radial velocities, but hardly any absorption features are visible, although their colours are consistent with being GCs. Figure 3 shows the S/N versus g-magnitude plot for A-, Band C-class objects in red, blue and black, respectively. As expected, almost all the class A and B objects have S/N>3, whereas class C objects are mostly fainter and, on average, have a lower S/N ratio. Few C class objects have S/N>10, however their absorption features were contaminated by sky lines. We only consider class A and B objects for our kinematic analysis, but we include the class C objects in our catalogue. As the last step, we applied the heliocentric correction to all the bona\ufb01de selected GCs radial velocities, based on the header information of their observation date. 4. Results A total of 4574 slits were de\ufb01ned in the 25 VIMOS pointings. Around 2400 of them were allocated to GC candidates and compact objects, \u223c800 slits to background galaxies and \u223c1000 slits to stars (Pota et al. 2018). In our analysis, the Esore\ufb02ex pipeline extracted 5131 spectra from the VIMOS data (some slits contained more than one object), and our radial velocity analysis resulted in detecting around 920 possible Fornax cluster GCs. For Article number, page 5 of 22 A&A proofs: manuscript no. paper1_catalog Fig. 4. Radial velocity comparison with previous measurements. The two dashed lines are drawn at \u00b1100 km s\u22121. the remaining spectra, around 1000 are classi\ufb01ed as background galaxies, and approximately 700 objects revealed velocities of foreground stars. About 2500 spectra were of poor spectral quality, having either extremely low S/N, or being a\ufb00ected by strong residual telluric and skyline features. We analyzed in detail the possible GC spectra. After visual inspection of the pPXF \ufb01ts (section 3), we classi\ufb01ed 839 spectra as class A and B objects, and 77 were classi\ufb01ed as class C objects. After accounting for duplicate objects, we obtained 777 unique GC radial velocity measurements for class A and B objects. In appendix C we present an excerpt of our VIMOS GCs catalogue, including all A-, Band C-class objects. The catalogue contains, despite the radial velocity, its error and S/N of the spectrum, also the photometric information in the u, g, r and i bands from the FDS (Cantiello et al. 2020). The full catalogue is available online. In the following subsections, we present our results that are based on the new GC catalogue. 4.1. Duplicate measurements We used the radial velocity measurements of the same objects observed in di\ufb00erent VIMOS masks as a measure to check the robustness of the derived radial velocities and as an estimate for the errors. In \ufb01gure 5, we show the radial velocity measurements and their di\ufb00erences for 62 duplicate targets as a function of g magnitude. The root mean square of the velocity di\ufb00erence is 104 km s\u22121, and the median o\ufb00set is -11 km s\u22121. In case an object has a velocity di\ufb00erence of more than 3\u03c3 of the corresponding uncertainty on the individual measurements, we take the velocity of the higher S/N spectrum; otherwise, we take the error weighted average velocity of two spectra. 4.2. Comparison with previous measurements Several past studies have probed the GC systems in the Fornax cluster. Schuberth et al. (2010) presented a catalogue of 700 GCs from observations with VLT-FORS2 and Gemini-GMOS. Bergond et al. (2007) measured the kinematics of 61 GCs in the intra-cluster space of the cluster based on FLAMES observations. Other studies (like Firth et al. 2007; Chilingarian et al. 2011) have Fig. 5. Velocity comparison of duplicate measurements. Red stars and black dots show the radial velocity from two di\ufb00erent measurements of the same object, as a function of g magnitude. The bottom panel shows the velocity di\ufb00erence between the two measurements. The solid and dashed lines are drawn at \u2206v = 0 and \u00b1 100 kms\u22121, respectively. targeted and analyzed the most massive compact stellar objects around NGC 1399. These literature velocity measurements of GCs provide us another way to verify and check our derived radial velocity analysis\u2019s robustness. Comparing our sample with Pota et al. (2018), we obtained a match for 369 objects. Out of those, 22 objects were found to have a velocity di\ufb00erence of more than 3\u03c3. Excluding the outliers, the RMS of the velocity di\ufb00erence is 72 km s\u22121 and the median o\ufb00set 32 km s\u22121. Here, the median o\ufb00set is de\ufb01ned as the median of the velocity di\ufb00erence distribution between our GCs radial velocities minus the matched literature GCs velocities. With the GC sample of Schuberth et al. (2010), we obtained a match for 103 objects, of which only 5 were found to have a velocity di\ufb00erence of more than 3\u03c3. Excluding these 5 outliers, we obtain an RMS of 80 km s\u22121 and median o\ufb00set of 43 km s\u22121. We visually inspected all the outliers in both samples and found that our \ufb01ts to the spectra look very reliable and therefore neglect the previous measurements of Pota et al. (2018) and Schuberth et al. (2010) for the outliers. In \ufb01gure 6 we show the velocity di\ufb00erences to both samples. Finally, we compared our velocity catalogue with all other available literature studies. Table 1 summarizes the number of matched objects with our velocity catalogue objects. Figure 4 shows the velocity comparison between velocities measured in this work and from the previously available catalogues. We speculate that the measured mean velocity o\ufb00sets between our and literature datasets might just be due to systematics in the zero points of the wavelength calibration, as it is common in multi-slit spectroscopy. All o\ufb00sets are minor and within the overall velocity scatter, and therefore, we did not attempt to correct for them. 4.3. Photometric properties To get the photometric properties of our GC sample, we matched it with the photometric ugri and gri catalogues presented by Cantiello et al. (2020). We get a photometric match for 700 and 770 objects with the ugri and gri catalogues, respectively. To separate our GC sample in blue and red GCs, we follow the procedure used by Angora et al. (2019) and Cantiello et al. (2020), namely Gaussian Mixture Modelling (GMM) implemented through the Article number, page 6 of 22 Avinash Chaturvedi et al.: Globular cluster kinematics in the Fornax cluster Fig. 6. Velocity measurement comparison with the GC sample of Schuberth et al. (2010) (left panel, blue dots) and that of Pota et al. (2018) (right panel, red dots) as function of g magnitude. The solid and dashed lines are drawn at \u2206v = 0 and \u00b1 100 kms\u22121, respectively. Fig. 7. Results of Gaussian Mixture Modeling. Left panel: Histogram and colour bi-modality of the GCs in g \u2212i colour distribution. Blue and red Gaussian curves are obtained from the GMM and represent the blue and red GC populations. Right panel: Same as left panel but for the u \u2212r colour distribution. Table 1. Matched number of objects from this study to previous studies, rms scatter and median o\ufb00set of the comparison (our\u2212previous work). Previous Study Matches RMS ( km s\u22121) Median o\ufb00set ( km s\u22121) Pota et al. (2018) 369 72 32 Schuberth et al. (2010) 104 80 43 Mieske et al. (2002) 13 102 -38 Drinkwater et al. (2000) 10 171 9 Hilker et al. (2007) 1 38 38 Kissler-Patig et al. (1999) 10 125 -69 Mieske et al. (2008) 5 38 -3 Bergond et al. (2007) 18 59 21 Firth et al. (2007) 11 68 33 Hilker & Puzia (priv.comm.) 20 84 36 Chilingarian et al. (2011) 4 34 2 python library sklearn (Pedregosa et al. 2012). We \ufb01tted a bimodal Gaussian distribution to the GC populations in the u \u2212r and g \u2212i colour-colour diagrams. Figure 7 shows the projected distributions of the bivariate Gaussian (and their components for blue and red GCs) on the g \u2212i and u \u2212r colour axes. A linear \ufb01t between the intersection of blue and red Gaussians for g \u2212i and u \u2212r is used to divide the GCs into the respective samples. Table 2 shows the results of our GMM. Out of 770 objects, our sample has 56% blue and 44% red GCs, as judged from the photometrically complete gri sample. Article number, page 7 of 22 A&A proofs: manuscript no. paper1_catalog Fig. 8. Radial velocity map of GCs within 1.5 square degrees of the Fornax cluster. Major galaxies are shown with green crosses. Left panel: GCs from this work are shown as dots. Squares and stars show GCs from Fahrion et al. (2020a) and previous literature measurements, respectively. Right panel: Smooth velocity map using the LOESS technique. The smoothing parameters are given in the legend of the plot. Fig. 9. Rotational velocity of all, red and blue GCs within 30 arcminutes. We modelled the full sample as well as a restricted sample, excluding the F3D GCs from Fahrion et al. (2020a) as most F3D GCs are bound to their respective host galaxies. Table 2. Bi-variate Gaussian parameters using GMM. Blue Red Parameter g \u2212i u \u2212r g \u2212i u \u2212r \u00b5 0.876 1.872 1.104 2.427 \u03c3 0.009 0.034 0.016 0.074 4.4. Radial Velocity Map Combining our radial velocity measurements with previous literature measurements and the recent catalogue presented by Fahrion et al. (2020a), brings the total number of con\ufb01rmed GCs in the Fornax cluster to 2341 objects. The catalogue of Fahrion et al. (2020a) is based on integral-\ufb01eld observations of the Fornax3D project (F3D, Sarzi et al. 2018) and provides the GC velocities in the inner regions of 32 Fornax cluster galaxies, many of them located in the cluster outskirts, and thus not shown in \ufb01gure 8, which displays the radial velocity of GCs from our sample within 1.5 square degrees. The combined sample of GCs provides a representative probe of the whole GC system in the core of Fornax. The GC distribution in the innermost one square degree around NGC 1399 is very uniform and geometrically complete. It amounts to more than 50% of our total GC sample. To better visualize and identify patterns in the velocity distribution, we smooth the radial velocity with the locally weighted regression method LOESS (Cleveland & Devlin 1988). We implemented it with the python version developed by Cappellari et al. (2013). LOESS tries to estimate the mean pattern by averaging the data into smaller bins. Normally, a linear or quadratic order polynomial is used in the LOESS technique. In our sample, some of the GCs in the phase space distribution were utterly isolated. Using a lower order polynomial could cause over-smoothing of distinct kinematic features. To prevent this, we used a 3rd order polynomial and a low value of smoothing factor of 0.1 (Cleveland 1979; Cleveland & Devlin 1988). The LOESS smooth radial velocity map is shown in the right panel of \ufb01gure 8. To check for any rotational signature in the GC system, we model the GC kinematics with a simple model that describes the rotational amplitude and velocity dispersion, similar to the work of Fahrion et al. (2020a) (see their section 4.2.1). To have a homogeneous phase-space distribution of GCs, we consider GCs within 30 arcminutes from the central galaxy NGC 1399. In \ufb01gure 9 we show the rotational amplitude and measured velocity dispersion for the full sample as well as red and blue GCs. We \ufb01nd a small rotational velocity of less than 30 km s\u22121 for the full sample and the blue GCs. Red GCs show a signi\ufb01cant rotational velocity of 60 km s\u22121 with a rotation axis of PA=70\u25e6(measured North over East). The rotation axis for the entire sample is close to the one of red GCs and is certainly dominated by them. In \ufb01gure 15, we show the rotation axis (black line) of the red GCs. For the red GCs, the ratio of Vrot/\u03c3 is 0.22, meaning a low but signi\ufb01cant rotational signature, similar to that of other massive galaxies. Only a few studies have examined the kinematics of the stellar body of NGC 1399; for example, Saglia et al. (2000) used longslit observations to obtain the stellar kinematics out to 1.6\u2019 of NGC 1399, giving a value of stellar Vrot/\u03c3 \u223c0.11. This low rotation measure is consistent with NGC 1399\u2019s nearly round shape (\u03b5 = 0.1), characterising this galaxy as a slow rotator. The central stellar kinematics of NGC 1399 cannot be straightforArticle number, page 8 of 22 Avinash Chaturvedi et al.: Globular cluster kinematics in the Fornax cluster Fig. 10. Distribution of GCs (red dots) and UCDs (yellow dots) in the colour-colour and colour-magnitude diagram. Left panel: The distribution of GCs in the (g \u2212r) vs (g \u2212r) space. The lower subplot shows the radial velocity as a function of (g \u2212i) colour. Right panel: Same as right panel, but in i mag vs. (g \u2212i) space. Fig. 11. Phase-space diagrams of radial velocity vs cluster-centric distance. In both panels the grey dots show the full sample, the limes crosses major galaxies within 300 kpc, and the dashed horizontal lines mark the systemic velocity of NGC 1399. Left panel: Velocity distribution for red GCs. Right panel: The same for blue GCs. Yellow dots indicate UCDs, and the lime crosses mark the major galaxies of the Fornax cluster. ward compared to the outer GC kinematics and rotation. They most probably re\ufb02ect the formation of the central stellar spheroid via violent relaxation of early mergers. The photometric PA of NGC 1399\u2019s major axis is \u223c112\u25e6degrees (within 1\u2019) and varies between 90-110\u25e6at outer radii (up to 20\u2019) (Iodice et al. 2016), which is more or less consistent with the East-West elongation of the extended GC system. More measurements of the outer stellar kinematics around NGC 1399 are needed to understand if the GCs and stellar halo components are kinematically coupled or decoupled. Previously, Schuberth et al. (2010) studied the rotation of GCs around NGC 1399 and found a rotation amplitude of 61\u00b135 km/s for the red GCs and 110-126 km/s for the blue GCs. In contrast to Schuberth et al. (2010), we did not \ufb01nd a strong rotational signature for the blue GCs. This might be due to our large and uniform sample of GCs, whereas the Schuberth et al. (2010) sample was limited to 10 arcminutes and geometrically not complete. We also notice di\ufb00erent patches of low(<1000 km s\u22121) and high-velocity regions (>1700 km s\u22121), elongated in east to west and north-east to south-west structures. We discuss the correlations between the photometric and kinematical properties of the GCs in the subsequent discussion section. 5. Discussion In this section, we connect the photometrically discovered intracluster GCs with the full sample of 2341 con\ufb01rmed GCs and study their phase-space distribution and radial velocity dispersion pro\ufb01le. 5.1. Colours, phase space and spatial distribution We study the properties of red and blue GCs separately. To divide the entire sample of 2341 GCs into red and blue sub-populations, we use the g \u2212i colour distribution since the shallower u-band photometry does not exist for all GCs. We adopt a value of g\u2212i = 0.978, obtained from the GMM (\ufb01g. 7, left panel) to separate the two sub-populations. The brightest compact objects of our catalogue are a mix of genuine massive globular clusters and Article number, page 9 of 22 A&A proofs: manuscript no. paper1_catalog Fig. 12. Velocity dispersion pro\ufb01les in the Fornax cluster core region as a function of projected distance from NGC 1399. Upper panel: The black line denotes the dispersion pro\ufb01le of the complete sample of 2341 GCs. The grey band marks 1\u03c3 uncertainty. Red and blue dots represent the values for the red and blue GCs, with 100 GCs per bin. The dashed blue and red lines represent the dispersion pro\ufb01les for the GC analysis of Schuberth et al. (2010) data. The green and orange dashed lines show the PNe and GC dispersion pro\ufb01les from Spiniello et al. (2018) and Pota et al. (2018), respectively. The horizontal band denotes the velocity dispersion of the Fornax cluster galaxies (Drinkwater et al. 2000). The vertical black dashed line marks the e\ufb00ective radius of NGC 1399 and the vertical grey dashed lines the projected distances of major galaxies (as labelled) from NGC 1399. Lower panel: The dispersion pro\ufb01le of ICGC candidates with two di\ufb00erent selections is shown. The pink line shows ICGCs and outer halo GCs selected further than 2re\ufb00away from major galaxies, and the light pink band represents the 1\u03c3 uncertainty. The dark red line represents ICGCs that were selected outside 4re\ufb00around major galaxies (see text for details), and the lighter red band denotes its 1 \u03c3 uncertainty. stripped nuclei, dubbed as ultra-compact dwarf galaxies (UCDs) in the literature (Hilker et al. 1999b; Drinkwater et al. 2000, 2003). For selecting UCDs, we use a magnitude cut of mi < 20 mag (Mieske et al. 2002) and found a total of 72 UCDs. In \ufb01gure 10, we show the distribution of GCs and UCDs in the magnitude, color (g \u2212i and g \u2212r) and velocity spaces. As can be seen from those plots, the UCDs are, on average redder than the GCs. This con\ufb01rms the \u2019blue tilt\u2019 of bright GCs and UCDs that was already found in photometric samples of rich GC systems (e.g. Dirsch et al. 2003; Mieske et al. 2010; Fensch et al. 2014). There exist some very blue and very red GCs, with (g \u2212i) < 0.6 and (g \u2212i) > 1.6, respectively. While the blue GCs might be explained by young to intermediate ages, the very red colours point to either very metal-rich populations, dust obscuration, or blends in the photometry. Future investigations are needed to clarify their nature. In \ufb01gure 11, we show the radial velocity of red (left panel) and blue (right panel) GCs as a function of the cluster-centric distance. Major galaxies around NGC 1399 are shown as lime crosses. We observe that most of the red GCs are centrally concentrated on the systematic velocities of these galaxies (taken from Iodice et al. 2019). Within 50 kpc from NGC 1399, red GCs homogenously span a range of relative velocities of \u00b1500 km s\u22121, and further outside follow a wedge shaped structure to smaller relative velocities till 150 kpc. Schuberth et al. (2010) had observed the wedge shaped feature of the red GCs con\ufb01ned within 50 kpc (see their Fig. 9, right panel). However, with the current larger sample of GCs, we notice that it extends out to larger distances. Most major galaxies at cluster-centric distances larger than 160 kpc have similar systemic velocities as NGC 1399. An interesting exception at \u223c220 kpc distance is NGC 1380, which has a high systemic velocity of \u223c1800 km s\u22121. Red GCs with similar high velocities are scattered out to \u00b150 kpc galactocentric distances in \ufb01lamentary structures around this galaxy, possibly suggesting a disturbance of its halo. Despite most red GCs being concentrated around major galaxies, there exists a noteworthy number of red GCs that seems not to be related to any particular galaxy. Those are candidates of intra-cluster GCs. In contrast to red GCs, blue GCs show a more complex and irregular pattern in the phase space diagram. In particular, between 60-150 kpc, they extend to larger relative velocities and \ufb01ll the intra-cluster regions between the galaxies. Apart from that, blue GCs occupy the outer halos of the major galaxies. Our UCD sample shows a radial velocity distribution in between 750-2500 km s\u22121, with a mean velocity close to the radial velocity of NGC 1399, with a velocity scatter of 312 km s\u22121, consistent with the fainter GCs. There also exists a dozen of red and blue GCs at low radial velocities of \u223c500 km s\u22121 at cluster-centric distances between 10-220 kpc. This was already noticed for the blue GCs by Richtler et al. (2004). Due to their high relative Article number, page 10 of 22 Avinash Chaturvedi et al.: Globular cluster kinematics in the Fornax cluster Fig. 13. Selection of potential ICGCs around NGC 1399 (\ufb01rst row) and NGC 1374 (second row). Left panel: the GC distribution within 5re\ufb00(blue dashed circle). The radius of 2re\ufb00is indicated as red dashed circle. Middle panel: the distribution of GCs in projected phase space. Red dots show the galactic GCs within 2re\ufb00and black dots the de\ufb01ned ICGCs. Vertical red and blue dashed lines indicate 2re\ufb00and 5re\ufb00, and the grey horizontal lines give the 1and 2-sigma scatter of GC velocities within 2re\ufb00around the systemic velocity of NGC 1374. Right panel: Velocity histograms of of ICGCs (black) and galactic GCs (red) are shown. The black dashed line marks the LOS velocity of NGC 1374 and the dashed grey lines the 1and 2-\u03c3 scatter of GCs radial velocities as also shown in the middle panel. Fig. 14. Radial velocity histograms of the full sample and the intracluster GCs. The vertical green dashed line indicates the radial velocity of NGC 1399. The vertical black, magenta, and dark red dashed lines indicate the mean velocities of \ufb01tted Gaussian to the three sets of GCs. velocity with respect to the Fornax cluster, exceeding 800 km s\u22121, they might constitute unbound GCs from galaxy encounters with highly radial orbits in the line-of-sight, or a sheet of foreground \u2019intra-space\u2019 GCs. 5.2. Velocity dispersion pro\ufb01le The large spatial coverage of our sample enables us to measure the velocity dispersion pro\ufb01le of the GCs out to 300 kpc. For this, we de\ufb01ne circular bins such that each bin has 100 GCs, and measure the velocity dispersion as the standard deviation of radial velocities in that bin. The uncertainty on the velocity dispersion is determined through a bootstrap technique. In each bin, we measure the velocity dispersion 1000 times and take its scatter as uncertainty. For the total sample, we obtain 23 bins, where the outermost bin has only 41 GCs. We followed the same procedure for red and blue GCs separately, resulting in 10 and 20 bins, respectively. In \ufb01gure 12 we show the velocity dispersion pro\ufb01le of our GC sample. The black line indicates the dispersion measurement for the full sample and the grey band denotes its 1\u03c3 uncertainty. Blue and red dots indicate the values for the blue and red GCs. The vertical grey dashed lines show the projected cluster-centric distances of NGC 1404 and other major galaxies. For reference and comparison, we have included the velocity dispersion measurements from previous studies as well, as indicated in the legend and caption. We have also measured the velocity dispersion pro\ufb01le of potential intra-cluster GCs (ICGCs) within the Fornax core region, shown as a magenta line in the lower panel of \ufb01gure 12, with the light pink band indicating its 1 \u03c3 uncertainty. The selection of the ICGCs was made by excluding GCs around major galaxies by performing cuts in the phase-space distribution. First, we calculate the scatter in the radial velocities of GCs within 2 e\ufb00ective radii (re\ufb00) of each galaxy, (taken from Iodice et al. 2019). We use \u00b12\u03c3 of this velocity scatter around the galaxy\u2019s LOS velocity as Article number, page 11 of 22 A&A proofs: manuscript no. paper1_catalog Red GCs All GCs Blue GCs Red GCs Fig. 15. GCs with con\ufb01rmed radial velocities (coloured dots) are plotted over the surface density map of photometric GC candidates from the FDS (Cantiello et al. 2020). Top panel: Shown is the full GC radial velocity sample. Middle panel: Radial velocity distribution of red GCs. The black line shows the rotation axis of the red GCs at PA=70\u25e6, measured north to east. Major galaxies are labelled in green. Bottom panel: The same for blue GCs. The density scale plotted on the bottom represents the number of GCs from the photometric sample per square arcminute. Article number, page 12 of 22 Avinash Chaturvedi et al.: Globular cluster kinematics in the Fornax cluster the lower and upper boundary to select the GCs belonging to each galaxy. The remaining GCs are classi\ufb01ed as ICGC candidates, being aware of the fact that this selection might include outer halo GCs that probably are still bound to their parent halos (see below). Figure 13 shows examples of the ICGC candidate selection for the central galaxy NGC 1399 and the galaxy NGC 1374. For the central galaxy, we clearly see a fraction of GCs with high relative velocities lying inside 2re\ufb00, which are identi\ufb01ed as the ICGCs. The true central concentration of ICGCs is di\ufb03cult to access since they might overlap in radial velocity with GCs of the central galaxy. We note that our ICGCs selection criteria only provides a rough separation between GCs bound to individual galaxies and those belonging to an unbound, or at least disturbed intra-cluster population. Bound GCs might actually reach out to larger e\ufb00ective radii, but also true ICGCs might be projected at similar velocities in front or behind a galaxy and thus are \u2018hidden\u2019 from detection. Only a detailed dynamical analysis of the mass pro\ufb01le around each galaxy can provide a cleaner sample of ICGCs. This is beyond the scope of this paper. In any case, according to our selection criteria, 719 GCs, almost 31% of the total sample, are classi\ufb01ed as ICGCs. This number probably is an upper limit of true ICGSs due to the abovementioned limitations of our selection criteria. Also, geometrical incompleteness of GC velocities within 2-4 re\ufb00around the major galaxies plays a role. Whereas the central regions are covered by MUSE observations, and thus GC counts are complete (Fahrion et al. 2020a) there, the outer halo regions are not fully covered by the VIMOS pointings, as can be seen in the uneven distribution of outer GCs around NGC 1374 (\ufb01g. 13, left panel). To produce a cleaner ICGC sample, we performed a similar selection as mentioned above but with a phase space cut at >4re\ufb00. This left us with a sample of only 286 ICGCs (12% of the total sample). The velocity dispersion pro\ufb01le of this set of GCs is shown as the dark-red band in the lower panel of \ufb01gure 12. Figure 14 shows the velocity distribution of the full and ICGCs samples. For all three samples, the mean velocity lies close to the radial velocity of NGC 1399. The velocity scatter of the full sample and ICGCs, selected at 2re\ufb00, is close to 300 km s\u22121, whereas ICGCs selected outside 4re\ufb00show a larger velocity scatter of 455 km s\u22121 around a mean velocity of 1400 km s\u22121. In the following, we describe the features and irregularities noticed in the velocity dispersion pro\ufb01les, starting from the center outwards: 1) Between 2 and 5 arcminutes: The dispersion pro\ufb01le takes a steep rise from 220 to 350 km s\u22121 within 1 re\ufb00of NGC 1399. Mostly blue GCs contribute to this rise. It is consistent with the rise previously reported by Schuberth et al. (2010). Red GCs show a constant velocity dispersion of \u223c270 km s\u22121 within 1 re\ufb00 of NGC 1399, in agreement with Schuberth et al. (2010) and Pota et al. (2018). 2) Between 5 and 10 arcminutes: The total dispersion pro\ufb01le \ufb02attens around a value of \u223c300 km s\u22121. While the dispersion pro\ufb01le of the blue GCs decreases, the one of the red GCs rises. This rise is caused by the superposition of the GCs of NGC 1404, which has a high systemic velocity of 1944 km s\u22121. Within these radii limits, Spiniello et al. (2018) have also reported a similar increase in the PNe velocity dispersion pro\ufb01le. The lower velocity dispersion of red GCs from Schuberth et al. (2010) can be explained by the increase of sample size in our study, which added several GCs with more extreme velocities. For the ICGCs velocity dispersion pro\ufb01le, we observe a value of \u223c500 km s\u22121at 8 arcmin. This is arti\ufb01cial and caused by the exclusion of GCs within 2 re\ufb00 of NGC 1399. Thus, we are left with GCs with extreme radial velocities, resulting in the large dispersion value. 3) Beyond 10 arcminutes: The dispersion pro\ufb01le remains \ufb02at around \u223c300 km s\u22121 until 18 arcmin, consistent with Pota et al. (2018) results. Further out, the GCs belonging to individual galaxies dominate the velocity dispersion values of all GCs and cause large variations from <200 to >300 km s\u22121. After a steep decrease from 500 to 300 km s\u22121, the velocity dispersion pro\ufb01le of ICGCs behaves smoother with nearly constant values around 290 km s\u22121 out to 40 arcmin. This value is relatively consistent with the velocity dispersion of cluster galaxies Drinkwater et al. (2000). A similar trend with PNe kinematics has been observed by Spiniello et al. (2018) out to 30 arcmin. Iodice et al. (2016), using g-band light distribution around NGC 1399, identi\ufb01ed a physical break radius at 10 arcmin, separating the total light pro\ufb01le into a central spheroid light of NGC 1399 and an outer exponential halo. The constant value and \ufb02attening of the ICGC dispersion pro\ufb01le beyond 12 arcmin gives the kinematical con\ufb01rmation to this physical break radius. 5.3. Globular clusters and planetary nebulae Spiniello et al. (2018) presented the kinematics of 1452 PNe out to 200 kpc in the Fornax cluster core, spatially extending the results presented in McNeil et al. (2010). Although the velocity dispersion pro\ufb01le of PNe overall follows the kinematics behaviour of the red GCs, slight di\ufb00erences in the pro\ufb01les can be found. In \ufb01gure 12, the green dashed line shows the velocity dispersion pro\ufb01le of PNe taken from Spiniello et al. (2018). Within 5 arcminutes, the velocity measurements we obtained for the red GCs show a slightly higher value than the PNe (this was true also in Spiniello et al. (2018), but the di\ufb00erence between the velocity dispersion values was smaller). In between 5-10 arcminutes, the PNe show a high dispersion peak value at \u223c380 km s\u22121, unlike our red GCs, and better match the value we measured for blue GCs. Between 10-20 arcmin, the velocity dispersion for both PNe and red GCs, decreases, with the red GCs showing a very low value at the projected distance of NGC 1387. Beyond 20 arcmin, the PNe velocity dispersion shows a \ufb02at behaviour at \u223c300 km s\u22121, slightly above that of blue and red GCs. In general, the PNe velocity dispersion pro\ufb01le follows closely that of all GCs beyond 10 arcmin, rather than that of red or blue GCs individually. This might suggest that PNe trace the behaviour of both stellar populations, the one of galaxies as well as of intra-cluster light. 5.4. Intracluster GC kinematics The \ufb01rst photometric wide-\ufb01eld search for GCs in the Fornax cluster by Bassino et al. (2006) reported the existence of an ICGC populations based on GC overdensities in regions between the central galaxy NGC 1399 and neighbouring galaxies. Later, Bergond et al. (2007) and Schuberth et al. (2008) kinematically identi\ufb01ed and quanti\ufb01ed the properties of some ICGCs. Through the FDS survey, D\u2019Abrusco et al. (2016) reported the discovery of an extended GC density distribution in the Fornax core region with several well de\ufb01ned overdense regions, and Iodice et al. (2016) discovered a faint stellar bridge coinciding with the GC over density between NGC 1399 and NGC 1387, con\ufb01rming the interaction between these two galaxies. Our extended and spatially homogeneous GC catalogue allows us to study the kinematical properties of the enhanced density regions of GCs in Fornax. In \ufb01g. 15, we plot our full GC radial velocity sample on top of a smoothed density distribution Article number, page 13 of 22 A&A proofs: manuscript no. paper1_catalog Fig. 16. Distribution of ICGCs selected with a phase space cut at >2re\ufb00. GC overdensity regions are named as in D\u2019Abrusco et al. (2016). The magenta boxes show the regions where we perform 2D KS tests. Black contours show the visibly selected regions to study the stream properties. Table 3. 2D KS test and properties of the ICGCs. Intra-cluster region p-value Median velocity [ km s\u22121] Velocity scatter [ km s\u22121] Blue to red GCs ratio (1) (2) (3) (4) (5) Reg A 0.37 1419 200 1.17 Reg C 0.72 1559 303 1.92 Reg F 0.84 1477 312 1.56 Reg G 0.66 1352 291 1.51 Stream A 0.48 1375 127 0.87 Stream A 2nd peak \u2013 1723 56 \u2013 Stream C 0.20 1384 117 2.03 Stream C 2nd peak \u2013 1824 128 \u2013 Stream F 0.98 1452 228 1.15 Stream G 0.54 1362 166 2.08 Notes: Column 3 and 4 show the mean velocity and velocity scatter of GCs within respective intra-cluster region. of photometric GC candidates by Cantiello et al. (2020). To create the smoothed density map, we use the non-parametric kernel density estimates based on python-scikit-learn kernel density routine by Pedregosa et al. (2011). From the FDS catalogue, a density of 0.75 GCs/arcmin2 is expected within the central region of the Fornax cluster. To include at least a couple of GCs in the density maps and to create the visual impression of the GCs streams, we adopted a Gaussian kernel bandwidth of 0.015 degrees, which is \u223c1 arcmin. The top, middle, and lower panels show the distribution of all, red and blue GC candidates, respectively. Con\ufb01rming the FDS survey \ufb01ndings of D\u2019Abrusco et al. (2016) and Cantiello et al. (2020), we also observe an elongated distribution of con\ufb01rmed GCs in the east-west direction, centred on NGC 1399. Looking at the radial velocity patterns in the smoothed velocity map in \ufb01g. 8, we \ufb01nd that, on the west side of NGC 1399, GCs have a relatively higher radial velocity than on the east side. Further on the east side of NGC 1399, in the over-dense G and F features, GCs show an extended, \ufb01lamentary spatial distribution. The azimuthal distribution of ICGCs selected outside 4re\ufb00of major galaxies is shown in \ufb01gure 17. It highlights the east-west elongation of ICGCs around NGC 1399. In the two lower panels of that \ufb01gure, where the azimuthal distribution is shown as a function of cluster-centric distance and radial velocity, respectively, Article number, page 14 of 22 Avinash Chaturvedi et al.: Globular cluster kinematics in the Fornax cluster Fig. 17. Azimuthal distribution of ICGCs selected outside 4re\ufb00radii around major galaxies (see text for details). Top panel: Histogram of the ICGC position angle (PA), with bin size of 30\u25e6. Middle panel: Clustercentric distance vs PA. Bottom panel: Radial velocity vs PA. Lime crosses indicate major galaxies. phase-space features in between galaxies become apparent. A detailed dynamical analysis of those features is beyond the scope of this paper. We investigated the spatial correlation between the photometric and our radial velocity catalogue. For this, we perform a 2-dimensional Kolmogorov-Smirnov (2D-KS) test (Peacock 1983) in the four GC overdensity regions named Reg. A, C, F and G following the same naming convention as in D\u2019Abrusco et al. (2016). Fig. 16 shows the phase-space distribution of the ICGCs selected with a cut of >2re\ufb00and indicates the rectangular regions around the GC overdensities. For all the regions, we get a p-value higher than 0.20, which means that the spatial distributions of photometrically selected and con\ufb01rmed GCs are correlated by more than 3\u03c3 signi\ufb01cance. Figure 18 shows the radial velocity histograms of ICGCs falling within these four overdense regions. The mean velocities are \u223c1450 km s\u22121, close to the radial velocity of NGC 1399 and the Fornax cluster itself. This suggests that the GCs in these regions are ICGCs, kinematically in\ufb02uenced by the Fornax cluster potential. In table 3, we list the p-values obtained from the 2D-KS tests for all regions and the \ufb01tted Gaussian mean and velocity scatter. These selected rectangular regions inhabit both red and blue GC populations, but on average, the blue GCs dominate in numbers. In contrast to this, GCs within the 2re\ufb00 radii of galaxies show, on average, a higher fraction of red GCs. We list the number ratio of blue to red GCs in table 3. With the small sample size of ICGCs, and given the caveats of the rough ICGC selection criteria mentioned in 5.2, it is hard to speculate about the nature of the GCs in the over-dense regions. Looking at \ufb01gure 16 it is quite clear that our spectroscopic sample provides kinematical information on the visible photometric streams in the overdense regions. Our 2D KS test performed for the selected rectangular regions, demonstrates that our spectroscopic sample is statistically coherent with the photometric sample. To get a hint on the possible progenitor galaxies of ICGCs and their physical properties, speci\ufb01cally, the ones which are tracing the visible streams (marked in \ufb01gure 16 with the black contours), we plot the radial velocity and g \u2212i colour histograms in \ufb01gure 18. We name these streams A, C, F and G. In the following we explain the features noticed within these streams: Stream A is a feature related to the faint stellar bridge reported by Iodice et al. (2016), connecting NGC 1387 and NGC 1399 (region A). In this stream, the GCs radial velocity distribution shows two peaks, one close to the radial velocity of the central galaxy NGC 1399 (at 1374 km s\u22121) and the other at 1723 km s\u22121. Both peaks show a low velocity scatter of values 127 km s\u22121 and 56 km s\u22121, respectively. The second peak is possibly arising from GCs on the east side of NGC 1387, which is interacting with NGC 1399. These GCs might be tidally stripped o\ufb00the halo of NGC 1387. In the radial velocity histograms, we mark the contribution of red GCs in red colour. We notice that red GCs mostly contribute to the \ufb01rst radial velocity peak, whereas the blue GCs dominate the second peak. This suggests that tidallystipped GCs, those that are outside the systemic Fornax cluster velocity, are mostly blue. In the g\u2212i colour histogram of stream A (bottom panel of \ufb01g. 18), we also observe two peaks, suggesting the presence of red as well as blue GCs. Studying the GC colour distributions of early-type galaxies in the Virgo cluster Peng et al. (2006) have shown that luminous galaxies (MB \u223c-21 mag) have mostly bimodal GC colour distributions, whereas low luminosity galaxies (MB \u223c\u221216) have dominant fractions of blue GCs. In stream A, we see a bimodality in the g \u2212i colour histogram with a larger fraction of red GCs. Comparing this kind of bimodality with results of Peng et al. (2006) suggests that GCs in streams A are mostly generated by the interaction of the luminous galaxy NGC 1387 and NGC 1399. Stream C in the overdense region C, consists of a chain of GCs in the vicinity of NGC 1380 and NGC 1380B. Cantiello et al. (2020) pointed out that this GC overdensity could result from the LOS projection of adjacent GC systems. Indeed, the GCs in the vicinity of NGC 1380 and NGC 1380B (but beyond 2re\ufb00 radii), have radial velocities larger than 1700 km s\u22121, consistent with the systemic velocities of both galaxies. In the GC radial velocity histogram of stream C we also observe two peaks, one close to the radial velocity of NGC 1380 and the other close to the NGC 1399 radial velocity. Similar to stream A, stream C GCs also show a bimodal g \u2212i colour histogram, with a higher fraction of the blue GC population, although the bimodality is not as clear due to the small sample size. In stream C, both radial velocity peaks are dominated by blue GCs with radial velocity scatters of \u223c110 km s\u22121. In stream C, both radial velocity peaks are dominated by the blue GCs with radial velocity scatters of around 110 km/s. In stream C, blue GCs are almost twice as abundant than red GCs. As shown in the studies of Peng et al. (2006), an asymmetrical distribution of GCs, with an inclination towards blue GCs, suggests that the GCs in stream C are generated by galaxies in the magnitude range \u221220 < MB < \u221219 mag. In stream F, GCs show a radial velocity distribution in between 700-1800 km s\u22121with a mean velocity and scatter of 1452 km s\u22121 and 228 km s\u22121, respectively. We \ufb01nd an equal fraction of blue to red GCs in stream F. Stream G harbours GCs in the velocity range 800-2000 km s\u22121, with a peak velocity close to the systemic velocity of Fornax and is mostly dominated by the blue GCs. Those GCs Article number, page 15 of 22 A&A proofs: manuscript no. paper1_catalog Fig. 18. Radial velocity and g \u2212i colour histograms of the intra-cluster regions. Top panel: radial velocity of GCs lying within the rectangular boxes A, C, F and G (left to right). Middle panel: radial velocity of GCs lying within the streams A, C, F, and G (left to right). The radial velocities of the red GCs are marked with red colour. Bottom panel: g \u2212i colour histogram of GCs lying within the streams A, C, F, and G (left to right). The black vertical dashed line marks the radial velocity of NGC 1399, the vertical green lines show the peak positions of the \ufb01tted Gaussians. For streams A and C, double Gaussians were \ufb01tted. comprise a kinematically coherent group and in the g \u2212i colour histogram, we observe a peak towards blue GCs, suggesting that the progenitors of GCs in stream G are low luminosity galaxies (Peng et al. 2006). Wee also notice that in the south-east of NGC 1404, next to the G feature, some GCs show radial velocities higher than 1700 km s\u22121, similar to the systemic velocity of NGC 1404. As previously shown by Bekki et al. (2003), and more recently through X-ray studies by Su et al. (2017), NGC 1404 su\ufb00ered from tidal interaction with NGC 1399 in the past few gigayears. Thus, tidally released GCs are expected around NGC 1404, and we now might see for the \ufb01rst time, the kinematical signature of those. Detailed dynamical models will be necessary to assess which GCs in the overall phase space distribution might have belonged to NGC 1404 in the past. Furthermore, we notice that GCs around NGC 1427A, on the south-west side of NGC 1399, show a stream-like distribution with a gradual decrease in radial velocity from 1500 km s\u22121 north of 1427A to 1100 km s\u22121 south of the galaxy. This kinematic feature might suggest that NGC 1427A is moving in south-north Article number, page 16 of 22 Avinash Chaturvedi et al.: Globular cluster kinematics in the Fornax cluster direction, loosing its GCs during its cruise through the core of the Fornax cluster (e.g. Lee-Waddell et al. 2018). Finally, we looked for the spatial distribution and numbers of red and blue GC sub-populations in the over-dense regions. As can be seen in \ufb01gure 15, blue GCs dominate the intra-cluster overdense regions between the Fornax cluster galaxies, whereas red GCs are more concentrated on the galaxies. The dominance of the blue (and thus mostly metal-poor) GCs in the Fornax IC regions and in the visually identi\ufb01ed streams suggests that the Fornax IC component results from the accretion of tidally stripped low mass galaxies. Our results are in accordance with the dominantly blue ICGCs population observed for the Virgo cluster (see Ko et al. 2017; Longobardi et al. 2018b). We list the number ratio of blue to red GCs in each region and the fours streams in table 3. 6. Conclusions We have re-analyzed VLT/VIMOS data of the central one square degree of the Fornax cluster, leading to produce radial velocity measurements of 777 GCs, which we present in a catalogue. Adding literature data, this provided us the largest and spatially most extended compilation of GC radial velocities in the Fornax cluster. This sample was used to kinematically characterize GCs in the core of the cluster. In the following, we highlight the main results of our work: 1) With the improved VIMOS ESO re\ufb02ex pipeline 3.3.0 and careful analysis of radial velocity measurements with pPXF over the full spectral range, we have doubled the number of GC radial velocity measurements on the same dataset that was previously analyzed by Pota et al. (2018). Combined with previously measured values from the literature, we gathered a sample of 2341 GC radial velocities in Fornax. 2) We used the Gaussian mixture modelling technique to divide the full sample of 2341 GCs into a blue (56%) and a red (44%) GCs sub-population. The phase space distribution of red GCs shows that most of them are bound to the major cluster galaxies, in particular the central galaxy NGC 1399. In contrast, blue GCs are spatially extended and show more irregular kinematics patterns. They occupy the outer haloes of galaxies and the intra-cluster space. 3) Using the radial velocities of GCs, we measured the dispersion pro\ufb01le out to a radius of 300 kpc, covering almost half of the virial radius of the Fornax cluster. Beyond 10 arcmin (\u223c58 kpc), the dispersion pro\ufb01le of all GCs \ufb02attens. This radius is therefore considered as the break radius separating the potential of NGC 1399 from that of the cluster. This result is strongly con\ufb01rmed by the dispersion pro\ufb01le of potential ICGCs, which shows a \ufb02at behaviour beyond 10 arcmin at a value of 300\u00b150 km s\u22121. 4) The radial velocity map of the full GCs sample kinematically characterizes the previously photometrically discovered ICGC population of the Fornax cluster. The di\ufb00erent over-dense GC regions are marked by streams of higher relative velocity GCs, giving \ufb01rst kinematical evidence of interactions between the central galaxy NGC 1399 and other major galaxies. 5) Finally, we notice that mostly blue GCs dominate the intracluster regions and trace sub-structures that connect NGC 1399 to its neighbouring galaxies. With the future goal to study the Fornax cluster\u2019s mass distribution and assembly history, the presented GC radial velocity catalogue is of unprecedented value in exploring the dynamical structure and evolution of the Fornax cluster and its member galaxies. Acknowledgements: Our sincere thanks to the anonymous referee for helpful feedback and suggestions that improved the manuscript\u2019s scienti\ufb01c content. The bulk of the velocities were derived from the FVSS data taken under the ESO programme 094.B-0687 (PI: Capaccioli). Our special thanks goes to Massimo Cappacioli who dedicated INAF GTO time to spectroscopic Fornax cluster projects. Some velocities of our full catalogue (including literature data) are based on so far unpublished FORS2 data taken under ESO programmes 078.B0632 and 080.B-0337 (PI: Hilker). A. Chaturvedi acknowledges the support from the IMPRS on Astrophysics at the ESO and LMU Munich. A. Chaturvedi also thanks Lodovico Coccato for helpful discussions. M. Cantiello acknowledges support from MIUR, PRIN 2017 (grant 20179ZF5KS). N.R. Napolitano acknowledges \ufb01nancial support from the \u201cOne hundred top talent program of Sun Yat-sen University\u201d grant N. 71000-18841229, and from the European Union Horizon 2020 research and innovation programme under the Marie Skodowska-Curie grant agreement n. 721463 to the SUNDIAL ITN network. G.v.d. Ven acknowledges funding from the European Research Council (ERC) under the European Union\u2019s Horizon 2020 research and innovation programme under grant agreement No 724857 (Consolidator Grant ArcheoDyn). C. Spiniello is supported by a Hintze Fellowship at the Oxford Centre for Astrophysical Surveys, which is funded through generous support from the Hintze Family Charitable Foundation. This research made use of Astropy (https://www.astropy.org)a community-developed core Python package for Astronomy (Astropy Collaboration et al. 2013, 2018).",
                    "introduction": "Understanding the assembly of galaxy clusters provides valuable insight into various aspects of cosmology, like galaxy evolution and formation, gravitational structure formation, intergalactic medium physics, etc. Galaxy clusters are the largest gravitation- ally bound systems, whose assembly is driven by early mergers of massive galaxies embedded in big dark matter (DM) halos and sequential accretion of galaxy groups (e.g. Kravtsov & Borgani 2012). During their growth, various physical processes act on the cluster galaxies, like tidal disturbances, ram pressure strip- ping, secular evolution, and gas accretion, which all contribute in shaping their luminous and dark matter distributions (Kravtsov & Borgani 2012; Duc et al. 2011; Amorisco 2019). Semi-analytic models of galaxy formation and evolution, combined with cos- mological N-body simulations of DM halos in the \u039bCDM frame- work, have shown that the amount of substructures in stellar halos and their dynamics directly probe two fundamental aspects of galaxy formation: the hierarchical assembly of massive galaxies and their DM halos (Cooper et al. 2013; Pillepich et al. 2015). The interaction processes leave dynamical imprints on the stellar populations of galaxies. In particular, tidal features are pre- served and easily identi\ufb01ed in the outer halos of galaxies, where the dynamical timescales are longer than in the inner parts (e.g. Napolitano et al. 2003). Observed disturbances include stellar streams and tidal structures in phase space (Romanowsky et al. 2012; Coccato et al. 2013; Longobardi et al. 2015). Therefore, stellar halos are crucial in understanding the formation and evolu- tion of galaxies. Due to the low surface brightness of the outer halos of galax- ies, kinematical details from integrated light at large radii are mostly inaccessible with current spectrographs. However, dis- crete tracers like globular clusters and planetary nebulae (PNe) play a signi\ufb01cant role in learning about the halos kinematics. These are bright sources that are easily detectable in the outskirts of galaxies (Dol\ufb01et al. 2021; Longobardi et al. 2015, 2018a; Hartke et al. 2018).PNe represent a post-main sequence evolu- Article number, page 1 of 22 arXiv:2109.08694v1  [astro-ph.GA]  17 Sep 2021 A&A proofs: manuscript no. paper1_catalog tionary stage of stars and are mainly associated with the stellar populations and integrated light of the galaxies (Douglas et al. 2007; Coccato et al. 2009; Napolitano et al. 2011; Spiniello et al. 2018). Globular clusters (GCs), on the other hand, are massive, compact, and mostly old star clusters, found in almost all major types of galaxies (e.g. Brodie & Strader 2006). Observations have shown that GCs exist in two major sub-populations: red (metal- rich) GCs and blue (metal-poor) GCs. The red GCs are found to have radial number density pro\ufb01les similar to the integrated light of their host galaxies, while blue GCs are spatially more extended into the intergalactic and intra-cluster regions and trace the metal-poor component of the stellar halos (Schuberth et al. 2010; Hilker et al. 2015; Cantiello et al. 2018; Pota et al. 2018). These two GC sub-populations also show di\ufb00erent kinemati- cal characteristics. In most cases, the red GCs follow the stellar population kinematics of their parent galaxies, whereas blue GCs show a more erratic and complex kinematic behaviour (Schuberth et al. 2010; Coccato et al. 2013; Napolitano et al. 2014; Cantiello et al. 2018; Pota et al. 2018). The GCs\u2019 colour bi-modality is mainly associated with their bimodal metallicity distribution, al- though the relation between colour and metallicity is not entirely linear (Cantiello et al. 2014; Fahrion et al. 2020b). The colour bi- modality and distinct kinematical behaviour have been explained as the result of a two-stage formation scenario for massive galax- ies (Ashman & Zepf 1992; Kundu & Whitmore 2001; Peng et al. 2006). Cosmological simulations suggest that massive early-type galaxies grow and evolve in these two stages: \ufb01rst, rapidly with a high star formation rate and early compact mergers (in-situ), and later through the continuous accretion of smaller systems that build up the extended halo populations. The red, metal-rich GCs are thought to have formed during the in-situ star formation process, whereas the blue, metal-poor GCs are added to the system via the accretion of low mass objects, like dwarf galaxies (Forbes et al. 1997; C\u00f4t\u00e9 et al. 1998; Hilker et al. 1999a; Kravtsov & Gnedin 2005; Tonini 2013; Forbes & Remus 2018). Various studies of GC populations in galaxy clus- ters revealed that there exist so-called intra-cluster GCs (ICGCs), which are not bound to any individual galaxy (Williams et al. 2007; Bergond et al. 2007; Bassino et al. 2006; Schuberth et al. 2008; Peng et al. 2011; Alamo-Mart\u00ednez et al. 2013). The ICGCs might represent the \ufb01rst GCs formed in a cluster potential or could be tidally released GCs from multiple galaxy interactions (White 1987; West et al. 1995; Yahagi & Bekki 2005; Madrid et al. 2018; Harris et al. 2020). Although their formation mechanism is still debated (Ramos-Almendares et al. 2018), their kinematics add additional constraints on the accretion and assembly history of their parent galaxy cluster. The above-mentioned properties of GCs make them privi- leged discrete tracers for the dynamical study of individual galax- ies, as well as the mass assembly of galaxy clusters. Recent ad- vancements in discrete dynamical modelling like Jeans dispersion- kurtosis, incorporating high-velocity moments (Napolitano et al. 2014), and chemo-dynamical modelling methods (Zhu et al. 2016a) allow the uni\ufb01cation of several physical properties of discrete tracers at once, like their positions, velocities, as well as colours and metallicities. This has brought a signi\ufb01cant improve- ment and produced better constraints on the mass modelling and orbital anisotropy of the tracers (Watkins et al. 2013; Zhu et al. 2016b,a). Recently, Li et al. (2020) used GCs kinematics to study the mass distribution and kinematics of the giant elliptical galaxy M87 in the centre of the Virgo cluster, based on 894 discrete tracers. The M87 GC system (GCS) and the core of the Virgo cluster are a well-explored environment in this respect. A very interesting and dynamically evolving environment is the Fornax galaxy cluster, the most massive galaxy overdensity within 20 Mpc after the Virgo cluster. It is an ideal target to study the e\ufb00ect of the environment on the structure and assembly of galaxies of any type in detail (Iodice et al. 2016, 2019). The earliest approach to dynamically model the Fornax central galaxy NGC 1399, was done by Kissler-Patig et al. (1999), Saglia et al. (2000) and Napolitano et al. (2002). Later, major and crucial work was presented by Schuberth et al. (2010), where they used 700 GCs within 80 kpc of the Fornax cluster as dynamical tracers to put constraints on the properties of the central DM halo. In the last decade, the GC system of the Fornax cluster has been examined in great detail photometrically. Various imaging surveys like the ACS Fornax Cluster Survey (ACSFCS) with the Hubble Space Telescope (Jord\u00e1n et al. 2007, also see Puzia et al. 2014), the Next Generation Fornax Survey (NGFS) (Mu\u00f1oz et al. 2015), and the Fornax Deep Survey (FDS) with the VLT Survey Telescope (VST) (Iodice et al. 2016) have added a wealth of information about galaxies and GCs in the Fornax cluster. Photometric studies from D\u2019Abrusco et al. (2016), and Iodice et al. (2019) have revealed that despite the regular appearance of the Fornax cluster, its assembly is still ongoing, as evidenced by the presence of stellar and GC tidal streams. Most recently, Cantiello et al. (2020) have produced the largest photometric catalogue of compact and slightly extended objects in the Fornax cluster, over an area of \u223c27 square degrees. Due to its proximity, Fornax provides a unique opportunity to map its complex kinematics from the core out to at least \u223c350 kpc using GCs as kinematic tracers. Using the radial velocities of GCs and PNe, the Fornax Cluster VLT Spectroscopic Survey (FVSS) has obtained an extended velocity dispersion pro\ufb01le of the central galaxy out to 200 kpc (Pota et al. 2018; Spiniello et al. 2018). This has allowed to connect the large-scale kinematics of the major galaxies to the small scale stellar halo kinematics of the central galaxy NGC 1399. A crucial missing information to comprehend the complete mass assembly of Fornax is to understand the origin and kinemat- ical behaviour of its intra-cluster population and of the disturbed outer halos of interacting cluster galaxies. Several studies have shown that ignoring the presence of substructures, which are generated by accretion and merger events, impact the dynamical mass estimates of clusters, leading to erroneous cosmological inferences (Old et al. 2017; Tucker et al. 2020). For example, studying the kinematics of stellar populations in the core of the Hydra I cluster, Hilker et al. (2018) reported that small scale varia- tions in the kinematics due to substructures can produce a notable change in the mass-modelling, leading to an overestimation of DM halo mass in the core of that cluster. Therefore, the identi\ufb01- cation and proper kinematical understanding of dynamically cold substructures and outer halos of interacting galaxies in clusters are essential to understand how these structures formed, assem- bled and evolved, and have to be taken into account for the mass modelling. Using a novel cold structure \ufb01nder algorithm, Gatto et al. (2020) made a \ufb01rst attempt to search for cold kinematical sub- structures in Fornax based on the GC and PNe data of Pota et al. (2018) and Spiniello et al. (2018). This has revealed the presence of at least a dozen of candidate streams in the combined kinemati- cal information of PNe and GCs dataset of the FVSS (Napolitano et al. in preparation). These substructures can then be subtracted from the underlying discrete radial velocity \ufb01eld in the Fornax core for unbiased dynamical models. Since the work of Schuberth et al. (2010) about ten years ago, a major dynamical study of the Fornax cluster is still missing, and so far no disturbed halo fea- Article number, page 2 of 22 Avinash Chaturvedi et al.: Globular cluster kinematics in the Fornax cluster Fig. 1. Individual and stacked reduced spectra for one example target. Red, green, and blue colours show the spectra for the three individual exposures. In black the \ufb01nal stacked spectrum is shown. No broadening is observed. tures of central cluster galaxies and no intra-cluster substructures were taken into account in a thorough dynamical model of the Fornax cluster core. The low recovery fraction of the GC radial velocity measure- ments from the earlier FVSS results (Pota et al. 2018) and the improvement of the VIMOS ESO pipeline motivated us to rean- alyze the VLT/VIMOS data of the Fornax Cluster. Here, in this work, we present the radial velocity catalogue of GCs over an area of more than two square degrees corresponding to 250 kpc of galactocentric radius. In forthcoming papers of this series (Chaturvedi et al., in prep.), we will discuss the identi\ufb01cation and properties of substructures and the mass-modelling of the Fornax cluster with the \ufb01nal goal to understand its mass-assembly and dark matter halo properties. This paper is organized as follows: In section 2 we describe the observations and data reduction. The radial velocity measure- ments are presented in section 3, and the results in section 4. In section 5, we discuss the results and present the photometric and spatial distribution of our GC catalogue. Section 6 summarizes our results and presents the scope of future work. In Appendices A and B we describe some tests performed for the radial velocity analysis and an object portfolio used for visual inspection. In Ap- pendix C we show an excerpt of the VIMOS data GC catalogue from this study. The full catalogue is available online. Throughout the paper, we adopt a distance to NGC 1399 of D\u223c19.95 Mpc (Tonry et al. 2001) which corresponds to a scale of 5.8 kpc per arcmin."
                }
            ],
            "Michael Hilker": [
                {
                    "url": "http://arxiv.org/abs/0805.1786v1",
                    "title": "Next Challenges in Bringing Artificial Immune Systems to Production in Network Security",
                    "abstract": "The human immune system protects the human body against various pathogens\nlike e.g. biological viruses and bacteria. Artificial immune systems reuse the\narchitecture, organization, and workflows of the human immune system for\nvarious problems in computer science. In the network security, the artificial\nimmune system is used to secure a network and its nodes against intrusions like\nviruses, worms, and trojans. However, these approaches are far away from\nproduction where they are academic proof-of-concept implementations or use only\na small part to protect against a certain intrusion. This article discusses the\nrequired steps to bring artificial immune systems into production in the\nnetwork security domain. It furthermore figures out the challenges and provides\nthe description and results of the prototype of an artificial immune system,\nwhich is SANA called.",
                    "authors": "Michael Hilker",
                    "published": "2008-05-13",
                    "updated": "2008-05-13",
                    "primary_cat": "cs.MA",
                    "cats": [
                        "cs.MA",
                        "cs.AI",
                        "I.2.11"
                    ],
                    "main_content": "Antivirus Software The antivirus software observes a node whether an infected file is accessed or a suspicious system call occurs. The intrusions are mostly described using a signature where pattern matching is used. When an intrusion is found asks the antivirus software the user how to proceed. Firewall The network traffic consists of packets where the firewall analyses the packet header in order to find intrusions. When an intrusion is found is the user consulted for further steps. Packet Filter In the network equipment is the packet filter installed. It analyses the packet header for intrusions. Furthermore, it defines a network security policy with arXiv:0805.1786v1  [cs.MA]  13 May 2008 allowed and disallowed tra\ufb03c, i.e. allowed and disallowed ports and network protocols. Intrusion Detection System Important nodes e.g. Internet gateway and email server require additional support because they are more likely an aim for attackers than normal nodes. Therefore, intrusion detection systems are used, which check each packet completely, observe the node for suspicious behavior, and report warnings and alerts directly to the administrator [3, 5, 21]. Other Systems Di\ufb00erent other protection systems exist, which perform certain tasks for network security. Examples are virus throttles slowing down the propagation of viruses [27] or automatic analyzing systems of infected nodes [20]. The protection system de\ufb01nes the used protection components, the con\ufb01guration, and the work\ufb02ows. Additionally, it de\ufb01nes in which way the administrator maintains the network, keeps the system up-to-date, and the response work\ufb02ows when an intrusion is identi\ufb01ed. Current protection systems use a fully centralized approach. Each node of the network has one or more client softwares, which are administrated using a single management server client-server architecture. The administrator installs and con\ufb01gures in each node antivirus software and \ufb01rewall, in the network equipment the packet \ufb01lters, and in important nodes the IDS. The client softwares are the already described components and observe the node for suspicious behavior. The alerts e.g. identi\ufb01cation of an intrusion are sent to the user of the node, who decides how to proceed. The warnings are sent to the management server and are manually evaluated by the administrator. The management server coordinates the client software in providing updates and administrative tasks. It also checks the nodes whether the client software runs or not. The di\ufb00erent client softwares do not collaborate as well as the messages from di\ufb00erent nodes are not combined evaluated in order to identify abnormal behavior. Furthermore, the system does not check itself for the identi\ufb01cation of not proper working or outdated components and it has serious problems with infected nodes. For the evaluation of protection system exist di\ufb00erent criteria [5, 19]: Completeness The protection system should secure the nodes of the network. Furthermore, it should secure all nodes against all known intrusions. Production Tolerant The production in the network should not be in\ufb02uenced by the security system reducing of the false-positives. E\ufb03ciency The resources should be used e\ufb03ciently so that the protection system does not require too many resources. Furthermore is this important to solve the packet loss problem where IDS stop checking packets when a certain load is reached [22]. Easy Usage The security system should use as many possible automatic work\ufb02ows so that the administration is reduced. Self-Checking The system should check itself regularly in order to identify infected nodes, not proper working or outdated security components, and abnormal behavior in the network. Adaptively In order to identify the current intrusions as well as modi\ufb01ed and novel intrusions, the security system should adapt to the current situation and provide adaptive work\ufb02ows to identify novel intrusions. Coping with upcoming Intrusions Novel intrusions analyze the protection system and use weak points, camou\ufb02age itself so that it cannot be detected anymore, and social engineering is more and more used where the normal users are mislead to provide internal information as e.g. passwords. Implementation, Maintenance, Updates, Extension These points should be simpli\ufb01ed so that the administrator is able to introduce novel techniques and updates into the system quickly. The system should check and repair itself, and the implementation should be fast. In addition, the system should provide a status snapshot when the administrator demands it. In the network security domain, common used protection systems use a centralized approach using the client-server architecture. The clients demand information from the server and the clients perform the tasks with a reporting to the server. Current protection systems have serious problems in each of these criteria and in coping with upcoming more and more intelligent and adaptive intrusions. Examples of these intrusions are the theoretical bradley virus [7] and metamorphic or polymorphic viruses that change its signature in every propagation [25]. The emerges out of the static architecture with standard pattern matching algorithm. Thus novel approaches should dynamically adapt to the current situation and perform di\ufb00erent analysis and combine the results and information to identify novel intrusions. Existing arti\ufb01cial immune systems for the networks security domain are discussed in the next section. 3. ARTIFICIAL IMMUNE SYSTEMS FOR NETWORK SECURITY The arti\ufb01cial immune system is a modeling of the human immune system for a speci\ufb01c application domain; in this article the domain is network security. Details about the human immune system are not explained in this article and it is referred e.g. to [16]. In the design and implementation of an arti\ufb01cial immune system, mostly a few parts of the human immune system are modeled. The article [8] de\ufb01nes and evaluates four di\ufb00erent methods approaching from the research in arti\ufb01cial immune systems [6]: Arti\ufb01cial Negative and Positive Selection The arti\ufb01cial cells are generated randomly and are afterwards evaluated whether they are tolerant to normal network tra\ufb03c or not negative selection and whether they detect abnormal network tra\ufb03c or not positive selection. Danger Theory The idea is that the arti\ufb01cial cells release signals describing their status, e.g. safe signals and danger signals. The various arti\ufb01cial cells use the signals in order to adapt their behavior. Arti\ufb01cial Clonal Selection and Hypermutation The arti\ufb01cial cells respond when an intrusion is found: it \ufb01rstly copies itself heavily so that the number of this arti\ufb01cial cell increases and the intrusion is found in several nodes. Second, the arti\ufb01cial cell mutate in order to identify the intrusion more properly, e.g. in adapting the internal patterns for \ufb01nding intrusions. Arti\ufb01cial Immune Networks These networks describe a mathematical model of antibodies and antigens that bind and interfere each other. The system reacts to the current situation of bindings and its strength. In [8] is stated that these four methods are the most promising as well as novel approaches of the arti\ufb01cial immune systems, which are signi\ufb01cant di\ufb00erent to existing approaches of computer science in general. However, the negative selection is not appropriate for anomaly detection identi\ufb01cation of intrusions according to behavior analysis [23]. The organization of the immune system is important and di\ufb00erent to the current protection systems in network security: the immune cells work autonomously as a mobile entity. The work\ufb02ows are fragmented in di\ufb00erent small tasks, which are performed by di\ufb00erent cells. The high number of cells ensures redundancies so that a partly breakdown does not in\ufb02uence the performance of the overall system. The lymph nodes are a meeting point between various cells and they respond to events in the network through releasing immune cells and antigens. The bone marrow and thymus releases continuously novel immune cells in order to keep the population up-to-date. The cell communication enables the collaboration between immune cells and the system manages itself so that the whole body is secured. The self-checking and -healing identi\ufb01es and removes not proper working immune cells. This organization should be used when an arti\ufb01cial immune system is deployed so that the fault tolerance and redundancies are available. For the network security domain exist di\ufb00erent approaches to use an arti\ufb01cial immune system or algorithms motivated by the human immune system: ARTIS/LISYS This arti\ufb01cial immune system secures a broadcast network against intrusions. The arti\ufb01cial cells reside in the nodes and check the network packets for certain patterns. A pattern is a string containing the information about the sourceand destination IP and port as well as the used network protocol. The arti\ufb01cial cells are generated according to the human immune system: the cells are randomly generated and the appropriate cells are selected using the positive and negative selection. More details about this approach can be found e.g. in [15]. LIBTISSUE Aickelin and his team implemented this arti\ufb01cial immune system simulator in a client/server architecture [2, 26]. The data collector are distributed over the clients and the analyzing part is centralized in the server. Herein, e.g. the dentritic cells of the innate immune system are implemented [9, 10] and approaches of the danger model [1]. CIDS Dasgupta introduces approaches to use an arti\ufb01cial immune system in the network security domain [4]. The used architecture is a multi-agent system with roaming agents performing di\ufb00erent tasks. However, the architecture is di\ufb00erent to the human immune system. Other approaches Other arti\ufb01cial immune systems for network security focus mostly on the multi-agent architecture without the biological-motivated architecture. In some approaches are e.g. a broadcast network used so that the arti\ufb01cial cells must not move or only the capturing of information is distributed and the analysis is centralized. An example is explained in [11] discussing the generation of immune algorithms for evolutionary detectors but the organization of the system is not discussed. In [17] is a blueprint of an arti\ufb01cial immune system described where several parts are similar in the SANA system introduced below. In [18] are several algorithms analyzed and a framework of an arti\ufb01cial immune system introduced. The next section describes challenges in the process of bringing an arti\ufb01cial immune system into production in the network security domain, which also copes with the upcoming requirements due to future trends in intrusions. 4. NEXT DESIGNING AND IMPLEMENTATION TASKS The architecture between arti\ufb01cial immune systems and common used protection systems is di\ufb00erent. In contrast to the client-server architecture of common used protection systems, the arti\ufb01cial immune systems implement a distributed architecture where lightweighted, mobile, and autonomous working arti\ufb01cial cells perform the required tasks. In order to run these cells in each node, some kind of middleware must be installed on each node, which handles the access to the resources of the node and also includes common used security components. The middleware should also ensure that only allowed arti\ufb01cial cells can access the resources and solve other security issues. Furthermore, the middleware should contain the knowledge for the normal production so that the arti\ufb01cial cells are lightweighted and platform independent. The middleware should distinguish the operating and security system so that legal evidences can be saved and the system is checked from outside. For the maintenance of the protection system are work\ufb02ows required. The administrator demands regularly a status snapshot of the system as well as the administrator wants to know the current status of the system. Therefore, all nodes should collect status information and specialized nodes provide quickly a summary status snapshot. However, the system should also analyze the warnings and alerts autonomously so that the load of the administrator is reduced. The administrator should be able to access all nodes and all components. The implementation of the system should be feasible and fast where extensions and novel techniques should be quickly deployed to all components of the system. Updates e.g. of the database of known intrusions are frequent and the system should include the updates as fast as possible e.g. through positive and negative selection. The installation of updates and extensions should be monitored so that unsuccessful installations are detected and reported. Infected nodes or not proper working components are a serious problem in current security systems. The arti\ufb01cial immune system should identify these components through self-checking work\ufb02ows. Furthermore, it should develop a strategy how to disinfect the nodes or to repair the components self-repairing and -healing. The information, which are gathered in this process, should be included in further protection processes learning of the system. Due to the enormous number of arti\ufb01cial cells and to enable novel work\ufb02ows, the information management must be more sophisticated implemented. The di\ufb00erent arti\ufb01cial cells perform only small tasks and several cells have to cooperate so that the goals are reached. Therefore, a communication protocol should be implemented where a cell informs a set of cells about a certain event point to multi-point communication. Then, the arti\ufb01cial cells should use the communication protocol for collaborative work where e.g. the danger theory can be used and self management organizes the arti\ufb01cial cells. Another point is that information from di\ufb00erent nodes and from di\ufb00erent analysis processes are used in order to identify suspicious behavior beside the standard processes of network security. A protection system should secure the network against all attacks where especially modi\ufb01ed or novel attacks are hard to prevent. Current protection systems use mostly the signature based approach extended with some heuristics and, thus, have serious problems with novel attacks. Arti\ufb01cial immune systems should be adaptive in order to cope with the more and more intelligent and adaptive intrusions. Therefore, both the arti\ufb01cial cells as well as the overall system should adapt to the current situation. The adaptively in arti\ufb01cial cells can e.g. implemented using the arti\ufb01cial clonal selection and hypermutation as well as internal measurements. These points are problems of protection systems and must be solved when an arti\ufb01cial immune system is deployed in the network security domain. SANA is a framework for an arti\ufb01cial immune system and is explained in the next section. 5. SANA ARTIFICIAL IMMUNE SYSTEM SANA is a framework for a distributed protection system where the architecture, design, and work\ufb02ows are mostly biological motivated [14] and the performance is increased due to an enhancement of the organization of the protection components. The security system is an arti\ufb01cial immune system using arti\ufb01cial cells as well as common used protection components in order to secure a network against intrusions. The protection components, e.g. antivirus softwares, \ufb01rewalls, packet \ufb01lters, intrusion detection systems, and arti\ufb01cial cells, use various approaches, which are both biological and non-biological inspired. The di\ufb00erent parts are discussed in detail: In the security environment run the di\ufb00erent common used protection components as well as the arti\ufb01cial cells. The security environment manages the access to the resources of the node. It provides a common interface for this access like a middleware between the node and the protection components, which work platform-independent. Furthermore, the security environment provides only the allowed components access to resources. For this is a distributed public key infrastructure used, where each component authorizes during the access to the resources. The security environment is so installed that an adversarial cannot use it for attacks. Therefore, the security environment is encrypted installed and the communication between the security environments is also encrypted. In SANA, the approach is to install the security environment as a virtual machine using hardware virtualization e.g. OpenVZ or KVM. A second virtual machine contains the operating system for the user. The underlying operating system is only used to utilize the virtual environments and is only changed when the hardware is changed. The security environment is allowed to check the underlying operating system and all other virtual machines where other virtual machines are not allowed to see other virtual machines. Then, an intrusion in the underlying operating system can be detected because this system changes only when the hardware changes. An intrusion in the normal operating system cannot see the security environment and this is also secured against attacks through integrity checks. The di\ufb00erent layers in the implementation are also visualized in \ufb01gure 1. The protection components consist of two types, which are installed in the security environment. The common used protection components like antivirus softwares, \ufb01rewalls, packet \ufb01lters, and intrusion detection systems are installed and registered in a security environment without any changes to the internal work\ufb02ows of the components. An arti\ufb01cial cell connects a common used security component to the security environment in order to translate the warnings and alerts, to inform the component about events, and to check and update the security component. The second type is the population of arti\ufb01cial cells [14]. Each cell is a lightweighted and mobile agent performing certain tasks in the security environments and moving through the network. The tasks are various: e.g. checking the packets, \ufb01les, or system calls for intrusions [13], identifying infected nodes [12], performing regular checks, and collecting status information. However, the cells can perform all tasks and novel techniques are deployed through novel arti\ufb01cial cells. E.g., the packet checking cells build up a distributed intrusion detection system protecting all nodes against intrusions packed in network packets. The warnings and alerts generated by the protection components are combined in a common log \ufb01le for each security environment. The information collected in the system are used to learn the system, e.g. to develop new strategies to defend the network self-learning. SANA uses lots of di\ufb00erent arti\ufb01cial cells, which are redundant installed in the network. The work\ufb02ows consist of several small tasks where each task is performed by one cell. For the collaboration is the arti\ufb01cial cell communication used, which is a robust, fault-tolerant, and e\ufb03cient communication protocol for point to multi-point communication. Two specialized nodes are added: the arti\ufb01cial lymph nodes supply the protection components of a small area with additional information and respond to important messages. Furthermore, the arti\ufb01cial lymph nodes decide when a message is sent to all nodes of the network and they collect information about the supplied network part. The second specialized node is the central nativity and training station (CNTS) that implements an arti\ufb01cial bone marrow and thymus. It generates and releases continuously novel arti\ufb01cial cells in order to keep the population of cells up-todate. Thereby, it also includes novel approaches of network security like enhancements and updates. In addition, it collects status information for the administrator and for further analysis. The various arti\ufb01cial cells move through the network autonomously. However, it must be always guaranteed that each node is properly secured. Therefore is the self-management used where each security component knows the reFigure 1: Implementation layers in a network node. The operating system and the SANA runtime environment in operating system layer 2 run in di\ufb00erent hardware virtualizations. The operating system in layer 1 changes only when the hardware changes. quired security it provides the security value. Each node calculates its security level basing on the security values and when this level falls below a certain threshold, it starts a noti\ufb01cation process. This process attracts cells from nearby nodes to move to this node and that cells in this node do not leave; however, the cells still work autonomously. An additional work\ufb02ow of the self-management organizes the cells, which \ufb02ow through the network and perform certain tasks, so that each node is regularly checked but not too often to save resources. Di\ufb00erent protection components work in the arti\ufb01cial immune system SANA and each component performs other tasks as well as gains other information. This information should be exchanged in order to identify abnormal behavior quickly. Therefore, the arti\ufb01cial cell communication is used to exchange messages between a sender and a set of receivers in a small area of the network. Important messages are also broadcasted to all receivers in the network or immediately to the administrator. Furthermore, the cells exchange every time step summary information about the current status in order to inform the nearby cells. All of these cells calculate a danger level and adapt their internal behavior accordingly implementation of the danger theory. Other adaptive work\ufb02ows are to identify also modi\ufb01ed intrusions using a similarity measurement and that the cells move to the area where the attacks are more likely to occur. SANA also identi\ufb01es infected nodes using a special type of arti\ufb01cial cells in reusing the information from components checking network packets. Then, the system quarantines these nodes and starts a disinfection process. The maintenance work\ufb02ows are di\ufb00erent to common used security systems. The arti\ufb01cial cells shutdown over time and the CNTS release novel cells over time. These novel cells include the newest information and techniques about intrusions and the population is always up-to-date. The other components are updated using updating cells, which \ufb02ow through the network and report each update; thus, unsuccessful updates and outdated components are identi\ufb01ed. Checking cells furthermore test the protection components and report not proper working components. These cells also check if a node is identi\ufb01ed with a certain intrusion. Novel approaches of network security are introduced using a novel type of arti\ufb01cial cells and are quickly released by the CNTS because they work platform-independent in the security environment. The administrator can always demand a status snapshot using the information collected by the CNTS and they can access each security environment using the network for more detailed information. The administrator can de\ufb01ne the granularity of the demanded information and the system collects the information using arti\ufb01cial cells and the information stored in the arti\ufb01cial lymph nodes and CNTS. Important messages are immediately sent to the administrator using the arti\ufb01cial cell communication. The maintenance work\ufb02ows are implemented through a management software, which enables access to all security environments and their security components. The administrator uses this management software to administrate SANA and its components and to observe the working of the nodes. Due to the virtualization of SANA\u2019s security environment and the operating system, they are no longer platform dependent. Consequently, the system is able to duplicate, halt, and transfer them over the network. This leads to a complete di\ufb00erent view of the system where a service oriented architecture is introduced. The arti\ufb01cial lymph nodes as well as the CNTS provide on demand security components as virtual machines, which are transferred to the demanding security environment when a certain event occurs to perform additional non-standard processes. Additionally, as infected identi\ufb01ed operating systems are duplicated in order to save the legal evidences and to move these to CNTS for further analysis to enhance the system. In addition, the operating systems can be organized as services so that an user works always with the same system and can also quickly move the operating system to other nodes. However, the latter issue is not in the scope of the SANA system. SANA\u2019s project status is that it is implemented on a network simulator as a proof-of-concept implementation. The automatic work\ufb02ows work well and the adaptive behavior increases the performance. Using the di\ufb00erent types of arti\ufb01cial cells are redundancies installed so that a partly breakdown does not in\ufb02uence the overall system. The results of SANA are explained in the next section. 6. RESULTS The performance of SANA is more than acceptable. Using the maintenance work\ufb02ows, the system can be easily updated and extended. The system processes the warnings and alerts automatically and uses this information in order to con\ufb01gure and adapt itself so that it copes with the current situation. Important information are quickly delivered to the administrator, who can in\ufb02uence the system. The status information are collected in the CNTS and the administrator can always access the information e.g. for further analysis. The self-management organizes the various arti\ufb01cial cells so that all nodes are properly secured and regular checks are performed on all nodes. The arti\ufb01cial cell communication works well so that the arti\ufb01cial cells can quickly and reliably exchange messages for collaboration. AGNOSCO a special type of arti\ufb01cial cells identifying infected nodes using the information gathered by components analyzing the network tra\ufb03c [12] helps to keep the system free of infections and improves the performance signi\ufb01cantly because common used systems mostly do not identify infected nodes. Furthermore, AGNOSCO uses the information from lots of protection components, which are distributed over nearly all nodes. Other cells perform regular checks in order to identify infections, not proper working components, and abnormal behavior self-checking. These cells report infections quickly and increase the performance because a not proper working protection components are a risk for the whole network. After identifying a problem, the system develops a strategy to solve it self-repairing and -healing. Examples are to add novel arti\ufb01cial cells for the identi\ufb01cation of new intrusions or to disinfect a node using an arti\ufb01cial cell. Otherwise, the system quarantines the node quickly and informs the administrator for disinfection. Most attacks towards networks are not only performed towards a single node but rather towards several nodes in order to \ufb01nd a weak point in the network e.g. IP-range scanning; to cope with this is the arti\ufb01cial clonal selection and hypermutation used. In order to \ufb01nd such attacks, SANA combines the information gathered in di\ufb00erent nodes for the identi\ufb01cation of abnormal attacks through a more sophisticated information management. One example is the already explained AGNOSCO approach. Other approaches are to combine summaries of the logs of di\ufb00erent nodes and analyze these in order to \ufb01nd patterns describing abnormal behavior. For cooperation and adaptively, the arti\ufb01cial cells exchange continuously summary status information in order to adapt their internal thresholds so that the overall system SANA adapts quickly to the current situation, which is a \ufb01rst implementation of the danger theory and will be extended in the near future. The distinguished installation through hardware virtualization enables several new features where especially the service oriented architecture (SOA) helps to demand the required components in order to react to the certain events like identi\ufb01cation of infections. The duplication of virtual machines works well and the intrusions can be stored in order to analyze them in detail and to use the legal evidences for legal analysis. The distinguished installation furthermore secures the security system against attacks because the normal operating system is not able to attack the security environment and the security environment is secured with integrity checks. For the evaluation of SANA, di\ufb00erent attack scenarios are implemented and simulated. SANA performs well and protects the network e\ufb03ciently: Worm, Virus, and Trojan Attacks A worm attacks the node over the network using some security holes. The worm mostly installs itself in the node infection called and performs certain tasks; the virus is installed when the host-programm is executed. Often, they open a backdoor so that other intrusions or hackers can occupy the node. SANA detects and removes the network packets containing the worm or virus, when it is known by SANA. Infected nodes are identi\ufb01ed and disinfected as well as backdoors are identi\ufb01ed by regular checks; the information are used in order to develop a protection strategy. Thus, SANA protects the network against worms as well as viruses and also disinfects it. Due to the regular checks is the performance higher than in common used protection systems. With the combined analysis of di\ufb00erent nodes and the status messages sent every time step are multi-step or multistage attacks identi\ufb01ed because each step is detected and reported to the nearby cells. Encrypted Tra\ufb03c Attacks These attacks install a backdoor in some node and connect to this node over the network with encrypted tra\ufb03c. The network packets can be only checked at the source and destination node of the connection where the source node is the hacker\u2019s node and normally not accessible. SANA uses a distributed IDS installed by the arti\ufb01cial cells and checks the network tra\ufb03c on all nodes. Thus, infected packets are identi\ufb01ed and removed at the destination node and the backdoor is identi\ufb01ed as well as removed by regular checks performed by arti\ufb01cial cells. Hacker Attacks The identi\ufb01cation of hacker attacks is more di\ufb03cult than identifying a worm or virus attack. For preventing a hacker attack, SANA uses at least the same work\ufb02ows as current protection systems. Additionally arti\ufb01cial cells check regularly the nodes for installed backdoors e.g. VPNserver with IPsec -, which are used by the hacker for further entries to the node. Also, other changes and additionally installed software is detected and reported to the administrator in order to secure the network more properly. Social Attacks This type of attack is performed by users with internal information, e.g. an unsatis\ufb01ed employee trying to gain internal information for further usage. The problem is to distinguish between the normal and abnormal network usage of such an user. However, some characteristics are e.g. that the user tries to access resources, which are normally not used by this user, and the user tries di\ufb00erent passwords generating login errors. Analyzing only the information from a single node is mostly not su\ufb03cient but combining the information from several nodes gives a hint in order to identify such an user. Therefore, SANA uses arti\ufb01cial cells analyzing the log \ufb01les of all nodes and identi\ufb01es these users. Physical Attacks The adversarial has physical access to the node. The adversarial can connect external storages, additional hardware, or start another operating system. SANA identi\ufb01es changes in the security environment and the hardware virtualizaton system through integrity checks and does not start the infected system. Furthermore, the neighbor nodes of a starting machine isolate the node until the security environments of the nodes synchronize and enable the network access. Without a running security environment is a network access not possible and the neighbor nodes report the nodes without proper security environment. Thus, physical attacks and changes in the security systems are detected and prevented. To sum up, SANA shows that a distributed approach like an arti\ufb01cial immune system enables additional features not provided by common used protection systems. These features are e.g. analysis combining information from lots of di\ufb00erent nodes, checking from outside through the installation of the security environment, and the cooperation between the numerous small components. Furthermore, the fast deployment of extensions and updates as well as the automatic work\ufb02ows without interaction with the user. The virtualization enables further features like the duplication of infected virtual machines. With theses features, the performance of SANA is signi\ufb01cantly better compared to common used protection systems because SANA also adapts to the current situation in the network as well as SANA can be quickly enhanced with novel approaches.. 7. CONCLUSION Arti\ufb01cial immune systems provide several advantages in protecting a network against intrusions compared to common used protection systems. Especially the architecture using lots of lightweighted, mobile, and autonomous arti\ufb01cial cells without a centralized server facilitates a more sophisticated information management and a self-checking for the identi\ufb01cation of abnormal behavior. The checking from outside as well as the quickly deployment is important for coping with upcoming intrusions. In order to bring an arti\ufb01cial immune system into production, several tasks have to be done where especially the implementation and the design are challenges. SANA is a framework of an arti\ufb01cial immune system and shows that the performance of arti\ufb01cial immune systems in the network security domain is more than acceptable. The next steps are to simulate more realistic attack scenarios and to discuss how to implement the security environment in each node. 8.",
                    "introduction": "Network security is the domain where a network is pro- tected against intrusions. These intrusions are automatic attacks like viruses, worms, and trojans as well as manual attacks performed by hackers or normal users trying to gain access to resources where they normally have no access. Dif- ferent various protection systems try to protect the network and its nodes where the protection system consists of several protection components. The protection components are a software or hardware solution using a speci\ufb01c type of tasks Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for pro\ufb01t or commercial advantage and that copies bear this notice and the full citation on the \ufb01rst page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior speci\ufb01c permission and/or a fee. BIONETICS 2007 December 10-12, 2001, Budapest, Hungary Copyright 200X ACM TBA ...$5.00. for detecting a set of intrusions. Examples are the host- based antivirus softwares, \ufb01rewalls, and maleware guards or the network-based packet \ufb01lters and intrusion detection sys- tems (IDS) [21]. These components run di\ufb00erent tasks like observing the \ufb01le access and system calls on a node or header and content scanning of packets. The protection system is mostly a collection of protection components lacking of col- laborative work and sophisticated information management in order to identify upcoming more and more intelligent and adaptive intrusions. The systems do not check itself or use the information in order to identify infected nodes - nodes with a running intrusion -, not proper working components, and abnormal behavior. Novel approaches are the arti\ufb01cial immune systems. These systems reuse the architecture, organization, and work\ufb02ows of the human immune system for various domains in com- puter science where this article focusses on the network se- curity domain. However, the current approaches in arti\ufb01- cial immune system are far away from productive work and mainly implement a few parts of the human immune system as an academic proof-of-concept implementation, which fo- cus on detecting a certain intrusion. The steps to bring an arti\ufb01cial immune system into production so that the secu- rity systems pro\ufb01t from the advantages are discussed in this article. Afterwards, the prototype SANA of an arti\ufb01cial im- mune system is introduced and its results in di\ufb00erent attack scenarios are discussed."
                }
            ],
            "Stephanie Tonnesen": [
                {
                    "url": "http://arxiv.org/abs/2308.00757v1",
                    "title": "You Are What You Eat: The Circumgalactic Medium Around BreakBRD Galaxies has Low Mass and Angular Momentum",
                    "abstract": "Observed breakBRD (\"break bulges in red disks\") galaxies are a nearby sample\nof face-on disk galaxies with particularly centrally-concentrated star\nformation: they have red disks but recent star formation in their centers as\nmeasured by the D$_n$4000 spectral index. In Kopenhafer et al. (2020), a\ncomparable population of breakBRD analogues was identified in the TNG\nsimulation, in which the central concentration of star formation was found to\nreflect a central concentration of dense, starforming gas caused by a lack of\ndense gas in the galaxy outskirts. In this paper we examine the circumgalactic\nmedium of the central breakBRD analogues to determine if the extended halo gas\nalso shows differences from that around comparison galaxies with comparable\nstellar mass. We examine the circumgalactic medium gas mass, specific angular\nmomentum, and metallicity in these galaxy populations. We find less gas in the\ncircumgalactic medium of breakBRD galaxies, and that the breakBRD\ncircumgalactic medium is slightly more concentrated than that of comparable\nstellar mass galaxies. In addition, we find that the angular momentum in the\ncircumgalactic medium of breakBRD galaxies tends to be low for their stellar\nmass, and show more misalignment to the angular momentum vector of the stellar\ndisk. Finally, we find that the circumgalactic medium metallicity of breakBRD\ngalaxies tends to be high for their stellar mass. Together with their low SFR,\nwe argue that these CGM properties indicate a small amount of disk feeding\nconcentrated in the central regions, and a lack of low-metallicity gas\naccretion from the intergalactic medium.",
                    "authors": "Stephanie Tonnesen, Daniel DeFelippis, Sarah Tuttle",
                    "published": "2023-08-01",
                    "updated": "2023-08-01",
                    "primary_cat": "astro-ph.GA",
                    "cats": [
                        "astro-ph.GA"
                    ],
                    "main_content": "Corresponding author: Stephanie Tonnesen stonnesen@flatironinstitute.org central (defined here as galaxies which are not identified as satellites, so analogous to the Milky Way as a central galaxy) galaxies whose CGM is less impacted by the surrounding environment. Because gas flowing from the CGM feeds star formation in galaxy disks, and supernovae feedback ejects mass and metals back into the CGM, observers have looked for correlations between the interstellar medium (ISM) cold gas content or star formation rate (SFR) of galaxies and the amount of cold gas in the CGM. Indeed, COS-GASS has found that the amount of cold gas in the ISM and CGM of galaxies is positively correlated (Borthakur et al. 2015). In addition, cold gas traced by Mg II has been found to positively correlate with galaxy SFR, with larger Mg II equivalent widths around blue galaxies than around red galaxies (Bordoloi et al. 2011), and larger Mg II covering fractions around star-forming arXiv:2308.00757v1  [astro-ph.GA]  1 Aug 2023 2 Tonnesen, DeFelippis & Tuttle galaxies compared to quiescent galaxies (Huang et al. 2021). However, cold gas traced by HI tells a less consistent story. While COS-Halos found very little difference in the amount of HI in the CGM of star-forming versus passive galaxies (Tumlinson et al. 2013), an SDSS selected sample of starburst and post-starburst galaxies observed stronger HI at large radius compared with the COS-Halos and COS-GASS samples containing galaxies with lower SFRs (Heckman et al. 2017). In addition to less cold gas generally being found around quiescent galaxies, O VI appears to be absent around the non-star-forming, more massive galaxies in the COS-Halos sample (Tumlinson et al. 2011), and is found in excess around late-type galaxies (see also Johnson et al. 2015; Chen & Mulchaey 2009). The dearth of \u223c105.5 K gas around quenched galaxies could indicate either a hotter CGM or non-equilibrium cooling (Oppenheimer et al. 2016). Star formation feedback may also have an effect on the spatial distribution of absorbers within the CGM. Several groups have observed that Mg II and O VI absorption tends to lie along the minor galaxy axis in star-forming galaxies, indicating feedback-driven outflows are correlated with cooler CGM gas (Bordoloi et al. 2011; Bouch\u00b4 e et al. 2012; Kacprzak et al. 2012, 2015; Nielsen et al. 2015; Schroetter et al. 2019; Martin et al. 2019). Low-metallicity gas inflowing from the intergalactic medium through the CGM tends to be observed along a galaxy\u2019s major axis (e.g. Crighton et al. 2013; Nielsen et al. 2015), corotating with the galactic disk, and possibly forming thick rotating \u201cdisks\u201d of halo gas before inspiraling (Steidel et al. 2002; Ho et al. 2017; Diamond-Stanic et al. 2016). Such cold extended disks in the CGM have also been found in zoom-in simulations run with several different hydrodynamical codes (Stewart et al. 2013, 2017). Simulations also find that the CGM is strongly connected to galaxy evolution via the gas cycle. IGM gas accretion through the CGM along the disk plane adds high angular momentum, metal-poor gas to fuel star formation (e.g. Dekel et al. 2009, 2013; van de Voort et al. 2011; Brook et al. 2011; Stewart et al. 2011; Brook et al. 2012; \u00a8 Ubler et al. 2014; Christensen et al. 2016; DeFelippis et al. 2017; Grand et al. 2019). Concurrently, gas expelled from the galaxy via feedback flows along the minor axis with low angular momentum (Brook et al. 2011, 2012; \u00a8 Ubler et al. 2014; Mitchell et al. 2020; DeFelippis et al. 2020). The gas along the minor axis then has higher metallicity as well as lower angular momentum than that aligned with the disk plane, thus far measured in the TNG cosmological suite of simulations (P\u00b4 eroux et al. 2020; Truong et al. 2021). We note that although the sample sizes are currently small, observations so far do not find the strong trend of metallicity varying with azimuthal angle identified in simulations (P\u00b4 eroux et al. 2016; Kacprzak et al. 2019; Pointon et al. 2019). In broad agreement with observations, simulations have found that the CGM systematically varies between star-forming and quenched galaxies. Recently, much of this work has been done using the TNG simulation suite that we examine in this paper (Marinacci et al. 2018; Naiman et al. 2018; Nelson et al. 2018a; Pillepich et al. 2018a; Springel et al. 2018). For example, using the TNG100 and TNG300 simulations, Nelson et al. (2018b) found more O VI mass around star-forming galaxies compared to quenched galaxies of the same mass. Fielding et al. (2020) found that in TNG100 quenched galaxies had hotter median temperatures in their inner CGM, but higher cold gas fractions in their outskirts. However, in agreement with previous work using the EAGLE simulations, quenched galaxies had lower total CGM mass (Davies et al. 2019, 2020), so did not necessarily have higher amounts of cold gas in comparison to the CGM of star-forming galaxies. Studying galaxies in the TNG100 simulations, DeFelippis et al. (2020) (D20) found that the angular momentum of the CGM is both larger and more aligned with the disk angular momentum in galaxies with high stellar angular momentum (high stellar angular momentum has been found to correlate with high SFR by Genel et al. (2015)). Interestingly, other authors have found that in the same simulation suite (TNG100), the angular momentum in the CGM is higher around quenched galaxies (Wang et al. 2022; Lu et al. 2022), although this result is for somewhat more massive galaxies than D20. While both observations and simulations are continuing to find connections between central galaxies and their surrounding CGM, it is still not clear how directly the state of the CGM reflects the gas and SF distribution in the galaxy disk. In this paper we search for this direct reflection by studying the CGM around a small sample of galaxies with unusual gas and SF distributions: Break Bulge, Red Disk galaxies (breakBRD), galaxies near z = 0 observationally identified to have centrally-concentrated SF using the Dn4000 break and red surrounding disks using (g \u2212r) color (Tuttle & Tonnesen 2020). Kopenhafer et al. (2020) identified breakBRD analogues in TNG100 (Marinacci et al. 2018; Naiman et al. 2018; Nelson et al. 2018a; Pillepich et al. 2018a; Springel et al. 2018), and found that the simulated analogues had a dearth of star-forming gas outside their central 2 kpc in addition to a dearth of star formation. Their central gas content and SFR was similar to a stellar mass matched The CGM of BreakBRD Galaxies 3 control sample, resulting in somewhat low global gas content and SFR, although they are not quenched. However, by tracking a breakBRD analogue sample identified at z = 0.5, K20 found that breakBRD galaxies are more likely to quench than galaxies in a mass-matched sample. Because of their unusually centrally-concentrated and globally low, but not quenched, SFR, it is interesting to examine the CGM of breakBRD galaxies. In this paper we focus on the CGM mass, angular momentum, and metallicity, all features of the CGM that have been shown to correlate with properties of central galaxies in cosmological simulations. We will determine if the CGM of breakBRDs is different from galaxies of similar stellar mass, with the dual goals of making predictions for future CGM observations of the observed breakBRD sample and completing our understanding of the breakBRD gas cycle by connecting the CGM gas to the disk gas. The paper is organized as follows. Section 2 first briefly introduces the TNG simulations (Section 2.1), discusses the breakBRD and comparison sample selections used in this paper (Section 2.2), and finally defines our cold CGM criteria (Section 2.3). We present our global CGM measures in Section 3. In Section 4 we examine the CGM in spatial detail using maps of the mass, angular momentum, and metallicity distribution around breakBRD galaxies and the comparison sample. We discuss our results with regards to the gas cycle in breakBRD galaxies and the CGM-galaxy connection in Sections 5.1 & 5.2, and make observational predictions in Section 5.3. Finally, we summarize our conclusions in Section 6. 2. METHOD 2.1. TNG100 The IllustrisTNG100 simulation (public data release: Marinacci et al. 2018; Naiman et al. 2018; Nelson et al. 2018a; Pillepich et al. 2018a; Springel et al. 2018)1 is part of a suite of cosmological simulations run using the AREPO moving mesh code (Springel 2010). TNG100 has a volume of 110.7 Mpc3 and a mass resolution of 7.5 \u00d7 106M\u2299and 1.4 \u00d7 106M\u2299for dark matter and baryons, respectively. The TNG suite implements upgraded subgrid models compared to the Illustris simulation (Vogelsberger et al. 2014; Genel et al. 2014); specifically, a modified black hole accretion and feedback model (Weinberger et al. 2017), updated galactic winds (Pillepich et al. 2018b), as well as the addition of 1 www.tng-project.org magnetohydrodynamics (Pakmor et al. 2011), all resulting in more realistic galaxies compared to the original Illustris simulation (e.g. Nelson et al. 2018a). 2.2. The BreakBRD and comparison sample selection As introduced above, breakBRD galaxies were first found in SDSS as unusual nearby (z < 0.05) galaxies that have star-forming central regions (using the Dn4000 break) embedded in red disks (using (g\u2212r) colors) (Tuttle & Tonnesen 2020). The BreakBRD analogue sample of galaxies was selected from within the TNG cosmological simulation, and is defined in Kopenhafer et al. (2020), but here we briefly summarize the main selection criteria. Our first criterion was that the subhalo stellar mass must lie within 1010 < M\u2217< 1012 M\u2299. We chose our lower mass limit in order to resolve galaxies and their central 2 kpc since our analysis requires looking directly at the central region of galaxies. We also ignored galaxies with M\u2217> 1012 M\u2299, as this is outside the mass range of the observed breakBRD sample, and we assumed these galaxies were mainly ellipticals. We required galaxies to have R0.5M > 2 kpc, where R0.5M is the stellar half mass radius. This requirement removed galaxies which did not have a well-resolved difference between the central region and the outskirts, and therefore would not be meaningful additions to our sample. To select our sample of breakBRD analogues from TNG, we then calculated star formation histories of all the galaxies in our massand size-defined parent sample. We use their star formation histories and the Flexible Stellar Population Synthesis (FSPS) code of Conroy et al. (2009) (updated in Conroy & Gunn 2010), with the Python interface from Foreman-Mackey et al. (2014), to generate mock spectra for the inner r < 2 kpc region, and g and r colors for the disk region (2 kpc < r < 2R0.5M) of our parent sample. To calculate the Dn4000 measure we apply the narrow definition from Balogh et al. (1999). Galaxies with Dn4000 < 1.4 in the inner 2 kpc comprise the Dn4000 selection. We also select galaxies with red outskirts using a color cut of g \u2212r > 0.655 in the 2 kpc < r < 2R0.5M region. Our final sample consists of galaxies that exhibit both a Dn4000 break in the bulge and a red disk, consisting of 235 galaxies at redshift z = 0.0 (out of 6092 massand size-selected galaxies). This sample is the complete breakBRD analogue sample. In this paper, we focus on the central galaxies in the breakBRD analogue sample, a subset of 88 galaxies. Throughout the paper, \u2018breakBRD galaxies\u2019 refers to 4 Tonnesen, DeFelippis & Tuttle 1.0 1.5 2.0 2.5 3.0 3.5 log j* [km/s\u00d7kpc] 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 1010 < M* < 1010.5 M BBRDs all halos Figure 1. Normalized histogram of j\u2217of central BBRD analogue galaxies (88 galaxies, blue histogram) and all central halos with stellar masses between 1010 1010.5 M\u2299(2132 galaxies, grey histogram). While the BBRD analogue population median j\u2217is somewhat lower than that of the comparison sample, a KS test has a p-value of 0.32, indicating that the distributions are not significantly different from each other. the subset of central breakBRD analogue galaxies (this is labeled BBRD in some figures). One of these galaxies has an abnormally large stellar mass of \u22482 \u00d7 1011 M\u2299 compared to the rest of the sample, so we exclude it from most of this analysis. The majority of the other 87 galaxies have stellar masses between 1010 1010.5 M\u2299, so for the detailed comparisons between the CGM of breakBRD galaxies and the general population in TNG in Section 4 our comparison sample consists of all central galaxies within this stellar mass range. We also split our galaxies into those with lowand high-j\u2217, where j\u2217is defined as the specific angular momentum of all of the stellar particles belonging to the galaxy (the same definition used in DeFelippis et al. (2020)). As shown in Genel et al. (2015), j\u2217is correlated with many galaxy properties, including star formation rate, where it is seen that quiescent galaxies tend to have lower j\u2217than star-forming galaxies. Kopenhafer et al. (2020) found that breakBRD galaxies tend to be transitioning from star forming to quiescent, even though they currently do not show a broad range of SFRs. Therefore while splitting the breakBRD sample by SFR is not a physically meaningful exercise and will not allow for straightforward comparison with the mass-matched comparison sample, splitting the sample by j\u2217allows us to split our sample in a way that may give insight into their evolutionary stage. In Figure 1 we show that the j\u2217distribution of the breakBRD analogue galaxies is quite similar to that of the central comparison sample. In order to more clearly see CGM differences correlated with j\u2217, we split our galaxy samples by selecting upper and lower quartiles of the j\u2217distribution of the central comparison sample of 2132 galaxies. This also selects a similar relative fraction of galaxies from the breakBRD analogue sample (20-25%). We note that, as discussed above, for the comparison sample j\u2217is correlated with sSFR, with the mean sSFR of 7.7 \u00d7 10\u221211 yr\u22121 and 1.1 \u00d7 10\u221210 yr\u22121 for low-j\u2217and high-j\u2217galaxies, respectively. However, the breakBRD sSFRs vary little with j\u2217: 3.4 \u00d7 10\u221211 yr\u22121 and 3.1 \u00d7 10\u221211 yr\u22121 for low-j\u2217and high-j\u2217galaxies, respectively. By comparing the CGM in these subsets of our samples, we can tease out what CGM properties are more strongly correlated with sSFR and what are more correlated with j\u2217(Section 5.2). 2.3. (Cold) Circumgalactic Medium Gas Selection In this work we compare the gas properties in the CGM of breakBRD analogues to the larger galaxy population. Here we define the CGM for each halo as all gas cells that are part of that halo, at least twice the stellar half-mass\u2013radius away from the center of the galaxy, and not bound to any satellite subhalo (i.e., the \u201csmooth\u201d component in DeFelippis et al. (2020)). Because the CGM consists of gas at a range of temperatures, in this paper we often consider the cold CGM separately from the hot CGM. Here we define the cold CGM as gas with temperatures below 105 K. For the mass range of our sample (M\u2217between 1010 1010.5 M\u2299), this is close to the definition of \u201ccold\u201d CGM in D20, defined as temperatures below half the virial temperature. Rather than use a mass-evolving definition for cold gas as in that work, here we choose 105 K because this temperature includes UV absorption lines that may be observed for comparison with our predictions about the state of the CGM and because including both \u201ccool\u201d and \u201ccold\u201d gas in our analysis includes a higher mass fraction of the CGM (Tumlinson et al. 2017). 3. GLOBAL CGM MEASURES In this section we compare the global CGM properties of central breakBRD galaxies to the larger population of central galaxies with comparable stellar masses. We first measure the total mass in the CGM, and then split it into cold gas as defined in Section 2.3 and the remaining hot gas. In Figure 2 we compare the breakBRD analogues to the central galaxy population. The breakBRD analogues are shown as the blue points, with the median value as a large blue square. For comparison, we show the running median in stellar mass bins 0.25 dex wide and 1-\u03c3 ranges of the distribution of MCGM of the central population as the black line and shaded region, The CGM of BreakBRD Galaxies 5 9.5 10.0 10.5 11.0 11.5 12.0 log M* [M ] 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.5 13.0 log MCGM [M ] 9.5 10.0 10.5 11.0 11.5 12.0 log M* [M ] 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.5 13.0 log MCGM, hot [M ] 9.5 10.0 10.5 11.0 11.5 12.0 log M* [M ] 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.5 13.0 log MCGM, cold [M ] Figure 2. The MCGM total (top panel), MCGM,hot (top panel), and MCGM,cold (bottom panel) vs M\u2217of central breakBRDs versus the central galaxy sample. The black line and shaded region are the running median and 1-\u03c3 ranges of the MCGM distribution of all central galaxies and the black points show the center of the stellar mass bins used which are 0.25 dex wide. The breakBRD galaxies are shown as blue points with the median value as the blue square. The comparison sample used in S 4 is chosen based on stellar mass (1010 \u2264M\u2217/M\u2299\u22641010.5), and denoted with vertical dashed lines. Both the hot and cold CGM mass tends to be somewhat lower than the CGM mass of most galaxies at the same stellar mass (KS tests between the breakBRD and comparison galaxies have p-values << 0.01). respectively. This allows us to visualize how total stellar mass effects the CGM in the breakBRD mass range while still including a few hundred galaxies in each bin. We also denote the mass range of the comparison sample introduced in Figure 1 and used in Section 4 with vertical dashed lines. From top to bottom we show the total MCGM, MCGM,hot, and MCGM,cold. In all cases, the breakBRD analogue sample tends to have lower CGM gas masses than the central galaxy sample. Although the breakBRD analogue sample has a large scatter, their median CGM mass lies at the lower 1-\u03c3 of the central sample, and the CGM masses are always below the upper 1\u03c3 scatter of the central sample (except for the total and hot MCGM of the most massive breakBRD analogue galaxy). We perform a two-sample KolmogorovSmirnov (KS) test to quantify the difference between the breakBRD analogue galaxies and the comparison sample between the dashed lines. For all three measures of the CGM mass, the p-value is orders of magnitude below 0.01, indicating that the CGM mass of breakBRD galaxies and the comparison sample are not drawn from the same distribution. In addition to the gas mass, we compare the angular momentum in the CGM of breakBRD galaxies to the central galaxy samples. In Figure 3 we find that the total angular momentum of hot gas in the CGM is quite similar to the central galaxy sample (top panel), which is quantitatively shown by the KS test p-value of 0.4. However, the angular momentum of cold gas tends to be slightly lower than that of the comparison central galaxy sample, with a p-value of 0.0003. The low jCGM,cold in breakBRD galaxies mainly reflects the low MCGM,cold in the sample. Indeed, we find that the jCGM MCGM relation in the breakBRD galaxies is quite similar to the relation in the comparison sample, defined in Section 2.2 as all central galaxies with M\u2217between 1010 1010.5 M\u2299 (not shown). Figure 3 simply sums the total angular momentum of the CGM, and does not account for how the direction of the CGM angular momentum relates to the angular momentum of the stellar disk. We will discuss angular momentum misalignment in detail for the cold gas in Section 4.2. Finally, we examine the metallicity of the CGM gas in breakBRD galaxies. In Figure 4 we show the massweighted average metallicity in the hot and cold CGM. The metallicity of both the hot and cold gas in the CGM of breakBRD galaxies tends to be higher than in the total central sample. In fact, the difference in the CGM metallicity between breakBRD and central galaxies is more significant than either the CGM mass or the jCGM, 6 Tonnesen, DeFelippis & Tuttle 9.5 10.0 10.5 11.0 11.5 12.0 log M* [M ] 2.5 3.0 3.5 4.0 4.5 5.0 log jCGM, hot [km/s\u00d7kpc] 9.5 10.0 10.5 11.0 11.5 12.0 log M* [M ] 2.5 3.0 3.5 4.0 4.5 5.0 log jCGM, cold [km/s\u00d7kpc] Figure 3. The jCGM,hot (top panel) and jCGM,cold (bottom panel) vs M\u2217of central breakBRDs versus the central galaxy sample. The lines and symbols are as in Figure 2. While the jCGM,hot is similar between the breakBRD and comparison samples (p-value of 0.4), the jCGM,cold differs (p-value well below a threshold of 0.01). with the average breakBRD value higher than the 1-\u03c3 region of the central sample. This is also reflected by the smallest p-values in a two-sample KS test, again several orders of magnitude below a 0.01 threshold indicating different distributions. 4. THE DISTRIBUTION OF THE CGM SURROUNDING BREAKBRDS In this section we examine the distribution of mass, angular momentum, and metals in the CGM in detail. We assume that the CGM around galaxies is symmetric above and below the disk as well as azimuthally, and varies as a function of cylindrical radius and height above the disk (in Appendix B we show the average variation from symmetry for our samples). We then map the CGM properties onto a grid with [z/Rvir, rxy/Rvir] cells that are [0.1,0.1] on each side. Cells are only shaded if they are \u2264Rvir from the disk and at least 25% of galaxies in the sample have mass in that region of their CGM. In addition to showing projected maps, we also show ei9.5 10.0 10.5 11.0 11.5 12.0 log M* [M ] 1.0 0.8 0.6 0.4 0.2 0.0 0.2 log ZCGM, hot [solar units] 9.5 10.0 10.5 11.0 11.5 12.0 log M* [M ] 1.0 0.8 0.6 0.4 0.2 0.0 0.2 log ZCGM, cold [solar units] Figure 4. The metallicity of hot (top panel) and cold (bottom panel) CGM gas vs M\u2217of central breakBRDs versus the central galaxy sample. A KS test comparing the breakBRD analoque sample to the comparison sample results in p-values well below a 0.01 threshold. ther the difference or ratio between the breakBRD and comparison sample in the rightmost plot in each row. As we define in Section 2.2, the comparison sample includes all central galaxies with stellar masses between 1010 1010.5 M\u2299. Here we also split the breakBRD and comparison sample into the high-j\u2217and low-j\u2217subsamples that are determined by the upper and lower j\u2217 quartiles of the comparison sample. As discussed in Section 2.2, because the breakBRD sample has a similar j\u2217 distribution to the comparison sample, these j\u2217values each select 20-25% of the breakBRD sample as well. 4.1. Mapping the Mass distribution We first compare the mass distribution of the CGM of the breakBRD and comparison central galaxy samples. In Figure 5 we plot the average mass distribution of the cold gas in the CGM of galaxies in the breakBRD sample and the central galaxies. The black lines are isodensity contours enclosing different percentages of the cold gas mass, which aid comparison of the CGM density profiles of different samples. The CGM of BreakBRD Galaxies 7 0 0.25 0.5 0.75 1 rxy/Rvir 0 0.25 0.5 0.75 1 z/Rvir M 99 90 50 all BBRDs 0 0.25 0.5 0.75 1 rxy/Rvir M 99 90 50 all halos 0 0.25 0.5 0.75 1 rxy/Rvir M all BBRDs / all halos 6 7 8 9 logM [solar units] 0.1 0.3 1 3 10 MBBRD/Mall 0 0.25 0.5 0.75 1 rxy/Rvir 0 0.25 0.5 0.75 1 z/Rvir M 99 90 50 high-j* BBRDs 0 0.25 0.5 0.75 1 rxy/Rvir M 99 90 50 all high-j* 0 0.25 0.5 0.75 1 rxy/Rvir M high-j* BBRDs / all high-j* 6 7 8 9 logM [solar units] 0.1 0.3 1 3 10 MBBRD/Mall 0 0.25 0.5 0.75 1 rxy/Rvir 0 0.25 0.5 0.75 1 z/Rvir M 99 90 low-j* BBRDs 0 0.25 0.5 0.75 1 rxy/Rvir M 99 90 50 all low-j* 0 0.25 0.5 0.75 1 rxy/Rvir M low-j* BBRDs / all low-j* 6 7 8 9 logM [solar units] 0.1 0.3 1 3 10 MBBRD/Mall Figure 5. The distribution of cold gas mass in breakBRD analogue versus central galaxies. From left to right the panels show breakBRD galaxies, the comparison sample (central galaxies with stellar masses between 1010 1010.5 M\u2299), and the ratio of the mass distribution. The upper panels show all BBRD galaxies (except the one with a stellar mass above 1011 M\u2299) and all galaxies in the comparison sample. The middle panels only show those galaxies in the high-j\u2217samples, and the bottom panels only show galaxies in the low-j\u2217sample. The black lines in each panel are isodensity contours of cold gas that are labeled by the percentage of cold gas mass they enclose. They are the same in all subsequent figures. The CGM of breakBRD galaxies tends to have less mass throughout, and be slightly more concentrated than the comparison sample. When we first look at breakBRD galaxies as a whole compared to the entire comparison central galaxy sample (top panels), we see that on average there is less cold gas mass throughout the halo. We also see some indication that the cold gas is less extended in breakBRD galaxies than the comparison sample by comparing the solid (BBRD galaxies) and dotted (comparison galaxies) lines denoting 90% and 99% of the CGM mass. The somewhat lower cold CGM mass throughout the halo agrees with Figure 2, which finds lower MCGM,cold in breakBRD galaxies relative to the comparison sample. In Appendix A we show the variation at any grid cell in our maps is comparable to the cold gas mass itself, indicating that the difference in the populations could be overlooked in comparisons between individual galaxies. When we split the sample into the highand low-j\u2217 samples we find that the high-j\u2217breakBRD galaxies have more centrally concentrated mass than comparison high8 Tonnesen, DeFelippis & Tuttle 0 0.25 0.5 0.75 1 z/Rvir j 99 90 50 all BBRDs j 99 90 50 all halos j all BBRDs all halos 0 0.25 0.5 0.75 1 rxy/Rvir 0 0.25 0.5 0.75 z/Rvir 99 90 50 0 0.25 0.5 0.75 1 rxy/Rvir 99 90 50 0 0.25 0.5 0.75 1 rxy/Rvir 2 3 5 10 15 [103 km/s\u00d7kpc] 0 15 30 45 60 75 90 105 120 [deg] 6 4 2 0 2 4 6 [103 km/s\u00d7kpc] 45 30 15 0 15 30 45 [deg] Figure 6. Top panels: The angular momentum distribution of the cold gas in the CGM of breakBRD versus comparison galaxies. Bottom panels: The misalignment angle of j\u2217and jCGM of the cold gas in the CGM of breakBRD versus central galaxies. Angular momentum is low and less well aligned with the stellar component in breakBRD galaxies. j\u2217galaxies, as seen most clearly by comparing the 90% mass lines. Although beyond 0.25 Rvir there is universally less mass in the CGM of breakBRD analogues, a somewhat bigger difference can be seen beyond 0.5 Rvir near the disk plane. The low-j\u2217mass distribution is very similar in the two populations, although again breakBRD analogue galaxies seem to have a slightly more centrally concentrated CGM and less overall cold CGM mass. 4.2. Mapping the CGM Angular Momentum As with the mass distribution, we map the specific angular momentum of CGM gas in Figures 6 & 7 (and discuss variation within the populations in Appendix A). Because the angular momentum can be in any direction, we also show the angular offset between the CGM angular momentum vector and the stellar angular momentum vector in the lower panels. In Figure 6 we find that breakBRD analogue galaxies tend to have lower specific angular momentum values than the comparison sample, particularly beyond 0.5 Rvir. The relative angular momentum in the CGM of breakBRD galaxies shows the most difference from the comparison sample farther out in the halo where there is much less mass, and near the disk plane. In the comparison sample, jCGM increases near the disk plane, unlike the breakBRD galaxies\u2019 jCGM. In addition to a lower magnitude, the direction of jCGM in breakBRD galaxies is generally more misaligned than the comparison sample. The misalignment difference is the most dramatic near the disk plane, and increases along the plane towards larger cylindrical radius. In Figure 7 we show the angular momentum maps for the high-j\u2217and low-j\u2217galaxy samples. In the highj\u2217galaxies, there are no strong differences, or consistent spatial trends when comparing the two samples, although there is a hint that the jCGM is slightly larger in the breakBRD galaxies. We highlight that the jCGM and angular momentum distribution in the high-j\u2217breakBRDs show less smooth gradients than the comparison sample, but that may be somewhat due to the much smaller sample size. On the other hand, low-j\u2217breakBRD galaxies show systematically different jCGM maps than the low-j\u2217comparison sample. First, the jCGM magnitude is smaller in the breakBRD galaxies, with the difference increasing with increasing radius. Second, low-j\u2217breakBRD galaxies show a much stronger misalignment between their jCGM and j\u2217vectors than the comparison sample, with some cells even showing counter-rotation. Indeed, the comparison between the low-j\u2217galaxies in the rightmost panels looks similar to the comparison between the total samples in Figure 6. This hints that the higher angular momentum and alignment in high-j\u2217breakBRD galaxies may be unusual for the population. The CGM of BreakBRD Galaxies 9 0 0.25 0.5 0.75 1 z/Rvir j 99 90 50 high-j* BBRDs j 99 90 50 all high-j* j high-j* BBRDs all high-j* 0 0.25 0.5 0.75 1 rxy/Rvir 0 0.25 0.5 0.75 z/Rvir 99 90 50 0 0.25 0.5 0.75 1 rxy/Rvir 99 90 50 0 0.25 0.5 0.75 1 rxy/Rvir 2 3 5 10 15 [103 km/s\u00d7kpc] 0 15 30 45 60 75 90 105 120 [deg] 6 4 2 0 2 4 6 [103 km/s\u00d7kpc] 45 30 15 0 15 30 45 [deg] 0 0.25 0.5 0.75 1 z/Rvir j 99 90 low-j* BBRDs j 99 90 50 all low-j* j low-j* BBRDs all low-j* 0 0.25 0.5 0.75 1 rxy/Rvir 0 0.25 0.5 0.75 z/Rvir 99 90 0 0.25 0.5 0.75 1 rxy/Rvir 99 90 50 0 0.25 0.5 0.75 1 rxy/Rvir 2 3 5 10 15 [103 km/s\u00d7kpc] 0 15 30 45 60 75 90 105 120 [deg] 6 4 2 0 2 4 6 [103 km/s\u00d7kpc] 45 30 15 0 15 30 45 [deg] Figure 7. The angular momentum distribution and alignment angle (jCGM versus j\u2217) of cold gas in breakBRD versus comparison galaxies, split into high-j\u2217(top panels) and low-j\u2217quartiles (bottom panels). The low-j\u2217breakBRDs show lower angular momentum and more misalignment than the comparison sample, reflecting the breakBRD population as a whole (Fig 6). 10 Tonnesen, DeFelippis & Tuttle 4.3. Mapping the CGM Metallicity Finally, in Figure 8 we show the metallicity distribution in the CGM of breakBRD galaxies and the comparison sample. As above, we first focus on the total populations before splitting them into highand low-j\u2217 samples. In all galaxies, we see that higher metallicity gas lies along the pole and lower metallicity gas lies closer to the disk plane, in agreement with previous work (e.g. Truong et al. 2021). However, in breakBRD galaxies, the CGM metallicity is consistently similar to or higher than in the comparison sample, as evidenced by the top right panel (albeit with galaxy-to-galaxy scatter, as shown in Appendix A). Unlike the mass and angular momentum distributions, there is no radial dependence along the disk plane on the metallicity difference between breakBRD and comparison galaxies. The high-j\u2217sample shows similar results, with a pronounced difference in the CGM metallicity of breakBRD and comparison galaxies, particularly along the polar axis and out to about 30\u25e6from the minor axis. Low-j\u2217 galaxies show similar metallicities in the breakBRD and comparison samples, showing no trend radially or as we look towards the polar or disk axes. 5. DISCUSSION In this section we first attempt to connect the breakBRD CGM properties to the star formation and gas distribution in breakBRD disks, then use the differences in the SFRs and j\u2217of the different breakBRD and comparison subpopulations to discuss what galaxy properties are most closely tied to CGM mass, angular momentum and metallicity. Finally, we make some general predictions for future observations of the CGM around central breakBRD galaxies. 5.1. The CGM as part of the breakBRD gas cycle In Kopenhafer et al. (2020), we found that breakBRD analogue galaxies have a centrally-concentrated star formation distribution. This comes as no surprise as they are defined to have red disks and star formation in the central 2 kpc. Importantly, we found that gas is also concentrated within the central 2 kpc. This concentration is due to low gas content beyond 2 kpc and normal gas mass in the central 2 kpc. We found similar results when looking specifically at the dense gas (star forming gas in TNG). In addition, breakBRD galaxies identified at z = 0 and tracked backwards have tended to lose gas mass since z = 0.5, particularly in their outskirts (beyond 2 R1/2), while other galaxies have tended to gain gas mass. While the CGM is an important reservoir of gas moving into and out of the disk, the timescales connecting gas in the outer CGM to the disk ISM can be long (e.g. Christensen et al. 2016). Therefore, in this section we pose connections between the CGM and disk gas distributions, but specifically tracking gas flows through the CGM into or out of the disk is beyond the scope of this paper. Despite this caveat, we can relate the differences between the CGM in the breakBRD and comparison sample in this paper to the galaxy properties found in Kopenhafer et al. (2020), and attempt to gain insight into the gas cycle of breakBRD galaxies. First, the high CGM metallicity in breakBRD galaxies is likely to indicate some combination of three scenarios: in the past more metals were being added to the CGM, less metals were (and are) leaving the CGM, or less low-metallicity gas is accreting into the system. Given that the mass in the CGM is low, trapping an excess of metal-rich gas is disfavored. Because the global SFR in breakBRD galaxies is low (K20), we do not think that an excess of metals are being added to the CGM. The enhanced metallicity along the polar axis, particularly of the high-j\u2217sample, could be from a small amount of metals added to the already low mass in the CGM. Therefore, we tentatively contend that the most likely scenario is that less low-metallicity gas historically accreted into the CGM of breakBRD galaxies, which may have resulted in higher metallicities even in the starforming and ejected gas. This scenario would also likely be reflected in an enhanced metallicity in the surviving disk, so could be tested in future work. The low angular momentum in the gas may also be related to a lower accretion rate into the CGM of breakBRD galaxies. The lower angular momentum in the total sample is most clearly seen in the CGM outskirts and near the disk plane, where we might expect accretion from the IGM to deposit mass and momentum. Interestingly, the high-j\u2217galaxies actually show higher angular momentum that is generally aligned with j\u2217. This may highlight the important role that feedback can play in maintaining angular momentum in the CGM, although we expect that much of the angular momentum in the CGM is gained from IGM accretion (DeFelippis et al. 2017). We now briefly look towards the future evolution of breakBRD analogues. The low CGM mass, particularly low cold gas mass, may indicate that these galaxies will run out of fuel for star formation and quench. This would agree with the Davies et al. (2020, 2019) results that central galaxies with low CGM gas fractions in TNG (and EAGLE) are more likely to be quenched. Indeed, K20 found that the majority of z =0.5 breakThe CGM of BreakBRD Galaxies 11 0 0.25 0.5 0.75 1 rxy/Rvir 0 0.25 0.5 0.75 1 z/Rvir Z 99 90 50 all BBRDs 0 0.25 0.5 0.75 1 rxy/Rvir Z 99 90 50 all halos 0 0.25 0.5 0.75 1 rxy/Rvir Z all BBRDs all halos 0.8 0.4 0 0.3 logZ [solar units] 0.75 0.5 0.25 0 0.25 0.5 0.75 Z [solar units] 0 0.25 0.5 0.75 1 rxy/Rvir 0 0.25 0.5 0.75 1 z/Rvir Z 99 90 50 high-j* BBRDs 0 0.25 0.5 0.75 1 rxy/Rvir Z 99 90 50 all high-j* 0 0.25 0.5 0.75 1 rxy/Rvir Z high-j* BBRDs all high-j* 0.8 0.4 0 0.3 logZ [solar units] 0.75 0.5 0.25 0 0.25 0.5 0.75 Z [solar units] 0 0.25 0.5 0.75 1 rxy/Rvir 0 0.25 0.5 0.75 1 z/Rvir Z 99 90 low-j* BBRDs 0 0.25 0.5 0.75 1 rxy/Rvir Z 99 90 50 all low-j* 0 0.25 0.5 0.75 1 rxy/Rvir Z low-j* BBRDs all low-j* 0.8 0.4 0 0.3 logZ [solar units] 0.75 0.5 0.25 0 0.25 0.5 0.75 Z [solar units] Figure 8. The metallicity distribution of cold gas in breakBRD versus comparison galaxies, with the complete samples in the top panels, and high-j\u2217and low-j\u2217samples in the middle and bottom panels, respectively. The metallicity is clearly the highest in high-j\u2217breakBRD galaxies along the minor axis. BRD analogues are quenched by z =0. Interestingly, the breakBRD sample shows a lower angular momentum than the comparison sample, while Lu et al. (2022) find that low SFR and quenched galaxies tend to have higher CGM angular momentum. We note that in that work the difference in the samples becomes clear at M\u2217 > 1010.5 M\u2299. In addition to the mass in the CGM being somewhat more centrally concentrated, the combination of lower angular momentum and higher misalignment between jCGM and j\u2217indicates that gas is more likely to enter the disk in the central regions (Trapp et al. 2022). Because the timeframe for infall from the CGM to the disk could be long (Oppenheimer et al. 2010; Ford et al. 2014; Christensen et al. 2016), and the low mass and angular momentum misalignment extend to the CGM outskirts, we would expect the centrally-star forming phase to be long-lived. Recall that K20 found that \u223c86% of central breakBRD galaxies identified at z = 0.5 quenched by z = 0 (compared to \u223c25% of the parent central sample), while \u223c26% of central breakBRD analogue galaxies identified at z = 0.1 have quenched by z = 0 (compared to \u223c4.5% of the parent central sample). Therefore we predict that these galaxies will remain centrally starforming until they become passive. 12 Tonnesen, DeFelippis & Tuttle 5.2. Connecting the CGM to Galaxy Properties As we discussed in Section 2.2, the central breakBRD sample has a similar distribution of j\u2217to the comparison sample, but a lower average sSFR than even the low-j\u2217 comparison sample. By comparing the different galaxy subsets in Section 4 we can briefly discuss what aspects of the CGM seem more unique to breakBRD galaxies, and what aspects are more closely connected to the j\u2217 or sSFR of galaxies. First, we note that the CGM mass around breakBRD galaxies is lower than either highor low-j\u2217comparison galaxies. As breakBRD galaxies have a lower median sSFR than either of the comparison subsamples, this agrees with other work that galaxies with lower SFRs have low CGM masses (Davies et al. 2020, 2019). Therefore, we argue that MCGM is likely more dependent on sSFR than on j\u2217. On the other hand, there are identifiable differences in the jCGM around breakBRD galaxies with high-j\u2217versus low-j\u2217. Reflecting the larger comparison sample, breakBRD high-j\u2217galaxies have higher jCGM that is better aligned with j\u2217. As one might expect, jCGM seems more strongly correlated with j\u2217than with the sSFR of galaxies. The metallicity is where our intuition and previous work does not align with our results. Previous work studying simulated galaxies in TNG has found that galaxies with higher sSFR tend to have stronger azimuthal metallicity gradients, with high metallicity along the minor axis and low metallicity near the galaxy plane (Truong et al. 2021). Indeed, that is what we see in the comparison sample, using our knowledge that the high-j\u2217sample has higher sSFR than the low-j\u2217sample. However, surprisingly, the highest metallicity along the minor axis and highest gradient from minor to major axis is in the high-j\u2217breakBRDs, which have lower sSFR than either of the comparison subsamples. Not only this, but low-j\u2217breakBRDs, which have similar sSFRs to high-j\u2217breakBRDs, do not show a metallicity gradient. This may indicate that the metallicity gradient is actually more dependent on j\u2217than sSFR. However, because the j\u2217distribution is quite similar between breakBRDs and the comparison sample, perhaps the metallicity gradient is most closely tied to jCGM. In the future this could be tested in TNG using larger samples with low sSFR and high jCGM. This would tell us whether or not the strong metallicity gradient could be unique to breakBRD galaxies, and therefore perhaps closely connected to the gas and SF concentration in the disk. 5.3. Observational Predictions While we do not make mock observations of our simulations, in this section we attempt to synthesize our results into observational predictions for the CGM around central breakBRD galaxies. First, we expect observations to find a more rapid falloff of CGM absorbers in number and strength as a function of impact parameter around breakBRD galaxies. This is due to the less extended cold gas mass in the CGM, seen in all central BBRDs, but most dramatically in high-j\u2217BBRDs. We note that as observations of the CGM in emission are likely only able to map the CGM closer to galaxies we would not expect a discernible difference based on gas mass. Based on the angular momentum of the cold CGM we predict that the velocities of absorbers in breakBRD galaxies will be lower than average. However, we see that the angular momentum is actually somewhat higher for high-j\u2217BBRD galaxies, showing that the scatter is large. We find that for most breakBRDs, the CGM will not be corotating with the disk, and in some cases, particularly in low-j\u2217galaxies, regions of the CGM are counterrotating with respect to the stellar disk. This differs both from the other galaxies in TNG100 and from observations: we predict observations will not find a thick corotating \u201cdisk\u201d of halo gas aligned with the galaxy disk (Steidel et al. 2002; Ho et al. 2017; Diamond-Stanic et al. 2016). Although we find that breakBRD analogues have a more metal-rich CGM than the comparison sample, there is still a significant overlap in CGM metallicity. Because of this, we expect that the difference in CGM metallicities would require either a large sample of absorption sight-lines or emission mapping of the CGM. However, we do predict that there is likely to be a more significant difference along the minor axis where the most metal-rich gas is found in all galaxies. We note that these observational predictions must be for a population comparison as shown in the distribution of global values in Figures 2 4 and in the maps of the variations between galaxies shown in Appendix A, there is overlap between the CGM properties of breakBRD galaxies and the larger population. 6. CONCLUSION In this paper we have studied the CGM of central breakBRD analogue galaxies identified in Kopenhafer et al. (2020). We have found a number of differences in the CGM gas properties of breakBRD galaxies from the general sample, even when splitting the populations into high-j\u2217and low-j\u2217subsamples. Our main results The CGM of BreakBRD Galaxies 13 are listed below: 1. BreakBRD galaxies tend to have a lower mass CGM, particularly when only considering cold CGM gas (Figure 2). The cold gas in the CGM of breakBRDs is on average less extended than in a comparison sample with similar stellar mass (Figure 5). 2. The angular momentum in the CGM of breakBRD galaxies is slightly low, mainly in cold gas (T < 105 K) (Figure 3). 3. By mapping the CGM angular momentum, we find that the most dramatic differences between the breakBRD and comparison sample are located near the galaxy disk, both in terms of lower angular momentum, and more misalignment between jCGM and j\u2217(Figure 6). We also find stronger systematic differences between the CGM of low-j\u2217 breakBRDs and comparison galaxies than in the CGM of high-j\u2217galaxies (Figure 7). 4. The metallicity of the CGM in breakBRDs is higher than in central TNG galaxies (Figure 4). This higher metallicity is seen throughout the CGM in BBRDs, with the most dramatic increase seen near the poles in high-j\u2217BBRDs (Figure 8). Together these differences between the CGM in breakBRD and comparison galaxies indicate that the lack of gas and SF in the outskirts of breakBRD galaxies could be connected to the state of the CGM: there is not enough gas in the CGM to sustain high SFRs through infall, yet the angular momentum is low and/or misaligned so gas reaching the disk is likely to do so near the center of the galaxy. The high metallicity in the CGM of breakBRD galaxies could be achieved by a small amount of metals mixing into the low-mass CGM. Overall, we argue that most of the unique properties of both the disk and CGM of breakBRD galaxies could be traced to low IGM accretion into the CGM (Section 5.1). We note that not all of our results are clearly consistent with this scenario, however. In particular we highlight the strong azimuthal metallicity gradient seen in high-j\u2217breakBRD analogues that is missing in the more strongly star-forming comparison samples as well as in the low-j\u2217breakBRD sample with similar SFRs. In Section 5.2 we discuss whether this may be connected to the higher jCGM in high-j\u2217breakBRDs. Opportunely, the high metallicity of the breakBRD CGM may allow for these differences to be detectable in the near future. Taking advantage of current measurements in absorption that allow line of sight detections, a proposed cubesat called Maratus would map in emission the extended CGM around past pencil beam detections in the far ultraviolet (Tuttle et al, in prep). Using primarily OVI, expected to be the brightest tracer of 105 \u2212106 K gas, the hope is that this proof of principal instrument would pave the way for upcoming large scale missions. Although directly measuring the angular momentum component would be complex, the differences in CGM metallicity as a function of galaxy properties will be important for disambiguating local and large scale trends. ACKNOWLEDGMENTS The authors first thank the referee, whose comments improved the paper. The authors would also like to thank the IllustrisTNG collaboration for making their data public. The data used in this work were hosted on facilities supported by the Scientific Computing Core at the Flatiron Institute, a division of the Simons Foundation, and the analysis was largely done using those facilities. SET acknowledges support from the National Science Foundation through grant AST-1813462. DD acknowledges support from the ANR 3DGasFlows Project (ANR-17-CE31-0017).",
                    "introduction": "1."
                },
                {
                    "url": "http://arxiv.org/abs/2102.13122v2",
                    "title": "An Improved and Physically-Motivated Scheme for Matching Galaxies with Dark Matter Halos",
                    "abstract": "The simplest scheme for predicting real galaxy properties after performing a\ndark matter simulation is to rank order the real systems by stellar mass and\nthe simulated systems by halo mass and then simply assume monotonicity - that\nthe more massive halos host the more massive galaxies. This has had some\nsuccess, but we study here if a better motivated and more accurate matching\nscheme is easily constructed by looking carefully at how well one could predict\nthe simulated IllustrisTNG galaxy sample from its dark matter computations. We\nfind that using the dark matter rotation curve peak velocity, $v_{max}$, for\nnormal galaxies reduces the error of the prediction by 30% (18% for central\ngalaxies and 60% for satellite systems) - following expectations from the\nphysics of monolithic collapse. For massive systems with halo mass $>$\n10$^{12.5}$ M$_{\\odot}$ hierarchical merger driven formation is the better\nmodel and dark matter halo mass remains the best single metric. Using a new\nsingle variable that combines these effects, $\\phi$ $=$\n$v_{max}$/$v_{max,12.7}$ + M$_{peak}$/(10$^{12.7}$ M$_{\\odot}$) allows further\nimprovement and reduces the error, as compared to ranking by dark matter mass\nat $z=0$ by another 6% from $v_{max}$ ranking. Two parameter fits -- including\nenvironmental effects produce only minimal further impact.",
                    "authors": "Stephanie Tonnesen, Jeremiah P. Ostriker",
                    "published": "2021-02-25",
                    "updated": "2021-10-20",
                    "primary_cat": "astro-ph.GA",
                    "cats": [
                        "astro-ph.GA"
                    ],
                    "main_content": "stonnes@gmail.com (ST) But there are virtues to considering simpler treatments that do not need to rely on sub-grid modeling and which are easily adaptable to analyzing large data sets. Of these, the simplest, perhaps, is the abundance matching scheme which is based on the fact that, in all variants of the LCDM modeling, galaxies live in more massive dark matter (DM) halos, quasispherical lumps of dark matter, which grow via gravitational instabilities from very low amplitude ( 10\u22125), gaussian perturbations imparted at very early times in a roughly power law distribution by unknown processes (thought to be related to inflation) ((e.g. Vale & Ostriker 2004, 2006, 2008). There is good agreement on how to compute the formation of these dark matter halos with several computational codes now able to make moderately high-resolution cosmic scale volumes containing accurate distributions of DM halos having well defined properties. Early analyses by Navarro et al. (1997) showed that these could be represented to a reasonable approximation by three numbers, a mass, a virial radius and a core radius, with the ratio of the latter two numbers represented as the concentration. To zeroth order observed galaxies can be represented by their stellar masses, or alternatively by their stellar luminosities. Thus, the simplest possible scheme for populating a volume in the universe with galaxies would be to populate it first with DM halos, and then make a rank ordered list of these with the most massive first. Next, one could take the same arXiv:2102.13122v2  [astro-ph.GA]  20 Oct 2021 2 volume from the real universe and rank order the observed galaxies by mass (or luminosity), and then simply assume that the more massive halos hosted more massive galaxies, putting in each halo the corresponding galaxy. This, almost ridiculously simple, scheme was pursued by Vale & Ostriker in three papers (Vale & Ostriker 2004, 2006, 2008; see also Kravtsov et al. 2004; Tasitsiomi et al. 2004). Using this scheme (or a variation thereof), one can take different variants of the LCDM model, compute the halo distribution, populate the halos with galaxies using the simple abundance matching scheme and then compare to observations. By construction, the luminosity functions must come out to be correct, but correlation functions (Conroy et al. 2006; Mar\u00edn et al. 2008; Guo et al. 2010; Trujillo-Gomez et al. 2011), pair counts (Berrier et al. 2006), magnitude gap statistics (Hearin et al. 2013; Ostriker et al. 2019), and galaxy-galaxy lensing (Hearin & Watson 2013) can be usefully compared to observations. Two immediate questions arise. First, is there a better zeroth order scheme than ranking by mass and matching. Several authors have considered this question. For example, while the DM in subhalos is quickly stripped once they are accreted onto halos, stripping of the more centralized galaxy starts later (Nagai & Kravtsov 2005), and in fact their optical sizes are observed to grow with cosmic time (cf van Dokkum et al. 2010), presumably due to the accretion of smaller satellite systems. Thus, Conroy et al. (2006) improved subhalo abundance matching by matching galaxies to halos at the time at which they are accreted onto a central halo. Even earlier, Kravtsov et al. (2004) proposed using the maximum circular velocity of (sub)halos, vmax, which is more stable than halo mass to stripping. Reddick et al. (2013) tested abundance matching models using several halo properties, and found that only vpeak (de\ufb01ned as the peak value of vmax over the history of the halo) or a combination of vmax for central galaxies and vpeak for satellite galaxies is able to reproduce observations of galaxy clustering. Indeed, Zentner et al. (2014) argues that abundance matching using vmax matches several observed galaxy statistics (Conroy et al. 2006; Hearin et al. 2013; Hearin & Watson 2013; Reddick et al. 2013) because halo mass alone does not determine the halo velocity pro\ufb01le. Xu & Zheng (2018) con\ufb01rmed that for the central galaxies in the original Illustris simulations, M\u2217is more tightly correlated with vpeak than with halo mass. They also \ufb01nd that at \ufb01xed vpeak, the correlation between M\u2217and other halo properties is removed. In He (2020), the author uses subhalo abundance matching and \ufb01nds that vpeak correlates best with the stellar mass at the epoch of vpeak in both central and satellite galaxies in EAGLE, Illustris, and IllustrisTNG. Stellar mass stripping of satellite galaxies results in increased scatter in the z = 0 M\u2217to vpeak relation. Chaves-Montero et al. (2016) \ufb01nd that vrelax, de\ufb01ned as the maximum of the circular velocity of a dark matter structure while it ful\ufb01ls a relaxation criterion, as evaluated along its entire history, correlates most strongly with M\u2217. Second, does there exist any \ufb01rst order re\ufb01nements of the mass-matching scheme that could be implemented, which would be easy to apply and would signi\ufb01cantly increase its accuracy. In fact, Lehmann et al. (2017) point out that while ranking by vmax is similar to ranking by halo mass, at \ufb01xed halo mass more concentrated halos have higher vmax (Klypin et al. 2011). They therefore use a parameterization from Mao et al. (2015) that includes both halo mass and concentration: V\u03b1 \u2261Vvir(Vmax Vvir )\u03b1 (1) where vmax is the maximal circular velocity of the halo and Vvir \u2261(GMvir Rvir )1/2 (2) They \ufb01nd that an \u03b1 \u223c0.57, with a scatter of 0.17 dex is the best \ufb01t to the SDSS clustering measurements, indicating that both the halo mass and the maximum circular velocity impact the stellar mass of galaxies. Identifying the variables causing the scatter in an abundance matching model also leads to a better understanding of the important physical processes in\ufb02uencing galaxy formation. For example, Matthee et al. (2017) matched galaxies in the hydrodynamic EAGLE simulation to those in the dark matter only simulations, and found that much of the scatter is due to halo concentration. Speci\ufb01cally, at a constant halo mass, higher concentration is correlated to higher stellar mass, likely because higher concentrations imply earlier formation times. However, they do not \ufb01nd a halo property than can explain the remaining scatter. Martizzi et al. (2020) considered the in\ufb02uence of formation time and environment on the scatter in the stellar mass to halo mass relation using IllustrisTNG. Sorting by the current subhalo mass, they \ufb01nd that the scatter in the relation for central galaxies is correlated more strongly with formation time, while the scatter for satellite galaxies is correlated more strongly with environment. On the other hand, Dragomir et al. (2018) compare the galaxy luminosity functions and the galaxy stellar mass function at di\ufb00erent environmental densities for SDSS observations and a subhalo abundance matching model applied to the Bolshoi-Planck simulation and \ufb01nd that the model predictions agree well with observations. In this paper we will try to both physically motivate and improve the simplest matching scheme. We will use IllustrisTNG to determine whether complicating the most simple form of subhalo abundance matching, ie matching stellar mass to a single halo property, reduces scatter in the assignment of galaxies to halos. We \ufb01rst verify the halo property 3 that produces the least scatter in the relation, vmax, considering the central and satellite populations separately and selecting di\ufb00erent mass ranges even in this initial step. We then provide a physical motivation for the parameters used in the optimal matching scheme. Then, similarly to Martizzi et al. (2020), we calculate how the scatter is reduced when we fold in a second halo feature. However, unlike these recent works, we test a wide range of possible parameters and possible combinations thereof. In Section 2 we describe our sample of galaxies and the variables we measure for each galaxy. In Section 3.1 we outline a theoretical basis for selecting the dark matter halo property on which to rank, and in section 3.2 we try out the simplest one parameter schemes and show that the physically motivated focus on peak velocity dispersion is best for normal galaxies but that total halo mass remains best for \ufb01rst brightest, massive, central systems as would be expected from the presented physical arguments. Section 4 broadens the treatment to include multiple variables including environment and then in Sections 5 and 6 we present an overall discussion of the results and possible tests of the scheme. Finally, in Section 7 we summarize our \ufb01ndings and conclusions. 2. METHODS 2.1. IllustrisTNG The IllustrisTNG100 (public data release: Nelson et al. 2019)1 is part of a suite of cosmological simulations run using the AREPO moving mesh code (Springel 2010). TNG100 has a volume of 110.7 Mpc3 and a mass resolution of 7.5 \u00d7 106M\u2299and 1.4 \u00d7 106M\u2299for dark matter and baryons, respectively. The TNG suite implements upgraded subgrid models compared to the Illustris simulation (Vogelsberger et al. 2014; Genel et al. 2014); speci\ufb01cally, a modi\ufb01ed black hole accretion and feedback model (Weinberger et al. 2017), updated galactic winds (Pillepich et al. 2018). TNG also includes magnetohydrodynamics (Pakmor et al. 2011). 2.2. Galaxy Selection We use galaxy populations from the IllustrisTNG 100 simulation described above. We consider galaxies at the z = 0 output with dark matter masses of \u22651011 M\u2299/h in the darkmatter only run (DMO) that are matched in the full hydrodynamical simulation with galaxies whose stellar mass is greater than 109 M\u2299/h. In detail, we \ufb01rst selected all galaxies in the DMO simulation with a dark matter mass greater than 1011 M\u2299/h. We then used the publicly available matching data to \ufb01nd the corresponding galaxy in the full hydro simulation. We use all 1 www.tng-project.org galaxies identi\ufb01ed with masses above 5 \u00d7 106 M\u2299/h, which clearly includes galaxies that are underresolved in the simulation. However, at our minimum dark matter halo mass, the lowest stellar mass of any galaxy in our sample is 7 \u00d7 107 M\u2299/h. In order to only include well-resolved galaxies, that are more likely to be in an observational sample, our \ufb01nal analysis only includes galaxies with stellar masses above 109 M\u2299/h. 2.3. Galaxy Environmental Measures We use nearby galaxies to measure the local environment. We include all galaxies with dark matter masses above 109 M\u2299/h within 1 Mpc, 2 Mpc, 5 Mpc, 8 Mpc or 15 Mpc of each galaxy. In order to have a more physical measure of the local mass density, we summed the total mass of all these galaxies. We also were able to separate galaxies into satellites or centrals using the GroupFirstSub identi\ufb01er in the IllustrisTNG DMO simulation. This allowed us to perform our \ufb01ts for the entire sample and for satellites and centrals separately, and, as we shall see, the two categories are signi\ufb01cantly di\ufb00erent in their properties. This gives us three samples: \u201call\", \u201ccentrals\" and \u201csatellites\". The fourth sample is labeled as \u201cmix\", which is the combined sample in which satellites and centrals are \ufb01t separately. 2.4. Concentration We use three measures of the concentration. First, from Bose et al. (2019) we use: cv \u2261 Vmax HoRmax (3) where vmax is the maximum velocity of the simulated rotation curve and Rmax is the radius at which Vc is maximal. Bose et al. (2019) show that this is equivalent to the concentration calculated using all the particles in a halo and assuming an NFW pro\ufb01le (see also Molin\u00e9 et al. 2017). Second, we use the ratio ch\u2261vmax/Vhal fmass, where Vhal fmass is the circular velocity at the half mass radius of the dark matter halo, calculated as pGMhal fmass/Rhal fmass. Finally, we use the ratio cR\u2261Rmax/Rhal fmass. 2.5. Percent Error We de\ufb01ne the error as: Error \u2261 P N | log(Mtrue/Mprediction) | N (4) so that for small errors our de\ufb01nition is equivalent to 0.43 times the average fractional error. 3. RANK ORDERING 4 In this section we discuss using rank ordering to match halos and galaxies. Speci\ufb01cally, we \ufb01rst present a straightforward theoretical sca\ufb00old for selecting the halo property best suited for rank ordering. Then, using IllustrisTNG we con\ufb01rm our derivation. 3.1. A Simple Theoretical Basis for Selecting the Ordering Halo Property We can begin with an assumption that stellar mass is related to the baryonic mass scaled to the dark matter mass, corrected by the fraction of matter that cools and forms stars in the center of the halo: M\u2217\u221dMpeak \u2126b \u2126d t form tcool, form (5) Here t form is the formation time of the halo and tcool, form is the time required for the baryons to cool and condense into a galaxy. This is simply putting in the form of an equation the classical idea of \u201cmonolithic collapse\" \ufb01rst proposed by Eggen et al. (1962). We can relate the mean density of the galaxy to its mass and radius: \u03c1max \u2261Mmax 4 3\u03c0r3 max (6) In which \u03c1max, Mmax, and rmax are the density, mass, and radius at which the circular velocity reaches vmax, where v2 max = GMmax rmax . We can relate tform to the halo density assuming standard gravitational collapse (Gunn & Gott 1972): G < \u03c1 >\u2261t\u22122 form (7) We can also relate tcool, form to density using energy conservation and the standard cooling equations: 3 2kTmax m \u2261GMmax rmax (8) The above equation de\ufb01nes Tmax. We subsequently can de\ufb01ne tcool, form as: \u039b(Tmax)\u03c12 max \u2261 3 2\u03c1maxkTmax tcool,form (9) Thus, tcool,form \u221d\u03c1\u22121 max f \u22121 where f\u2261\u039b(Tmax)/Tmax, and t form \u221d\u03c1 \u22121 2 max. If we use these relations in Equation 5, we \ufb01nd that M\u2217\u221dMpeak\u03c1 1 2 max f \u221d( Mmax rmax ) 3 2 f \u221dv3 max f (10) For low mass halos for which f is nearly proportional to Tmax this indicates a steep dependence on M\u2217on vmax, which \ufb02attens for higher mass galaxies with higher Tmax. We highlight that this derivation is based on the assumption of spherical collapse of the halo and pure radiative cooling. We do not consider any complicating processes that we know a\ufb00ect galaxies in the universe, such as mergers or feedback from star formation or AGN. In fact, we might expect this relation between M\u2217and v3 max f to break down more often for higher mass galaxies, as they have been found to have later growth times where these assumptions clearly breakdown (Behroozi et al. 2013). For \ufb01rst brightest systems, sitting in massive halos from which they can accrete satellites, one would expect Mpeak to be more relevant, and, as we have noted, both observations (e.g. van Dokkum et al. 2010) and LCDM theory argue that hierarchical accretion is the dominant process for \ufb01rst brightest galaxies. Indeed, we can go a step farther and ask the basis for and the value of the transition mass above which \u201cnormal\" growth of the stellar component from a cooling collapse becomes di\ufb03cult. This was addressed in a paper by Rees & Ostriker (1977)(eqn 20) in an elementary discussion of the maximum mass of cosmic gas that can cool and collapse in a dynamical time. They did not include the important effects of dark matter in their treatment and obtained a mass of [( \u210fc Gm2 p )2( e2 \u210fc)5( mp me ) 1 2 ]mp\u223c1012 M\u2299in baryons. Had the effects of dark matter been included the value of the baryonic, transition mass would have been reduced somewhat, but the corresponding dark matter mass would have approximated 1012.5 M\u2299. In fact, the mass function of galaxies in the standard Press-Schechter parameterization declines exponentially above a certain critical mass, the stellar mass being roughly 1011 M\u2299and the corresponding halo mass being roughly 1012.5 M\u2299. Consequently, we have both an observational and a physical basis for expecting that galaxies above some critical mass will grow primarily by accreting satellites and cannot be formed easily by a monolithic collapse. Thus, while matching based on vmax will be best for normal systems, we can expect that, for \ufb01rst brightest galaxies in massive clusters, Mpeak should be the best metric. 3.2. Rank Ordering in IllustrisTNG Here, we test these theoretical predictions using the IllustrisTNG simulation. As described in Section 2.2, we use a sample of galaxies with dark matter mass greater than 1011 M\u2299/h in the DMO simulation and stellar masses above 109 M\u2299/h in the full hydrodynamical simulation. We rank-ordered our selected galaxies by total mass and the stellar mass separately for each of our samples: \"all\" (11927), \"satellites\" (2337), and \"centrals\" (9590). We have used three simple proxies for dark matter halo mass in our ranking schemes: the current dark matter mass, MDM, the peak dark matter mass, Mpeak, and the current vmax. These are shown in order from the top to bottom panels in Figure 1. We show the total mass proxy and stellar mass for each of 5 our galaxies as orange \u201co\". The blue lines show the predicted stellar mass using the rank-ordering method for each of our samples. We highlight that M\u2217is the current stellar mass at z = 0, including any mass loss from star particles due to stellar evolution (Vogelsberger et al. 2013; Leitner & Kravtsov 2011; Wiersma et al. 2009). Within \u223c3 Gyr of formation, 45% of a star particle\u2019s mass can be lost due to stellar evolution (Leitner & Kravtsov 2011), inserting a factor of \u223c2 into Equation 10. However, we cannot simply include a constant term into the relation between current stellar mass and halo mass (or vmax) because of the time-dependence of stellar evolution, and the fact that mass recycled from earlier stellar populations may be required to form later generations of stars. The time-dependence of stellar mass loss would move galaxies with earlier formation times to lower M\u2217as they have had more time to recycle stellar mass back to gas mass. However, we note that earlier formation times are correlated with higher stellar mass at a constant halo mass (e.g. Matthee et al. 2017), so stellar evolution likely only \ufb02attens this relation. We see that the scatter decreases as we move from using MDM to Mpeak, although the M\u2217\u221dM(3/4) halo for higher masses holds for both variables. We also highlight that the rankorder line for satellite galaxies is much closer to that for centrals when we use Mpeak than when we use MDM. The scatter continues to decrease when we use vmax as our dark matter halo mass proxy, particularly at lower masses (lower vmax). To guide the eye we have overplotted simple power-law relations between M\u2217and vmax. The results shown in Figure 1 are quanti\ufb01ed using the percent error as described in Section 2.5 (eqn 4), with the results shown in Table 1. We see that while using the current MDM in the matching scheme is reasonably accurate for central galaxies, it is much less accurate for satellite systems. Therefore, we also consider the peak mass of the halo, Mpeak. Using Mpeak should correct for mass loss from satellite galaxies due to tidal stripping. Because dark matter is distributed to a larger radius than the stars in a galaxy, it will be more strongly stripped. Therefore, while we expect Mpeak to be very similar to MDM for central galaxies, it can vary by a considerable amount for satellites. Indeed, we see in Table 1 that the improvement for centrals is very small when using Mpeak rather than MDM, but it is dramatic for satellite galaxies. We also consider vmax, as tidal stripping is found to have little e\ufb00ect on this property, likely because the maximum rotational velocity is reached at relatively low radii. Using vmax for our variable we \ufb01nd that the error for central galaxies has improved by more than 15%, although the correlation between vmax and stellar mass for satellites is somewhat weaker than the correlation between Mpeak and stellar mass. However, beFigure 1. The stellar mass of galaxies versus possible variables to use for ranking. Blue lines show the predicted stellar mass using the rank-ordering method for each of our samples. Top panel: Ranking using the current dark matter halo mass has the most scatter. Middle panel: Using Mpeak for ranking reduces scatter, and the rank ordering predictions for satellite and central galaxies is much closer. Bottom panel: Ranking using vmax reduces scatter dramatically, particularly for lower mass (lower vmax) halos, as quanti\ufb01ed in Table 1. 6 cause most of our galaxies are centrals, vmax remains the best single variable for rank-ordering our galaxy sample. We stress that, because of the shape of the mass function, any relation between stellar mass and halo mass will be dominated by the lowest-mass galaxies. Therefore, we also consider separately only galaxies whose mass in the DMO simulation is greater than 1012 M\u2299/h in order to remove the bulk of low mass galaxies while still retaining a sample with \u223c200 satellite galaxies. Unsurprisingly, we \ufb01nd that, as in the full sample, ordering using MDM is reasonably accurate for central galaxies, but much less so for satellite systems. Again, we \ufb01nd a large improvement in the ranking scheme for satellite galaxies using Mpeak. However, unlike in the full sample, vmax is the worst ranking variable for central galaxies with halo masses above 1012 M\u2299/h. This agrees well with our theoretical argument that at large masses Mpeak will be the best ranking variable due to merging. With this empirical support for the trends predicted in our model, we also develop a straightforward variable, using the physical intuition from above, that vmax will be the best ranking variable for low mass galaxies and Mpeak will be the best ranking variable for high mass galaxies (Section 3.1). For this variable we normalize both vmax and Mpeak to their values at a \u201cpivot mass\" of Mpeak = 1012.7 M\u2299. We call these variables vnorm \u2261vmax/vmax,12.7 and mnorm \u2261Mpeak/1012.7. We then rank order our galaxies using the parameter based on these normalized values: \u03c6 \u2261vnorm + mnorm (11) Using this parameter, low mass galaxies depend more strongly on vmax, while high mass galaxies depend on Mpeak. Both the exact value of the pivot mass and the powers of vnorm and mnorm were selected to minimize error while \ufb02eshing out our theoretical sca\ufb00old. As shown in Table 1, using this parameter \u03c6 gives some improvement on the \ufb01t to the central galaxies in our sample, and dramatically reduces the error for the satellite galaxies. Using this variable for the mix of all galaxies reduces the error by a substantial 33% when compared with rank ordering by MDM. 4. USING SECONDARY VARIABLES TO IMPROVE RANK ORDERING We now attempt to minimize the scatter in the \u03c6 M\u2217relation using other features of dark matter halos. These features are listed in Table 2. We have roughly grouped the halo properties into those related to the halo mass (MDM, Mpeak, vdisp\u2261dark matter velocity dispersion, and vmax), size (rmax\u2261 vmax radius and rDM\u2261dark matter half mass radius), shape (concentration using the three methods described in Section 2.4), formation time (the lookback time to Mpeak, to when the halo reaches 50% of its z=0 mass, and to when the halo reaches 85% of its z=0 mass), and surrounding environment (using the mass of dark matter halos within various radii). In this section we \ufb01rst describe the method we use to include secondary features, and then discuss the results. 4.1. Method of Correction We \ufb01rst plot our feature as a function of our best single variable \u03c6, and \ufb01nd the running median of the feature using a window size of 50 galaxies. We have tested using other window sizes (25 and 100 galaxies as well as a constant \u2206log(\u03c6) bin of \u00b10.3 around each galaxy) and \ufb01nd similar results in our percent improvement. The top panel of Figure 2 shows this plot using the environmental density MDM,r<2Mpc variable. Clearly there is a trend of increasing environmental density as a function of \u03c6, and it di\ufb00ers for satellites and centrals. Because we use the rolling median, we need to remove the \ufb01rst and last 25 values, so we are left with an \"all\" sample of 11877, a \"centrals\" sample of 9540, and a \"satellites\" sample of 2287 galaxies. Removing these galaxies has little impact on the percent errors using the rank ordering method for each sample (a change of less than 1%). We then plot Mtrue/Mrank as a function of \u2206log(feature), which is the di\ufb00erence between the log(feature) for each dark matter halo and the log(featurerollingmedian) found at each \u03c6. In the bottom panel of Figure 2 we show how Mtrue/Mrank is related to the scatter in MDM,r<2Mpc. This relation is \ufb01t using \ufb01rst, second and third order polynomial \ufb01ts. Finally, we correct our prediction for the stellar mass using our chosen \ufb01t as below (the second order polynomial \ufb01t shown tends to give the best results): log(M\u2217,pred) = log(M\u2217,rank)+ \u03b1\u2206log( feature)2 + \u03b2\u2206log( feature) + \u03b3 (12) Finally, we calculate the percent error of the new prediction. This value for each feature and galaxy population is shown in Table 2. 4.2. Results All of our quantitative results are shown in Table 2. The most glaring result is that most corrections do not result in a large improvement of the percent error from ranking using \u03c6. Using random resampling of 70% of our data sets (\u201call\",\u201ccentral\", and \u201csatellites\") 60 times, we \ufb01nd a distribution of errors with means matching the values listed for \u03c6 of the complete sample in Table 1, and standard deviations of 0.001, 0.001, 0.002, and 0.0009 for \u201call\", \u201ccentrals\", \u201csatellites\" and \u201cmix\" samples, respectively. With this in mind we 7 Number of galaxies (MDM > 1011 M\u2299) 11927 9590 2337 11927 11927 Galaxy Sample All Centrals Satellites Mix % Improvement Rank Ordering using MDM 0.198 0.130 0.279 0.159 \u2013 Rank Ordering using Mpeak 0.136 0.127 0.133 0.128 19 Rank Ordering using vmax 0.116 0.106 0.137 0.112 30 Rank Ordering using \u03c6 \u2261vnorm + mnorm 0.111 0.101 0.119 0.105 34 Table 1: The percent error (eqn 4) of the ranking method using a single variable chosen to be either MDM (at z = 0), Mpeak, vmax (at z = 0), and \u03c6 \u2261vnorm + mnorm (eqn 11) for the dark matter mass for the di\ufb00erent samples (a \ufb01t to all galaxies, only centrals, only satellites, and mix of all galaxies \ufb01tting the centrals and satellites separately). We use a galaxy sample with dark matter mass in the DMO simulation greater than 1011M\u2299/h that is matched to any galaxy in the hydrodynamical run with stellar mass greater than 109M\u2299/h. The \ufb01nal column shows the percent improvement of ranking by the selected variable compared to MDM (at z = 0) on the \u201cmix\" sample. We see that ranking using the single variable \u03c6 reduces the error 34% compared to matching by MDM (at z = 0). Number of galaxies (MDM > 1011 M\u2299) 11927 9590 2337 11927 11927 Galaxy Sample All Centrals Satellites Mix % Improvement \u03c6 + vdisp 0.112 0.102 0.117 0.105 0 \u03c6 + vmax 0.111 0.101 0.117 0.104 1 \u03c6 + MDM 0.105 0.101 0.110 0.103 2 \u03c6 + Mpeak 0.111 0.101 0.117 0.104 1 \u03c6 + rmax 0.111 0.101 0.118 0.105 0 \u03c6 + rDM 0.105 0.100 0.114 0.103 2 \u03c6 + cv 0.111 0.101 0.118 0.105 0 \u03c6 + ch 0.109 0.101 0.117 0.104 1 \u03c6 + cr 0.109 0.101 0.116 0.104 1 \u03c6 + tpeak 0.105 0.101 0.110 0.103 2 \u03c6 + t50 0.106 0.099 0.116 0.102 3 \u03c6 + t85 0.104 0.099 0.111 0.101 4 \u03c6 + MDM,r<1Mpc 0.104 0.100 0.115 0.103 2 \u03c6 + MDM,r<2Mpc 0.103 0.099 0.113 0.102 3 \u03c6 + MDM,r<5Mpc 0.105 0.099 0.115 0.102 3 \u03c6 + MDM,r<8Mpc 0.107 0.100 0.116 0.103 2 \u03c6 + MDM,r<15Mpc 0.109 0.100 0.117 0.104 1 \u03c6 + MDM,r<2Mpc + t85 0.101 0.097 0.108 0.099 6 Table 2: The percent error using two variables: the \u03c6 ranking method plus the listed corrections. We use the galaxy sample with dark matter mass greater than 1011M\u2299/h that is matched to any galaxy in the hydro run with stellar mass greater than 109M\u2299/h. Note that MDM,r<XMpc is the mass of all halos within that radius from the DMO simulation with MDM > 109M\u2299, including the mass of the halo from which the measurement originates. All halo properties are measured using the DMO simulation. Here the \ufb01nal column shows the percent improvement on the \u201cmix\" sample of using the correction variable in addition to rank-ordering by \u03c6 in comparison to only rank-ordering by \u03c6. can look more closely at the improvement when adding a second feature to our matching scheme. In some more detail, it is not surprising that all of the halo features describing halo mass do not improve the \ufb01t to central galaxies at all. These are well-\ufb01t by our \u03c6 variable. However, interestingly, the error is reduced for the satellite sample when we include a MDM correction. This may be because we have largely ignored satellite galaxy evolution by choosing vmax and Mpeak as the components of \u03c6. Including MDM may start to include the later evolution of these galaxies. We \ufb01nd universally small improvement when considering our variables describing halo size (rmax and rDM) and shape (concentration). Although previous work has shown that the scatter in abundance matching is related to concentration (e.g. Matthee et al. 2017), it is not surprising that concentration does not improve the scatter when ranking using our \u03c6 variable. This is because \u03c6 includes vmax, which is already related to concentration (Klypin et al. 2011). Interestingly, there is some improvement in the error when folding formation time into the stellar mass estimate. For example, t85 is the halo feature that results in the smallest percent errors across all of our samples: \u201call\" galaxies, \u201ccentrals\", \u201csatellites\", and the \u201cmix\" sample. As discussed above, although we \ufb01nd that earlier formation times are cor8 Figure 2. The top and bottom panels show the \ufb01rst and second steps used to include a secondary halo feature to reduce the scatter in rank ordering halos (Section 4.1). Here we use the MDM,r<2Mpc environmental measure, written as M2Mpc. Top: First we plot this variable as a function of \u03c6, our rank-ordering variable. Here we show the total sample (\u201call\") as well as the centrals and satellites (\"sats\") separately. The points are color-coded as centrals and satellites. Bottom: Using the scatter from a rolling median, we can \ufb01nd that the ratio of the true stellar mass of the galaxy to the rankordered assigned mass has a dependence on MDM,r<2Mpc. The points are not color-coded for satellites and centrals, as for the \u201call\" \ufb01t we use all of the galaxies in the sample. We can then correct our stellar mass using this dependence. Notice that the rolling median for the total sample is similar to that for the separated satellite and central samples. related with higher stellar mass at a constant \u03c6 (in agreement with previous work), stellar evolution causing mass loss over several Gyr may \ufb02atten this relationship. Finally, using environment to correct for the stellar mass also has a small impact on the overall error. Despite this, we note that including the mass from galaxies within 2-5 Mpc seems to produce a slightly better correction than smaller or larger environment windows. 4.2.1. Correcting Using A Combination of Environment and Formation Time Finally, we use our \ufb01ts for each of our strongest individual corrections, t85 and MDM,r<2Mpc, to create a combined correction on the rank-ordering technique. M\u2217,pred = log(M\u2217,rank)+ (\u03b1M2\u2206log(MDM,r<2Mpc)2 + \u03b2M2\u2206log(MDM,r<2Mpc)+ (\u03b1t85\u2206log(t85)2 + \u03b2t85\u2206log(t85) + \u03b3 (13) We use the curve\ufb01t module in scipy to perform a leastsquares \ufb01t to the above equation, and \ufb01nd that we can reduce the error using both MDM,r<2Mpc and t85 as shown in the \ufb01nal line of Table 2. 4.3. Verifying our Results Here we use two methods to verify our results on the improvement using multiple halo features to determine stellar mass. 4.3.1. Random Forest Regression Now that we have gained insight into the level of improvement that can be gained by using more than one feature of dark matter halos in the abundance matching technique, we turn to machine learning to provide an independent check of our modeling and ranking scheme. Using Random Forest Regression (RFR) allows us to rank the features according to their e\ufb00ect on the model output, and has the additional bene\ufb01t of expanding the space of available models beyond polynomial \ufb01tting. For this work we use scikit-learn (Pedregosa et al. 2011). First, we are able to reproduce the percent error on the entire sample using only our de\ufb01ned \u03c6 feature (0.111), and in a two-feature setting where we add a central/satellite galaxy label (0.105). We check the rest of our ranking parameters from Table 1 and verify that \u03c6 produces the best ranking variable to match DM halos to galaxies. Also, we con\ufb01rm that our \u03c6 variable produces lower error values than the combination of vmax and Mpeak. We also use our four selected halo features that we found produced the best match between the DMO and hydrodynamical simulations, \u03c6, MDM,r<2Mpc, t85, and the central/satellite label. Using an optimized RF regressor, the expected test set error is 0.098 with a standard deviation of 0.0013, quite similar to the percent error we \ufb01nd ranking the satellites and centrals separately using \u03c6 and applying our analytic correction using MDM,r<2Mpc and t85. This is reassuring because it shows that our results are only very mildly dependent on the modeling assumptions. 9 All Centrals Satellites Mix \u03c6 0.111,0.111 0.102,0.101 0.120,0.117 0.105,0.104 \u03c6 + MDM,r<2Mpc 0.104,0.104 0.099,0.099 0.114,0.112 0.102,0.101 \u03c6 + t85 0.104,0.104 0.099,0.100 0.111,0.109 0.101,0.102 \u03c6 + MDM,r<2Mpc + t85 0.101,0.100 0.097,0.097 0.109,0.104 0.099,0.097 Table 3: The median percent error on ten iterations using a training and test sample. For each sample and \ufb01tting method we list the training then test sample values. We can also include all the features and use a parameter optimization technique to \ufb01nd the minimum possible error of a Random Forest Regression. We \ufb01nd a minimum error of 0.092 using eight randomly selected features, creating 100 trees (nestimators) with a maximum depth of 14 branches (maxdepth). However, there are more than 30 combinations within one standard deviation (0.0015), including one using only 4 features. We can conclude that there may be many similarly relevant predictors in our feature list. This supports our analytic reasoning that several of our halo features are reasonable proxies for halo mass, and we have already noted that our other halo features can be separated into only a few types of variables (halo size, concentration, formation time, and environment). Indeed, if we optimize the RFR including one feature of each type we can reach an error of 0.095 (\u03c6, MDM,r<2Mpc, t50, rDM, and cv). This is within two standard deviations of the four halo parameters we use in our analytic model, and so does not indicate a dramatic improvement. Comparing our results to the errors found using the RFR machine learning technique gives us assurance that our analytic method for including extra halo features is reasonable, and that our conclusions are not strongly model-dependent. While continuing to add features can reduce the error on the matching scheme, we do not \ufb01nd other clear DM halo features that dramatically improve upon our analytic method. 4.3.2. Cross-Validation In order to obtain another view on whether increasing the number of halo features improves our estimate of stellar mass we can use cross-validation. This can be used to determine how meaningful our derived improvements are when used to predict the stellar mass of galaxies. Cross-validation is speci\ufb01cally designed to trade o\ufb00overand under-\ufb01tting to give the highest prediction accuracy. For this, we randomly select 80% of our sample as our test set, on which we perform the \ufb01tting processes as described. We use the remaining 20% as our test set to determine if the percent error on the stellar mass prediction improves when including more features. Speci\ufb01cally, we select 80% of our total sample for the \u201call\" \ufb01ts, and then 80% of the central and satellite samples, in order to determine the \u201ccentral\", \u201csatellite\", and \u201cmix\" \ufb01ts. We performed this cross-validation routine ten times using ten di\ufb00erent random subsets of the data, and universally \ufb01nd improvement in both the training and test sets when using MDM,r<2Mpc, t85, or their combination. In Table 3, we list the median percent error values for the ten sets of training and test samples. We can conclude that we have not yet over\ufb01t using these halo features, and our improvement in predicting stellar masses from halo masses is real, albeit small. 5. DISCUSSION What have we learned from this exercise? The zeroth order conclusion is that a matching scheme based on the maximum velocity in a dark matter halo is a good single predictor of the \ufb01nal stellar mass for normal galaxies, whether they are central galaxies or satellites. The typical error in the prediction (in the IllustrisTNG100 simulations) is 11.6 percent in log(M\u2217) compared to 19.8 using MDM, and the dependence of stellar mass on vmax is unsurprisingly log (M\u2217) \u223c(3.8 \u00b1 0.02) log(vmax) (using bootstrap resampling with 70% of the data set), close to the Faber-Jackson relation (Faber & Jackson 1976). This result is just what one would have expected from the simplest physical argument that estimates the amount of gas that can be turned into stars in the standard Gunn & Gott (1972) collapse of a dark matter halo. But, for high mass systems comparable to the \ufb01rst brightest galaxies in clusters living in halos more massive than 1012.7 M\u2299, the accretion of satellite systems will signi\ufb01cantly increase the stellar mass and the most relevant halo parameter is simply the peak dark matter mass, Mpeak. Using a single variable, \u03c6 (Equation (11)), which incorporates both features reduces the error to 10.5% when satellites and centrals are ranked separately. These prescriptions should be easy to implement and can replace the simplest, halo mass based initial matching schemes when estimating the expected galaxy stellar masses given a dark matter simulation. If one wants to go farther and improve the best zeroth order scheme by \ufb01rst order corrections then we have found that a roughly 6% improvement is possible. Interestingly, environmental considerations that we considered did not lead to signi\ufb01cant improvement even in satellite galaxies, and the best single variable for improvement was t85, the time at which a halo reached 85% of its peak mass. However, an almost mindless combination of the two variables (vmax, Mpeak) worked best. We further found that a simple linear combination based on these two variables en10 ables predictions to a typical accuracy of 10.5 percent error in log(M\u2217). 6. TESTS All of these results are based on simulated data and it is important to test them in the real world. We have been able to think of two tests that might be applied to help determine whether the proposed matching scheme provides a signi\ufb01cant improvement over the simplest matching scheme. First one constructs a standard LCDM, dark matter only simulation and, using a standard halo \ufb01nding algorithm, makes a catalog of dark matter halos labeling each of them with the \ufb01nal dark matter mass, MDM, the peak dark matter mass Mpeak over the history of the halo and the current halo maximum circular velocity vmax. Then, to test the classic matching scheme (as has been done before \u2013 Conroy et al. 2006), one takes a representative volume and rank orders the halos by MDM, takes catalog values for a comparable volume (from, say, the Sloan Digital Sky Survey) and rank orders the observed galaxies by (for example) g or r magnitudes and then identi\ufb01es each DM halo with the matched by ranking, real galaxy. This gives one an arti\ufb01cial catalog of galaxies each tagged with a position, a velocity and a g or r optical magnitude. Then one would \u201cobserve\u201d this synthesized catalog and construct two spatial distribution functions, a galaxy-galaxy spatial correlation function (Conroy et al. 2006; Hearin et al. 2013; Hearin & Watson 2013; Reddick et al. 2013) and a void distribution function (e.g. Walsh & Tinker 2019). These could then be compared to the known galaxy-galaxy spatial correlation functions and the known void distribution functions with both one parameter functions speci\ufb01ed as a function of magnitude. The magnitude distribution itself is of course correct by construction. Then comparing \u2013 say \u2013 the autocorrelation length as a function of galaxy magnitude between the real and synthesized data sets allows one to determine the fractional error as a function of galaxy magnitude. Then one would go back to the original DM halo catalog and, using (Mpeak,vmax), construct for each halo the value of \u03c6 = (vmax/v1) + (Mpeak/(M1)) (Equation 11), where (v1, M1) are the values of (vmax, Mpeak) for the average halo of mass 1012.7 M\u2299. Now, with each halo tagged with its value of \u03c6, one can rank order the synthetic sample by \u03c6 and attach visual magnitudes to each galaxy by the same method as was done using MDM. Now one has a new catalog to observe with respect to spatial distribution metrics and can again \ufb01nd the fractional error in \u2013 for example \u2013 the spatial autocorrelation length as a function of visual brightness and compute the error by comparing to real observed data. This procedure would give us a quantitative estimate as to how well the matching scheme was working compared to both reality and the previous simpler matching scheme which has had considerable success. And, unlike the exercises in this paper, the tests would not be dependent on the accuracy of our current galaxy formation algorithms, which, while well tested, su\ufb00er from the \u201ccon\ufb01rmation bias\u201d inevitable when uncertain modelling parameters are adjusted to \ufb01t observations. We look forward to pursuing these independent tests in future work. 7. CONCLUSIONS In this paper we have examined schemes to populate a synthesized dark matter only set of cosmological simulations with galaxies to see if we could devise a simple and accurate scheme. We took as our starting point a matching scheme (Vale & Ostriker 2004, 2006, 2008) which, while almost naively simple has had some success. In that scheme, one rank orders DM halos by \ufb01nal mass and rank orders real galaxies in a similar cosmic volume by luminosity and attaches to the kth ranked halo the kth ranked galaxy. Table 1 represents of one parameter e\ufb00orts which we compared to the computed luminosities in the IllustrisTNG simulated galaxy catalog. Table 2 summarizes our results with two parameter \ufb01ts where we used combinations of velocity dispersion, mass and environmental density. We did not \ufb01nd that adding an environmental variable produced a signi\ufb01cant improvement over simpler schemes nor did we \ufb01nd that any of the two parameter \ufb01ts that we investigated were statistically signi\ufb01cantly superior to the one parameter \ufb01ts. What we did discover was that a new single variable, \u03c6 (cf equation 12), which combines information from both mass and velocity variables, provides a quite signi\ufb01cant improvement over the basic ranking scheme using \ufb01nal dark matter mass, the error being reduced by about 33% percent. In our examination of the physical basis for the success of this new variable we examined simple arguments starting with the over half century old paper by Rees & Ostriker (1977). There is a critical mass for galaxies \u2013 the mass above which it cannot cool by normal radiative processes in roughly a free fall time. That mass corresponds roughly to 1012.7 M\u2299which we designate as M1. Below this mass there is a simple analytic argument that asks if a gaseous object can cool in its own free fall time and is equivalent to M\u2217\u223cv3 max f. For masses above M1 growth only occurs by accretion of satellites and that is proportional to M. So, we designed a metric, \u03c6, which is dominated by velocity for low mass objects and dominated by mass for high mass objects more massive than M1. This single variable, based on the physical motivation given above, seems to provide a matching scheme superior to others which we have tested. We did try other combinations of (Mpeak,vmax) and found none superior to the simple variable, \u03c6, that we had tested. So our bottom line is that the variable, \u03c6 (Equation 11), is the best single variable to use in predicting the stellar mass of galaxies, given their halo properties. 11 ACKNOWLEDGMENTS We would like to thank the referee for helpful comments that improved the paper. ST would like to thank Claire Kopenhafer and Tjitske Starkenburg for their help and scripts in reading in and analyzing TNG outputs, Viviana Aquaviva for her Machine Learning class and comments on the draft, and Dan Foreman-Mackey for discussions and comments on cross-validation. ST gratefully acknowledges support from the Center for Computational Astrophysics at the Flatiron Institute, which is supported by the Simons Foundation. The data used in this work were hosted on facilities supported by the Scienti\ufb01c Computing Core at the Flatiron Institute, a division of the Simons Foundation. 12",
                    "introduction": "1."
                },
                {
                    "url": "http://arxiv.org/abs/2102.05061v1",
                    "title": "It's Cloud's Illusions I Recall: Mixing Drives the Acceleration of Clouds from Ram Pressure Stripped Galaxies",
                    "abstract": "Ram Pressure Stripping can remove gas from satellite galaxies in clusters via\na direct interaction between the intracluster medium (ICM) and the interstellar\nmedium. This interaction is generally thought of as a contact force per area,\nhowever we point out that these gases must interact in a hydrodynamic fashion,\nand argue that this will lead to mixing of the galactic gas with the ICM wind.\nWe develop an analytic framework for how mixing is related to the acceleration\nof stripped gas from a satellite galaxy. We then test this model using three\n\"wind-tunnel\" simulations of Milky Way-like galaxies interacting with a moving\nICM, and find excellent agreement with predictions using the analytic\nframework. Focusing on the dense clumps in the stripped tails, we find that\nthey are nearly uniformly mixed with the ICM, indicating that all gas in the\ntail mixes with the surroundings, and dense clumps are not separate entities to\nbe modeled differently than diffuse gas. We find that while mixing drives\nacceleration of stripped gas, the density and velocity of the surrounding wind\nwill determine whether the mixing results in the heating of stripped gas into\nthe ICM, or the cooling of the ICM into dense clouds.",
                    "authors": "Stephanie Tonnesen, Greg L. Bryan",
                    "published": "2021-02-09",
                    "updated": "2021-02-09",
                    "primary_cat": "astro-ph.GA",
                    "cats": [
                        "astro-ph.GA"
                    ],
                    "main_content": "Corresponding author: Stephanie Tonnesen stonnesen@flatironinstitute.org predicted by the GG72 picture, gas has been observed to be stripped from the outside-in (Gullieuszik et al. 2017; Pappalardo et al. 2010; Abramson et al. 2011; Merluzzi et al. 2016; Fossati et al. 2018; Cramer et al. 2019). In addition, high-density gas with a higher \u03a3g may survive in the disk while lower-density gas is stripped. This has been observed in molecular clouds surviving in the disk of NGC 4402 (Crowl et al. 2005), and predicted in simulations (Tonnesen & Bryan 2009). This differential stripping may be followed by differential acceleration, in which low density gas is pushed to higher velocities than more dense gas (Tonnesen & Bryan 2010; Jachym et al. 2017). However, thinking of the boundary between the ICM and ISM as impermeable denies the nature of the hydrodynamic interaction between the two fluids. This boundary is often unstable to a variety of hydrodynamic or hydromagnetic instabilities, which can drive mixing and the development of intermediate temperature and density gas at constant pressure (Begelman & Fabian 1990). For example, Rayleigh-Taylor and Kelvin-Helmholtz instabilities may completely destroy a cold clump subjected to a hot wind (Chandrasekhar 1961; Agertz et al. 2007). In addition, non-ideal processes may drive mixing: heat conduction can evaporate cold gas into the ICM (Cowie & Songaila 1977; Cowie & McKee 1977). Shock heating of the cool gas may allow these mixing proarXiv:2102.05061v1  [astro-ph.GA]  9 Feb 2021 2 cesses to act more quickly in stripped tails. In addition to heating cold gas, radiative cooling can lead to entrainment of the hot ICM onto cold gas and mixing in surviving cold gas clouds (Klein et al. 1994; Mellema et al. 2002; Scannapieco & Br\u00fcggen 2015; Gronke & Oh 2018, 2019). In addition, if we apply the ram pressure model simply requiring ram pressure to overcome the gravitational restoring force per area on small scales, then it becomes clear that dense clouds, with their large restoring forces and low surface areas, should not be susceptible to stripping, leaving dense molecular clouds impervious to ram pressure. Nevertheless, both observations (Moretti et al. 2018, 2020; Sivanandam et al. 2010; Jachym et al. 2014, 2019; Cramer et al. 2019) and simulations (e.g., Tonnesen & Bryan 2010) demonstrate that dense gas is present in the stripped tail.1 This puzzle has been remarked on in other contexts \u2013 for example, Thompson et al. (2016) pointed out (in the context of cold clumps in galactic winds) that clouds are destroyed more rapidly than they are accelerated to the surrounding wind speed, at least in the absence of strong radiative cooling, a statement which has been veri\ufb01ed by high-resolution simulations (Schneider & Robertson 2018). There is also observational evidence of gas mixing in stripped tails. When comparing the expected gas mass of ram pressure stripped galaxies to the mass of gas that is observed in the disk and tail, observers often \ufb01nd lower masses (e.g. Vollmer & Huchtmeier 2007; Ramatsoku et al. 2019; 2020), possibly indicating stripped gas is mixing into the ICM. Observations also \ufb01nd that the metallicity in the stripped gas is often between that of the ISM and ICM (Fossati et al. 2016; Gullieuszik et al. 2017; Bellhouse et al. 2019). In this paper, we propose a model of ram-pressure that is driven by mixing processes, rather than a traditional contact force exerted between by the low-density wind and the highdensity cloud. In particular, we write down a few straightforward relations based on this supposition (and some simple ideas about energy conservation) which describe how galactic gas is removed and accelerated from a disk in a rampressure-stripping wind. We then compare it to the acceleration of gas from galaxies in wind-tunnel ram-pressurestripping simulations. In our comparison we examine all of the stripped gas, but also focus in one section on dense clouds that therefore have longer conduction, viscous stripping, and Kelvin-Helmholtz timescales. Thus we are focusing on the gas that is the most likely to remain unmixed with the ICM in a classic \u201cpushing\" scenario. 1 The ram-pressure literature sometimes di\ufb00erentiates between ram-pressure and viscous-stripping, with the implication that a non-ideal viscous force is responsible for removing denser material; however, a coherent physical picture of viscous stripping has not been developed to date. This idea, that the acceleration of cold clouds by hot \ufb02ows is fundamentally driven by mixing, has received some additional support by two recent works, one examining the in\ufb02ow of cold gas on to a galactic disk (Melso, Bryan & Li 2019), and another exploring galactic out\ufb02ows at high resolution (Schneider et al. 2020). We begin by introducing our mixing model for gas stripping and acceleration in Section 2. In order to test the predictions from our model, in Section 3 we describe our simulations (Section 3.1) and how we identify and measure properties of clouds in the tail (Section 3.2). We then test our model predictions through comparisons with all the gas behind the simulated galaxies as well as with denser clouds (Section 4). In Section 5 we discuss the survival of the clouds in our simulated stripped tails. We use cloud properties to determine to what extent the surrounding ICM in\ufb02uences stripped gas in Section 6. We discuss the implications of our results in Section 7, focusing on caveats in Section 7.4. Finally, in Section 8 we summarize our conclusions. 2. GAS ACCELERATION VIA MIXING In this section we introduce a simple mixing model to try to describe the properties of a cloud of mass \u03b4M in the downstream wake. The cloud is assumed to be a coherent identity that is identi\ufb01ed as a single (cold) object in the wake (to inform comparison with the simulations below). This cloud can be thought of being composed of gas with two sources: (1) the cold ISM, at rest with respect to the galaxy (our reference frame), and (2) the hot ICM wind with velocity vwind. We denote the masses of those two sources contributing to the cloud as MISM and MICM, respectively. Note that the gas from these two sources may not come from contiguous regions in either the ISM or the ICM. Mass conservation implies MISM + MICM = Mtotal. De\ufb01ning fraction mass contributions fISM = MISM/Mtotal and fICM = MICM/Mtotal, we can rewrite this as fISM + fICM = 1. (1) Determining the resulting velocity of the gas which ends up in the cloud is, of course, more challenging (which we assume to be well mixed, a question directly addressed in the simulation investigations explored later in the paper). However, our overriding assumption is that acceleration of the cloud is done through the process of mixing, and that mixing of the hot (wind) phase into the cold cloud leads to a gain of mass, momentum and energy. Here, we explore two simple models, one based on momentum conservation neglecting the potential of the host galaxy, and a second approach based on energy conservation. If we ignore any external forces on the gas during the mixing process (as well as any gravitational torques), then a simple application of momentum conservation implies that the 3 cloud velocity would be given by vm = fICMvwind (2) where we use subscript m to denote the momentum conservation estimate (see also Gronke & Oh 2018; Schneider et al. 2020). In principle, we could include the gravitational forces, but this would require a knowledge of the trajectory of the gas elements throughout it\u2019s evolution, which requires more assumptions. In addition, vwind should more accurately be the velocity after being processed through the bow shock (if present), which reduces the momentum of the gas by a factor which depends on the Mach number M = vwind/cs (where cs is the sound speed in the hot gas). For low Mach numbers and subsonic \ufb02ow this is negligible, and even for the highest velocity case we explore, we \ufb01nd that the ICM \ufb02ow velocity in the vicinity of active cloud entrainment is only mildly reduced from vwind. The other extreme is to assume a form of energy conservation. On \ufb01rst blush, this seems problematic, both because radiative loses are clearly important and also because of work done on this gas during its evolution, however we can make simple assumptions as to the amount of energy lost due to radiative cooling as well as assume that no work is done during the mixing. We express this with: fICMv2 wind   1 + 2 (\u03b3 \u22121)M2 ! \u2212fISMv2 esc = v2 e + fICM\u03c7   2 (\u03b3 \u22121)M2 ! v2 wind (3) The left-hand side is the \u2018before\u2019 state; the \ufb01rst term represents the total enthalpy plus kinetic energy of the wind gas, while the gas in the galaxy only contributes a term due to its gravitational potential energy, expressed in terms of the escape velocity (vesc). We neglect any gravitational contribution for the ICM wind as well as for the cloud after stripping, under the assumption that they are su\ufb03ciently far from the galaxy. In the \u2018after\u2019 state on the right-hand-side, we assume that the gas is cold and so only has a kinetic component (in this case, we denote the \ufb01nal cloud velocity as ve to emphasize the energy formulation behind the estimate). We account for the radiative losses with the second expression on the right-hand-side. Our ignorance as to the amount of energy radiated is expressed in terms of the ratio to the incoming enthalpy, such that \u03c7 = 1 is the minimum energy loss according to our assumption that the gas is cold in the \u2018after\u2019 state. Making the \u03c7 = 1 assumption simpli\ufb01es this to ve = \u0010 fICMv2 wind \u2212fISMv2 esc \u00111/2 = \u0010 fICM \u0010 v2 wind + v2 esc \u0011 \u2212v2 esc \u00111/2 (4) This implies a minimum amount of mixing from the ICM wind to launch a cloud, since ve only becomes real and positive when fICM > fICM,crit = v2 esc/(v2 wind + v2 esc). For fICM values below this critical fraction, we assume ve = 0. We expect the momentum conservation formulation to fail at low values of fICM (or low vwind) when we can\u2019t ignore the gravitational deceleration, but to be increasingly accurate for unbound gas. On the other hand, when the energy formulation exceeds the momentum prediction, that implies that thermal pressure gradients are accelerating the gas and doing work above and beyond the momentum content of the in\ufb02owing gas. This seems unlikely when mixing is operating in the strong cooling limit, as high-resolution models of the hot/cold interface show no pressure gradient (Fielding et al. 2020). Therefore, we expect the energy conservation argument to fail for high values of fICM. One simple way to combine this to estimates is simply to take the minimum predicted velocity of each: vcloud = min (vm, ve) (5) It is this simple model that we will compare to simulations in the rest of this paper. The cloud velocity in this model depends on the ICM fraction of the clouds (fICM), in addition to the wind and escape velocities. We illustrate these relationships in Figure 1. The primary (thick black) curve in this plot shows the model just derived (Eq. 5), with dashed and dot-dashed thin lines showing vm and ve, respectively. We also explore changing vwind and vesc: a perusal of the three lines in this illustration shows that the velocity-ICM fraction relationship is a\ufb00ected in different ways by these parameters. We vary the escape velocity by changing the cylindrical radius from which gas is stripped (called the stripping radius throughout the paper) \u2013in the \ufb01ducial model (black) this is 20 kpc, and we reduce this to 2.5 kpc in the silver comparison line in the cartoon (a perusal of the galaxy potential described in Section 3.1 and Tonnesen & Bryan (2009) connects the disk radius to the escape velocity). The wind velocity increases from 1000 km/s in the \ufb01ducial case to 1500 km/s for the \u201cfast wind\" comparison (grey line). We see that changing the radius from which gas is being stripped more strongly a\ufb00ects the velocity-ICM fraction relationship at low velocities and levels of mixing, as the silver line lies along the black line (seen as the narrower line). However, changing the wind velocity increases the velocity of stripped gas at all mixed fractions. In its most simple form, as described above, our model does not predict the distance of the cloud from the disk, largely because this depends of the rate of mixing of the gas in the past. However, if we assume a mixing rate for clouds we can make a straightforward prediction for the height of the cloud from the disk. We make the simplest possible as4 Figure 1. An illustration of our analytic model, showing the predicted gas velocity versus the fraction of gas originating in the ICM (a gas cloud at fICM = 0 only contains gas from the galaxy while one at fICM = 1 contains only ICM gas). The thick solid line shows vcloud(fICM) from Equation 5, while the dashed and dash-dot lines show where vm and ve are larger than vcloud, for the \ufb01ducial model (see text). In addition to the \ufb01ducial model, we show a model with a fast wind (grey line) and one in which the gas is stripped from a smaller radius (silver line), where it must escape from a location deeper in the potential well. We also use colored segments to show the locations along these tracks corresponding to the fICM value that gas at a height ranging from 12 to 18 kpc (above the disk) would have for di\ufb00erent assumptions of the cloud mass and wind velocity, as noted in the legend. sumption, that clouds mix at a constant linear rate: fICM(t) =  t t\ufb01nal ! fICM(t\ufb01nal) (6) Here t is the current time and t\ufb01nal is the time at which the cloud reaches fICM(t\ufb01nal). Mixing occurs by the accretion of all of the wind that hits the cloud. The time it takes to reach a chosen fICM(t\ufb01nal) depends on the cloud mass (Mcloud,\ufb01nal) and (e\ufb00ective) cross-sectional area (Acloud), as well as the wind velocity (vwind): t\ufb01nal = fICM(t\ufb01nal)Mcloud,\ufb01nal \u03c1windAcloudvwind (7) We note that our assumptions that all ICM mass that hits the cloud is accreted and that Acloud is constant with time are simpli\ufb01cations. As discussed in Fielding et al. (2020) shear is likely important for mass transfer, as well as the cloud shape (Ji et al. 2019; Gronke & Oh 2020). Then, because we have the velocity as a function of the mixed fraction, we have the velocity of the cloud material2 as a function of time. vcloud(t) = \uf8f1 \uf8f4 \uf8f4 \uf8f4 \uf8f4 \uf8f4 \uf8f2 \uf8f4 \uf8f4 \uf8f4 \uf8f4 \uf8f4 \uf8f3 vwind fICM t t\ufb01nal t > t2 h fICM t t\ufb01nal (v2 wind + v2 esc) \u2212v2 esc i1/2 t2 > t > t1 0 t1 > t (8) where t1 = t\ufb01nalv2 esc/( fICM(v2 wind+v2 esc)) is the time required for fICM(t) to reach the critical value mentioned earlier ( fICM,crit), and t2 = t\ufb01nalv2 esc/( fICMv2 wind) is the time when the momentum and energy predictions are the same (i.e. ve(t) = vm(t)). Finally, we can solve for the distance (zcloud(t)) by integrating the velocity over time: zcloud(t) = 2 3(v2 esc fICM q )1/2t\ufb01nal \uf8ee \uf8ef \uf8ef \uf8ef \uf8ef \uf8ef \uf8f0  t2 t\ufb01nal \u2212 q fICM !3/2\uf8f9 \uf8fa \uf8fa \uf8fa \uf8fa \uf8fa \uf8fb +vwind fICM 2t\ufb01nal \u0010 t2 \u2212t2 2 \u0011 (9) where q = v2 esc/(v2 wind + v2 esc). If t < t2, then the last term is dropped and t2 \u2192t. These relationships are illustrated in Figure 2, where we show the impact on the position of a \ufb01ducial cloud as we vary one property of the cloud at a time. Unlike Figure 1, this is a single snapshot, so the height of each cloud varies depending on its properties. When an ICM wind has been acting on a galaxy, gas at a smaller radius is deeper in the galaxy potential and therefore has higher vesc (as discussed in Section 3.1 and Tonnesen & Bryan 2009), so in the same amount of time (and for \ufb01xed fICM) it will not make it as far as our \ufb01ducial cloud. In the paper we call this the stripping radius, and in Figure 2 this is shown as Rstrip. Also, a more massive cloud will be closer to the disk (red in Figure 2), while a larger radius cloud (with \ufb01xed mass) will be farther from the disk (yellow in Figure 2). Using these simple assumptions, we can return to Figure 1 and determine where along the ICM-fraction velocity track clouds will be as a function of height, using equation 9. In our schematic diagram we illustrate this relation using the height range from 15 kpc. We vary the three parameters as listed in Figure 2 so as to show the impact of vesc, cloud radius, and cloud mass, modifying one parameter at a time while keeping the others \ufb01xed. The orange bars describe 105 M\u2299clouds with 80 pc radii being accelerated by the \ufb01ducial density wind. Less massive clouds mix and accelerate more quickly than heavier clouds (compare the orange to red 2 We stress that we are not trying to model the cloud as a single entity during its evolution, since the gas which ends up in a cloud at a given t\ufb01nal may have a complicated previous history and is likely to come from multiple paths; therefore, these quantities should be thought as \u201ce\ufb00ective\" values, characteristic of the cloud\u2019s gas history. 5 fiducial cloud:  rcloud = 80 pc  Mcloud = 105 Msun Rstrip = 20 kpc large vesc cloud:  rcloud = 80 pc  Mcloud = 105 Msun Rstrip = 2.5 kpc 10x massive cloud:  rcloud = 80 pc Mcloud = 106 Msun Rstrip = 20 kpc 2.5x radius cloud:  rcloud = 200 pc Mcloud = 105 Msun Rstrip = 20 kpc Edge-on slice of galaxy  during stripping \u00e0 high z(t) \u00e0 low z(t) Rstrip, small Rstrip, fiducial \u00e0 low z(t) Figure 2. An illustrative cartoon showing the importance of cloud properties for the acceleration of gas from a galaxy due to ram pressure stripping, as predicted by Eq. 9. For context, the background greyscale is the maximum density within a 2.4 kpc slab from run HDHV, taken at a single snapshot in time. Cartoon \u201cclouds\" (shown as colored circles) with di\ufb00erent properties are depicted on top of this map and are labelled by their properties. Each cloud di\ufb00ers from the \ufb01ducial cloud (orange) in one parameter, with the others held constant: in particular, we \ufb01x fICM, and vary vesc (orange and silver), mass (red), and radius (yellow); we have written how each variable a\ufb00ects the distance as a function of time (z(t) from Equation 9) for \ufb01xed fICM. The colors are chosen to match those in Figure 1 (we use purple to di\ufb00erentiate the large vesc parameters, although the cloud is orange and silver as in Figure 1). Note that we are using this image only as a background to show the context; the individual colored circles do not refer to speci\ufb01c clouds in this simulation. regions along the black \ufb01ducial relation), and clouds with larger radii mix more quickly than smaller ones (compare the orange to yellow regions). In addition, in Figure 1 we change two wind parameters: the wind velocity and density. We have already discussed that changing the wind velocity changes the whole velocity-ICM fraction track, and we also see that this results in gas moving more quickly at any height above the disk (compare the two orange regions in the black and grey lines). Also, with a faster wind, less mixed-in ICM mass is required to accelerate the gas to the same height, so the ICM fraction of a cloud is reduced with respect to a cloud. Increasing the density of the wind increases the rate of mixing and energy/momentum input into the cloud, so given the same wind velocity a denser wind will result in clouds moving more quickly and being more well-mixed at any height above the disk (compare the orange and cyan regions along the black \ufb01ducial cloud relation). Having developed and explored this simple model, in the next section, we carry out a set of high-resolution simulations of ram-pressure stripping with three di\ufb00erent wind parameters and explore how well it performs. 3. METHOD To follow the gas, we employ the adaptive mesh re\ufb01nement (AMR) code Enzo (Bryan et al. 2014) which solves the \ufb02uid equations including gravity and optically thin radiative cooling. The code begins with a \ufb01xed set of static grids and automatically adds re\ufb01ned grids as required in order to resolve important features in the \ufb02ow. Our simulated region is 300 kpc on a side with a root grid resolution of 256 cells. We allow an additional 5 levels of re\ufb01nement, for a smallest cell size of 37 pc. The re\ufb01nement criteria is based on gas mass, with a resolution of \u223c1.9 \u00d7 104 M\u2299(HDHV), \u223c2.9 \u00d7 104 M\u2299(HDLV), and \u223c3.5 \u00d7 104 M\u2299(LDLV), meaning that whenever a cell exceeds this mass it is re\ufb01ned into 8 small sub-cells. The simulation includes radiative cooling using the GRACKLE (Version 3) cooling tables including metal cooling and the UV background from HM2012 (Smith et al. 2017). 6 3.1. Simulation Initialization Our galaxy is placed at a position corresponding to (150,150,75) kpc from the corner of our cubical 300 kpc computational volume, so that we can follow the stripped gas for more than 200 kpc. The galaxy remains stationary throughout the runs, with the disk aligned in the x-y plane. The ICM wind \ufb02ows along the z-axis in the positive direction, with the lower x, y, and z boundaries set for in\ufb02ow and upper x,y, and z boundaries set as out\ufb02ow. We model a massive spiral galaxy with a \ufb02at rotation curve of 200 km s\u22121. It includes a gas disc that is resolved to the maximum level (37 pc). The galaxy model also includes the static potentials of the stellar disc, stellar bulge and dark matter halo, directly following the set-up of Roediger & Bruggen (2006). Speci\ufb01cally, we model the stellar disc using a Plummer-Kuzmin disc (see Miyamoto & Nagai 1975), using a radial scale length of 3.5 kpc, a vertical scale length of 0.7 kpc and a total mass of 1.15 \u00d7 1011 M\u2299. The stellar bulge is modeled using a spherical Hernquist pro\ufb01le (Hernquist 1993) with a scale length of 0.6 kpc and a total mass of 1010 M\u2299. The dark matter halo is modeled using the spherical model of Burkert (1995), with an equation for the analytic potential as given in Mori & Burkert (2000). The dark matter halo has a scale radius of 23 kpc and a central density of 3.8 \u00d7 10\u221225 g cm\u22123. We describe our disk setup in detail in Tonnesen & Bryan (2009, 2010). To identify gas that has been stripped from the galaxy we also follow a metallicity value that is initially set to 1.0 inside the galaxy and 0.3 outside. Because we do not include star formation in this simulation, the metallicity can also be used to determine the origin of the gas in each cell, in particular we can track the ratio of galactic gas to ICM gas on a cell-by-cell basis. In this paper we discuss three simulations. In all three runs, as in our earlier work (Tonnesen & Bryan 2009, 2010, 2012), we impose a delay of 100 Myr before the wind enters the box in order to allow multiphase gas to self-consistently develop in the disk via radiative cooling. All of the ICM winds have temperatures of 7.08 \u00d7 107 K. We vary the velocity and density as shown in Table 3.1. The low density, low velocity wind (LDLV) has a velocity of 1000 km s\u22121 (M \u223c0.79) and a density of 5 \u00d7 10\u221228 g cm\u22123. The high density, low velocity wind (HDLV) has a velocity of 1000 km s\u22121 (M \u223c0.79) and a density of 1.2 \u00d7 10\u221227 g cm\u22123. Finally, the high density, high velocity wind (HDHV) has a velocity of 3230 km s\u22121 (M \u223c2.5) and a density of 1.2 \u00d7 10\u221227 g cm\u22123. The minimum and maximum ram pressure parameters were chosen to roughly correspond to the ICM wind parameters of two jelly\ufb01sh galaxies observed in the GASP sample (GAs Stripping Phenomena in Galaxies with MUSE; Poggianti et al. 2016): JO204 (LDLV) and JO201 (HDHV) (Gullieuszik et al. 2017; Bellhouse et al. 2017), with the middle simulation a test of Name Velocity Density km s\u22121 g cm\u22123 LDLV 1000 5 \u00d7 10\u221228 HDLV 1000 1.2 \u00d7 10\u221227 HDHV 3230 1.2 \u00d7 10\u221227 Table 1. The wind velocity and density of the three simulations discussed in this paper. Figure 3. The distribution of the minimum temperature found in clumps in the all three simulations (number of clouds per logarithmic temperature bin). The colors denote height above the galaxy disk. We have not di\ufb00erentiated between the three simulations as they all have a similar minimum in their temperature distribution. The y-axis scale is set to log to highlight the minimum in the distribution at all heights above the disk, at about 30 000 K (dashed vertical line). Clouds are required to have a minimum temperature below this value. the impact of changing a single wind variable rather than both density and velocity. 3.2. Cloud Selection In this paper, we examine both the state of all of the gas in the wake (Section 4.1) as well as focusing just on the dense gas (Section 4.2), which is more observationally accessible. In order to \ufb01nd higher-density \u201cclouds\" in our tails, we used the clump \ufb01nder routine in yt (Turk et al. 2011). This uses level sets to \ufb01nd connected cells with values above a given selection criteria. We searched for clouds using the gas density, starting with 10\u221226 g cm\u22123 and increasing the density by a factor of two for each level set. This minimum density is relatively arbitrary, and we use other characteristics of the clumps, as described below, to make a more physicallymotivated cloud selection. In brief, we required a minimum number of cells and a low minimum temperature in the clump to include it in our analysis. In more detail, the clump \ufb01nder algorithm will \ufb01nd clumps down to a single cell, and indeed, we \ufb01nd that about half of 7 our raw clump sample have fewer than 10 cells. In order to eliminate clumps that are actually small density perturbations in the di\ufb00use stripped tail, we only keep those identi\ufb01ed with at least 10 cells in total (we note that we have repeated this work using clumps with at least 300 total cells and \ufb01nd the same trends, with some results shown in Appendix A). We also \ufb01nd that clumps have a bimodal distribution in their minimum temperature, as shown in Figure 3. As we are attempting to choose cold, dense clouds rather than simple overdensities in the tail gas, we only include clumps whose minimum temperature is below 30 000 K. We note that, when we impose these two selection criteria, the lowest maximum density of any cloud across all three simulations is more than 4 \u00d7 10\u221226 g cm\u22123, so our minimum search density (10\u221226 g cm\u22123) does not have a strong impact on the number of clouds we identify. To orient the reader, a density of 4 \u00d7 10\u221226 g cm\u22123 will be re\ufb01ned to \u223c300 pc, and only densities reaching \u223c4 \u00d7 10\u221223 g cm\u22123 will be re\ufb01ned to 37 pc, i.e. the centers of the most dense clouds. During the clump \ufb01nding procedure we also save several cloud properties. We \ufb01nd the maximum and minimum values of density, temperature, and the ICM fraction within the cloud. Using all of the cells identi\ufb01ed as belonging to our clouds, we also save the mass-weighted mean cloud position and velocity in addition to the physical characteristics listed above. In summary, our \ufb01nal set of \u201cclouds\" are ten or more connected cells consisting of gas at least an order of magnitude denser than the ICM that have minimum temperatures more than three orders of magnitude lower than that of the ICM. This makes us con\ufb01dent that our clouds are physically distinct entities rather than just being ephemeral overdensities in the wake. We identify these clouds in three evenly spaced regions: 12-18 kpc above the disk, 82-88 kpc above the disk, and 152158 kpc above the disk. Throughout the paper these heights will be identi\ufb01ed as 15 kpc, 85 kpc, and 155 kpc. These regions were selected so that we can easily compare gas properties as a function of height above the disk, and because they span the range of tail lengths seen in observations. We tested our results using di\ufb00erent height bins (10-20 kpc, 76-86 kpc, and 160-170 kpc) with no qualitative change to our results. We perform this clump identi\ufb01cation at each output (10 Myr apart) for each simulation. We do not attempt to follow any individual clump, but identify the population of clumps in our simulations in the three regions at each output. In Figure 4 we show density projections of \u201cearly\" and \u201clate\" illustrative outputs from each simulation, with colored lines indicating the three narrow height ranges we analyze, as described above. Here we are using \u201cearly\" and \u201clate\" to denote the timeline of the development of the tail. Speci\ufb01cally, the \u201cearly\" output is close to the output at which the most clouds are found in the 15 kpc region, and the \u201clate\" output is close to the output at which the most clouds are found in the 155 kpc region (as seen in Figure 10). In order to directly compare the simulations, and highlight di\ufb00erences in the tails, we chose to show the 360 Myr snapshot for all three. This same output is also used in Figures 5 7. The tail structure varies as a function of height and time within a simulation, and di\ufb00ers across simulations at the same time. At earlier times clouds are tightly packed in the tails, while at later times clouds are less densely distributed. This is true even looking at a single height above the disk (for example within the red 15 kpc region). The wind properties have a signi\ufb01cant impact: for example, at 360 Myr, dense gas in the HDHV tail has reached 155 kpc from the disk, while in the LV runs it has barely reached 85 kpc. Even within the LV runs the gas distribution is di\ufb00erent: denser clumps are seen at larger distances in HDLV than in LDLV. We also note that the ICM of the HD runs is denser than in LDLV, leading to the darker background density seen in the projections. 4. TESTING THE MIXING MODEL Our simple analytic mixing model, developed in Section 2, predicts a relationship between stripped cloud velocity and mixed fraction, modulo wind velocity and galaxy escape velocity. In this section we use the three simulations described in Section 3.1 to test these predictions. 4.1. All Gas We begin by looking at the properties of all gas in the tail before turning to dense clouds (which connect more directly with observations) in the next section. The gas velocity in our mixing model depends only on the ICM fraction of gas (for \ufb01xed vesc and vwind), and therefore can be tested using all of the gas behind the galaxy in our simulations. According to our model, this \u201ctail\" gas will consist of a range of ICM fractions, from nearly pure galactic gas that was loosely bound to the galaxy and moving slowly, all the way to nearly pure ICM gas moving at the wind speed. In Figure 5, we see that, indeed, gas behind the galaxy has a range of ICM fractions. In this \ufb01gure we plot the velocityICM fraction relation in the HDHV run at three heights above the disk (15 kpc, 85 kpc, and 155 kpc). Each of these plots use an output taken shortly after any dense clouds are identi\ufb01ed at those heights. In black we overplot the analytic relation between ICM fraction and velocity using a stripping radius of 3 kpc (used to determine vesc), as this is about the radius of the gas disk at the end of the simulation. We see that at any height above the disk, gas tends to have a broad range of ICM fractions, and generally falls along the analytic relationship between ICM fraction and velocity. As we move farther from the disk, the minimum velocity and ICM fractions are shifted to higher values. This agrees well with 8 Figure 4. Images of projected density for an early (upper panels) and late (lower panels) output from each of our simulations. Each projection is 185 kpc by 110 kpc. The regions on which we focus in this paper are denoted by the colored lines (which are re\ufb02ected in later \ufb01gures). Gas behind galaxies shows a range of densities and tail morphologies as a function of height above the disk, time since stripping began, and wind paramaters. 9 Figure 5. The gas velocity-fICM relation at three di\ufb00erent heights (and times), as labelled, above the disk in run HDHV. There is more mixing of gas as we move farther from the disk. Despite this, the gas at all heights falls along a similar velocity ICM fraction line. The solid line in each panel is from equation 5. Figure 6. All gas between 15 kpc in HDHV at an early time (170 Myr) and later time (360 Myr). The black line shows the model prediction using a stripping radius of 3 kpc. At early times there is gas that is less mixed than at later times. More energy is required to remove gas from inner radii, which results in the higher ICM fractions at later times. our model prediction that continual mixing occurs as gas is driven away from the disk, therefore our lowest ICM fractions will be found near the disk. We note that the tail gas from 15 kpc in HDHV shows a maximum velocity (\u223c2500 km/s) that is lower than our input wind velocity (3230 km/s). This is because the wind velocity in HDHV is supersonic and creates a large bow shock, de\ufb02ecting the incoming wind along the xand y-axes in addition to the z-axis. At later times, much of the gas is stripped, the bow-shock shrinks, and gas \ufb02ows more directly along the z-axis, the direction of gas in\ufb02ow at the edge of the box. As 10 Figure 7. Gas from 15 kpc at an early (top panels) and later (bottom panels) time in the LV runs: LDLV (230 Myr and 360 Myr) and HDLV (210 Myr and 360 Myr). In each run the majority of gas falls near the analytic line. Gas with low ICM fractions tends to be moving with higher velocities at earlier times. Also, in comparison to the HDHV run, the LV gas tails show a much broader velocity distribution at a given ICM fraction. we show below, the slow velocities in the z-direction of high fICM gas is not a long-lived e\ufb00ect. In Figure 6 we examine how the velocity-ICM fraction relation changes over time in our simulations. We plot this relation in the HDHV run 15 kpc above the disk at an early (170 Myr) and late (360 Myr) time. The amount of gas in the tail changes (as we will explore in more detail later in the paper), but here we highlight the fact that, at all times in our simulations, most of the gas in the tail falls approximately along our analytic relation. By examining the minimum ICM fraction of gas from 15 kpc as a function of time, Figure 6 illustrates the importance of the escape velocity in the velocity-ICM fraction relation. We \ufb01nd that at early times some gas is moving slowly with low ICM fractions, while at late times there is only gas moving quickly with higher mixed fractions. This re\ufb02ects the decreasing stripping radius, and the resulting increase in escape velocity, as a function of time. The impact of the stripping radius on the ICM fraction and velocity of gas can be seen in Figure 1 by comparing the orange bars in the \ufb01ducial and small stripping radius lines. We note that at later times the velocity of lowfICM gas tends to fall below the analytic line. In comparison with the larger distances in Figure 5, we \ufb01nd that this occurs most dramatically near the disk. We posit two likely reasons for this lower velocity gas. First, there continues to be a small bow shock near the disk, and the gas \ufb02ow is not completely in the z-direction. We also \ufb01nd that at early times the disk 11 is being stripped rapidly and shrinking, but at late times the disk size stabilizes. Therefore gas that is stripped is more likely to be near the disk edge and somewhat protected from the wind. We discuss this more below. Now that we have carefully compared the HDHV run to our analytic model, in Figure 7 we verify that this relationship holds in all three of our runs. Here, in two columns we have plotted the gas 15 kpc above the disk in LDLV and HDLV, in each case choosing a time shortly after dense clouds are identi\ufb01ed (upper panels) and at 360 Myr (lower panels) to match the projections in Figure 4. The disk stripping radii for the model lines are chosen to be 20 kpc (LDLV) and 15 kpc (HDLV), as these are near the surviving disk radius at early times for the three runs. We note that at early times, gas with a low ICM fraction is moving more quickly than the analytic line, likely due to gas stripped from a large galactic radii, while at 360 Myr more of the gas lies along or below the line, indicating stripping from small radii. This agrees well with our model prediction illustrated in Figure 1. The generally good agreement between the model predictions and the gas distribution in these plots demonstrate the basic success of the picture. While the overall predictions are veri\ufb01ed, we highlight two points of disagreement between the LV runs and our model predictions. First, at the early times shown in Figure 7, the gas velocity is slightly larger than predicted, and this is true even for pure ICM gas (at the right edge of the upper two panels), which have speeds in excess of the in\ufb02ow velocity (1000 km/s for the LV runs). We see in the lower panels of Figure 7 that this excess velocity is less pronounced at later times. The second, more dramatic, disagreement between the simulations and the model in the LV runs is the gas component with high ICM fractions and low, even negative, velocities (in the lower-right of each panel). To look at these discrepancies in more detail, in Figure 8 we plot the z-velocity of the gas, as a function of cylindrical radius for gas within the same 15 kpc height range of the disk in the HDLV run (to match the HDLV panel in Figure 7). Rather than the total mass in each histogram cell, we have color-coded these two plots using the mean ICM fraction (top) and the mean gas density (bottom) in each cell of the histogram. First we describe the general gas distribution in these panels. In the inner regions, gas only has negative velocities \u2013 this indicates the disk\u2019s \u201cshadow\", where it blocks the \ufb02ow of the ICM wind. There is then a region between \u223c15-30 kpc with gas at a wide range of velocities, indicating that the majority of the tail is found at these radii, and \ufb01nally at very large radii we see pure ICM gas at the in\ufb02ow velocity. We now see that gas moving at the highest velocities (even higher than the input wind velocity) is near the border between the disk \u201cshadow\" and the tail region, at the edge of Figure 8. These panels both plot the gas velocity in the wind direction against the cylindrical radius (for all gas in the 15 kpc bin) from the disk in the HDLV simulation at 210 Myr into the simulation. The upper and lower panels are color coded by the mean ICM fraction and gas density in each histogram cell, respectively. We see that the high ICM fraction, low density gas in the inner tail region is moving quickly, and that the low density gas in the disk \u201cshadow\" has negative velocities. the disk. Visual inspection suggests that this is due to vortices created by the wind \ufb02owing past the surviving disk, with some smaller vortices created by dense clouds in the tail. When the vortex velocity aligns with the wind velocity we see our maximal velocities. At early times a particularly large vortex forms that results in a large amount of gas at high velocity while at later times the majority of ICM-like gas is moving at the in\ufb02ow velocity. We do not see these fast \ufb02ows in the HDHV run because the galaxy is stripped quickly to a 12 small radius so there are not large vortices containing a signi\ufb01cant amount of mass. We can also clearly see in Figure 8 that gas with high ICM fractions and negative velocities is falling back in the shadow of the disk (i.e. at small galactocentric radius). It falls o\ufb00of our predicted fICM-velocity relation because the primary mode of acceleration of this gas is gravitational acceleration rather than mixing. The resulting infall velocity is of order 300 km/s, a value which is set by the acceleration of the galaxy and is unrelated to the wind velocity. The remaining gas disk is very small in HDHV, and so there is no fallback in that run (as seen by the lack of negative velocities in Figure 5). Interestingly, the gas in the shadow of the disk is generally low density, which likely allows it to be more easily shifted to di\ufb00erent radii due to disordered motion or vortices (there may be occasional fallback of clouds but this is a minor e\ufb00ect in these runs). When we focus on just the dense gas in the bottom panel, we see a very clear relationship between radius and velocity, again illustrating the importance of the stripping radius (and thus escape velocity) on gas acceleration. In summary, our simple model is an excellent prediction of the gas velocity-ICM fraction relation, and the di\ufb00erences between the model and simulations can be explained by the hydrodynamical interaction of a wind hitting a disk. 4.2. Focusing on Dense Clouds While it is commonly accepted that low-density gas in ram pressure stripped tails mixes with the ICM, dense clouds are often assumed to consist of galactic gas that maintains its integrity as it is being accelerated by the wind. Therefore, in this section we focus directly on comparing our model predictions to dense clouds in the tail. As we did with all of the gas in our tail, we compare the cloud velocity to the ICM fraction in our clouds in Figure 9. The contours in each panel show the cloud velocity versus ICM fraction for clouds identi\ufb01ed at early times in each simulation. The clouds are de\ufb01ned using contiguous regions of dense gas, as described in Section 3.2, and the contours show the number of clouds in any bin. We use clouds identi\ufb01ed in a limited range of outputs because the radius from which gas is stripped decreases over time so the e\ufb00ective escape velocity for clouds at a given height increases over time. As our model uses a single escape velocity, we choose a narrow range in time to decrease this variation. We also note that we are not tracking individual clouds in our simulations, so we cannot determine the relationship between clouds at di\ufb00erent distances and outputs. Therefore, we use the \ufb01rst 4 outputs (5 at 155 kpc in order to have more than 150 clouds in LDLV) at each height that have any identi\ufb01ed clouds in an attempt to follow a similar population of clouds moving away from the disk. Figure 9. The velocity as a function of the ICM fraction of clouds. The contours show the density of clouds per linear range in velocity and gas fraction. As in Figure 7, the panels from top to bottom are the three runs: LDLV, HDLV, and HDHV. Clouds from the \ufb01rst 4 (15 and 85 kpc) or 5 (155 kpc) outputs at which they are identi\ufb01ed in each simulation and height are shown. For the analytic model, the cloud radius is set to 80 pc, and the mass ranges from 2\u00d7105 to 4\u00d7105 M\u2299. For LDLV and HDLV the wind velocity is set to be 1000 km/s, and for HDHV the wind velocity is set to be 3230 km/s. Simulations are generally in good agreement with the analytic model. 13 In order to overplot a model line we made several choices for parameters based on our simulations. First, we chose a stripping radius in order to calculate the escape velocity. We do this by computing the distance to the x=y=0 line (through the disk center). Based on this analysis, we identi\ufb01ed stripping radii of 30 kpc, 20 kpc, and 10 kpc for LDLV, HDLV, and HDHV, respectively. These values are meant to be representative of the radius from which gas has been stripped, and as such are smaller than the original disk radius but larger than the surviving disk radius. Thus these values are smaller than the initial stripping radius and larger than the radius from which gas is stripped at late times. Note that the line does not change dramatically due to the minor change in stripping radius between LDLV and HDLV. The wind velocity and escape velocity sets the shape of our curves, as shown in Figure 1. We also examined the size and mass of clouds and chose a cloud mass ranging from 2 \u00d7 105 to 4 \u00d7 105 M\u2299for all three simulations. This is based on the measured mass distribution of our selected clumps, which ranges from about 5 \u00d7 104 to 1 \u00d7 106 M\u2299, with the peak of the mass distributions in all simulations at about 2 \u00d7 105 M\u2299. A cloud radius cannot be directly measured, as the clouds are not spherical. Indeed, we expect them to be extended along the wind direction. We choose a radius of 80 pc based on the measured volumes of the clouds, recognizing that this could vary by a factor of several (from 1 cell across to a radius of 600 pc, corresponding to a spherical cloud at our maximum measured volume of 3 \u00d7 1064 cm3). Using these assumptions allows us to predict where along each curve the clouds will fall when 15 kpc, 85 kpc, and 155 kpc above the disk (Equations 8 & 9). This is shown by the thick shaded regions along the curves. Despite the simplicity of our model, we again \ufb01nd good agreement with the simulations. In particular, the fICMvelocity relations follow quite well the predictions of the model and there is qualitative agreement in that higher cloud height corresponds to larger cloud velocities and higher mixed fractions. However, there is some disagreement with the predictions in detail, which we can separate into two general trends: shifts above or below the model curve, and shifts along the model curve. We \ufb01rst focus on the shift of the simulated output o\ufb00the model curve. First, we note that this only occurs in the two LV runs near the galaxy disk. As we have discussed with regards to Figure 1, there are two main variables that change the shape of the velocity-ICM fraction curve in our model: the wind velocity and the galaxy escape velocity. Including the galaxy escape velocity in our model results in a lower velocity at a given ICM fraction than we see in our simulations. However, we note that even simply using a linear relationship due to momentum transfer would still predict velocities slightly below the peak of the HDLV contours. We next focus on our predictions for where along the velocity-ICM fraction curve gas should lie as a function of height above the disk. We note that the LV runs show good agreement between the predictions and simulations, although the model has a slight shift towards higher velocities and ICM fractions as a function of height. In the HDHV simulation, these predictions di\ufb00er much more dramatically, with the di\ufb00erence between the simulation and model increasing with height above the disk. This could be for several reasons. First, we assumed a constant cloud mass, which is likely not the case \u2013 clouds could be constantly accreting gas and fragmenting, processes which are not included in our simple model. Indeed, as we discuss in the next section, we expect that not all clouds survive. On the same note, we assume a constant 80 pc radius. The clouds could be very elongated along the wind direction and be narrower than we model, which would shift our model shaded regions to lower velocities and ICM fractions. Finally, for simplicity we assume that the ICM fraction of cloud gas changes linearly with time, but as the velocity difference between the cloud and ICM decreases, the mass deposition rate should also decrease, leading to a slower increase in the ICM fraction. As we see in HDHV, this should lead to a shift in our model towards lower velocities and ICM fractions, particularly at large distances above the disk. 5. CLOUD SURVIVAL Beyond our model, the evolution of clouds in stripped tails is important for understanding gas mixing and cooling as well as star formation in the ICM. As we have discussed in the Introduction, there remains debate about whether dense gas is removed from the disk and survives in the tail, or whether dense gas can form within that tail from lowerdensity galactic gas that is more easily stripped. In this section, we directly address the evolution of clouds in our simulations, \ufb01rst empirically by examining cloud properties in the simulations as a function of height, and then theoretically by comparing the cooling and destruction (crushing) times of clouds. 5.1. Cloud Number and Mass As a Function of Height Above the Disk Because we cannot track individual clouds in our simulations, the most straightforward way to determine if clouds survive in the stripped tail is to simply count the number of clouds at di\ufb00erent heights above the disk. However, because clumps could fragment or merge, summing the total mass in clouds, or the mass \ufb02ux, may be a more useful measure of the evolution of dense gas in the tail. All of these metrics are shown in Figure 10. We note that clouds move at a range of velocities (as shown in Figure 9), and so comparing gas at di\ufb00erent heights is not likely to give us the exact 14 Figure 10. The number of clouds (top panels) and the total mass in clouds (bottom panels) as a function of time in the three simulations, in each of the three height ranges previous de\ufb01ned. Note that the xand y-axis ranges di\ufb00er across the panels. The bottom panel shows the mass \ufb02ux through each 6 kpc region as a function of time measured from the time of peak \ufb02ux (Time Tpeak). Although the number and mass of clouds is highest in each simulation close to the disk, in HDLV the number of and mass in clouds may increase from \u223c85 kpc to \u223c155 kpc, and the mass \ufb02ux increases as a function of height above the disk. same cloud population. However, with that caveat in mind we make rough comparisons using the peak of the distributions at any height. Clearly, in all simulations, the number of clouds decreases as we compare the 15 kpc height range to either 85 kpc or 155 kpc. Thus, many clouds are not surviving intact as they are being accelerated through the tail by the ICM wind. In agreement with this interpretation, we also see that the total mass in clouds decreases as we look farther from the disk. However, when we compare the number of clouds at 85 kpc to that at 155 kpc, the fate of clouds becomes less clear. In both the LDLV and HDHV simulations, the number of, and mass in, clouds at their peaks decrease from 85 kpc to 155 kpc. In contrast, the peak number of clouds found at 155 kpc in the HDLV run is actually larger than the peak found at 85 kpc, and this increase in the number of clouds is re\ufb02ected in an increase in the total mass in clouds. While clouds may be both destroyed and formed in any of the simulated tails, the increase in cloud number and mass in the HDLV wind 15 Figure 11. The ratio of the minimum to the maximum ICM fraction versus the minimum ICM fraction for clouds in the three simulations. In all runs, the minimum ICM fraction increases as a function of height above the disk, indicating continued mixing of stripped and surrounding gas. Also, the ICM fraction within each cloud tends to be nearly uniform (and becomes increasingly uniform with height above the disk). indicates that clouds are likely to be forming in the tail, with a net increase in the number of clouds beyond \u223c85 kpc above the disk. Because the cloud velocity varies as a function of height above the disk (and there is a range of cloud velocities at any given height as shown in Figure 9), we also look at the mass \ufb02ux in clouds for a physically-motivated view of the cloud \ufb02ow as a function of height. This is shown in the bottom panels of Figure 10; here we have shifted the \ufb02uxes for the three di\ufb00erent heights such that their peaks are coincident at t = 0 in order to ease comparison of their amplitudes and widths. This con\ufb01rms that the LDLV and HDHV runs have a lower \ufb02ux of cold gas as we go away from the disk, while the HDLV run shows a growing \ufb02ux with height. We will discuss a possible mechanism for this growth in Section 5.2. Using the number of clouds as a function of height, we have argued that many clouds are destroyed as they move away from the disk. Next, we focus on the ICM fraction in order to determine whether clouds far from a galaxy originated in the disk or formed from the stripped gas. As we showed in comparison to our model in Figure 9, the mean ICM fraction in gas clouds increases with height above the disk in all runs, following our analytic framework that mixing is critical to acceleration. In Figure 11 we look more carefully at the distribution of the ICM fraction inside clouds by plotting the ratio of the minimum to the maximum ICM fraction of all the cells composing each cloud versus the minimum ICM fraction found in the cloud. We see that in general the ratio is close to one, meaning clouds are well-mixed. Even though the scatter plot shows that the cells composing some clouds can have a range of ICM fractions, particularly in the HDHV run, the histograms demonstrate that the distribution peaks at high values (close to unity). Importantly, we highlight that as we move farther from the galaxy, the minimum ICM fraction increases. Thus it is clear that mixing between the stripped and surrounding gas occurs throughout our clouds and no unmixed gas survives to large distances. In fact, as we move farther from the galaxy, the ratio of the minimum to maximum ICM fraction moves closer to unity. This is particularly notable in the case of HDLV, which shows an increase in the number and mass of clouds from \u223c85 kpc to \u223c155 kpc. Even though the total mass of clouds is increasing, it is not due to stripped clouds simply accreting ICM gas. In other words, in all three simulations there is no surviving core of pure \u201cgalactic material\" that is being accelerated while the outer layers of the clouds are mixing. We note that this result is robust even when only selecting clouds with at least 300 cells, as shown in Appendix A. 5.2. The Wake as a Whole 16 Figure 12. Mass versus time for gas in the entire box (\u201call\"), within 10 kpc of the disk plane (\u201cdisk\"), and from 10-224 kpc above the disk (\u201cwake\"). Each panel shows the gas mass for which fICM < 0.5 (cyan) or \u03c1 > 2\u00d710\u221226 g cm\u22123 (green). In each simulation the mixing of disk gas with the ICM results in a di\ufb00erent amount of dense gas relative to the low-fICM gas. Note that gas begins to leave the simulation volume after 670 Myr for the LV runs and 260 for the HDHV run and so care should be taken interpreting results after those times (shaded to guide the eye). The di\ufb00erence between the green and cyan dashed lines in the HDLV run signi\ufb01es substantial condensation of ICM gas. As we have shown in the previous section, it is useful to compare cloud properties at di\ufb00erent distances from the stripped galaxies. However, we must be careful not to assume that clouds move together in clumps, or in other words that clouds found in the 15 kpc region at one output will later be found together 85 kpc from the disk. This is visually clear when we consider the di\ufb00erent distribution of clouds as a function of time in Figure 4, and is also predicted by the velocity range of clouds shown in Figure 9. It is informative, then, to step back and measure the amount of dense and unmixed gas as a function of time in the simulations as a whole to see if they follow our expectations. In Figure 12 we do just that. For each simulation, the mass of gas with fICM < 0.5 is shown in cyan (i.e. gas originating primarily from the galaxy), and the mass of gas with \u03c1 > 2\u00d710\u221226 g cm\u22123 is shown in green (i.e. dense gas of all origins). The linestyles denote di\ufb00erent spatial regions of the simulation. The early rapid increase in the dense gas (in the \ufb01rst 20 Myr of the simulation) comes from the relaxation of the disk, as dense clouds form out of the initially smooth disk gas. Before exploring the rami\ufb01cations of these plots, we note a technical point, which is the \ufb02ow of gas out of the simulation volume. Because we are only showing here dense or low fICM gas, it is not clear whether decreasing mass corresponds to gas leaving the simulation volume, or transitioning into another state. However, we can resolve this di\ufb00erence by noting that in both LV runs the total amount of gas in the simulation decreases after about 670 Myr, and in HDHV the total amount of gas in the simulation decreases after about 260 Myr, indicating that at these late times more gas is leaving the box than is \ufb02owing into it (shown as the shaded regions in each panel). This explains most or all of the late-time decrease in wake gas for both HD runs. If we \ufb01rst consider the mass of gas with fICM < 0.5 (with a primarily galactic origin), we see that in all simulations, at early times (at t \u223c200 Myr for the LV runs and t \u223c150 Myr for the HV run), the total gas mass in the box increases as pure ICM gas is beginning to mix with the disk gas. Comparing the wake to the disk gas masses, we see that most of the increase in gas mass is occurring behind the disk (in the wake). This agrees well with our main prediction that mixing drives gas acceleration. We also see a rapid drop in the wake mass as gas that is stripped continues to mix to high fICM values, as seen in Figure 11. When we examine the dense gas in the simulation we see a somewhat di\ufb00erent story. In all simulations, the amount of dense gas in the disk region decreases as the amount of dense gas in the wake increases, indicating that dense gas is stripped from the galaxy. However, the total amount of dense gas and the ratio between dense and low fICM gas di\ufb00ers dramatically in the di\ufb00erent simulations. In comparing the dense gas mass to the low fICM gas mass we will move from right to left in the panels. In HDHV there is never an increase in the total dense gas mass after the wind hits the disk. When we compare the wake gas mass measured using fICM or by our density cut, the HDHV curves are similar in width, but the amount of low fICM gas in the wake is higher than the amount of dense gas, indicating that in general mixing is heating stripped gas. However, HDLV seems to tell the opposite story. The total dense gas mass nearly doubles from the initial mass to the peak mass, and reaches much higher values than the total low fICM gas. The dense gas peak in the wake is much broader and higher than the fICM peak, indicating that as gas mixes it continues to cool. This indicates that we are seeing signi\ufb01cant gas condensation out of the ICM, driven by the mixing from clouds stripped out of the galaxy. Finally, the LDLV run does not necessarily tell a single story of mixing. As with HDHV, the total low fICM gas rises while the total dense gas falls, and in the wake the peak low fICM gas is higher than the peak dense gas. Interestingly, if 17 we look closely at the wake gas in LDLV, the mass of dense gas has a slightly broader time pro\ufb01le than the mass of low fICM, and there is more dense gas than low fICM gas in the wake after 600 Myr. This may speak to late cooling of mixing gas, reminiscent of (but weaker than) the HDLV run. To summarize this section and the previous one, we \ufb01nd that in all three simulations, fICM of clouds increases with distance from the disk, demonstrating mixing. Importantly, this does not seem to correspond to universal cloud destruction or accretion. In more detail, as we move beyond 15 kpc from the disk, clouds seem to be destroyed in two simulations: the number and mass of dense gas in clouds continues to decrease throughout the wake and in time in both LDLV and HDHV. However, looking farther in the wake in HDLV we see that the mass of clouds increases at large distances, and this is re\ufb02ected in the total dense mass in the wake. 5.3. The Cooling versus Destruction time of Clouds We also consider the survival of clouds in the stripped tails more theoretically by comparing the cooling and destruction, or \u201ccrushing\" times of the clouds. To calculate the cooling time of the gas we use the cooling rates from the grackle cooling tables implemented in our simulations. Since, as we have shown, the metallicity varies little in the clouds, we use the average metallicity in the cooling calculation. We calculate the cloud crushing timescale as (e.g., Klein et al. 1994): tcc = r\u03c1cloud \u03c1ICM Rcloud vdi\ufb00 (10) For our calculation, \u03c1cloud is the maximum cloud density, \u03c1ICM is the in\ufb02owing ICM density, vdi\ufb00is the cloud velocity in the wind direction subtracted from the input wind velocity, and we assume spherical clouds and use the cloud volume to calculate Rcloud. In Figure 13 we plot the ratio of the cooling and crushing times as a function of mean cloud density. We calculate the cooling times of the clouds with two di\ufb00erent assumptions. In the top panels we use the minimum temperature of the cloud and the maximum density to calculate the maximum H number density using \u00b5 = 1. In the bottom panels we use the \u201cmixing\" temperature and density (with \u00b5 = 0.6) from Gronke & Oh (2018; GO18). The distributions are similar, but we \ufb01nd that low density clouds are closer to tcool = tcc using this second de\ufb01nition, and therefore are more likely to be destroyed before they cool. This is largely because of the dependence of the cooling rate on density squared, which results in faster cooling rates for higher density gas. Only our densest clouds have temperatures cooler than the peak of the cooling curve, so the rate is not generally strongly dependent on temperature. Thus, while the cooling rate is quite similar for the cloud and the mixing layer, the cooling time is longer in the mixing layer because of the higher temperature. However, using either formalism we (marginally) \ufb01nd that most clouds will cool before they are destroyed. We also note that the ratio tcool/tcc of clouds at di\ufb00erent heights above the disk have very similar distributions. However, in both the HDLV and HDHV simulations, clouds with higher densities extend to lower tcool/tcc when they are close to the galaxy. In addition, the fraction of clouds with tcool/tcc > 1 increases as we look farther from the disk in HDHV. We highlight that HDLV has the least gas above the tcool = tcc threshold, and extends to the most extreme (small) tcool/tcc ratios. The HDLV simulation has an ICM wind in which the number and mass of clouds increases from \u223c85 kpc to \u223c155 kpc, and in which the dense gas in the entire box increases over time. This is qualitatively consistent with the small tcool/tcc ratios. How does this theoretical calculation align with our \ufb01ndings in Section 5.1, that clouds do not (generally) survive intact in the tail? In the GO18 picture, even clouds that accrete gas \ufb01rst seem to lose dense gas mass, and only then cool and accrete gas in tails very late in the simulation (more than ten cloud crushing times at the highest density ratios). Therefore, it is likely that the clouds that eventually accrete mass in a GO18 scenario are well-mixed throughout, consistent with our Figure 11. However, both the number and mass of clouds in our simulations decreases from 15 kpc above the disk to larger distances. In GO18, higher density ratios between the surroundings and the cloud result in longer lag times before the dense cloud mass starts to increase. In our ICM wind simulation, with higher density ratios than simulated in GO18 (or Gronke & Oh 2019), the growth rate of these clouds may be even slower (comparing the ICM density to the average cloud densities from Figure 13, our clouds range from density ratios of \u223c100 104). The cloud crushing times range from 3\u00d7105 years (the shortest crushing time in the HDHV run) to 108 years (the longest crushing time in HDLV). However, the distribution of crushing times in HDHV peaks at 2.5\u00d7106 years while both LV runs peak between 1-2\u00d7107 years. Even using the maximum cloud velocities from Figure 9, the travel time from 15 kpc to 155 kpc above the disk is more than ten cloud crushing times for the majority of clouds. Therefore, only if the growth times of our clouds are more than ten cloud crushing times may we need to follow our clouds longer in order to see growth, or at density ratios of \u223c104 clouds may not accrete gas from their surroundings. In all three simulations, as we have shown, our clouds straddle the tcool = tcc line. By using the maximum density for our clouds we are choosing the maximum possible crushing time for our comparison. Further, we are using the mass density of the gas and an estimated \u00b5 as a proxy for H 18 Figure 13. The ratio of tcool/tcc versus the mean density of the cloud for all three simulations. As in Figure 9, the contours are based on the density of clouds in each two-dimensional histogram bin. In the top panels we use the maximum density and minimum temperature of the cloud to compute the cooling time, and generally \ufb01nd that these clouds should cool. However, in the lower panels we use the mixing temperature and density as in Gronke & Oh (2018) and \ufb01nd that these clouds lie much closer to the tcool = tcc boundary (marked as a dashed line). Comparing the nearest (red contours) to the most distant clouds (blue contours), we see that while the distributions of tcool/tcc have a large amount of overlap, in both HD simulations clouds near the disk extend to much lower tcool,mix/tcc ratios. number density in our cooling time calculation. These approximations could shift our clouds above or below the line of equality. We are performing high resolution simulations of individual clouds to follow their evolution in detail and verify these calculations (Smith et al, in prep and Abruzzo et al., in prep). 6. THE INFLUENCE OF THE ICM ON CLOUD PROPERTIES In this paper we have used three simulations to support our model for ICM-mixing as the driver for gas acceleration in ram pressure stripped tails. While we have discussed some di\ufb00erences in tail properties as a function of height above the disk and across the di\ufb00erent simulations, in this section we focus on the impact of the ICM properties on cloud properties. We \ufb01nd that both the ICM density and velocity in\ufb02uence the gas in the stripped tail. 6.1. ICM Density First, we compare the LDLV and HDLV simulations to discuss the e\ufb00ect of the ICM density on cloud properties. In Figure 9 we showed that at the same height, the clouds in HDLV are moving slightly faster than those in LDLV, and in Figure 4, we see that HDLV has a longer dense tail than LDLV at the same simulation time. In our model, this follows from the fact that there is more mass in the higher density wind resulting in quicker mixing for HDLV clouds. We also \ufb01nd that the maximum number and mass of clouds in any height bin is larger in the HDLV run than in the LDLV simulation. While this must, to some extent, re\ufb02ect the fact that the ram pressure (\u03c1v2) is about twice as high in HDLV than in LDLV, and there is therefore more stripped gas that could cool to dense clumps, we argue that that is not the whole story. If we compare the relative number of clouds as a function of distance from the galaxy we see a dramatic di\ufb00erence in the two runs. From Figure 10, we can see that, at their respective peaks, there are about six times as many clouds at 15 kpc from the disk as 85 kpc above the disk in LDLV, while there are about two times as many clouds near the disk when doing the same comparison for the HDLV run. The di\ufb00erence is even more dramatic when we compare the number of clouds at 155 kpc in the two LV runs. The maximum number and mass of clouds in HDLV is larger at 155 kpc than at 85 kpc, in stark contrast to the continued decline in the number and mass in clouds as a function of height in LDLV. In addition, if we track the total dense gas mass within the entire simulation, as in Figure 12, we \ufb01nd that the dense gas mass increases in HDLV and decreases in LDLV. 19 This suggests that a higher density ICM leads to more cloud condensation due to stripped gas mixing. This is consistent with the results of section 5.3 \u2013 in particular, when we look closely at Figure 13, we see that LDLV has the largest population of clouds for which tcool,mix \u22640.01tcc. Examining the ICM fractions of dense gas in the HDLV and LDLV simulations can give us insight into whether mixing or another process such as compression is driving the differences in cloud mass in HDLV and LDLV. Clouds in the HDLV tail tend to have higher ICM fractions, with the difference becoming more pronounced at larger height from the galaxy, as seen in both Figures 9 & 11. This again follows our model as more mass from the wind will have impacted a cloud in a higher density ICM. The di\ufb00erent ICM densities do not have a dramatic impact on the minimum-to-maximum ICM fraction ratio, although there is a slight tendency for clouds in the LDLV run to have closer to uniform ICM fractions. Therefore cloud mixing occurs in a similar fashion in both simulations. Comparing the time evolution of low fICM gas to dense gas in Figure 12 also indicates a signi\ufb01cant di\ufb00erence in how mixing e\ufb00ects gas in the stripped tails due to ICM density. In both runs the low fICM gas increases \ufb01rst, then as gas continues to mix with the ICM the low fICM gas mass decreases. In LDLV the dense gas mass decreases when the low fICM gas decreases, indicating that mixing in low density ICM results in gas heating. On the other hand, in the higher density ICM of HDLV, low fICM gas mass decreases while dense gas mass continues to increase, indicating that mixing in HDLV results in gas condensing into clouds. In summary, we argue then that stripped gas in a higher density surrounding medium accretes more of the ICM, resulting in gas with higher fICM, and the formation of more high-density clouds, particularly at larger distances from the galaxy. 6.2. ICM velocity We can now compare HDLV and HDHV to discuss the e\ufb00ects of the ICM wind velocity on the stripped gas. Unsurprisingly, the most clear di\ufb00erence is that stripped gas is moving faster in the high velocity run. Comparing the number and total mass of clouds as a function of height, we see that although the maximum number of clouds near the disk in HDHV is higher than in HDLV, as we would expect since the higher ram pressure in HDHV will strip more gas, the number drops by a slightly larger factor from 15 kpc to 85 kpc in HDHV than in HDLV at their peaks. However, the di\ufb00erence is dramatic at the largest distance we probe\u2013155 kpc from the disk, there are more clouds in HDLV than in HDHV at their peaks. This indicates that the fast, high-Mach number HDHV wind does not allow dense clouds to survive (or form) as easily as HDLV3. Indeed, we also see this in the mass of dense gas in the wake as a function of time \u2013 the mass drops dramatically in HDHV while it increases in HDLV (Figure 12). This agrees with our \ufb01nding in Figure 13 that more clouds have shorter tcc than tcool. Interestingly, the gas composing HDHV clouds has a large range of ICM fractions, particularly close to the galaxy (Figure 11). Perhaps the range in ICM fractions within a cloud is a signature of the clouds being destroyed, as indicated by the short cloud crushing times. We also \ufb01nd that at the same ICM density the faster wind (HDHV) results in clouds with lower minimum ICM fractions (in other words, less mixing between the stripped and surrounding gas). This supports our analytic model that the faster ICM will add more momentum to stripped gas per unit mass. In addition, almost all identi\ufb01ed clouds in HDHV have minimum fICM less than 0.5. In combination with the fact that the mass of low fICM gas in the wake is always more than the mass of high density gas (Figure 12), this again highlights that mixing is likely to heat cold, dense gas into the di\ufb00use ICM. 7. DISCUSSION 7.1. The Importance of the ICM In previous work we have argued that the ICM is important in setting the properties in the tail, from the X-ray luminosity to the star formation rate (Tonnesen et al. 2011; Tonnesen & Bryan 2012). We found that both the X-ray luminosity of the stripped tail and the star formation rate in stripped gas will increase as the ICM pressure increases due to the near-pressure equilibrium of the stripped and surrounding gas. These conclusions were largely based on the \u03c1-T diagrams of the stripped gas, which found higher density gas at all temperatures in a higher-pressure ICM. In this paper, we focus on the properties of overdense clumps in the tail. As we have discussed, we \ufb01nd agreement with our previous conclusion that a higher density ICM produces more high density clouds. Here we look more closely at our clouds to determine whether they are likely to be gravitationally bound or pressure con\ufb01ned. To do this we compare estimates of the cloud internal energy and the gravitational potential: U = 3 2kboltzTmean Mcloud \u00b5mH (11) Ug = GM2 cloud rcloud (12) In which Tmean is the mass-weighted average temperature, Mcloud is the total mass of the cloud, and rcloud is the cloud 3 However, as we do not track individual clouds we cannot discount the possibility that there is a larger range of cloud velocity in HDHV that is spreading an increasing number of clouds more thinly across the length of the tail. 20 radius assuming a spherical cloud with the volume of cells included in the identi\ufb01ed cloud. We are ignoring turbulent energy and assuming all internal energy is thermal. Figure 14 shows the distribution of these two quantities for the clouds in all three simulations at all three heights. From this, we see that most of the clouds in all three simulations are pressure con\ufb01ned (Ug \u226aU). In our higher-density ICM runs (HDLV and HDHV), some of the most massive clouds lie very close to the line of equality. These clouds seem to be largely pressure con\ufb01ned, which agrees with our earlier \ufb01ndings of near-pressure equilibrium in the stripped tail and ICM, although we cannot rule out a part of these clouds being gravitationally unstable. Indeed, when we select only clumps with at least 300 cells, as in Appendix A1, we \ufb01nd a much higher fraction of massive clouds lie close to the line of equality, supporting the idea that regions of massive clouds may be gravitationally unstable. Because our model for gas acceleration requires the mixing of ICM and ISM gas, we have carefully examined the mixed fraction of dense clumps. In Figure 11 we saw evidence that the surrounding ICM is not just compressing the stripped material towards pressure equilibrium, but is mixed throughout the stripped gas, even in the most dense clouds. In fact, we see that this mixing is more e\ufb03cient in the HDLV run than the LDLV run, indicating that a higher density (and therefore higher pressure) ICM mixes more with the stripped tail. The mixing of the stripped and surrounding gas can either result in the cooling of hot gas or the heating of cold gas. Clouds tend to lie close to the tcool,mix = tcc line, indicating that they may be able to survive for signi\ufb01cant amounts of time. In addition, as we have mentioned in Section 5.3, the density ratio of clouds to the ICM ranges from 103 105. Therefore, in a picture in which the mass accretion of dense clouds takes more time for higher density ratios as in GO18 (at \ufb01xed tcool,mix/tcc), the cooling onto these clouds could take more than 1 Gyr (10 cloud crushing times of 108 years). These results lead us to a picture in which stripped gas quickly mixes with the ICM. This happens more quickly when the surrounding gas has a higher density (and therefore pressure). We posit that this plays out in di\ufb00erent ways in the HDLV and HDHV runs. In pressure equilibrium, cold gas will have higher densities so the cooling time will be shorter and clouds will be more likely to survive. We see this in the HDLV run in the low tcool,mix/tcc clouds in Figure 13 and in the increasing number and mass of clouds from \u223c85 kpc to \u223c155 kpc. However, although the cloud densities are similar in the HDHV run, the velocity di\ufb00erence between the cloud and the ICM is also larger, leading to a lower tcc, and therefore more clouds reside above the tcool,mix=tcc line in Figure 13. Therefore, when stripped gas has mixed with a large fraction of ICM gas (i.e. fICM \u22730.5), these clouds are Figure 14. The internal energy of clouds versus the gravitational potential of clouds. As in Figure 9, the contours are based on the density of clouds in each two-dimensional histogram bin. The panels are organized as in Figure 9, and have a line at x = y. We see that the internal energy of the clouds is higher than the gravitational potential, indicating that these clouds are pressure con\ufb01ned. destroyed (Figure 12). This is why we do not see clouds with high ICM fractions in Figure 11. Therefore the interplay of ICM density and velocity will determine whether gas mixing results in dense clouds or diffuse gas. 7.2. Making Predictions for observations 21 We make a clear prediction that gas that is moving faster will be more highly mixed with the surrounding ICM, which should be re\ufb02ected in the metallicity of stripped gas. This may, in fact, be the case in stripped galaxies, for example in the system JO201 (Bellhouse et al. 2019). However, in order to use this model to determine the three dimensional distance and velocity of observed clouds, we would need to fold in the metallicity of the ISM as a function of the radius from which it was stripped. As this becomes more well-constrained, our predictive power will increase. We have also found that for galaxies moving at the same velocity with regards to the ICM, a higher density ICM will lead to tails moving at higher velocities and to more dense clouds at large distances from the galaxy. We also argue that at the same ICM density, dense clouds are less likely to be found at large distances in tails stripped from galaxies with high velocities. Although this is a relative relation, it is possible that it could be used to compare the likely ICM conditions surrounding galaxies undergoing ram pressure stripping and help to break degeneracies resulting from only observing the line of sight velocity and projected distance from the cluster center. 7.3. Star Formation in Stripped Tails Although we do not include star formation in these simulations and only focus on dense gas, in observations of stripped tails some of the best evidence for cold dense clouds is the HII regions resulting from star formation. However, currently there are no clear cases of stars formed more than \u223c100 kpc from a stripped disk (Poggianti et al. 2019), yet we \ufb01nd dense clouds out to at least \u223c155 kpc. There are several possible explanations for this. On the observational side, stars at such a large distance from the disk may not be as clearly associated with a stripped tail because all lower density gas will have been mixed and heated until it is indistinguishable from the ICM. On the simulation side, we \ufb01rst recall that our clouds are pressure con\ufb01ned, and our rough estimate \ufb01nds that tcool \u223c tcc, so many of our clouds could be destroyed before they would cool and form stars. Also, it is possible that star formation in dense gas closer to the disk will heat nearby gas and cause it to mix into the surrounding medium more e\ufb03ciently than we \ufb01nd in our simulations. A highly-resolved simulation including star formation is required to determine how far from the disk stars will form. However, despite these caveats, based on our results we would predict that star formation is most likely to occur in the stripped tails of galaxies moving slowly in a high-density ICM. This might translate into more star formation from stripped galaxies with circular orbits close to the cluster center. 7.4. Caveats In this section, we brie\ufb02y discuss a number of shortcomings of our simulations, \ufb01rst discussing the impact of spatial resolution, before turning to other physical e\ufb00ects that we have not included. 7.4.1. Resolution Although our resolution of up to \u223c40 pc allows for many cells across the galaxy disk, individual clouds in the tail are not well-resolved. We require at least 10 cells in a cloud, but in order to begin to resolve an individual cloud, \u223c105 would be required (32 cells across the cloud radius). However, the individual clouds we identify are objects in the \ufb02ow and have already been processed by turbulence and cooling, while the resolution requirement of clouds in cloud-crushing simulations refers to the initial cloud size \u2013 such simulations also generally \ufb01nd structure in their partially mixed clouds down to the grid scale. Therefore, we argue that the in-situ cloud sizes are not necessarily a good estimate of the resolved nature of the simulations. We examine the impact of resolution in more detail in Appendices A and B, where we look at the properties of clouds as a function of their resolution as well as an additional set of simulations performed at lower resolution. The overall conclusion is that, while detailed properties do change, the overall results are remarkably robust to changes in resolution. However, we note that if a cloud does fragment into small pieces, as in the \u201cshattering\" scenario of McCourt et al. (2018), because we are not resolving the cstcool length scale, the fragments would mix into the surrounding medium at the grid scale. Our clouds are not in precise pressure balance with the ICM, perhaps making a shattering scenario more relevant (see discussion in Gronke & Oh 2020). Future simulations of clouds surrounded by gas at these high density and temperature ratios are required to predict the ICM densities and temperatures at which clouds will mix into the ICM or will accrete gas from the ICM. In this paper we only claim that higher ICM density is likely to result in longer cloud survival, while higher relative ICM velocity will result in faster cloud mixing. 7.4.2. Missing Physics We run these simulations using only hydrodynamic equations, which means that we may be missing relevant physics for gas mixing. For example, we have no magnetic \ufb01elds. Gronke & Oh (2020) and others (e.g. Sur et al. 2014; McCourt et al. 2015; Cottle et al. 2020) include magnetic \ufb01elds in their simulations that study the growth of cold clouds through the entrainment of the surrounding material. Their magnetic \ufb01elds increase the velocity of clouds, suppress the KH instability, and stretch the cold gas along the \ufb01eld lines. Importantly, they \ufb01nd that magnetic \ufb01elds have little impact on the overall mass growth rate. In contrast, in plane-parallel simulations, 22 Ji et al. (2019) \ufb01nd that magnetic \ufb01elds suppress cold gas growth through entrainment. While it is not clear whether magnetic \ufb01elds would suppress or enhance the growth of cold clouds, it is likely that they would stabilize them against mixing to some degree. Along with a magnetic \ufb01eld, we do not include thermal conduction. Cloud survival has been studied including isotropic heat conduction. Bruggen & Scannapieco (2016) include both radiative cooling and heat conduction in simulations of clouds being ejected in galactic out\ufb02ows. They \ufb01nd that while the outer envelope is evaporated, the central region cools and stretches into dense \ufb01laments (in agreement with simulations that only include radiative cooling: Mellema et al. 2002; Fragile et al. 2004; Orlando et al. 2005; Johansson & Ziegler 2013). These clouds are accelerated only at early times because their cross-section decreases dramatically as the outer layers evaporate, so they move more slowly than simulated clouds without heat conduction. Clouds with heat conduction also lose mass more quickly than those with only radiative cooling. The authors do highlight that this time can be lengthened if there are magnetic \ufb01elds perpendicular to the temperature gradient (Cowie & McKee 1977; Cox 1979). Vollmer et al. (2001) argue that magnetic \ufb01elds could increase the evaporation time by nearly an order of magnitude, although the actual value is highly uncertain. In previous work, we have found that in order for the length of tails in our simulations to agree with observations, heat conduction must not be e\ufb03cient (Tonnesen & Bryan 2010; Tonnesen et al. 2011). As with increased resolution, we think that including these physical e\ufb00ects will not alter the trends we have found in this paper. Interestingly, recall that in the HDHV run, the cloud velocities far from the disk are below our analytic prediction. This may be explained by the single-cloud results that with radiative cooling clouds stretch into narrower \ufb01laments over time, while our analytic model assumes a constant cloud cross-sectional area. 8. CONCLUSIONS We have presented an analytic model describing how gas is unbound and accelerated away from a galaxy due to mixingmediated ram pressure stripping. The model is based on the idea of mixing driving momentum transfer, rather than a traditional ram \u201cforce\". To verify this model and to highlight the impact of the ICM velocity and density, we also present three \u201cwind-tunnel\" simulations of a galaxy undergoing ram pressure stripping in which we identify and examine clouds in the tail. Our main conclusions are as follows: 1. We present a model in which the acceleration of gas from a galaxy is due to mixing with the ICM, and is based on a mix of energy and momentum deposition into galactic gas from the ICM (Section 2). The model makes clear predictions that gas with higher velocities and at larger distances from the disk will be more wellmixed with the ICM (Figures 1 & 2). 2. We compare our model to three simulations in which we have varied the ICM velocity and density. We \ufb01nd excellent agreement with the ICM fraction-velocity relation for all gas in the stripped tail (Section 4.1). 3. When we focus only on the dense clouds in our simulations we still \ufb01nd good agreement, even when we fold in a model for the distance a cloud has traveled (Figure 9). 4. Clouds are nearly uniformly mixed with the ICM, meaning that in our simulations there is no cloud \u201ccore\" that survives intact from the galaxy. The ICM fraction in dense clouds increases as a function of height from the disk (Figure 11). Comparing simulations, we \ufb01nd that at the same wind velocity, clouds are more well-mixed in a higher density ICM. At the same ICM density, clouds are more well-mixed in a slower wind. 5. Both the number and mass of gas in dense clouds decreases as a function of height above the disk (Figure 10), suggesting that clouds generally do not survive in the tail. However, in the HDLV run, the number and mass of clouds increases from \u223c85 kpc to \u223c155 kpc above the disk, indicating that some clouds survive and accrete gas from their surroundings. Stripped gas mixing with the ICM results in decreasing dense gas mass in HDHV and LDLV, but in HDLV mixing adds dense gas mass to the simulation (Figure 12). Importantly, we have shown in this paper that dense clouds in stripped tails are part of the continuum of gas in the tails. Our mixing-driven model for gas acceleration in the tail applies equally well to low-density and high-dense gas. This is an important departure from the simple picture that intact clouds can survive being \u201cpushed\" from the galaxy by an ICM wind. Indeed, this leads to the observational prediction that the metallicity of dense clouds should decrease as the distance from the galaxy increases (absent enrichment due to additional star formation in the tail). Because mixing drives the formation and acceleration of the stripped gas, the question to ask when comparing the different temperature and density distributions of tails becomes clear: will mixing with the ICM result in more gas being able to cool into dense clouds, or will it heat the stripped gas until it is indistinguishable from its surroundings? We have shown that a higher density ICM will tip the balance towards more dense cloud formation, while higher relative ICM velocities will destroy clouds and add the stripped gas to the di\ufb00use surroundings. 23 Our results on cloud survival and mixing are based on comparing simulations with di\ufb00erent ICM properties, however we also consider cloud survival more theoretically by calculating their crushing and cooling times. We \ufb01nd that clouds fall near the tcool,mix = tcc line when we use the cooling time of the mixing layer of our clouds (Figure 13), indicating that cloud survival cannot be universally predicted even within a single stripped tail (or that the process of cloud evolution drives clouds close to this relation). Given the diversity of observed stripped tails, some with dense gas and even star formation, while others only contain more di\ufb00use gas in their tails, the question of what causes dense gas survival and collapse to stars is important to understanding the physics at play in the ICM. While our results are an important step outlining the competition between velocity and density, predicting the survival of dense gas in stripped tails in detail will require more theoretical work \u2013 in particular, a suite of simulations that resolve individual clouds and include star formation as well as non-ideal MHD processes such as conduction. ACKNOWLEDGMENTS We would like to thank the referee for helpful comments that improved the paper. The authors gratefully acknowledge support from the Center for Computational Astrophysics at the Flatiron Institute, which is supported by the Simons Foundation. ST thanks the GASP collaboration for useful discussions about gas acceleration in stripped tails. GLB acknowledges \ufb01nancial support from NSF (grant AST-1615955, OAC-1835509), and NASA (grant NNX15AB20G), and computing support from NSF XSEDE. The simulations used in this work were run on facilities supported by the Scienti\ufb01c Computing Core at the Flatiron Institute, a division of the Simons Foundation. APPENDIX A. CLUMP RESOLUTION In this appendix we discuss individual cloud resolution by comparing the properties of clumps that include at least 300 cells to our entire set, which includes clumps with as few as 10 cells. In Figure A1 we repeat Figure 11 using only those clumps with at least 300 cells. The most striking, although unsurprising, di\ufb00erence is that there are many fewer clumps using this selection criteria. We also note that the ratio between the minimum and maximum ICM fractions within each clump tends towards lower values. Again, because we select larger clumps we would expect this result. Interestingly, the di\ufb00erences between the ICM fraction minimum-to-maximum ratio as a function of height above the disk are clearer when we focus on larger clouds. Speci\ufb01cally, clumps identi\ufb01ed at 15 kpc above the disk tend to have lower ratios, in other words be less well-mixed, than those at 85 kpc or 155 kpc. This agrees well with our conclusions that mixing is driving cloud acceleration and that unmixed cores are not surviving to large distances. In Figure A2 we recreate the bottom panels of Figure 13 to determine whether the trends we see for the whole cloud sample continue when only considering the largest clouds. As one would expect, when focusing on larger clouds the tcool,mix/tcc decreases. As tcc increases with cloud radius, even at the same cloud density we would expect a lower tcool,mix/tcc, as we see. When we look at only the largest clumps in our tails, we see that the vast majority lie well below the line of equality, indicating they will grow in mass rather than destroyed. However, we note that the number, mass, and mass \ufb02ux of large clouds decreases from 15 kpc to 155 kpc in both LDLV and HDHV. We also note that there still does seem to be a di\ufb00erence in the tcool,mix/tcc distributions in the large clouds, with HDLV values tending to be lower. B. SIMULATION RESOLUTION In this section, we examine the impact of the maximum resolution in the simulations on the evolution of mixed and dense gas in the tails. We have rerun all three simulations using lower resolution. LDLV and HDLV were run with a maximum resolution of 160 pc, and HDLV was run with a maximum resolution of 320 pc. In Figure B3, we repeat Figure 12 with the lower resolution simulations. First, we highlight the striking similarity in the LDLV and HDHV simulations at high (40 pc) and low (160 pc or 320 pc) resolution. At lower resolution, we see that there is always more low fICM gas in the simulation than there is dense gas, and this is re\ufb02ected in the wake. This indicates that in general, as gas mixes it is heated and di\ufb00uses into the ICM. However, as with the higher resolution runs, HDLV tells a di\ufb00erent story. Here the mass of dense gas in the wake is larger than the mass of low fICM gas, indicating that gas mixes and cools. Interestingly, we do not see the growth of high-density gas in the wake as in the higher 24 Figure A1. The same as Figure 11, but only including clumps with at least 300 cells. The same trends hold as in the full clump sample, and we can clearly see that individual clumps tend to be more uniformly mixed (have minimum-to-maximum ratios closer to unity) farther from the disk. Figure A2. The same as the bottom three panels in Figure 13, but only including clumps with at least 300 cells. These larger clumps tend to lie well below the line of equality. Figure B3. As Figure 12, but for simulations run at either 160 pc (LDLV and HDLV) or 320 pc (HDHV) resolution. We see that particularly for LDLV and HDHV the unmixed and dense gas trends are remarkably similar to the 40 pc resolution runs. Although the speci\ufb01cs of HDLV di\ufb00er at the lower resolution, the fact that more dense gas than unmixed gas exists in the wake at late times is consistent with the higher resolution results. resolution simulation. We highlight that at lower resolution we \ufb01nd the same qualitative trends\u2013mixing gas does not become dense in LDLV and HDHV, while mixing gas can become dense in HDLV.",
                    "introduction": "1."
                },
                {
                    "url": "http://arxiv.org/abs/1903.08178v1",
                    "title": "The Journey Counts: The Importance of Including Orbits when Simulating Ram Pressure Stripping",
                    "abstract": "We investigate the importance of varying the ram pressure to more\nrealistically mimic the infall of a cluster satellite galaxy when comparing ram\npressure stripping simulations to observations. We examine the gas disk and\ntail properties of stripped cluster galaxies in eight \"wind-tunnel\"\nhydrodynamical simulations with either varying or constant ram pressure\nstrength. In simulations without radiative cooling, applying a varying wind\nleads to significantly different density and velocity structure in the tail\nthan found when applying a constant wind, although the stripping rate, disk\nmass, and disk radius remain consistent in both scenarios. In simulations with\nradiative cooling, the differences between a constant and varying wind are even\nmore pronounced. Not only is there a difference in morphology and velocity\nstructure in the tails, but a varying wind leads to a much lower stripping\nrate, even after the varying wind has reached the ram pressure strength of the\nconstant wind. Also, galaxies in constant and varying wind simulations with the\nsame gas disk mass do not have in the same gas disk radius. A constant wind\ncannot appropriately model the ram pressure stripping of a galaxy entering a\ncluster. We conclude that simulations attempting detailed comparisons with\nobservations must take the variation of the ram pressure profile due to a\ngalaxy's orbit into consideration.",
                    "authors": "Stephanie Tonnesen",
                    "published": "2019-03-19",
                    "updated": "2019-03-19",
                    "primary_cat": "astro-ph.GA",
                    "cats": [
                        "astro-ph.GA"
                    ],
                    "main_content": "2014; Kapferer et al. 2009). Perhaps the strongest indicator of ram pressure stripping is single-sided gas tails, as observed in HI, H\u03b1, Xray, and molecular emission (e.g. Irwin & Sarazin 1996; Oosterloo & van Gorkom 2005; Haynes et al. 2007; Chung et al. 2007, 2009; Kenney et al. 2008; Yoshida et al. 2008; Yagi et al. 2010; Sun et al. 2006; Jachym et al. 2014, 2017; Boselli et al. 2018; Lee & Chung 2018; George et al. 2018; Moretti et al. 2018a; Moretti et al. 2018b; Poggianti et al. 2019). Recently, Poggianti et al. (2016) found ram pressure stripping candidates by identifying unilateral disturbances in optical emission. With the advent of integral field units, detailed observational maps of galaxies have become possible. For example, Merluzzi et al. (2013; 2016) used the integral field spectrograph WiFeS and imaging data to map the kinematics and physical conditions of the ionized gas and stellar populations of galaxies with signatures of ram pressure stripping in the Shapley supercluster. Using MUSE (Multi Unit Spectroscopic Explorer) spectroscopy, other researchers have mapped other cluster galaxies (e.g. Fossati et al. 2016; Poggianti et al. 2017; Bellhouse et al. 2017; Gullieuszik et al. 2017; Moretti et al. 2018a). In addition, numerical simulations can be used to predict observational signatures of stripped galaxies. For example, Bekki (2014) ran several simulations, varying galaxy and cluster mass as well as galaxy orbits and inclinations, to study how ram pressure stripping generally affects star formation rates and H\u03b1 emission. This work concluded that star formation rates and H\u03b1 distributions in the galaxy disk are affected by ram pressure in a variety of ways depending on the galaxy mass, inclination angle, and ram pressure strength. On the other hand, simulations have also been used to determine if observed galaxies have been ram pressure stripped. This has been done extensively for Virgo cluster galaxies using an N-body code (Vollmer et al. 2001; 2003; 2006; 2008; 2009; 2012). For example, in Vollmer et al. (2008), the authors model 4 ram pressure profiles, arXiv:1903.08178v1  [astro-ph.GA]  19 Mar 2019 2 each with 4 di\ufb00erent disk-wind inclination angles to \ufb01nd a best match to NGC 4501. More recently, Merluzzi et al. (2013) focus on a galaxy in the Shapley supercluster, and use N-body/hydrodynamical simulations to verify their proposed ram pressure stripping scenario. They run a grid of more than 100 simulations, varying the inclination angle between the galaxy and the ICM wind, the wind velocity, and the gas disk scale height (see also Merluzzi et al. 2016). In this paper we consider one aspect of simulating ram pressure stripping in galaxies: varying ram pressure over time to mimic the infall of a satellite galaxy. The importance of varying ram pressure has been studied with regards to gas removal in elliptical galaxies for decades. Takeda et al. (1984) \ufb01nd that as a galaxy falls into the cluster gas stripping can be quite e\ufb03cient, removing much of the galaxy\u2019s gas from the outside-in in the form of a smooth blob of stripped gas. Toniazzo & Schindler (2001) model a range of orbits and \ufb01nd that stripping is most e\ufb03cient when ram pressure increases strongly to a high value, and otherwise gas stripping proceeds more slowly. Recently Roediger et al. (2015a,b) have examined the stripping of elliptical galaxies in detail using M89 as a reference point, and \ufb01nd that the details of the remaining gas and tail properties depend on the galaxy potential, initial gas distribution, galaxy orbit and orbital stage as well as ICM plasma properties. Signi\ufb01cant work has also been done studying the importance of varying ram pressure on stripping of spiral galaxies. In addition to work speci\ufb01cally modeling individual galaxies (e.g. Vollmer et al. 2001; 2003; 2006; 2008; 2009; 2012), Jachym et al. (2007, 2009) \ufb01nd that the total amount of ICM sweeping past stripped galaxies is more important than the peak ram pressure encountered, and that while more highly inclined disks tend to have less gas removed this di\ufb00erence is eliminated in strongly stripped galaxies that encounter a large ICM column density. Roediger & Bruggen (2007) \ufb01nd that in an orbiting galaxy, gas is lost more slowly than in an instantaneous prediction, although the remaining radius and total gas mass stripped is similar to the Gunn & Gott (1972) analytic estimate as long as the inclination is not high. Roediger & Bruggen (2008) \ufb01nd that the tail mass distribution depends on the galaxy orbit. However, because a galaxy\u2019s orbit is uncertain, it is often ignored when comparing observations to simulations (e.g. Tonnesen et al. 2011; Merluzzi et al. 2013; 2016; Gullieuszik et al. 2017). Particularly if a galaxy is still falling into a cluster, and so has only experienced increasing ram pressure, this simpli\ufb01cation may be based on the assumption that because ram pressure stripping is a fast process, only the peak ram pressure a galaxy experiences determines the amount of gas stripped. In this work we focus on whether constant ram pressure stripping simulations can be used to model observed orbiting galaxies by directly comparing simulations with a constant ram pressure to those with a varying ram pressure, focusing on the \ufb01rst infall of a galaxy, so only increasing the ram pressure. We \ufb01nd that a constant ram pressure cannot simultaneously reproduce both the disk and tail properties produced by a varying ram pressure pro\ufb01le. Therefore, we argue that simulators must include varying ram pressure due to galaxy infall in order to directly compare with observed galaxies. The organization of this paper is as follows. In Section 2 we describe our simulation method, with Sections 2.1 and 2.2 detailing the galaxy model and the individual simulation parameters, respectively. We then examine the results of our simulations, \ufb01rst focusing on the stripping rate in Section 3.1. In the following results sections we focus on properties of the disk (Sec 3.2) and tail (Sec 3.3) that can be compared to observations. We compare simulations with and without radiative cooling to understand the physics behind our results in Section 4. Finally, we summarize our conclusions in Section 5. 2. METHODOLOGY We use the adaptive mesh re\ufb01nement (AMR) code Enzo (Bryan et al. 2014). To follow the gas, we employ an adaptive mesh for solving the \ufb02uid equations including gravity. The code begins with a \ufb01xed set of static grids and automatically adds re\ufb01ned grids as required in order to resolve important features in the \ufb02ow. Our simulated region is 160 kpc on a side with a root grid resolution of 2563 cells. In the central 80 kpc we allow an additional 4 levels of re\ufb01nement, for a smallest cell size of 39 pc. We re\ufb01ne the grid based on the local gas density, and choose parameters that re\ufb01ne most of the galactic disk to 39 pc resolution. Simulations including radiative cooling use the Sarazin & White (1987) cooling curve, with no star formation or heating processes. To mimic e\ufb00ects that we do not model directly (such as stellar and supernovae feedback, subgrid turbulence, UV heating, magnetic \ufb01eld support, or cosmic rays), we cut o\ufb00the cooling curve at a minimum temperature Tmin so that the cooling rate is zero below this temperature. In these simulations we use Tmin = 8000 K. To analyze our data we use yt, a toolkit for analyzing and visualizing quantitative data (Turk et al. 2011). We use yt to create projections and slices, as well as to select disk gas both spatially and using gas density and/or a passive tracer. yt is then able to perform analysis tasks on the selected data. 2.1. The Galaxy Our galaxy is placed at the center of our computational volume, and remains stationary throughout the runs. The lower x, y, and z boundaries are all set to in\ufb02ow in the ICM wind runs, and the wind direction varies depending on the run. The upper x, y, and z boundaries are set to out\ufb02ow. We model a massive spiral galaxy with a \ufb02at rotation curve of 205 km s\u22121. It consists of a gas disk that is followed using the adaptive mesh re\ufb01nement algorithm (including self-gravity of the gas), as well as the static potentials of the stellar disk, stellar bulge, and dark matter halo. We follow Roediger & Br\u00a8 uggen (2006) in our modeling of the stellar and dark matter potential and gas disk. Speci\ufb01cally, we model the stellar disk as a Plummer-Kuzmin disk (Miyamoto & Nagai 1975), the stellar bulge as a spherical Hernquist pro\ufb01le (Hernquist 1993), and the dark matter halo as the spherical Burkert (1995) model (see Mori & Burkert 2000 for the analytic potential). We describe our disk model in detail in Tonnesen & Bryan (2009, 2010). In this paper our stellar disk has a radial scale length of 3.5 kpc, a vertical scale length of 0.7 kpc and a total mass of 1.15\u00d71011 M\u2299; the 3 TABLE 1 Run ID Rad. Face-on Wind Initial Max. Cooling? Wind? Pro\ufb01le? Press. RP RCVW yes no vary 9.84e-14 1.337e-11 RCFOVW yes yes vary 9.84e-14 1.337e-11 RCCW yes no const 2.79e-12 1.337e-11 RCFOCW yes yes const 2.79e-12 1.337e-11 RCFOCWL yes yes const 2.09e-12 1.001e-11 RCFOCWD yes yes const 2.79e-12 1.337e-11 NCFOVW no yes vary 9.84e-14 1.337e-11 NCFOCW no yes const 2.79e-12 1.337e-11 Details of the simulations discussed in this paper. All units are cgs. 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 Time (Gyr) 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Pressure (10\u221211 dyne cm\u22122) Ram Pressure Thermal Pressure RCFOVW RCFOCW RCFOCWL RCFOCWD Fig. 1.\u2014 Ram pressure and thermal pressure as a function of time near the simulation box edge at the midplane of the disk. The dashed lines are the constant wind runs (CW) and the solid line is the varying wind run (VW). Although we only show the measured values for the radiatively cooled cased with a face-on wind (\u201cRCFO\u201d), the runs with wind coming in at an angle and without radiative cooling show nearly identical pro\ufb01les. The ram pressure is in thicker magenta lines and the thermal pressure is in thinner orange lines. Note that the ram pressure is measured as the density multiplied by the total velocity squared, which means that before the wind hits the galaxy there can be \u201cram pressure\u201d measured from gas cooling onto the galaxy. We clearly see that the thermal pressure is less than the peak ram pressure across all runs. The ram pressure reaches its peak value after about 1.2 Gyr in the CW runs and 3.1 Gyr in the VW runs. stellar bulge has a scale length of 0.6 kpc and a total mass of 1010 M\u2299; and the dark matter halo has a scale radius of 23 kpc and a central density of 3.8 \u00d7 10\u221225 g cm\u22123. The gas disk has a mass of 8\u00d71010 M\u2299, and radial and vertical scale lengths of 7 kpc and 0.9 kpc, respectively. To identify gas that originated in the galaxy we follow a passive tracer that is initially set to 1.0 inside the galaxy and 10\u221210 outside. 2.2. The Simulations In this paper we discuss eight simulations, summarized in Table 1. All of the simulations initially have the same galaxy density pro\ufb01les, and allow the galaxy to evolve in a static surrounding medium. In seven of our simulations, after 1 Gyr we generate an ICM in\ufb02ow. The one simulation with a delayed wind is denoted with a \u201cD\u201d. For the six runs that include radiative cooling, denoted by \u201cRC\u201d in the Run ID (see Table 1), this time allows cool, dense gas to form in the galaxy (\u03c1 \u226510\u221222 g cm\u22123). This naturally generates a multiphase ISM (see Tasker & Bryan (2006) and Tonnesen & Bryan (2009) for more discussion of the ISM properties). Six of the simulations use a wind that is moving along the rotation axis of the galaxy (denoted by \u201cFO\u201d), while two simulations model a wind at a 53\u25e6angle. Three of the simulations have a wind that increases in strength (denoted by \u201cVW\u201d). Four simulations have a constant wind: three at the maximum ram pressure of the varying winds, and one at 75% of the maximum varying ram pressure (denoted by \u201cCW\u201d or \u201cCWL\u201d). In Figure 1 we show the di\ufb00erent wind ram pressure strength pro\ufb01les for comparison. Note that our varying wind pro\ufb01les (\u201cVW\u201d) are stripped for an extra Gyr at the maximum ram pressure for comparison purposes. The ICM conditions are selected such that the initial wind has a Mach number of about two so that the initial wind hitting the galaxy is well described by the shockjump conditions. Together with our ram pressure pro\ufb01les, the Mach number sets our initial thermal ICM pressure as denoted in Table 1. Although the initial thermal ICM pressures di\ufb00er by more than an order of magnitude because the initial ram pressure in the \u201cVW\u201d runs is lower, the thermal pressure is always much lower than the peak ram pressure experienced by the galaxies (see also Figure 1). To brie\ufb02y summarize our nomenclature, all runs are identi\ufb01ed as \u201cRC\u201d or \u201cNC\u201d, indicating radiative cooling or no cooling. Also, all runs either have \u201cVW\u201d or \u201cCW\u201d indicating varying wind or constant wind. Finally, many of our simulation names include \u201cFO\u201d indicating that the wind is face-on. Although our results are general and do not depend on the details of the varying wind, we brie\ufb02y explain how we derive the ram pressure pro\ufb01le here. We model a galaxy orbiting a cluster using galpy, a python package for orbital dynamics (Bovy 2015, http://github.com/jobovy/galpy). We model the cluster as an NFW potential with a virial mass of 4.41e14 M\u2299, and virial radius of 1.55 Mpc. We use a concentration of 4, as this is a reasonable \ufb01t to most clusters (Mandelbaum et al. 2008). We assume that the cluster is spherically symmetric and static in order to simplify the model. We can then create a series of possible orbits, and choose one for this work. The ICM density is modeled as a beta-pro\ufb01le. The peak ram pressure that we model is found when the galaxy velocity is 1500 km/s as it infalls 1.4 Mpc from the cluster center, so this particular galaxy orbit would have increasing ram pressure as the galaxy continued towards pericenter passage. The wind begins 2 Gyr before this point, at a distance of 2.9 Mpc from the cluster center (within 2 virial radii of this cluster). 3. RESULTS 3.1. Gas Disk The importance of ram pressure stripping as a galaxy quenching mechanism strongly depends on the amount of gas it can remove from the disk. Therefore, we \ufb01rst consider the amount of gas removed by these di\ufb00erent wind pro\ufb01les. In Figure 2 we plot the disk gas mass, 4 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 Time (Gyr) 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 Gas Mass within \u00b110 kpc (1010 M\u2299) RCVW RCCW RCFOVW RCFOCW RCFOCWL RCFOCWD NCFOVW NCFOCW Fig. 2.\u2014 The gas mass as a function of time for all seven runs performed for this work. As in Figure 1, the solid and broken lines denote the VW and CW runs, respectively. Line color denotes run type as in the legend. Note the dramatic di\ufb00erence in the gas mass between the VW and CW runs, particularly for the simulations that include radiative cooling. 0 5 10 15 20 25 30 35 40 Radius (kpc) 10-27 10-26 10-25 10-24 10-23 10-22 Density ( g cm3 ) RCFOVW, 3.12 Gyr RCFOCW, 1.23 Gyr RCFOCWL, 1.25 Gyr RCFOCWD, 3.24 Gyr NCFOVW, 3.12 Gyr NCFOCW, 1.58 Gyr Fig. 3.\u2014 Average gas density pro\ufb01les within the central \u00b12 kpc of the disk plane. The times are chosen so that the varying wind (VW) and constant wind (CW) simulations have the same amount of gas mass in the disk. In the RC simulations, it is clear that the radius is larger in the CW runs than in the VW run, while in the NC simulations the radius is very similar in the VW and CW runs. de\ufb01ned as gas with a tracer fraction of more than 0.5 within \u00b1 10 kpc of the disk plane, as a function of time. We \ufb01rst focus on the runs that include radiative cooling (RC runs in cyan and magenta), and it is clear that stripping proceeds signi\ufb01cantly di\ufb00erently depending on the wind pro\ufb01le. First, the total gas mass lost is dramatically di\ufb00erent, with much more gas removed in the CW cases. However, even the rate of gas removal is quite di\ufb00erent depending on the wind pro\ufb01le. With a constant wind (CW), stripping proceeds quickly, and most of the gas removal has occurred less than 1 Gyr after the initial onslaught. On the other hand, stripping proceeds slowly with a VW. Even in the last Gyr of the VW runs, when we hold the ram pressure constant at a value that is the same or higher than the CW(L/D) runs, the mass loss rate is lower than in the \ufb01rst few 100 Myrs post-wind of the CW runs. The amount of gas lost once the VW wind has reached maximum (at \u223c3 Gyr in the simulation) corresponds to the amount of gas lost in the \ufb01rst \u223c200 Myr post-wind in the CW runs, and is di\ufb00erent in the face-on and angled runs. In fact, the total gas mass lost after 3 Gyr of stripping (total simulation time of 4 Gyr) is less than the gas mass removed after 500 Myr in the CW cases. We highlight that even with a lower ram pressure, the RCFOCWL galaxy quickly loses much more gas than the RCFOVW galaxy over the length of the simulation. Clearly, an increasing ram pressure strips less gas than a constant ram pressure in a radiatively cooled disk. We have also run a simulation that has been allowed to radiatively cool and form dense clumps for an extra 2 Gyr before being hit with a constant wind (RCFOCWD). Indeed, the original thermal pressure surrounding this galaxy is higher than the ram pressure experienced by RCFOVW until \u223c2.25 Gyr into the varying-wind simulation (1.25 Gyr after the wind hits the galaxy), and the thermal pressure of the stripping wind in RCFOCWD is also higher than that in RCFOVW. Despite this, the gas disk mass evolves in a similar fashion to RCFOCW(L). This indicates that it is not merely time gas is allowed to cool in the simulation, or the surrounding thermal pressure, but the pro\ufb01le of the ram pressure impacting the galaxy that causes the di\ufb00erent gas mass loss rates. We highlight that although much of this paper is focused on simulations with a face-on wind, the di\ufb00erences hold for galaxies inclined to the wind direction (RCVW compared to RCCW). Because most ram pressure stripped galaxies have some inclination with respect to the ICM wind, verifying these results is important. The CW runs re\ufb02ect the results in Roediger & Bruggen (2005), that higher inclination angles have slightly less gas stripped. The disk mass within the VW runs is always within 5%, indicating that the inclination angle may have even less impact on the gas stripping with increasing ram pressure. The story is di\ufb00erent in the cases without radiative cooling (\u201cNC\u201d runs in green). In the CW run, gas mass removal continues at a high rate throughout the simulation, although the slope decreases slightly with time. In the VW run, the rate of gas mass loss increases with time as the ram pressure strength increases. Indeed, for the last Gyr of the VW run, when the ram pressure is held at the maximum (CW) value, the gas removal rate between the CW and VW runs is very similar. While the total gas mass loss is higher in the CW run than in the VW run, if we compare the VW and CW runs 1 Gyr after the ram pressure reaches its maximum value (4 Gyr into the VW simulation and 2 Gyr into the CW simulation), the total gas loss in NCFOVW is larger by only \u223c10% than the gas loss in NCFOCW. Without radiative cooling, the peak ram pressure drives the rate of gas stripping with little to no in\ufb02uence from the ram pressure pro\ufb01le. Varying the ram pressure strength has a signi\ufb01cant impact on the total gas loss of ram pressure stripped galaxies that include radiative cooling. 3.2. Gas Pro\ufb01le We next consider the gas pro\ufb01le in the galaxy disk, focusing on the FO runs for clarity. This provides a clear 5 1 1 30 20 10 0 10 20 30 x (kpc) 30 20 10 0 10 20 30 z (kpc) 3120 Myr 10-3 10-2 Projected Density \u00b3 g cm2 \u00b4 30 20 10 0 10 20 30 x (kpc) 30 20 10 0 10 20 30 z (kpc) 1230 Myr 10-3 10-2 Projected Density \u00b3 g cm2 \u00b4 30 20 10 0 10 20 30 x (kpc) 30 20 10 0 10 20 30 z (kpc) 1250 Myr 10-3 10-2 Projected Density \u00b3 g cm2 \u00b4 30 20 10 0 10 20 30 x (kpc) 30 20 10 0 10 20 30 z (kpc) 3120 Myr 10-3 10-2 Projected Density \u00b3 g cm2 \u00b4 30 20 10 0 10 20 30 x (kpc) 30 20 10 0 10 20 30 z (kpc) 1610 Myr 10-3 10-2 Projected Density \u00b3 g cm2 \u00b4 30 20 10 0 10 20 30 x (kpc) 30 20 10 0 10 20 30 z (kpc) 1620 Myr 10-3 10-2 Projected Density \u00b3 g cm2 \u00b4 RCFOVW RCFOCW RCFOCWL Disk Mass Match Disk Radius Match Fig. 4.\u2014 Projections of gas density in the RC simulations. The top panels compare the density projections when the gas masses in the disks are the same, and the bottom panels compare when the gas disk radii are the same. When the mass in the disks agree, the gas in the CW tails is concentrated closer to the disk. At later times in the CW runs, when the gas disk radius agrees with the VW run, the gas in the tail is more evenly distributed throughout the tail. See discussion in Section 3.3.1 and Figure 5 0 10 20 30 40 50 60 70 80 Height above disk (kpc) 0.0 0.2 0.4 0.6 0.8 1.0 Tail Mass fraction ( > 6 kpc) Disk Radius Match Disk Mass Match Fig. 5.\u2014 The cumulative distribution of tail gas along the wind direction in the RC simulations. The sum begins 6 kpc above the disk and ends at the edge of the box. The black line is the distribution along the RCFOVW tail at 3.12 Gyr. The dashed (dash-dotted) lines show the gas distribution in the RCFOCW(L) tails when the disk gas mass or radius is the same (red or magenta). The gas distribution of the VW and CW tails does not agree at either of these sets of times. comparison between simulations and observations: the extent of the gas disk. In addition, we can compare the radial gas density distribution in the disks. We choose the output from the VW simulations at which the wind at the galaxy midplane has reached its peak value, 3.12 Gyr into the simulation. We then compare the VW case at 3.12 Gyr to the CW runs when they have the same amount of gas mass in the disk (RCFOCW at 1.23 Gyr, RCFOCWL at 1.25 Gyr, RCFOCWD at 3.24 Gyr, and NCFOCW at 1.58 Gyr). In Figure 3 we show the azimuthally-average disk gas pro\ufb01le measured using all of the disk gas within \u00b12 kpc of the disk plane. We compare the gas pro\ufb01les of galaxies when the gas mass is the same in the VW and CW runs (within 0.5%). Clearly, in the RC simulations, the disk mass does not determine the gas radius. However, in the NC simulations, the gas radius is quite similar at the times at which the VW and CW runs have the same gas mass (within 0.6%). Examining the gas density pro\ufb01le as a function of galaxy radius, we see that in the RC simulations the galaxies in the CW runs have lower average density in the inner regions than the VW run. This is despite the fact that we have made sure to select times at which the surrounding ram pressures are the same (or lower in the RCFOCWL run). This is because the initial lower ram pressure that the RCFOVW run experiences cannot remove all but the outermost gas, so instead compresses it so that it more quickly radiatively cools into dense structures. At later times, when the ram pressure reaches its peak value, the more central gas is too dense to be quickly removed. This is in contrast to the CW runs, in which the strong ram pressure is able to remove much of the low density gas before compressing it. The compression 6 1 1 RCFOVW RCFOCW RCFOCWL Disk Mass Match Disk Radius Match Fig. 6.\u2014 Gas mass distribution as a function of height above the disk and velocity in the wind (z) direction. The colorbar range is chosen to highlight tail gas at the expense of losing some contrast in gas moving slowly near the disk. The di\ufb00ering ram pressure pro\ufb01les is evidenced in the di\ufb00ering velocities along the tail\u2013in the CW runs the tails have higher velocities at larger distances from the galaxy. of the disk gas in RCFOVW is a continuous process as the ram pressure increases, as evidenced by the fact that stripping in RCFOCWD proceeds quickly starting at 3.2 Gyr into the simulation despite the fact that the gas disk has been allowed to cool into clumps in a relatively highpressure static ICM. RCFOCWD has a radial gas density pro\ufb01le much more similar to RCFOCW(L) than to RCFOVW. While a compression wave still runs through the disk in the NC runs, because they cannot radiatively cool, there is no long-term density increase (see Figure 16 in Tonnesen & Stone 2014). We discuss this in detail below in Section 4. 3.3. Gas Tail Current comparisons between observations and simulations demand agreement between both disk and tail properties to use simulations to interpret observations. The gas tail can give important clues to a galaxy\u2019s stripping or interaction history, both in the distribution of gas along the direction of motion (in the wind tunnel simulation this is the wind direction) or in the plane of the sky, and in the velocity distribution of gas in the tail. For example, in Merluzzi et al. (2016), simulations with a constant wind are not able to simultaneously reproduce both the extent of the tail and the truncation of the gas disk for one of the observed galaxies, and thus the authors conclude that ram pressure stripping alone cannot account for the observed gas removal. Therefore, in order to use a CW simulation in place of one that includes a varying wind from a galaxy\u2019s orbit, both disk and tail observables must agree. In this section, we compare the tail properties of the VW case at 3.12 Gyr to the CW runs at two times: when they have the same gas mass in the disk (RCFOCW at 1.23 Gyr, RCFOCWL at 1.25 Gyr, and NCFOCW at 1.58 Gyr), and when they have the same gas disk radius (RCFOCW at 1.61 Gyr, RCFOCWL at 1.62 Gyr, and NCFOCW at 1.58 Gyr). Because RCFOCWD is so similar to the RCFOCW(L) runs, with qualitatively identical comparisons with RCFOVW, we do not discuss it here. 3.3.1. Radiative Cooling Runs Before we focus on the tail properties, it is worthwhile to recall that the CW runs have been stripped for relatively short amounts of time when the gas disk masses and radii agree with the VW run at 3.12 Gyr. In fact, when the CW galaxies have the same gas disk mass as the VW galaxy, stripping has just begun (\u223c100 Myr) and the galaxies will continue to quickly lose gas mass for another \u223c400 Myr. When the gas disk radii agree, gas removal from the CW galaxies has begun to slow, and we are looking at a later stripping stage. In Figure 4 we compare the density projections of RCFOVW with the RCFOCW and RCFOCWL runs. The top panels compare when the gas masses within \u00b1 10 kpc of the disk plane are the same, and the bottom panels compare when the disk radii measured using the gas pro\ufb01les are the same. We clearly see that the gas density distribution in the VW case di\ufb00ers from the CW cases. When the gas mass agrees across the runs, the tails in the CW runs are broader, re\ufb02ecting the larger 7 surviving disk (see Figure 3). In the CW tails there is more high density gas closer to the disk (within 20 kpc), which may re\ufb02ect the fact that the wind has been stripping the CW galaxies for only 100 Myr, in comparison to the 2 Gyr of stripping in the VW run. There has not been enough time in the CW runs for stripped gas, particularly high-density gas that moves more slowly away from the disk (Tonnesen & Bryan 2010), to reach large distances. However, we do note that all three tails have gas that is denser than the surrounding ICM extending to the edge of the projection. When the gas radii agree across the runs (the bottom panels), we see that there is more high-density gas throughout the CW tails. This is 400 Myr later in the CW runs, during which time gas has continued to be removed from the disk at a relatively constant high rate (Figure 2), so we would expect more gas distributed throughout the tail. However, from the projections it is di\ufb03cult to determine whether the gas distribution is different or if the higher density simply re\ufb02ects that there is more gas in the CW tails when the disk radii are the same. We examine the gas tail quantitatively in Figure 5, which plots the cumulative mass distribution of gas in the tail along the wind direction starting at 6 kpc above the disk plane out to the edge of the simulated box (the lower boundary choice has no qualitative e\ufb00ect on the results). When the disk mass is the same in the VW and CW runs, the bulk of the stripped gas is found closer to the CW(L) disks. Conversely, when the VW and CW runs have the same gas disk radii, the tail mass in the CW runs is more evenly-distributed along the tail, with more mass farther from the disk. We next consider whether the di\ufb00erent tail gas distributions are re\ufb02ected in the tail gas velocity, which is another observed property of stripped galaxies. In Figure 6 we plot the distribution of gas mass with a tracer fraction of at least 0.25 as a function of distance above the disk and velocity in the wind direction. Here we only focus on the re\ufb01ned region of the box, within 40 kpc of the disk, as this region better resolves the velocity structure in the tail. When the gas mass agrees, we \ufb01rst see that there is more gas close to the disk. In addition, much of the stripped gas in the CW tails is accelerated to higher velocities within 4-10 kpc than in the VW tail. While this is most dramatic in the RCFOCW run, it can also be seen in the RCFOCWL run even though the ram pressure strength is lower than in the RCFOVW panel. The faster velocity of tail gas continues to the edge of the re\ufb01ned region, 40 kpc from the disk. Also, the CW runs have a broader velocity distribution that extends to much higher (\u223c2x) velocities when focusing on the higher-mass contours (\u22651039 g). In the bottom panels, we see that when the gas disk radius agrees well between the VW and CW cases, the \ufb02ow of most of the gas in the tail is also similar. However, there tends to be more fallback in the VW run, and more gas moving at high velocities in the CW runs. This may be because the ram pressure has been stronger and the wind faster for longer in the CW runs, even when the maximum wind velocity is lower (in RCFOCWL). We will discuss this in more detail in Section 4. Neither the gas density nor the velocity distribution 40 20 0 20 40 x (kpc) 40 20 0 20 40 z (kpc) 3120 Myr 10-3 10-2 Projected Density \u00b3 g cm2 \u00b4 40 20 0 20 40 x (kpc) 40 20 0 20 40 z (kpc) 1580 Myr 10-3 10-2 Projected Density \u00b3 g cm2 \u00b4 Fig. 7.\u2014 Projections of gas density in the NC simulations. The top panel shows NCFOVW 3.12 Gyr into the simulation, and the bottom panel shows NCFOCW when the disk properties (gas mass and radius) agree with the NCFOVW run. The gas distribution in the projection is quite di\ufb00erent in the VW and CW tails. in the tails agree when comparing radiatively cooled stripped galaxies in simulations with constant and varying ICM winds. 3.3.2. No Cooling Runs As we discussed in Section 3.2, without radiative cooling the disk masses and radii of the VW and CW simulations both agree using a single pair of outputs (VW at 3.12 Gyr, CW at 1.58 Gyr). We now compare the stripped tails at those outputs. In Figure 7 we show density projections of the simulations, as in Figure 4. Clearly the morphology of these tails are quite di\ufb00erent, with the CW run having a much more \ufb02ared tail. In the CW tail, the high density gas near the disk is more evenly distributed in projected radius, while in the VW tail the higher density gas tends to be found at larger cylindrical radii. Also, more higher density gas is found in the CW tail at all heights above the disk starting at about 4 kpc. The cumulative mass distributions of gas in the tail along the wind direction are quite similar, but the di\ufb00ering density distributions of gas in the VW and CW tails means that these tails look quite di\ufb00erent. Finally, we consider the velocity distribution of gas in 8 1 1 Fig. 8.\u2014 Gas mass distribution as a function of height above the disk and velocity in the wind (z) direction. The top and bottom panels show the NCFOVW and NCFOCW runs, respectively. As in the RC simulations, the stripped tail has a higher velocity far from the galaxy in the CW run compared to the VW run. the tail. In Figure 8 we plot the distribution of gas mass with a tracer fraction of at least 0.25 as a function of distance above the disk and velocity in the wind direction. As in Figure 6, we only focus on the re\ufb01ned region of the box, within 40 kpc of the disk. The tail in the VW run has a signi\ufb01cant component with negative velocities that stretches at least 40 kpc from the disk, while very little gas is falling back in the CW run. In the CW run much more gas is moving at high velocities, possibly because it has been a\ufb00ected by a fast-moving ICM for longer than the VW run (as in the RC simulations). As with the simulations with radiative cooling, neither the gas density nor the velocity distribution in the tails agree when comparing stripped galaxies in non-cooling simulations with constant and varying ICM winds. 4. COMPARING SIMULATIONS WITH AND WITHOUT RADIATIVE COOLING In this paper, we have run simulations that include radiative cooling (RC) and those that do not (NC). While clearly radiative cooling is an important process occurring in ram pressure stripped galaxies like those we simulate, we know that we are not including several important physical processes. For example, we are only including radiative cooling down to \u223c104 K. We do not include star formation and subsequent energy input from supernovae and stellar feedback. We also ignore heating from the UV background, cosmic rays, or the surrounding ICM. Turbulent scales below our resolution are not considered, and we do not include magnetic \ufb01elds. It is useful to highlight how the subgrid physics we implement in our simulations may a\ufb00ect our results as we draw conclusions and compare to observations. Therefore, here we consider the di\ufb00erent results in our RC and NC simulations. One main di\ufb00erence is that the RCFOVW and RCFOCW(L/D) runs have di\ufb00erent stripping rates and gas pro\ufb01les, while in the NCFOVW and NCFOCW the disks are quite similar (Figures 2 & 3). Radiative cooling allows the disk to collapse and dense clouds to form even before the wind hits the disk, (seen at later times by comparing Figures 4 and 7). When the ICM wind impacts the galaxy, it compresses gas in the galaxy, as noted in Sections 3.1 & 3.2. This compression wave can be important to the evolution of the galaxy with radiative cooling. In the VW run, because the initial ram pressure is quite low, this results in radiative cooling of gas that was previously too low density to quickly cool but cannot yet be removed. By the time the peak ram pressure is impacting the galaxy in the varying wind run, more gas is too dense to be stripped. In Figure 3 we see that the inner density pro\ufb01le of RCFOVW has higher density gas than the RCFOCW(L/D) runs. This is also the case when comparing the gas pro\ufb01les at the times when the gas radii agree. However, before the wind hits the disks, the inner density of the RCFOVW galaxy is less than in the RCFOCW(L/D) galaxies, supporting the picture of dominant cooling in RCFOVW versus dominant stripping in RCFOCW(L/D). Because the initial surrounding thermal pressure in RCFOCWD is higher than the ram pressure experienced by RCFOVW until \u223c2.25 Gyr into the varying-wind simulation (1.25 Gyr after the wind hits the galaxy), see Figure 1, the additional compression of the disk gas in the RCFOVW simulation due to the increasing ram pressure is important to the gas stripping. While a compression wave is likely to drive cooling and collapse of gas in a disk, we are not including heating sources that could mitigate the e\ufb00ect of cooling. Also, without star formation or feedback, dense clouds survive for a signi\ufb01cant period of time (the entire simulation unless destroyed by the wind), which may allow more time for the clouds to travel towards the center of the disk and thus factor into the di\ufb00erent density pro\ufb01les (e.g. Schulz & Struck 2001; Tonnesen & Bryan 2009; 2012). Despite these caveats, the di\ufb00erences in the disk properties between the RCFOVW and RCFOCW(L) runs is enough to question the detailed comparison of constant-wind simulations with observations for any individual galaxy. Although the level of agreement between disks in the VW and CW runs depends on radiative cooling, the results regarding the stripped tail are independent of whether cooling is implemented. A simulation using a constant wind will not reproduce the tail properties of a simulation with a varying wind. When disk properties agree, although the total time that the constant wind has been stripping the galaxy is shorter than that of the varying wind, the constant wind has had a longer time at the peak velocity. This allows some of the gas to be accelerated to higher velocities, a phenomenon we point 9 out for both the RC and NC runs in Figures 6 and 8. We also note that any length of time at a constant ram pressure is unphysical for nearly all galaxy orbits. Finding agreement in disk properties between simulations with constant and varying winds does not indicate that tail properties, seen most strongly in the velocity pro\ufb01les, will agree. This robust result does not depend on the exact physics implemented in a simulation. This is well understood in terms of the multi-stage stripping described by, e.g. Schulz & Struck (2001) and Roediger & Hensler (2005). Initially gas is removed from the disk, but remains bound to the galaxy and may \u201chang\u201d behind the galaxy, especially when it is shielded from the ICM wind by the remaining gas disk. With continued ram pressure, most gas is this region is eventually stripped, but some gas falls back towards the disk. Roediger & Hensler (2005) show that stronger ram pressure decreases both the amount of time that gas remains bound in the halo and the fraction of gas that falls back to the disk. For our simulations, this means that because the VW runs spend most of the simulation before our comparison time at 3.12 Gyr with ram pressure well below those of the CW run, more gas will hang for longer in the halo, leading to slower velocities throughout the VW tail. Another dramatic di\ufb00erence in the velocity of tail gas is the fact that there is more fallback in the VW runs, as seen in both the RC and NC runs in Figures 6 & 8. This may be because the snapshots of the VW runs are taken \u223c2 Gyr after the wind has hit the disk, while the comparison times of the CW runs are no more than 600 Myr after the wind has hit the disk. As discussed in Roediger et al. (2015), after an impulsive onset of a wind there can be a several-hundred Myr relaxation phase (depending on the size of the object and the \ufb02ow velocity) before stripping reaches a quasi-steady state in which a back\ufb02ow develops behind the unstripped gas. The VW runs should be well into the quasi-steady stripping phase, while the CW runs may not yet have developed the back\ufb02ow velocity structure. Indeed, if we consider the velocity of stripped gas in the CW runs at 3.12 Gyr we see very similar levels of fallback. The rapidly shrinking disk in the radiatively cooled CW runs exacerbates the di\ufb00erence in the tail velocities. As pointed out in Roediger et al. (2015), as the shielding region shrinks, more gas can be directly accelerated by the ICM wind. In the radiatively cooled simulations, the disk radius of the CW runs continues shrinking for about 1 Gyr after the wind hits the disk, while the radius of the gas disk in the VW run changes very little after about 2.5 Gyr into the simulation, before the ram pressure reaches its peak. Therefore, when we compare the tails, the CW disks are shrinking and more gas is being pushed from behind the galaxies while the VW disk size remains relatively constant. 4.1. Resolution While we do not perform a resolution test in this series of simulations, previous work has discussed the effects of resolution at length. For example, Roediger & Bruggen (2006) found that changing resolution has very little e\ufb00ect on wind-tunnel simulations without radiative cooling. Tonnesen & Bryan (2009) found that in windtunnel simulations with radiative cooling, lower spatial resolution runs have larger cold clouds with lower maximum densities. This means a smoother disk and stripping rates closer to those of disks with no radiative cooling. Tonnesen & Bryan (2010) considered the e\ufb00ects of lower resolution on stripped tails with radiative cooling, and found that less resolution results in shorter tails, both from easier mixing of stripped gas into the ICM and from less low-density gas accelerated quickly from the disk. They also found more fallback in lower resolution runs, possibly because the remaining disk shields the stripped gas more e\ufb00ectively with less fragmentation. Therefore, we predict that lowering the resolution of the radiatively cooled runs would weaken our results, but only with very low resolution would we reach the results of the no-cooling runs. 5. CONCLUSIONS In this paper we examine a series of hydrodynamical simulations to determine whether considering the varying ram pressure strength due to the orbit of a satellite galaxy is important when using simulations to interpret observations. Speci\ufb01cally, we compare simulations with increasing ram pressure to those with a constant ram pressure. Our main results are as follows: 1) In simulations that include radiative cooling, the amount of gas removed from the disk and rate of removal is dramatically di\ufb00erent in a constant versus a varying wind. More gas is removed more quickly from a constant wind. Even once the varying wind reaches the peak ram pressure, the gas removal rate is lower than in the constant wind simulations (Figure 2). 2) In radiative cooling simulations, when the gas mass is the same in simulations with a constant and varying wind, the radius of the surviving gas disks di\ufb00er (Fig. 3). 3) The agreement of disk properties, such as gas mass or radius, between simulations with di\ufb00erent wind properties does not indicate that the tail properties, such as density or velocity structure, will be similar. This occurs whether or not radiative cooling is included in the simulations (Section 3.3). It is apparent that a simulation that uses a constant wind cannot accurately reproduce a galaxy that has been ram pressure stripped by an increasing wind. Importantly, in this paper, we examine simulations that include radiative cooling and those that do not, and \ufb01nd that the cooling implementation does not a\ufb00ect our result. Thus, we stress that simulations, particularly those with a constant wind, should be used carefully and sparingly as tools to interpret speci\ufb01c observations of galaxies. Using simulations to interpret observations of individual systems requires sampling a large set of parameters. The wind angle, ram pressure strength, and gas disk scale height will a\ufb00ect the resulting stripped galaxy\u2019s gas density and velocity structure (e.g. Merluzzi et al. 2013, 2016). In this paper we have shown that including an increasing ram pressure also has an e\ufb00ect. More complications are certainly possible, for example, a varying wind angle may e\ufb00ect the tail morphology and velocity structure. Also, a clumpy or turbulent ICM may e\ufb00ect the e\ufb03ciency of stripping and mixing. The surrounding gravitational potential, both from the cluster and nearby galaxies, are also likely to a\ufb00ect the stripped tail. Testing the e\ufb00ects of more complicated ICM and orbital models on cluster galaxies will not only allow us to test how galaxies are a\ufb00ected by their surroundings, 10 but also to determine the extent to which we can use ram pressure stripped galaxies to probe the nature of the surrounding ICM\u2013its turbulence, pressure, and magnetic \ufb01eld. I would like to thank the referee, Elke Roediger, for comments that greatly improved the paper. I would also like to thank the GASP team for useful discussions about ram pressure stripping, and Greg Bryan for helpful conversations and comments on the paper. The simulations were run with computing resources provided by mies. ST was partially supported by the Alvin E. Nashman Fellowship in Theoretical Astrophysics.",
                    "introduction": "1. Cluster satellite galaxies may undergo a number of in- teractions that are speci\ufb01c to dense environments. These include interactions between the intracluster medium (ICM) and the galaxy, such as ram pressure stripping and starvation (Gunn & Gott 1972; Larson, Tinsley & Cald- well 1980), and gravitational interactions such as those between galaxies, like harassment (Moore et al. 1996), and between a galaxy and the cluster potential, such as tidal stripping (Merritt 1984; Gnedin 2003). The rela- tive in\ufb02uence of these mechanisms in transforming galaxy morphology, color, and gas content remains unclear, with large surveys helping to disentangle the various drivers (e.g. Moran et al 2007; van den Bosch et al. 2008). An alternative way to gauge their relative importance, and to get a deeper understanding of the processes them- selves, is to look for observational signs of the di\ufb00erent interactions in individual galaxies. There are a few signatures that can be used to di\ufb00er- entiate between gas-stripping mechanisms like ram pres- sure stripping and gravitational interactions. For exam- ple, late-type galaxies in the center of the Virgo cluster have smaller H I disks than stellar disks, indicating an interaction that does not a\ufb00ect the stellar component of galaxies (Cayatte et al. 1990; Warmels 1988; but see Smith et al. 2012 for simulations showing gas dragging the stellar disk). Studies of H I de\ufb01ciency have shown that galaxies in clusters have less neutral hydrogen than their counterparts in the \ufb01eld (see the review by Haynes et al. 1984). Ram pressure stripped galaxies should therefore have small gas disks and correspondingly lower star formation rates (Gavazzi et al. 2006; Koopmann & Kenney 2004). However, ram pressure stripping may also increase star formation rates in the surviving gas disk (Dressler & Gunn 1983; Evrard 1991; Fujita 1998; Smith et al. 2010; Poggianti et al. 2004; 2009; 2017; Fu- jita & Nagashima 1999; Tonnesen & Bryan 2012; Bekki"
                },
                {
                    "url": "http://arxiv.org/abs/1707.03409v1",
                    "title": "Probing the Dependence of the Intergalactic Medium on Large Scale Environment Using the Low Redshift Lyman Alpha Forest",
                    "abstract": "We examine the statistics of the low-redshift Ly-alpha forest in an adaptive\nmesh refinement hydrodynamic cosmological simulation of sufficient volume to\ninclude distinct large-scale environments. We compare our HI column density\ndistribution of absorbers both with recent work and between two highly-refined\nregions of our simulation: a large-scale overdensity and a large-scale\nunderdensity (on scales of approximately 20 Mpc). We recover the average\nresults presented in Kollmeier et al. (2014) using different simulation\nmethods. We further break down these results as a function of environment to\nexamine the detailed dependence of absorber statistics on large-scale density.\nWe find that the slope of the HI column density distribution in the 10$^{12.5}$\n$\\le$ N$_{HI}$/cm$^{-2}$ $\\le$ 10$^{14.5}$ range depends on environment such\nthat the slope becomes steeper for higher environmental density, and this\ndifference reflects distinct physical conditions of the intergalactic medium on\nthese scales. We track this difference to the different temperature structures\nof filaments in varying environments. Specifically, filaments in the\noverdensity are hotter and, correspondingly, are composed of gas with lower HI\nfractions than those in underdense environments. Our results highlight that in\norder to understand the physics driving the HI CDD, we need not only improved\naccounting of the sources of ionizing UV photons, but also of the physical\nconditions of the IGM and how this may vary as a function of large-scale\nenvironment.",
                    "authors": "Stephanie Tonnesen, Britton D. Smith, Juna Kollmeier, Renyue Cen",
                    "published": "2017-07-11",
                    "updated": "2017-07-11",
                    "primary_cat": "astro-ph.CO",
                    "cats": [
                        "astro-ph.CO",
                        "astro-ph.GA"
                    ],
                    "main_content": "than 5. In K14, the authors put forward several plausible solutions to the PUC, including increased AGN fractions and ionizing radiation escape fractions relative to the HM12 predictions which they deemed unlikely but have been examined further in the literature (e.g Khaire & Srianand 2015a,b; who also increase the star formation rate density at z < 0.5 above that of HM12). Another possible solution was put forward by Gurvich et al. (2016) using the Illustris simulation including AGN feedback. They find that for their simulation, the HI CDD in the range NHI = 1012.5 to 1014 cm\u22122 agrees well with observations due partly to a slightly higher adopted value of \u0393 (Faucher-Gigu\u2018ere et al. 2009) but primarily from the inclusion of AGN feedback. The authors note that their simulation begins to diverge from observations at NHI > 1013.5 cm\u22122, perhaps indicating excessively strong AGN feedback unphysically reducing the number of absorbers (Gurvich et al. 2016). Prompted by this literature, we set out to understand two elements of the PUC which have not been clarified. Firstly what, if any, role does the underlying hydrodynamic scheme play in determining the HI CDD? One of the possible (but deemed unlikely) resolutions presented for completeness in K14 was the possible effect of the underlying hydrodynamics scheme which could play a role in the PUC. Those authors quoted results for their smoothed particle hydrodynamics (SPH) simulations which are thought to be robust in the regime of the IGM (certainly at the 50% level), but it was not directly tested at low redshift whether there could have been an unexpected and far larger effect. We do that test here. Secondly, we wished to use the unique nature of our simulation to determine whether the environment would affect the intergalactic medium to an extent that the HI CDD could differ across different regions of the universe. 2 In this paper we examine Ly\u03b1 absorbers with HI column densities between 1012.5 1014.5 cm\u22122 in a largescale (\u223c20 Mpc) overdensity and underdensity cosmologically simulated using the adaptive mesh re\ufb01nement (AMR) Eulerian hydrodynamical code Enzo (Bryan et al. 2014). These simulations provide us with an opportunity to compare Ly\u03b1 absorbers in di\ufb00erent largescale environments within the same fully hydrodynamical cosmological simulation performed at sub-kpc resolution. Comparing di\ufb00erent environments within the same simulation where all physical processes are modeled in the same way minimizes the degrees of freedom of the numerical problem. In Section 2 we describe our simulations, and brie\ufb02y mention our galaxy selection technique in Section 2.1. We then discuss our methods for creating sightlines through our simulations and spectrally identifying Ly\u03b1 absorbers in Section 2.2, and explain our method for \ufb01nding individual Ly\u03b1 absorbing clouds in Section 2.3. Our \ufb01rst result is a spectrally-determined HI CDD, in Section 3. In Section 4 we examine individual absorbing clouds we \ufb01nd along our sightlines (Section 4.1), the gas properties of those clouds (Section 4.2) and where the clouds tend to be found (Section 4.3). In Section 5 we synthesize our absorbing cloud results to determine the impact of environment on Ly\u03b1 clouds. Finally, in Section 6 we summarize our conclusions, and discuss directions for both observational and theoretical future work. 2. METHOD For the details of our simulations, we refer the reader to Cen (2012a), although for completeness we reiterate the main points here. We perform cosmological simulations with the AMR Eulerian hydrodynamical code Enzo (Bryan 1999; Bryan et al. 2014). We use cosmological parameters consistent with the WMAP7-normalized LCDM model (Komatsu et al. 2011): \u2126M = 0.28, \u2126b = 0.046, \u2126\u039b = 0.72, \u03c38 = 0.82, Ho = 100 h km s\u22121 Mpc\u22121 = 70 km s\u22121 Mpc\u22121, and n = 0.96. We \ufb01rst ran a low resolution simulation with a periodic box of 120 h\u22121 Mpc on a side, and identi\ufb01ed two regions: an overdensity centered on a cluster and an underdensity centered on a void at z = 0. We then resimulated each of the two regions separately with high resolution, but embedded within the outer 120 h\u22121 Mpc box to properly take into account large-scale tidal \ufb01eld e\ufb00ects and appropriate \ufb02uxes of matter, energy and momentum across the boundaries of the re\ufb01ned region. The overdense re\ufb01ned region is 21 \u00d7 24 \u00d7 20 h\u22123 Mpc3. The central cluster is \u223c2 \u00d7 1014 M\u2299with a virial radius (r200) of 1.3 h\u22121 Mpc. The underdense re\ufb01ned region is somewhat larger, at 31 \u00d7 31 \u00d7 35 h\u22123 Mpc3. At their respective volumes, they represent +1.8\u03c3 and -1.0\u03c3 \ufb02uctuations. Although these are large-scale overand underdense environments, there are galaxies at a range of local densities in both boxes, and there is substantial overlap of local densities between the two volumes (Tonnesen & Cen 2012). In both re\ufb01ned boxes, the minimum cell size is 0.46 h\u22121 kpc, using 11 re\ufb01nement levels at z = 0. The initial conditions for the re\ufb01ned regions have a mean interparticle separation of 117 h\u22121 kpc comoving, and a dark matter particle mass of 1.07 \u00d7 108 h\u22121 M\u2299. While we do not perform a resolution study here, we refer our readers to Tepper-Garc\u00b4 \u0131a et al. (2012). They show that the HI column density distribution between 1012.5 \u2264NHI/cm\u22122 \u22641014.5, one of the major results of our paper, is well converged using dark matter particle masses of 4.1 \u00d7 108 h\u22121 M\u2299(a factor of 4 more massive than the dark matter particle mass in our simulation). The simulations include a metagalactic UV background (Haardt & Madau 1996) supplemented with an X-ray Compton heating background from Madau & Efstathiou (1999), a model for shielding of UV radiation by neutral hydrogen (Cen et al. 2005), and metallicitydependent radiative cooling (Cen et al. 1995). The fraction and density of neutral hydrogen is directly computed within the simulations. Star particles are created in gas cells that satisfy a set of criteria for star formation proposed by Cen & Ostriker (1992), and reiterated with regards to this simulation in Cen (2012a). Each star particle has a mass of \u223c106 M\u2299, which is similar to the mass of a coeval globular cluster. Once formed, the stellar particle loses mass through gas recycling from Type II supernovae feedback, and about 30% of the stellar particle mass is returned to the ISM within a time step. Supernovae feedback is implemented as described in Cen (2012a): feedback energy and ejected metal-enriched mass are distributed into 27 local gas cells centered at the star particle in question, weighted by the speci\ufb01c volume of each cell. We allow the whole feedback process to be hydrodynamically coupled to surroundings and subject to relevant physical processes, such as cooling and heating, as in nature. The simulation used in this paper has compared several galaxy properties that depend critically on the feedback method to observations and found strong agreement (Cen 2012a-b; Cen 2013). For example, Cen (2012a) found excellent agreement between simulated and observed damped Ly\u03b1 systems, and Cen (2012b) found that the properties of O VI and O VII absorbers also agree well with observations. We do not include a prescription for AGN feedback in this simulation, and as a result, our simulation overproduces luminous galaxies at the centers of groups and clusters of galaxies. 2.1. Galaxies As has been discussed in earlier work (e.g. Tonnesen & Cen 2012; 2014; 2015), we use HOP (Eisenstein & Hut 1998) to identify galaxies using the stellar particles. HOP uses a two-step procedure to identify individual galaxies. First, the algorithm assigns a density to each star particle based on the distribution of the surrounding particles and then hops from a particle to its densest nearby neighbor until a maximum is reached. All particles (with densities above a minimum threshold, \u03b4outer) that reach the same maximum are identi\ufb01ed as one coherent group. The densest star particle is considered the center of the stellar group, or galaxy. In the second step, groups are combined if the density at the saddle point which connects them is greater than \u03b4saddle. We use HOP because of its physical basis, although we expect similar results would be found using a friends-of-friends halo \ufb01nder. HOP has been tested and shown to be robust (e.g. Tonnesen, Bryan, & van Gorkom 2007). 2.2. Sightlines and Spectra 3 We follow the general method described in K14 to calculate sightlines and spectra through our simulated regions. We use the z=0.1 outputs of both re\ufb01ned region simulations. In each re\ufb01ned box, we then extract 2500 sightlines that span 0.008 in redshift. This width spans a large fraction of the re\ufb01ned region while ensuring that the same structures are not sampled repeatedly in a sightline. Speci\ufb01cally, we use yt1 to create the sightlines and spectra across our re\ufb01ned regions. yt is a python package for analyzing and visualizing volumetric, multi-resolution data from astrophysical simulations and observations (Turk et al. 2011). We randomly generate sightlines that are completely contained within the re\ufb01ned region of our simulation, allowing the rays to wrap around the re\ufb01ned region. In the overdense region, we only allow our sightlines to span 21 \u00d7 18 \u00d7 20 h\u22123 Mpc3 so that they are crossing truly highly-re\ufb01ned structures. We generate a synthetic spectrum for each ray and derive HI column densities from the spectrum using the methods described below. For creating an absorption spectrum from the simulation data, we use the absorption spectrum generator in yt (Turk et al. 2011). We create arti\ufb01cial sight lines from simulation data by extracting all grid cells intersected the ray. We gather all relevant \ufb01eld data for each grid cell, including density \ufb01elds for appropriate ions, velocities, and the temperature. Spectra are generated by depositing a Voigt pro\ufb01le for each element of the ray, where the column density is the density of relevant ion multiplied by the path length through each cell and the Doppler parameter is given by the cell temperature. The lines are shifted from their rest wavelengths by a combination of the line-of-sight peculiar velocity and Hubble expansion. For the redshift, the start of the ray is assumed to be at the redshift of the dataset and the redshift is increased according to the comoving radial distance along the ray. In practice, spectral features identi\ufb01ed as single lines are the result of multiple elements in the ray. This functionality has now been subsumed by the Trident package (Hummels et al. 2016), and we refer the reader there for a detailed description of the method. Because we are only interested in Ly\u03b1 in this work, we only include the Ly\u03b1 line in the synthetic spectra and assume zero noise. While unrealistic, this sets an upper limit on the number of detectable lines. As the simulation includes non-equilibrium atomic H/He chemistry, we are able to provide the neutral H densities directly to the spectrum generator. Automated spectral \ufb01tting is done using the method of Egan et al. (2014, E14), also a part of the yt package. This method uses the least squares \ufb01tting algorithm provided by the SciPy optimize library, to \ufb01nd an optimal combination of column density, Doppler parameter, and redshift for any contiguous region of a spectrum below 99% of the continuum \ufb02ux. Additional components are added, up to a maximum of 8, if the reduced \u03c72 error of the optimal \ufb01t is above 10\u22124. To aid the \ufb01tting routine, we allow for only a range of acceptable parameters, (1011 < NHI < 1022 cm\u22122), Doppler parameter (1 < b < 300), and redshift (0.1 < z < 0.4). These settings are broader than the range of parameters of the \ufb01tted lines. This method can be compared directly to observations, 1 http://yt-project.org/ because it uses the redshift of Ly\u03b1 absorbing gas to determine whether it is combined into a single absorption feature or separated into several features. This procedure thus closely resembles the procedure followed by observers when analyzing real data. 2.3. Selecting Individual Clouds In order to examine the properties of individual absorbers along a sightline, we select dense HI clouds, using a method similar to the \u2018contour method\u2019 described in E14. To do this, we \ufb01nd local maxima in HI number density by selecting a cell with the peak HI density within \u00b1 300 kpc from that point. This peak HI number density must be greater than 10\u221213 cm\u22123 (although as we discuss below, this requirement does not a\ufb00ect our results). We then select the edges of the absorbers by \ufb01nding the closest cell that is either a local minimum within \u00b1 300 kpc or has an HI number density that is nHI,min/nHI,peak = {0.1,0.5,0.9} of the peak value. We use the maximum or minimum found over several cells, here selected to be \u00b1 300 kpc, to smooth out small density \ufb02uctuations between cells, even in regions far from galaxies that are not re\ufb01ned to the maximum level. As a straightforward check of our method, we plotted the HI density pro\ufb01les of several absorbers and found that from peak to minimum they were \u2265250 kpc, which means that the minimum absorber size was not likely dictated by the criterium that there be >300 kpc between neighboring minima (or maxima). Multiple peaks are rarely seen in our visual inspection of HI absorber pro\ufb01les, so we are identifying single clouds. We will call absorbers selected in this manner clouds throughout the paper in order to di\ufb00erentiate them with absorbers found using the spectrum as described above. Because we are not including redshift information in our cloud selection and allow for broad absorbers with little variation between the peak and minimum HI density, we do not expect that every cloud will be identi\ufb01ed using the yt absorption spectrum routine. Indeed, this is what we \ufb01nd when compare our two routines. To do this, we \ufb01rst select individual HI clouds along 200 lines of sight. Then for each cloud, we run the yt absorption spectrum generator routine on the small section of the sightline that contains the cloud. Thus we can determine whether the yt routine would identify each individual HI cloud. We show in Figure 1 the histograms of clouds that are identi\ufb01ed using nHI,min/nHI,peak = 0.1, and overplot the number of those clouds that are re-identi\ufb01ed using yt to create a spectrum of that section of the sightline and identifying the Ly\u03b1 line as described in Section 2.2. We \ufb01nd reasonable agreement in the HI cloud column densities measured using both methods. In both the overdense and underdense regions, \u223c85% of clouds that are re-identi\ufb01ed with the yt routine have absorption spectrum column densities within 20% of the HI cloud column density. In the overdense (underdense) region about 7% (16%) of the re-identi\ufb01ed HI clouds have multiple spectral peaks. There is no clear reason for the di\ufb00erences between cloud re-identi\ufb01cation in the two environments. We \ufb01nd that the number of HI clouds re-identi\ufb01ed with the yt routine does not change when we vary the \ufb01tting parameters discussed in Section 2.2 (for example, the initial guess for the \ufb01tting routine of the column density or b parameter, or changing the range of allowed column den4 12.5 13.0 13.5 14.0 14.5 NHI 0 20 40 60 80 100 120 140 160 Number of Absorbers Manually selected HI Clouds Clouds re-identified from spectrum 12.5 13.0 13.5 14.0 14.5 NHI 0 20 40 60 80 100 Number of Absorbers Manually selected HI Clouds Clouds re-identified from spectrum Fig. 1.\u2014 Histograms comparing manually selected HI clouds and those that are subsequently identi\ufb01ed as Ly\u03b1 absorbers by creating an absorption spectrum using yt. 200 sightlines were used in this comparison in both the overdense (top panel) and underdense (bottom panel) re\ufb01ned regions. Clouds selected in either manner show the same di\ufb00erence in the HI CDD between di\ufb00erent environments. sities or redshifts). However, if we only select HI clouds whose peak HI number density is greater than 9\u00d710\u221212 cm\u22123 (which corresponds to a neutral fraction of 1.4 \u00d7 10\u22125 at three times the mean baryon density), then in the overdense and underdense boxes, respectively, 99% and 82% of clouds are identi\ufb01ed as Ly\u03b1 absorbers using the yt absorption spectrum generator routine. We vary the peak number density simply to illustrate that, as we expect, HI clouds with lower peak densities are more dif\ufb01cult for the yt absorption spectrum routine to identify. Whether we use our \ufb01ducial peak HI number density minimum, this high minimum, or no minimum, the comparisons we discuss in this paper remain qualitatively the 12.5 13.0 13.5 14.0 14.5 log(NHI/cm\u22122)) 100 101 102 103 d2N/dlog(NHI)dz overdense median overdense quartiles underdense median underdense quartiles Danforth 2016 K14 HM01 K14 HM01B Fig. 2.\u2014 The HI CDD for our sightlines. We generated 15 sets of 2500 sightlines with \u2206z= 0.008. The red and blue lines are the median number of absorbers in the overdense and underdense regions, respectively. The orange and cyan lines denote the upper and lower quartiles for the overdense and underdense regions. The HI CDD in the overdense region is steeper than in the underdense region. same. We make use of both our spectrally identi\ufb01ed absorbers as well as the manually identi\ufb01ed clouds. The spectrally identi\ufb01ed absorbers are most useful for comparing with observational datasets. However, for exploring the physical conditions giving rise to the absorption, and thus to gain further physical insight into the environmental dependence of absorption, we will use the statistics from our manually identi\ufb01ed cloud population. Comparing Figures 2 and 3, we \ufb01nd that either absorber selection method \ufb01nds that the distribution of HI column densities di\ufb00ers between the overdense and underdense environments. We \ufb01rst turn our attention to comparison with observations and prior work. 3. THE HI COLUMN DENSITY DISTRIBUTION We \ufb01rst create an HI Column Density Distribution (CDD) for comparison with K14 and observations. As in K14, this is de\ufb01ned to be the mean number of absorbers per logarithmic interval of column density per unit redshift path length, for the simulated Ly\u03b1 forest. In the z=0.1 output of both of our re\ufb01ned regions, we generated 15 sets of 2500 sightlines with \u2206z= 0.008. We then identi\ufb01ed absorbers in each of those 15 sets of sightlines using the technique described in Section 2.2. In Figure 2 we show the resulting HI CDD for each re\ufb01ned region. In blue and cyan we show the median and quartile range, respectively, of our 15 sets of sightlines in the underdense region, and in red and orange we show the median and quartile range, respectively, of our 15 sets of sightlines in the overdense region. We have also included two of the K14 HI CDDs, speci\ufb01cally those that use the Haardt & Madau (2001) UV background (HM01; yellow) and the Haardt & Madau (2001) UV background plus blazars (HM01B; magenta). In green we include the observational results from Danforth et al. (2016). 5 First, we \ufb01nd that in general we show broad agreement with observational results, particularly at column densities below 1014 cm\u22122, as well as with the K14 HM01 prediction as discussed in K14. We note, however, that our UV background is a hot HM01, or HM01 plus an X-ray Compton heating background, which produces a systematically \u201cthinner\u201d forest than the more recent Haardt & Madau (2012) and Faucher-Gigu\u2019ere et al. (2009) UV backgrounds (see Figure 1 in K14). The HM01 UV background is signi\ufb01cantly larger than some more recent direct measurements of the local metagalactic UVB (Adams et al. 2011). We also note that the slope of our CDD in either re\ufb01ned region is steeper than observed by Danforth et al. (2016), particularly at high columns. Our simulation is unique in that we can compare two highly-resolved regions around a large-scale overdensity and underdensity. We note that the e\ufb00ect of the different environment becomes manifest at columns greater than 1013.5 cm\u22122 and that below this column, the effect of large-scale overdensity is less obvious, although still distinct. We \ufb01nd that the HI CDD in the overdense region is steeper than in the underdense region. This is driven partly by the absence of low-column density (NHI < 1013.5 cm\u22122) absorbers in underdense void regions, but more clearly by the absence of high-column density NHI > 1013.5 absorbers in the overdense volume. We note that we \ufb01nd the same qualitative results when we vary the simulation data we collect. For example, our results did not di\ufb00er if we used 50 sets of 2500 sightlines or 7 sets of 2500 sightlines, if we increased the \u2206z of each sightline to 0.016, or if we used a larger overdense box that included some underre\ufb01ned regions. 4. EXAMINING ABSORBING CLOUDS IN DETAIL We now examine HI fabsorbers in these two regions to determine whether there are di\ufb00erences in their properties that could drive the di\ufb00erences in the HI CDD. In order to determine if cloud properties di\ufb00er in the two environments, we identify individual HI clouds as we discuss in Section 2.3. For the following results we use all of the HI clouds identi\ufb01ed in 7 sets of 2500 lines of sight. As we have shown above, our HI cloud selection scheme does not correspond directly to spectral absorbers. We \ufb01rst create a CDD of all of the HI clouds found in these 17,500 lines of sight. Figure 3 shows this CDD for the three cloud de\ufb01nitions in each of the re\ufb01ned regions. The overdense box is denoted by red lines and the underdense box is denoted by blue lines. The linestyle designates whether the clouds are {0.1,0.5,0.9}\u00d7npeak. As with the spectrally-determined HI CDD in Figure 2, the slope in the overdense region is steeper than the slope in the underdense region for all but our smallest clouds (nHI,min/nHI,peak = 0.9). Therefore, looking directly at the HI clouds should provide physical insight into environmental causes that may drive the di\ufb00erences in the spectrally-observed HI CDDs. 4.1. Cloud Size In Figure 4 we plot the length of HI clouds, binned by NHI. The colors are as in Figure 3, with the lines denoting the median values and the shaded regions spanning the upper to lower quartiles of the nHI,min/nHI,peak = 0.1 clouds. The larger clouds ({0.1,0.5}\u00d7npeak) have consistently broader lengths in the overdense region up 12.5 13.0 13.5 14.0 14.5 log (NHI [cm\u22122]) 102 103 104 Number of absorbers over under 0.1 0.5 0.9 Fig. 3.\u2014 The number of HI clouds selected by \ufb01nding a local nHI maximum and calculating the total column density between cells with {0.1,0.5,0.9} of the peak value. The overdense box is denoted by red lines, and the underdense box is denoted by blue lines. The linestyle, {solid, dashed, dash-dot} designates the HI minimum of the clouds: {0.1,0.5,0.9}\u00d7npeak. HI clouds selected this way show a steeper slope in the number of absorbers as a function of NHI in the overdense box than in the underdense box for the clouds that include gas with densities down to {0.1,0.5} of the peak value. to the highest column densities (log(NHI/cm\u22122) \u226514). However, the di\ufb00erences between the cloud sizes are not dramatic, and there is a large overlap in the range of cloud size values, as shown by the shaded quartile regions. The smallest clouds, nHI,min/nHI,peak = 0.9, are nearly identical in size in the two environments across the entire column density range. We can compare our cloud lengths to E14. We \ufb01nd that our largest absorbers, those with nHI,min/nHI,peak = 0.1, tend to be larger than the E14 clouds at all column densities. Clouds selected with nHI,min/nHI,peak = {0.5, 0.9} are larger at lower column densities and smaller at higher column densities than E14 clouds. Part of this is that E14 uses a density cuto\ufb00of nHI,peak \u226510\u221212. Indeed, we \ufb01nd, unsurprisingly, that increasing our density cuto\ufb00for the peak value also decreases our absorber sizes, as you need a smaller pathlength of higher density gas to reach the same total column density. However, we reiterate from Section 2.3 that our relative relationships between absorbers in the two environments do not change depending on our nHI,peak cuto\ufb00and it is the relative environmental dependence we wish to probe. 4.2. The Gas Properties of Absorbing Clouds Di\ufb00erences in the sizes of clouds that have the same HI column density may re\ufb02ect intrinsic di\ufb00erences in the gas that forms these Ly\u03b1 absorbing clouds. We now examine this directly. In the top panel of Figure 5 we show the average cloud temperature binned by NHI. Our results are the same if we use the median temperature or an average temperature weighted by cell density or column density. When comparing clouds selected using the same density criteria (the same nHI,min/nHI,peak value), the temperature of the clouds in the overdense region 6 Fig. 4.\u2014 The length of HI clouds, binned by NHI. The colors are the same as in Figure 3. The lines denote the median value in a bin and the shaded region spans the quartile range of the nHI,min/nHI,peak = 0.1 clouds. is always higher than the temperature of the clouds in the underdense region. In most bins the clouds in the overdense region are hotter by a factor of at least 1.5. In fact, for clouds with log(NHI/cm\u22122) > 12.9 the density criteria does not matter, and clouds in the overdense region are hotter than clouds in the underdense region. We might expect hotter clouds to be larger, and indeed, as we have shown, clouds in the overdense region tend to be larger than clouds in the underdense region. We \ufb01nd that the sizes of our nHI,min/nHI,peak = 0.1 clouds are broadly consistent with straightforward Jeans-length arguments that scale with the thermal velocity (e.g. eqn. 2 in Peeples et al. 2010) and indicate a typical size of \u223c 800 h\u22121kpc for IGM temperatures of 104K, with cloud lengths generally ranging from 0.6-1.4 Jeans lengths. In the bottom panel of Figure 5 we plot the average HI fraction in the absorbing clouds binned by NHI. As with the temperature measurement, when comparing clouds selected using the same density criteria, the HI fraction of the clouds in the overdense region is always lower than the HI fraction of the clouds in the underdense region. However, we note that the HI fractions of the smallest clouds (nHI,min/nHI,peak = 0.9) are quite similar at higher column densities. Because HI clouds tend to be hotter in the overdense region, it follows that they would have lower HI fractions. This also explains the size di\ufb00erence in clouds in the di\ufb00erent environments: hotter clouds have lower neutral fractions, so must be larger to reach the same column density. These HI absorbing clouds could be formed from gas that has been ejected from galaxies due to feedback or from gas that has never been impacted by out\ufb02ows. In order to determine which of these scenarios is more likely, we examine the gas metallicity of the absorbing clouds. In Figure 6, we plot the average metallicity of our absorbing clouds binned by log(NHI/cm\u22122). In both the overdense and underdense region, the metallicities are quite low until at least log(NHI/cm\u22122) > 13.9. Below this column density, even the upper quartile of all clouds does not reach a metallicity of 10\u22123. Even at higher column densities the median value of metallicity remains Fig. 5.\u2014 Gas properties of absorbing clouds, binned by NHI. The colors are the same as in Figure 3. The lines denote the median value in a bin and the shaded region span the quartile range of the nHI,min/nHI,peak = 0.1 clouds. Top panel: The average temperature of absorbing clouds, binned by NHI. The temperature of clouds in the overdense region is consistently higher than those of clouds in the underdense region. Bottom panel: The average HI fraction of absorbing clouds, binned by NHI. The HI fraction of clouds in the overdense region is consistently lower than those of clouds in the underdense region. below 10\u22123 in all clouds except those in the highest bin selected using (nHI,min/nHI,peak = 0.9) in the overdense environment. Our clouds are largely very low metallicity, so would generally not result in metal detections in observations. This is roughly in agreement with available observations. Stocke et al. (2006) \ufb01nd that all of their O VI detections are within 1.15 Mpc of the nearest galaxy in regions surveyed to at least L\u2217, but even within this close distance only \u223c30% of Ly\u03b1 absorbers have O VI detections. Many of our clouds are more distant that 1.15 Mpc from any galaxy in our simulation (which identi\ufb01es galaxies down to below 109 M\u2299). In fact, most of our low-column density clouds are beyond 1.15 Mpc from the nearest galaxy (log(NHI/cm\u22122) < 13.1). Danforth et al. (2016) do not give distance information for their observed Ly\u03b1 absorbers, but \ufb01nd that 3% of 12.5 < log(NHI/cm\u22122) 7 Fig. 6.\u2014 The average metallicity of HI clouds, binned by NrmHI. The colors are the same as in Figure 3. The lines denote the median value in a bin and the shaded region spans the quartile range. The metallicity of clouds in either environment is quite low. < 13.5 Ly\u03b1 absorbers have metal detections, and this fraction rises to only 22% for 13.5 < log(NHI/cm\u22122) < 14.5 Ly\u03b1 absorbers. As discussed by several authors (eg. Werk et al. 2013, 2014; Danforth et al. 2016), the drop in detection rate with decreasing column density may be because absorber metallicity decreases with decreasing column density, as we \ufb01nd, or because the same metal fraction is increasingly di\ufb03cult to detect at low column densities. Low metallicity indicates that in most cases, the gas creating the absorbers has not recently been ejected from galaxies. Therefore this gas has either had very little interaction with out\ufb02ows, or was ejected at early times and has thoroughly mixed with the surrounding intergalactic medium (as discussed in Tepper-Garc\u00b4 \u0131a et al. 2012). This is particularly interesting when we compare absorbing clouds in the two environments. Although all of the clouds have low metallicity, in all but the highest column density bins the median metallicity of the absorbing clouds in the overdense box is lower than the median metallicity of clouds in the underdense box. When we combine this information with the fact that the average temperature of clouds in the overdense box is higher than the temperature of those in the underdense box (Figure 5), we conclude that these clouds are likely to have been shock heated through structure formation rather than galactic feedback. 4.3. Where are Absorbing Clouds? In order to create a complete picture of absorbing clouds, we must determine where they reside with respect to galaxies. We calculate the distance to the nearest HOP-identi\ufb01ed galaxy (see Section 2.1). We also calculate the distance to the nearest central galaxy, which is de\ufb01ned as a galaxy that is not within two r200 of any more massive galaxy, using the stellar mass as identi\ufb01ed with HOP. In order to \ufb01nd the smallest distance to any possible galaxy, we do not require a minimum stellar mass for our galaxies. Our results are qualitatively the same whether or not we include satellite galaxies, so we will focus on the distance to central galaxies. Fig. 7.\u2014 The distance between absorbing clouds and the nearest central galaxy, binned by NHI. The colors are the same as in Figure 3, although for clarity we only show the largest clouds (nHI,min/nHI,peak = 0.1). The lines denote the median value in a bin and the shaded region spans the quartile range. All of our clouds are quite distant from the nearest galaxy. In Figure 7 we plot the distance between absorbing clouds and the nearest central galaxy, binned by NHI. We see that in any NHI bin, the absorbing clouds in the overdense region are closer to galaxies than clouds in the underdense region. This is expected as there are many more galaxies in the overdense region. It is notable that the median distance for clouds in all but the highest column density bin is more than 500 kpc. This is in qualitative agreement with the observational \ufb01nding of the distances between Ly\u03b1 absorbers and nearby galaxies by Stocke et al. (2006). We \ufb01nd that the median stellar masses of the nearest galaxies in any NHI bin are below 2\u00d71010 M\u2299in either environment, and thus the absorbers tend to be more than 2 virial radii from the nearest galaxy. In fact, the median mass of galaxies closest to the absorbing clouds is low enough that they may not even produce a strong accretion shock (Dekel & Birnboim 2006; Keres et al. 2005). The Ly\u03b1 forest is formed well outside the circumgalactic medium of galaxies. In the overdense region, we also speci\ufb01cally checked the distance between absorbing clouds and the cD galaxy at the center of the most massive cluster in the simulation. We \ufb01nd that 75% of the clouds are more than 5 Mpc from the cD galaxy, or more than 2.5 rvir from the cluster center. The environment within the cluster is not determining the properties of absorbing clouds within the overdense region. 5. ENVIRONMENTAL EFFECTS ON LY\u03b1 ABSORBERS Why are absorbers in the overdense and underdense environments di\ufb00erent? We have found that the most dramatic di\ufb00erence in absorbing clouds is that their temperature is higher in the overdense region than in the underdense region. However, the low metallicity of absorbers and their large distance from nearby galaxies indicate that neither SN feedback nor halo accretion shocks account for this di\ufb00erence. In Figure 8 we show slices from the overdense and underdense re\ufb01ned regions of our simulation in the left and 8 Fig. 8.\u2014 Projections of thin slabs of part of the re\ufb01ned regions. The slabs are \u223c1.5 Mpc deep and 23 Mpc on a side. The right panels are of the overdense region and the left panels are of the underdense region. Top Panels: Projected temperature weighted by density. Second Panels: Projected density of all gas. Third Panels: Projected HI fraction of the gas weighted by density. Bottom Panels: Projected HI number density. The number densities shown span the column density of absorbing clouds we discuss in this paper. right panels, respectively. The top panels are projections of gas temperature weighted by density, the second panels are of total gas column density, the third panels are of the HI fraction weighted by density, and the bottom panels are the HI column density. The slices are about 1.5 Mpc in width, which is somewhat larger than most of the Ly\u03b1 absorbing clouds we \ufb01nd (Figure 4). These slices are of a subsection of the re\ufb01ned regions, with 23 Mpc sides. The slices highlight the cluster in the overdense region and contain the top of the void in the underdense region. If we focus \ufb01rst on the cluster in the overdense region, we see that for this very massive halo the accretion shock has heated the gas to temperatures at which, despite a high gas column density, the HI column density is very low. In general, we do not \ufb01nd Ly\u03b1 absorbers around massive halos with a strong accretion shock, in agreement with our \ufb01nding that absorbers tend to have temperatures below 105 K. Instead, we \ufb01nd that high HI column density tends to resides in \ufb01laments (1012.5 1014.5 cm\u22122). In the temperature projection the \ufb01laments are quite wide, more than 1 Mpc, with temperature gradients that indicate shocking from 9 Fig. 8 (Cont.).\u2014 Third and Fourth panels of Figure 8 structure formation. The high density regions of the \ufb01laments are narrower, and only in the center, cooler regions is there signi\ufb01cant HI column density. In the underdense region, we also see that much of the gas with HI column densities between 1012.5 1014.5 cm\u22122 resides in \ufb01laments. However, these \ufb01laments are much narrower in the temperature map, and rarely show signs of shocking in their temperature structure. We posit that the environment impacts Ly\u03b1 absorbers in the formation of cool gas in \ufb01laments between galaxies. Structure formation in the overdense region results in large collapsed structures outside of halos that have their own shocks that heat gas. This hotter gas has lower HI fractions and therefore lower HI column density. In Figure 9 we illustrate this point using the narrow projection of gas density from Figure 8. We have overplotted the positions of absorbing clouds whose HI peak density is within the central \u223c300 pc of the slab (for clarity as the results do not change if we vary the line of sight range along which we select absorbers). The colors of the spheres denote the column density of the absorbing cloud while the radius is half of the length of the absorber. We see that several large, low-column density absorbing clouds lie along the comparatively hotter \ufb01laments in the overdense region, while the low-column density absorbers in the (cooler) \ufb01laments in the under10 Fig. 9.\u2014 As in Figure 8, these are projections of the gas density in thin slabs of part of the re\ufb01ned regions. The slabs are \u223c1.5 Mpc deep and 23 Mpc on a side. The right panel is of the overdense region and the left panel is of the underdense region. The circles denote Ly\u03b1 absorbing cloud positions whose peak HI density is within the central \u223c300 pc of the slab. The circle color and size denote the absorber column density and size, respectively. dense region tend to be smaller. This di\ufb00erence in absorbers is above and beyond any di\ufb00erences that would be driven by UV background sources. In fact, UV sources might vary with environment in a way that is likely to exacerbate the di\ufb00erences between overdense and underdense environments. For example, quasars tend to reside in higher density regions, so would be more likely to ionize gas in the overdense region. Because the overdense region has more galaxies, ionization from star formation and AGN feedback would be more likely to impact absorbers in overdense environments. 6. CONCLUSIONS In this paper we have used a cosmological hydrodynamical simulation to examine the Ly\u03b1 forest in detail. We focused on two re\ufb01ned regions, an overand underdensity, representing +1.8\u03c3 and -1.0\u03c3 \ufb02uctuations in order to determine if the environment a\ufb00ects the nature of the absorbing gas. Our results are as follows: 1) We \ufb01nd very good agreement between our spectral HI column density distribution (CDD) and those in K14, indicating that our results on the HI CDD are robust and that resolution and simulation code have little impact on the HI CDD (Section 3). 2) The HI CDD in the overdense environment is steeper than in the underdense environment, which is most dramatically seen in the smaller number of high density absorbers in the overdense versus underdense environment (NHI \u22651013.7 cm\u22122) (Figure 2). 3) We \ufb01nd that there are physical di\ufb00erences in individual Ly\u03b1 absorbing clouds in the two environments, speci\ufb01cally that clouds in the overdense region are larger, hotter, and have lower HI fractions than those in the underdense region (Figures 4 5). 4) In both environments, the metallicity of Ly\u03b1 absorbing clouds is quite low, indicating that the gas was not recently expelled from galaxies. At lower column densities (NHI < 1014 cm\u22122), the metallicity is lower in clouds in the overdense region than in clouds in the underdense region (Figure 6). 5) Ly\u03b1 absorbers tend to reside far from galaxies (Figure 7), and even high column density clouds (NHI \u22651014 cm\u22122) are more than two virial radii from their nearest galaxy neighbor. In fact, much of the Ly\u03b1 forest resides along \ufb01laments between galaxies (Figure 8). We conclude that the environmental di\ufb00erence in the HI CDD slopes is driven by the temperature di\ufb00erences of the absorbing clouds. In the overdense region, the higher temperature and lower HI fraction means that clouds must be larger to have the same column density as clouds in the underdense region. We \ufb01nd that Ly\u03b1 absorbing clouds tend to be far from galaxies and reside in cool regions of \ufb01laments. Because \ufb01laments are naturally narrow structures, absorbers cannot be arbitrarily large. This results in a steeper HI CDD slope in the overdense region, which tends to require larger clouds. In earlier work, K14 termed the large di\ufb00erence between the the HI CDD predicted using HM12 on hydrodynamic cosmological simulations and the observed HI CDD the Photon Underproduction Crisis. We reiterate that the mismatch between observations and simulations points to a substantial and exciting gap in our current understanding of the low-redshift universe. As highlighted by Shull et a. (2015), a single UV background generically fails to reproduce a su\ufb03ciently large range of the HI CDD. Multiple partial matches between theoretical and observational HI CDDs highlight the types of sources 11 that must be observed in more detail and modeled with the highest \ufb01delity possible. Both the amplitude and the slope of the HI CDD are important clues to the exchange of energy between galactic and intergalactic scales. The HI CDD provides a key diagnostic of these largely degenerate models, and with further observational and theoretical constraints, can become even more useful. For observers, constraining the SFRD and QSO luminosity functions to better than a factor of two will dramatically decrease the current leeway in simulations, as will a more well-de\ufb01ned escape fraction from galaxies as a function of redshift and galaxy mass. Although we \ufb01nd that gravitational shocks are a stronger energy source heating the IGM than feedback at z=0 (also Cen & Chisari 2011), simulators\u2019 continued e\ufb00orts in correctly modeling the heating of gas through both stellar and AGN feedback, and the mixing of this gas into the IGM, is important for understanding IGM heating and ionization. Radiative transfer codes will be important to determine the range of in\ufb02uence of QSOs. We recommend that some simulations, where AGN feedback is implemented to be an important source of heat and ionizing photons even at z=0, be confronted with constraints provided by observations of Ly\u03b1 absorbers in di\ufb00erent environments, as we perform here, to understand their plausibility. Finding agreement across a broad range of Ly\u03b1 absorber column density (at least the entirety of 1012.5 1014.5 cm\u22122) is another important assessment of how well simulations reproduce observations. Knowing to what extent \ufb02ux sinks as well as sources can e\ufb00ect the HI CDD is critically important for narrowing in on the precise magnitude and origin of heat and ionizing photons in the local universe. Computing resources were in part provided by the NASA HighEnd Computing (HEC) Program through the NASA Advanced Supercomputing (NAS) Division at Ames Research Center and in part by a grant from the Ahmanson Foundation. The research is supported in part by NSF grants AST-1108700, AST15-15389 and NASA grant NNX12AF91G. ST was supported by the Alvin E. Nashman Fellowship in Theoretical Astrophysics.",
                    "introduction": "1. The high-redshift Ly\u03b1 forest has long been used for cosmology owing to its relatively simple structure theo- retically and observationally (e.g., Cen et al. 1994; Zhang et al. 1995; Hernquist et al. 1996; Miralda-Escude et al. 1996; Rauch et al. 1997; Weinberg 1998; Peeples et al. 2010). This structure, \ufb01rst understood using cosmolog- ical hydrodynamics simulations, emerges from the ther- modynamic conditions of Hydrogen within the cosmic web and depends only on cosmological parameters and atomic physics through the ionization and recombination rates of Hydrogen. While the values for cosmological pa- rameters have become exquisitely precise, the same is not true for the metagalactic ionization rate, \u0393, at any redshift. Kollmeier et al. (2014; K14) highlighted the use of the low-redshift Ly\u03b1 forest as a cosmic calorimeter and probe of the low redshift ionizing \ufb02ux, which is noto- riously di\ufb03cult to measure. While standard practice at high redshift, K14 found that the metagalactic photoion- ization rate required by their simulations to match the observed properties of the low-redshift Ly\u03b1 forest is a factor of \ufb01ve larger than the values predicted by state of the art ionization models of Haardt & Madau (2012; HM12) \u2014 a discrepancy between models and observa- tions they termed the \u201cPhoton Underproduction Crisis\u201d (PUC). This is illustrated when comparing the column density distribution (CDD) of Ly\u03b1 forest absorbers from their simulations, adjusted to di\ufb00erent values of \u0393, with data from HST. Prompted by K14, other authors also found they required higher photoionization rates than HM12 (e.g. Shull et al. 2015; Emerick et al. 2015; Puchwein et al. 2015), although, in Shull et al. (2015) the particular boosts required was a factor of 2-3 rather"
                },
                {
                    "url": "http://arxiv.org/abs/1509.05039v1",
                    "title": "Don't Forget the Forest for the Trees: The Stellar-Mass Halo-Mass Relation in Different Environments",
                    "abstract": "The connection between dark matter halos and galactic baryons is often not\nwell-constrained nor well-resolved in cosmological hydrodynamical simulations.\nThus, Halo Occupation Distribution (HOD) models that assign galaxies to halos\nbased on halo mass are frequently used to interpret clustering observations,\neven though it is well-known that the assembly history of dark matter halos is\nrelated to their clustering. In this paper we use high-resolution\nhydrodynamical cosmological simulations to compare the halo and stellar mass\ngrowth of galaxies in a large-scale overdensity to those in a large-scale\nunderdensity (on scales of about 20 Mpc). The simulation reproduces assembly\nbias, that halos have earlier formation times in overdense environments than in\nunderdense regions. We find that the stellar mass to halo mass ratio is larger\nin overdense regions in central galaxies residing in halos with masses between\n10$^{11}$-10$^{12.9}$ M$_{\\odot}$. When we force the local density (within 2\nMpc) at z=0 to be the same for galaxies in the large-scale over- and\nunderdensities, we find the same results. We posit that this difference can be\nexplained by a combination of earlier formation times, more interactions at\nearly times with neighbors, and more filaments feeding galaxies in overdense\nregions. This result puts the standard practice of assigning stellar mass to\nhalos based only on their mass, rather than considering their larger\nenvironment, into question.",
                    "authors": "Stephanie Tonnesen, Renyue Cen",
                    "published": "2015-09-16",
                    "updated": "2015-09-16",
                    "primary_cat": "astro-ph.GA",
                    "cats": [
                        "astro-ph.GA",
                        "astro-ph.CO"
                    ],
                    "main_content": "linked to the SFR from cold gas accretion. This model is focused only on the central galaxies in halos, as these are the only galaxies for which we could expect a relationship between gas and dark matter halo mass based on the two-mode theory of gas accretion (Kere\u02c7 s et al. 2005; Dekel & Birnboim 2006). A number of possible interactions can affect the gas, stellar, and dark matter mass of a satellite galaxy, as discussed in Boselli & Gavazzi (2006). Crain et al. (2009) use the GIMIC simulations\u2013 hydrodynamical \u201cre\u201d-simulations of the Millennium simulation at (-2, -1, 0, +1, +2)\u03c3 of the mean density on the scale of \u223c20 Mpc\u2013to determine whether halo mass is responsible for the differences in the SFR density (SFRD) in different environments. They find that the SFR to halo mass ratio is the same in all environments, and conclude that halo mass determines the rate at which galaxies form stars. Because of the difficulty in directly modeling the baryonic physics that drives gas cooling, star formation, and feedback, and using the theory that halo mass is the fundamental parameter that determines other galaxy properties, more analytic models have been used to connect galaxies to dark matter halos. In particular, standard Halo Occupation Distribution models (HODs) assume that halo mass is the fundamental parameter determining the stellar mass and internal processes of galaxies, and do not include any dependence on the larger environment in which the halo resides. These models are frequently used to make mock catalogues to interpret galaxy clustering measurements (e.g. Kauffmann et al. 1997; Jing et al. 1998; Benson et al. 2000; Seljak 2000; Peacock & Smith 2000; Ma & Fry 2000; Scoccimarro et al. 2001; Berlind & Weinberg 2002; Zheng et al. 2005; Tinker et al. 2008). Because the halo mass function depends on environment\u2013more massive halos form in higher density regions of the universe, called halo bias (e.g. 2 Kaiser 1984)\u2013these methods also reproduce the empirical \ufb01nding that higher stellar mass galaxies reside in regions of higher galaxy density. For example, Abbas & Sheth (2006) compare galaxy clustering in the SDSS DR4 (Mr < -21) to measurements in mock catalogues created using HODs and to measurements from an analytic halo model calculation. The authors argue that the three samples agree well enough that correlations between galaxy properties can be entirely explained by the variation of the halo mass function in di\ufb00erent environments (see also Skibba et al. 2006). Tinker et al. (2008) compare observed void statistics to those obtained using a standard HOD, and \ufb01nd that the sizes and emptiness of voids are in excellent agreement. However, more than the halo mass distribution has been shown to depend on the environment. Gao et al. (2005) use the Millennium Simulation to \ufb01nd that the \u039bCDM paradigm predicts that the clustering of dark matter halos depends not only on their mass but also on their formation time (the time at which the halo mass of the main progenitor has reached half of the \ufb01nal halo mass), an e\ufb00ect often called assembly bias. Speci\ufb01cally, low-mass halos (Mhalo < 6.15\u00d71012 h\u22121 M\u2299) that assemble early are much more strongly clustered than those that assemble late (see also Harker et al. 2006; Gao & White 2007; Wechsler et al. 2006; Wetzel et al. 2007). Clustering, measured using the 2-point autocorrelation function, increases with increasingly early formation times, and the signal is stronger as the length scale increases. Fakhouri & Ma (2009; 2010) \ufb01nd that the formation time of dark matter halos in the Millennium Simulation is earlier with increasing environmental density, measured using the dark matter mass within 7 Mpc of a galaxy. They further \ufb01nd that mass growth proceeds di\ufb00erently in di\ufb00erent environments, with more mergers in high-density regions and more di\ufb00use accretion in low-density regions. As Gao et al. (2005) point out, galaxy properties may depend on the assembly history of halos, and therefore models that ignore the age dependence of clustering do so at their peril. Berlind et al. (2006) examine SDSS groups and \ufb01nd that central galaxy color is correlated with clustering, but only for the most massive (>1014 M\u2299) galaxy groups. Groups with less red central galaxies cluster more than groups with redder central galaxies. They conclude that massive halos that formed earlier contain redder galaxies than more recently-formed halos. However, Yang et al. (2006) use the emissionand absorption-line strength in a galaxy\u2019s spectrum to study the SFR of the central galaxies of SDSS groups. They \ufb01nd that group halos at all masses with central galaxies with lower SFRs are more clustered than groups with highly star-forming central galaxies. Although Berlind et al. (2006) point out that emissionand absorption-line strength in a luminous red galaxy does not necessarily re\ufb02ect its g \u2212r color, it is not clear why these two groups get these seemingly opposing results. Much work has been performed studying assembly bias using SAMs or HODs. For example, Gonzalez & Padilla (2009) use a SAM to study the e\ufb00ect of the environment on galaxy SFRs. They \ufb01nd that most of the di\ufb00erences in the SFR between galaxies in di\ufb00erent large-scale environments can be explained by the environmental dependence of the halo mass function. Further, they conclude that assembly bias is the most likely candidate driving the small di\ufb00erences in the populations beyond those explained by the halo mass function. Croton et al. (2007) come to a di\ufb00erent conclusion using a SAM built into the Millennium Simulation. They compare the two-point autocorrelation functions for the galaxies formed in their SAMs to a population that has been shu\ufb04ed randomly into halos of the same mass (maintaining the relative separation between the central and its satellites). Shu\ufb04ing reduces the clustering of the entire sample. They then change their shu\ufb04ing scheme to also account for halo formation time (t50%) or concentration in addition to halo mass, but \ufb01nd that neither of these halo properties can account for the clustering differences seen in the SAM population versus the shu\ufb04ed population. They conclude that another unknown aspect of halo assembly or environment must be causing a large fraction of the bias. Zentner et al. (2014) \ufb01nd that assembly bias a\ufb00ects HOD modeling by comparing the HOD \ufb01ts to mock catalogues with and without assembly bias. They \ufb01nd that reasonable levels of assembly bias in the population can lead to systematic errors in the galaxy-halo connection inferred using standard HOD models, and conclude that incorporating assembly bias e\ufb00ects into future HODs should be a priority. Jung, Yee & Li (2014) use a SAM to study whether the stellar mass of galaxies with the same halo mass is a\ufb00ected in regions of di\ufb00erent large-scale (7 h\u22121 Mpc) density. They \ufb01nd a small di\ufb00erence, speci\ufb01cally that low-mass (<1012 M\u2299) halos have slightly higher stellar masses in high-density environments. In this paper we compare halo mass growth, stellar mass assembly and the star formation histories of galaxies from z=6 to z=0 in a large-scale (\u223c20 Mpc) overdensity and underdensity cosmologically simulated using the adaptive mesh re\ufb01nement (AMR) Eulerian hydrodynamical code Enzo (Bryan et al. 2014). At their respective volumes, they represent +1.8\u03c3 and -1.0\u03c3 \ufb02uctuations. These simulations provide us with an opportunity to compare di\ufb00erent large-scale environments within the same fully hydrodynamical cosmological simulation performed at sub-kpc resolution. It is important to compare across di\ufb00erent environments within the same simulation, as all physical processes are modeled in the same way. Our goal is to determine whether the stellar mass of galaxies is universally related to the halo mass of galaxies, or if it also depends on environment. After a brief description of our simulations (Section 2), we discuss our galaxy selection technique and our method for determining quantities for each galaxy in Section 2.1. In our results we compare the formation histories of galaxies in di\ufb00erent environments, binned either by their \ufb01nal halo mass (Section 3.1) or stellar mass (Section 3.2). In Section 4 we discuss several possible causes for the higher stellar masses found in galaxy halos in the overdense environment, ending with our comprehensive interpretation in Section 4.7. We then compare our results to other theoretical work on this issue (Section 5). Finally, in Section 6 we summarize our conclusions and discuss the implications of our results. 3 2. METHOD For the details of our simulations, we refer the reader to Cen (2012), although for completeness we reiterate the main points here. We perform cosmological simulations with the AMR Eulerian hydrodynamical code Enzo (Bryan 1999; Bryan et al. 2014). We use cosmological parameters consistent with the WMAP7-normalized LCDM model (Komatsu et al. 2011): \u2126M = 0.28, \u2126b = 0.046, \u2126\u039b = 0.72, \u03c38 = 0.82, Ho = 100 h km s\u22121 Mpc\u22121 = 70 km s\u22121 Mpc\u22121, and n = 0.96. We \ufb01rst ran a low resolution simulation with a periodic box of 120 h\u22121 Mpc on a side, and identi\ufb01ed two regions: an overdensity centered on a cluster and an underdensity centered on a void at z = 0. We then resimulated each of the two regions separately with high resolution, but embedded within the outer 120 h\u22121 Mpc box to properly take into account large-scale tidal \ufb01eld e\ufb00ects and appropriate \ufb02uxes of matter, energy and momentum across the boundaries of the re\ufb01ned region. The overdense re\ufb01ned region, or C box, is 21 \u00d7 24 \u00d7 20 h\u22123 Mpc3. The central cluster has an M200 of \u223c2 \u00d7 1014 M\u2299with a virial radius (r200) of 1.3 h\u22121 Mpc. The underdense re\ufb01ned region, or V box, is somewhat larger, at 31 \u00d7 31 \u00d7 35 h\u22123 Mpc3. At their respective volumes, they represent +1.8\u03c3 and -1.0\u03c3 \ufb02uctuations where \u03c3 is the density variance on the volume of the C and V boxes. Although these are large-scale overand underdense environments, these high-resolution boxes are much larger than the cluster or the void at their centers. Thus, there are galaxies at a range of local densities in both boxes, and there is substantial overlap of local densities between the two volumes (Tonnesen & Cen 2012). In both re\ufb01ned boxes, the minimum cell size is 0.46 h\u22121 kpc, using 11 re\ufb01nement levels at z = 0. The initial conditions for the re\ufb01ned regions have a mean interparticle separation of 117 h\u22121 kpc comoving, and a dark matter particle mass of 1.07 \u00d7 108 h\u22121 M\u2299. The simulations include a metagalactic UV background (Haardt & Madau 1996), a model for shielding of UV radiation by neutral hydrogen (Cen et al. 2005), and metallicity-dependent radiative cooling (Cen et al. 1995). The fraction and density of neutral hydrogen is directly computed within the simulations. Star particles are created in gas cells that satisfy a set of criteria for star formation proposed by Cen & Ostriker (1992), and reiterated with regards to this simulation in Cen (2012). Brie\ufb02y, A star particle is created if the gas in a cell at any time meets the following three conditions simultaneously: (1) contracting \ufb02ow, (2) cooling time less than dynamical time, and (3) Jeans unstable. A star particle of mass m\u2217= c\u2217mgas\u2206t/t\u2217is created (the same amount is removed from the gas mass in the cell), where \u2206t is the time step, t\u2217= max(tdyn,107 yr), tdyn = p 3\u03c0/(32G\u03c1tot) is the dynamical time of the cell, mgas is the baryonic gas mass in the cell, and c\u2217= 0.03 is the star formation e\ufb03ciency. Each star particle has a mass of \u223c106 M\u2299, which is similar to the mass of a coeval globular cluster. Once formed, the stellar particle loses mass through gas recycling from Type II supernovae feedback, and about 30% of the stellar particle mass is returned to the ISM within a time step. Supernovae feedback is implemented as described in Cen (2012): feedback energy and ejected metal-enriched mass are distributed into 27 local gas cells centered at the star particle in question, weighted by the speci\ufb01c volume of each cell, which is to mimic the physical process of supernova blastwave propagation that tends to channel energy, momentum, and mass into the least dense regions (with the least resistance and cooling). We allow the whole feedback process to be hydrodynamically coupled to surroundings and subject to relevant physical processes, such as cooling and heating, as in nature. The simulation used in this paper has compared several galaxy properties that depend critically on the feedback method to observations and found strong agreement (Cen 2011a-c; Cen 2012). We do not include a prescription for AGN feedback in this simulation, and as a result, our simulation overproduces luminous galaxies at the centers of groups and clusters of galaxies. This is discussed in detail in Cen (2011c), who shows that the luminosity function of the simulated galaxies agrees well with observations at z=0 except at the high-luminosity end. When Cen (2011c) adds an AGN feedback correction in the post-simulation analysis that most strongly a\ufb00ects halos with masses greater than 1013 M\u2299or galaxies with stellar masses above 4\u00d71012 M\u2299, the simulated luminosity function also agrees with observations at the high luminosity end. We do not include any post-simulation AGN correction because of uncertainties in its implementation, particularly across a large redshift range (see discussion in Tonnesen & Cen 2014), and as all of the galaxies we examine in this paper have halo masses less than 1013 M\u2299, we would expect the correction to be minor in any case. 2.1. Galaxies We use HOP (Eisenstein & Hut 1998) to identify galaxies using the stellar particles. HOP uses a two-step procedure to identify individual galaxies. First, the algorithm assigns a density to each star particle based on the distribution of the surrounding particles and then hops from a particle to its densest nearby neighbor until a maximum is reached. All particles (with densities above a minimum threshold, \u03b4outer) that reach the same maximum are identi\ufb01ed as one coherent group. The densest star particle is considered the center of the stellar group, or galaxy. In the second step, groups are combined if the density at the saddle point which connects them is greater than \u03b4saddle. The minimum number of star particles in a group that HOP will return as a galaxy is 20, but this lower mass limit of 2\u00d7107 M\u2299is well below the lowest mass of the galaxies followed in this paper at z=0, which is well above 109 M\u2299. We use HOP because of its physical basis, although we expect similar results would be found using a friends-of-friends halo \ufb01nder. HOP has been tested and is robust using reasonable ranges of values (e.g. Tonnesen, Bryan, & van Gorkom 2007). In this paper we measure the stellar mass (M\u2217), dark matter halo mass (Mhalo), and SFR of galaxies. Stellar mass is determined by adding the mass of each star particle identi\ufb01ed by HOP to belong to a galaxy. The dark matter halo mass is calculated by summing the mass of all the dark matter particles out to r200 (the radius within which the average density of the dark matter halo is 200 times the critical density). We also categorize our galaxies into centrals and satellites. Central galaxies are those galaxies that are not within r200 of any more massive galaxy, using the stel4 lar mass as identi\ufb01ed with HOP. Satellite galaxies are de\ufb01ned as within r200 of a more massive galaxy. Our qualitative results do not depend on our speci\ufb01c choice of radius, and are qualitatively the same if we use a radius of 2 r200. In this paper, because we are studying the connection between halo mass and stellar mass, we only focus on central galaxies. Lackner et al. (2012) describe in detail the merger trees that we will use in this paper, updated to include additional redshift outputs. Brie\ufb02y, the method tracks the stellar particles from one galaxy to another in sequential redshift slices. If most of the stars in galaxy B at redshift 0.05 are in galaxy A at redshift 0, then we consider galaxy B to be the parent of galaxy A. If several galaxies contribute stars to galaxy A, the galaxy that contributes the most stellar mass to galaxy A is the main progenitor. A galaxy can be tracked to the minimum stellar mass identi\ufb01ed by HOP, \u223c2\u00d7107 M\u2299, and this sets the minimum initial mass possible for galaxies we track. We note that not all galaxies are initially identi\ufb01ed with such a small set of particles. In this paper we follow the stellar and dark matter mass histories of galaxies, so select only galaxies that have been tracked through the merger trees from a minimum redshift. As we are examining whether galaxy stellar mass grows di\ufb00erently in lowversus high-density environments, we focus on galaxies that can be tracked to at least a redshift of 1. We compared these results to a sample that could be tracked to at least a redshift of 3 to include the peak of the SFRD (Hopkins & Beacom 2006; Karim et al. 2011; Seymour et al. 2008; Brinchmann et al. 2004; Reddy & Steidel 2009; Bouwens et al. 2007), and found no qualitative di\ufb00erences in our results. In fact, we also \ufb01nd that if we compare the entire set of HOP-identi\ufb01ed galaxies in each environment (as in Section 5), we \ufb01nd the same results as when we focus on our tracked samples of galaxies. This is an important veri\ufb01cation exercise because demanding that a galaxy can be tracked to z=1 is essentially demanding that a galaxy has a stellar mass of at least 2\u00d7107 M\u2299by that redshift. Particularly in our lowest mass bin, this will tend to select galaxies with higher z=0 stellar masses. Because we \ufb01nd the same results when we include all galaxies at individual outputs, we know that this selection criterium does not e\ufb00ect our results. However, as one of the goals of this paper is to consider the growth of galaxies over time, we focus on the tracked sample. 3. RESULTS 3.1. Matching Halo Mass In order to compare the properties of galaxies over time, we have two galaxy samples: those in the largescale underdensity (V box) and those in the large-scale overdensity (C box), both of which must be tracked to at least z=1. Recall that in this paper we only consider central galaxies. While this includes most galaxies in the V box (more than 90% of galaxies at z=0), at lower masses in the C box there are a large fraction of satellite galaxies (\u223c35% at z=0), so the mass growth of the galaxies we follow is not necessarily representative of the C box population as a whole. In order to present our results the most clearly, we have binned both samples by halo mass at z=0. We have veri\ufb01ed that the speci\ufb01c mass ranges do not a\ufb00ect our results: we have selected our samples in several di\ufb00erent ways and found that our results are robust, even when we use C box samples that have slightly lower halo masses than their V box counterparts. We consider four mass bins, with Mhalo/M\u2299between 10111011.5, 1011.5-1011.9, 1011.9-1012.3, and 1012.3-1012.9. In Figures 1-5 we show several properties of our galaxies over our tracked redshift range. In all \ufb01gures, the solid lines are the median value of the sample, and the shading denotes the middle range of values (25-75 percentiles). The V box galaxies (underdense environment) are shown in blue and the C box galaxies (overdense environment) are shown in red. The vertical lines are the median redshift at which the halo has grown to half of its \ufb01nal mass (formation time). Until our minimum tracking redshift, z=1, new galaxies can be added to the set, which may decrease the median halo or stellar mass values. This can result in the sometimes dramatic di\ufb00erences in median values as galaxies are added to the sample, particularly in the lowest mass bin. These jumps are not important to our results, which as we have discussed are insensitive to our sample selection, including the redshift to which we track galaxies. In order to speed post-processing of our galaxy parameters, we use coarse radial bins to determine r200, and do not calculate the average overdensity continuously. This means that the halo mass can vary, as seen particularly at late times in the underdense box, because a small difference in the radial density pro\ufb01le can result in a large variation in our r200 due to the bin size, and therefore Mhalo may vary. These variations also do not a\ufb00ect our results. 3.1.1. Halo Mass First we consider the halo mass of our galaxy samples in Figure 1. We can compare the formation time (or halo age) of our tracked galaxies in the overdense and underdense environments. As in Gao et al. (2005), we de\ufb01ne the age of a halo using the redshift at which the mass of the main progenitor halo is 50% of the \ufb01nal halo mass. Our outputs are in redshift steps of 0.05 and 0.1 in the C and V box, respectively, which sets our uncertainty on the halo age of any individual galaxy. If we do not start tracking a galaxy until after it has reached half of its \ufb01nal mass, we set the formation time to the earliest time tracked. We compare our median formation time including these estimated values to a median formation time calculated using only the formation times for galaxies that we begin tracking when they are less than 50% of their \ufb01nal halo mass, and \ufb01nd that for the three highest bins the change is minuscule. The lowest bin, that tends to begin tracking galaxies at later times, shifts to earlier median formation times when only the smaller sample is used. In the lowest mass bin, from 1011-1011.5 M\u2299, the formation times go from being similar in the two environments to being at higher redshifts in the overdense sample. If we compare across di\ufb00erent masses in the same environment, we \ufb01nd that in our underdense samples, as in Behroozi et al. (2013), the halo age decreases as halo mass increases. This is evident when comparing the highest mass bin to any of the lower mass bins. In contrast, the overdense galaxy samples tend to have slightly decreasing formation times with increasing mass until the 5 Fig. 1.\u2014 The median halo mass of tracked galaxies from a possible maximum redshift of six. Galaxies are binned according to halo mass at z=0. The solid lines are the median value of the sample of tracked galaxies, and the shading denotes the middle range of values (25-75 percentiles). The V box galaxies (underdense environment) are shown in blue and the C box galaxies (overdense environment) are shown in red. The vertical lines are the median redshift at which the halo has grown to half of its \ufb01nal mass. Our galaxy sample selection has selected galaxies with similar z=0 halo masses in the V and C boxes. See Section 3.1 for details and Section 3.1.1 for discussion. most massive halo bin (1012.3-1012.9 M\u2299), which has the oldest formation time. It is possible that our selection criterion that a galaxy must remain a central galaxy to z=0 eliminates the older low-mass galaxies, which will effect the median formation time in the overdense environment more strongly because a higher fraction of galaxies are satellites. Comparing between galaxies of the same halo mass in underdense versus overdense environments, we \ufb01nd that in general halos in the overdense region have older or similar formation times than galaxies in the underdense environment. This tendency agrees with the halo bias Fig. 2.\u2014 The median stellar mass of tracked galaxies binned by halo mass at redshift 0. Lines are as in Figure 1. The C box galaxies in the overdense environment (red) tend to have higher \ufb01nal stellar masses than the V box galaxies in the underdense environment (blue), and the crossover redshift from lower to higher stellar masses increases with increasing redshift. See Section 3.1.2 for discussion. \ufb01ndings of Gao et al. (2005), that more clustered halos tend to collapse \ufb01rst. As we expect, the biggest di\ufb00erence is in the highest mass bin (1012.3-1012.9 M\u2299), where we are the least likely to exclude halos from our sample because they become satellites. We \ufb01nd that, in agreement with the similar halo ages, the halo growth curves are very similar in the lower mass bins (1011-1011.5 M\u2299and 1011.5-1011.9 M\u2299), particularly after about z=2.5. However, in the highest Mhalo bin, the C box galaxies\u2019 halo growth \ufb02attens from about z=1, while the galaxies in the V box continue to grow more massive. In summary, in agreement with previous N-body simulations (e.g. Gao et al 2005 and see our Introduction), we \ufb01nd evidence of assembly bias. Also, in the highest 6 Fig. 3.\u2014 The median stellar mass to halo mass ratio (SMHM) of tracked galaxies binned by halo mass at redshift 0. Lines are as in Figure 1. The galaxies in the overdensity (C box, red lines) have higher SMHM ratios than those in the underdensity (V box, blue lines). This result holds even comparing between galaxies in di\ufb00erent mass bins. See Section 3.1.2 for discussion. mass bin (1012.3-1012.9 M\u2299), we see a hint that at low redshift (z<1) the dark matter mass growth of massive halos \ufb02attens in galaxies in the overdense environments in comparison to halos in the underdense environment. 3.1.2. Stellar Mass In Figure 2 we focus on the stellar mass of our galaxies. In the overdense (C box) environment, the stellar mass growth from z=1 to z=0 is the steepest in the lowest halo mass bin (1011-1011.5 M\u2299), indicating a trend of downsizing in stellar mass growth with decreasing redshift. In all mass bins in the underdense environment and in the upper three mass bins in the overdense sample the stellar mass growth from z\u22641 is similar. However, the galaxies in the underdense environment grow more than the galaxies in the overdense environment in all but the lowFig. 4.\u2014 The median SFR of tracked galaxies binned by halo mass at redshift 0. Lines are as in Figure 1. The SFRs of galaxies in the overdensity (C box, red lines) tend to be lower than those of galaxies in the underdensity (V box, blue lines) at z\u22654, but become higher at lower redshifts. See Section 3.1.3 for discussion. est mass bin, indicating that stellar growth shifts from overdense to underdense regions over time. In all of the halo mass bins, the median stellar mass of galaxies in the overdense box is higher than that of galaxies in the underdense box by z=0. In all but the highest mass bin (1012.3-1012.9 M\u2299), the median stellar mass in the C box galaxies begins lower than the median stellar mass for the V box galaxies. The redshift at which the C box stellar mass crosses the V box stellar mass tends to decrease with decreasing mass\u2013from the highest mass bin always having higher stellar mass galaxies in the C box to a crossover at z\u223c1 in the lowest mass bin. However, the stellar mass growth at very low redshift (z\u22641) is generally \ufb02atter in the C box galaxies than in the V box galaxies, indicating less recent star formation, in agreement with observations (e.g. Szomoru et al. 1996). The stellar mass to halo mass (SMHM) ratio, shown 7 Fig. 5.\u2014 The median sSFR of tracked galaxies binned by halo mass at redshift 0. Lines are as in Figure 1. Galaxies follow the sSFR-stellar mass relation. Comparing galaxies with the same z=0 halo mass, we \ufb01nd that at early times the sSFR of galaxies in the overdensity (C box, red lines) is higher with respect to the sSFR of galaxies in the underdensity (V box, blue lines) than at z=0. See Section 3.1.3 for discussion. in Figure 3, also re\ufb02ects the higher stellar mass in halos in the overdense environment. In general, even when comparing across di\ufb00erent halo mass bins, we see that the SMHM ratio is higher in the overdense environment, showing that the halo mass distribution does not e\ufb00ect this result. In other words, by z=0, the SMHM ratio of overdense galaxies in any mass bin is higher than the SMHM ratio of underdense galaxies in any halo mass bin. Comparing within each environment, we \ufb01nd that the SMHM ratio at z=0 is the highest for galaxies with the highest halo masses, unlike previous results (e.g. Moster et al. 2012, Guo et al. 2010, Behroozi et al. 2013 and references therein) that the peak SMHM ratio will be found for galaxies with halo masses of about 1012 M\u2299. These previous results use several methods to match results to existing data, and we do not call their overarching SMHM results, that do not consider di\ufb00erent largescale environments, into question. Indeed, our SMHM ratio tends to be too high. This may indicate that our feedback mechanisms are ine\ufb03cient, particularly at the lowest and highest masses, which we will discuss in detail below in Section 4.6. We conclude that the lowest mass and highest mass halos have the most cold gas that is able to form stars, either by never shock-heating accreting gas to high temperature or by having a high enough central density to cool gas and form stars. As our feedback prescription is the same across all environments, the di\ufb00erences between galaxies in the overdense and underdense regions should be real and not due to our particular numerical methodology, although we cannot eliminate the possibility that our speci\ufb01c feedback scheme could smooth out or exacerbate any di\ufb00erences between galaxies in di\ufb00erent environments. We conclude that the SMHM ratio di\ufb00ers in these di\ufb00ering large-scale environments, with central galaxies in overdense environments having higher SMHM ratios than those of central galaxies in underdense environments. 3.1.3. Star Formation Rate We next focus on the SFRs of the galaxies in Figure 4. For all galaxy samples but the highest mass galaxies in the underdense environment, the SFR initially increases to an early peak, then decreases to z=0. This follows our expectations, because as shown in Cen (2011c) our simulated SFR density history agrees well with observations that show a peak between z=2-3 followed by a declining SFRD. When we compare galaxies of the same mass in different environments, we \ufb01nd that for all but the highest mass galaxies, the SFR in galaxies in the overdense environment begins lower than the SFR in galaxies in the underdense environment. The SFR of the C box galaxies increases with respect to the SFR of the V box galaxies as the universe ages, eventually overtaking the SFR of V box galaxies. The redshift at which the C box SFR becomes higher than the V box SFR tends to decrease for decreasing halo mass. In our highest mass bin (1012.31012.9 M\u2299), the C box SFR begins higher than the V box SFR, but decreases quickly after z=1. In Figure 5 we see that in either environment at z=0 our galaxies follow the sSFR-stellar mass relation, with lower mass galaxies having higher sSFRs. We also see that at early times the sSFR of galaxies in the overdense environment tends to be somewhat higher than the sSFR of galaxies in the underdense environment. At late times, the z=0 sSFR is either similar in the two environments, or higher in the V box than in the C box, probably re\ufb02ecting the sSFR-M\u2217relation. This may also agree with the Szomoru et al. (1996) observational result that galaxies in the Bootes Void tend to lie above the Tully-Fisher relation using the B-band magnitude. The comparison between the star formation histories of these galaxies align with the comparative stellar mass growth of these galaxies. 3.2. Matching Stellar Mass In order to compare the properties of galaxies using a more easily observed quantity, we verify our results when 8 we bin galaxies by their stellar mass at z=0. We \ufb01nd that, as when we bin by halo mass, galaxies in the overdense region tend to have higher SMHM ratios. Unlike when we bin by halo mass, we \ufb01nd that the SFRs and sSFRs in the two environments are more similar by z=0, as we might expect given that the \ufb01nal stellar mass is quite similar. However, the z=0 SFR and sSFR of our massive galaxies in the underdense region tends to be slightly higher than in the overdense region. Thus, depending on the stellar masses of the galaxies we compare, the sSFR is the same across di\ufb00erent environments, or galaxies of the same mass are bluer in underdense environments than in overdense environments (Yang et al. 2006; Rojas et al. 2004; Grogin & Geller 1999,2000; Szomoru et al. 1996). 4. DISCUSSION We will now discuss several possible causes of this difference in the SMHM ratio in galaxies in di\ufb00erent environments. Finally, we will propose our synthesized picture of how higher-density large-scale environments could produce galaxies with high SMHM ratios. 4.1. Formation Time We \ufb01rst discuss whether the formation time, de\ufb01ned as in Gao et al. (2005) and marked with vertical lines in Figures 1-5, is related to the increased SMHM ratios in the overdense environment. We see a clear trend that the C box galaxy populations tend to have earlier formation times and higher SMHM ratios. Although the sample used in this paper of overdense galaxies is slightly more massive than the galaxies in the underdense region, we have veri\ufb01ed that this result does not depend on the mass distribution of the two samples by selecting an overdense galaxy sample that has slightly lower masses than the underdense sample. However, we \ufb01nd that more subtle di\ufb00erences in formation time are not clearly related to the \ufb01nal SMHM ratios. Examining Figure 3, we see that the two largest di\ufb00erences in the SMHM ratios are in the halo mass bins from 1011.5 1011.9 and 1011.9 1012.3. These mass bins have the smallest di\ufb00erences in the formation times between the overdense and underdense populations. The largest di\ufb00erence in formation times is in the highest mass bin (1012.3-1012.9 M\u2299), and the di\ufb00erence between the \ufb01nal SMHM ratios in the two environments is among the smallest. To summarize, we \ufb01nd that galaxies in the overdense environment have both earlier formation times and higher SMHM ratios than galaxies in the underdense environment. However, an earlier formation time does not necessarily lead to a higher SMHM ratio, as seen by comparing the galaxies in the underdense environment in Figure 3, and, as we discussed above, a larger di\ufb00erence in formation times does not force a larger di\ufb00erence in SMHM ratio. 4.2. Tidal Stripping of DM Halos? Several recent works have argued that assembly bias, the earlier formation times of halos in higher density environments, can be explained by the increased tidal interactions with neighbors in higher density environments. N-body simulations have shown that at late times, the tidal \ufb01eld from massive neighbors can halt halo growth and even in some cases reduce halo mass (Avila-Reese et al. 2005; Maulbetsch et al. 2007; Wang et al. 2006; Diemand et al. 2007; Hahn et al. 2009; McBride et al. 2009; Wang et al. 2011). Wang et al. (2007) specify that halos in overdense environments cannot accrete dark matter because of the high velocity dispersion of the dark matter. These works generally \ufb01nd that tidal e\ufb00ects are strongest for low-mass halos. We might expect to see several signatures of this e\ufb00ect on our results. First, we would expect slower late-time growth of halos in the overdense region compared to halos in the underdense region. Secondly, we would expect that within the overdense box, low mass halos would have slower late-time growth than high mass halos. Finally, we would expect tidal e\ufb00ects to cause the largest di\ufb00erence between galaxies in the overdense versus underdense environment for galaxies with the lowest halo mass. In agreement with our \ufb01rst prediction, we see that the highest halo mass bin (1012.3-1012.9 M\u2299) shows slower growth in the Mhalo of the galaxies in overdense regions at late times (z<1; Figure 1). Also, as discussed above (Section 4.1), we also \ufb01nd that the formation time of galaxies in the higher density environment tends to be earlier than in the lower density environment. However, when we test the second prediction by comparing di\ufb00erent mass ranges within the overdense box, we do not \ufb01nd the expected trend. As discussed in Section 3.1.1, the halo age is the oldest for the highest halo mass bin in the overdense box, indicating that the latetime halo growth of low mass halos is larger than that of the highest mass halos. If we focus on halo growth from z=1 to z=0, we \ufb01nd that most mass bins increase by about the same factor. A caveat to this result is that the smaller-scale environment within the large-scale overdensity is not necessarily the same surrounding galaxies of di\ufb00erent masses. In fact, the number of galaxies within 2 Mpc of the tracked galaxies decreases with decreasing halo mass, so a careful comparison may show that in the same smaller-scale density \ufb01eld, lower mass halos grow more slowly at late times. Finally, against our third expectation, the di\ufb00erence between the stellar mass of the lowest mass galaxies (1011-1011.5 M\u2299) is clearly the smallest of any of the mass bins, and the similarity of the SMHM ratio supports that \ufb01nding. Higher mass bins (1011.5-1011.9 M\u2299 and 1011.9-1012.3 M\u2299) have the largest SMHM ratio difference. Therefore, while we \ufb01nd evidence that tidal truncation of accretion and/or tidal stripping of dark matter halos is occurring in the overdense environment by comparing the late-time growth of halos, because the di\ufb00erence in formation time is not the largest for low-mass galaxies and because the di\ufb00erence in the z=0 SMHM ratio is the smallest for low-mass galaxies, we do not think that tidal e\ufb00ects are the main driver of our results. 4.3. Local Galaxy Density Tidal e\ufb00ects on galaxies may come from local halos, and we have not normalized for the local galaxy density. Indeed, in all of the mass bins, the galaxies in the overdensity (C box) have a larger median number of galaxies within 2 physical Mpc (pMpc) of the tracked sample than the galaxies in the underdensity (V box). In order to determine if the local galaxy density within 2 pMpc 9 Fig. 6.\u2014 The SMHM ratio (left) and the number of galaxies within 2 pMpc of galaxies (number of nearby neighbors plus the galaxy itself), with an additional criterium for the overdense (C box) sample that the z=0 number of nearby galaxies is less than or equal to 2 (3 including the galaxy). Even if we select C box galaxies with lower local densities than that of V box galaxies, the SMHM ratio remains higher. See Section 4.3 for discussion. is in fact causing the di\ufb00erences in the SMHM ratios, we select a subset of C box galaxies in each mass bin that \ufb01t the additional criteria that at z=0 the number of galaxies within 2 pMpc of the C box galaxy is three or less, including the galaxy itself, meaning two or fewer neighbors. We choose the upper limit of two neighbors because the median number of neighbors in the V box sample is two in our middle two mass bins (1011.5-1011.9 M\u2299and 1011.9-1012.3 M\u2299), one in our lowest mass bin, and four in our highest mass bin. Thus we can compare this \u201dlow local-density\u201d C box sample to the complete, unchanged, V box sample. In Figure 6 we show the SMHM ratio and number of galaxies within 2 pMpc in this much reduced sample. The small sample size of C box galaxies is most dramatic in the highest halo mass bins. In the highest mass bin (1012.3-1012.9 M\u2299) there is only one galaxy in the C box sample until z=1.2, and only two galaxies thereafter. The second highest bin also only has two galaxies in the C box (1011.9-1012.3 M\u2299), and the third bin has three (1011.5-1011.9 M\u2299). The C box samples in the lowest mass bin, 1011-1011.5 M\u2299, has 22 galaxies. Due to these small samples, the conclusions we can draw are necessarily tentative. While at early times the C box galaxies always have more neighbors, by z=1 the numbers are similar in the two environments, and by z=0 the number of neighbors in the underdense environment is generally slightly more than in the overdense environment (by construction, due to our selection criteria). We note that this may indicate more mergers in the higher density environment, in agreement with Fakouri & Ma (2009). However, even us10 ing this speci\ufb01cally selected sample, the SMHM ratio is higher in the overdense (C box) sample. Therefore, when examining a z<1 galaxy sample, simply forcing the number of galaxies to be the same in 2 Mpc regions is not enough to damp out larger-scale environmental e\ufb00ects. 4.4. Satellites We next brie\ufb02y consider whether satellites could have an e\ufb00ect on the SMHM ratio. First, satellites will add to the total dark matter mass within one virial radius before the stellar particles merge to be identi\ufb01ed as a single object by HOP, so more satellites might lead to lower SMHM ratios. It is also possible that gravitational e\ufb00ects from an orbiting satellite could drive gas towards the center of the central galaxy and increase the SFR, resulting in higher SMHM ratios. However, the di\ufb00erences in the number of satellites between the overdense and underdense samples are quite small. None of the central galaxies in the lowest mass bin have satellites identi\ufb01ed by HOP (which identi\ufb01es stellar groups of 20 particles, or about 2\u00d7107 M\u2299). In the second lowest halo mass bin, the median number of satellites is always zero, although the 75 percentile can extend to one satellite in both the C and V box samples. In the second highest mass bin the median number of satellites varies between 0 and 1, with the overdense sample tending to have more. Finally, in the highest mass bin, after z\u223c3 the galaxies in the underdense sample have a median number of 1-2 satellites while the galaxies in the overdense sample have a median number of satellites between 0-1.5 (a median of 1.5 can occur with an even number of galaxies in the sample). While satellites may have something to do with the lower SMHM ratio in the underdense galaxies in the highest mass bin, it is unlikely that they play a role for the majority of galaxies. 4.5. Gas supply a\ufb00ected by the large-scale environment? We now discuss whether the gas supply available to form stars in galaxies of the same halo mass may differ in di\ufb00erent environments. Clearly, the dark matter density in the overdense region is higher than in the underdense region. If baryons generally trace dark matter, there must be therefore more gas available in the overdense region. Indeed this is the case in our simulation, as the global baryon fraction di\ufb00ers by less than 5% in the C and V boxes. The question is then: why does more gas form stars in halos in the overdense region? In recent work, Cen (2014) has found that the number of cold streams feeding galaxies correlates with the SFR. Therefore, we posit that if galaxies in the overdense environment have more cold streams, then more gas may be able to form stars. Cen (2014) also argues that streams have higher densities in environments that are e\ufb00ected by gravitational heating. In our higher density environment, individual galaxy halos are more likely to collapse within denser \ufb01laments or Zeldovich pancakes, which may result in more higher density cold streams. However, Fakhouri & Ma (2010), examining the dark matter-only Millennium Simulation, \ufb01nd that although there is more di\ufb00use dark matter around halos in highdensity environments, the accretion rate of di\ufb00use dark matter is higher in low-density environments. They propose that this may be because di\ufb00use material is dynamically hotter in high-density environments, and therefore unable to accrete onto halos. Although determining the environmental dependence of galaxy accretion from cold streams is beyond the scope of this paper, in future work we will compare the cold streams accreting onto galaxies in overdense versus underdense regions. 4.6. Stronger Feedback We can now discuss the possible e\ufb00ects of including AGN feedback or changing the strength of SN feedback on our results. Including AGN feedback would have the most e\ufb00ect on high-mass galaxies (Mhalo \u22651013 M\u2299), which are not the focus of this work. While there would be some effect on the galaxies in our highest mass bin, it would be quite small (as these halos are <1013 M\u2299). Also, this e\ufb00ect would be smaller at earlier times, before the AGN became massive, although Schaye et al. (2010) \ufb01nd that AGN feedback begins a\ufb00ecting the SFR of massive galaxies as early as z\u223c3. However, we note that the stellar mass of the C box galaxies in the highest halo mass bin is always (to z\u223c6, the entire time that galaxies are tracked in the simulation) higher than the stellar mass of the V box galaxies. Therefore, we conclude that including AGN feedback would not strongly a\ufb00ect our results. As discussed above, we posit that much of the di\ufb00erence in the stellar mass of galaxies in underdense versus overdense environments is due to di\ufb00ering gas supply. Therefore, decreasing the energy input from supernovae feedback would not bring the stellar masses of galaxies in these di\ufb00erent environments into agreement and might increase the di\ufb00erence. On the other hand, increasing the strength of SN feedback may bring the stellar masses of galaxies in these di\ufb00erent environments into better agreement. As shown in Figure 12 of Cen (2011c), the speci\ufb01c cold gas in\ufb02ow rate is always higher than the sSFR, in both the C and V boxes, which is likely due to SN feedback regulating star formation rates. Therefore, it may be possible to eliminate any di\ufb00erences with environment if we were to increase the strength of our feedback to lower the SFR at all halo masses. As increasing the feedback strength would a\ufb00ect halos in both the overdense and underdense environments, we expect that a small change would not be enough to bring the stellar masses into agreement. Therefore we are hesitant to invoke increased feedback to remedy this di\ufb00erence, as in several papers we have compared our simulations to observations and found good agreement. For example, the SFRD in our two extreme regions brackets the observed global SFRD (Cen 2011c), and dramatically affecting the SFR of galaxies in our simulations would have a signi\ufb01cant e\ufb00ect on this measurement. As shown in Cen (2011c), the speci\ufb01c cold gas in\ufb02ow rate is higher than the sSFR for galaxies in both the C and V boxes, indicating self-regulation of SF. However, the di\ufb00erence between the speci\ufb01c in\ufb02ow rate and the sSFR is highest at high redshift (z>3), and at these high redshifts V galaxies have a higher in\ufb02ow to sSFR ratio. Therefore, we \ufb01nd that SN feedback is making SF less e\ufb03cient in galaxies in the underdense environment. Because our current feedback scheme seems to a\ufb00ect the gas consumption rate in V galaxies more strongly than in C galaxies, we infer that increasing the feedback strength 11 would only exacerbate the di\ufb00erence in the populations. Although we cannot use SAMs to make strong predictions for hydrodynamical simulations, we note that in Jung et al. (2014) the authors vary their star formation feedback strength by a factor of four and \ufb01nd no qualitative di\ufb00erence in their result for low mass halos that galaxies in dense environments have higher stellar masses than galaxies in underdense environments. Finally, even if we devised a feedback prescription that eliminated the di\ufb00erences in SFR and therefore stellar mass in halos in di\ufb00erent large-scale environments, our results are interesting because they indicate that gas accretion di\ufb00ers across di\ufb00erent large-scale environments, and is not solely dependent on halo mass. 4.7. How environment a\ufb00ects the SMHM ratio We conclude that the SMHM ratio depends on more than the halo mass or local (2 pMpc or less) galaxy density at z=0. Our results point to a picture in which the combination of earlier formation times, enhanced interactions, and more \ufb01laments are the likely causes of the increased SMHM ratios in galaxies in higher density environments. First, formation time plays a role. Galaxies in the overdense region have earlier formation times. An earlier formation time means that the galaxies in the overdense region grow more quickly at earlier times, when all galaxies have higher SFRs and more star-forming gas available. Therefore, their higher halo mass at z>1 allows them to form more stars when rates are high. As we are considering halos that all have z=0 masses below 1013 M\u2299, the halos are not massive and hot enough to quench cold accretion and/or star formation at early times. Second, interactions with nearby neighbors play a role. Galaxies in overdense environments have more nearby neighbors, particularly at early times. In Figure 6, where we have forced the z=0 number of neighbors in the C box to be less than in the V box, we see that at early times the SMHM ratio is lower and the number of neighbors is higher in the galaxies in the overdense region than in those in the underdense region. The SMHM ratio increases in the C box galaxies relative to the V box galaxies, as the number of neighbors decreases in the C box to equal the number of neighbors are V box galaxies. As discussed in Cen & Safarzadeh (2014), interactions \ufb01rst drive enhanced star formation in massive galaxies, then at later times a\ufb00ect lower mass galaxies. In agreement with this scenario, in Figure 6 (and Figure 3) the SMHM ratio of the C box galaxies crosses that of the V box galaxies at later times for lower mass galaxies. Finally, \ufb01lamentary structure a\ufb00ects galaxy growth. As we discuss in Section 4.5, Cen (2014) \ufb01nds that number of \ufb01laments correlates with SFR. Overdense regions are likely to have more \ufb01laments that can feed galaxies through smooth accretion and increase SFRs. In particular, the growth in both the stellar and dark matter mass of galaxies in the overdense region happens at earlier times, when \ufb01lamentary accretion is more likely to be able to strongly increase the mass of galaxies, and gas consumption into stars is more e\ufb03cient (Cen 2011c). At later times, \ufb01lamentary accretion becomes less important in general, which is why \ufb01laments can impact the SMHM ratio even of galaxies in the large scale overdensity that are in local underdensities by z=0. The relative SMHM ratios of galaxies in di\ufb00erent environments depends on the mass of the galaxies. In the two most massive bins in Figure 3 the di\ufb00erence between the SMHM ratio in the two environments peaks before z=0. This is because gas accretion and star formation have slowed in the high mass galaxies in the overdense environment, but are still continuing in the high mass galaxies in the underdense environment. The di\ufb00erence in the SMHM ratio remains similar from z=1 to z=0 in the second mass bin (1011.5-1011.9 M\u2299), and is increasing for galaxies in the lowest mass bin. We see this trend with mass re\ufb02ected in Figure 5, that the sSFR in the highest mass bin is lower in the overdense than in the underdense environment, while at the lowest halo masses the sSFR is similar in the overdense environment. Therefore, we suspect that for even higher masses, by z=0 the di\ufb00erence in SMHM ratio would be entirely wiped out by the higher sSFR in the low density environment. In summary, the environment a\ufb00ects the formation time of halos, which in turn a\ufb00ects how gas-rich the universe is when they are massive enough to quickly accrete gas and form stars. Also, galaxies in higher density largescale environments have a larger number of neighbors, particularly at early times. These interactions can drive gas instabilities and star formation. Finally, galaxies in higher density environments are likely fed by more, and higher density, \ufb01laments. 5. COMPARISON WITH OTHER WORK Much of the work performed examining how environment, often measured through clustering, a\ufb00ects galaxy properties has been performed using SAMs. A dark matter-only N-body simulation is used and galaxies are assumed to populate halos from early times. The assembly history of the halos, such as smooth accretion and mergers, is also assigned to the galaxy. For example, the accretion of gas follows the accretion of dark matter using the global baryonic fraction, then cools at a prescribed rate until it can form stars. The internal processes of galaxies, such as gas cooling, star formation and feedback processes, are generally simpli\ufb01ed prescriptions that are tuned so that the z=0 population matches observed galaxy populations (e.g. as described in Jung, Lee & Yi 2014). Using such a SAM, Jung et al. (2014) \ufb01nd a small difference in regions of di\ufb00erent large-scale (7 h\u22121 Mpc) density, speci\ufb01cally that low-mass (<1012 M\u2299) halos have slightly higher stellar masses in high-density environments. Our results qualitatively agree with those of Jung et al. (2014), although they \ufb01nd a much smaller di\ufb00erence in the stellar mass of galaxies in overdense versus underdense regions, and only for low-mass halos (1011-1011.5 M\u2299/h). They show that in their simulation this is because there is more cold gas in low-mass halos in higher density environments. We have also posed this as an explanation for our di\ufb00erent stellar masses. However, we see a much larger e\ufb00ect for a much broader range of galaxy masses. We consider a few possible explanations. First, Jung et al. (2014) considers environment on the scale of 7 h\u22121 Mpc while we are considering environment measured on \u223c25 Mpc scale. Although Jung et al. (2014) tested that scales from 3-9 h\u22121 Mpc did not e\ufb00ect their results, Gao et al. (2005) found that as12 Fig. 7.\u2014 The halo sSFR (SFR/MDMhalo) as a function of dark matter halo mass. Each point is the median value of 50 galaxies binned by halo mass. The shaded region shows the 25-75% range of values. The red denotes the C box galaxies, and the blue denotes the V box galaxies. We overplot results from Crain et al. 2009 in the z=0 panel for comparison. From left to right the redshifts are z=3.1, 1.0, 0. The halo sSFR tends to be higher for galaxies in the overdensity (C box) than in the underdensity (V box). As the redshift decreases, the di\ufb00erence between C box galaxies and V box galaxies become more dramatic. See discussion in Section 5. sembly bias increases with increasing length scale, and Jung et al. (2014) do not extend to the scale we use to de\ufb01ne environment. Secondly, we directly calculate the cooling rate using the gas chemistry, and perhaps gas is more metal-rich in the overdense environment and so can cool more quickly. Indeed, Cen (2013) \ufb01nds that gas \ufb02owing into halos (with negative radial velocities) tends to have higher metallicity in the overdense C box than in the underdense V box. It is possible that metals can escape lower density \ufb01laments more easily therefore resulting in less metal-enrichment of galaxies in low density environments. This is an extension of the discussion of metal enrichment of clusters via \ufb01laments by Rasmussen & Ponman (2009). However, we suspect that the most important di\ufb00erence is that we directly calculate any hydrodynamical e\ufb00ects from neighbors. As we discuss in Section 4.7, we believe that one driver of our results is interactions with nearby galaxies (most of which are not satellites) driving gas instabilities and in\ufb02ows that increase SFRs. This is a process that is not treated in SAMs. We can also compare with the other hydrodynamical simulation that compares galaxies in di\ufb00erent environments, and \ufb01nd that our results di\ufb00er from those in Crain et al. (2009). The GIMIC simulations use GADGET3 to hydrodynamically \u201cre\u201d-simulate regions of the Millennium simulation at (-2, -1, 0, +1, +2)\u03c3 (on the scale of \u223c20 Mpc) of the mean density to determine what drives di\ufb00erences in the SFRD. While the peaks of their curves are between z=2-3, in agreement with our results, they \ufb01nd a smaller di\ufb00erence in the normalization of the SFRD curves in the highand low-density environments. Other properties of their galaxy populations di\ufb00er from ours. For example, Crain et al. (2009) do not \ufb01nd much di\ufb00erence in either the shape or the magnitude of the stellar mass functions in their over dense versus under dense regions. However, while they reproduce the overall number of galaxies more massive than 109 M\u2299, their stellar mass functions do not match the observed shape of the z=0 stellar mass function of Li & White (2009) (as discussed in their Figure 3). We note that this group has since run the \u2018Evolution and Assembly of GaLaxies and their Environments\u2019 (EAGLE) simulation project, which has an excellent \ufb01t to the z=0 galaxy stellar mass function (Schaye et al. 2015). However, the EAGLE simulations do not compare di\ufb00erent large scale environments, so we cannot compare our work to these simulations. In Figure 3 of Cen (2011) the luminosity function of galaxies in the combined C and V boxes is shown to be a good \ufb01t to Blanton et al. (2003), although the highest luminosity, i.e. most massive, galaxies require a post-processing addition of AGN feedback to match observations. In addition, Kreckel et al. (2011) focus only the V box, and reproduce the luminosity function of void galaxies found by Hoyle et al. (2005). The void luminosity function differs from the total luminosity function both in that the normalization of the low luminosity end drops by more than an order of magnitude and the knee of the function shifts. In this paper we track galaxies over time rather than look at the galaxy population at individual redshifts. However, in order to determine whether we would get the same results, in Figure 7 we make a halo sSFR \ufb01gure similar to Figure 8 in Crain et al. (2009). Here we look at z=3.1,1.0, and 0. We bin our galaxies by halo mass, with 50 galaxies in a bin, except the highest mass bin has between 50-100 galaxies. In red we plot the C box galaxies and in blue we plot the V box galaxies. The solid lines and symbols are the median values and the shaded region denotes the central 25-75% of values. We brie\ufb02y note that the low mass galaxies at z=0 have masses below our lowest mass bin in Figures 1-6, and most of these galaxies are not tracked even to z=1. The precipitous drop in the sSFR is quite probably due to poor resolution of these galaxies, or may possibly indicate that the environment is dramatically a\ufb00ecting the SFRs of these galaxies beyond two virial radii of their nearest neighbor or that these are splashback galaxies. The dashed lines at z=0 show some of the Crain et al. (2009) data. First, our halo sSFR agrees well with the high mass end of the halo sSFR in Crain et al. (2009), but is relatively \ufb02at with halo mass and does not drop at lower masses. We speculate that this is because we do not include kinetic feedback as in the GIMIC simulations, 13 so we do not have a sudden drop below about 1012 M\u2299 from gas blow-out. Unlike Crain et al. (2009), we \ufb01nd that at lower redshifts the halo sSFR is clearly di\ufb00erent in di\ufb00ering environments, across all of the halo masses we probe. Even at z=3.1, we see a hint that the halo sSFRs of galaxies in the overdense environment is larger than that of galaxies in the underdense environment. At earlier redshifts, the sSFRS in the two environments are indistinguishable. The reason for these di\ufb00erences is di\ufb03cult to determine as the simulations are quite di\ufb00erent. Crain et al. (2009) use GADGET3, a smooth-particle hydrodynamics code. Their gravitational softening length is \ufb01xed in physical space at z\u22643 to 1 h\u22121 kpc in the intermediate resolution runs (from which most of their results are drawn), which is twice our resolution scale. Their cosmology is matched to the Millennium Simulation, so is also di\ufb00erent from ours. As discussed above, they also employ kinetic rather than thermal feedback. 6. CONCLUSIONS In this paper we have used a cosmological hydrodynamical simulation to examine the stellar mass to halo mass ratio of central galaxies in two di\ufb00erent large-scale (\u223c20 Mpc) environments. When we focus on the growth of dark matter halos (Figure 1), we reproduce the assembly bias found by Gao et al. (2005)\u2013galaxy halos in overdense environments have earlier formation times than those in underdense environments. Importantly, we have found that the halo mass alone cannot determine the SMHM ratio of galaxies. Speci\ufb01cally, in the large-scale overdensity central galaxies with halo masses from 1011-1012.9 M\u2299have higher SMHM ratios than galaxies in a large-scale underdensity (Figure 3). Even when we force the number of galaxies within 2 pMpc at z=0 in the overdense regions to be similar to or smaller than the number of surrounding galaxies in the underdense region, we cannot erase this di\ufb00erence. We posit that this result is due to the earlier formation times of halos in a large-scale overdensity and to the larger number of nearby galaxies and \ufb01laments at early times. Because the halos in overdense environments are more massive at early times, they can accrete gas and therefore form stars more quickly than those in underdense environments. Although at later times the V box halos grow more quickly than the C box halos, by that time there is generally less gas accretion, so SFRs are necessarily lower and the SMHM ratio does not equalize. In addition, particularly at early times, halos in overdense environments have a larger number of neighbors, which can drive instabilities in the gas and increase the SFR of central galaxies. Finally, there are more \ufb01laments feeding galaxies in higher density environments, particularly at early times. We \ufb01nd that the z=0 sSFR of galaxies is higher in the underdense region, in agreement with observational results (Rojas et al. 2004; Grogin & Geller 1999,2000; Szomoru et al. 1996). To test our results more robustly, we need more detailed observations of the SFR and stellar masses of a large sample of galaxies in deep, large voids. In particular, more comparisons of the TullyFisher relation using red bands to determine stellar mass would be useful. One di\ufb03culty will be to make sure we are comparing only central galaxies in both underdense and overdense environments. Di\ufb00erent SMHM ratios in di\ufb00erent large-scale environments means that assigning stellar masses based entirely on halo masses in simulations may not produce a realistic galaxy population, and including the z=0 local density in the stellar mass assignment will not compensate for the di\ufb00erent environments in which the galaxies previously evolved. The authors would like to thank Dr. Claire Lackner for the use of her merger trees, and Dr. Robert Crain for sharing his data. They would also like to thank the referee for comments that greatly improved the clarity of the paper. Computing resources were in part provided by the NASA HighEnd Computing (HEC) Program through the NASA Advanced Supercomputing (NAS) Division at Ames Research Center. The research is supported in part by NSF grant AST-1108700 and NASA grant NNX12AF91G. ST was supported by the Lyman Spitzer, Jr. Postdoctoral Fellowship and the Alvin E. Nashman Fellowship in Theoretical Astrophysics.",
                    "introduction": "1. In a \u039b cold dark matter (\u039bCDM) universe (Komatsu et al. 2011), the mass function and distribution of dark matter halos is well-understood. Dark matter only sim- ulations show that halos form in \ufb01laments that are con- nected at nodes containing (a) massive halo(s). This compares well with observations that show galaxies in \ufb01l- aments, sheets, clusters and superclusters (e.g. Springel et al. 2006). Connecting the stellar component of galaxies to dark matter halos can be di\ufb03cult because galaxy growth de- pends on both internal and external factors. Gas accre- tion and mergers can drive galaxy star formation, while feedback from active galactic nuclei (AGN), supernovae and stellar winds can delay or stop growth. Many of these processes are di\ufb03cult for cosmological hydrodynamical simulations to resolve, such as the radiative cooling of gas into molecular clouds, star formation, and energy in- jection into the interstellar medium from supernovae and AGN. Despite these complications, halo mass has been closely linked to a galaxy\u2019s stellar mass and star formation. An- alytic models of galaxy formation through smooth gas accretion found that there is an upper mass threshold at which accreted gas is shocked to temperatures from which it can no longer cool within a Hubble time and \ufb01le star formation, determining the mass at which galaxies must be red (Rees & Ostriker 1977; Silk 1977; Binney 1977; White and Rees 1978). Recent numerical hydro- dynamical cosmological simulations by Kere\u02c7 s et al. 2005 (see also Ocvirk et al. 2008) have updated this model, showing that cold gas accretion can occur in halos with a range of masses, but the amount of cold gas in a galaxy is determined by its dark matter halo mass, Mhalo. There- fore, one would expect a galaxy\u2019s Mhalo to be directly"
                },
                {
                    "url": "http://arxiv.org/abs/1408.4521v1",
                    "title": "The Ties that Bind? Galactic Magnetic Fields and Ram Pressure Stripping",
                    "abstract": "One process affecting gas-rich cluster galaxies is ram pressure stripping,\ni.e. the removal of galactic gas through direct interaction with the\nintracluster medium. Galactic magnetic fields may have an important impact on\nthe stripping rate and tail structure. We run the first magnetohydrodynamic\nsimulations of ram pressure stripping that include a galactic magnetic field,\nusing 159 pc resolution throughout our entire domain in order to resolve mixing\nthroughout the tail. We find very little difference in the total amount of gas\nremoved from the unmagnetized and magnetized galaxies, although a magnetic\nfield with a radial component will initially accelerate stripped gas more\nquickly. In general, we find that magnetic fields in the disk lead to slower\nvelocities in the stripped gas near the disk and faster velocities farther from\nthe disk. We also find that magnetic fields in the galactic gas lead to larger\nunmixed structures in the tail. Finally, we discuss whether ram pressure\nstripped tails can magnetize the ICM. We find that the total magnetic energy\ndensity grows as the tail lengthens, likely through turbulence. There are\nmicroGauss-strength fields in the tail in all of our MHD runs, which survive to\nat least 100 kpc from the disk (the edge of our simulated region), indicating\nthat the area-filling factor of magnetized tails in a cluster could be large.",
                    "authors": "Stephanie Tonnesen, James Stone",
                    "published": "2014-08-20",
                    "updated": "2014-08-20",
                    "primary_cat": "astro-ph.GA",
                    "cats": [
                        "astro-ph.GA",
                        "astro-ph.CO"
                    ],
                    "main_content": "clusters. These simulations of RPS only include magnetic fields in the ICM and neglect galactic magnetic fields. Including magnetic fields in the galaxy and the ICM is important to understanding the physics behind observations of ram pressure stripped galaxies. For example, enhancement of radio continuum emission has been observed in cluster galaxies, as well as an enhanced, though still tight, radio-to-far infrared (FIR) correlation (Gavazzi 1991; Niklas et al. 1995; Andersen & Owen 1995). Because the radio is enhanced relative to the FIR emission, Scodeggio & Gavazzi (1993) and Rengarajan et al. (1997) argue that the increase in radio continuum emission cannot be entirely explained by enhanced star formation in cluster galaxies, and claim that therefore magnetic field compression by the ICM is also likely to be at work. Using spatial information, Murphy et al. (2009) compare maps of the FIR-radio correlation between Virgo and normal galaxies. Based on the FIR emission and expectations from field galaxies, they find radio deficits in galaxies undergoing ram pressure stripping along the face of the interaction between the galaxy and the ICM. In agreement with earlier works, they find that cluster galaxies have enhanced global radio emission, but they are the first to connect this enhanced global emission with local radio deficits in ram pressure stripped galaxies. This was then seen and discussed in the context of detailed multi-wavelength observations of several Virgo galaxies (Vollmer et al. 2009; 2010; 2013). The scenario proposed by these authors is that low density gas and its associated magnetic fields and relativistic electrons are more easily stripped. The observed enhanced radio emission is produced when mini-shocks accelerate cosmic rays in the ISM. On the other hand, Pfrommer & Dursi (2010) argue that magnetic draping of the intracluster magnetic field can explain the radio deficit observations. Including galactic magnetic fields may also be important in the study of stripped tails. In fact the first 2 stripped tails were observed in radio continuum emission (Gavazzi & Ja\ufb00e 1987), indicating magnetic \ufb01elds in the stripped gas. Recently Sun et al. (2006; 2007) found a ram pressure stripped \u201cdouble-tail\u201d in X-ray emission, which they argue may be due to con\ufb01nement from magnetic \ufb01elds. Zhang et al. (2013) report on another double-tailed stripped galaxy in the same cluster (Ruszkowski et al. 2014 report that they reproduce a double tail with an intracluster magnetic \ufb01eld, and intend to determine the brightness of this feature in future work). In addition, stripped tails have the same metallicity as their parent galaxy, and thus may be important to the enrichment of the ICM (this has been observed in, e.g. Kenney et al. 2014). It is still under debate whether, in general, the ICM has a smooth, \ufb02at distribution of metals beyond a central cD-dominated peak (e.g. Werner et al. 2013; Leccardi & Molendi 2008; Fujita et al. 2008; Ezawa et al. 1997); metallicities that, beyond the cDdominated central region, fall slowly with increasing radius (e.g. Finoguenov et al. 2000; Baldi et al. 2007; Matsushita 2011); or if the ICM metallicity \ufb02uctuates on both small and large scales, as observed in A3667 (Lovisari et al. 2009). Fluctuations in the ICM metallicity indicate recent enrichment, and RPS could then be an important enrichment mechanism (Domainko et al. 2006). Including magnetic \ufb01elds is important to understanding the rate at which stripped material mixes with the ICM. The magnetic \ufb01eld in the tail may also be important, as it may help to magnetize, or maintain magnetic \ufb01elds in, the ICM (for a discussion of possible sources of the intracluster magnetic \ufb01eld see Brandenburg & Subramanian 2005). Several observations indicate that intracluster magnetic \ufb01elds are \u223c\u00b5G, possibly rising to nearly 10 \u00b5G in cluster centers (e.g. Pratley et al. 2013; Feretti et al. 2012; Bonafede et al. 2009; Murgia et al. 2009; Guidetti et al. 2008; Govoni et al. 2006; Govoni & Feretti 2004; Clarke, Kronberg & B\u00a8 ohringer 2001; Eilek & Owen 2002; Clarke 2004; Vogt & En\u00dflin 2003, 2005). Clarke, Kronberg & B\u00a8 ohringer (2001) \ufb01nd that within about 500 kpc from the cluster center the area-covering factor of magnetic \ufb01elds is about unity. Subramanian et al. (2006) calculate using a simple analytical model that while galaxy wakes \ufb01ll a small fraction of the volume of a cluster they could have an area covering factor near unity. Arieli et al. (2011) use a cosmological simulation in which they assume a constant 3 \u00b5G galactic magnetic \ufb01eld and analytically model stellar out\ufb02ows and ram pressure stripping from galaxies to study whether galactic gas can magnetize the ICM. The authors \ufb01nd that without allowing for \ufb01eld ampli\ufb01cation or dissipation, winds and stripping can magnetize the ICM to an average \ufb01eld strength of 0.9 \u00b5G in the central 100 kpc. Studying the magnetic \ufb01eld strength and dissipation rate in tails in detail is necessary to determine the level to which stripped tails can magnetize the ICM. In this paper, we run a set of high resolution simulations to understand the e\ufb00ect of galactic magnetic \ufb01elds on ram pressure stripped disks and tails. Here we focus on the e\ufb00ects of galactic magnetic \ufb01elds, and therefore we do not include added physics such as radiative cooling or conduction. Running an ideal MHD simulation is the \ufb01rst step in constraining the physical processes at work in the ICM that can a\ufb00ect stripped tails. These constraints will come through comparisons of the \ufb01eld strength and structure in simulated and observed stripped tails, and in the mixing rate of stripped gas with the ICM. This is a \ufb01rst step because non-ideal plasma transport processes such as anisotropic viscosity and conduction could have important e\ufb00ects on the mixing rate of the stripped tail of gas, the energy dissipation rate, and the propagation and decay of turbulence in the tail (Braginskii 1965; Lyutikov 2007, 2008; Schekochihin et al. 2009). The paper is structured as follows. After a brief introduction to our methodology, we provide the details of our galaxy model in Section 2.1, and of the ICM in Section 2.2. We then discuss whether and how including a galactic magnetic \ufb01eld a\ufb00ects the disk and tail (\u00a73), \ufb01rst focusing on how magnetic \ufb01elds a\ufb00ect the stripping rate in the disk (\u00a73.1) and then how they a\ufb00ect the stripped tail (\u00a73.2). In Section 4 we focus directly on the magnetic \ufb01eld in the stripped tail, and discuss to what extent ram pressure stripped tails can add to the magnetization of the ICM. In Section 5 we compare our results to previous simulations and observations. Finally, we conclude in \u00a76 with a summary of our results and discuss future work. 2. METHODOLOGY We use the MHD grid code Athena (Stone et al. 2008). To follow the gas, we employ a mesh for solving the \ufb02uid equations including gravity. In our implementation we use a single grid throughout the box with a cell size of 159 pc. Much of the post-processing analysis of these simulations was performed using yt, an open-source analysis toolkit (Turk et al. 2011). 2.1. The Galaxy Our galaxy is placed at a position corresponding to (83,83,52) kpc from the corner of our (166,166,151) kpc computational box (in one of our runs, described below and labeled DIP, the box is slightly narrower, with the disk (68,68,62) kpc from the corner of our (136,136,160) kpc domain), so that we can follow the stripped gas for about 100 kpc. The galaxy remains stationary throughout the runs. The ICM wind \ufb02ows along the z-axis in the positive direction, with the lower z boundary set for in\ufb02ow and upper z boundary set as out\ufb02ow. The x and y boundaries are set to out\ufb02ow in all four runs. We describe our disk in detail in Tonnesen & Bryan (2009; 2010), but repeat the salient points here. We choose to model a massive spiral galaxy with a \ufb02at rotation curve of 200 km s\u22121. It consists of a gas disk that is followed using the mesh algorithm (excluding self-gravity), as well as the static potentials of the (preexisting) stellar disk, stellar bulge, and dark matter halo. We directly follow Roediger & Br\u00a8 uggen (2006) in our modeling of the stellar and dark matter potential and gas disk. In particular, we model the stellar disk using a Plummer-Kuzmin disk (see Miyamoto & Nagai 1975), the stellar bulge using a spherical Hernquist pro\ufb01le (Hernquist 1993), and the dark matter halo using the spherical model of Burkert (1995). This dark matter halo model is compatible with observed rotation curves (Burkert 1995; Trachternach et al. 2008). The equation for the analytic potential is equation (2) in Mori & Burkert (2000). Our stellar disk has a radial scale length of 4 kpc, a vertical scale length of 0.25 kpc and a total mass 3 of 1011 M\u2299; the stellar bulge has a scale length of 0.4 kpc and a total mass of 1010 M\u2299; and the dark matter halo has a scale radius of 23 kpc and a central density of 3.8 \u00d7 10\u221225 g cm\u22123. The gas disk has about 10% of the mass in the stellar disk, and radial and vertical scales of 7 kpc and 0.4 kpc, respectively. To identify gas that has been stripped from the galaxy we also follow a passive tracer that is initially set to 1.0 inside the galaxy and 10\u221210 outside. Speci\ufb01cally, the passive tracer is assigned in the initial problem set-up so that all gas with densities higher than the ICM density is set to one. As gas from the disk is mixed into the ICM this allows us to determine, for each cell, the fraction of gas that originated in the disk (which we call the tracer fraction). In the following analysis, we will use a minimum tracer fraction of 25% to \ufb01nd gas stripped from the galaxy (as in Tonnesen et al. 2011; Tonnesen & Bryan 2012). 2.1.1. The Galactic Magnetic Fields We analyze four simulations in this paper, in which we vary the initial galactic magnetic \ufb01eld. Our baseline is a purely hydrodynamic run, Hydro. We also examine two runs with toroidal magnetic \ufb01elds of di\ufb00erent initial strengths: TORL and TORH. Finally, we have run a simulation with a dipole \ufb01eld that has been compressed in the z-direction and stretched along the disk plane: DIP. In order to initialize a divergence-free magnetic \ufb01eld, we input the vector potential, and calculate the magnetic \ufb01eld within the run. In the TORL and TORH runs we forced the magnetic \ufb01eld to be zero outside of the disk by setting the vector potential to a constant at a threshold Az. We selected a vector potential such that our magnetic \ufb01eld was weak in the center of the galaxy where the velocity is changing rapidly, peaked a couple kpc from the center (well within the stripping radius), and then fell o\ufb00gradually with increasing radius. The vector potential follows equations 1-4 in the disk. Ax = Ay = 0 (1) Az = \u221aazfe(\u22126Rcyl)\u00d7 (\u22126sin(2.5Rcyl) \u22122.5cos(2.5Rcyl)) (62 + 2.52) (2) azf = ao(\u2212|z| + 1)80 (3) ao(T ORL) = 1000, ao(T ORH) = 4000 (4) In the DIP run we began with a dipole vector potential, then forced it to decrease more rapidly in the z-direction and more slowly in the Rcyl-direction than a true dipole magnetic \ufb01eld. In order to allow for closed magnetic \ufb01eld lines we did not set the vector potential to a constant outside of the disk. Instead, in order to slow the growth of the magnetic \ufb01eld at the disk edges, we allow the surrounding ICM to rotate with the disk out to 2.4 Rdisk (\u223c62 kpc). The vector potential is described by equations 5-7. Ax = \u2212aoyR2 cyl ((z2 + 0.01)3r3 sph) (5) Ay = aoxR2 cyl ((z2 + 0.01)3r3 sph) (6) Az = 0, ao = 3.0 \u00d7 10\u22128 (7) In Figure 1, we show slices of the magnetic \ufb01eld magnitude including representative streamlines through the y=0 and z=0 planes of the galaxies. We see that the central regions of the galaxies tend to have high magnetic \ufb01eld strengths in comparison to the 2-7 \u00b5G measured in the Milky Way (e.g. Men et al. 2008; Mao et al. 2012). However, the strength of magnetic \ufb01elds in nearby spiral gas-rich galaxies with high star formation rates range from 20-30 \u00b5G in the spiral arms, and starburst galaxies can have total \ufb01elds of 50-100 \u00b5G (see review by Beck 2009). Therefore, while our simulated magnetic \ufb01elds may be somewhat strong for Milky Way measurements, they are not unphysical. We also note that by a radius of 5 kpc the peak magnetic \ufb01eld magnitude in DIP is at or below 3 \u00b5G, and by 15 kpc the magnetic \ufb01eld in TORL peaks at \u223c3 \u00b5G. While the magnetic \ufb01eld in TORH is stronger than we would expect for a Milky Way type galaxy, it will allow us to place upper limits on the importance of the magnetic \ufb01eld strength to our results. We consider the DIP and TORH runs to be our strong magnetic \ufb01eld cases because both have \u00b5G \ufb01elds extending to the edge of the disk (the top panels of Figure 1). Our magnetic \ufb01eld morphologies are simpli\ufb01ed in order to slow the growth of instabilities, which we discuss below. For example, we do not include small-scale random \ufb01elds (discussions in, e.g. Beuermann et al. 1985; Sun et al. 2008). We also either cut-o\ufb00(TORL and TORH) or severely lower (DIP) the strength of our magnetic \ufb01elds at the disk edge\u2013to maintain a lower magnetic pressure than thermal pressure at the disk edge in order to reduce disk expansion and to reduce magnetic \ufb01eld growth from the velocity di\ufb00erential between the disk and the ICM. Observed magnetic \ufb01elds tend to have a planar component that follows the spiral arms, with the \ufb01eld often strongest in the regions between the optical arms (Beck 2009 and references therein). There have also been observations of an X-shaped vertical \ufb01eld in the halos of disk galaxies (Beck 2009 and references therein). As we do not include radiative cooling or spiral density waves, it is sensible to begin with straightforward disk \ufb01elds. We choose the \ufb01eld morphologies described above in order to use reproducible, divergence-free \ufb01elds that vary slowly due to instabilities. In Figure 2 we show the initial \u03b2=PTherm/(B2/8\u03c0) values in our disks. We have used TORH to set the color scale, as it has the lowest minimum \u03b2 of 0.1246. The minimum \u03b2 values for TORL and DIP are 1.99 and 0.97, respectively. We highlight where \u03b2=1 using a pink contour. The added magnetic pressure does not have a strong effect on the disk in either the TORL or DIP runs, as it is generally well below that of the thermal pressure. However, in the TORH run the magnetic pressure along the central plane of the disk from a radius of \u223c2 -15 kpc is larger than the gas pressure by up to a factor of eight, so the disk quickly pu\ufb00s up (recall that the gas thermal pressure is initially set to balance the gravitational potential). In fact, the gas disk expands to more than 5 kpc from the disk plane by t=25 Myr, before the ICM wind hits the disk. This is why the disk gas measured 4 1 Fig. 1.\u2014 Slices along the yand z-axis for the initial conditions of the TORL, TORH, and DIP runs. The color scale is the magnetic \ufb01eld strength, the black lines are streamlines of the magnetic \ufb01eld lines, and the white line shows the edge of the disk de\ufb01ned by where the density drops to that of the ICM. Fig. 2.\u2014 Slices along the y-axis for the initial conditions of the TORL, TORH, and DIP runs from top to bottom. The color scale is \u03b2=PT hermal/(B2/8\u03c0), The pink contour is \u03b2=1 (for TORH and DIP, the two runs with \u03b2\u22651), and the white line shows the edge of the disk de\ufb01ned by where the density drops to that of the ICM. within 5 kpc of the disk plane begins decreasing the earliest in the TORH run, as seen in Figure 5. By later times (\u223c150 Myr after the wind has hit the disk), this di\ufb00erence does not a\ufb00ect how much gas remains in the disk. The extra magnetic pressure in the TORH run also results in the thicker disk in the projections in Figure 4 and in the higher velocities of high-density disk gas 50 Myr after the wind has hit the disk, in Figure 7. Our initial conditions are not in magnetostatic equilibrium, so we see evolution in the magnetic \ufb01eld strength and structure, and in the gas distribution of the disk. While our DIP run begins with a magnetic \ufb01eld with only cylindrical radial and vertical components, due to di\ufb00erential rotation in the disk the azimuthal component grows with time. This increases the magnetic pressure with time, and can be seen most clearly by the increase in the maximum pressure of the DIP run with time, and the increasing z-velocity of central, high-density, disk gas (Figures 7 & 8). The e\ufb00ect is strongest in the central regions of the disk, where it will have little e\ufb00ect on the stripping pro\ufb01le of the galaxy. However, the evolving magnetic \ufb01eld does make us unable to use the DIP run when we discuss the e\ufb00ect of compression by the ICM wind on the magnetic \ufb01eld strength in the central regions of the disk (Section 5.2). These disks are unstable to the magnetorotational instability (MRI) (Balbus & Hawley 1991) for most of their radius, beyond \u223c4 kpc, where the angular velocity begins decreasing outwards (Hawley & Balbus 1999a,b). The local growth rate of the MRI is proportional to the local orbital frequency (Hawley 2001), so the instability grows the most quickly near the center of the disk. At 4 kpc, the orbital period is 120 Myr, and at the edge of the disk the orbital period is 800 Myr, so while the inside of the disk will have more gas mass and higher densities (seen in the increase in high density gas in the late panels in the DIP run in Figure 7), there will be very little expansion of the outer edge of the disk. Even at 16 kpc, the initial stripping radius of the disk, the orbital period is 490 Myr, so disks do not expand much in our simulation. If a disk remained on a relatively circular orbit for a long period of time, the MRI might result in more gas removal at late times because of disk expansion. 2.2. The ICM All four of the simulations we discuss in this paper initially embed a galaxy in a static, high-pressure medium with \u03c1 = 9.152 \u00d7 10\u221229 g cm\u22123 and T = 4.15 \u00d7 106 K. The boundary conditions generate a constant unmagnetized ICM in\ufb02ow along the inner z-axis, which is always face-on to the galaxy. The wind parameters 5 are Pram = \u03c1v2 ICM = 6.4 \u00d7 10\u221212 dynes cm\u22122, and vICM = 1413 km s\u22121. The ICM wind has a T = 4 \u00d7 107 K and \u03c1 = 3.2 \u00d7 10\u221228 g cm\u22123, and therefore P = 1.76 \u00d7 10\u221212 dynes cm\u22122. These are the same ICM parameters as in Tonnesen & Bryan (2009; 2010; 2012). 3. THE EFFECTS OF A GALACTIC MAGNETIC FIELD In Figure 3, we show slices at y=0 of the fraction of gas that originated in the disk in our TORH (upper panel) and Hydro (lower panel) simulations, 750 Myr after the ICM wind has hit the disk. Clearly we follow a range of mixing levels throughout the tails within our simulated region. The structure in the tail indicates that disordered motions are mixing the gas in both the hydrodynamical and MHD runs. In the TORH run, the eddy structures are larger than in the Hydro run, and much more nearly unmixed gas (more than 75% of the gas in the cell originated in the disk) survives to the edge of our simulated region, \u223c100 kpc above the disk plane. While Figure 3 is useful to see the tail structure in detail, density projections can be more directly compared to observations. Therefore, for reference in the following discussions, we include 5 density projections for each of our runs in Figure 4. Each column is a di\ufb00erent simulation and each row steps through time, as noted in the caption and in Figures 5 and 6. The \ufb01rst row, 50 Myr after the wind has hit the disk, shows that there is little initial di\ufb00erence between the Hydro and TOR (L & H) cases, but the tail is already more extended in the DIP run. This behavior is caused by the magnetic \ufb01eld threading radially through the disk into the surrounding low-density gas in the DIP run. As the low density gas is swept up by the wind, magnetic tension will increase the total pressure removing the disk gas. 170 Myr after the wind has hit the disk (second row), the Hydro and TORL simulations are very similar, but the stronger magnetic \ufb01eld in the TORH disk results in less \ufb02aring through most of the tail. The DIP run also has less \ufb02aring in the tail, and an organized \u201cstreak\u201d-pattern in the stripped gas that can be seen criss-crossing in the tail due to the radial component of the magnetic \ufb01eld. At 310 Myr (third row), the strong magnetic \ufb01eld cases (TORH and DIP) have shorter dark blue tails (mid-range densities) than the Hydro and TORL runs, and this continues to be true 360 Myr after the wind has hit the disk. However, at 360 Myr after the wind has hit the disk, the surface area of higher density gas (yellow and green) above the disk is larger in the TORH and DIP runs than in the Hydro and TORL runs. 500 Myr after the wind has hit the disk (bottom row), higher density gas is clearly seen farther above the disk in the TORH run (light blue and green), and in a careful examination, light blue higher column density regions can be seen in the DIP run even farther along the tail than in the TORH run, out to \u226565 kpc above the disk. 3.1. The Gas Disk In this section we discuss the di\ufb00erences in the gas residing in the disk in our four simulations. Disk gas is de\ufb01ned as gas with a tracer fraction greater than 0.6 and within a cylinder with 28.6 kpc radius and 10 kpc height (\u00b15 kpc from the disk plane). Our choice of limiting tracer fraction does not have any qualitative impact on our results. The gas disk mass using a tracer fraction of 0.25 is always less than 2% di\ufb00erent than 0.9. We see in Figure 3 that most of the gas near the disk has a tracer fraction more than 0.9, and the transition from 0.9 to 0 occurs over a short distance at the disk edges. Gas that falls back tends to have a lower tracer fraction (be more mixed with the ICM), but the center of infalling clumps have high tracer fractions so a limiting value of more than 0.75 would need to be chosen to have much impact on the measured radius. The phase plots do change when we dramatically vary the minimum tracer fraction used to de\ufb01ne disk gas\u2013there is more low-density gas when we use 0.25, and almost no gas with densities below 2 \u00d710\u221227 g cm\u22123 when we choose 0.9. However, the red and orange contours remain unchanged and the comparisons between the di\ufb00erent runs remain unchanged. 3.1.1. The Disk Mass In Figure 5, we plot the amount of gas in the disk as a function of time for all four runs. The wind hits at t \u223c 30 Myr (t \u223c35 Myr in the DIP run). The vertical lines denote the times at which density projections are shown in Figure 4, and a selection of these times will be used in the phase plots throughout the paper. We \ufb01rst highlight the similarities between the four cases. In all four cases there is an initial stripping event lasting between 110-170 Myr with the fastest stripping rate in the simulation. All four simulations then undergo fallback onto the disk. As we have discussed in earlier work (Tonnesen & Bryan 2009, 2010; also Schulz & Struck 2001), fallback occurs when stripped gas that is still gravitationally bound to the galaxy moves into the protected lee of the disk and is no longer pushed by the wind. At 300 Myr after the wind has hit the disk the stripping rate begins to slow and to have less dramatic fallback episodes. Also, after 300 Myr of stripping there is very little di\ufb00erence in the amount of disk gas in the four runs, with the largest di\ufb00erence between runs being less than 10% of the total gas disk mass. At later times gas is removed by continuous stripping processes, e.g. Kelvin-Helmholtz instabilities or viscous stripping, as discussed in Tonnesen & Bryan (2009). Including either a toroidal (TORL or TORH) or poloidal (DIP) magnetic \ufb01eld has little e\ufb00ect on the rate of this instabilitydriven gas removal. The main di\ufb00erence in these runs is that more gas falls back in the strong magnetic \ufb01eld cases (TORH and DIP) than in the weak \ufb01eld cases (Hydro and TORL). We suspect that this is because the stronger magnetic tension initially con\ufb01nes the stripped gas to a more collimated tail behind the disk (as seen by the narrower tails in the second column of Figure 4). This allows more gas to be in the shadow of the disk for added fallback. There is an initial di\ufb00erence in the TORH run due to the initial conditions of the \ufb01eld, as discussed in Section 2.1.1. The TORH disk seems to lose mass the most quickly, even though the magnetic \ufb01eld does not extend beyond the disk and the \ufb01eld is toroidal, so magnetic tension should not initially play a role in gas stripping. In agreement with this expectation, the dark blue column density gas in the \ufb01rst TORH and Hydro projections looks nearly identical (Figure 4). However, TORH has a strong magnetic \ufb01eld, such that the magnetic pressure in the inner \u223c15 kpc pu\ufb00s up the disk so that some gas is more than 5 kpc from the disk plane, leading to a de6 Fig. 3.\u2014 A slice of the fraction of gas that originated in the disk in our TORH (upper panel) and Hydro (lower panel) simulations, 750 Myr after the ICM wind has hit the disk. The color scale shows the fraction of gas in any cell that originated from the disk. The range of mixing levels is broad at most heights above the disk, ranging from \u223c0.2 to more than 0.5. Much more nearly unmixed gas (more than 75% of the gas in the cell originated in the disk) survives to the edge of our box in the TORH run, \u223c100 kpc above the disk plane. The slice is about 81\u00d7107 kpc 7 Fig. 4.\u2014 Density projections for all four runs. From left to right the columns show the Hydro, TORL, TORH, and DIP runs. Each row shows a di\ufb00erent time after the wind has hit the galaxy: 50 Myr, 170 Myr, 310 Myr, 360 Myr, 500 Myr. 8 0 200 400 600 800 1000  Myr 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 Mgas (1010  M \u2299) Hydro TORL TORH DIP Fig. 5.\u2014 The amount of gas in the disk as as function of time. The disk gas is de\ufb01ned as gas with a tracer fraction greater than 0.6 and within a cylinder with radius 28.6 and height 10 kpc (\u00b1 5 kpc from the disk plane). The wind hits the disks at t\u223c30 Myr, so 50 Myr after the wind has hit the disk is at 80 Myr on the x-axis of this \ufb01gure. The vertical dashed lines denote the times at which we show density slices in Figure 4. Although the initial stripping seems to depend on the magnetic \ufb01eld strength, by about 310 Myr after the wind has hit the disk (the third vertical line), the amount of gas remaining in the disk is very similar in all four runs. crease in the disk gas measurement (which is de\ufb01ned to only include gas within 5 kpc of the disk plane) before the ICM wind can strip the disk. This can also be seen in Figure 4 when comparing the light blue and green gas above the central region of the disk in TORH to any other simulation. At later times (beyond 300 Myr) this lower-density gas is stripped from all four galaxies, so the TORH run evolves similarly to the other runs. Although the highest density gas (red in the projection) also has a larger scale height in the TORH run, it remains within 5 kpc of the disk plane, and so does not a\ufb00ect this comparison between the runs. 3.1.2. The Disk Radius The disk radius is calculated as the largest radius at which gas with a tracer fraction greater than 0.6 resides within 5 kpc of the disk plane. As with the gas mass shown in Figure 5, the stripping and fallback cycle leads to variations in the gas radius. Through comparison with Figure 5 we \ufb01nd that fallback coincides with an increase in gas mass at large galactic radius. Comparing with the \ufb01nal three rows in Figure 4, we see that the fallback at large radius is clumpy and asymmetric. We also examine disk symmetry by \ufb01nding the maximum radius in four quadrants of each disk. For the \ufb01rst 250 Myr of stripping, before the \ufb01rst fallback peak in Figure 5, the four quadrants in each disk have visually identical (to within the width of the line) maximum radii. After this time in the simulations, there is a radial variation of about 2 kpc between the largest and smallest quadrants at any given time, although the variation can be up to \u223c10 kpc for short times (tens of Myr) near the peak in radius at \u223c400 Myr. In this face-on ICM-ISM interaction, fallback, not stripping, drives asymmetry. Fig. 6.\u2014 The disk radius as a function of time, calculated as the largest radius at which gas with a tracer fraction greater than 0.6 resides within 5 kpc of the disk plane. The minimum radius reached in the initial stripping in all four cases is very similar. The bulk of the gas near the disk plane (|z| < 5 kpc) stays within the initial stripping radius, between 15-19 kpc for all the runs. The peaks are from material that has been stripped falling back towards the disk plane. The peak radius, reached in the initial fallback period, is largest in the Hydro case, as might be expected with no magnetic \ufb01eld con\ufb01nement. The initial minimum radius is reached at nearly the same time as the \ufb01rst minimum in disk gas mass from the initial stripping, but the peak in radius is somewhat later than the fallback peak in gas mass. This may be because material falls towards the disk then splashes outward along the disk plane from the added pressure. Although the fallback looks dramatic in Figure 6, the bulk of the disk gas mass remains within the initial stripping radius, which can be seen in the constant size of the red regions in the projection plots in Figure 4. The radial variations with time continue throughout all of our runs, although they seem to be settling towards the initial stripping radius. As discussed above, the gas removal at later times is due to Kelvin-Helmholtz instabilities or viscous stripping. As the ICM wind \ufb02ows around the disk there is a component of the wind moving along the disk plane, so these processes may draw disk material to larger radii before the wind accelerates the gas from the disk plane, resulting in the small variations seen in the disk radius on short timescales. There is very little di\ufb00erence in all four runs, but we see the e\ufb00ect of the strong magnetic \ufb01elds in TORH by the smaller maximum radius reached by gas falling back onto the disk. As discussed with regards to the the TORH run in the second row of Figure 4, the magnetic tension inhibits the radial expansion of the stripped gas. 3.1.3. A Closer Look at the Disk Gas In Figure 7 we show disk gas mass as a function of density and z-velocity. In this \ufb01gure, disk gas is gas with a tracer fraction greater than 0.6 and within a cylinder of radius 31 kpc and height 10 kpc (\u00b1 5 kpc from the galaxy plane). At 50 Myr there is no signi\ufb01cant di\ufb00erence between the Hydro and TORL runs, but we see more clearly the 9 Fig. 7.\u2014 Mass contours of disk gas as a function of density and velocity in the wind direction (z-velocity). Disk gas is gas with a tracer fraction greater than 0.6 and within a cylinder of radius 31 kpc and height 10 kpc (\u00b1 5 kpc from the galaxy plane). The columns, from left to right, are from the Hydro, TORL, TORH, and DIP runs. Each row is a di\ufb00erent time after the wind has hit: 50 Myr, 170 Myr, 310 Myr, 500 Myr. While all four runs show strong similarities, the di\ufb00erences indicate the impact of including magnetic \ufb01elds. See the discussion in Section 3.1.3. di\ufb00erences in the TORH and DIP runs that we have discussed with regards to Figure 4. The blue contours in TORH are very similar to those in TORL and Hydro, indicating that gas at the edge of the disk is being stripped at the same rate in all three runs. However, there is more gas with negative velocities, particularly at 10\u221226<\u03c1<10\u221225, and there is more high-density gas with large positive velocities. This indicates that magnetic pressure is driving expansion of dense (and therefore central) disk gas. Low-density gas (\u03c1<10\u221227) in the DIP run has reached a larger maximum velocity by 50 Myr, indicating that the magnetic \ufb01eld threading radially through the disk and into the surrounding medium is increasing the acceleration of the lower-density stripped gas. At 170 Myr, the DIP run still has gas being removed from the disk at the highest velocities. Here it is clear that the gas in the TORH run is being accelerated the most slowly, possibly due to pressure support from the magnetic \ufb01eld. There is also less fallback in the TORH run, shown as less gas with negative velocities, particularly at \u03c1<10\u221226. Indeed, including any magnetic \ufb01eld in the disk results in slower fallback at this early time, as the Hydro run has the largest negative velocities. At 310 Myr, the Hydro and TORL runs remain very similar. At densities below 10\u221225, the blue and green contours of DIP also look quite similar to the Hydro run, indicating that magnetic tension is no longer accelerating stripping in DIP. In fact, at this later time when continuous stripping processes dominate gas removal, a comparison of the yellow and orange contours indicates that the bulk of the gas with a density of a few 10\u221227 is being accelerated more slowly in the DIP run than in the Hydro and TORL runs. However, the gas at \u03c1\u226510\u221225 g cm\u22123 has a broader z-velocity distribution in the DIP run than in the Hydro and TORL runs. The TORH run has similar di\ufb00erences from the Hydro and TORL runs. As in the DIP run, the bulk of the gas at \u03c1<10\u221225 g cm\u22123 is 10 accelerated more slowly by the wind, but this di\ufb00erence is more pronounced when comparing TORH and Hydro (the di\ufb00erence is seen at all contour levels). Also, the gas at \u03c1\u223c10\u221225 g cm\u22123 has a broader z-velocity distribution in the TORH run than in the Hydro or TORL runs. The dense gas in the TORH and DIP runs is expanding due to pressure from the galactic magnetic \ufb01elds, the same \ufb01elds that may be inhibiting the removal of low-density material by the ICM wind. Finally, at 500 Myr, the lower-density gas (\u03c1<10\u221225 g cm\u22123) in the DIP run has a very similar velocity distribution to that in the Hydro and TORL runs, and indeed Figure 5 indicates that the stripping rate at later times is very similar in all four runs. At higher densities the velocity distribution of gas is broader because the di\ufb00erential rotation in the inner part of the disk has strengthened the magnetic \ufb01eld, and magnetic pressure drives some gas from the disk center. In TORH, which has the strongest initial magnetic \ufb01eld throughout the disk, less gas is accelerated quickly from the disk, although clearly the di\ufb00erence is not large enough to di\ufb00erentiate the gross stripping rate in TORH from that in TORL and Hydro, as seen in Figure 5. As in DIP, the stronger central magnetic \ufb01eld results in a broader velocity distribution in the center of the disk, but this gas is too tightly bound to be stripped. It may also be physically informative to consider the pressure of the disk gas. In Figure 8 we show the mass contours of disk gas as a function of pressure and velocity in the wind direction (z-velocity) 310 Myr after the wind has hit the disk. We have drawn a vertical line on each plot at Pcrit = Pram + PThermal,ICM = 8.16\u00d710\u221212 dyne cm\u22122. Gas with pressure above this critical pressure cannot be removed from the disk. This is because in our initial conditions, we set the pressure gradient to balance the gravitational potential in the disk z-direction, which links the disk pressure to the gravitational restoring force that binds that gas to the galaxy. In any line through the disk along the wind direction, if the maximum gas pressure (thermal plus nonthermal) is greater than Pcrit, gas cannot be removed by ram pressure. Even continuous stripping mechanisms will lower the pressure of the gas through mixing as they remove gas from the disk. It is not obvious that when radiative cooling and other sources of pressure are included, this result will hold, but if gas pressure can still be considered a proxy for the gravitational restoring force, then this would be a more direct way to determine whether gas can be stripped from a cluster galaxy. Of course, determining the total pressure of galactic gas is di\ufb03cult, because non-thermal pressure support can play a large role in balancing the galaxy\u2019s gravitational potential. In summary, the stripping rate from the disk depends very little on either the morphology or strength of the magnetic \ufb01eld. However, a poloidal \ufb01eld (DIP) that connects high-density to low-density gas can increase the early acceleration of stripped gas. At later times when continuous stripping processes dominate gas removal, stronger magnetic \ufb01elds seem to bind gas more tightly to the disk, resulting in the slower z-velocities of the bulk of the gas in the disk. However, even global magnetic \ufb01elds that are stronger than those found in the Milky Way do not have a drastic e\ufb00ect on the stripping amount or radius, nor do they strongly a\ufb00ect the density of the gas that can be removed from the disk. 3.2. The Gas Tail In this section we focus on the gas tail, to determine if a magnetic \ufb01eld a\ufb00ects its structure and evolution. Throughout this section, tail gas is de\ufb01ned as gas more than 10 kpc above the disk with a tracer fraction greater than 0.25. 3.2.1. The Tail Velocity Structure In Figure 9, we plot gas mass as a function of height above the disk and velocity in the wind direction (zvelocity). We de\ufb01ne tail gas as gas more than 10 kpc above the disk with a tracer fraction greater than 0.25. As in the velocity structure of disk gas, there are not many dramatic di\ufb00erences in the velocity structure of the tail gas between the Hydro and MHD runs. This is an important result because it means that estimates of tail velocities and lengths based on hydrodynamical simulation results do not have to be dramatically revised. However, it is worthwhile to examine the velocity structure closely to determine any e\ufb00ects of magnetic \ufb01elds. 170 Myr after the wind has hit the disk, all four runs are just past their \ufb01rst disk gas mass minimum (Figure 5). In Figure 9, TORH has more gas with negative velocities at \u223c20 kpc above the disk, although DIP does not show more fallback than in the TORL and Hydro runs. It is possible that most of the infalling gas in DIP is between 5-10 kpc above the disk at this time so is not included in either \ufb01gure. In Hydro the stripped gas at \u223c20 kpc is moving with higher velocities than in the MHD runs, evidenced by both the orange and green contours. However, more than 20 kpc above the disk, TORH has the most stripped gas farthest from the disk and moving at the highest velocities of any of the four runs, with DIP close behind. This is clearly shown in the orange and yellow contours. 310 Myr after the wind has hit the disk, the Hydro run has the longest orange contour, possibly indicating the survival of dense gas to \u223c70 kpc above the disk. Recall that the survival of dense gas to large distances in the Hydro run is also shown in the dark blue contours in the third row of Figure 4. There is a slight indication that TORH and DIP have more fallback than Hydro and TORL, which agrees with the gas mass as a function of time in Figure 5\u2013fallback is just \ufb01nishing in TORH and DIP, while gas removal has already restarted in Hydro and TORL. While the gas at \u223c40 kpc above the disk is moving at similar velocities in all four runs, again there is more gas at high velocities within 20 kpc of the disk in the Hydro run. Finally, 500 Myr after the wind has hit the disk, the velocity structure in the TORH tail looks quite di\ufb00erent than in the other three tails. TORH has very little gas with negative velocities, while the majority of the gas from 20-40 kpc above the disk in the Hydro and TORL runs and from 15-25 kpc in the DIP run has negative velocities. There is also less gas in the tail from 80-100 kpc above the disk in the TORH run than in any of the other three runs (also see Figure 4), and the gas at those large distance has the broadest z-velocity distribution of any of the runs. As in the top panels of this \ufb01gure, more 11 Fig. 8.\u2014 Mass contours of disk gas as a function of pressure and velocity in the wind direction (z-velocity) 310 Myr after the wind has hit the disk. Disk gas is gas with a tracer fraction greater than 0.6 and within a cylinder of radius 31 kpc and height 10 kpc (\u00b1 5 kpc from the galaxy plane). The magnetic pressure has extended the pressure range in these \ufb01gures to both higher and lower total pressure than the Hydro run. As in the \ufb01gure above, there is very little di\ufb00erence in the gross characteristics of the velocity structure of the disk gas in the four runs. Only gas with lower total pressure than the sum of the ram pressure and ICM thermal pressure (dash-dot vertical line) is stripped. We can see evidence of magnetic pressure driving disk expansion in the larger velocity range of gas with P > 10\u221211. Fig. 9.\u2014 Mass contours of tail gas as a function of height above the disk and velocity in the wind direction (z-velocity). Tail gas is gas more than 10 kpc above the disk with a tracer fraction greater than 0.25. There is little di\ufb00erence between the four runs. Hydro has more gas moving quickly close to the disk, but there is some indication that at larger distances the gas tends to move more quickly in the MHD runs. See Section 3.2.1. than 20 kpc above the disk, gas tends to be moving more quickly from the galaxy in TORH and DIP than in Hydro and TORL. In brief, including magnetic \ufb01elds in the tail does not narrow the velocity width of the tail in the wind direction. It also does not dramatically a\ufb00ect the bulk \ufb02ow of the gas, although we note two points that are consistent in all three outputs we examine in detail: \ufb01rst, within 20 kpc of the disk, the Hydro run has more gas accelerated to high velocities, and second, more than 20 kpc above the disk, the tail gas in the TORH and DIP runs tends to be moving away from the disk at velocities equal to or greater than the tail gas in the Hydro run. We posit that these di\ufb00erences are because near the disk the magnetic \ufb01eld slows the acceleration of gas, but farther from the galaxy the magnetic \ufb01eld in the tail allows larger coherent structures to survive that are then swept up by the ICM wind rather than mixed into the 12 ambient ICM. In Figure 3 this may be seen at 310 Myr in the green contours lying closer to the disk in TORH and DIP than in TORL and Hydro, and at 500 Myr in the dense gas (light blue) seen farther from the disk in the MHD runs than in Hydro. In order to determine how this may a\ufb00ect observable tails, we need to include radiative cooling, which we will include in a future work. 3.2.2. Density and Temperature Structure of the Tail In Figure 10, we plot the mass of gas in the stripped tail as a function of density and temperature. As in Figure 9, tail gas is de\ufb01ned as gas more than 10 kpc above the disk plane with a tracer fraction greater than 0.25. Our \ufb01rst row shows the density-temperature structure of gas 170 Myr after the wind has hit the galaxy. At this time the density range of the gas is similar in all four runs, with the high-temperature, low-density tail gas matching the temperature and density of the ICM wind. TORH and DIP have more low-temperature (<105 K) gas residing in the tail, although it is unclear whether in the Hydro and TORL runs this cold gas has been mixed into the ICM or simply has not yet reached 10 kpc above the disk. 310 Myr after the wind has hit the galaxy, at the fallback peak in TORH and DIP in Figure 5, there is more cool (<106 K), higher-density (\u03c1>10\u221226 g cm\u22123) gas in all three MHD runs than in the Hydro run. By 500 Myr after the wind has hit the galaxy, there is clearly much more cool (<106 K), higher density (\u03c1>10\u221226 g cm\u22123) gas in the tail in the TORH run than in any of the other three runs. We see that in all runs, at 170 Myr the density and temperature distribution of tail gas extends to higher densities and lower temperatures than at later times. In order for gas to be removed from this density-temperature plane it must mix with the ICM, leave the box, or fall back to within 10 kpc of the disk. Therefore to explain the di\ufb00erence between TORH and the other runs at 500 Myr the inclusion of the magnetic \ufb01eld must lower the mixing rate of stripped gas, lower the velocity of stripped gas, impede fallback, or drive some combination of these three possibilities. We show in Figure 3 that at very late times (750 Myr after the wind has hit the disk), more unmixed gas survives to large distances from the disk in TORH than in Hydro. While this indicates that the magnetic \ufb01eld inhibits mixing, this is one slice from a complicated \ufb02ow, as is clear from Figures 4 and 9. Examining Figure 9, we \ufb01nd that the velocity of the stripped gas tends to be larger \u226520 kpc above the disk in TORH than in Hydro. Thus, throughout most of the tail, including a magnetic \ufb01eld increases the tail velocity, making more likely that stripped gas will leave the TORH box. However, within 20 kpc of the disk, the wind accelerates gas the most quickly in the Hydro run and there tends to be more gas within 15 kpc with negative z-velocities in TORH and DIP than in Hydro. If anything, Figures 5 and 9 indicate that TORH has more fallback from 170 Myr to 310 Myr than Hydro. We \ufb01nd that the MHD runs will be at least as likely as the Hydro run to remove gas from the tail through fallback near the disk or acceleration out of the simulated domain. Therefore, it is worthwhile to examine more directly whether the magnetic \ufb01eld impedes gas mixing. To do this, we plot the tail gas mass as a function of magnetic \ufb01eld magnitude and tracer fraction in Figure 11. 170 Myr after the wind has hit the disk the initial, fast stripping has just ended in all three runs, so the gas in the tail was relatively recently removed from the disk and very little gas originating in the disk has left the simulation box. In the top panels of Figure 11, gas with the highest magnetic \ufb01eld magnitude is also the least mixed. At least part of this is because gas from the more central regions of the disk, with stronger magnetic \ufb01elds, is stripped at later times. This interpretation can explain the di\ufb00erences that we see between the top panels of the three runs: TORL and TORH have the same magnetic \ufb01eld structure in their disks and in both tails the magnetic \ufb01eld strength drops by a factor of about 6 from the unmixed maximum contour level to the mixed maximum contour at a tracer fraction of about 0.4. However, the magnetic \ufb01eld in DIP only drops by about a factor of two from the unmixed to the mixed peak, and the magnetic \ufb01eld strength is much more constant throughout the disk in DIP than in the toroidal \ufb01eld runs (Figure 1). Recall that from one output to the next, the gas we are examining is changing. We expect that gas that is recently stripped has a high tracer fraction, then at later times will have a lower tracer fraction as it mixes with the surrounding ICM (moving to the left in the panels in Figure 11). At 310 Myr, more gas in TORL has a tracer fraction of 0.6 than in the TORH or DIP runs, which have most of their tail gas at higher tracer fractions. At 500 Myr, TORH clearly has more gas residing at higher tracer fractions than either TORL or DIP. As we know from Figure 5, the stripping rate starting at about 310 Myr is very similar across all the simulations, so the stripped gas from 310 Myr to 500 Myr has had a similar time in which to mix with the ICM. This is a strong indicator that gas mixes more slowly in the strongest magnetic \ufb01eld case, and the initial \ufb01eld morphology in the disk has little a\ufb00ect on the tail. In Figure 12 we also consider this problem by examining observable gas properties, the density and magnetic \ufb01eld strength. At early times, 170 Myr after the wind has hit the disk, all three runs have a similar range and distribution of gas density. By 500 Myr after the wind has hit the disk, only the TORH run has gas in the tail with densities greater than 3\u00d710\u221226 g cm\u22123. Tonnesen & Bryan (2010) \ufb01nd that high density gas in the tail moves more slowly, so this gas is the least likely to have left the simulated box. Further, fallback is also dominated by lower density gas that can be more easily pushed into the shadow of the disk by disordered motion (Figure 7 and Tonnesen & Bryan 2010). Therefore, it is likely that in TORL and DIP the high density gas has mixed with the lower density ICM and that the stronger magnetic \ufb01eld in TORH inhibits mixing. It is important to note that we do not include explicit di\ufb00usion in our simulation. This a\ufb00ects gas mixing and sets our magnetic Prandtl number to 1. We highlight that because we do not include di\ufb00usion, mixing between magnetized galactic gas and unmagnetized intracluster gas can only occur on scales smaller than our cell size. See Ruszkowski et al. (2014) for a detailed discussion of mixing in ideal MHD simulations. A magnetic Prandtl number of one means that the viscous dissipation length is the same as the resistive dissipation length, so our velocity structures will be the same 13 Fig. 10.\u2014 Mass contours of tail gas as a function of density and temperature. Tail gas is de\ufb01ned as in Figure 9. As time passes, there is more high-density gas in the tail in the magnetic \ufb01eld cases than in the Hydro run, indicating that mixing acts more slowly if magnetic \ufb01elds thread the tail gas. size as our magnetic \ufb01eld structures. Since \u03b7 << \u03bd in intracluster plasma (e.g. Brandenburg & Subramanian 2005), the ICM has large Pm (as does the ISM). Simulations that vary the magnetic Prandtl number indicate that this di\ufb00erence could e\ufb00ect the magnetic \ufb01eld in our tails. For example, Fromang et al. (2010) found that MRI turbulence is not sustained when Pm\u22641. Also, at larger Pm, turbulent \ufb02ows may produce more magnetic energy, closer to equipartition with kinetic energy (Subramanian et al. 2006 and references therein), although values of Pm as large as those expected in intracluster gas have not been simulated. Bovino et al. (2013) \ufb01nd that at the large Pm and Rm values expected in the ICM the turbulent growth rate is much larger than at Pm\u223c1. Therefore, our Pm=1 may result in weaker magnetic \ufb01elds in our stripped tails and faster decay of turbulence than we would expect in observed tails evolving in a high-Pm ICM. 4. MAGNETIZING THE ICM Thus far we have focused on how a galactic magnetic \ufb01eld will a\ufb00ect the gas in the disk and tail. However, the magnetic \ufb01eld in the tail should be examined in its own right, as it may help to magnetize the ICM. 4.1. Growth of Magnetic Field in the Stripped Tail In Figure 13 we plot the total magnetic energy (top panel) and average magnetic \ufb01eld strength (bottom panel) in the tail and in the disk. The DIP run is in red, the TORH run in blue, and the TORL run in green. The solid lines denote the values in the tail (more than 10 kpc above the central plane of the galaxy) and the dash-dotted lines show the values in the disk (a cylindrical region with h = 10 kpc and r = 28.6 kpc). The total magnetic energy is the sum of B2/8\u03c0 in each cell times the cell volume. Focusing \ufb01rst on the disk magnetic energy, we \ufb01nd that both of the galaxies with a toroidal \ufb01eld have relatively constant magnetic energy in the disks. This is not surprising as the strongest magnetic \ufb01elds reside within the stripping radius of the disk (\u223c15 kpc). We also see that the magnetic energy density in the disk in the DIP run increases with time. As we discussed in Section 2.1.1, this is because the magnetic \ufb01eld is not in a steady state and a toroidal component grows with time due to radiallyvarying velocity. The total magnetic energy in the tail in all three simulations generally increases with time, particularly for the \ufb01rst 500 Myr. This is quite interesting as we have made no correction for material leaving the box in this \ufb01gure. Material stripped from the disk will continue to add gas with stronger magnetic \ufb01elds, and turbulent stretching of the magnetic \ufb01eld will increase the total magnetic energy in the tail. Indeed, in our weakest MHD run, TORL, the magnetic energy in the tail is larger than the magnetic 14 Fig. 11.\u2014 Mass contours of tail gas as a function of tracer fraction and B magnitude. Tail gas is de\ufb01ned as in Figure 9. The columns from left to right are TORL, TORH, DIP. At later times it become clear that there is more unmixed gas in the TORH tail than in either of the other tails. Fig. 12.\u2014 Mass contours of tail gas as a function of density and B magnitude. Tail gas is de\ufb01ned as in Figure 9. The columns from left to right are TORL, TORH, DIP. TORH, with the strongest magnetic \ufb01eld, has much more high-density gas at 500 Myr than the other two MHD runs. 15 Fig. 13.\u2014 Top Panel: The total magnetic energy in the disk (dotdashed lines) and tail (solid lines) for the three MHD runs. There is a dramatic increase in the magnetic energy in the tails over time, and the tails add magnetic energy to the ICM. Bottom Panel: The average magnetic \ufb01eld in a cell in the disk (dot-dashed lines) and tail (solid lines) for the three MHD runs. energy in the disk later than about 400 Myr after the wind has hit the disk. However, we note that as shown in the bottom panel of Figure 13, the mean magnetic \ufb01eld strength in the tail is always less than in the disk. Again, this is because the magnetic \ufb01eld strength increases towards the center of the disk, where ram pressure is not strong enough to remove the disk gas in our simulations. The mean magnetic \ufb01eld in our tails is between 0.3-0.6 \u00b5G, which is within a factor of a few of the observationally-determined intracluster magnetic \ufb01eld strengths outside of cluster centers. 4.2. MicroGauss Fields in the ICM In this section we consider whether magnetic \ufb01elds of \u2265\u00b5G strength exist in our stripped tails, as several observations indicate that intracluster magnetic \ufb01elds are \u223c\u00b5G (e.g. Bonafede et al. 2009; Clarke, Kronberg & B\u00a8 ohringer 2001). From Figures 11 & 12 we know that \u00b5G \ufb01elds do exist in our tail. In Figure 14 we show slices of the magnetic \ufb01eld strength 750 Myr after the wind has hit the disk in the TORH and TORL runs, which have the strongest (TORH) and weakest (TORL) magnetic \ufb01elds in the tail. The structure of the B \ufb01eld in the TORH slice resembles the structure in our mixing slice in Figure 3. This is as we would expect for turbulence to be driving both the increase in our magnetic energy density and mixing between stripped gas and the ICM. From a visual inspection of Figure 14 it is clear that the correlation length of the \ufb01eld in the tail is smaller than galaxy scales. This is somewhat smaller than the scale indicated by Faraday rotation observations, which imply lengths of 10-20 kpc (e.g. Clarke et al. 2001; Eilek & Owen 2002; Clarke 2004). Using a power-law \ufb01t to the B-\ufb01eld observed with Faraday rotation measure and fractional polarization images of the radio galaxy in A2199 Vacca et al. (2012) \ufb01nd the best \ufb01t for the maximum scale of magnetic \ufb02uctuations to be 35 kpc. However, Vogt & En\u00dflin (2003, 2005) \ufb01nd correlation lengths of less than 5 kpc in three clusters and generally argue that the magnetic \ufb01eld correlation length is in fact 2-4 times shorter than the rotation measure \ufb02uctuation scale with which it is often equated. In a re-examination of one of those clusters, Kuchar & En\u00dflin (2011) argue that there is magnetic power up to at least 8 kpc length scales. To directly compare our magnetic \ufb01eld length scales to observations we will need to perform mock observations on a much larger volume of a cluster or observations would need to pinpoint stripped tails in clusters. In Figure 9, the width of the orange contour indicates that the turbulent velocity is a few hundred km/s. The turbulent velocities in the x and y directions seem to be similar based on slices of the x-, y-, and zvelocity. Thus, for the lower-density gas in our tail, 4 \u00d710\u221228 g cm\u22123, and a conservative estimate of the turbulent velocity magnitude of \u221a 3\u00d7100 km/s, the average magnetic \ufb01eld strength through equipartition should be about 1 \u00b5G. This is a factor of 2-3 higher than we \ufb01nd in the tail (bottom panel of Figure 13), so equipartition is either not reached in this system, or would only be reached after the gas has left our simulated region. In Figure 15, we plot the volume fraction of gas with \u2265\u00b5G magnetic \ufb01elds in the tails in the DIP (red), TORH (blue), and TORL (green) simulations. The dashed lines show the fraction from 10-50 kpc above the disk, and the solid lines show the fraction from 50-100 kpc. The volume fraction is similar, so the magnetic \ufb01eld strength does not fade with distance from the disk. Also, the total volume of \u2265\u00b5G gas increases as we move farther along the tail, although sometimes with a time lag between the near and more distant tail regions. We clearly see that the volume fraction of \u2265\u00b5G gas depends strongly on the galactic magnetic \ufb01eld strength by comparing the fraction in TORH and TORL, so either the turbulence is much stronger in TORH than in 16 Fig. 14.\u2014 Slices of the magnetic \ufb01eld strength 750 Myr after the wind has hit the disk in the TORL (left panel) and TORH (right panel) runs. We chose these two runs because they have the lowest (TORL) and highest (TORH) amount of gas with magnetic \ufb01eld strengths of at least a \u00b5G. The image region is 94 \u00d7 102 kpc. The right panel can be compared to the top panel in Figure 3. Fig. 15.\u2014 The volume fraction of gas with \u2265\u00b5G magnetic \ufb01elds in tails in the DIP (red), TORH (blue), and TORL (green) simulations. The dashed lines show the fraction from 10-50 kpc above the disk, and the solid lines show the fraction from 50-100 kpc. The volume fraction is similar, so the total volume of \u00b5G gas increases as we move farther along the tail, although sometimes with a time lag between the near and more distant tail regions. TORL (which does not seem to be the case looking at the velocity structure in Fig. 9), or the seed \ufb01eld from the disk is more important than a turbulent dynamo in determining the magnetic \ufb01eld strength in the tail. 5. DISCUSSION 5.1. Comparison with previous work We compare our results to earlier work that has examined similar properties of ram pressure stripped disks and tails. First, we \ufb01nd that the remaining disk gas mass and radius in our simulations agree well with the non-cooling hydrodynamic runs in Tonnesen & Bryan (2009) and Roediger & Br\u00a8 uggen (2006). The di\ufb00erences between our results and theirs are because we use the tracer fraction rather than a density cut to de\ufb01ne our disk gas and because we use the maximum radius at which high tracer fraction gas can be found to de\ufb01ne our radius (rather than the minimum radius at which low density gas can be found). Also, our tail is very similar to the non-cooling tail in Tonnesen & Bryan (2010), morphologically, in density-temperature space, and in velocity structure. The range of resolutions used, 40-80 pc in Tonnesen & Bryan (2009; 2010), 159 pc in this work, and 500 pc in Roediger & Br\u00a8 uggen (2006) highlights that these results are insensitive to resolution. Ruszkowski et al. (2014) examined the impact of intracluster magnetic \ufb01elds on stripping of disk galaxies, but did not include galactic magnetic \ufb01elds. Because they use a di\ufb00erent galaxy model, we cannot compare our results directly to theirs and can only make qualitative comparisons. They \ufb01nd that including a magnetic \ufb01eld in the ICM changes the stripping rate from that of the pure hydrodynamic case with a face-on wind. The initial stripping rate is the same (for the \ufb01rst \u223c100 Myr), then the MHD run has slower stripping to a maximum di\ufb00erence in the disk gas of less than 15%, at which point the 17 MHD stripping rate increases such that \u223c550 Myr after the wind has hit the disk the MHD and hydrodynamical runs have the same amount of gas in the disk. The authors posit that the slower stripping for \u223c400 Myr is due to the magnetic draping layer that forms on, and protects, the face of the galaxy. This is a process quite separate from any that we simulate, so there is no tension between the two results. Unlike Ruszkowski et al. (2014), we do not \ufb01nd a dramatic di\ufb00erence in the morphology of our tails with and without magnetic \ufb01elds. The di\ufb00erences observed in Ruszkowski et al. (2014) may occur because they also include radiative cooling, a process that dramatically affects tail structure, as discussed in detail in Tonnesen & Bryan (2010). This paper compares, in hydrodynamic and magnetohydrodynamic runs, the morphology of gas in the tail, the \u03c1-T distribution of gas in the tail, and examines how stripped gas may be mixed into the ICM, all without including radiative cooling. However, Tonnesen & Bryan (2010; also Tonnesen et al. 2011) have stressed the necessity of including radiative cooling in order to reproduce HI, H\u03b1, and X-ray observations of ram pressure stripped tails. Including radiative cooling, however, can result in disks and tails that are clumpier than those observed (Tonnesen & Bryan 2009; Ruszkowski et al. 2014) and may miss the more di\ufb00use ISM that would become di\ufb00use stripped gas. While, as these authors have shown, this low-density gas will not be observed in HI and H\u03b1 emission, understanding how this gas mixes with the ICM is very important to understanding how ram pressure stripping will pollute the ICM with metals and magnetic \ufb01elds. Our examination of how magnetic \ufb01elds a\ufb00ect the di\ufb00use gas tail is a step in understanding that process. In this paper, we only consider a face-on wind geometry. The role of the inclination angle in disk gas stripping has been considered in previous work (e.g. Quilis et al. 2000; Vollmer et al. 2001; Schulz & Struck 2001; Roediger & Br\u00a8 uggen 2006; J\u00b4 achym et al. 2009), so here we do not focus on tilted disks. However, we can brie\ufb02y discuss the possible impact of galactic magnetic \ufb01elds on the ram pressure stripping of tilted disks. The previous works listed above have generally found that inclination angle does not have a strong impact on the amount of gas stripped from a disk until the wind is close to edge-on, at which point much less gas is removed from the galaxy. We see no reason for the inclusion of galactic magnetic \ufb01elds to change these results. As we have found, the stripping rate of gas that is bound by magnetic \ufb01elds does not di\ufb00er from the stripping rate of the purely hydrodynamical case, so we would not expect this result to change with galaxy inclination. However, as we have discussed, the disk in TORH has expanded in the z-direction due to the strong magnetic pressure. In the highly inclined case, we would expect more gas removal in the TORH run because the more distant gas has a weaker gravitational restoring force from the disk. We expect that at high inclination angles the height of the disk gas above the galaxy plane is more important than whether there are magnetic \ufb01elds. 5.2. Comparison With Observations As we discussed in our introduction, Murphy et al. (2009) compare maps of the FIR-radio correlation between ram pressure stripped and normal galaxies, and \ufb01nd radio de\ufb01cits along the face of the interaction between the galaxy and the ICM. They believe that these radio de\ufb01cits are due to the sweeping out of low density gas and the corresponding magnetic \ufb01elds rather than compression towards the disk plane because there is no ridge of strong radio emission between the radio de\ufb01cit and the galaxy mid plane. We look for physical insight into these observations by examining the magnetic \ufb01eld magnitude of disk gas as a function of distance below the disk. We can only look at the TORL and TORH runs, because in the DIP run the di\ufb00erential rotation in the disk increases the central magnetic \ufb01eld strength, leaving us unable to determine whether any of the increase in the magnetic \ufb01eld strength is due to compression from the ICM wind. In Figure 16, we plot contours of the amount of gas mass within a 5 kpc radius cylinder around the disk center as a function of magnetic \ufb01eld magnitude and zdistance below the disk plane. The range of |B| magnitude at a single distance below the disk is due to the range in galactic radius. We choose to focus on the small central region so that the \ufb01gure does not become more complicated by a larger range of magnetic \ufb01eld values. We show the output before the wind hits the disk, the output at which the wind hits the disk (the shock front in the ICM has just passed the disk plane), 25 Myr after the wind has hit the disk, and 500 Myr after the wind has hit the disk. Immediately as the wind hits the disk, we see that the magnetic \ufb01eld strength increases as a shock propagates through the disk. This increase in |B| magnitude corresponds to an increase in density from the shock. However, this increase is short-lived, and by 25 Myr after the wind has hit the disk there is no enhancement of the magnetic \ufb01eld (or density). As predicted in Murphy et al. (2009) and Vollmer et al. (2010), lower density gas is swept away. The edges continue to be ablated, so gas that is not quickly swept away mixes with the nonrotating ICM and is eventually removed, as can be seen by the shrinking of the disk in the z-direction from 25 Myr to 500 Myr after the wind has hit the disk. 6. CONCLUSIONS We have run high-resolution galaxy simulations including galactic magnetic \ufb01elds in order to understand how galactic magnetic \ufb01elds a\ufb00ect ram pressure stripping and mixing into the ICM. We compare a hydrodynamical simulation to two simulations with toroidal galactic magnetic \ufb01elds (TORL and TORH) and a run with a dipolelike magnetic \ufb01eld (DIP). Our main conclusions are: 1. Magnetic \ufb01elds in the galactic disk do not dramatically change the stripping rate or amount of gas removed from Milky Way-type galaxies. Even including a \ufb01eld with a radial component that links high and lowdensity gas does not e\ufb00ect the initial stripping rate due to magnetic tension dragging gas from the disk at the \ufb01eld strength we simulate. The stripping pro\ufb01les in all four runs are nearly identical beyond 360 Myr after the wind has hit the disk (Figure 5). 2. The density and pressure of gas in the disk is also very similar in all four runs, although we see some evidence that a magnetic \ufb01eld inhibits the acceleration of stripped gas at later times. Speci\ufb01cally, we \ufb01nd that 18 Fig. 16.\u2014 Mass contours of central disk gas that lies below the disk mid plane as a function of B Magnitude and distance from the disk plane. Here central disk gas is de\ufb01ned as gas within the central 5 kpc radius with a tracer fraction of more than 0.6. The top row is TORL and the bottom is TORH. Each column is a di\ufb00erent time step: t=25 Myr, the output immediately before the wind hits the disk, t=30 Myr, the output at which the wind hits the disk (reaches the mid plane of the disk), t=55 Myr, or 25 Myr after the wind has hit the disk, and t=530 Myr, or 500 Myr after the wind has hit the disk. As the wind initially hits the disk the B magnitude increases as a compression wave moves across the disk. However, by 25 Myr after the wind hits the disk, there is no increase in the B magnitude anywhere on the wind-facing side of the central disk. In the last column we see that this remains true throughout the simulations. in the TORH and DIP runs the bulk of the gas being removed by the ICM wind leaves the disk with lower velocities than in the TORL and Hydro runs (Figures 7 & 8). 3. The velocity structure in the tail is very similar in all four runs, with two consistent di\ufb00erences: \ufb01rst, within 20 kpc of the disk, the Hydro run has more gas accelerated to high velocities than any MHD run, and second, more than 20 kpc above the disk, the majority of gas in the tail in the TORH and DIP runs is moving away from the disk at velocities equal to or greater than the tail gas in the Hydro run (Figure 9). 4. More dense gas survives in the MHD tails from 170 Myr to 310 Myr (Figure 10). By 500 Myr, the di\ufb00erence between the MHD and Hydro runs has shrunk, but persists throughout the simulations. We use Figures 11 and 12 to determine that this is because the magnetic \ufb01eld in the stripped tail inhibits mixing with the surrounding ICM. 5. The magnetic energy in the tail increases with time as the volume of the tail increases (Figure 13). We \ufb01nd that the mean magnetic \ufb01eld in the tail seems to plateau between 0.3-0.6 \u00b5G, and up to 15% of the volume of the tail has magnetic \ufb01eld strengths of at least 1 \u00b5G, but this depends on the strength of the magnetic \ufb01eld in the disk. Indeed, the \ufb01eld strength in the tail seems to depend more on the galactic magnetic \ufb01eld strength than on turbulent enhancement. 6. We examine the magnetic \ufb01eld on the wind-facing side of our disk and \ufb01nd that the magnetic \ufb01eld only brie\ufb02y (\u223c25 Myr) increases due to compression from the shock front traveling through the disk, and otherwise the magnetic \ufb01eld strength is de\ufb01cient in comparison to the \ufb01eld strength before the wind hits. This is in good agreement with the observational \ufb01ndings of Murphy et al. (2009), and does not require ram pressure to a\ufb00ect the star formation rate in galaxies. Although the tails that we are modeling are disordered \ufb02ows that vary with time, we \ufb01nd that including magnetic \ufb01elds will allow mostly unmixed gas to survive to larger distances from the disk-both by inhibiting mixing and by allowing for more acceleration of the tail gas by the ICM wind. We also \ufb01nd initial evidence that ram pressure stripping can magnetize the ICM. While only 5-15% of the gas has \u00b5G magnetic \ufb01eld, we see from Figure 14 that a much larger fraction of the tail has 0.1 \u00b5G \ufb01eld strengths, and that the mean \ufb01eld in the tail is at least 0.3 \u00b5G, which is within a factor of a few of the observationally-inferred intracluster magnetic \ufb01eld strength outside the cluster core. As we discuss (\u00a73.2.2), because our magnetic Prandtl number of 1 is orders of magnitude below Pm in the ICM and ISM, turbulence in our simulated tails likely strengthens the magnetic \ufb01eld much less than in nature. It is also worth noting that our ram pressure strength and ICM velocity were selected from a sample of galaxy orbits in a cosmologically-simulated cluster (with M200\u223c4\u00d71014 M\u2299) taken from about the virial radius (Tonnesen et al. 2007; Tonnesen & Bryan 2009). As shown in Figure 5, these galaxies are stripped of less than 60% of their gas, leaving their inner disks intact. As galaxies experience higher ram pressure, particularly closer to the cluster center, they may be completely stripped, polluting the ICM with stronger magnetic \ufb01elds. Our tails are at least 100 kpc long and more than 30 kpc wide, so could contribute to a large area-covering fraction in a cluster. Assuming no overlap, there would 19 need to be about 165 tails that are 30 kpc in diameter and 200 kpc long within 1 Mpc for an area covering factor of unity. Solanes et al. (2001) \ufb01nd 171 HI de\ufb01cient galaxies within 1 Abell radius (1.5 h\u22121 Mpc) in the Virgo cluster. If all of these galaxies have been ram pressure stripped with \u223c200 kpc tails, similar to but longer than we are able to simulate in our small domain, magnetic \ufb01elds in stripped tails would have an area-covering factor of \u223c25% with 2 Mpc of the Virgo cluster center. This may be a lower estimate of the number of galaxies that can contribute to the intracluster magnetic \ufb01eld, because if magnetic \ufb01elds thread through galactic gas halos, galaxies that are not HI de\ufb01cient could also contribute magnetic energy to the ICM. We can test if strong stripping is necessary to add signi\ufb01cant magnetic energy to the ICM by simply rerunning our simulations with slower and lower-density winds. In the future we will simulate a larger box to determine how long unmixed gas survives in the ICM, predicting how long strong metallicity gradients will survive in cluster gas. While in this work we are using ideal MHD, we also plan to include anisotropic conduction, which may a\ufb00ect the heating and mixing of the tail gas relative to that in the hydrodynamic simulation. Determining tail lengths and magnetic \ufb01eld strength and correlation length in the tails is important for determining how much of the magnetic \ufb01eld measured in clusters could come from ram pressure stripped galaxies. Future observational constraints on the magnitude, volume \ufb01lling factor and correlation length of the intracluster magnetic \ufb01eld will allow us to more clearly determine the fraction of the total intracluster magnetic \ufb01eld that can be attributed to magnetized stripped tails. We acknowledge support from NSF grant PHY1144374 and from Princeton University through the Lyman Spitzer, Jr. Fellowship. Computations were performed on resources provided by the Princeton Institute for Computational Science and Engineering. We thank Professor Greg Bryan for useful discussions, and Professor Ming Sun and Professor Je\ufb00rey Kenney for useful comments. We also thank our anonymous referee for comments and suggestions that improved the quality of this paper.",
                    "introduction": "1. As galaxies orbit within a cluster, their interstellar medium (ISM) may interact directly with the intraclus- ter medium (ICM), the hot halo of gas bound by the cluster gravitational potential. This type of interaction may take the form of ram pressure stripping (RPS), in which the ISM is removed through momentum transfer by the ICM (Gunn & Gott 1972). ISM-ICM interac- tions also include continuous stripping by thermal evap- oration, Kelvin-Helmholtz instabilties, or turbulent vis- cous stripping (Cowie & Songaila 1977; Chandrasekhar 1961; Nulsen 1982). ISM-ICM interactions have been well-studied using hy- drodynamic simulations (e.g. Abadi et al. 1999; Schulz & Struck 2001; Roediger & Hensler 2005; Roediger & Br\u00a8 uggen 2006; Roediger & Br\u00a8 uggen 2007; Quilis, Moore & Bower 2000; Kronberger et al. 2008; Kapferer et al. 2009; J\u00b4 achym et al. 2009; Tonnesen & Bryan 2009, 2010, 2012; Tonnesen et al. 2011; sticky particle simulations in e.g. Vollmer et al. 2001; Vollmer et al. 2002). Work including radiative cooling has found that stripped tails can extend several hundred kpc (Kronberger et al. 2008; Kapferer et al. 2009; Tonnesen & Bryan 2010; Tonnesen et al. 2011), in agreement with HI observations of some cluster galaxies (e.g. Oosterloo & van Gorkom 2005). However, very little work has been done using magne- tohydrodynamic (MHD) simulations. Ruszkowski et al. (2014) include ICM magnetic \ufb01elds and radiative cool- ing, and \ufb01nd that intracluster magnetic \ufb01elds a\ufb00ect the tail morphology. The clumpy gas in a hydrodynamic ra- diatively cooling tail is smoothed to a more \ufb01lamentary structure when intracluster magnetic \ufb01elds are included. Pfrommer & Dursi (2010) argue that their MHD simula- tions show that observations of polarized intensity con- tours on the face of ram pressure stripped galaxies can be used to determine the orientation of magnetic \ufb01elds in"
                },
                {
                    "url": "http://arxiv.org/abs/1405.1049v1",
                    "title": "On the Reversal of SFR-Density Relation at z=1: Insights from Simulations",
                    "abstract": "Recent large surveys have found a reversal of the star formation rate\n(SFR)-density relation at z=1 from that at z=0 (e.g. Elbaz et al.; Cooper et\nal.), while the sign of the slope of the color-density relation remains\nunchanged (e.g. Cucciati et al.; Quadri et al.). We use state-of-the-art\nadaptive mesh refinement cosmological hydrodynamic simulations of a 21x24x20\n(Mpc/h)$^3$ region centered on a cluster to examine the SFR-density and\ncolor-density relations of galaxies at z=0 and z=1. The local environmental\ndensity is defined by the dark matter mass in spheres of radius 1 Mpc/h, and we\nprobe two decades of environmental densities. Our simulations produce a large\nincrease of SFR with density at z=1, as in the observations of Elbaz et al. We\nalso find a significant evolution to z=0, where the SFR-density relation is\nmuch flatter. The color-density relation in our simulations is consistent from\nz=1 to z=0, in agreement with observations. We find that the increase in the\nmedian SFR with local density at z=1 is due to a growing population of\nstar-forming galaxies in higher-density environments. At z=0 and z=1 both the\nSFR and cold gas mass are tightly correlated with the galaxy halo mass, and\ntherefore the correlation between median halo mass and local density is an\nimportant cause of the SFR-density relation at both redshifts. We also show\nthat the local density on 1 Mpc/h scales affects galaxy SFRs as much as halo\nmass at z=0. Finally, we find indications that the role of the 1 Mpc/h scale\nenvironment reverses from z=0 to z=1: at z=0 high-density environments depress\ngalaxy SFRs, while at z=1 high-density environments tend to increase SFRs.",
                    "authors": "Stephanie Tonnesen, Renyue Cen",
                    "published": "2014-05-05",
                    "updated": "2014-05-05",
                    "primary_cat": "astro-ph.GA",
                    "cats": [
                        "astro-ph.GA",
                        "astro-ph.CO"
                    ],
                    "main_content": "star-forming SDSS galaxies to star-forming galaxies in the GOODS-S and GOODS-N fields at z\u223c1. They find a reversal of the SFR-density relation: specifically that the median <SFR> decreases with increasing galaxy density in the local sample, while at z\u223c1, the median <SFR> first increases with increasing galaxy density before peaking and then decreasing again at the highest densities. They claim that the increase of <SFR> with local galaxy density is caused by increases of both M\u2217and sSFR with galaxy density. Because in general sSFR decreases with increasing M\u2217(e.g. Blanton et al. 2003; Baldry et al. 2004), they conclude that at z\u223c1 the environment must enhance the SFR of galaxies in order for sSFR to increase while M\u2217increases. Cooper et al. (2008; C08) also observed the reversal of the SFR-density relation by comparing a local SDSS sample to the z\u223c1 DEEP2 sample (not limited to starforming galaxies), but came to a somewhat different conclusion. Because they find that the sSFR decreases with local density at both z\u223c0 and z\u223c1, they conclude that the reversal of the SFR-density relation is mainly due to the different luminosity-density (and mass-density) relations of the blue galaxies in their samples at the two redshifts: at z\u223c1 MB increases with local density, while at z\u223c0, MB is constant with local density. Several observations of individual clusters at z\u223c1.5 find that they already have a significant passive galaxy population (e.g. McCarthy et al. 2007; Kurk et al. 2009; Wilson et al. 2009; Strazzullo et al. 2010), indicating that at least the color-density relation extends beyond z\u223c1. Further, using an early release of the UKIDSS UltraDeep Survey, Chuter et al. (2011) find a strong relationship between rest-frame (U \u2212B) color and galaxy environment to z\u223c1.5, with red galaxies residing in significantly denser environments than blue galaxies on scales 2 below 1 Mpc. Using a more complete UKIDSS UltraDeep Survey data release, Quadri et al. (2012; Q12) use a mass-selected sample to show that galaxies with quenched SF tend to reside in dense environments out to as least z\u223c1.8. Speci\ufb01cally, they \ufb01nd that the quiescent fraction increases with local density, even at high redshift. It is di\ufb03cult to synthesize these observational results into a single coherent picture, as they use di\ufb00erent wavelengths to measure color and/or SFR, use di\ufb00erent methods to measure local density, observe di\ufb00erent \ufb01elds and de\ufb01ne their galaxy samples di\ufb00erently. In addition, semianalytic models (SAMs) have not reproduced observations of the reversal of the SFR-density or color-density relations (E07; Cucciati et al. 2006; 2012). In this paper we present the SFR-density, sSFRdensity, and quiescent fraction of galaxies at z = 0 and z = 1 in a hydrodynamic cosmological simulation. We choose these redshifts in order to compare our results to recent work, speci\ufb01cally E07, C08, and Q12. We focus on one region centered around a cluster within a large simulation with box side of 120 h\u22121 Mpc, with size 21\u00d7 24\u00d720 h\u22123 Mpc3, which gives us a broad range of local environments to study. Our goal is to gain physical insight into what sets galaxy SFRs by comparing the SFR, sSFR, and quiescent fraction as a function of environmental density on the same galaxy sample. After a brief description of our simulations (Section 2.1), we discuss our galaxy selection technique and our method for determining quantities for each galaxy in Section 2.2. In Section 2.3 we de\ufb01ne our local density parameter. In Section 3 we compare our results to E07 (Section 3.1), C08 (Section 3.2) and Q12 (Section 3.3). We then discuss and interpret our results in terms of the halo mass (\u00a74.1), and highlight why our results di\ufb00er from those based on semi-analytic models in Section 4.2. Finally, we summarize our main conclusions (\u00a75). 2. METHODOLOGY 2.1. The Simulations For the details of our simulations, we refer the reader to Cen (2012), although for completeness we reiterate the main points here. We perform cosmological simulations with the adaptive mesh re\ufb01nement (AMR) Eulerian hydrodynamical code Enzo (Bryan 1999; O\u2019Shea et al. 2004; Joung et al. 2009). We use cosmological parameters consistent with the WMAP7-normalized LCDM model (Komatsu et al. 2011): \u2126M = 0.28, \u2126b = 0.046, \u2126\u039b = 0.72, \u03c38 = 0.82, Ho = 100 h km s\u22121 Mpc\u22121 = 70 km s\u22121 Mpc\u22121, and n = 0.96. We \ufb01rst ran a low resolution simulation with a periodic box of 120 h\u22121 Mpc on a side, and identi\ufb01ed a region centered on a cluster at z = 0. We then resimulated the region with high resolution, but embedded within the outer 120 h\u22121 Mpc box to properly take into account large-scale tidal \ufb01eld e\ufb00ects and appropriate \ufb02uxes of matter, energy and momentum across the boundaries of the re\ufb01ned region. The re\ufb01ned region we discuss in this paper is 21\u00d724\u00d720 h\u22123 Mpc3 centered on a cluster of \u223c2\u00d71014 M\u2299with a virial radius (r200) of 1.3 h\u22121 Mpc. We emphasize that this highly-resolved box is much larger than the cluster at its center, and that therefore there are galaxies in a range of local densities. In Tonnesen & Cen (2012) we compare the local densities of galaxies in this re\ufb01ned region to a di\ufb00erent re\ufb01ned region in the same large periodic box centered around a void, and showed that there is substantial overlap in the distribution of local densities found in the two very di\ufb00erent large-scale environments. We consider two re\ufb01ned simulations of the same region that di\ufb00er in their level of maximum re\ufb01nement. In the re\ufb01ned region in the low resolution simulation, the minimum cell size is 0.46 h\u22121 kpc, using 11 re\ufb01nement levels at z = 0. The initial conditions for the re\ufb01ned region include a mean interparticle separation of 117 h\u22121 kpc comoving and a dark matter particle mass of 1.07\u00d7108 h\u22121 M\u2299. In the high resolution simulation, the minimum cell size is 0.114 h\u22121 kpc, using 13 re\ufb01nement levels at z = 0, with an initial mean interparticle separation of 58.6 h\u22121 kpc comoving and a dark matter particle mass of 1.5\u00d7107 h\u22121 M\u2299. We only have the z=1 output of the HR simulation, because it has not yet run to z=0. The simulations include a metagalactic UV background (Haardt & Madau 1996), a model for shielding of UV radiation by neutral hydrogen (Cen et al. 2005), and metallicity-dependent radiative cooling (Cen et al. 1995). The fraction and density of neutral hydrogen is directly computed within the simulations. Star particles are created in gas cells that satisfy a set of criteria for star formation proposed by Cen & Ostriker (1992), and reiterated with regards to this simulation in Cen (2012). Once formed, the stellar particle loses mass through gas recycling from Type II supernovae feedback, and about 30% of the stellar particle mass is returned to the ISM within a time step. Supernovae feedback is implemented as described in Cen (2012): feedback energy and ejected metal-enriched mass are distributed into 27 local gas cells centered at the star particle in question, weighted by the speci\ufb01c volume of each cell, which is to mimic the physical process of supernova blastwave propagation that tends to channel energy, momentum, and mass into the least dense regions (with the least resistance and cooling). We allow the whole feedback process to be hydrodynamically coupled to surroundings and subject to relevant physical processes, such as cooling and heating, as in nature. The low resolution simulation used in this paper has compared several galaxy properties that depend critically on the feedback method to observations and found strong agreement (Cen 2011a-c; Cen 2012). We do not include a prescription for AGN feedback in this simulation, and as a result, our simulation overproduces luminous galaxies at the centers of groups and clusters of galaxies. This is discussed in detail in Cen (2011c), who shows that the luminosity function of the simulated galaxies agrees well with observations at z=0 except at the high-luminosity end. When Cen (2011c) adds an AGN feedback correction in the post-simulation analysis for halos with masses greater than 1013 M\u2299or for galaxies with stellar masses above 4\u00d71012 M\u2299, the simulated luminosity function also agrees with observations at the high luminosity end. In the low resolution run, each star particle has a mass of \u223c106 M\u2299, which is similar to the mass of a coeval globular cluster. In the high resolution run, each star particle has a mass of \u223c105 M\u2299. 2.2. Galaxies 3 We use HOP (Eisenstein & Hut 1998) to identify galaxies using the stellar particles. HOP uses a two-step procedure to identify individual galaxies. First, the algorithm assigns a density to each star particle based on the distribution of the surrounding particles and then hops from a particle to its densest nearby neighbor until a maximum is reached. All particles (with densities above a minimum threshold, \u03b4outer) that reach the same maximum are identi\ufb01ed as one coherent group. In the second step, groups are combined if the density at the saddle point which connects them is greater than \u03b4saddle). We use HOP because of its physical basis, although we expect similar results would be found using a friends-of-friends halo \ufb01nder. This has been tested and is robust using reasonable ranges of values (e.g. Tonnesen, Bryan, & van Gorkom 2007). After we identify galaxies using stellar particles, we create our sample using only well-resolved galaxies within our re\ufb01nement region. First, we restrict our sample to galaxies that have resided in the re\ufb01ned region since the beginning of the simulation. To do this, we require that all of the dark matter particles within the virial radius (in detail, we use r200, the radius within which the average density is 200 times the critical density, which is directly calculated using simulation output) of each galaxy be the low-mass dark matter particles with which we populated the re\ufb01ned region of our simulation. Second, we only consider those galaxies with a stellar mass greater than 5\u00d7109 M\u2299. We choose this lower limit to our stellar mass because we have found that above this mass our sample is more than 75% complete (Cen 2014). We have tested that including lower mass galaxies down to 108 M\u2299has little quantitative and no qualitative e\ufb00ect on our results. Implementing these two criteria leaves 61% of the originally identi\ufb01ed galaxies at z=0 in the low resolution run. We plotted projections of the star particles of each of the galaxies identi\ufb01ed by HOP at z=0 in order to verify \ufb01rst that HOP was identifying galaxy-like objects (with a stellar density peak), and second, that HOP was not grouping multiple galaxies together. Only a few of the galaxies above our minimum mass that HOP identi\ufb01ed had density pro\ufb01les without a strong density peak, and a small number of HOP-identi\ufb01ed galaxies in fact had two density peaks, and one had three peaks. Both of these problems add up to a misidenti\ufb01cation of only 2%. In this paper we measure the stellar mass (M\u2217), dark matter halo mass (Mhalo), cold gas mass (Mcold), SFR, MB, and g \u2212r color. Stellar mass is determined by adding the mass of each star particle identi\ufb01ed by HOP to belong to a galaxy. The dark matter halo mass is calculated by summing the mass of all the dark matter particles out to r200. The cold gas mass is de\ufb01ned slightly di\ufb00erently in the low resolution versus the high resolution simulation due to di\ufb00erences in how the galaxy data sets were originally made, although as we now discuss the di\ufb00erences are minor for the purposes of this paper. In the low resolution simulation, Mcold is the sum of all HI gas within r200. As noted in Section 2.1, the fraction and density of neutral hydrogen is directly computed within the simulations. The high resolution data set includes values of the total gas within 100 kpc and 300 kpc with a temperature less than 105 K. Because this gas is at the peak of the cooling curve it quickly cools to \u223c104 K, and there is therefore little e\ufb00ective di\ufb00erence in the temperatures of the two cold gas de\ufb01nitions. However, rather than use one or the other of these set radii, in order to compare with the Mcold from the low resolution run we want to include all of the cold gas within r200. Therefore, in order to estimate the cold gas within the virial radius of galaxies in the high resolution simulation, we separate the galaxies into low-mass galaxies with Mhalo < 2.5\u00d71011M\u2299(and therefore virial radii at or less than 100 kpc), high-mass galaxies with Mhalo > 6\u00d71012M\u2299(and virial radii at or greater than 300 kpc), and galaxies that fall between these two extremes. The two extreme cases are simple, and Mcold is either the gas within 100 kpc for the low-mass galaxies or within 300 kpc for the high-mass galaxies. For all other galaxies, we use the halo mass to determine the fraction of gas between 100-300 kpc that we will include in Mcold, using Mcold = M100kpc + (Mhalo/6\u00d71012)\u00d7(M300kpc-M100kpc). With these de\ufb01nitions, Mcold is consistent between the lowand high-resolution simulations at z=1. The luminosity of each stellar particle at each of the Sloan Digital Sky Survey (SDSS) \ufb01ve bands is computed using the GISSEL stellar synthesis code (Bruzual & Charlot 2003), by supplying the formation time, metallicity and stellar mass. MB is calculated as MB = Mg + 0.313\u00d7(Mg\u2212Mr)+0.2271 (Lupton 2005). The SFR for a galaxy is calculated based on the creation time and mass of each star particle. 2.3. Local Density We choose to use dark matter mass to de\ufb01ne the local environment because it is a fundamental measure of the local mass in a region. Further, using dark matter mass is not plagued by the uncertainties in using galaxy counts as a measure of local density. In simulations the galaxy number count could be a\ufb00ected by resolution issues that may a\ufb00ect galaxy number counts, while in observational samples local galaxy counts may be a\ufb00ected by projection e\ufb00ects due to lack of means to distinguish between peculiar velocity and Hubble velocity. We de\ufb01ne the local environment by measuring the dark matter mass in spheres with a comoving radius of 1 h\u22121 Mpc. In this paper we focus on how galaxy SFRs and gas content may be a\ufb00ected on scales larger than the virial radius (all halos except the cluster halo have virial radii less than 1 h\u22121 Mpc), for example whether residing in collapsed \ufb01laments and pancakes would a\ufb00ect these properties (Cen 2011c). This is done by summing the dark matter mass directly, not demanding that it is within the virial radius of any galaxy. We randomly select 27 000 positions within the re\ufb01ned region (with a 2 h\u22121 Mpc bu\ufb00er at each edge) to be the center of the spheres. Thus we oversample our box and end up with a total of 27 000 environments that we probe, which we di\ufb00erentiate by the dark matter mass in the sphere, Msph. However, not every r=1 h\u22121 Mpc sphere will contain a galaxy, so when we determine galaxy properties as a function of environment, we only consider those spheres that contain galaxies. This technique of choosing random spheres in space rather than spheres centered on galaxies di\ufb00ers from that used by many observers, however, E07 compare average 4 SFRs found in regions centered on galaxies to those found in regions centered on grid points independent of galaxy positions, and \ufb01nd negligible di\ufb00erence between the two techniques. 3. RESULTS 3.1. The reversal of the <SFR>-density relation We \ufb01rst determine whether our SFR-density relation evolves from z=0 to z=1. To facilitate comparisons to E07 we use similar galaxy selection criteria and methods. E07 study the evolution of the SFR-density relation by comparing local SDSS galaxies to the GOODS-S and GOODS-N \ufb01elds at z \u223c1. They use a magnitude cut in both samples, MB \u2264-20, which they state is equivalent to a stellar mass cuto\ufb00of M\u2217\u2265109 M\u2299at z=0.8 and M\u2217\u22651010 M\u2299at z= 1.2 (the two extremes of their high-redshift range). The local galaxy density is determined by counting all the galaxies within boxes centered on each galaxy of 1.5 comoving Mpc on a side, in a velocity interval \u2206v = \u2206z/(1 + z), \u2206z =0.02. E07 only include star-forming galaxies in their sample, down to SFRUV limits of 0.5 M\u2299yr\u22121 for the z\u223c1 sample. They use the star-forming galaxy sample and SFRs calculated in Brinchmann et al. (2004) for the low-redshift SDSS sample. E07 \ufb01rst calculates an average SFR (<SFR>) and local galaxy density in boxes centered on every galaxy. Then they group the galaxies into local density bins and \ufb01nd the median of the distribution of <SFR>. They \ufb01nd that the median <SFR> decreases with increasing galaxy density in the SDSS sample, but, at z\u223c1, the median <SFR> \ufb01rst increases with increasing galaxy density before peaking and then decreasing at the highest local densities. These results are not reproduced by a SAM using the Millennium simulation. In the SAM, there is never a reversal of the SFR-density relation, just a gradual \ufb02attening (it is not \ufb02at by z=1). When only examining galaxies with 5\u00d71010 < M\u2217/M\u2299< 5\u00d71011, E07 \ufb01nds that the sSFR increases with increasing local density. They claim that the increase of <SFR> with local density is due to increases of both M\u2217and sSFR with galaxy density. Because in general sSFR decreases with increasing M\u2217(e.g. Blanton et al. 2003; Baldry et al. 2004), they \ufb01nd it likely that the environment enhances the SFR of massive galaxies. In order to examine comparable galaxy samples, we examine galaxies from our z=1 and z=0 outputs and use the same magnitude cut as E07 (MB \u2264-20). As discussed in Section 2.2, we also only include galaxies with M\u2217> 5\u00d7109 M\u2299. All galaxies that ful\ufb01ll our magnitude and mass criteria are included in our sample. Recall that the MB cut in E07 is equivalent to an M\u2217cuto\ufb00of 109 M\u2299and 1010 M\u2299at z=0.8 and z=1.2, respectively, so the lower mass cut is well-matched to the GOODS-S and GOODS-N samples. We separate our galaxies into local density (Msph) bins as de\ufb01ned in Section 2.3. We then plot <SFR> as in E07, \ufb01rst calculating the average SFR (<SFR>) in each r=1 h\u22121 Mpc sphere, then binning the spheres by local density (Msph) so that each bin has at least 100 spheres in each simulation output, and \ufb01nally \ufb01nding the median <SFR> in each local density bin. Results are shown as blue \u20dd(z=0 low resolution (LR)), orange \u25b3(z=1 LR), and red \u2207(z=1 high Fig. 1.\u2014 The median values of the <SFR> in bins de\ufb01ned by dark matter mass (Msph) as a measure of local density. The shaded regions denote the 25th-75th percentiles of the <SFR> distribution at z=0 LR (blue) and z=1 HR (red). This \ufb01gure plots galaxies with MB \u2264-20, and 5\u00d7109 < M\u2217/M\u2299. We overplot values from the E07 paper\u2013in magenta and purple we plot the GOODS-S and GOODSN samples, respectively, and in cyan we plot the SDSS sample. We de\ufb01ne the highest local density measurement in the GOODS-N bin to be in a DM halo of \u223c1.5\u00d71013 M\u2299, and assume that \u03a3gal \u221d Msph. resolution (HR)) in Figure 1. The horizontal bars denote the Msph bin sizes. The shaded regions enclose the 25th to the 75th percentiles of the z=1 HR (red) and z=0 LR (blue) samples, denoting the (lower and upper) limits of the upper and lower quartiles of the data. We \ufb01nd that in the z=1 HR output, the <SFR> increases with increasing local density from Msph\u223c5\u00d71011 M\u2299to Msph\u223c1013 M\u2299, then decreases towards the highest Msph. In the z=1 LR output, the <SFR> increases up to the highest Msph. At z=0 the <SFR>-density relation is nearly \ufb02at until the highest Msph bin, at which point the <SFR> increases. We compare the <SFR> in the lowest and highest Msph bins, and \ufb01nd that the comparison is quite di\ufb00erent in the z=1 and z=0 samples. At z=1 the <SFR> in the highest Msph bin is nearly an order of magnitude more than the <SFR> in the lowest Msph bin, while at z=0 the <SFR> in the highest Msph bin is three times that in the lowest Msph bin. In Figure 1 we include all galaxies that ful\ufb01ll our luminosity and mass criteria, including both star-forming and passive galaxies. However, our result that the <SFR>density relation is much steeper at z=1 than at z=0 is robust to whether or not we include only star-forming galaxies. If we limit our sample to galaxies with SFR > 0.5 M\u2299yr\u22121 (at both z=0 and z=1), the median <SFR> is unchanged up to Msph = 3\u00d71012 M\u2299, and the median <SFR> in our \ufb01ve highest density bins increases by at most 33% in the z=1 (HR or LR) outputs, and by as much as a factor of two in our z=0 output. The z=1 <SFR> remains universally higher than the z=0 <SFR>. For comparison, we also plot values from E07 Figure 5 Fig. 2.\u2014 Top: The median and mean values of the <sSFR> in bins de\ufb01ned by dark matter mass (Msph) as a measure of local density. This panel plots galaxies with MB \u2264-20, and 5\u00d71010 < M\u2217/M\u2299, as in the bottom panel of Figure 20 from E07 (the E07 values are overplotted). To show that this result is not dominated by massive galaxies, we overplot galaxies with 5\u00d71010 < M\u2217/M\u2299 < 5\u00d71011 as dash-dotted lines. The <sSFR> increases, then decreases. Bottom: The median values of the <M\u2217> in Msph bins. As in E07, we include galaxies with MB \u2264-20, and 5\u00d7109 < M\u2217/M\u2299, and \ufb01nd that the mass of galaxies increases with local density (Msph). 8. The qualitative agreement between the trends at z=1 is clear, although there is a large amount of uncertainty in the alignment and stretch in the x-axis. In order to compare our density measure (Msph) directly with that used in E07, we re-scale the E07 density values. The largest group in the E07 z=0.8-1.2 sample has LX[0.5-2 keV] = 2\u00d71042 erg s\u22121, so is about 2-3\u00d71013 M\u2299(Stanek et al. 2006). Thus, we choose the highest local density bin in the GOODS-N sample to be in a Msph bin centered at 1.5\u00d71013 M\u2299, and assume that there is a one-to-one relationship between the 2D (\u03a3gal in E07) and 3D (Msph in this work) local density measures\u2013i.e. \u03a3 \u221d\u03c1. In agreement with observed local mass-density relations (e.g. Balogh et al. 2001; Blanton et al. 2003), E07 \ufb01nd that the average stellar mass of 0.8<z<1.2 galaxies increases as a function of local density (top panel of their Figure 20). Based on the relationship between mass and sSFR (e.g. Blanton et al. 2003; Baldry et al. 2004), this indicates that the sSFR of galaxies should decrease as a function of increasing local density. However, when they consider only massive galaxies at z=1, speci\ufb01cally 5\u00d71010 < M\u2217/M\u2299< 5\u00d71011, the average sSFR increases as a function of local density (bottom panel of their Figure 20). Thus, E07 conclude that the local environment causes the increase in the <SFR> at higher local densities at z=1. In order to determine if our results conform to the interpretation in E07, in the top panel of Figure 2 we plot the median of the <sSFR> of the massive galaxies in our sample (5\u00d71010 < M\u2217/M\u2299) binned by local density (Msph). Because our lack of AGN feedback will increase the SFR in massive galaxies, thus causing an increasing <sSFR>-density relation, we also plot the <sSFR>density relation for 5\u00d71010 < M\u2217/M\u2299< 5\u00d71011 galaxies. We choose this mass range because it matches the masses studied in E07 and because the SFRs we measure would not be lowered by AGN feedback. The lower mass range is shown as the dashed lines connecting the smaller symbols. We also overplot values from Figure 20 in E07, scaled by a factor of two. We scale the values so that the relative shapes from the observations and simulations can be easily compared. In the bottom panel of Figure 2 we plot the median <M\u2217> of the 5\u00d7109 < M\u2217/M\u2299total sample, which also increases with increasing Msph (the median <M\u2217> of the 5\u00d71010 < M\u2217/M\u2299sample also increases with increasing Msph). We overplot the M\u2217values from E07, multiplied by two. Because our simulated <SFR> values are similar to those in observations (cf. Figure 1), our lower <sSFR> values indicate that our simulated stellar masses are too high. Indeed, we \ufb01nd better agreement between the simulated and observed stellar masses when we multiply the observed M\u2217by two. Our <sSFR> increases by about a factor of two while the <sSFR> in E07 increases by a factor of about four. Further, the shape of our sSFR-density relation is quite di\ufb00erent from that in E07 as it is \ufb02at from 1012<Msph/M\u2299<5\u00d71012. However, as in E07, we \ufb01nd that although M\u2217increases, sSFR does not decrease up to at least Msph\u223c5\u00d71012. This is true for either mass range or resolution we consider. Since we expect an increase in M\u2217to drive a decrease in sSFR, our <sSFR>density relation may be \ufb02atter than that in E07 because our <M\u2217>-density relation increases more steeply (Figure 2). We \ufb01nd that our stellar masses tend to be larger and increase more quickly with increasing local density. We speculate that rerunning our simulation with a lower star formation e\ufb03ciency might lower early SFRs, producing lower-mass galaxies. 3.2. Comparing the SFR-density and sSFR-density relations We next use a galaxy sample matched to that in C08 to compare the SFR-density relation to the sSFR-density relation. As in C08, in this section at each redshift we use the same galaxy sample when we measure the SFR and sSFR as a function of density. C08 used SDSS galaxies at low redshift and the DEEP2 sample at z\u223c1. The colorindependent completeness limit of the DEEP2 survey at 6 Fig. 3.\u2014 The median values (with the shaded area denoting the 25th-75th percentiles) of the sSFR and SFR in local density bins de\ufb01ned by dark matter mass. This \ufb01gure uses a redshift-dependent magnitude cut that is MB \u2264-20.53 at z=1 and MB \u2264-19.16 at z=0, following C08. We again only include galaxies with 5\u00d7109 < M\u2217/M\u2299. We overplot estimated values from C08\u2013the DEEP2C sample in purple, and the SDSS-B sample in cyan. In order to compare the shapes of the relations, the sSFR in the DEEP2C sample is scaled by a factor of 4 (divided by 4), and the SFR in the DEEP2-C sample is scaled by a factor of 3. We de\ufb01ne the highest local density measurement in DEEP2 to be in a DM sphere of 2\u00d71013 M\u2299, and assume that \u03a3gal \u221dMsph. z = 1.05 is MB \u2264-20.6, so in their DEEP2-C sample they use a redshift-dependent magnitude cut that is MB \u2264-20.53 at z=1 and MB \u2264-19.16 at z=0 (SDSS-B sample). We choose to compare to this magnitude-limited observed sample because the magnitude limit acts to remove the lowest-mass galaxies from their sample (see C08 Figure 7). This results in a closer match to the mass range in our simulated sample, which, as discussed in Section 2.2, has a minimum stellar mass of 5\u00d7109 M\u2299. Our median sSFR and SFR as a function of local density (Msph) are shown in Figure 3. As in C08, we simply take the median SFR or sSFR of all galaxies that fall into Fig. 4.\u2014 The median values of MB of blue galaxies in Msph bins\u2013 our measure of local density. As in Figure 3, we only plot galaxies with 5\u00d7109 < M\u2217/M\u2299, but do not use a minimum brightness cut and instead use a color cut: g \u2212r < 0.64 at z=0 and g \u2212r < 0.57 at z=1. The MB of galaxies in each Msph bin are similar at z=0 and z=1 HR, and decrease with increasing local density. a bin of local density (Msph) (rather than the median of the average SFR or sSFR in each Msph as in Section 3.1). As in the previous \ufb01gures, the z=0 LR is blue \u20dd, z=1 LR is orange \u25b3, and z=1 HR is red \u2207. The horizontal lines denote the Msph bin sizes. The shaded regions enclose the region between the 25th and 75th percentiles of the z=1 HR (red) and z=0 LR (blue) samples. Our bins are selected to include at least 100 galaxies. We overplot estimates of the values from Figures A1 & A2 in C08. As in Sec. 3.1, we re-scale the observed density measure to compare directly with our own density measure, Msph. The DEEP2 survey does not probe clusters, but includes somewhat larger groups at z\u223c1 than the GOODS \ufb01elds (Gerke et al. 2005), so we align Msph with the density measure in C08 such that the highest local density measurement in DEEP2 is in a DM sphere of 2\u00d71013 M\u2299. We again assume that there is a one-to-one relationship between the 2D (\u03a3gal in C08) and 3D (Msph in this work) local density measures. We \ufb01nd that sSFR decreases with increasing local density (Msph) at both z=0 and z=1 (top panel of Figure 3). The z=0 sSFR-density relation is in very good agreement with the C08 SDSS-B sample\u2019s relation. The shape of both the z=1 LR and HR sSFR-density relations match that of the DEEP2-C sample, although the absolute value of the sSFR is low by a factor of 4 (LR) to 8 (HR). In order to quantitatively match the observed sSFR in C08 (and SFR), we would need to raise our SFRs, which would probably require changing some of the variables in our star formation prescription. While it is di\ufb03cult to predict how changing our thresholds for star formation or our star formation e\ufb03ciency would affect our simulation at low redshift, it is possible that, for example, lowering the star formation e\ufb03ciency could delay star formation in our simulation, resulting in lowermass galaxies and more gas available for higher SFRs at later times. Testing a series of these values in our 7 zoom-in boxes is beyond the scope of this work, but an array of lower-resolution cosmological simulations with these types of variations have been compared using a smoothed-particle hydrodynamics (SPH) code in Schaye et al. (2010). Changing our star formation e\ufb03ciency would similarly a\ufb00ect halos of all masses and in all environments, so we expect the redshift dependence of the SFR-density relation to be robust to changes in the star formation e\ufb03ciency. In the bottom panel of Figure 3, at z=0, our SFRdensity relation is nearly \ufb02at until Msph > 1.3\u00d71013 M\u2299, at which point the SFR drops steeply with Msph. While the C08 result (SDSS-B sample) drops by a similar fraction, it does so more smoothly and gradually. At z=1, our SFR-density relation rises and falls more than in C08, but at Msph\u22652\u00d71012 M\u2299, the shape of our SFR-density relation is in decent agreement with C08. As with the <SFR>-density relation (Figure 1), we \ufb01nd that at z=1 the 75th percentile of the SFR of galaxies initially increases dramatically (by a factor of more than 5) as Msph increases to 8\u00d71012 M\u2299, while in this \ufb01gure the 25th percentile of SFR stays \ufb02at. In contrast, at z=0 the 75th percentile of the SFR of galaxies increases by less than a factor of 3. This indicates that a population of strongly-star-forming galaxies is driving the increasing SFR-density relation at z=1. C08 \ufb01nd that their observed reversal of the SFRdensity relation is largely due to the fact that the mean MB of the blue galaxies in their samples decreases with local density at z=1 but is \ufb02at with local density at z=0. They \ufb01nd that MB is correlated with M\u2217, with scatter, so we can loosely rewrite their result to say that the M\u2217of the blue galaxies in their sample increases with local density at z=1 but is \ufb02at at z=0. Blue galaxies dominate their z=1 sample, so the increase in SFR with increasing local density re\ufb02ects the MB-density relation (or M\u2217-density relation). C08 claim that at z=1 only their highest local density bin has enough red galaxies to \ufb02atten the SFRand MB-density relations. At z=0, blue galaxies do not completely dominate the sample, so an increasing fraction of red galaxies will cause the median SFR to decrease with local density. Also, MB does not vary strongly with local density, so there is no strongly star-forming population driving an increase in the median SFR with increasing local density. In Figure 4 we plot the median MB versus Msph for blue galaxies (g \u2212r < 0.64 at z=0 and g \u2212r < 0.57 at z=1, see Figure 5) with 5\u00d7109 < M\u2217/M\u2299(no minimum brightness cut). There are several points to discuss in comparing our MB-density relation to that in C08 (their Figure 17). First, in our simulations MB decreases (and M\u2217increases) with local density (Msph) at both redshifts. In the z=1 HR sample the median MB of galaxies in the lowest Msph bin agrees with that in C08, but quickly moves to brighter MB values as the local density increases. The z=1 LR blue sample always has brighter median MB values than either the z=1 HR or the C08 galaxies, and MB increases the most steeply in the z=1 LR blue sample. At z=0 the median MB of our simulated galaxies is always brighter than that of the C08 SDSS sample, and decreases with increasing local density. As we do not include dust in our simulations, we would expect our galaxies to be somewhat brighter than those in C08 (somewhere between 0.5-1.2 dex; Shao et al. 2007). Also, the same adjustment to our simulation that we have proposed earlier in this Section may bring our results into closer agreement with those of C08\u2013decreasing star formation e\ufb03ciency will increase the MB of galaxies. 3.3. The color-density relation We now \ufb01nd the red fraction of the simulated galaxies as a function of local density (Msph) at z=0 and z=1. In Figure 5 we plot the g \u2212r color distribution of the galaxies in our three outputs (5\u00d7109 < M\u2217/M\u2299). There is a bimodal distribution in all of the galaxy samples, and we have chosen to split the blue (star-forming) and red (quiescent) populations at g \u2212r = 0.64 at z=0 and g \u2212r = 0.57 at z=1. As our simulation does not have dust, this single color-cut is su\ufb03cient to di\ufb00erentiate star-forming from quiescent galaxies. We tested that varying the value of the color-cut by 10% has little quantitative impact on our results. We plot the fraction of red (quiescent) galaxies in our samples in Figure 6. At both z=1 and z=0, the fraction of red galaxies increases with increasing Msph. Although there is little evolution in this \ufb01gure from z=1 to z=0, in the z=1 LR sample, the fraction of red galaxies is always smaller than in the z=0 sample, and the z=1 HR sample does not reach the maximum red fraction found in the z=0 sample. We compare our results to those of Q12, who use a mass-selected sample (log(M\u2217/M\u2299) > 10.2) from the UKIDSS Ultra-Deep Survey to plot the quiescent fraction (quiescent galaxies are de\ufb01ned using a color-color cut) of galaxies as a function of local density in di\ufb00erent redshift ranges. They \ufb01nd that even in their highest redshift bin (1.5<z<2.0), the fraction of quiescent galaxies increases with local density. As shown in Figure 6, our results clearly qualitatively agree with those of Q12 (and many others; e.g. McCarthy et al. 2007; Kurk et al. 2009; Wilson et al. 2009; Chuter et al. 2011). As with our previous comparisons to observations, the alignment of the observed galaxy density and Msph is somewhat arbitrary. While our main conclusion is that the color-density relation exists at both z=0 and z=1, we now address the quantitative di\ufb00erences between our quiescent fraction and the observed quiescent fraction in Q12. Our red fraction is too low in low local density (Msph) regions and too high in high local density (Msph) regions in comparison to Q12. This is not an uncommon di\ufb00erence between simulations and observations, and has been seen, for example, in Tonnesen et al. (2007). Some of this may be due to the local density measure used by Q12: the distance to the 8th nearest neighbor. They use photometric redshifts, which have large uncertainties, and interlopers may damp out strong trends in the data (see discussion in Q12). Focusing on our simulation, we have no dust reddening our star-forming galaxies. Although Q12 use a color-color selection in order to limit the number of dusty star-forming galaxy interlopers in their quiescent sample, their quiescent fraction may still be slightly high. Also, we may have too much cold gas in galaxies in lower density regions due to the well-studied cooling \ufb02ow problem (e.g. Fabian 1994; McNamara 2002; Croton et al. 2006), which may lead to low levels of star formation in galaxies that would otherwise have no star formation. In high 8 0.0 0.2 0.4 0.6 0.8 g r 0 10 20 30 40 50 N z=0 LR  0.0 0.2 0.4 0.6 0.8 g r 0 10 20 30 40 50   z=1 LR 0.0 0.2 0.4 0.6 0.8 g r 0 20 40 60 80 100 120   z=1 HR Fig. 5.\u2014 The g \u2212r color distribution of galaxies at the z=0 LR output, the z=1LR output, and the z=1 HR output (from left to right). The panels show all galaxies with 5\u00d7109 < M\u2217/M\u2299. The bimodal distribution is visible in all panels. The red dashed lines denote the g \u2212r color we have chosen to split the blue (star-forming) from the red (passive) galaxies: 0.64 at z=0 and 0.57 at z=1. 1011 1012 1013 1014 1015 Msph (M \u2299) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 fred z=0 LR \u20dd z=1 LR \u25b3 z=1 HR \u2207 M \u2217>1010.2  M \u2299 Q12 0.5 <z <1 \u22c6 1 <z <1.5 \u25b3 z=0 LR \u20dd z=1 LR \u25b3 z=1 HR \u2207 M \u2217>1010.2  M \u2299 Q12 0.5 <z <1 \u22c6 1 <z <1.5 \u25b3 z=0 LR \u20dd z=1 LR \u25b3 z=1 HR \u2207 M \u2217>1010.2  M \u2299 Q12 0.5 <z <1 \u22c6 1 <z <1.5 \u25b3 1011 1012 1013 1014 1015 Msph (M \u2299 h3  Mpc\u22123 ) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 fred z=0 LR \u20dd z=1 LR \u25b3 z=1 HR \u2207 M \u2217>109.7  M \u2299 MB <-20 z=0 LR \u20dd z=1 LR \u25b3 z=1 HR \u2207 M \u2217>109.7  M \u2299 MB <-20 z=0 LR \u20dd z=1 LR \u25b3 z=1 HR \u2207 M \u2217>109.7  M \u2299 MB <-20 Fig. 6.\u2014 The fraction of red (quiescent) galaxies in bins of Msph (local density). Top: We use the same low-mass cut as in Q12, so include all galaxies with 1010.2 < M\u2217/M\u2299. We overplot the results from the Q12 paper that bracket z=1. Bottom: Using the same galaxy sample as in Figure 1. The red fraction is much lower in this MB \u2264-20 sample, but still increases with increasing Msph at both z=0 and z=1. density environments, like the inner regions of clusters, cold gas may be used too quickly to form stars, and, as we have suggested above, decreasing the star formation e\ufb03ciency may also reduce this discrepancy between our simulation and observations. We \ufb01nd that changing our galaxy selection criteria has no qualitative e\ufb00ect on our results. We changed the color-cut di\ufb00erentiating blue (star-forming) and red (passive) galaxies and the mass range of galaxies we included in our galaxy samples, and only included central galaxies in our sample. Perhaps most importantly, in the bottom panel of Figure 6 we plot the red fraction of galaxies that ful\ufb01lled the E07 criteria: MB \u2264-20 and 5\u00d7109 < M\u2217/M\u2299 < 1012. E07 also \ufb01nd that that the color-density relation still exists at z=1. 4. DISCUSSION 4.1. Physical Insight Our \ufb01rst main result is that we reproduce the reversal of the SFR-density relation from z=0 to z=1. We conclude that this is because at z=1 the entire 25th-75th percentile range of SFRs at a given environment shifts upward with increasing local density (Msph), shown as the shaded region in Figures 1 & 3. In z=1 HR there are relatively more highly star-forming galaxies (the 75th percentile) and relatively fewer galaxies with low SFRs (the 25th percentile bottom of the shaded region) up to a peak at Msph\u223c1013 M\u2299in Figure 1. While there is a population of highly star-forming galaxies in the highest density bin in our sample at z=0, there are not enough galaxies with high SFRs to drive a dramatic increase in the median SFR. As we argue in \u00a73.2, this agrees with the observational \ufb01nding by Cooper et al. (2006) of a population of brighter blue galaxies in high local density environments at z\u223c1. We also \ufb01nd that, using the same galaxy sample that shows an evolution in the SFR-density relation, there is an increasing fraction of red, quiescent galaxies as Msph 9 increases (bottom panel of Figure 6). Until the red fraction increases to 50% of the galaxies in the sample, much of the median SFR value will depend upon the distribution of the SFRs of the star-forming galaxies. Indeed, we can see that the red fraction of galaxies that ful\ufb01ll the E07 criteria (MB \u2264-20, 5\u00d7109 < M\u2217/M\u2299) never reaches 50% at z=1 (Figure 6). Therefore, there is no tension between the observations of the median SFR increasing with local density and the observations of the fraction of quiescent galaxies increasing with local density\u2013they are measuring two di\ufb00erent aspects of the galaxy population. This result has been pointed out observationally in E07. 4.1.1. What drives the SFR-density relation? We now look for a better understanding of why a much higher fraction of galaxies have high SFRs in higher density environments at z=1 than at z=0. To do this we will discuss our \ufb01ndings in the context of a current standard theory of gas accretion and star formation. First, we expect that a galaxy\u2019s cold gas reservoir is the fuel for star formation and therefore is an important factor in determining its SFR. One current standard theory of gas accretion (e.g. Kere\u02c7 s et al. 2005; Dekel & Birnboim 2006) contends that the amount of cold gas in a galaxy is determined by its dark matter halo mass, Mhalo. Therefore, one would expect the Mhalo-Msph relation to re\ufb02ect the SFR-Msph and Mcold-Msph relations. In order to compare our results with this theory we must focus only on central galaxies in their halos, as these are the only galaxies for which we could expect a relationship between gas and dark matter halo mass based on the two-mode theory of gas accretion. A number of possible interactions can a\ufb00ect the gas, stellar, and dark matter mass of a satellite galaxy orbiting within a larger galaxy\u2019s halo, as discussed in Boselli & Gavazzi (2006). For satellite galaxies we \ufb01nd that the <SFR> increases with density by a factor of 1.6 at z=1 LR, is \ufb02at with density at z=1 HR and decreases by a factor of 2 with density at z=0. See Cen (2011c) for a detailed examination of why star formation ceases in satellite galaxies in this simulation. In the top panel of Figure 7, we plot the median of the <SFR> for only central galaxies in the simulation, which are the most massive galaxies in their halo. These are galaxies that are beyond two virial radii from any more massive galaxy. Most galaxies in our sample are central galaxies, but the fraction of satellites increases with Msph (local density) until about half of the galaxies in the highest Msph bin are satellites (27% at z=0 LR, 68% at z=1 LR and 53% at z=1 HR). Note that because of the large range in <SFR>, we plot the y-axis on a logarithmic scale. When we focus only on central galaxies our results do not qualitatively change and we still see a dramatic change with redshift in the <SFR>-density relation. In the middle panel of Figure 7 we examine the cold gas reservoir by plotting <Mcold> as a function of Msph. This value measures the amount of gas that is, or will likely soon be, available for star formation. For the low resolution outputs, this is the neutral HI gas that is within the r200 of the parent halo, and for the high resolution output, this is the gas with T < 105 K that is within 100 kpc of the galaxy (see Section 2.2). As we expected, the shape of <Mcold> agrees well with that of Fig. 7.\u2014 The <SFR>, <Mcold> and <Mhalo> of central galaxies with MB\u2264-20 and 5\u00d7109 < M\u2217/M\u2299< 1012 as a function of Msph. Blue (\u20dd) is low-resolution run at z=0, yellow (\u25b3) is the lowresolution run at z=1, and red (\u2207) is the high-resolution run at z=1 Top: Median (shaded region is 25th-75th percentiles) <SFR> in each sphere binned by local density. Middle: Median (shaded region is 25th-75th percentiles) <Mcold> in each sphere binned by local density. The galaxies with the highest SFR tend to have the highest Mcold. Bottom: Median (shaded region is 25th-75th percentiles) of average mass in dark matter halos of central galaxies in each Msph (dark matter sphere) bin. the <SFR> in all three outputs. In the bottom panel of Figure 7 we plot the average dark matter halo mass (<Mhalo>) of galaxies at each Msph. As de\ufb01ned in Section 2.2, the dark matter halo mass is the M200 of the central halo\u2013all the mass encompassed in a region with \u03c1DM/\u03c1crit >200. A key point to remember is that Msph is not usually the mass of a single halo, it is the mass in a sphere with a radius of 1 comoving h\u22121 Mpc (Section 2.3). For reference, the M200 of a single halo with r200 = 1 h\u22121 Mpc is \u223c7\u00d71013 h\u22121 M\u2299. We \ufb01rst notice that at a speci\ufb01c local density (Msph), 10 galaxies tend to reside in similar mass halos at z=1 and z=0. For all three outputs, the general shape of the <Mhalo> curve agrees with the general shape of the <SFR> curve and the <Mcold> curve. However, starting at Msph\u223c4\u00d71012 M\u2299, the di\ufb00erence between the halo masses at z=1 and z=0 is smaller than the di\ufb00erence in the <SFR> and <Mcold>. Interpreting the panels of Figure 7 within the cold-hot two mode theory of gas accretion, it seems that SFR depends on the amount of cold gas, which in turn depends strongly on the halo mass. The cold gas mass increases from the lowest halo masses to higher halo masses because there is simply more gas in more massive halos, although Mcold/M\u2217decreases with increasing halo mass. The fraction of cold gas with respect to the total amount of gas in the halo decreases with increasing halo mass, as found in Kere\u02c7 s et al. (2005), and we see that from the penultimate to the \ufb01nal bin <Mhalo> increases by a higher fraction than either <SFR> or <Mcold> in all three outputs. Kere\u02c7 s et al. (2005) \ufb01nd that hot mode accretion dominates in halos above 1011.4 M\u2299, the median halo mass of galaxies residing in environments with Msph\u223c2.5\u00d71012 M\u2299, the highest density as which we \ufb01nd agreement between the z=1 and z=0 outputs. In this interpretation, the lower fraction of cold gas accretion could be reducing the cold gas available at z=0 with respect to z=1, therefore lowering SFRs at higher halo mass because of reduced supply. This interpretation could be tested by examining higher redshifts and determining how the gas supply and SFR evolve. If Keres et al. (2005) are correct that at z=3 the cold gas fraction decreases with increasing halo mass (although the fraction is consistently higher than at lower redshift) our results suggest that the SFR-density relation should be steeper with increasing density and halo mass at higher redshifts. This would be a good test of whether cold accretion indeed decreases with halo mass at high redshift. 4.1.2. A Closer Examination of Halo Mass In the above section, we have shown that we can \ufb01t our data into a theory in which SFR depends on Mhalo and Mhalo depends on Msph. However, this scenario does not explain the increasing sSFR with increasing Msph show in Figure 2. Therefore in this section we will look directly at how the environment, Msph, a\ufb00ects galaxies with the same Mhalo. To compare the importance of Mhalo to Msph in determining galaxy SFRs we split our central galaxy sample (central galaxies with MB \u2264-20 and 5\u00d7109 < M\u2217/M\u2299) into low local density (Msph < 3\u00d71012 M\u2299) and high local density (Msph > 5\u00d71012 M\u2299) subsamples. This brackets the Msph bin at which the z=1 and z=0 values diverge in Figure 1. In Figures 8 & 9 we then plot galaxy properties in these two sub-samples as a function of Mhalo at z=1 (Figure 8: we only plot the galaxies in the HR simulation for easier viewing, and \ufb01nd the same qualitative results for the LR output) and at z=0 (Figure 9). It is useful to plot SFR and Mcold to compare the absolute values at di\ufb00erent local densities, and plotting SFR and Mcold divided by M\u2217allows us to normalize for the di\ufb00erent M\u2217distributions in the high and low density subsamples. Clearly there will not be halos more massive than 3\u00d71012 M\u2299residing in regions with Msph < 3\u00d71012 M\u2299, so the low density data set stops at that mass. For completeness, we show the higher Mhalo galaxies in the high-density subset. We see that at z=1 (Figure 8), the low-density and high-density samples lie close together. In particular, SFR increases by a factor of more than 5 as Mhalo varies, but at a constant Mhalo the di\ufb00erence between the lowand high-density samples is always less than a factor of 1.5. The sSFR is very \ufb02at with Mhalo such that the di\ufb00erence between the lowand high-density samples at a single Mhalo can be greater than the di\ufb00erence between galaxies in di\ufb00erent Mhalo bins, particularly in the two highest Mhalo bins. However, the absolute value of the di\ufb00erence of the median sSFR in the highand low-density samples is always small. The Mcold of the lowand high-density samples seems to be very di\ufb00erent at high Mhalo, but some of this is probably due to the higher mass of galaxies at higher local densities, which is corrected for in the Mcold/M\u2217plot. In addition to the median Mcold and Mcold/M\u2217tending to be higher at high Msph than at low Msph, we see a tendency in all panels for the 25th-75th percentile range of the high-density galaxy sample to be higher than that of the low-density galaxy sample. At z=0 (Figure 9), the lowand high-density samples lie close enough to one another that again it is di\ufb03cult to immediately determine whether the environment directly impacts the SFR and/or Mcold of galaxies. In both the SFR and Mcold panels, the main di\ufb00erence between lowand high-density galaxies is the larger 25th-75th percentile range of galaxies in high-Msph regions. However, when comparing SFR to sSFR and Mcold to Mcold/M\u2217, it becomes clear that the SFR and Mcold of high-Msph galaxies is enhanced by a larger fraction of high-M\u2217 galaxies. The di\ufb00erences between the low-density and high-density medians normalized by M\u2217are larger than the absolute SFR and Mcold. Indeed, the di\ufb00erence between the sSFR of lowand high-density galaxy samples in the lowest or highest Mhalo bin is similar to the difference between the sSFR in neighboring Mhalo bins. In addition, opposite to the trend at z=1, the 25th-75th percentile range of values di\ufb00ers in the sSFR plot with a consistently higher range of sSFRs in the low-density subsample than in the high-density subsample. Also, when we normalize for M\u2217, we see that in the two lowest Mhalo bins, the di\ufb00erence in median Mcold/M\u2217between galaxies in lowand high-density environments is twice that between galaxies in the same environment. It seems that at z=0 local density has a similar level of impact on the SFR and Mcold of galaxies as the halo mass itself, particularly for lower mass halos (Mhalo<1011.8 M\u2299). When comparing Figures 8 and 9, we see that the difference between lowand high-density galaxies in any individual Mhalo bin tends to show the opposite trends at the two redshifts. At z=0, galaxies in high local density regions tend to have lower SFR, sSFR, Mcold and Mcold/M\u2217than galaxies in low local density regions. In contrast, at z=1, galaxies in high local density regions tend to have higher sSFR and Mcold/M\u2217than galaxies in low local density regions. At z=1 Mhalo is a much stronger driver of galaxy SFR and Mcold than Msph, and we have provided clear evidence that the e\ufb00ect of the environment becomes more important at lower redshift. 11 Fig. 8.\u2014 Galaxy properties as a function of Mhalo at z=1 (HR) for central galaxies only. We split the galaxy sample (MB < -20 and 5\u00d7109 < M\u2217/M\u2299) into low local density (Msph < 3\u00d71012 M\u2299: purple circles) and high local density (Msph > 5\u00d71012 M\u2299: green triangles) samples. In general, the SFR and Mcold change more strongly with Mhalo than with local density (Msph). However, galaxies at higher local densities may have slightly higher SFRs and Mcold. 4.2. The Use of Hydrodynamical Simulations Why does our fully hydrodynamical simulation succeed in reproducing the observed increase in <SFR> with increasing local density at z=1 while SAMs do not (as shown in Elbaz et al. 2007)? Before we consider how the inclusion of hydrodynamics will a\ufb00ect our results, we consider the di\ufb00erence in dark matter resolution in our simulation versus the Millennium simulation. In our low resolution re\ufb01ned region, dark matter particles are \u223c108 M\u2299, about an order of magnitude better than the mass resolution of the Millennium simulation. Thus, we can resolve smaller dark matter halos. As we show in the bottom panel of Figure 7, the increase in the median galaxy halo mass is one of the main causes of the increasing SFR with increasing Msph at z=1. In the lowest Msph, while we \ufb01nd <Mhalo>\u223c1-2\u00d71011 M\u2299, the number of \u223c1011 M\u2299halos in the Millennium simulation may be signi\ufb01cantly under-estimated due to mass resolution. Guo et al. (2011) compare the dark matter halo mass functions in the Millennium simulation and in MS-II, which has more than two orders of magnitude better resolution. They \ufb01nd that at Mhalo= 1011 the mass density of halos in MS is 75% that in MS-II (while at Mhalo= 1012 they nearly agree). If, due to this resolution-dependent underdensity of low-mass halos, <Mhalo> is forced to be an order of magnitude higher at low local densities, there may be no increase in <SFR> with increasing local density. It may be possible to check whether resolution is the main issue by determining if SAMs can reproduce the reversal of the SFR-density relation when halos from the Millenium-II simulation are included in the analysis. Our di\ufb00erent results may also be due to di\ufb00erences in the treatment of gasphysics, including SNe feedback processes and large-scale structure collapse induced shock heating. We \ufb01nd some correlation between Msph and the Mcold and SFR of galaxies (Figures 7, 8, & 9). Cen (2011c) discusses how gravitational heating can be important outside of virialized regions, for example in collapsed \ufb01laments and pancakes. This may be more likely to a\ufb00ect the reservoir of cold gas available to galaxies in high-density large-scale environments. Because we self-consistently include gravitational heating, our simulations include these a\ufb00ects while SAMS cannot. 4.3. AGN Feedback and Resolution Here we will address the e\ufb00ects of AGN feedback and resolution on our results. First, as discussed in Section 2.1, we do not include AGN feedback in this anal12 Fig. 9.\u2014 As Figure 8, but for galaxies at z=0. The di\ufb00erences between galaxies at lowand high-densities are more pronounced at this lower redshift, and indicate that SFR and Mcold are both lower in galaxies in higher local density regions. ysis. Cen (2011c) included a feedback prescription in which star formation is suppressed by a factor f = 1/(1 + (Mh/1013M\u2299)2/3) post simulation, which results in better agreement between the simulated and observed z=0 r-band luminosity functions. This suppression factor only has a large e\ufb00ect on galaxies in halos with masses at or above 1013 M\u2299, so as is clear from Figure 7, it only has a strong e\ufb00ect on the highest density bin. This AGN feedback implementation lowers the <SFR> in Figure 1 by 45% in the \ufb01nal bin of z=1 LR, resulting in a \ufb02at <SFR>-density relation across the two highest density bins. The change is 30% in \ufb01nal bins of the z=1 HR and z=0 outputs, and the shape of the <SFR>-density relation stays unchanged. The general shape of Figure 3 also remains unchanged, although the decrease of SFR and sSFR is slightly steeper in the \ufb01nal two bins for all outputs, which is at densities higher than observed in C08. The di\ufb00erences in all of our other \ufb01gures when we include this AGN feedback are also minor with no qualitative change in our results. While it is useful to point out that our results do not change when we include this form of AGN feedback, because of uncertainties in how AGN feedback should be implemented it is more clear to present our results without post-processing. Importantly, it is not clear that using the same relation between AGN feedback and halo mass is appropriate at z=0 and z=1 (see discussion in the review by Kormendy & Ho 2013 & references therein). If black holes grow before bulges, then the AGN might be more massive at z=1 than at z=0. Kormendy & Ho (2013) argue that black holes are twice as massive relative to the bulge mass using z\u22652 quasars (but see, e.g., Schulze & Wisotzki 2014; Kisaka & Kojima 2010). If the suppression of SF by AGN feedback is directly proportional to AGN mass, then we can test the importance of this di\ufb00erence by suppressing SF by an extra factor of two at z=1. Even if we suppress star formation in the z=1 outputs by a factor of two more than at z=0, the di\ufb00erence between z=1 and z=0 remains. Testing every permutation of star formation suppression by AGN feedback is beyond the scope of this paper, but the fact that our results remain unchanged when including these two possible forms of AGN feedback lead us to believe that the large di\ufb00erence in the SFR-density relation we \ufb01nd at z=1 and z=0 is robust to variations in the prescription used to implement AGN feedback. Resolution can have several impacts on our results, and we are able to examine these e\ufb00ects by comparing our results in the z=1 LR output to the z=1 HR output. Overmerging, discussed in detail in reference to these simulations in Lackner et al. (2012), is a resolution issue in which a lower resolution is in general more conducive to 13 merging among galaxies in crowded environments, such as clusters of galaxies (White 1976; Moore et al. 1996). Because overmerging will have more of an e\ufb00ect at larger local densities, the higher resolution run may naturally have a \ufb02atter M\u2217-density relation. As we see in the bottom panel of Figure 2, overmerging does not seem to have caused a di\ufb00erence between the low resolution and high resolution runs by z=1. If overmerging occurs between z=1 and z=0, and results in galaxies that are too massive at z=0, the simulated SFRs will be higher than observed SFRs-which is indeed what we see in our comparisons. However, lowering the SFRs in our simulation at z=0 will only serve to increase the di\ufb00erence in the relation between the two redshifts, so will only strengthen our result. Resolution may also impact the e\ufb00ect of SN feedback on galaxies. In our implementation of supernovae feedback, energy is channeled into the 27 gas cells surrounding the star particle. With lower resolution, this energy input will not heat the gas to as high temperatures and may allow it to cool relatively more quickly, hence may result in a reduced negative feedback e\ufb00ect in comparison to the higher resolution simulation. As with overmerging, we see that this cannot be a large e\ufb00ect up to z=1 because the low and high resolution runs have similar galaxy mass distributions. However, at z=1 the SFRs, particularly at high densities and in higher mass halos, are larger in the low resolution run than in the high resolution run. By this late in the simulation the galaxies may be massive enough that in the high density central regions of halos rapid cooling is occurring. While in the high resolution run supernovae feedback may result in lower SFRs, the lower resolution run has higher SFRs. It is noteworthy that the di\ufb00erence in the low and high resolution runs at z=1 begins at higher Msph than the di\ufb00erence between the z=1 outputs and the z=0 output. These di\ufb00erences due to resolution do not outweigh the di\ufb00erences in the SFR-density relation at low and high redshift. It is not immediately clear how a di\ufb00erence in supernovae heating would a\ufb00ect z=0 SFRs. If more gas is able to cool in the low resolution run and supernovae continue to heat the gas more e\ufb03ciently in the high resolution run, the SFRs may be higher than in a high resolution run. However, if more of the available gas is used quickly in the low resolution run, the SFRs may be lower at z=0 in the lower resolution run because of a lack of fuel. Schaye et al. (2010) \ufb01nd a lower SFR at late times (z\u22641) in higher resolution runs, in agreement with our \ufb01ndings. As they use a lower resolution SPH simulation and a different feedback scheme, we cannot simply assume their results apply to our simulation, but as we have noted above, a lower SFR at z=0 better matches observations and strengthens our results. 5. CONCLUSION In this paper we examine the SFR-density and colordensity relations at z=0 and z=1 in high resolution cosmological simulations with a re\ufb01ned region of size 21\u00d724\u00d720 h\u22123 Mpc3 centered on a cluster of mass \u223c3 \u00d7 1014M\u2299at z=0. This re\ufb01ned region has a large range of local densities, which allows us to separate the halo-scale from the larger-scale environment. We have utilized the high resolution (0.114-0.46 h\u22121 kpc) in these simulations to examine the SFR of a large sample of galaxies in detail to determine how galaxy properties are related to environment on a 1 h\u22121 Mpc scale at z=0 versus z=1. Our results are summarized below. 1) At z=1, our simulations produce SFRs that increase strongly with increasing local density, as in the observations of E07 (Figure 1). We also \ufb01nd strong evolution in our SFR-density relation from z=1 to a much \ufb02atter SFR-density relation at z=0. In addition, we reproduce the results of Cooper et al. (2008) that the sSFR decreases with increasing density at both z=1 and z=0 (Figure 3). However, as in Elbaz et al. (2007), when we only consider the massive galaxies in our sample, 5\u00d71010 < M\u2217/M\u2299, both sSFR and M\u2217increase with local density (Msph) up to \u223c3\u00d71012 (Figure 2). We \ufb01nd that the increase in median SFR with increasing local density (Msph) at z=1 is caused by an increasing fraction of highly-star forming galaxies at a given local density at higher local densities. Massive (5\u00d71010 < M\u2217/M\u2299) star-forming galaxies drive the increasing SFR-density relation. This agrees with observations of a population of z\u223c1 galaxies with high SFRs at high local density (Cooper et al. 2006; Cooper et al. 2008). 2) Using a galaxy sample matched to Quadri et al. (2012) or to Elbaz et al. (2007), we \ufb01nd that the red fraction increases as a function of local density (Msph) at both z=0 and z=1 (Figure 6). There is no tension between the dramatic di\ufb00erence in the SFR-density relation at z=1 compared to z=0 and the consistency of the color-density relation. 3) We \ufb01nd that the relationship between median Mhalo and local density (Msph) is an important cause of the redshift-dependent behavior of the SFR-density relation (Figure 7). The SFR and Mcold values at z=0 begin to diverge from those at z=1 at lower Msph, \u223c4\u00d71012, than the Mhalo values diverge, at Msph\u223c8\u00d71012. We also show that the local environment on scales of 1 h\u22121 Mpc is more important at z=0 than at z=1, and a\ufb00ects galaxy SFRs as much as halo mass at z=0 (Figures 8 & 9). Finally, we \ufb01nd indications that the role of environment reverses from z=0 to z=1: at z=0 high-density environments depress galaxy SFRs, while at z=1 high-density environments may serve to raise SFRs. We thank an anonymous referee for thoughtful and helpful comments that greatly improved the paper. We thank Dr. David Elbaz for providing observational data to us. Computing resources were in part provided by the NASA HighEnd Computing (HEC) Program through the NASA Advanced Supercomputing (NAS) Division at Ames Research Center. This work is supported in part by grant NASA NNX11AI23G.",
                    "introduction": "1. In the nearby universe, the morphology, color, star for- mation rate (SFR), and mass of galaxies is correlated with local environmental density. Speci\ufb01cally, galaxies tend to be earlier types, more massive, redder and to have lower SFRs and speci\ufb01c SFRs (sSFR \u2261SFR/M\u2217) in higher density environments (Dressler 1980; Oemler 1974; Balogh et al. 2001; Blanton et al. 2003; Hogg et al. 2004; Balogh et al. 1998; Hashimoto et al. 1998; G\u00b4 omez et al. 2003). While galaxy morphology, color, and SFR also depend on mass (e.g. de Vaucouleurs 1960; de Vaucouleurs 1962; Strateva et al. 2001; Blanton et al. 2003; Baldry et al. 2004), Kau\ufb00mann et al. (2004) bins galaxies by mass and \ufb01nds that star formation history (SFH) depends on the local density at any galaxy stellar mass. The \ufb01rst evidence that the galaxy population in clus- ters may evolve with redshift was found by Butcher & Oemler (1978), who observed that galaxies in clusters beyond z\u223c0.4 tend to be bluer than galaxies in nearby clusters. However, the Butcher & Oemler observations did not compare the cluster to the \ufb01eld populations at high redshift, while later observations showed that galax- ies in all environments had higher SFRs in the past (Lilly et al. 1996; Madau et al. 1996; Wilson et al. 2002). Us- ing large surveys able to probe a range of environments at high redshifts, recent observations have found that the SFR-density and color-density relations may be re- versed at z\u223c1 compared to those at z\u223c0 (e.g. Cucciati et al. 2006; Elbaz et al. 2007; Cooper et al. 2008; Ideue et al. 2009; Salimbeni et al. 2009; Tran et al. 2010; Gr\u00a8 utzbauch et al. 2011; Popesso et al. 2011). For example, Elbaz et al. (2007; E07) compare local"
                },
                {
                    "url": "http://arxiv.org/abs/1203.0308v1",
                    "title": "Star Formation in Ram Pressure Stripped Tails",
                    "abstract": "We investigate the impact of star formation and feedback on ram pressure\nstripping using high-resolution adaptive mesh simulations, building on a\nprevious series of papers that systematically investigated stripping using a\nrealistic model for the interstellar medium, but without star formation. We\nfind that star formation does not significantly affect the rate at which\nstripping occurs, and only has a slight impact on the density and temperature\ndistribution of the stripped gas, indicating that our previous (gas-only)\nresults are unaffected. For our chosen (moderate) ram pressure strength,\nstripping acts to truncate star formation in the disk over a few hundred\nmillion years, and does not lead to a burst of star formation. Star formation\nin the bulge is slightly enhanced, but the resulting change in the\nbulge-to-disk ratio is insignificant. We find that stars do form in the tail,\nprimarily from gas that is ablated from the disk and the cools and condenses in\nthe turbulent wake. The star formation rate in the tail is low, and any\ncontribution to the intracluster light is likely to be very small. We argue\nthat star formation in the tail depends primarily on the pressure in the\nintracluster medium, rather than the ram pressure strength. Finally, we compare\nto observations of star formation in stripped tails, finding that many of the\ndiscrepancies between our simulation and observed wakes can be accounted for by\ndifferent intracluster medium pressures.",
                    "authors": "Stephanie Tonnesen, Greg L. Bryan",
                    "published": "2012-03-01",
                    "updated": "2012-03-01",
                    "primary_cat": "astro-ph.CO",
                    "cats": [
                        "astro-ph.CO"
                    ],
                    "main_content": "We use the adaptive mesh refinement (AMR) code Enzo. To follow the gas, we employ an adaptive mesh for solving the fluid equations including gravity (Bryan 1999; Norman & Bryan 1999; O\u2019Shea et al. 2004). The code begins with a fixed set of static grids and automatically adds refined grids as required in order to resolve important features in the flow. Our simulated region is 311 kpc on a side with a root grid resolution of 1283 cells. We allow an additional 6 levels of refinement, for a smallest cell size of 38 pc. We refine the grid based on the local gas mass, such that a cell was flagged for refinement whenever it contained more than about 4900 M\u2299. We found that these parameters quickly refined most of the galactic disk to 38 pc resolution. The run also refined much of the wake to a spatial resolution of about 76 pc, and the dense clouds to 38 pc. The simulation includes radiative cooling using the Sarazin & White (1987) cooling curve extended to low temperatures as described in Tasker & Bryan (2006). To mimic effects that we do not model directly (such as turbulence on scales below the grid scale, UV heating, magnetic field support, or cosmic rays), we cut off the cooling curve at a minimum temperature Tmin so that the cooling rate is zero below this temperature. In the simulations described here we use Tmin = 300 K, below the threshold for neutral hydrogen formation. In previous work (Tonnesen & Bryan 2009; 2010), we have explored the impact of adopting a Tmin value of 8000 K, finding the effect to be relatively small. 2.1 Star Formation and Feedback Implementation Star formation occurred in our finest grid cells (38 pc) when two criteria were met: 1) the gas density in a cell exceeded a critical overdensity (in our runs, this was set to a density of about 3.85 \u00d7 10\u221225 g cm\u22123), and 2) the gas temperature was below 1.1 \u00d7 104 K. The reader may note that this set of criteria is missing two commonly used requirements for star formation (e.g. Cen & Ostriker 1992): (1) there is a convergent flow, and (2) the mass in the cell exceeds the Jean\u2019s mass. We chose not to require a convergent flow because we intend to look for star formation in the stripped gas tail and may not be able to resolve the internal structure of the clouds in the tail accurately. In a previous paper (Tonnesen & Bryan 2010), we have shown that dense gas can be accelerated to nearly 1000 km s\u22121. In addition, we have dropped the requirement that the mass in the cell must exceed the Jeans mass because with this condition, our minimum temperature floor could prevent star formation except in the densest cells. Using our minimum allowed gas density and maximum temperature for star formation, the Jeans mass is 300 times the mass in a cell. We fulfill the Truelove criterion (1997) using those parameters, but will discuss the limits of our resolution in more detail in Section 4.4.1. The implementation of star formation and feedback is explained in detail in Tasker & Bryan (2006), and our summary here directly reflects that paper (but is included for completeness). When the gas in a cell meets our requirements for star formation, some of the gas is turned into a star particle. The mass of the star particle is: m\u2217= \u01eb \u2206t t \u2206t tdyn \u03c1gas\u2206x3 (1) in which \u01eb is the star formation efficiency, \u2206t is the timestep, tdyn is the local dynamical time, \u03c1gas is the gas density and \u2206x is the cell size. The efficiency parameter was chosen to match the Kennicutt-Schmidt relation (as in Tasker & Bryan 2006). The star formation and feedback parameters we use are given in Table 1. If the above requirements are met and the resulting star particle will have a mass above a minimum mass, m\u2217min, it is formed. This mass is chosen so that a large number of small star particles will not slow down the simulation. However, if the star particle would have a smaller mass, the probability that it will form is equal to the ratio of the mass of the projected star particle to m\u2217min. If the star particle is then formed, its mass is the minimum of m\u2217min and 80% of the mass in the gas cell. Thus, the probability of forming stars in any individual cell is low, but this algorithm still produces stars at the specified rate. This is done by keeping track of the amount of mass in cells that fulfilled all of the star formation criteria except the minimum mass requirement. When the mass of the unformed stars reaches the minimum mass, star particles will form even if they are below the specified minimum mass. In order to make sure that we were not missing any stars formed in the larger volume of the stripped tail, we allowed for a smaller minimum mass in our simulation with ram pressure stripping. As we will show, this lower m\u2217min does not change the star formation in the disk, but we did find that the lower minimum was necessary to form the correct amount of stars in the tail. We also include stellar feedback from Type II supernova explosions. Not only may this be important for regulating star formation in the galactic disk (e.g. Tasker & Bryan 2006; Robertson et al. 2004), but feedback from star formation in a stripped gas tail could enhance the rate at which stripped gas mixes with the ICM. Star formation in a molecular cloud is likely to be spread out over a dynamical time, and so in order to calculate the timeline of feedback, stars in a particle are considered to form according to the relation: c \u20dd2011 RAS, MNRAS 000, 1\u2013?? 4 S. Tonnesen and G. L. Bryan Variable Value \u03c1min 3.85 \u00d7 10\u221225 g cm\u22123 Tmax 1.1 \u00d7 104 K \u01eb 0.5% m\u2217min 104 M\u2299(SFNW) 102 M\u2299(SFW) \u01ebSN 10\u22125 Table 1. Star Formation and Feedback Parameters mstar(t) = m\u2217 Z t tSF (t \u2212tSF) \u03c4 2 exp \u2212(t \u2212tSF) \u03c4 dt, (2) where tSF is the time at which the star particle was formed and \u03c4 = max(tdyn, 10 Myr). As in Tasker & Bryan (2006), over a time period of a few \u03c4, 10\u22125 of the rest-mass energy of the stars is added to the thermal energy of the gas in the cell in which the star particle has been created. This corresponds to approximately 56 solar masses of stars formed for each 1051 erg SN. 2.2 The Galaxy Our galaxy is placed at a position corresponding to (155.5,155.5,68.42) kpc from the corner of our cubical 311 kpc computational volume, so that we can follow the stripped gas for more than 200 kpc. The galaxy remains stationary throughout the runs. The ICM wind \ufb02ows along the z-axis in the positive direction, with the lower z boundary set for in\ufb02ow and upper z boundary set as out\ufb02ow. The x and y boundaries are set to out\ufb02ow in all three cases. We chose to model a massive spiral galaxy with a \ufb02at rotation curve of 200 km s\u22121. It consists of a gas disk that is followed using the adaptive mesh re\ufb01nement algorithm (including self-gravity of the gas and any newly formed stars), as well as the static potentials of the (pre-existing) stellar disk, stellar bulge, and dark matter halo. We directly follow Roediger & Br\u00a8 uggen (2006) in our modeling of the stellar and dark matter potential and gas disk. In particular, we model the stellar disk using a Plummer-Kuzmin disk (see Miyamoto & Nagai 1975), the stellar bulge using a spherical Hernquist pro\ufb01le (Hernquist 1993), and the dark matter halo using the spherical model of Burkert (1995). This dark matter halo model is compatible with observed rotation curves (Burkert 1995; Trachternach et al. 2008). The equation for the analytic potential is in Mori & Burkert (2000). We describe our disk in detail in Tonnesen & Bryan (2009, 2010). Brie\ufb02y, our stellar disk has a radial scale length of 4 kpc, a vertical scale length of 0.25 kpc and a total mass of 1011 M\u2299; the stellar bulge has a scale length of 0.4 kpc and a total mass of 1010 M\u2299; and the dark matter halo has a scale radius of 23 kpc and a central density of 3.8\u00d710\u221225 g cm\u22123. The gas disk has about 10% of the mass in the stellar disk, and radial and vertical scales of 7 kpc and 0.4 kpc, respectively. To identify gas that has been stripped from the galaxy we also follow a passive tracer that is initially set to 1.0 inside the galaxy and 10\u221210 outside. In the following analysis, we will use a minimum tracer fraction of 25% to \ufb01nd gas stripped from the galaxy (our conclusions do not change if we use 10% instead). 2.3 The Simulations All three of the galaxies we discuss in this paper initially evolve in a static, high-pressure medium with \u03c1 = 9.152 \u00d7 10\u221229 g cm\u22123 and T = 4.15 \u00d7 106 K, to allow cool, dense gas to form in the galaxy. This naturally generates a multiphase ISM (see Tasker & Bryan (2006) and Tonnesen & Bryan (2009) for more discussion of the ISM properties). In our simulation without star formation, after 155 Myrs we reset the boundary conditions to generate a constant ICM in\ufb02ow along the inner z-axis, which is always face-on to the galaxy. We chose this time so that the galaxy would have formed high density gas clouds (\u03c1 > 10\u221223 g cm\u22123) by the time the wind hits the galaxy (190 Myr after the start of the simulation). In our comparison case with star formation, we delay the onset of the wind by about 18 Myr in order to allow the galaxy to evolve for more than 200 Myr before the wind hits the disk. We do this for two reasons: \ufb01rst, because Tasker & Bryan (2006) found that the star formation rate in the disk settles to a relatively constant value after about 200 Myr of star formation, and second, because at that point in our simulations the azimuthally-averaged relation between gas surface density and SFR surface density agrees with that found in Kennicutt (1989, 1998). While we could have chosen to wait longer, this change would have no qualitative e\ufb00ect on our conclusions. In this paper we discuss three simulations. All of these runs have the same initial conditions (same galaxy density pro\ufb01les evolving in a static ICM with \u03c1 = 9.152 \u00d7 10\u221229 g cm\u22123 and T = 4.15 \u00d7 106 K and a cooling curve following Sarazin & White (1987) extended to Tmin = 300 K). Two of these simulations include star formation, SFNW and SFW. SFNW evolves in a static ICM, while SFW initially evolves in a static ICM and is later stripped by a higher-density ICM wind. The \ufb01nal simulation we discuss in this paper is NSFW, which is the same simulation as SFW without star formation. NSFW is the Tmin = 300 K case discussed in our earlier paper, Tonnesen & Bryan (2010). In both wind cases, Pram = \u03c1v2 ICM = 6.4 \u00d7 10\u221212 dynes cm\u22122, and vICM = 1413 km s\u22121. The ICM wind has a T = 4 \u00d7 107 K and \u03c1 = 3.2 \u00d7 10\u221228 g cm\u22123. 2.4 Projections Enzo outputs the density and temperature of the gas in each cell. To transform these values into H I column density and H\u03b1 intensity, we used Cloudy, version 08.00 of the code, last described by Ferland et al. (1998). Using a grid of temperatures and densities, we calculated the hydrogen neutral fraction and H\u03b1 emissivity. In the Cloudy calculation, we included cosmic microwave background radiation, the cosmic ray background, bremsstrahlung radiation from the ICM and the 2005 version of the Haardt & Madau (2001) z = 0 metagalactic continuum, as implemented by Cloudy. We found that including a local interstellar radiation \ufb01eld emission resulted in somewhat lower amounts of neutral gas. Since much of our gas is very distant from the galaxy, we decided not to include this radiation. We also found that removing bremsstrahlung radiation did not signi\ufb01cantly change any of the values we considered. We chose to calculate the neutral fraction and H\u03b1 emissivity (from collisionally heated di\ufb00use gas; emission from c \u20dd2011 RAS, MNRAS 000, 1\u2013?? Star Formation in Ram Pressure Stripped Tails 5 HII regions will be dealt with separately) for a thin planeparallel gas cloud of width 100 pc. We selected this width because it corresponds roughly to the cell size of most of the gas in the highly resolved tails, and accounts approximately for radiative transfer e\ufb00ects. If we assumed the radiative thin limit, it would slightly decrease the amount of H I we predict, and slightly increase the H\u03b1 emission for dense, low-temperature gas. Ideally, we would include the radiation \ufb01eld with radiative transfer directly in the simulation, but this is not yet feasible (and only has a slight impact on the dynamics); instead we post-process these results to get reasonable predictions for the ionization fraction and H\u03b1 emissivity (see Furlanetto et al. 2005 for a discussion of various approaches in the context of Ly\u03b1 emission). For a more detailed discussion, we refer the reader to Tonnesen & Bryan (2010). 3 RESULTS 3.1 Star Formation in the Galactic Disk We will \ufb01rst compare the star formation in the galactic disks of the SFNW and SFW cases to determine if and how ram pressure stripping a\ufb00ects disk star formation. We de\ufb01ne the disk to extend 2 kpc from the the central disk plane, which includes all of the star formation in the SFNW run. First, in the top panel of Figure 1 we plot the star formation rate (SFR) as a function of time for the SFNW and SFW runs. For the \ufb01rst 220 Myr the SFRs are nearly identical. The higher m\u2217min in SFNW only makes the SFR slightly less smooth over time, and does not a\ufb00ect the agreement of SFNW and SFW. Shortly after the ICM wind hits the SFW galaxy disk, its SFR drops precipitously. This \ufb01gure clearly shows that ram pressure stripping quickly lowers the SFR and does not induce even a short-lived burst of star formation (at least at the level of ram pressure modeled here). While our exact star formation recipe results in a SFR in our models that is high for an isolated Milky-Way sized spiral galaxy, we emphasize that it is the comparison between SFNW and SFW that is important in this work. In the bottom panel of Figure 1 we plot the radius including 95% of the new stars formed in the disk against time. As in the panel above, we \ufb01nd that the two cases are nearly identical for the \ufb01rst 200 Myr. However, it takes \u223c 70 Myr longer than for the SFR (until \u223c290 Myr) for the star-formation radii to diverge. This is likely because dense clouds have formed up to 17 kpc from the disk centre that cannot be instantly stripped by the ICM wind. It is only after these clouds have formed stars or been ablated \u2014 had their own edges stripped by the wind until they are destroyed or are of low enough density to be removed from the disk by the ICM wind \u2014 that the star-formation radius drastically drops. In the two previous \ufb01gures we focused on the total star formation rate. Now we will look at how star formation rate relates to the gas surface density. Even though the star formation rate does not spike when the wind hits the galaxy, it could be high relative to the surface density of the gas remaining in the disk. In Figure 2 we plot the Schmidt-Kennicutt relationship of each galaxy for each timestep (Schmidt 1959; Kennicutt 1989). We focus on the Figure 1. The top panel plots star formation rate (SFR) as a function of time in the simulated galaxy with no wind (SFNW, black line) and in the galaxy that is hit by an ICM wind after about 210 Myr (SFW, red line). About 10 Myr after the wind hits the disk, the SFR of the galaxy begins quickly decreasing, and continues to decrease throughout our run, as the disk gas is stripped. The bottom panel plots the disk radius (in kpc) that includes 95% of the new stars formed as a function of time for the same runs as in Figure 1. Once the wind hits the SFW galaxy (red), this outer star forming radius decreases, but not as quickly as the SFR (Figure 1), probably because some dense clouds in the disk cannot be stripped by the wind, so instead form stars. outputs at times later than 250 Myr (shown as diamonds in this \ufb01gure), as this is both when the SFR becomes constant in the SFNW case (see Fig. 1), and also after the SFW galaxy begins being ram pressure stripped. Limiting ourselves just to those points after 250 Myr, we can see that the Schmidt-Kennicutt relationship closely follows the observed relation in both cases, plotted as the solid line (2.5 \u00d7 10\u22124 (\u03a3gas/ 1 M\u2299pc\u22122)1.4). At the latest times in the SFNW galaxy, the galaxy evolves only very slowly in gas surface density or SFR surface density. The SFW galaxy has a slightly increasing gas surface density with time because the outer, lower-density regions are being stripped. In Figure 3 we plot a \u201clocal\u201d Schmidt Law\u2013the SFR surface density against the gas surface density in rings with 1 kpc width. This relationship is plotted for a single time snapshot\u2013460 Myr into the simulation, or 250 Myr after the wind hits the SFW galaxy. We choose this late time because it maximizes the di\ufb00erence between the SFR and the starformation radius of the SFW and SFNW galaxies (as seen in Figure 1). However, clearly the local relationships between SFR surface density and gas surface density are very similar in both runs. They even seem to \ufb02atten at about the same c \u20dd2011 RAS, MNRAS 000, 1\u2013?? 6 S. Tonnesen and G. L. Bryan Figure 2. The Kennicutt-Schmidt relation of the two simulated galaxies. For each timestep we calculate the gas and SFR surface density within the radius containing 95% of the new star formation for that timestep. Plus symbols are used for the \ufb01rst 250 Myr, before the disk has completely settled, and then diamonds are used thereafter. At early times, the star formation relation lies below the line denoting the observed Kennicutt-Schmidt relation (Kennicutt 1989), while at late times the galaxies lie very close to the Kennicutt-Schmidt Law. Figure 3. The star formation-surface density relation computed in rings with widths of 1 kpc. The SFNW run is shown with black diamonds and SFW is the red triangles, both shown at a time 250 Myr after wind hits disk (460 Myr into the simulation). The solid line is the empirical Kennicutt relation (2.5 \u00d7 10\u22124 (\u03a3gas/ 1 M\u2299 pc\u22122)1.4) (Kennicutt 1989), and the dash-dotted line denotes the gas surface density at which Leroy et al. (2008) found the local star formation e\ufb03ciency \ufb02attens. gas surface density, \u223c20 M\u2299pc\u22122, which is in remarkably good agreement with the gas surface density at which the local SF e\ufb03ciency \ufb02attens as observationally found by Leroy et al. (2008) (14 \u00b1 6 M\u2299pc\u22122; see their Figure 5). The most notable di\ufb00erence between our two runs is that the SFW galaxy has fewer points than the SFNW galaxy. This could be because either the gas density is zero in a 1 kpc ring in the galaxy, or the SFR surface density is zero. In fact, both the gas density and SFR surface density are very low outside of a radius of about 12 kpc, continuing to hold to a correlation between gas and SFR surface density. Thus far we have found that including a ram pressure stripping wind decreases the total SFR and focuses the SF towards the centre of the galaxy (Figure 1), but only slightly increases the gas surface density in the disk and does not change the relationship between gas surface density and SFR surface density (Figures 2 and 3). We \ufb01nally consider the total amount of newly formed stellar mass in the disk and in the bulge of the galaxy. As shown in the top panel of Figure 4, the total stellar mass formed in the disk, since the beginning of the simulation, is nearly identical in SFNW and SFW for the \ufb01rst 200 Myr, but once the wind hits the disk, the two lines begin to diverge. By the end of the SFW simulation, the SFW galaxy has about 7 \u00d7 108 M\u2299less stellar mass in its disk. If we focus only on the (newly formed) bulge stars, as de\ufb01ned by all of the stars formed since the simulation began in a sphere with a 3.4 kpc radius from the galaxy centre (this includes 80% of the mass in the spherical Hernquist bulge we initially used to determine our galaxy potential), we \ufb01nd that including the wind leads to more stars in the galactic bulge, as shown in the bottom panel of Figure 4. As we have discussed in Tonnesen & Bryan (2009), we \ufb01nd that gas clouds that are not stripped are able to spiral towards the centre of the disk (initially seen by Schulz & Struck 2001). It is this in\ufb02ow of gas within the disk that adds most of the stars to the bulge (rather than stellar fallback). Our bulge-to-total ratio of new stars is 0.1 in the SFNW galaxy and 0.2 in the SFW galaxy. However, this galaxy initially had a stellar disk mass of 1011 M\u2299and a stellar bulge mass of 1010 M\u2299, so the the new stars change the bulge-tototal ratio of stellar mass by at most a few percent. In summary, we \ufb01nd that ram pressure stripping lowers the SFR of a galaxy without an initial burst, despite the fact that our stripping ICM has a higher pressure than the static ICM. The relationship between gas density and SFR is similar in both simulations, with a slight increase in the total gas surface density for the SFW run, as would be expected from both the ram pressure and the higher-pressure surrounding ICM. Finally, although ram pressure does cause SFW to form more stars in the bulge and less stars in the disk than SFNW, it is not enough to overcome the initial mass pro\ufb01le of the galaxy. The galaxy would have to have about 2 orders of magnitude less stellar mass for the di\ufb00erence in star formation to have a signi\ufb01cant e\ufb00ect on the bulge-to-total mass ratio. 3.2 Gas in the Galactic Disk We will now examine if including star formation and feedback a\ufb00ects the remaining gas disk of a ram pressurestripped galaxy. First we plot the amount of gas in the disk as a function of time for all three simulations in Figure 5. Gas is counted as being in the disk if it has a tracer fraction of more than 0.6 and is within 2 kpc of the disk central plane. Focusing on SFNW (the black solid line), we see that including star formation results in disk gas being used to form new stars throughout the simulation. Comparing the two ram pressure stripped galaxies (SFW: red dash-dotted c \u20dd2011 RAS, MNRAS 000, 1\u2013?? Star Formation in Ram Pressure Stripped Tails 7 Figure 4. The top panel shows the total amount of newly formed stellar mass in the disk (i.e. within 2 kpc of the disk plane), as a function of time. Shortly after the wind hits the galaxy on the right, the star formation rate decreases, and by the end of the SFW run, it has about 7 \u00d7 108 M\u2299less stellar mass in the disk than the SFNW run. The bottom panel plots mass of newly formed bulge stars, as a function of time. If we focus only on the bulge \u2013 all stars within 3.4 kpc of the galaxy centre \u2013 we see that ram pressure does lead to more stars in the bulge. However, the di\ufb00erence does not signi\ufb01cantly change the B/T ratio, which begins at 0.1 with MBulge = 1010 M\u2299and MDisk = 1011 M\u2299. line and NSFW: blue dashed line), we see that after 250 Myr of stripping (the end of each line), the galaxies lose very similar amounts of gas. The SFW run has about 109 M\u2299less gas left in the disk than the NSFW galaxy, which is less than the amount of gas that formed stars (1.4 \u00d7 109 M\u2299), so 4 \u00d7 108 M\u2299less gas was actually removed from SFW than from NSFW by the ICM wind. We conjecture that this is because dense gas clouds near the outer edges of the disk formed stars in SFW rather than being ablated and eventually stripped by the ICM wind. This picture of outer gas clouds being either stripped (NSFW) or forming stars (SFW) also agrees with Figure 6, where we plot the radius of dense gas in the disk in all three simulations (see also Tonnesen & Bryan 2008). This is the radius of gas with a density above 10\u221224 g cm\u22123. For each timestep we consider twelve wedge-shaped sections of the disk and measure the largest radius at which there is gas with a density above 10\u221224 g cm\u22123. Each of these individual measurements are shown as dash-dotted lines. We also plot the mean radius of all wedges against time as the thick solid line. In all three cases, we see the collapse of the disk gas into dense clouds as the early increase in the radius of this Figure 5. The amount of gas in the disk in all three simulated galaxies. The SFW galaxy has less gas than the NSFW galaxy after being stripped for 250 Myr, but only by 109 M\u2299. This is less than the 1.4 \u00d7 109 M\u2299of stars that form throughout the SFW simulation. dense gas. The ram pressure stripping wind a\ufb00ects both the disk with and the disk without star formation in a similar fashion: the gas disks have similar ranges of measured radii and a similar mean radius of about 18-19 kpc. We next consider how star formation a\ufb00ects the density and temperature distribution of gas in the galactic disk. In Figure 7, we show contours of gas mass in the disk, as a function of gas density and temperature. These are all 250 Myr after the wind has hit the galaxy (or simply 460 Myr into the SFNW simulation). Including star formation and feedback spreads the distribution of high density (\u03c1 > 10\u221223 g cm\u22123) gas in the disk to include lower densities and higher temperatures. This may lower the surface density of gas in the galaxies with star formation, making it easier to strip. Finally we consider the velocity structure of the gas in the disk. In Figure 8, we plot contours of gas mass in the disk (de\ufb01ned as before), as a function of density and gas velocity in the wind direction, for the same time as in Figure 7. First, we note that the velocity spread in the SFNW run indicates the density and velocity of the disk gas that is accelerated due to the inclusion of thermal feedback from supernovae (i.e. only gas with \u03c1 \u226410\u221224 g cm\u22123 is a\ufb00ected). Gas accelerated by this process likely explains most of the di\ufb00erences between the SFW and NSFW cases. The most obvious di\ufb00erence is in the gas with negative velocities \u2013 while in the NSFW runs, most of the gas with negative velocities is likely the fallback of stripped gas into the central region of the disk, in the SFW simulation a portion of the gas is also accelerated due to feedback. A smaller e\ufb00ect is seen in the positive velocity gas \u2013 the same density gas can have a higher positive velocity in the SFW case than in the NSFW case. However, this \ufb01gure tells us that the gas being stripped (with large positive velocities) has densities less than 10\u221223 g cm\u22123, so the di\ufb00erences that star formation and feedc \u20dd2011 RAS, MNRAS 000, 1\u2013?? 8 S. Tonnesen and G. L. Bryan Figure 6. The maximum radius of gas with a density above 10\u221224 g cm\u22123 as a function of time. Dash-dotted lines show this radius for each of twelve wedges of the disk, while the solid line is the mean of the wedges. From left to right, the panels show SFNW, SFW, and NSFW. Being stripped by the ICM wind lowers the galaxy radius, but including star formation does not have much a\ufb00ect on the radius of the dense gas that remains in the disk (at least for 250 Myr of stripping). Figure 7. Contours of gas mass in the disk (de\ufb01ned as gas with a tracer fraction of more than 0.6 and a height above the disk of less than 2 kpc), as a function of gas density and temperature. These are all shown 250 Myr after the wind has hit the galaxy (or simply 460 Myr into the simulation with no ICM wind). Including star formation and feedback allows gas in the disk to have lower densities and higher temperatures which may make gas in the disk with star formation easier to strip. back cause in the density and temperature distribution of disk gas (Figure 7) do not strongly a\ufb00ect gas that will be stripped. Although we do not carry out a series of runs with higher ram pressures that also include star formation (due to prohibitively long run times), we have analyzed simulations with higher ram pressures (but without star formation) in Tonnesen et al. (2011). In that case, with a ram pressure of 4 \u00d7 1011 dynes cm\u22122, gas with densities as high as 6 \u00d7 10\u221223 g cm\u22123 can be stripped. We predict that star formation would result in that galaxy being stripped more quickly than in our simulations with no star formation. Including star formation only has a slight e\ufb00ect (\u223c10%) on the amount of gas left in the disk (Figure 5) and has very little e\ufb00ect on the residual size of the unstripped gas disk (Figure 6). We do \ufb01nd noticeable di\ufb00erences in the densitytemperature and z-velocity distributions of the gas in the disk, likely due to feedback from star formation. 3.3 Gas in the Stripped Tail We turn now to the gas in the stripped tail. First, as with the disk gas, we plot contours of gas mass as a function of density and temperature in Figure 9. This \ufb01gure is a snapshot 250 Myr after the wind has hit the disk, including all of the gas more than 10 kpc above the disk with a tracer fraction above 0.25 (i.e only gas that originated in the disk). It is immediately clear that the gas density and temperature distributions in the tail are very similar whether or not the simulation includes star formation. In the SFW panel we have denoted the range of temperatures and densities at which gas may form stars. The NSFW contours reach somewhat lower densities at low temperatures. In Figure 10 we plot contours of gas mass as a function of velocity in the wind direction and height above the disk. Once again, the distributions are very similar, although on closer inspection there is a slight di\ufb00erence in the placement of the highest c \u20dd2011 RAS, MNRAS 000, 1\u2013?? Star Formation in Ram Pressure Stripped Tails 9 Figure 8. Contours of gas mass in the disk as a function of velocity in the wind direction and gas density, 250 Myr after the wind has hit the galaxy. Including star formation and feedback causes gas in the disk to have negative and positive velocities. In addition, at any density, the run that includes star formation has slightly more gas at higher velocities. Figure 9. Contours of gas mass in the tail (tracer fraction of more than 0.25 and height greater than 10 kpc), as a function of gas density and temperature, both at a time 250 Myr after the wind has hit the galaxy. Including SF and feedback has a minimal e\ufb00ect on the \u03c1-T distribution of the tail. The dotted red lines denote the minimum mass and maximum temperature necessary for stars to form from a gas cell. contour (see also Figure 11), and the SFW tail has a narrower velocity distribution at large distances from the disk. We can see how the similarity in density, temperature, and velocity plays out in observables, speci\ufb01cally H I column density and H\u03b1 emission. In Figure 11 we display the projections of the SFW run on the left and the NSFW run on the right. For these plots, we restrict ourselves to di\ufb00use H\u03b1 emission, neglecting the contribution from HII regions (see the next section for the stellar contribution). Unlike the previous \ufb01gures, here the tails look somewhat di\ufb00erent, with the SFW tail having much of its dense gas farther from the disk than the NSFW tail. The small di\ufb00erence in the highest contour of Figure 10 has resulted in a signi\ufb01cantly di\ufb00erent distribution of bright H I and H\u03b1 emission. These di\ufb00erences in the distribution of the stripped gas are due to feedback near the disk. Thermal feedback results in gas out\ufb02ows above and below the disk. This means that some gas that will be removed from the galaxy is already moving away from the galaxy in the direction of the ICM wind. This is why dense gas is farther from the disk in the SFW simulation than in the NSFW simulation. There is not much star formation in the stripped tail, as we will show below, so it does not have such a large e\ufb00ect on the morphology of the tail. As we would expect from the similarity between SFW c \u20dd2011 RAS, MNRAS 000, 1\u2013?? 10 S. Tonnesen and G. L. Bryan Figure 10. Contours of gas mass in the tail as a function of gas velocity in the wind direction and height above the disk. These are both 250 Myr after the wind has hit the galaxy. Including star formation results in the bulk of the stripped gas being farther above the disk, although the range of z-velocities is very similar both cases. and NSFW in Figure 9, the range of H I column densities and H\u03b1 intensities are the same in the two tails. The total emission from the tails is also very similar. Including star formation results in slightly less H I gas (20% less), possibly because some of the most dense gas turns into stars. The (di\ufb00use) H\u03b1 emission is only 2% higher when including star formation and thermal feedback. Although we do not show a projection here because the X-ray brightness is too low to be observed, including star formation reduces the X-ray luminosity by only a small amount, 13%. 3.4 Star Formation in the Stripped Tail Finally, we consider star formation in the tail. In Figure 12 we plot the z-velocity of the tail stars against the height above the disk for a single output 250 Myr after the wind has hit the disk. We plot these points over the contours of gas mass. The escape velocity from the galaxy as a function of height above the disk is shown by a red dash-dotted line. We see that most of the stars are moving more slowly than the bulk of the stripped gas at that height. This is because the stars are moving at the velocity of the gas when they are formed, but then are no longer accelerated by the ICM wind and begin to slow down due to the galaxy\u2019s potential. Most of the stars with negative velocities are near the disk, but some stars out to \u223c60 kpc have negative velocities, indicating that they are falling back onto the disk. If we ran the simulation for long enough (inside a large box) we would expect all of the stars below the red line to begin to eventually fall back towards the disk. For most of these stars to be tidally stripped by the cluster potential (which we have not considered so far), the tidal radius would Figure 12. The z-velocity and height above the plane of the star particles are shown as diamonds (showing only those with heights above 1 kpc) are overplotted on the SFW gas contours from Figure 10. The edges of the gas contours are overplotted in green for clarity. The stars begin with the velocity of the gas in the tail from which they are formed, and then slow down as they are no longer accelerated by the wind. need to be about 60 kpc. If our galaxy were in the Virgo cluster, which has a velocity dispersion of about 700 km s\u22121, it would therefore need to be about 200 kpc from the cluster centre. In Coma, which has a velocity dispersion of about 1000 km s\u22121, the galaxy would need to be about 300 kpc from the cluster centre for tidal stripping to unbind a signi\ufb01cant number of stars. In Figure 13 we show projections of the stellar surface density and the surface brightness of H\u03b1 from HII regions. c \u20dd2011 RAS, MNRAS 000, 1\u2013?? Star Formation in Ram Pressure Stripped Tails 11 Figure 11. Projections of HI column density (top row) and H\u03b1 intensity (bottom row). The galaxy with star formation and feedback (SFW) is on the left, and without (NSFW) is on the right. Including star formation results in slightly longer tails. First we focus on the left panel, the stellar mass surface density. We see that there are a few clumps of \u223c3 \u00d7 104 M\u2299 kpc\u22122, which are aligned with where the recent star formation has taken place (compare to the right panel). There is also a more di\ufb00use component with surface densities about an order of magnitude less. We can estimate if we should see these tails in deep images of clusters. Each star particle is the size of a small cluster of stars that is formed at the same time using a Salpeter mass function ranging from 0.1-100 M\u2299. Mengel et al. (2002) \ufb01nd the Lv/M for young star clusters to range from 0.5-2 for ages ranging from 106-108 yr. If we assume the highest Lv/M, the surface brightness of the bright knots of \u223c3 \u00d7 104 M\u2299kpc\u22122 is \u223c29.5 mag/arcsec2. This is well within the range of V-band surface brightness of the ICL, and dimmer than the ICL observed by Mihos et al. (2005). The dimmer, more di\ufb00use stellar component c \u20dd2011 RAS, MNRAS 000, 1\u2013?? 12 S. Tonnesen and G. L. Bryan that is clearly connected to the disk would be very di\ufb03cult to distinguish from the general ICL. In the right panel of Figure 13 we show a projection of the surface brightness of H\u03b1 from HII regions. Our simulation outputs the mass and formation time of each star particle, from which it is easy to compute a SFR. The simulation does not directly calculate an H\u03b1 luminosity, so in order to compare with observations of HII regions (which are observationally distinguished from di\ufb00use H\u03b1 emission because they are small bright regions), we must assume that newly-formed (within 10 Myr) star particles produce H\u03b1 emission from HII regions. We use the observationally determined relation between the (recent) star formation rate and H\u03b1 luminosity from Kennicutt (1998): SFR (M\u2299yr\u22121) = 7.9\u00d710\u221242L(H\u03b1) (erg s\u22121). In this calculation we are simply assuming that H\u03b1 emission only measures the SFR within the last \u223c10 Myr. We compute the equivalent star formation rate by selecting only star particles which are younger than 10 Myr (and hence will have associated gas and bright H\u03b1 emission). As in previous work (Tonnesen & Bryan 2009; 2010), we \ufb01nd that ram pressure stripping cannot remove the densest clouds in the disc without breaking them apart. Stars formed in the tail must therefore be created from the less dense gas that has cooled and condensed in the tail. Disk gas (that is not in dense clouds) with a range of densities is stripped continuously, so there is a range of gas densities throughout the tail. Accordingly, the time it takes for radiative cooling and compression by the ICM, and consequent star formation to occur, varies throughout the tail as well. Figures 7 and 8 show that gas with \u03c1 < 10\u221224 can be stripped from the disk and that some gas at these lower densities has T < 105. Because of these low temperatures, this gas will cool and condense into clouds rather than mix into the ICM (as discussed in Tonnesen & Bryan 2010, 2011). The exact temperature and density of the gas will determine how long this takes, which is why there is a large spread in the height of stars above the disk. This is illustrated in the two lines in the upper panel of Figure 14, which shows the SFR in the tail above either 2 kpc (the black solid line), or 20 kpc (the red dashed line). Star formation in the tail occurs throughout the simulation from close to the disk (\u223c2 kpc) to far from the disk (well beyond 20 kpc, see also Figure 13). Hester et al. (2010) also \ufb01nd that this scenario of star-forming clouds condensing within the stripped tail agrees well with their observation of a tail from a galaxy in the Virgo cluster. There are clearly stars in the tail, and if unbound, they can contribute to the ICL. We evaluate this possibility with Figure 14, which shows the cumulative amount of stars formed in the tail. We \ufb01nd that 250 Myr after the SFW galaxy has begun to be stripped by the ICM wind, there is about 4.2 \u00d7 106 M\u2299of stellar mass more than 20 kpc above the galaxy. From Figure 12 we know that this is an overestimate of the number of stars that will escape this galaxy. Therefore we \ufb01nd it unlikely that ram pressure stripping is a large contributor to the ICL, as 4.2 \u00d7 106 M\u2299is less than 1% of the stellar mass formed in the disk. Figure 14. The top panel shows the SFR in the tail gas either above 2 kpc (solid black line) or above 20 kpc (dashed red line). There is star formation throughout the tail. At early times the SFR rate is very low, in rough agreement with the observations of Gerhard et al. (2002) and Cortese et al. (2003; 2004). The bottom panel plots the amount of stellar mass more than 20 kpc above the disk vs time. Although there certainly are stars in the tail, this amount of stellar mass will not be a large fraction of the ICL even if it all escapes into the ICM. 4 DISCUSSION 4.1 Comparison with previous work We compare our results with the simulations in K09, as they both make predictions for star formation in the tails of rampressure stripped galaxies. As we discuss in the introduction, K09 ran 12 simulations of ram pressure stripped galaxies, varying the ICM density and velocity. Our simulation is most similar to their run 2, which has an ICM density slightly above ours (5 \u00d7 10\u221228 g cm\u22123 rather than 3.2 \u00d7 10\u221228 g cm\u22123) and a wind velocity slightly below ours (1000 km s\u22121 vs 1413 km s\u22121). The amount of gas stripped is very similar \u2013 in 250 Myr about 65% of the original gas mass is stripped from the K09 simulation (their \ufb01gure 15), while our SFW run has about 58% of the gas mass stripped (Figure 5). Given that the SFW galaxy is more massive than the K09 galaxy, this is reasonably good agreement. K09 \ufb01nd that tail gas with T > 106 K has a mean density of about 10\u221224 g cm\u22123, while our mean density is lower, at \u223c2 \u00d7 10\u221225 g cm\u22123. This is both because our surrounding ICM density is lower and because we are including all gas with a tracer fraction above 0.6 in this measurement, which we would expect to skew our results to lower densities. The results regarding the stripped gas are similar between SFW and K09. However, our star formation results are very di\ufb00erent from the K09 results. In direct opposition to our results, c \u20dd2011 RAS, MNRAS 000, 1\u2013?? Star Formation in Ram Pressure Stripped Tails 13 Figure 13. Projections of stellar surface density on the left and the surface brightness of H\u03b1 in HII regions on the right (computed from stars formed in the last 10 Myr, see text). We smooth both projections using a 1 kpc gaussian. Both old (stars formed within the stripped gas but older than 10 Myr) and new stars are well-distributed throughout the tail, re\ufb02ecting the range of densities and dynamical times of stripped gas. they \ufb01nd that adding a ram pressure stripping wind results in more stars being formed in the simulation. In the run most similar to ours, after 250 Myr there are nearly as many stars formed in the wake as in the disk, while in our SFW run only about 1% of the new stars formed are in the tail. We checked whether a di\ufb00erence in our threshold density for star formation could have a large e\ufb00ect on the star formation rate in our simulations. To do this, we ran a comparison simulation identical to SFW in which we allowed stars to form if gas had a density above 3.85 \u00d7 10\u221226 g cm\u22123, a factor of 10 below our standard prescription. The results were quite similar to our standard run. The SFR in the disk had di\ufb00erences of less than 10% at every output. After 460 Myr, the total stellar mass in the disk with the lower density star-formation threshold was only 4% larger than in the SFW disk, and the amount in the bulge was only 4% lower than in the SFW bulge. The tail results di\ufb00ered a bit more: about 50% more stars were formed in the tail over the length of the simulation. This makes sense \u2013 decreasing the star formation threshold substantially increases the amount of gas that can form stars (see Figure 9), but the gas has a longer dynamical time so the net change in star formation is not large. This increase in stellar mass formed in the stripped tail is not nearly large enough to account for the di\ufb00erence between our results and those of K09. Increasing our star formation e\ufb03ciency would probably increase the stellar mass in the tail, but this could a\ufb00ect our agreement with the empirical Schmidt-Kennicutt Law. Our simulations are very di\ufb00erent, so there are many possible reasons for di\ufb00erent results, and we will list a few of the most salient di\ufb00erences now. First, K09 use GADGET2, an SPH code, and include a subgrid model that increases the gas pressure at high density. Their galaxy is less massive than ours, with a circular velocity of 160 km s\u22121. It is also more gas-rich, with a gas fraction of 25% of the total disk mass. They allow radiative cooling to 104 K, and the maximum temperature at which gas can form stars is 106 K. Their star formation prescription, like ours, is proportional to the dynamical time of the gas. The reason for the very di\ufb00erent predicted star formation rates in the tail is hard to pin down, but we suggest two key di\ufb00erences. First, the subgrid model in the Springel & Hernquist (2003) prescription has a very sti\ufb00equation of state in dense gas, while our dense gas typically is cold and has a low thermal pressure. Second, inspection of the K09 results suggests that stripped gas does not mix with the ICM, resulting in a high fraction of the stripped gas ending in large, cold clumps. We note that SPH has di\ufb03culties in resolving instabilities at interfaces (Agertz et al. 2007), resulting in undermixing and reduced stripping. This, combined with the sti\ufb00equation of state and the high ICM pressure, lead to large star formation rates in the stripped gas. 4.2 Comparison With Observations We will \ufb01rst compare our results to observations of ram pressure stripped galaxies in the Virgo cluster, which have largely been identi\ufb01ed due to their H I tails (but have relatively little star formation). We will then compare our results to observations of H II regions and/or stellar tails associated c \u20dd2011 RAS, MNRAS 000, 1\u2013?? 14 S. Tonnesen and G. L. Bryan with galaxies that are likely undergoing ram pressure stripping in more massive clusters. Finally, we discuss the key physics that control the star formation rate in our simulated tails. 4.2.1 Virgo Tails As we have discussed in the Introduction, eleven galaxies in Virgo have clear stripping signatures in H I observations, but only four have been found to have star formation either from UV emission or H II regions. This begs the question of whether we should expect star formation in our stripped tail. To answer this question we will compare our results to some of these observations. Let us \ufb01rst consider the galaxies that have star formation in their tails. Cortese et al. (2003) found an H II region 3 kpc from the disk in the stripped tail of NGC 4402. Their measured H\u03b1 luminosity results in a SFR (using the Kennicutt (1998) equation) of 2.3 \u00d7 10\u22123 M\u2299yr\u22121. Our simulated ram pressures are similar to that likely experienced by Virgo galaxies, and we have SFRs of tail gas (more than 2 kpc above the disk) ranging up to 6 \u00d7 10\u22122 M\u2299 yr\u22121 (over the 250 Myr that the galaxy is being stripped). If we choose an early output, our SFR agrees with the observations of Cortese et al. (2003; 2004). However, Crowl & Kenney (2008) use stellar populations in the disk to predict that this galaxy has been stripped for nearly 200 Myr. This means that we overpredict both the SFR and the distance to which star formation would be observed in this galaxy. Of course, because we are not actually modeling this galaxy, our galaxy velocity is slightly higher than that expected by Crowl et al. (2005), and our galaxy is being stripped face-on rather than at an angle. Our ICM density is very similar to that near NGC 4402 (Schindler et al. 1999). Similarly, NGC 4330, NGC 4522, and NGC 4438 have ongoing star formation in their stripped tails (Abramson et al. 2011; Kenney & Koopmann 1999; Boselli et al. 2005). As in NGC 4402, the observed stars in the tails are closer to the galaxy than the more extended tails we simulate. Finally, we discuss IC 3418, which has not been observed in H I, but has a UV and H\u03b1 tail (Martin et al. 2005; Hester et al. 2010). IC 3418 is likely to be in a higherdensity ICM than we model by about a factor of 5. This UV tail extends 17 kpc from the disk, and the authors calculate a lower limit for the SFR of 6 \u00d7 10\u22123 M\u2299yr\u22121 (because they do not correct for any dust extinction). They use the star formation truncation time to estimate that this galaxy has been stripped for 100 Myr. After 100 Myr of stripping, our stellar tail is about 20 kpc, in good agreement with this observation. However, our simulated SFR is still a factor of \u223c3 above that in IC 3418. There are, in addition, seven galaxies that do not have any stellar light associated with their H I tails. Six of these galaxies are at or beyond 700 kpc from M87, and so may be in lower-pressure ICM regions than we simulate. The exception is NGC 4388, which, based on the models of Vollmer & Huchtmeier (2003), may be in a similar, or higher, density region of the ICM than we use in our simulations. Although we are not attempting to directly model any single galaxy, in general we have a higher SFR in our tail and a longer stellar tail than in most of these galaxies. There are a number of reasons we \ufb01nd higher star formation in our stripped tail. (i) We may be overestimating the amount of star formation in the tail due to our star formation method. We could lower the SFR in our tail by changing our star formation criteria\u2013while we saw in Section 4.1 that lowering the star formation density threshold by an order of magnitude only changed the amount of star formation by 50%, we could raise the threshold to the point where there was very little star formation in the tail. (ii) We may also be overestimating the survival of star-forming clouds to large distances above the disk, a point we will discuss in more detail in Section 4.4.2. (iii) We may also have more star formation in our tail because we have a face-on wind that can strip more gas, or (iv) because we are modeling a higher-pressure ICM than surrounds most of the observed galaxies with H I tails in Virgo. This point will be discussed in more detail below. 4.2.2 Stellar Tails in Massive Clusters Turning to more massive clusters, Yoshida et al. (2008) observed \u201c\ufb01reballs\u201d around a merger galaxy in the Coma cluster. They \ufb01nd that these blue or H\u03b1 emitting \ufb01laments are found on one side of the galaxy, extending up to 80 kpc from the disk. The morphology of this tail of \u201c\ufb01reballs\u201d is roughly in agreement with our simulation. They \ufb01nd that the H\u03b1 knots and \ufb01laments are farther from the disk than the blue knots and \ufb01laments, which also tends to be the case in our tail (Figure 13), but is not as clear-cut as in the case of RB 199. However, they only \ufb01nd 13 knots and \ufb01laments, while it is clear that we have many more star particles. Further, they estimate the mass of the stars in their tail to add up to 108 M\u2299\u2013at least a factor of 25 larger than the stellar mass in our stripped tail (but see below). Recently Yagi et al. (2010) observed 14 galaxies with stellar H\u03b1 clouds in tails in the Coma cluster. Their images show a range of possible tails, some of which look more like our simulated tail than others. A number of their tails show very linear trails of either young stars or H II regions, which is in qualitative agreement with the right panel of Figure 13. Finally, Sun et al. (2007) focus on the H II regions in the stripped tail of ESO 137-001. They \ufb01nd 29 H II regions with H\u03b1 luminosities ranging from 1038 to 1040 erg s\u22121. They calculate that the total mass of all the H II regions should be about 107 M\u2299, and using the Kennicutt (1998) relationship between H\u03b1 luminosity and SFR estimate an instantaneous SFR of about 0.7 M\u2299yr\u22121. This includes a bright H II region slightly less than 2 kpc above the disk, and without this H II region the SFR would be about 0.53 M\u2299yr\u22121. Both are larger than what we \ufb01nd, by about an order of magnitude. Why do we predict signi\ufb01cantly less star formation in the stripped tail than in these observations? Yoshida et al. (2008) determine an ICM density much like the one in our simulation, so there should not be an increased SFR in tail gas due to higher ICM density. A possible explanation is that RB 199 has the disturbed morphology of a merger remnant, which may have moved large star-forming clouds farther from the centre of the galaxy to regions where they could be more easily stripped by ram pressure. We may have less stellar mass in our tails than in ESO 137-001 and most of the galaxies observed by Yagi et al. (2010) because we simulate a lower density ICM than in those regions of the Coma and Norma clusters. Kapferer et c \u20dd2011 RAS, MNRAS 000, 1\u2013?? Star Formation in Ram Pressure Stripped Tails 15 al. (2009) found that increasing the ICM density increased the star formation in the tail, which might cause stripped clouds to be compressed more quickly. This agrees with observations of the lower H\u03b1 luminosities of H II regions in ram pressure stripped galaxies in the lower-density ICM of the Virgo cluster (Kenney & Koopmann 1999; Cortese et al. 2004), as highlighted in the previous section. In order to test this idea using our simulations, we can make a rough estimate of the star formation rate of gas in the tail in our two simulations modeled after ESO 137001, and examined in detail in Tonnesen et al. (2011) (running these simulations including star formation at the same resolution as SFW is too computationally costly). From equation (1) we can calculate the star formation rate simply by knowing the gas mass and density in a cell, using tdyn = (3\u03c0/32G\u03c1)1/2 and recalling that we have an e\ufb03ciency of 0.5%. We \ufb01rst test this method by comparing the star formation rate estimated in this way to the measured rate for SFNW and SFW. First, we consider just the disk gas, and \ufb01nd that, averaged over time, the estimated rate is within 1% of the measured rate, with a variation ranging from 10% too large, to 2% too small. More importantly, in the tail of the SFW run, the estimated rate is within about 10% of the measured rate, with a similar level of scatter. Now that we have con\ufb01rmed that the errors in our estimation scheme are low in comparison to the measured rates, we can predict the star formation rate in our two simulations using similar ICM conditions to those around ESO 137-001 (Sun et al. 2006; 2010; see Tonnesen et al. 2011 for details of these runs). Using the gas between 2 and 40 kpc above the disk in order to match the observations of Sun et al. (2006), we predict a SFR of 0.094 M\u2299yr\u22121 (for the T3vl run, which had somewhat lower ram and thermal pressures) and 0.32 M\u2299yr\u22121 (for the T3vh run, which had higher pressures). We see that the T3vh estimate is within a factor of \u223c2.5 of the observed Sun et al. (2007) value of 0.7 M\u2299yr\u22121 (or within a factor of 2 of the corrected value of 0.53 M\u2299yr\u22121, beyond 2 kpc above the disk), while the T3vl estimate is in poorer agreement. As discussed in Tonnesen et al. (2011), the T3vl case also does not agree with the non-detections of H I in the tail, and these star formation estimates lend more credibility to our claim that T3vh is a stronger match to the observations of ESO 137-001. We also predict that there will be star formation in the stripped tail between 40-80 kpc with a SFR of about 0.075 (T3vh, 0.51 for T3vl) M\u2299yr\u22121, which, if correct, will make it very di\ufb03cult to observe. 4.2.3 What drives the rate of star formation in the tail? Finally, in this section we try to determine the key physical e\ufb00ect that determines the star formation rate in the tail. To do this, we compare the T3vl and SFW runs \u2013 the velocities in the two runs are similar, and although the di\ufb00erent ram pressures (T3vl is about a factor of 10 larger than the SFW run) lead to di\ufb00erent mass loss rates, we can compare the two runs when there are similar amounts of gas in the tail. When we do that, the T3vl run still produces a much larger (estimated) star formation rate, indicating it is not simply the amount of stripped gas. Instead, we argue that, the enhanced rate is largely due to the increased thermal pressure in the ICM. Since the cold tail gas is largely in pressure equilibrium with the ICM, increasing the ICM pressure moves that gas to higher density (see Figure 9), increasing the star formation rate. Of course, the amount of stripped gas is also important, which is controlled by the ram pressure strength, but once the gas is stripped, it is largely the ICM pressure which controls the star formation rate in the wake. 4.3 Star Formation Recipe As noted in Section 2.1, we allow stars to form in gas with densities greater than 3.85 \u00d7 10\u221225 g cm\u22123 and temperatures below 1.1 \u00d7 104 K. We do not; however, require that the mass of the cell exceeds the Jeans mass, or that the cooling time be less than the dynamical time, as used in, for example, Tasker & Bryan (2006). If we used more strict star formation criteria, we would expect our star formation rate to decrease, although based on inspection of Figure 7, the density criteria would have to change by more than an order of magnitude before the mass of gas able to form stars would be signi\ufb01cantly a\ufb00ected. Nevertheless, we note that our more generous star formation criteria make our conclusions regarding intracluster light and the change of the bulge-to-disk ratio conservative. In addition, we note that our results are based on a comparison between the SFR in SFNW and SFW and so should not be a\ufb00ected by our exact star formation recipe. Our star formation recipe may have a greater impact on the SFR we measure in the stripped tail of gas. We discuss this in Section 4.1, but it is worth reiterating here. If we used more strict star formation criteria, we may indeed see less star formation in the tail, possibly in better agreement with observations of Virgo galaxies. While it is possible to change our calculated values of the SFR by changing our star formation recipe, our conclusion that higher ICM pressure results in more star formation is robust. 4.4 Resolution 4.4.1 Star Formation This work has included star formation in order to determine how ram pressure stripping a\ufb00ects star formation rates in the disk and tail of a stripped galaxy. Therefore it is important to discuss how resolution may a\ufb00ect our results. As we discussed above (Section 2.1), star formation can occur in gas with densities greater than 3.85 \u00d7 10\u221225 g cm\u22123 and temperatures below 1.1 \u00d7 104 K. This corresponds to a Jeans length of about 1.9 kpc, which is resolved by 50 cells at the \ufb01nest level of resolution. These cases meet the Truelove criterion (Truelove et al. 1997), which requires a minimum of four cells per Jeans length. However, there is some gas with much higher densities and lower temperatures in both the disk and tail (Figures 7 & 9). Some of this high density gas has a Jeans length of less than 10 pc, so our simulations may include arti\ufb01cial fragmentation that could increase our star formation rate. Our densest gas is found in the galaxy disk, and we have found that our galaxies do lie on the Kennicutt-Schmidt relation. Further, our newly formed stellar mass closely matches that predicted by Equation 2.1. However, this does not prove that we do not have arti\ufb01cial fragmentation on small scales in high-density clouds, and so our exact measures for the SFR in the galaxy disks could be incorrect. The comparisons between the SFNW and SFW c \u20dd2011 RAS, MNRAS 000, 1\u2013?? 16 S. Tonnesen and G. L. Bryan disks should not be a\ufb00ected. The tail gas has a much lower density and will largely not be a\ufb00ected by arti\ufb01cial fragmentation. The actual values for the SFR found in the tail should be more reliable, which is most pertinent for this paper. In galactic disks, improving the resolution allows the gas to fragment faster and into smaller clumps, leading to higher densities and larger star formation rates. We found this e\ufb00ect in Tonnesen & Bryan (2009), when we simulated disks with 20, 40 and 80 pc minimum resolution. We found that high density gas formed faster, and the highest density reached was larger as the resolution increased, although by 40 pc, gas easily reached star forming densities. This e\ufb00ect was also demonstrated explicitly in Teyssier et al. 2010, who carried out merger simulations with low and high resolution, arguing that high resolution was required to correctly obtain the star formation rate. Although their high-resolution simulation had signi\ufb01cantly better spatial resolution (10 pc) than described here, it had signi\ufb01cantly worse mass resolution (4\u00d7104M\u2299compared to 5\u00d7103M\u2299). Since mass resolution is important in resolving clump formation, we conclude that our simulations probably do not signi\ufb01cantly underestimate the star formation rate. This is in agreement with the results of Tasker & Bryan (2006), who carried out simulations with 25 and 50 pc, and found that although the higher resolution simulations produced small clumps, the net star formation rate was similar in the two runs. At our current resolution (38 pc) we see individual clumps in both the disks and tails (our spatial and mass resolution is intermediate between their two resolution runs). 4.4.2 Cloud Survival Although we refer the reader to our previous papers for an in-depth discussion of how resolution may e\ufb00ect cloud survival (e.g. Tonnesen et al. 2011), it is important to note that we do not fully resolve the dense clouds in our disk or in the stripped tail. We have found that decreasing the resolution decreases the number of dense clouds formed, and the maximum density of the clouds formed. Also, based on the fact that a lower resolution simulation discussed in Tonnesen et al. (2011) emits less H\u03b1 per cloud, we expect that the edges of the clouds are more di\ufb00use with lower resolution. The density gradient at the edge of a cloud may a\ufb00ect its survival, as discussed in detail in Nakamura et al. (2006) and Yirak et al. (2009), who \ufb01nd that a low density gradient results in slower growth of instabilities, which can retard cloud destruction. Deep, high resolution observations in H I of tails that have young stars and H II regions will allow us to determine how many dense clouds form, and how long they survive, in order to better constrain our simulations. 5 CONCLUSIONS We have run high-resolution galaxy simulations including radiative cooling and star formation with thermal feedback in order to understand how ram pressure stripping can in\ufb02uence the stellar disk and whether ram pressure stripping can contribute a large fraction of stars to the ICL. Our main conclusions are: 1. Including star formation and thermal feedback does not signi\ufb01cantly a\ufb00ect the remaining gas disk and the stripped gas tail. The results from our previous simulations without star formation do not need to be much modi\ufb01ed when star formation is included. A possible caveat to this is that star formation and feedback can a\ufb00ect the density distribution of very dense gas, with \u03c1 > 10\u221223 g cm\u22123 (see Figure 7, where the gas is pu\ufb00ed up and spread to lower densities), which might then make it susceptible to very strong ram pressure \u2013 stronger than modeled here, but see Tonnesen et al. (2011). 2. Ram pressure stripping acts to quickly reduce the total SFR of the galaxy, with a timescale of a few hundred Myr. We \ufb01nd no increase in the star formation rate either due to the increase in the surrounding pressure or the shock of the ram pressure stripping wind. The relationship between star formation rate and gas surface density (the -Schmidt relation) remains consistent whether or not a galaxy is being ram pressure stripped. 3. Ram pressure stripping slightly increases the stellar mass of the galactic bulge relative to a galaxy forming stars in a static ICM. However, this e\ufb00ect is very small and does not signi\ufb01cantly change the bulge-to-total ratio in our model galaxy. 4. We \ufb01nd that star formation does occur in the tail. This occurs not because dense (molecular) clouds are stripped wholesale, but instead because the relatively low density gas that is stripped can cool and condense into dense clouds in the turbulent wake. We predict both the di\ufb00use H\u03b1 and stellar H\u03b1 production rates in the tail. 5. Some of the stars formed in the tail are unbound from the galaxy and will become part of the intracluster light. However, the total stellar mass added to the ICL from stripped gas is only \u223c4.2 \u00d7 106 M\u2299. 6. We compare the star formation rate we \ufb01nd in the tail to observations, and \ufb01nd that in the stripped tails of Virgo galaxies, the observed star formation rate in the tail is lower than we predict. In more massive clusters, the star formation rate in stripped tails can be about an order of magnitude higher than our predictions. We argue, based on these comparisons and estimations of star formation rates in previous simulations (that varied the ram pressure and thermal pressure strengths but that did not self-consistently include star formation), that the star formation rate in the tail depends both on how much gas is stripped, and also on the ICM pressure. Higher ICM pressures create more cold, dense gas in the wakes, resulting in higher star formation rates, consistent with observational trends. As we discuss in the text of this paper, a few of our results may be very dependent on our galaxy model and ICM parameters. Our third conclusion, that ram pressure does not have a large e\ufb00ect on the B/T ratio, may depend on our disk model. First, if our galaxy was much less massive, then we might expect the disk to be even more quickly stripped and to dim faster, while the bulge growth may remain very similar. This could a\ufb00ect the bulge-to-disk ratio. Later-type galaxies do tend to be less massive and are the very galaxies for which it is most important that the bulge mass grows in order to produce an S0 (Solanes et al. 1989). In addition, as we note, a more dense and/or more quickly moving wind can strip gas with higher densities. Therefore, although in this case including star formation had very little e\ufb00ect on the total amount of gas stripped from the disk, at higher ram pressures we might expect more gas c \u20dd2011 RAS, MNRAS 000, 1\u2013?? Star Formation in Ram Pressure Stripped Tails 17 to be stripped from simulated galaxies that included star formation and feedback. It would be interesting to explore star formation and feedback in models with a range of ram pressure strengths. Our \ufb01fth conclusion, that ram pressure stripping does not add a signi\ufb01cant amount of stellar mass to the ICL, deserves more attention. This simulation models ICM densities and velocities of galaxies found at about the virial radius of a \u223c4 \u00d7 1014 M\u2299cluster (Tonnesen et al. 2007). If we estimate the amount of star formation in our simulations from Tonnesen et al. (2011), which have a higher ICM pressure modeled after the observations by Sun et al. (2006, 2007, 2010), we predict that the SFR increases by a factor of about 10. If we assume that this means there will be 10 times as much total stellar mass added to the ICL, we still conclude that even in the centres of large clusters like Norma (ESO 137-001 is about 200 kpc from the centre of the Norma cluster), less than 1% of the stripped gas turns into stars to be added to the ICL. Sun et al. (2010) argued that ram pressure stripping could contribute a signi\ufb01cant fraction of the ICL if 10% of stripped gas forms stars, which is clearly not predicted by our simulations. However, we did \ufb01nd that increased ICM pressure does increase the star formation rate of stripped gas. Therefore, it is possible that in regions of very high ICM pressure (T \u223c107 K and \u03c1 > 10\u221226 g cm\u22123), 10% of stripped gas could form stars. Arnaboldi & Gerhard (2010; references therein) write that recent studies have found that the ICL contains between 10% and 30% of the stellar mass in a cluster. The stellar mass in our simulated galaxy is 1011 M\u2299, and the amount of stars added to the ICL is about 4 \u00d7 106 M\u2299. Even in the centre of Norma, the stellar mass added to the ICL is likely to be less than 108 M\u2299. We \ufb01nd that ram pressure stripping will contribute a very small fraction of the total stellar mass in the ICL. We predict that observers will continue to \ufb01nd that strong features in the ICL are red, indicating stars stripped from galaxies rather than star formation in the ICL (Rudick et al. 2010). Further, we predict that ram pressure will not generally form starburst galaxies. Finally, the bulge in our galaxies grows through gas spiraling in through the disk. This may lead to more rotation in the bulge, a signature that could discriminate between this bulge growth method and, for example, one directly from mergers. We acknowledge support from NSF grants AST0547823, AST-0908390, and AST-1008134, as well as computational resources from NASA, the NSF Teragrid, and Columbia University\u2019s Hotfoot cluster. We thank Jacqueline van Gorkom and Je\ufb00rey Kenney for useful discussions. We also thank our anonymous referee for comments and suggestions that improved the quality of this paper.",
                    "introduction": "As galaxies orbit within a cluster, their interstellar medium (ISM) may interact directly with the intracluster medium (ICM), the hot halo of gas bound by the cluster gravitational potential. This is often thought of as a gas-only a\ufb00air, in which stars remain una\ufb00ected. For example, ram pressure stripping (and related processes) by the ICM is only able to remove a galaxy\u2019s gas (Gunn & Gott 1972). Although stars are not directly a\ufb00ected, there is increasing evidence that ISM-ICM interactions do impact star formation. In general, galaxies in clusters have lower star formation rates than galaxies of the same morphological type in the \ufb01eld (e.g. Hashimoto et al. 1998; Rines et al. 2005; Balogh et al. 1998; although Gom\u00b4 ez et al. (2003) found that a galaxy\u2019s star formation rate depended more on local galaxy density than on cluster membership). Gavazzi et al. (2006) found that the star formation rate in cluster galaxies was related to the amount of H I: galaxies with normal H I had twice the H\u03b1 equivalent widths of H I de\ufb01cient galaxies. Koop- mann & Kenney (2004) found that Virgo spirals are form- \u22c6E-mail: stonnes@astro.princeton.edu (ST)); gbryan@astro.columbia.edu (GLB) ing stars primarily in the centres of their disks, which can be explained by the outer gas disk having been stripped by the ICM. In a more recent study of ten Virgo spiral galaxies, Crowl & Kenney (2008) \ufb01nd that the star formation history and quenching time of \ufb01ve of their galaxies is consistent with ram pressure stripping in the cluster centre, while the other \ufb01ve have more complicated histories. Although there is evidence linking ISM-ICM interac- tions to star-formation quenching, the question of whether interactions with the ICM could also induce star formation in a galactic disk remains open. For example, star formation could be triggered by the increase in surrounding pressure when a galaxy enters a high-density ICM (Dressler & Gunn 1983; Evrard 1991; Fujita 1998; Smith et al. 2010). Fujita & Nagashima (1999) found ram pressure induced star forma- tion in simulated galaxies. Observations of post-starburst galaxies in clusters in- dicate that star formation can be induced by environmen- tal processes (Dressler & Gunn 1983), although the exact mechanism is still unknown. Post-starburst galaxies reside preferentially in clusters at z = 0.3 \u22120.6 (e.g. Poggianti et al. 1999, Poggianti et al. 2004; Tran et al. 2004; but see Balogh & Bower 2003). Although most observations at both lower and higher redshift have found k+a fractions in- c \u20dd2011 RAS 2 S. Tonnesen and G. L. Bryan creasing with decreasing galaxy density (e.g. Zabludo\ufb00et al. 1996; Hogg et al. 2006; Goto 2007; Yang et al. 2008), Pog- gianti et al. (2004) \ufb01nd a large population of low-luminosity post-starburst galaxies in Coma. Tran et al. (2003) exam- ined E+A galaxies in three intermediate-redshift clusters and found that the majority were not associated with merg- ers. By considering the spatial distribution of post-starburst galaxies in clusters, some observers have found evidence that both the star formation quenching and earlier starburst could be related to interactions with the ICM (Poggianti et al. 2004; Poggianti et al. 2009; Ma & Ebeling 2008). By investigating whether and how ram pressure strip- ping by a dense ICM can a\ufb00ect star formation in a galaxy, we can shed light on what drives the evolution of cluster galax- ies. From z\u223c0.5 to z=0, much of the morphological evolution in clusters has been from spirals to S0s (Dressler et al. 1997). In order for a spiral galaxy to evolve into an S0, both spec- troscopic and morphological changes must take place: the galaxy must become red, it must lose spiral structure in its disk, and the bulge-to-disk ratio must increase. Ram pressure stripping, through gas removal, can cause a galaxy to become red. Passive spirals, red spirals without star formation, have been observed to reside preferentially in clusters (Moran et al. 2007; Poggianti et al. 1999). A galaxy- ICM interaction is the likely mechanism for forming passive spirals because these galaxies have had their gas removed but are morphologically spirals (because their stellar disks are relatively undisturbed). If passive spirals are precursors to S0s, then a galaxy-ICM interaction is a step in the evo- lution of normal spirals into S0s. Ram pressure stripping can also result in a disk galaxy losing its spiral arms. Bekki et al. (2002) used simulations to show that if gas is no longer accreted by a galaxy, it will lose its spiral arms in about 3.5 Gyr. This is in good agreement with observational and model estimates for how long morphological transformation may take (e.g Kodama & Smail 2001; Poggianti et al. 1999; but see Moran et al. 2007 for a shorter estimate). Finally, a galaxy\u2019s bulge-to-disk (B/D) ratio can in- crease either by fading the disk or growing the bulge. Ram pressure stripping can result in the disk of a galaxy fading. Fading the disk of a galaxy with a B/D = 0.2 will result in a galaxy with a B/D = 0.5, so an Sb galaxy, after disk fading, will have the B/D ratio of an S0 galaxy (Fujita & Nagashima 1999; Solanes et al. 1989). Solanes et al. (1989) \ufb01nd that the bulge luminosities of Sa galaxies are similar to those of S0s, and all galaxy types have a range of luminosities, so it is not universally necessary to increase the bulge luminosity to transform a spiral to an S0. However, if the slow fading of the disk was the only mechanism at work, the total lu- minosity of S0s should be less than that of spirals, which is not generally the case (Burstein et al. 2005). Christlein & Zabludo\ufb00(2004) compared the bulge and disk luminosi- ties of cluster galaxies, and concluded that S0s in clusters form by growing the bulge of spiral galaxies. Therefore it is important to know whether ram pressure can induce star formation that may grow a galaxy\u2019s bulge. There can also be star formation in a ram pressure stripped tail of gas, even though molecular clouds are con- sidered too dense to be directly stripped from a galactic disk. It is still unclear how common star formation in stripped gas tails is, as many tails observed in H I do not have any as- sociated star formation. For example, several one-sided H I tails have been observed in Virgo. Chung et al. (2007) found 7 one-sided tails between 0.6-1 Mpc in projected distance from M87. Oosterloo & van Gorkom (2005) found a \u223c110 kpc H I tail associated with NGC 4388. NGC 4438 was orig- inally believed to be an interacting galaxy (e.g. Hibbard & van Gorkom 1990; Kenney et al. 1995; Vollmer et al. 2005), but more recent work has concluded that it is likely only ram pressure stripped. NGC 4522 is 1 Mpc from M87, and Kenney et al. (2004) conclude that it is being ram pressure stripped by an overdense or moving region of the ICM. Fi- nally, NGC 4402 also has an H I tail (Crowl et al. 2005). Of these eleven galaxies with clear stripping signatures in H I observations, only four have been found to have star formation either from UV emission or H II regions. The four H I tails with star formation tend to have short stellar tails with low star formation rates. Abramson et al. (2011) \ufb01nd 9 UV emitting regions near NGC 4330, for a total of 4.55 \u00d7 106 M\u2299of extragalactic stars. Cortese et al. (2003; 2004) found an H II region 3 kpc above the disk of NGC 4402 in the Virgo cluster. Similarly, NGC 4522, and NGC 4438 have ongoing star formation in their stripped tails close to the galaxy (Kenney & Koopmann 1999; Boselli et al. 2005). NGC 4438 has the most distant UV emission out to nearly 30 kpc from the disk (Boselli et al. 2005). Although Gerhard et al. (2002) \ufb01nd an H II region near NGC 4388 in the Virgo cluster, this H II region is not near the long H I tail observed by Oosterloo & van Gorkom (2005), and there have been no stars found associated with the stripped H I. There have been an increasing number of recent obser- vations of star formation in stripped gas tails. Long trails of star-forming knots were observed in two massive galaxy clusters by Cortese et al. (2007), extending as far as 80 kpc from one of the galaxies. Cortese et al. (2007) \ufb01nd that a combination of tidal and ram pressure stripping are a\ufb00ect- ing the galaxies. In the Coma cluster, Yoshida et al. (2008) found a complex of H\u03b1 \ufb01laments and clouds extending up to 80 kpc from the E+A galaxy RB 199. They also con- clude that the most likely gas removal scenario involves a combination of a merger and ram pressure stripping. Yagi et al. (2010) \ufb01nd another 13 galaxies with young stars or H\u03b1 clouds in tails. Finally, ES0 137-001, which we discussed in detail in Tonnesen et al. (2011), has 35 HII regions extend- ing more than 30 kpc from the disk. These HII regions are spatially correlated with a ram pressure stripped tail of gas (Sun et al. 2006, 2007, 2010). Hester et al. (2010) found H\u03b1 emission indicative of star formation in the UV tail of IC 3418 (Martin et al. 2005), a low surface brightness galaxy in the Virgo Cluster. In a series of 12 SPH simulations including ram pressure stripping and star formation, Kapferer et al. (2009) found that stars can form in their ram pressure-stripped tail out to hundreds of kiloparsecs from the disk. In fact, using fast, high-density ICM winds, the authors found more stars form- ing in the stripped tail than in the remaining disk. The star formation rate increased due to enhanced external pressure provided by the ICM. They also found that stars formed in the tail could fall back into the stellar bulge. Clearly, the standard lore that galaxy-ICM interactions do not result in stars outside of the galaxy has been over- turned. In fact, if star formation in stripped tails is common, c \u20dd2011 RAS, MNRAS 000, 1\u2013?? Star Formation in Ram Pressure Stripped Tails 3 ram pressure stripping could contribute a signi\ufb01cant fraction of the Intracluster Light (ICL). In this paper, we run a set of high resolution simulations (about 40 pc resolution, which is small enough to marginally resolve giant molecular clouds) to understand whether ram pressure can induce star formation in a galactic disk, pro- ducing starburst galaxies or increasing the mass of the bulge, and whether stars can form in a stripped gas tail and add to the ICL. The paper is structured as follows. After a brief intro- duction to our methodology, we provide the general charac- teristics of our simulation (\u00a72.1-2). We introduce the param- eters of our speci\ufb01c simulations in \u00a72.3. In \u00a72.4 we discuss how we make projections of observables. We then discuss our results (\u00a73), \ufb01rst focusing on how star formation a\ufb00ects the disk and then the stripped tail. In \u00a74 we compare our results to observations and previous simulations. We discuss the possible e\ufb00ects of our resolution in \u00a75. Finally, we con- clude in \u00a76 with a summary of our results and predictions for observers."
                },
                {
                    "url": "http://arxiv.org/abs/1111.0636v2",
                    "title": "Effects on Galaxy Evolution: Pair Interactions versus Environment",
                    "abstract": "In a hierarchical universe, mergers may be an important mechanism not only in\nincreasing the mass of galaxies but also in driving the color and morphological\nevolution of galaxies. We use a large sample of ~1000 simulated galaxies of\nstellar mass greater than 10^9.6 solar masses (for ~4800 observations at\nmultiple redshifts) from a high-res (0.46 h^{-1} kpc) cosmological simulation\nto determine under what circumstances being a member of a pair influences\ngalaxy properties at z <= 0.2. We identify gravitationally bound pairs, and\nfind a relative fraction of blue-blue, red-red, and blue-red pairs that agrees\nwith observations (Lin et al. 2010). Pairs tend to avoid the extreme\nenvironments of clusters and void centres. While pairs in groups can include\ngalaxies that are both blue, both red, or one of each color, in the field it is\nrare for pair galaxies to both be red. We find that physically bound pairs\ncloser than 250 h^{-1} kpc tend to have higher sSFRs than the galaxy population\nas a whole. However, the sSFR of a bound galaxy relative to galaxies in a\ncomparable local density environment (determined by the distance to the fifth\nnearest neighbor, rho_5), differs depending on the local density. In regions of\nhigh rho_5 the bound population has a higher fraction of star-forming (bluer)\ngalaxies, whereas there is very little difference between bound and unbound\ngalaxies in low rho_5 regions. This effect on the star-forming fraction may be\ndriven by the higher fraction of bound HI-rich galaxies compared to unbound\ngalaxies, particularly at high local densities. It appears that being in a pair\nhas an incremental, but not overwhelming, effect on the star formation rate of\nthe paired galaxies, compared to the more pronounced trend where galaxies\noverall have low sSFR (are red) in clusters and higher sSFR (blue) at the\ncentre of voids. This trend depends most strongly on rho_5.(abridged)",
                    "authors": "Stephanie Tonnesen, Renyue Cen",
                    "published": "2011-11-02",
                    "updated": "2012-07-05",
                    "primary_cat": "astro-ph.CO",
                    "cats": [
                        "astro-ph.CO"
                    ],
                    "main_content": "2.1 Simulation Details For details of our simulations, we refer the reader to Cen (2010), although for completeness we reiterate the main points here. We perform cosmological simulations with the adaptive mesh refinement (AMR) Eulerian hydrodynamical code Enzo (Bryan 1999; O\u2019Shea et al. 2004; Joung et al. 2009). We use cosmological parameters consistent with the WMAP7-normalized LCDM model (Komatsu et al. 2011): \u2126M = 0.28, \u2126b = 0.046, \u2126\u039b = 0.72, \u03c38 = 0.82, Ho = 100 h km s\u22121 Mpc\u22121 = 70 km s\u22121 Mpc\u22121, and n = 0.96. We first ran a low resolution simulation with a periodic box of 120 h\u22121 Mpc on a side, and identified two regions: one centred on a cluster and one centred on a void at z = 0. We then resimulated each of the two regions separately with high resolution, but embedded within the outer 120 h\u22121 Mpc box to properly take into account large-scale tidal field effects and appropriate fluxes of matter, energy and momentum across the boundaries of the refined region. The cluster refined region, or C box, is 21 \u00d7 24 \u00d7 20 h\u22123 Mpc3. The central cluster is \u223c2 \u00d7 1014 M\u2299with a virial radius (r200) of 1.3 h\u22121 Mpc. The void refined region, or V box, is somewhat larger, at 31 \u00d7 31 \u00d7 35 h\u22123 Mpc3. Although we name these two regions based on whether they contain the cluster or void, we emphasize that these highresolution boxes are much larger than the cluster or the void at their centres. Thus, there are galaxies at a range of local densities in both boxes, and there is substantial overlap of local densities between the two volumes. In both refined boxes, the minimum cell size is 0.46 h\u22121 kpc, using 11 refinement levels at z = 0. The initial conditions for the refined regions have a mean interparticle separation of 117 h\u22121 kpc comoving, and a dark matter particle mass of 1.07 \u00d7 108 h\u22121 M\u2299. The simulations include a metagalactic UV background (Haardt & Madau 1996), a model for shielding of UV radiation by neutral hydrogen (Cen et al. 2005), and metallicity-dependent radiative cooling (Cen et al. 1995). The fraction and density of neutral hydrogen is directly computed within the simulation. The computed H I gas roughly corresponds to all cold gas with temperature less than about 2 \u00d7 104 K, above which collisional ionization becomes important, causing the ionized hydrogen to be the dominant ionization state. Star particles are created in cells that satisfy a set of criteria for star formation proposed by Cen & Ostriker (1992), and supernovae feedback is included (Cen et al. 2005). Each star particle has a mass of \u223c106 M\u2299, which is similar to the mass of a coeval globular cluster. 2.2 The Galaxy Sample 2.2.1 Galaxy Sample Selection We use HOP (Eisenstein & Hut 1998) to identify galaxies using the stellar particles. This has been tested and is robust using reasonable ranges of values (e.g. Tonnesen, Bryan, & van Gorkom 2007). In order to choose only well-resolved galaxies, we only consider those galaxies with a stellar mass greater than 109.6 M\u2299. In the C box, this leaves 61% of the originally identified galaxies, and in the V box this leaves 49% of the galaxies. We also demand that all of the dark matter particles in each galaxy be highly refined\u2013so each galaxy must have resided in the refined region since the beginning of the simulation. In Table 2, we show the number of galaxies above our minimum mass at each output in each box, and see that this number tends to decrease with decreasing redshift. While the fraction of galaxies with M\u2217> 109.6 M\u2299is highest in the z = 0 boxes, the number of galaxc \u20dd2011 RAS, MNRAS 000, 1\u201324 4 S. Tonnesen and R. Cen ies that began in the re\ufb01ned region and have stayed in the re\ufb01ned region has decreased. In the C box, this is due to both mergers and galaxies leaving the re\ufb01ned region, while the underdensity of the V box results in galaxies leaving the re\ufb01ned region. We plotted projections of the star particles of each of these galaxies in order to verify \ufb01rst that HOP was identifying galaxy-like objects (with a density peak), and second, that HOP was not grouping multiple galaxies together. In both the Cluster and Void boxes, only a few of the galaxies above our minimum mass that HOP identi\ufb01ed had density pro\ufb01les without a strong density peak, eliminating 8 galaxies in the C box and 7 galaxies in the V box over all the redshift outputs. In addition, in the C box 47 HOP-identi\ufb01ed galaxies in fact had two density peaks, and one had three \u201cgalaxies\u201d. In the Void box a total of 13 HOP-identi\ufb01ed galaxies had two density peaks. Both of these problems add up to a misidenti\ufb01cation of only 2% in each box. If we treat multiple density peaks in HOP-identi\ufb01ed galaxies as multiple galaxies, we have 4858 galaxies above the minimum mass constituting our \u201ctotal\u201d galaxy population over all redshift outputs (C box z = 0.0, 0.05, 0.1, 0.15, and 0.2 for a total C box galaxy population of 3324; V box z = 0.0, 0.05, 0.15, and 0.2 for a total V box population of 1534). 2.2.2 HOP multi-peak sample All of the HOP-identi\ufb01ed galaxies with multiple density peaks make up our HOP multi-peak sample (HOP has combined multiple galaxies into one). We will discuss each of the galaxy pairs from the HOP multi-peak sample as if observers would identify them as mid-merger or strongly interacting pairs (we do not include the largest cluster cD galaxy in any of our pair samples, including the HOP multipeak sample). These galaxies are likely to be observationally identi\ufb01ed as interacting for the same reason that HOP identi\ufb01es them as a single galaxy \u2013 they have either a small gap between or overlapping stellar populations, and frequently have tidal streams connecting the galaxies. The high-density stellar cores of the galaxies are within about 30 kpc of one another. We also checked the velocities of these galaxies and \ufb01nd that they are gravitationally bound and not simply close passes. 2.2.3 Galaxy Characteristics For details on the properties of our galaxy sample, see Cen (2011). In particular, Cen (2011) compares the evolution of the SFR density from the C and V runs to observations and \ufb01nds strong agreement. Cen (2011) also compares the SDSS r-band galaxy luminosity function at z = 0 to observations and \ufb01nds excellent agreement at Mr > -22. We do overproduce large galaxies, and including AGN feedback can bring the luminosity function into agreement even at high luminosities (as shown in Figure 3 of Cen (2011)). In the top panel of Figure 1, we plot the colour distribution of our total galaxy sample (recall our \u201ctotal galaxy sample\u201d is composed of all galaxies with Mstar > 109.6 M\u2299). We see that there is a bimodal distribution of colours as in observations, and the total range of g \u2212r colours in our simulations is similar to the observed range of galaxy colours 0.0 0.2 0.4 0.6 0.8 g\u2212r 0 50 100 150 200 250 300 350 N 9.5 10.3 11.1 11.9 12.7 log(M \u2217) (M \u2299) -0.10 0.10 0.30 0.50 0.70 g\u2299r 0 4 8 12 16 20 24 28 32 36 Figure 1. Top Panel: A histogram of the colour distribution of all the galaxies in both the C and V boxes above our minimum mass. The distribution is bimodal, and has more blue galaxies than red galaxies. Part of this may be explained by comparing the galaxies at z = 0.2 (purple line) to galaxies at z=0 (orange line). The galaxies at earlier times are more plentiful and bluer. The split between the blue and red population happens at around the same colour as in observations: g\u2212r = 0.65. Bottom Panel: A twodimensional histogram of galaxy colour and mass. The bimodal distribution is also seen in this panel, and we see that high-mass galaxies tend to be redder than low-mass galaxies. See Section 2.2.1 for discussion. (e.g. Blanton et al. 2003; Patton et al. 2011). However, the blue peak is slightly bluer (about 0.05-0.1 magnitudes) and the red peak is about 0.1 magnitudes bluer than in Blanton et al. (2003), and our distribution is narrower (particulary on the red end of the distribution). In the bottom panel of Figure 1, we plot the twodimensional histogram of galaxy colour and mass. Again, we see the bimodal distribution of the panel above, and we also see that our bluest galaxies tend to be low-mass, and our high-mass galaxies are redder than low-mass galaxies, in broad agreement with observations (Baldry et al. 2004). This mass-colour relation has begun to be understood in a cosmological context by considering the gas properties of c \u20dd2011 RAS, MNRAS 000, 1\u201324 Galaxy Evolution: Pair Interactions versus Environment 5 galaxy halos: high stellar mass galaxies have higher mass halos containing hot gas that either cools slowly before it can form stars, or cannot radiatively cool to form stars, while galaxies in low-mass halos are able to directly accrete cold gas that can quickly form stars (e.g. Dekel & Birnboim 2006; Kere\u02c7 s et al. 2005). The ratio of the number of galaxies in the blue cloud to that on the red sequence depends on the uncertain weightings for the C and V boxes, making a direct comparison to observations di\ufb03cult. In the bottom panel of Figure 1 we see that there are a few unrealistically large galaxies\u2013these are mainly at the centre of our cluster or at the centres of groups. The inclusion of AGN feedback, as mentioned above and in Cen (2011), would largely mitigate this discrepancy between our simulations and observations. We can partially explain the di\ufb00erences between the colour distribution of our sample from z = 0 to z = 0.2 to the Blanton et al. (2003) observations (at z = 0.1) by comparing the histograms from the z = 0 (orange line) and z = 0.2 (purple line) outputs. The z = 0.2 output is bluer at both peaks, and contains more galaxies (see also Table 2). We expect our (large) galaxies to become more red with time, as cold gas can no longer be accreted by galaxies as they grow or enter larger halos or overdense large-scale structure (Cen 2011). The fact that both blue and red galaxies were bluer in the past has been observed (e.g. Blanton 2006, although for a larger redshift range). In addition, these di\ufb00erences may be in part due to the fact that we do not include dust reddening for our galaxies, in part because we do not include all of the physical processes that could a\ufb00ect the colours of these galaxies (such as feedback from AGN and SN Ia), and perhaps in a large part because our total galaxy sample (across both the C and V boxes) is not necessarily equal to the global average sample. For these reasons we will focus mainly on comparative studies within our simulations, which should be much less dependent on these uncertainties. Kreckel et al. (2011) closely examine galaxies in the same V box as our simulation, and in fact we use the void centre point that they identi\ufb01ed. Their work di\ufb00ers from ours in that they have one fewer level of re\ufb01nement (two times less resolution), and use somewhat di\ufb00erent criteria in their HOP galaxy identi\ufb01cation. This results in di\ufb00erences of less than a factor of two in the measured properties of our populations. By far the biggest di\ufb00erence is that they include galaxies well below our lower mass limit in their analysis. The luminosity of each stellar particle in each of the \ufb01ve Sloan Digital Sky Survey (SDSS) bands is computed using the GISSEL stellar synthesis code (Bruzual & Charlot 2003), by supplying the formation time, metallicity and stellar mass. Collecting luminosity and other quantities of member stellar particles, gas cells and dark matter particles yields the following physical parameters for each galaxy: position, velocity, total mass, stellar mass, gas mass, mean formation time, mean stellar metallicity, mean gas metallicity, star formation rate, and luminosities in the \ufb01ve SDSS bands. 3 CAN OBSERVERS PICK OUT PAIRS? In this paper we will compare our results to observational trends in order to gain physical insight into what causes pairs to be di\ufb00erent from galaxies without a bound companion. It is worthwhile \ufb01rst to ask whether observers are in fact picking out real pairs since they do not have realspace three dimensional information. In order to determine whether the observational selection criteria for pairs actually choose galaxies that are close to one another and/or that are gravitationally bound to one another, we choose \u201cprojected pairs\u201d using a few sets of criteria used in recent observational work. The least stringent criterion for choosing projected pairs is from Perez et al. (2009), who use a projected distance (rp) of less than 100 kpc h\u22121 and relative line-of-sight velocities \u2206v < 350 km s\u22121. We also use two criteria from Patton et al. (2011), who use a relative line-ofsight velocity criterion of \u2206v < 200 km s\u22121, and a rp upper limit of either 60 kpc h\u22121 or 30 kpc h\u22121. We choose projected pairs using the x-y, x-z, and y-z planes in our simulation for both our C box and V box, and the velocity di\ufb00erence perpendicular to the plane as our line of sight velocity. In Table 1 we show the number of pairs we \ufb01nd for each selections criterium across all projections and all redshifts. We \ufb01rst consider whether galaxies that are close in projected distance and radial velocity are in fact close when considering all three dimensions in real space. As shown in Figure 2, none of the three sets of criteria consistently select galaxies that are actually close to one another. The top panel is a two-dimensional histogram of the projected pairs that are within 100 kpc and 350 km s\u22121. As larger projected distances are allowed, more projected pairs actually have large three-dimensional distances. Sixteen of these projected pairs are more than 8 h\u22121 Mpc apart (one with a projected distance of less than 20 kpc). The projected pairs with the largest three-dimensional distances are from the C box (the largest three-dimensional distance in the V box is \u223c3 h\u22121 Mpc). This is because C box projected pairs contain both galaxies within the cluster that happen to have small line-of-sight velocity di\ufb00erences and pairs between a cluster member and a foreground or background galaxy that have small line-of-sight velocity di\ufb00erences. This highlights the well-known concern that choosing projected pairs may produce spurious pairs near clusters where there is a high density of galaxies (Mamon 1986; Alonso et al. 2004; Perez et al. 2006a), but we also \ufb01nd spurious pairs in our lowerdensity large scale environment. In the bottom panel we plot projected pairs found using the most stringent criterion from Patton et al. (2011): \u2206v < 200 km s\u22121 and rp < 30 h\u22121 kpc. Red symbols are C galaxies, and the blue are V galaxies. Even this most strict criterion \ufb01nds galaxy projected pairs that are separated by large three-dimensional distances. In the rest of this paper, we will be considering only galaxies that are gravitationally bound, which we de\ufb01ne as a pair of galaxies whose total kinetic energy in the centreof-mass frame is less than 90% of its potential energy. This de\ufb01nition will be discussed in greater detail below (Section 4). Here we calculate whether the projected pairs identify bound galaxies. In Figure 3 we plot the kinetic energy versus the potential energy. Again, the top panel is for the least strict pair selection criterion, and the bottom panel shows each pair selected with the most strict criterion. As a more strict selection criterion is used, more galaxies are bound (\u223c11% using the most strict criterion). Also, projected pairs in the C box are more likely to have a positive total energy. A similar analysis has been undertaken by Perez et al. c \u20dd2011 RAS, MNRAS 000, 1\u201324 6 S. Tonnesen and R. Cen Table 1. Number of Projected Pairs Box rp < 100 kpc h\u22121 rp < 60 kpc h\u22121 rp < 30 kpc h\u22121 (all projections) \u2206v < 350 km s\u22121 \u2206v < 200 km s\u22121 \u2206v < 200 km s\u22121 (all redshifts) C 1512 513 201 V 280 144 62 10\u22122 Projected Distance (Mpc h\u22121 ) 10\u22122 10\u22121 100 101 3D Distance (Mpc h\u22121 )      0.009      0.015      0.025       0.04       0.07 Projected Distance (Mpc h\u22121 )      0.009       0.04       0.19       0.88       4.03 3D Distance (Mpc h\u22121 ) 0 2 4 6 8 10 12 14 16 Number of Pairs Figure 2. The two-dimensional and three-dimensional distance between projected pairs selected in our simulation. The top panel shows a two-dimensional histogram of projected pairs chosen to be within 100 kpc and 350 km s\u22121. The bottom panel shows only the pairs that are within 30 kpc and 200 km s\u22121. Blue symbols are from the V box and red are from the C box. Clearly any of these pair-selection criteria allow for a large range of actual distance. 1056 1057 1058 1059 1060 1061 1062 1063 Potential Energy (erg) 1056 1057 1058 1059 1060 1061 1062 Kinetic Energy (erg) 3.2e+55 7.9e+56 2e+58 5e+59 1.3e+61 3.2e+62 Potential Energy (erg) 2.8e+55 7.1e+56 1.8e+58 4.5e+59 1.1e+61 2.8e+62 Kinetic Energy (erg) 0 2 4 6 8 10 12 14 16 18 Number of Pairs Figure 3. The kinetic energy plotted against the potential energy of the pair system. The line denotes K =0.9 |W| (a K=|W| line is essentially the same). The colours and symbols are as in Figure 2. These criteria do not necessarily identify bound pairs. (2006a). In order to determine if projected pairs are indeed pairs, they use a three-dimensional distance criterion of 100 h\u22121 kpc. They \ufb01nd that using the least strict selection criterion (\u2206v < 350 km s\u22121 and rp < 100 h\u22121 kpc), 27% of projected pairs are spurious. We \ufb01nd about 60% of our proc \u20dd2011 RAS, MNRAS 000, 1\u201324 Galaxy Evolution: Pair Interactions versus Environment 7 jected pairs have three dimensional distances > 100 h\u22121 kpc. Using our gravitationally bound criterion, we \ufb01nd that 48% of the identi\ufb01ed projected pairs are in fact spurious. This large spurious fraction is dominated by the C box projected pairs, which have a spurious fraction of 55%. If we only include the projected pairs in the V box and the HOP multi-peak sample, we have a spurious pair fraction of only 12%. Again, this agrees with the idea that projected pairs are more likely to produce spurious pairs in higher-density environments (Mamon 1986; Alonso et al. 2004; Perez et al. 2006a). Perez et al. (2006a) determine local density from the projected distance to the \ufb01fth nearest neighbor with Mr < -20.5 and radial velocity di\ufb00erences lower than 1000 km s\u22121. If we only include galaxies at low local densities we can agree with the Perez et al. (2006a) results. However, in order to do this we must only consider regions with \u03c15 \u22641 h3 Mpc\u22123, which as we will show in Section 7, includes only half of the total or pair galaxy population. Further, at these low local densities we consider only \u223c44% of our projected pairs. The transition from blue to red galaxies seems to occur in higher density regions\u2013therefore, when considering if being a member of a pair is important to galaxy evolution we must consider these regions, and will lose important information by simply discarding high local density regions from our analysis. 4 BOUND PAIRS In order to \ufb01nd galaxy pairs in our simulation, we calculate whether a pair of galaxies is physically bound (we will stress that not all close galaxies are gravitationally bound in Section B). To do this we calculate the kinetic energy of the pair using the galaxies\u2019 velocities relative to the centre of mass velocity. We also include the velocity due to the Hubble expansion from the centre of mass of the pair in the calculation of their velocities relative to the centre of mass. When calculating the potential energy of the pair, we also consider the positive energy due to the Hubble expansion of the matter between the galaxies. Our potential energy equation takes this form: W = \u2212GM1M2 d + 3 10H2r2 \u00d7 (4 3\u03c0\u03c1mr3), (1) where r = 0.5d and \u03c1m = \u03c1crit \u00d7 \u2126m. Because we demand that our potential energy be negative, this puts an upper limit on the distance between bound galaxies (that is mass-dependent). We consider pairs that are slightly more tightly bound than simply |W | > K, so we choose a limit of 0.9|W | > K. Our results do not qualitatively vary even if we use an upper limit of 0.5. This does mean that we can have widely separated galaxies that are bound under our criteria (see Figure 4). While very widely separated galaxies will not merge within a Hubble time, and are distant enough that we would expect them to show no e\ufb00ects from being bound, for completeness we keep them in our sample. As we will discuss below, we include distance cuts to focus on pairs that are more likely to be interacting. Although we search for pairs, we also \ufb01nd groups\u2013either multiple galaxies bound to the same larger galaxy, or bound galaxies in which one is also directly bound to another, larger, galaxy. In the rest of this paper, the term pair refers to a galaxy that is gravitationally bound to at least one other galaxy\u2013it includes galaxies that are a member of a single pair or a member of a larger group. We do not include galaxies bound to the cluster cD in our count, as this would defeat our purpose of understanding when and how being a member of a pair in\ufb02uences galaxy properties rather than simply being inside of a cluster. Here we de\ufb01ne the cD to be the central dominant galaxy of our largest cluster. We also have groups that contain a central dominant galaxy, to which we do allow galaxies to be bound. In Table 2, we show the number of galaxies that are bound to at least one other galaxy for each of our criteria (as some galaxies are bound to multiple galaxies, the number of \u201cpairs\u201d is not simply half the number of bound galaxies). We also de\ufb01ne subsets of pairs by imposing a distance upper limit to our bound pairs (as mentioned in the Introduction, we use the physical distance between galaxies). Note that the criteria are inclusive: the d < 0.25 Mpc h\u22121 galaxies are a subset of the d < 0.5 Mpc h\u22121 galaxies, which are a subset of the K |W | < 0.9 galaxies. We reiterate that in our pair selection, we only consider galaxies with M\u2217\u2265109.6 M\u2299, which constitute our \u201ctotal\u201d galaxy population. We will also discuss the HOP multi-peak sample, listed in the \ufb01nal column of Table 2. This population was chosen di\ufb00erently than the other pair samples, and therefore is not a subset of the bound pair populations. Of course, if a HOP multi-peak galaxy is also bound to other galaxies, both members of the HOP pair are included in that set of bound pairs. 5 PAIR DEMOGRAPHICS 5.1 Redshift Distribution A perusal of Table 2 quickly shows that both the total number of galaxies and the number of pair galaxies (as de\ufb01ned, galaxies that are gravitationally bound to at least one other galaxy) increases with redshift. In fact, the fraction of pair galaxies at any given output also increases with redshift. This means that trends that we see when comparing the total population to the pair population may in part be attributable to trends of the total population with redshift. When considering the total galaxy populations, we \ufb01nd that, on average, galaxies at higher redshift have bluer colour distributions, higher SFRs, and reside in regions of higher local density. This is all in good agreement with observations (e.g. Blanton et al. 2003; Blanton 2006; Martin et al. 2007). We also \ufb01nd that at higher redshifts galaxies tend to have lower stellar masses, and there are fewer galaxies with very low MHI/M\u2217. These trends can be explained by continued mass growth through star formation, and continued heating of the cosmic gas. We address this issue in more detail and \ufb01nd that our results are not due to the redshift distribution of our pair galaxies (Appendix A). It is also worth noting that we are examining some of the same galaxies at multiple redshifts. Therefore it is important to consider what is simply the evolution of the same population over time, as more gas is turned into stars and galaxy masses increase, and what is due to gravitational interactions between pair galaxies. We also address this issue by considering each redshift output individually, and discuss these results in Appendix A. c \u20dd2011 RAS, MNRAS 000, 1\u201324 8 S. Tonnesen and R. Cen Table 2. Number of Galaxies Box redshift all galaxies K |W | < 0.9 d<0.5 Mpc h\u22121 d<0.25 Mpc h\u22121 HOP multi-peak C 0 547 228 102 24 14 C 0.05 680 352 234 155 14 C 0.1 694 399 255 172 24 C 0.15 699 403 262 181 23 C 0.2 704 421 280 201 22 V 0 296 73 32 10 4 V 0.05 412 190 107 75 4 V 0.15 418 206 112 71 10 V 0.2 408 210 112 70 8 5.2 Mass ratios and Distances Observationally it has been found that star formation tends to be more enhanced between closer pairs and pairs with an even mass ratio (Nikolic et al. 2004; Woods & Geller 2007; Ellison et al. 2008). Therefore, it is useful to keep in mind the mass ratios and distances between our pair galaxies (our pair galaxies are all galaxies that are gravitationally bound to at least one other galaxy). In Figure 4 we plot the mass ratio of the pair against the distance between the two pair galaxies. The top panel are the V box bound galaxies, and the bottom panel are the C box bond galaxies. There are some widely separated bound pairs (most of the widely separated pairs are group members), which will result in less tidally-induced star formation. We will account for this using our distance cuts described above. There are also some pairs with high mass ratios in both the C and V boxes. Considering only close bound galaxies reduces the fraction of high mass-ratio pairs, and we \ufb01nd that limiting pairs to more even mass ratios (\u22645) does not qualitatively change any of our results from simply using close bound pairs. 5.3 Where are Pairs? As Table 2 quanti\ufb01es, pairs compose slightly more than half of the galaxy population in the C box and slightly less than half of the galaxy population in the V box (as de\ufb01ned in Section 4, pairs are all galaxies that are gravitationally bound to at least one other galaxy, so a pair galaxy may be a member of a group). At all redshift outputs, there is a higher fraction of bound galaxies in the C box than in the V box. This may have to do with the fact that in the C box there are galaxies that are bound to many other galaxies in groups, while at any output in the V box there are less than half as many groups with at least 4 members as in the C box. This agrees with the Barton et al. (2007) conclusion that pairs tend to reside in larger dark matter halos (Ngalaxies > 2). We bin galaxies using either distance from the cluster cD (C box) or void centre (V box), shown in Figure 5. We use the void centre identi\ufb01ed in Kreckel et al. (2011). In this \ufb01gure we use bin sizes of 0.6 h\u22121 Mpc, and using smaller or larger bin sizes increases or decreases the scatter, respectively, but has no e\ufb00ect on the visible trends. The solid lines are the pair fraction in di\ufb00erent distance bins. The black dot-dashed line is the cumulative fraction of all galaxies (the total galaxy samples in the C or V boxes) as a function of distance from the cD or void centre. The red or blue dotdashed lines are the cumulative fraction of bound galaxies as a function of distance from the cD or void centre. We also plot the cumulative fraction of galaxies that are members of a projected pair (\u2206v < 350 km s\u22121 and rp < 100 kpc h\u22121) as magenta dash-dot lines. First we focus on the C box galaxies (left panel). The total population (black dot-dash line) is concentrated in the cluster\u2013more than 25% of the galaxies are within 2 Abell radii of the cD (rA = 1.5 h\u22121 Mpc), and nearly all of the galaxies are less than 10 h\u22121 Mpc from the cD. The pair distribution is di\ufb00erent from the total galaxy distribution, with few bound galaxies near the cD (the red dash-dot line). This is not surprising, as galaxies in clusters tend to have large relative velocities. However, the pair fraction (the thick solid red line) remains nearly constant below 60% between 3-6 h\u22121 Mpc from the cD, so we do not see evidence of an increase in the fraction of bound galaxies in the infalling population\u2013galaxies are not \u201cpre-processed\u201d in pairs or groups immediately (within 5 h\u22121 Mpc of the cD) before entering the cluster. We predict that about 4050% of galaxies will enter the cluster in groups or pairs. At 2 Abell radii the pair fraction is \u223c55% and has been \ufb02at for a few Mpc. The pair fraction continues to decrease to \u223c37% at the virial radius. This range overlaps the Moss (2006) observational \ufb01nding that 50%-70% of galaxies entering clusters are members of pairs or have recently merged. We agree with the semi-analytic results of De Lucia et al. (2011) that 40-60% of galaxies are isolated when they enter a cluster (also McGee et al. 2009). We \ufb01nd fewer isolated galaxies entering our cluster than the 70% in the simulations of Berrier et al. (2009). Both De Lucia et al. (2011) and McGee et al. (2009) discuss possible reasons for these discrepancies. Also, our simulations di\ufb00er in several respects from all three of these works: we include gas and all hydrodynamical e\ufb00ects as well as radiative cooling and feedback processes, identify galaxies using stellar particles instead of dark matter particles, and de\ufb01ne pair galaxies as those that are gravitationally bound. At larger distances from the cD, 6-15 h\u22121 Mpc, bound galaxies are the majority of the total population. This is because there are many groups in the C box, in which several galaxies are bound to the central galaxy. We do not see a similar phenomenon in the cluster because we do not include galaxies bound to the cD in our pair catalogue. Therefore, 3-6 h\u22121 Mpc from the cD is the c \u20dd2011 RAS, MNRAS 000, 1\u201324 Galaxy Evolution: Pair Interactions versus Environment 9       0.01        0.07        0.52          3.7 Distance (Mpc h\u22121 )        0.5          5.7         65.2          744   Mass Ratio       0.01        0.07        0.52          3.7 Distance (Mpc h\u22121 )        0.5          5.7         65.2          744   Mass Ratio 0 2 4 6 8 10 12 14 16 0 1.5 3 4.5 6 7.5 9 10.5 Number of Pairs Figure 4. This \ufb01gure displays the mass ratio and distances between our identi\ufb01ed pair galaxies (0.9|W| > K). The top panel is the V box galaxies, and the bottom panel is the C box galaxies. There is a large range in both quantities, but as we consider closer pairs the mass ratio tends to decrease. See Section 5.2 for discussion. closest to an average \u201c\ufb01eld\u201d population, because it is outside the cluster and groups in the C box. Finally, we see that projected pairs (magenta line) are the most centrally-concentrated population of all three. In dense regions like clusters there is more chance for galaxies to be superposed on the sky but not necessarily bound, which is the case for most projected pairs in our C box (Section 3). There are no V box galaxies within 5 h\u22121 Mpc of the void centre, and the \ufb01rst pair is 5 h\u22121 Mpc beyond the \ufb01rst galaxy. The projected pairs begin farther yet from the void centre. At large distances from the void centre, one is e\ufb00ectively looking at \u201c\ufb01eld galaxies\u201d. The galaxy pair fraction in the V box beyond r \u223c15 h\u22121 Mpc is comparable to that 0   10   20   30   40 Dist. from Void Centre (h\u22121  Mpc) Void 0 5 10 15 Dist. from cD (h\u22121  Mpc) 0.0 0.2 0.4 0.6 0.8 1.0 Pair Fraction Cluster Figure 5. This \ufb01gure illustrates where pairs are in the C and V boxes with respect to the cluster or void centre. The thick lines are the pair fraction in bins that are 0.6 h\u22121 Mpc wide. We overplot a few representative binomial error bars (to 95% certainty). The dash-dot lines denote the cumulative fraction of di\ufb00erent subsets of galaxies. The black line is the cumulative distribution function of all of the galaxies above the minimum mass in each box. The red (blue) line denotes the cumulative distribution function (CDF) of the C (V) pairs. The magneta line denotes the CDF of projected pairs. Pairs do not dominate the highest or lowest density regions, instead congregating in the groups in the C box. See Section 5.3 for discussion. of the C box pair fraction between r \u223c3-6 h\u22121 Mpc, which highlights the fact that there is no increased pair fraction near the cluster edge. The pair fraction in the V box has a large scatter because of the smaller number of galaxies in that region. Overall, the similarity in the pair fractions in the V box and the \u201d\ufb01eld\u201d region of the C box agrees with the observational result of Szomoru et al. (1996) that small-scale clustering is the same in voids and large-scale higher-density regions. In Figure 6 we show the pair fraction as a function of local density, which is de\ufb01ned as \u03c15 = 5/(4\u03c0d3 5/3), where d5 is the (physical) distance to the \ufb01fth nearest neighbor in h\u22121 Mpc. Notice that this is similar to calculations of local density used by observers (e.g. Perez et al. 2009), but here we calculate a three-dimensional galaxy density. As always, we only use galaxies above our minimum stellar mass in the calculation of local galaxy density. In red we plot the pair fraction in the C box, in blue the V box, and the black dashed line is the total pair fraction across both boxes. We use large (0.45 dex) bins of local density in order to minimize scatter, but we can still see the e\ufb00ects of small numbers of galaxies in each bin. The spike in the pair fraction in the C box at the second-lowest local density bin shown is arti\ufb01cially high due to the small number of galaxies in that bin. Between local densities of 0.1 and 100 galaxies h3 Mpc\u22123 the pair fraction in the C box is between 50% and 60%, which is somewhat below the pair fraction in the V box between a galaxy density of 0.1 and 3. This may be because the V box galaxies tend to have more even mass ratios (few extremely massive galaxies at the centres of groups), which will maximize the potential energy between any pair. In addition, we plot the distribution of the galaxies across both boxes in each local density bin. In black we plot the fraction of all galaxies (the total galaxy samples in the C plus V boxes), in green the fraction of all gravitationally bound galaxies, and in magenta the fraction of all projected pair galaxies. Several noticeable features are seen. c \u20dd2011 RAS, MNRAS 000, 1\u201324 10 S. Tonnesen and R. Cen 10\u22123 10\u22122 10\u22121 100 101 102 103 \u03c15  (h3  Mpc\u22123 ) 0.0 0.2 0.4 0.6 0.8 1.0 Pair Fraction Figure 6. The galaxy pair fraction as a function of the local galaxy density. The thick lines are the pair fraction in local density bins. We overplot a few representative binomial error bars (to 95% certainty).As in Figure 5, red is C box, blue is V box, and here the black dashed line is the total fraction. The red spike at low densities is due to the small number of galaxies at low local density in the C box. The dash-dot lines denote the distribution functions of di\ufb00erent subsets of galaxies with respect to local density: black for the distribution function of the total galaxy population, green for all bound pairs, and magneta for projected pairs. This \ufb01gure illustrates that pairs tend to reside in mid-local density regions, particularly avoiding the lowest local densities. See Section 5.3 for discussion. First, as expected, we see that the total population has a broader distribution of local densities than either the bound or projected pair galaxies, and a much larger fraction of the total galaxy population is at lower local densities (\u03c15 < 0.1 h3 Mpc\u22123) than that at which bound or projected pairs are found. Bound galaxies (green) are rarely found in the lowest density regions, and drop at least as sharply as the total population at the highest densities (\u03c15 > 10 h3 Mpc\u22123). Projected pairs (magenta) are also rare at low densities. However, the projected pair distribution peaks at densities that are higher than either the total or bound population, and a higher fraction of the projected pair population is found at the highest local densities. 5.4 Wet, Dry, and Mixed Mergers We now ask where wet, dry and mixed mergers occur. Given the colour-magnitude diagram in Figure 1, it is sensible to divide the whole population into red and blue sequences at g \u2212r = 0.65, as in observational work (e.g. Lin et al. 2008; Patton et al. 2011 use a line with slope -0.01 that passed through g \u2212r = 0.65 at Mr = -21). With this colour cut we denote blue-blue pairs as wet, red-red as dry, and bluered as mixed (pairs are de\ufb01ned in Section 4 to be galaxies gravitationally bound to at least one other galaxy). We \ufb01nd that 59% of pairs are wet, 13% are dry, and 28% are mixed (C box: 48% wet pairs, 17% dry pairs, 35% mixed pairs; V Table 3. Number of Wet, Dry, and Mixed Pairs Box redshift wet dry mixed C 0 88 42 56 C 0.05 154 45 126 C 0.1 173 84 138 C 0.15 189 61 127 C 0.2 212 54 136 V 0 42 0 5 V 0.05 133 0 14 V 0.15 154 1 18 V 0.2 171 0 11 box: 91% wet pairs, <1% dry pairs, 9% mixed pairs \u2013 the numbers separated by redshift and box are in Table 3). The ratios between the types of pairs are in good agreement with the observational results of Lin et al. (2010), who \ufb01nd 56% wet pairs, 15% dry pairs, and 29% mixed pairs. However, there are di\ufb00erences between our sample and the Lin et al. (2010) sample. For example, we have a broader range of local density. If we use the same range of local density relative to our median \u03c15 (0.45) as in Lin et al. (2010) (one order of magnitude below and two orders of magnitude above the median), we \ufb01nd 60% wet pairs, 11% dry pairs, and 29% mixed pairs, still consistent with the Lin et al. (2010) fractions. The Lin et al. (2010) sample includes galaxies with -21 < MB+1.3 < -19, whereas we include massive galaxies above their range. As we have discussed in Section 2.2, star formation is over-estimated for the most massive galaxies, and our slightly higher fraction of wet pairs may be due to this. In Figure 7 we plot the histograms of the wet (blue), mixed (green), and dry (red) pairs as a function of distance from the cluster centre or void centre, and of local galaxy density. Both the clustercentric distance and local density of the major member of the pair are used to represent those of the pair. For this reason it is easy to pick out the two largest groups in the C box in the middle panel\u2013at about 8 h\u22121 Mpc and 9-9.8 h\u22121 Mpc from the cluster centre. One of them has a red central galaxy and therefore the pairs are either dry or mixed (at \u223c9.8 h\u22121 Mpc), and the other has a blue central galaxy so the pairs are either wet or mixed (at \u223c8 h\u22121 Mpc). The group with the blue central galaxy has more blue galaxies, and the group with the red central galaxy has more red galaxies (seen in the top two panels of Figure 7). This colour conformity is consistent with the \u2019galactic conformity\u2019 observed in Weinmann et al. (2006), that the morphology of the central galaxy in a halo is correlated with the morphology of the satellite galaxies (this was recently examined in terms of gas availability in Kau\ufb00mann et al. 2010). Ignoring these two groups, we can see that dry pairs are closer to the cluster centre, in general agreement with the colour-density relation. Wet and mixed pairs are spread much more evenly in distance from the cD, although there are very few wet pairs within the virial radius of the cluster (1.3 h\u22121 Mpc), and no wet pairs within the virial radius at z \u22640.05. In the V box (the lowest panel), there are no pairs within 10 h\u22121 Mpc of the void centre, and no mixed pairs until nearly 20 h\u22121 Mpc from the void centre. The number c \u20dd2011 RAS, MNRAS 000, 1\u201324 Galaxy Evolution: Pair Interactions versus Environment 11 0 2 4 6 8 10 12 14 16 Distance from Cluster center (h \u00001  Mpc) 0 20 40 60 80 100 120 140 N 10 15 20 25 30 35 40 45 Distance from Void center (h \u00011  Mpc) 0 10 20 30 40 50 60 N 10-3 10-2 10-1 100 101 102 103 \u00025 (h3  Mpc \u00033 ) 0 20 40 60 80 100 120 140 N Figure 7. Histograms of pairs as a function of local density and distance from the cD or the void centre. Red denotes dry pairs, blue denotes wet pairs, and green denotes mixed pairs. The differences in the distributions of dry and wet pairs are easy to pick out by eye. See Section 5.4 for discussion. of pairs increases with distance from the void centre until we reach the edge of the V box. If we consider the local galaxy density of the pairs in the upper panel of Figure 7, we can more easily pick out the group with the red central galaxy, which has a local density of about 10 h3 Mpc\u22123. At later times (at z\u22640.05), both groups have this local density. However, at earlier times the red group has even higher local densities and the blue group has lower local densities. Focusing on the rest of the pairs, we see that wet pairs reach the lowest local densities (\u03c15 \u223c 0.005). We also \ufb01nd that dry pairs are rare outside of group environments (\u03c15 < 3), although we might \ufb01nd more dry pairs if we had a larger red galaxy population (if, for example, we included AGN feedback, see Section 2.2.1). Our overall \ufb01nding is that, while all three types of pairs can occur in groups, dry pairs are extremely rare in \ufb01eld environments. If pairs end in mergers, the following physical picture emerges: dry mergers should occur only in group or cluster environments, while wet and mixed mergers can occur at all local galaxy densities. Wet mergers will dominate at the lowest local densities (\u03c15 < 0.1). At the other environmental extreme, dry mergers dominate within the virial radius of a cluster. This is in general agreement with the observations of Lin et al. (2010). 6 PAIRS COMPARED TO THE TOTAL GALAXY POPULATION In this section we compare properties of pair galaxies (we de\ufb01ne pairs in Section 4 to be galaxies bound to at least one other galaxy\u2013excluding the cD in our largest cluster) to those of the entire galaxy population. First consider the stellar mass of the galaxies. We \ufb01nd that, on average, the stellar mass of bound galaxies is larger than that of the total population at a \ufb01xed local density. This is true whatever subset of bound galaxies we consider (all pairs, d < 500 h\u22121 kpc, d < 250 h\u22121 kpc, or the HOP multi-peak sample). Because galaxy mass may have a strong in\ufb02uence on galaxy properties (Visvanathan & Sandage 1977; Schweizer & Seitzer 1992; Blanton et al. 2003; Baldry et al. 2004; and see Figure 1), we performed all of our analysis twice: once with the entire galaxy sample as our control, and once using a sample that was matched to the stellar mass distribution of the bound sample. Each bound sample was separately matched, therefore the comparison samples are not identical. After going through this process we \ufb01nd that the di\ufb00erences between the pair and total samples are somewhat smaller when we match stellar mass, although the sign remains the same. In this section, we will present our results using the entire galaxy sample for comparison. 6.1 Star Formation Rate Galaxy colour is often used as a proxy for star formation rate (see the references in the Introduction). We have considered both the colour and speci\ufb01c SFR (sSFR \u2261SFR/M\u2217), and \ufb01nd analogous results when comparing pairs to the total population. Therefore we will focus on the sSFR, as it is a more fundamental parameter and calculated directly in the simulation, whereas colour is subject to other less well modeled processes, such as dust reddening. We will now discuss the di\ufb00erences in the sSFR between the pair and the total galaxy population. As we discussed in Section 2.2.1, we will compare trends we \ufb01nd in our simulations to observational trends rather than attempt to directly compare our simulated galaxies to observed galaxy populations. In Figure 8 we plot the cumulative distribution function (CDF) of the sSFR of di\ufb00erent subsets of the simulated galaxies. The dash-dotted lines remain the same in all six panels, describing the total galaxy population in the C box c \u20dd2011 RAS, MNRAS 000, 1\u201324 12 S. Tonnesen and R. Cen (red), V box (blue) and including the total combined population in the C and V boxes (black). Overlaid on these curves we plot the CDFs of bound galaxies, with each panel showing a di\ufb00erent subset. To make the distributions of the higher sSFR galaxies more clear, we zoom in on the high sSFR end in the bottom panels. The sSFR distributions of the total galaxy populations in the two boxes di\ufb00er. The V galaxies have a much higher fraction of high sSFR galaxies, although the maximum sSFR in both boxes is very similar. About 35% more of the galaxies in the V box have sSFR > 10\u221211 yr\u22121 than in the C box. Clearly sSFR (and therefore galaxy colour) depends on environment, a point we will return to in Section 7. Note that the bound (and to a lesser extent, the total galaxy) CDFs are dominated by the C box galaxies, given the numbers shown in Table 2. Focusing on the bound galaxies, we see that the CDF tilts towards higher sSFR as we move from the entire bound sample to subsets with distance cuts. This is largely due to changes in the CDF of the C box in the low sSFR end (< 5 \u00d7 10\u221211). In the lower panels, it is clear that there is very little change in the distribution of higher sSFR galaxies between the C box total bound population (0.9|W| > K) and the C box bound population with d < 250 h\u22121 kpc. If we focus on the V box, we \ufb01nd that the bound galaxy distribution appears very similar to that of the total V galaxy population, but with slightly more galaxies at both the high and low sSFR ends. In contrast to the C box galaxies discussed above, the sSFR distribution of the low sSFR V box bound galaxies varies very little as we consider only pairs with small separations (\u223c2% at 10\u221211 yr\u22121). The most noticeable change in the V pair CDFs is a larger fraction of high sSFR galaxies (+5% at 10\u221210 yr\u22121). The HOP multi-peak sample has a clearly larger high sSFR fraction than the total population for both the C and V boxes, although it is more pronounced in the V box. The sSFRs in these strongly interacting galaxies are among the highest of the total galaxy population. There are also galaxies with low sSFRs in the HOP multi-peak sample, indicating that being a member of a strongly interacting pair does not necessarily lead to strong star formation. When we match this sample for stellar mass we see the exact same trends. Tidal interactions may be causing a substantially higher fraction of HOP multi-peak galaxies to have high sSFRs than pairs with larger separations. Of course, companioninduced interactions are not the only cause of blue galaxies with high sSFRs; in fact, the galaxy with the highest sSFR (1.75 \u00d7 10\u22129 yr\u22121) is not bound to any other galaxy. Quantitatively, among the 39 galaxies with the highest sSFRs (\u2265 3 \u00d7 1010 yr\u22121), we \ufb01nd only 8 of them to be members of the bound d < 250 h\u22121 kpc, 6 to be a member of the HOP multi-peak sample, and 1 to have been a member of the HOP multi-peak sample in the previous output (and therefore likely to have just merged). In Figure 8 we \ufb01nd red HOP multi-peak galaxies with low sSFRs that span the entire stellar mass range and the entire range of mass ratios in the HOP multi-peak sample. To brie\ufb02y summarize, we \ufb01nd a slightly higher fraction of low sSFR bound galaxies than that of the total sample (compare the black dash-dotted line to the black solid line in the \ufb01rst panel of Figure 8). This is in agreement with 10 \u00044 10 \u00053 10 \u00062 10 \u00071 10 \b0   MHI/M \t 0.0 0.2 0.4 0.6 0.8 1.0 CDF All Pairs All galaxies All C All V Pairs C Pairs V Pairs 10  4 10 \u000b3 10 \f2 10 \r1 100 101 MHI/M \u000e             Pairs d < 0.25 h \u000f1  Mpc Figure 9. Left panel shows the MHI/M\u2217distribution of the galaxies, for pairs and the total galaxy population in the C box, V box, and across both the C and V boxes. Right panel shows the CDFs for closer pairs with d < 250 h\u22121 kpc. Linestyles are as in Figure 8. See Section 6.2 for discussion. Patton et al. (2011). Including any distance cut results in a pair population with higher sSFR. This is at least partly because the distance cuts remove more group galaxies, which are likely to have lower sSFR (and therefore be redder) due to the dense environment in which they reside. We \ufb01nd a larger population of high sSFR (extremely blue) galaxies in the HOP multi-peak pairs than in the total sample, which qualitatively agrees with the results of Patton et al. (2011). We do not \ufb01nd a larger fraction of low sSFR (extremely red) galaxies using any of our pair samples. 6.2 Cold Gas Mass In addition to determining whether star formation is a\ufb00ected by being a member of a pair or group, we now investigate whether the cold gas mass of bound galaxies is di\ufb00erent from the total population. As mentioned in Section 2.1, the H I density is directly followed within the simulation. We consider the H I gas fraction in Figure 9, as it tells us about the fuel available for star formation in these galaxies. We use the H I gas mass within one virial radius. We are unable to accurately separate the gas that belonged to each component galaxy in the HOP multi-peak sample, and so do not consider that sample in this section. In the C box, the H I gas fraction for all pairs has a similar distribution to the general C population. It is notable that close pairs have a higher fraction (70% vs 60%) of somewhat H I gas rich galaxies (MHI/M\u2217\u226510\u22123) than the total C population. It is equally interesting to note that the fraction of pairs (\u223c4%) with high H I mass fractions (MHI/M\u2217 \u22650.1) appears little changed by being a pair member or a close pair member. As in the C box, V box pairs have a very similar H I gas fraction to the general V population. However, unlike the C box pairs, bound pairs in the V box with smaller separations (d < 250 h\u22121 kpc) have a dramatically higher fraction of extremely H I rich galaxies: 20% of close pairs have MHI/M\u2217 \u22651, whereas only 4-5% of galaxies in the total V population or the entire V pair population have MHI/M\u2217\u22651. Overall, we \ufb01nd that galaxies in closer pairs have higher c \u20dd2011 RAS, MNRAS 000, 1\u201324 Galaxy Evolution: Pair Interactions versus Environment 13 10 \u001012 10 \u001111 10 \u001210   sSFR             CDF Pairs d < 0.25 h \u00131  Mpc 10 \u001412 10 \u001511 10 \u001610   sSFR 0.0 0.2 0.4 0.6 0.8 1.0 CDF All Pairs Pairs C Pairs V Pairs 10 \u001712 10 \u001811 10 \u001910 10 \u001a9 sSFR             HOP combined All galaxies All C All V 10 \u001b10 10 \u001c9 sSFR           CDF Pairs d < 0.25 h \u001d1  Mpc 10 \u001e10 10 \u001f9 sSFR 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1.0 CDF All Pairs All galaxies All C All V Pairs C Pairs V Pairs 10  10 10 !9 sSFR           HOP combined Figure 8. Top three panels show the sSFR distribution of the galaxies. The CDFs for the total galaxy population in the C box, V box, and across both the C and V boxes are shown in all three panels as the red, blue, and black dash-dotted lines, respectively. Left panel shows the CDF for all bound galaxy pairs. The middle panel shows a subset of those pairs are that less than 250 h\u22121 kpc apart. The right panel shows galaxies that were identi\ufb01ed by HOP as a single galaxy because their stellar clumps signi\ufb01cantly overlap. The bottom three panels zoom in to the high sSFR end. Note that the galaxies in the C box have a di\ufb00erent sSFR CDF than galaxies in the V box (Section 6.1). Closer bound galaxies have a higher sSFR than more distant ones, and close pairs (d < 250 h\u22121 kpc) have a slightly higher fraction of galaxies with sSFR > 10\u221210 yr\u22121 than galaxies in the total population. HOP multi-peak galaxies have a higher fraction of galaxies with high sSFRs, and the C HOP multi-peak galaxies also have fewer galaxies with low sSFRs (See Section 6.1). MHI gas fractions than the general population: the P values for the KS tests comparing the bound galaxies to either the total or the mass-matched sample are below 0.1 for all pairs with d < 500 h\u22121 kpc. This indicates that close interactions increase cold gas formation via gravitationally induced hydrodynamical e\ufb00ects and radiative cooling. Observations indicate that galaxy interactions can cause in\ufb02ows in ionized gas (Rampazzo et al. 2005) and neutral gas (e.g. Hibbard & van Gorkom 1996). In addition, observations \ufb01nd that interacting galaxies have lower metallicities in the central regions and have lower metallicity gradients in the disc (Kewley et al. 2006; Kewley et al. 2010). Together these \ufb01ndings indicate that low metallicty gas in\ufb02ows come from outer regions of the halo to the disk and central galaxy. Recall from Figure 8 that the fraction of higher-sSFR galaxies does not start to increase until we focus on the HOP multi-peak sample. This may mean that gas is cooling from the halo in the d < 250 h\u22121 kpc sample, but is not transmitted into a higher SFR until galaxies are still closer. Our simulations suggest this physical picture holds for about 50% of the close pairs (d < 250 h\u22121 kpc) in the V box with MHI/M\u2217\u22650.2. 7 THE LOCAL ENVIRONMENT OF BOUND GALAXIES In higher density environments, observed galaxies tend to be more massive, redder (lower sSFR), and have less H I gas (Hubble & Humason 1931; Oemler 1974; Dressler 1980; Balogh 2001; Blanton et al. 2003; Solanes et al. 2001; Haynes, Giovanelli, & Chincarini 1984). By simply comparing the total galaxy population in the C box to that in the V box, it is clear that our simulated galaxies follow these relationships well (e.g. Figures 8 and 9). Therefore, we must determine if the di\ufb00erences between pairs (as de\ufb01ned in Section 4, a pair galaxy is gravitationally bound to at least one other galaxy that is not the cD of the largest cluster) and the total galaxy population may be attributed to an environmental di\ufb00erence between bound c \u20dd2011 RAS, MNRAS 000, 1\u201324 14 S. Tonnesen and R. Cen 10 \"3 10 #2 10 $1 100 101 102   %5 (h3  Mpc &3 )             CDF Pairs d < 0.25 h '1  Mpc 10 (3 10 )2 10 *1 100 101 102   +5 (h3  Mpc ,3 ) 0.0 0.2 0.4 0.6 0.8 1.0 CDF All Pairs All Gals All C All V Pairs C Pairs V Pairs 10 -3 10 .2 10 /1 100 101 102 103 05 (h3  Mpc 13 )             HOP combined Figure 10. CDFs of the local density, \u03c15, of galaxies. See Figure 8 for a description of the panels. Bound galaxies tend to reside in local densities above that of the corresponding total population. See Section 7 for discussion. and unbound galaxies. We show in Figure 5 that there are fewer pairs in regions close to the cD (< 3 h\u22121 Mpc) than in regions more distant from the cluster. This may be part of the reason that the bound galaxies in this large scale environment have fewer galaxies with low sSFRs than the general galaxy population in the C box: simply because pairs are more remote from the cluster (see Figure 8). Similarly, we \ufb01nd that bound galaxies in the V box tend to be farther from the void centre than the general population. This could explain why bound galaxies in this low-density large-scale environment tend to have lower sSFRs than the general V galaxy population\u2013although very close bound galaxies in the V box do not conform to this trend (Figure 8). Even though pairs avoid the centre of the cluster and void, Figure 6 shows that in both the C and V boxes the local galaxy density of bound galaxies spans a large range. To look more closely at the local environment of bound galaxies versus the total population, Figure 10 shows the CDFs of our galaxy pair and total populations. We see that V box pairs tend to reside in regions of higher density (a factor of \u223c2) than the total V population, whereas in the C box the environments are nearly identical, bearing mind that bound pairs with the cD galaxy of the cluster are intentionally removed from the bound pair populations in the C box in our analysis.. The closest pairs (d < 250 kpc h\u22121) in both the C and V boxes reside in a higher range of local galaxy density than the total samples. This is also true if we compare the bound galaxies to the total sample that is matched in mass. The only KS test with a P value larger than 0.1 compares the total C population matched in mass to all the pairs in the C box. Clearly, bound galaxies tend to reside in higher local density environments than unbound galaxies. The fact that there is a higher fraction of close pairs than pairs with larger separations in high-density environments suggests either that dense environments are more conducive to the formation of close pairs, or that in general pairs have a lifetime on order of the Hubble time and move closer together as they migrate to denser environments, or a combination of these two factors. In the C box, bound galaxies have a strong tendency to have higher sSFRs and be more H I-rich, which is opposite to what one would predict from the fact that bound galaxies reside in higher density environments. It is less clear whether the V box bound galaxies are in\ufb02uenced by the fact that they tend to reside in higher density environments than the total population. First, there is an excess of galaxies with low sSFRs in all V bound galaxy populations except the HOP multi-peak sample. This trend could be explained by the environment. However, in the d < 250 kpc h\u22121 galaxies and the HOP multi-peak galaxies there is an excess of high sSFR galaxies as well. The V bound population tends to have more H I-rich galaxies, which would not be caused by a dense environment. Combining these facts, it seems that most of the di\ufb00erences between the bound and total galaxy populations may be driven by pair e\ufb00ects rather than local environment. We will now test this more carefully. 7.1 Fraction of Star-Forming Galaxies Relative to Their Environment We can look more closely at the e\ufb00ects of the large-scale, local, or very local (being a member of a close bound pair, where a pair galaxy is any galaxy that is gravitationally bound to at least one other galaxy that is not the cD of the largest cluster) environment on the star-formation properties of galaxies. We de\ufb01ne the fraction of galaxies having sSFR > 10\u221211 yr\u22121 as the star-forming fraction. This is the lowest sSFR denoting the green valley used by Heinis et al. (2009). In the upper panel of Figure 11 we plot the starforming fraction in four bins of local density, which were chosen so that the second bin contained a large number of galaxies from both the C and V boxes, and the third bin extends to the highest local density in the V box (\u223c83 h3 Mpc\u22123). The comparison \u201ctotal\u201d population has been matched to the mass distribution of the close pair sample. We use close pairs (d < 250 kpc h\u22121 including the HOP multi-peak sample). The horizontal lines are the widths of the local density bins, and vertical lines denote the binomial error for the sample in that bin using a 95% con\ufb01dence level. In the lower panel of Figure 11, we plot the total galaxy population from each box separately. The C box total population are the red symbols, and the V box total population are the blue symbols. We note that we have a small number of galaxies in the lowest and highest density bins from the C box, and in the third density bin from the V box. We can make several comparisons using Figure 11. c \u20dd2011 RAS, MNRAS 000, 1\u201324 Galaxy Evolution: Pair Interactions versus Environment 15                 0.0 0.2 0.4 0.6 0.8 1.0 fraction galaxies sSFR >= 10\u221211 10\u22123 10\u22122 10\u22121 100 101 102 103 104 \u03c15  (h3  Mpc\u22123 ) 0.0 0.2 0.4 0.6 0.8   fraction galaxies sSFR >= 10\u221211 Figure 11. The fraction of star-forming galaxies in four bins of local density. Top Panel: the black points are the star-forming fractions of the total comparison population, and the green lines are the star-forming fraction of the close pairs (d < 250 kpc h\u22121 galaxies plus HOP multi-peak galaxies) for the combined C plus V boxes. Bottom Panel: The red points are the fractions of mass-matched C box total galaxy sample, and the blue points are those of the mass-matched total V box sample. The horizontal lines denote the width of the local density bin, and the vertical lines are the 95% con\ufb01dence binomial error bars. Note the only clear di\ufb00erence between pairs and the matched sample is in the star-forming fraction at the highest densities. See Section 7 for discussion. First, we can determine how di\ufb00erent local densities a\ufb00ect the star-forming fraction of the total galaxy population by comparing the black symbols. Second, we can determine how the large-scale structure a\ufb00ects the star-forming fraction by comparing the solid red (C box) and blue (V box) markers. Finally, we can check how being a member of a pair a\ufb00ects the star-forming fraction by comparing the green and black symbols in the top panel. Addressing the \ufb01rst point, we \ufb01nd that the fraction of star-forming galaxies decreases with increasing local density. This is true whether we are considering the total galaxy population (black symbols), or the total pair population (green symbols). This is also true when considering the C box or V box galaxies separately (bottom panel). This is in excel                0.0 0.05 0.1 0.15 0.2 0.25 fraction galaxies sSFR >= 10\u221210 10\u22123 10\u22122 10\u22121 100 101 102 103 104 \u03c15  (h3  Mpc\u22123 ) 0.0 0.05 0.1 0.15 0.2 0.25 fraction galaxies sSFR >= 10\u221210 Figure 12. The fraction of starburst galaxies in close pairs (d < 250 kpc h\u22121 galaxies plus HOP multi-peak galaxies) compared to a sample of the total population matched to the mass distribution of the pairs. See Figure 11 for an explanation of the symbols. See Section 7 for discussion. lent agreement with observations where there is a consistent trend of galaxies becoming progressively redder with lower sSFRs from voids to \ufb01laments to clusters (Rojas et al. 2004, 2005; Kau\ufb00man et al. 2004; G\u00b4 omez et al. 2003). Focusing on the C and V box galaxies separately leads us to our second question: how does the large-scale structure a\ufb00ect the star-forming fraction? In the bottom panel, the trend with local density is much stronger for the C box galaxies, which drops by about 55% compared to the \u223c20% drop in the V box over the same local density range (the \ufb01rst three bins). This drop remains nearly identical (30% di\ufb00erence versus 35% di\ufb00erence) when we match the local density distributions (P value of 0.93) and the mass distributions (P value of 0.78) of the C and V galaxies within the third density bin (the bin with the largest di\ufb00erence between the C and V box total galaxy populations). In the two lower density bins, the V box and C box galaxies have similar starforming fractions, and the V box galaxies are less a\ufb00ected by local density than the C box galaxies only in the third density bin, where the error bars on the V box galaxies are quite large. The lower star-forming fraction at similar \u03c15 (1 c \u20dd2011 RAS, MNRAS 000, 1\u201324 16 S. Tonnesen and R. Cen < \u03c15 < 83) may indicate that C box galaxies are more likely to be in larger groups than V box galaxies. Although to \ufb01rst order \u03c15 is a measure of halo mass, in large halos there can be a large range of \u03c15. For example, even within one Abell radius of the cluster centre (1.5 h\u22121 Mpc), \u03c15 can be as low as 1.5 h3 Mpc\u22123. We \ufb01nd that in general the local density has a stronger a\ufb00ect on the star-forming fraction than whether a galaxy is in the C box (large-scale overdensity) or V box (large-scale underdensity). However, at higher local densities, there is a signi\ufb01cant di\ufb00erence between C and V box galaxies, which may be indication of some e\ufb00ects on intermediate scales ( 1 Mpc), such as whether or not a galaxy is close to the cluster (or a group). Finally, we consider whether being a member of a pair a\ufb00ects the star-forming fraction. In the top panel we compare the total population (black) to the close pairs (d < 250 kpc h\u22121 including HOP multi-peak galaxies in green) in the C plus V boxes. In the two lowest density bins, the populations have the same star-forming fraction within the error bars. In the two highest local density bins, the star-forming fractions of the pairs are higher than the star-forming fraction of the total population (although the error bars in the highest bin are large). We checked these results using only the HOP multipeak sample, and while the error bars are much larger, we \ufb01nd the same trends. We also considered whether simply being near another galaxy could cause this increase in the star-forming fraction by comparing the close bound galaxies to the close unbound galaxies (see Appendix B). Although with four close unbound galaxies in the V box our results are dominated by the C box galaxies, we still \ufb01nd the same trends\u2013the star-forming fraction decreases with local density and in the two lower-density bins the bound galaxy star-forming fraction agrees within the errors with that of the close unbound galaxies. In the highest local density bin the bound galaxy star-forming fraction is signi\ufb01cantly higher than that of unbound close galaxies. We have also examined the median sSFR of starforming galaxies in Appendix C. We \ufb01nd that the starforming fraction does not strongly depend on galaxy mass and the local density distribution of pairs versus the total sample in Appendices D & E. To summarize all of the information in Figure 11, we \ufb01nd two main e\ufb00ects on the star-forming fraction. First, the fraction of star-forming galaxies is most strongly dependent on local density (\u03c15), dropping by about 80% (from nearly 100% to about 20%) from our lowest to highest density bin (i.e. from voids to clusters). Second, being a member of a bound pair a\ufb00ects the star-forming fraction of the galaxy population only at the highest local densities, with a boost in the star-forming fraction of more than 10%. We believe the \ufb01rst conclusion to be very robust and it is indeed a fundamental environmental e\ufb00ect. The second e\ufb00ect is more di\ufb03cult to decipher physically for the following reason. It could be that the local environment indeed plays the primary role to produce the seen e\ufb00ect. Alternatively, one might envision the following picture. Galaxies tend to move to higher local density environments with time, whether they are isolated, in pairs, or in groups. Pairs may form at some intermediate local density. With time these pairs move to higher density regions and at the same time become more closely separated. If a portion of these close pairs results in more enhanced star formation, it could explain, at least in part, the seen trend. Such a picture is also consistent with the higher fraction of close pairs in higher density environments (Figure 10). However, we would expect the HOP multi-peak sample to have a higher fraction of star-forming galaxies at any local density, and we only \ufb01nd a di\ufb00erence of that sort in the highest local density bin. We defer a more careful examination of this issue to a future study. 7.2 Fraction of Starburst Galaxies Relative to Their Environment In Figure 12 we plot the fraction of galaxies with sSFR > 10\u221210 yr\u22121 in four bins of local density, which as before are chosen so that the second lowest density bin contained a large number of galaxies from both the C and V boxes, and the second highest density bin reached the maximum local density of V box galaxies. This sSFR is the limit used by Heinis et al. (2009) to denote the bottom of the blue cloud, which we call starburst galaxies. If we compare close pairs (d < 250 h\u22121 kpc bound including HOP multi-peak galaxies) to the mass-matched total galaxy sample, we can clearly see that the values are the same to well within the errors. In fact, these errors are large enough that we can only say that the fraction of starburst galaxies decreases with increasing local density (by about 10%). The fraction of starburst galaxies is a\ufb00ected less than the fraction of star-forming galaxies by both local density and whether a galaxy is a member of a close pair. 7.3 Fraction of H I-Rich Galaxies Relative to Their Environment In Figure 13 we plot the fraction of galaxies with MHI/M\u2217 >= 0.1, which we will call the H I-rich fraction, with the comparison sample matched for both mass and local density to the pair sample. As with the star-forming fraction, the bound galaxies di\ufb00er from the comparison population only in the highest local density bins. The pairs have a higher H I-rich fraction, which is consistent with having a higher star-forming fraction of galaxies, as seen earlier. But, unlike the star-forming fraction, the H I-rich fraction is consistently higher in the V box than in the C box. This indicates that galaxies in the V box have easier access to cold gas, which, by comparison to the star-forming fraction, does not necessarily result in high star-formation rates. 7.4 Comparison to Observations We will now brie\ufb02y compare our results to the observations of Ellison et al. (2010). Ellison et al. (2010) consider whether environment changes the e\ufb00ect of being in a close pair. In direct opposition to our results, they \ufb01nd that star formation is more enhanced for close pairs at low projected local density, with no increase in the median sSFR for projected pairs in their highest local density bin. Using projected local density, we still \ufb01nd results opposite to theirs. A number of factors may have contributed to this di\ufb00erence. The main physical di\ufb00erence between our simulation c \u20dd2011 RAS, MNRAS 000, 1\u201324 Galaxy Evolution: Pair Interactions versus Environment 17                 0.0 0.2 0.4 0.6 0.8 1.0 fraction galaxies MHI/M \u2217 >= 0.1 10\u22123 10\u22122 10\u22121 100 101 102 103 104 \u03c15  (h3  Mpc\u22123 ) 0.0 0.2 0.4 0.6 0.8   fraction galaxies MHI/M \u2217 >= 0.1 Figure 13. The fraction of H I-rich galaxies in close pairs (d < 250 kpc h\u22121 galaxies plus HOP multi-peak galaxies) compared to a sample of the total population matched to the mass and local density distribution of the pairs. The symbols are the same as in Figure 11. Once again, the samples di\ufb00er signi\ufb01cantly in the two highest local density bins. See Section 7 for discussion. and their observation is that pairs in our simulation are physically bound, while observed projected pairs may contain interlopers. In particular, the paired galaxies in the higher density bins in Ellison et al. (2010) may contain a high fraction of unpaired interlopers (as we have shown earlier), which may lower the sSFR of their pair population in high density regions. To illustrate how this a\ufb00ects our results, we \ufb01nd that the fraction of star-forming projected pairs in our third local density bin (1 < \u03c15 < 83) is 49%, which is below the 60% star-forming fraction of close pairs (d < 250 kpc h\u22121 galaxies plus HOP multi-peak galaxies), and within the error bar of the total galaxy population shown in the top panel of Figure 11. The sample used in Ellison et al. (2010) is much larger than our sample, so the close pairs at which they see this increase in sSFR are within 30 kpc h\u22121 70 . This corresponds roughly to our HOP multi-peak sample, which is too small to make any robust conclusions. In the two lowest density bins, we have 16 and 26 HOP multi-peak galaxies, respectively. Therefore, we may not have a large enough sample to identify the speci\ufb01c signal observed by Ellison et al. (2010). There are also di\ufb00erences related to the method used to calculate local density. We use all of the galaxies in each box to determine the projected local density for this rough comparison, but Ellison et al. (2010) choose galaxies within a line-of-sight velocity of 1000 km s\u22121. Also, we calculate local density using all the galaxies with M\u2217> 4 \u00d7 109 M\u2299 in our simulation, while Ellison et al. (2010) use only galaxies with Mr < -20.6. If we were to only include galaxies with Mr < -20.6, we would eliminate 48% of our C box galaxies and 60% of our V box galaxies. A direct comparison between our galaxies and those observed by Ellison et al. (2010) using the same projected local density bins is not robust, because we only have eleven paired galaxies in the lowest density bin used by Ellison et al. (2010) (log \u03a3 < -0.55). When we split our galaxy population into three evenly log-spaced bins in projected local density (the same process as in Ellison et al. (2010)), we see the same trends as when we use the threedimensional local density. 8 SSFR AND BOUND PAIR SEPARATION Another possible explanation for the di\ufb00erences in the bound pair (as de\ufb01ned in Section 4, a pair galaxy is gravitationally bound to at least one other galaxy that is not the cD of the largest cluster) and total populations is that bound galaxies are interacting. Because even our closest pairs use a rather large distance bin (d < 250 kpc h\u22121), we could be diluting a signal that depends on the distance between galaxies. Observations of close interacting pairs at low redshifts \ufb01nd that they are a blue population (e.g. Condon et al. 1982; Keel et al. 1985; Kennicutt et al. 1987; Wong et al. 2011; Patton et al. 2011), which is consistent with the blue galaxy population in our d < 250 kpc h\u22121 bound galaxies. It is noteworthy that the HOP multi-peak sample is composed of strongly interacting galaxies, as we discussed earlier (Section 2.2.1, and have a larger blue population than the total galaxy population. We can perform a quantitative check by noting that galaxies may be gravitationally strongly interacting if they are closer than the tidal distance, which we estimate as the Roche radius: d = 160h\u22121kpc \u00d7 ( Mminor 1012M\u2299) 1 3 \u00d7 (2 \u00d7 (Mmajor Mminor )) 1 3 . (2) In Figure 14, we plot the number density of pairs in the (Distance/Roche radius) sSFR two-dimensional plane. Note that the Roche radius is recalculated for every pair or group using the above equation. The top left panel is the major member of the pair in the C box, the bottom left panel is the minor member of the pair in the C box, the top right panel is the major member of the pair in the V box, and the bottom right panel is the minor member of the pair in the V box. The (Distance/Roche radius) bins are evenly spaced in log. The sSFR bins are evenly spaced in log above 10\u221213 yr\u22121, and the two bins below 10\u221213 yr\u22121 contain all of the galaxies with sSFR lower than 10\u221213 yr\u22121. We also split the x-axis into three separate groups: non-star forming, star-forming, and starburst galaxies, and split the y-axis into two regions: inside or outside the Roche radius. Each of these six bins is c \u20dd2011 RAS, MNRAS 000, 1\u201324 18 S. Tonnesen and R. Cen -13 -12 -11 -10 -9 log(sSFR)       0.03       0.07       0.15       0.33       0.71       1.54       3.35       7.29 Distance / Roche radius 156 408 22 346 679 25 0 2 4 6 8 10 12 14 16 -13 -12 -11 -10 -9 log(sSFR)       0.03       0.07       0.15       0.33       0.71       1.54       3.35       7.29 Distance / Roche radius 3 106 20 26 355 26 0 1.5 3 4.5 6 7.5 9 10.5 12 13.5 -13 -12 -11 -10 -9 log(sSFR)       0.03       0.07       0.15       0.33       0.71       1.54       3.35       7.29 Distance / Roche radius 374 192 20 378 578 94 0 3 6 9 12 15 18 21 24 27 -13 -12 -11 -10 -9 log(sSFR)       0.03       0.07       0.15       0.33       0.71       1.54       3.35       7.29 Distance / Roche radius 39 65 25 22 295 90 0 1.5 3 4.5 6 7.5 9 10.5 12 Figure 14. Galaxy pair number in the (Distance/Roche radius) \u2013 sSFR plane. The top left panel is the major member of the pair in the C box, the bottom left panel is the minor member of the pair in the C box, the top right panel is the major member of the pair in the V box, and the bottom right panel is the minor member of the pair in the V box. The sSFR histograms are evenly spaced in log space, except that the two bins below 10\u221213 yr\u22121 simply contain all the galaxies with sSFR below 10\u221213 yr\u22121. In addition, we split each \ufb01gure into six bins, separating non-star forming, star-forming, and highly star-forming galaxies that are inside or outside the Roche radius. There is no strong trend of sSFR with galaxy distance. There is a slight indication that the major galaxy in a pair may be more likely to be highly star-forming if the bound galaxy is within the Roche radius. labeled with the number of galaxies it contains. Examining the orbits of all of these bound galaxies is beyond the scope of this paper, but we do note that it is possible that galaxies that are currently outside of the Roche radius may have been closer at some point in the past. From these histograms, we see that there is no strong trend of sSFR with galaxy distance. If we focus only on the larger bins, there is some indication that the major galaxy in a pair may be more likely to be a starburst galaxy if the minor bound galaxy is within the Roche radius, although the numbers of galaxies in the sSFR > 10\u221210 yr\u22121 bins are small. The major bound galaxies are slightly less likely to have low sSFR (sSFR < 10\u221211 yr\u22121) if the minor galaxy is within its Roche radius. These points could indicate that a major galaxy with the minor member of the pair within its Roche radius is able to accrete cold gas either from the minor member of the pair, or from gas in the nearby environment. The minor bound galaxy is more likely to have a sSFR < 10\u221211 yr\u22121 if it is within the Roche radius of the major galaxy, and slightly less likely to have a sSFR > 10\u221210 yr\u22121. Thus, we do not see evidence of tidal triggering of starformation in the smaller galaxy in a pair. Instead, it seems that being bound to a larger galaxy decreases the sSFR. We cannot say whether this is due to a gravitational interaction with the major member of the pair or if these galaxies are simply entering higher density environments, where any of a number of other mechanisms could redden the galaxy (e.g. harassment or ram pressure stripping, as discussed in the Introduction). Finally, if we consider all galaxies (major and minor) that are in pairs, we \ufb01nd that galaxies with the minor member inside the Roche radius are about 10% less likely to be star-forming (sSFR > 10\u221211 yr\u22121) than galaxies with the minor pair outside the Roche radius. Therefore, although close pairs may be gravitationally interacting, we conclude that to \ufb01rst order these interactions are not resulting in the di\ufb00erent sSFRs of close bound galaxies (d < 250 h\u22121 kpc plus HOP multi-peak galaxies) relative to the global galaxy population that we see in Figure 11. 9 A COHERENT PHYSICAL EXPLANATION On large scales, global structures, such as around a rich cluster of galaxies or a void region, are expected to evolve di\ufb00erently, with the large-scale overdensity playing the role of a dynamic \u201cclock\u201d. In this sense, a large-scale overdense region is dynamically more advanced than a large-scale underdense region. This is in accord with one\u2019s intuitive expectation, for example, that a cluster is dynamically more developed than a \ufb01eld region that is yet to collapse, which in turn is more advanced than a void region that may still be experiencing expansion. This macroscopic view is in line with the di\ufb00erences we see when comparing the C and V box total galaxy c \u20dd2011 RAS, MNRAS 000, 1\u201324 Galaxy Evolution: Pair Interactions versus Environment 19 populations. C box galaxies are more massive and have lower sSFRs and less cold gas than the V box population. It seems that local overdensity, as parameterized by \u03c15, plays a more important role with respect to star formation, galaxy colour, gas cooling, etc, at least at z = 0 0.2 range examined here. We suggest that the local overdensity effectively determines the thermodynamic properties of the gas, primarily dictated by the strength of the converging shocks due to the collapse of embedding large-scale structures. For example, in cluster environments the gas is heated to a high temperature commensurate with the depth of the potential well of the cluster, whereas in large-scale \ufb01laments and sheets the temperature is determined by the 2-d or 1-d Zel\u2019dovich pancake collapse of the corresponding large-scale density \ufb02uctuations. To zero-th order, a local density measure, such as \u03c15, is a measure of the local gas temperature or perhaps more importantly the amount of cold gas (Cen 2011); at a \ufb01xed galaxy halo mass, a higher \u03c15 corresponds to a lower amount of cold gas than a lower \u03c15. If we place this in the nomenclature of cold and hot mode accretion, \u03c15 e\ufb00ectively measures the \u201chalo\u201d mass of the embedding structure of the galaxy in question (although this is not necessarily limited to virialized systems). There are also a number of interactions that can occur in large halos that may remove a galaxy\u2019s gas, as discussed in the Introduction. Once a galaxy\u2019s gas has been exhausted or removed in these massive, hot halos, there is no simple mode for replenishing the reservoir (but see Kau\ufb00mann et al. 2010). Within this context we can understand the trend of galaxies having more cold gas, and higher sSFRs in low density regions than in high density regions for the general galaxy population. We see the trend of increasing starforming fraction with decreasing \u03c15 in Figure 11. As we have shown, bound galaxy pairs tend to avoid cluster environments as well as void regions (Figures 5 and 6). As a result of this \u201cselection\u201d e\ufb00ect, bound galaxy pairs tend to be redder than void galaxies but bluer than cluster galaxies. However, this e\ufb00ect alone does not explain all the trends we have found for galaxy pairs. Gravitational interactions between bound galaxies cause an additional, subtle physical e\ufb00ect that is dependent on local overdensity. At a relatively high \u03c15, hot gas is more dominant in or surrounding a galaxy halo. In this case, in our simulation close galaxy-galaxy interactions induce shocks, gas compression and cooling of hot gas that causes a noticeable increase in the amount of cold gas, which in turn causes the interacting galaxies to have a higher star formation rate. Thus, galaxy pairs in relatively high density regions tend to be bluer and more H I-gas rich than the general galaxy population at the same density. On the other hand, at a relatively low \u03c15 the amount of hot gas is negligible compared to the much larger amount of cold gas available. Thus, any cooling of the hot halo caused by close galaxy-galaxy interactions does not substantially increase the amount of cold gas. Indeed, some of the initially cold gas could be shock-heated to hot gas or disrupted during the interactions. Consequently, galaxy pairs in relatively low density regions tend to have colours and H I-fractions similar to the total population in those regions. Whether the cooling of hot halo gas in\ufb02uences the sSFR of galaxies depends on whether the galaxies at that local density are rich or poor in H I. In our pair galaxies, the replacement of direct cold gas accretion with cooling gas from the hot halo can be most directly seen by examining Figure 13. The H I fraction decreases as the local density increases, and only at the highest local densities do bound galaxies have higher H I fractions than the comparison population. This cooling from the hot halo is a smaller e\ufb00ect than the strong dependence of H I gas content on local density, as evidenced by the smaller di\ufb00erence between the fraction of H I-rich bound and matched samples in the highest density bin compared to the di\ufb00erence between the \u201ctotal\u201d populations in the middle and highest density bins. The properties of close unbound galaxies support this scenario. They have redder colours and lower H I fractions than the bound galaxies, which are undergoing a more extended interaction. Also, unbound close galaxies are in higher density environments, and because of the strong correlation we \ufb01nd between local density and galaxy colour we would expect them to be redder. 10 CONCLUSION We have examined the galaxies formed in a large, 120 h\u22121 Mpc cosmological simulation in detail in two zoomed-in boxes: one centred on a void of size 31 \u00d7 31 \u00d7 35 h\u22123 Mpc3 and the other on a cluster of size 21 \u00d7 24 \u00d7 20 h\u22123 Mpc3. The two re\ufb01ned regions have an overlapping range of local densities, which allows us to separate local and large-scale environmental e\ufb00ects. We have utilized the high resolution (0.46 h\u22121 kpc) in these regions to examine galaxies in detail to determine how being a member of a pair (as de\ufb01ned in Section 4, a pair galaxy is gravitationally bound to at least one other galaxy that is not the cD of the largest cluster) a\ufb00ects galaxy properties and whether these e\ufb00ects depend on environment. We now summarize our results and conclusions. 1) We use the three-dimensional information provided by our simulation to determine whether the observational criteria used to choose projected pairs identify physically bound pairs. We \ufb01nd that these criteria yield pair samples that include a larger fraction of spurious pairs than in previous work (Perez et al. 2006a found 27% spurious fraction to our 48%). If we only consider projected pairs in the lowerdensity V box, we \ufb01nd a much lower spurious pair fraction of 12%. In qualitative agreement with previous work, we \ufb01nd that the fraction of spurious pairs increases in dense regions. In order to agree with Perez et al. (2006a), we must only consider regions with \u03c15 \u22641 h3 Mpc\u22123, which is less dense than group environments. In order to understand if pair interactions may redden galaxies, it is important to consider higher local densities where a larger fraction of the galaxy population is red. The high fraction of spurious pairs at high densities (58% at \u03c15 > 1 h3 Mpc\u22123) may have masked the trends we \ufb01nd for pair galaxies as a function of local density in some observed samples. 2) We \ufb01nd that, of all pairs, (59%,13%, 28%) are wet, dry and mixed pairs, respectively, which are in excellent agreement with the corresponding fractions of (56%, 15%, 29%) found in observed galaxy pairs by Lin et al. (2010). In Figure 7 we show that the environments of these pairs are consistent with the colour-density relation. 3) We see no evidence that, considering the bound population as a whole, being closer than the Roche radius enc \u20dd2011 RAS, MNRAS 000, 1\u201324 20 S. Tonnesen and R. Cen hances the sSFR of gravitationally bound pair galaxies (Section 8). 4) Largely independent of being in a galaxy pair or not, the strongest trend we \ufb01nd is environmental, where the average sSFR is a monotonic increasing function of local environmental density, de\ufb01ned by \u03c15. This trend is in broad agreement with observations from SDSS. The likely physical cause for this trend is the underlying trend of higher gas temperature in higher density regions due to formation of massive halos or large scales structures such as pancakes and \ufb01laments (Kere\u02c7 s et al. 2005, Dekel & Birnboim 2006; Cen 2011), which dictates the cold gas supply. This may also have to do with the many interactions that can occur in high density regions: galaxy-cluster, galaxy-galaxy, and galaxy-intracluster medium interactions can all remove galaxy\u2019s cold gas (e.g. Merritt 1984; Moore et al. 1996; Gunn & Gott 1972; Larson et al. 1980). 5) Being a pair galaxy has a secondary but signi\ufb01cant e\ufb00ect on star formation rate and cold gas on pair galaxies. We \ufb01nd that galaxies in close pairs tend to have higher sSFR in high density environment than the non-paired galaxies at the same environment density (e.g., in and near galaxy clusters). Such an enhancement for pairs is not seen in low density environments (e.g., in the centre of a void); in fact, the opposite is seen there. As a result, we \ufb01nd that pairs in high density environments tend to have fewer low sSFR galaxies than non-pairs, where pairs in low density environments have the opposite trend. However, very close pairs (rp < 50 kpc, the HOP multi-peak sample) always have an elevated fraction of high sSFR galaxies, regardless of their environment. Analogous statements apply to H I gas in galaxies. 6) Interactions between close pairs a\ufb00ects galaxies at high local densities by cooling gas out of the hot halo, as evidenced by the higher MHI/M\u2217of close pairs in higher local density bins rather than in lower local density bins where cold \ufb02ow accretion is more common and hot gas is largely absent (Figure 13 and Section 9). Our results indicate that observationally \ufb01nding galaxy pairs without resorting to searches for tidally-disturbed galaxies can be di\ufb03cult. That said, we do \ufb01nd similar results\u2013a general increase in sSFR as galaxy pairs move closer together. We predict that if observers look for pairs speci\ufb01cally in and near voids, they will \ufb01nd that in these large-scale underdensities, the pair population will not have a larger fraction of star-forming galaxies than the total void population (although we do see hints that the strongly starforming fraction may be increased in pairs in voids in Figure 12). Finally, we introduced this paper by claiming that mergers may increase the mass of star-forming galaxies, drive the evolution of star-forming galaxies into red and dead galaxies, and hierarchically build massive red galaxies through dry mergers. Do our results and the physical explanation we put forth in Section 9 support that claim? The answer appears to be no, as we will now discuss. First, we \ufb01nd that the majority of our close pairs (d < 250 h\u22121 kpc galaxies plus d < 50 h\u22121 kpc galaxies\u2013the HOP multi-peak galaxies) are star-forming. If we assume that these close pairs will merge, this indicates that close pair interaction of galaxies do not quench star formation prior to the merger. The fraction of strongly star-forming galaxies is very similar between the close bound pairs and total galaxy populations, indicating no signi\ufb01cantly strong bursts of star-formation prior to merging. Second, the fuel for star formation (MHI/M\u2217) increases as the separation of the galaxy pair decreases. This suggests that at least during the pair interaction period prior to the \ufb01nal merger the gas reservoir is increased rather than decreased, even though star formation rate is higher for closer pairs. In other words, there is no sign of pair interactions causing cold gas exhaustion. Third, although the close pairs (d < 250 kpc h\u22121 plus galaxies with separations of 30-50 kpc h\u22121\u2013the HOP multipeak sample) have some of the highest sSFRs of the entire galaxy population, they only account for 15 of the 39 highest sSFRs. This shows that pairs (including very close pairs) do not monopolize starbursts. Could the remaining (24 out of 39) highest sSFR non-pair galaxies be post-merger galaxies? We \ufb01nd that of the 17 galaxies with sSFR \u22653 \u00d7 10\u221210 yr\u22121 that we can track back at least one output (galaxies at z \u2264 0.15 and that had M\u2217> 109.6 M\u2299in the previous output), only one galaxy is post-merger (had been a member of a close pair the output before, but is no longer a member of a pair). Altogether, this evidence suggests that in general neither mergers nor pre-merger interactions quench star formation either through heating cold gas or a burst of star formation. The \u223c40% (15/39) of starbursting galaxies that are in pairs falls in the range of poststarburst galaxies observed to be merging or tidally-interacting: about 50% in Poggianti et al. (1999) and 25% in Zabludo\ufb00et al. (1996). In fact, rather than pair interactions driving a starburst that exhausts a galaxy\u2019s reservoir of cold gas, we \ufb01nd that close pairs (d < 250 h\u22121 kpc galaxies plus galaxies with separations of 30-50 kpc h\u22121\u2013the HOP multi-peak sample) have a higher (MHI/M\u2217). The higher star-forming fraction of close pairs, particularly at higher local densities (and therefore in more massive halos) may suggest that the small amount of star formation and H I observed in otherwise red and dead disturbed galaxies is created from cooling of hot halo gas in interacting elliptical galaxies (Donovan et al. 2007), and therefore \u201cdry\u201d mergers may hierarchically grow larger red galaxies as well as induce small amounts of star formation. Donovan et al. (2007) frequently \ufb01nd a peculiar morphology in the H I associated with their observed red elliptical galaxies, possibly indicating a recent tidal disturbance. Are mergers responsible for the colour-density relation? Available evidence suggest the answer is no. We see no evidence of close pair interactions causing accelerated removal of cold gas reservoir. Nor do we see evidence of pair interactions causing star formation to cease in the outskirts of clusters of galaxies, before their entry into clusters. All evidence points to the opposite of what the colour-density relation suggests. Nevertheless, our galaxies are in broad agreement with the observed colour-density relation, which strongly suggests that it is the environment, rather than pair-interactions/mergers, that is responsible for the colourdensity relation. This could be due to any of several interactions that can occur in high-density environments: galaxycluster, galaxy-galaxy, and galaxy-intracluster medium interactions can all remove galaxy\u2019s cold gas (e.g. Merritt 1984; Moore et al. 1996; Gunn & Gott 1972). Also, residing in a massive halo means that galaxies do not have access to cold \ufb02ows that can replenish their gas reservoir, so they will eventually be unable to form stars (Larson et al. 1980; Kere\u02c7 s c \u20dd2011 RAS, MNRAS 000, 1\u201324 Galaxy Evolution: Pair Interactions versus Environment 21 et al. 2005). We shall devote a more detailed investigation to this important issue. We would like to thank Dr. M.K.R. Joung for help on generating initial conditions for the simulations and running a portion of the simulations and Greg Bryan for help with Enzo code. ST would like to that Jacqueline van Gorkom for helpful comments on this paper. We would like to thank our referee for comments that greatly improved the quality of the paper. Computing resources were in part provided by the NASA HighEnd Computing (HEC) Program through the NASA Advanced Supercomputing (NAS) Division at Ames Research Center. This work is supported in part by grant NNX11AI23G.",
                    "introduction": "Observations of galaxy populations at di\ufb00erent redshifts in- dicate that the red sequence has roughly doubled in mass from z \u223c1 to 0, while the mass in the blue cloud remains relatively unchanged (Bell et al. 2004; Willmer et al. 2006; Faber et al. 2007; Martin et al. 2007; Ruhland et al. 2009). Gravitational interactions between galaxies can in\ufb02uence their star formation rate (SFR), gas content, and morphol- ogy. As such, they can increase the mass of star-forming galaxies, and be an important mechanism causing the evolu- \u22c6E-mail: stonnes@astro.princeton.edu (ST); cen@astro.princeton.edu (RC) tion of blue, star-forming galaxies into red and dead galaxies. Slow interactions that result in mergers will have a stronger impact on galaxy properties (but see Moore et al. 1996 for a discussion of the possible impact of many quick galaxy interactions). Dry mergers between gasless galaxies can also cause the hierarchical build-up of massive red galaxies. Galaxy-galaxy interactions may drive the evolution of blue galaxies into red galaxies by causing a burst of star for- mation that may exhaust the gas in the merging pair and result in a more massive red galaxy. Larson & Tinsley (1978) identi\ufb01ed interacting galaxies as peculiar galaxies, and de- termined that many of these galaxies had recently under- gone a burst of star formation. Shortly thereafter, a number of observers found bursts of star formation associated with c \u20dd2011 RAS 2 S. Tonnesen and R. Cen tidal interactions (e.g. Condon et al. 1982; Keel et al. 1985; Kennicutt et al. 1987). Since then there has been much more observational work verifying and expanding on these results. For example, Park et al. (2008) \ufb01nd that tidal e\ufb00ects can ac- celerate the consumption of gas in galaxies and transform late types into early types. In addition, the level of star formation rate enhancement increases for closer pairs (e.g. Alonso et al. 2004, 2006; Ellison et al. 2008), more gas-rich pairs (Nikolic et al. 2004; Woods & Geller 2007), and more evenly matched mass-ratio pairs (Woods & Geller 2007; El- lison et al. 2008; but also see Nikolic et al. 2004). In addition to an increase in the total mass of red sys- tems over time, there is also evidence of an environmental dependence of the red to blue galaxy ratio. Since about z \u223c 0.4 red galaxies have dominated the galaxy populations of dense regions, such as clusters (Butcher & Oemler 1978). Cooper et al. (2008), using the DEEP2 Galaxy Redshift Survey, \ufb01nd that the red fraction is higher in regions of high density to beyond a redshift of 1. If galaxy mergers are the main way to quench star formation and turn galax- ies from blue to red, then it might be expected that pairs would be found in or near groups and clusters in order to match the morphology-density and colour-density relations (Oemler 1974; Dressler 1980). Lin et al. (2010) examine the local densities in which wet, dry and mixed mergers occur and \ufb01nd that they broadly agree with the predictions of the colour-density relation. Using simulations, Barton et al. (2007) \ufb01nd that a higher fraction of close pairs than of the unpaired galaxy population lie in dark matter halos con- taining more than two galaxies. If these pairs merge, then this supports the idea that mergers are an important process driving the colour-density relation. Although in this paper we will only focus on the inter- actions between bound galaxies, it is important to note that the colour-density and morphology-density relations may also be caused by a number of other possible interactions. In addition to pair interactions, galaxies in groups and clus- ters can undergo a number of fast interactions with other satellite galaxies, resulting in galaxy harassment (Moore et al. 1996). A galaxy can also interact with the cluster poten- tial, which can strip material from the galaxy or induce star formation (Merritt 1984; Byrd & Valtonen 1990). Finally, a galaxy can interact directly with the intracluster medium, which can remove gas through ram pressure stripping (Gunn & Gott 1972), thermal evaporation (Cowie & Songaila 1977), Kelvin-Helmholtz instabilities (Chandrasekhar 1961), or vis- cous stripping (Nulsen 1982). Many of these processes could also only cause starvation, or the removal of halo gas, which will slowly redden a galaxy as it exhausts its gas reservoir through star formation (Larson, Tinsley & Caldwell 1980). While the mechanisms described above depend on a dense environment to a\ufb00ect individual galaxies, the oppo- site may be true for mergers. The high velocity dispersion in clusters makes them unfriendly environments for pairs (e.g. Ostriker 1980; Makino & Hut 1997), and it has been proposed that \u201cpre-processing\u201d of galaxies before they enter clusters can cause the morphology-density relation (Zablud- o\ufb00& Mulchaey 1998; Zabludo\ufb002002; Mihos 2004). For example, galaxies in groups and \ufb01eld pairs can undergo slower encounters that are more likely to result in merg- ers. Moss (2006) observe galaxies in 8 low-redshift clusters, and \ufb01nd that 50-70% of the infall population was interact- ing or showed a disturbed morphology indicating a recent merger. This agrees with the results of McGee et al. (2009) and DeLucia et al. (2011), who use semi-analytic models and the Millennium Simulation (Springel et al. 2005) to \ufb01nd that 40-60% of galaxies with stellar masses above 109 M\u2299 enter clusters with no companions. Berrier et al. (2009), us- ing a somewhat di\ufb00erent method, examine 53 clusters in dark-matter only N-body simulations and \ufb01nd that 70% of galaxies with total masses above 1011.5 M\u2299fall into clusters with no companions. There continues to be a large amount of observational work on how interactions a\ufb00ect the SFR of galaxies in a range of environments. Wong et al. (2011) measure star for- mation rate enhancements of 15-20% in isolated pairs, and also \ufb01nd marginal evidence for increasing enhancement with decreasing redshift. Barton et al. (2007) examine isolated close pairs and \ufb01nd that SFR can be boosted by a factor of 30. They argue that studies of pairs in denser environments are \ufb02awed because local galaxy density does not accurately determine whether galaxies are in their own halo or are satel- lite galaxies. Despite this concern, there has been signi\ufb01cant observational work on how the larger-scale environment can a\ufb00ect the SFR of interacting galaxies using local galaxy den- sity. Lambas et al. (2003) and Alonso et al. (2004) determine that pairs need to be closer in groups than in the \ufb01eld for the interaction to trigger enhanced star formation. Ellison et al. (2010) examine whether pairs behave di\ufb00erently in di\ufb00erent local density environments, which they determine by using the projected distances to the fourth and \ufb01fth nearest neigh- bors. They \ufb01nd that in low density environments (log \u03a3 < -0.55), interacting pairs trigger star formation, while pairs in high-density environments do not have enhanced star for- mation (log \u03a3 > 0.15). Using SDSS data, Perez et al. (2009) compare pair galaxies to control samples that were matched for dark matter halo mass, stellar mass, redshift, and local galaxy density (within the distance to the \ufb01fth nearest neigh- bor, \u03a35). They \ufb01nd that although star formation is higher in pairs in low local density regions than in high local density regions, it is more enhanced in pairs in mid-range density regions relative to unpaired galaxies. They suggest that this is evidence for galaxy pre-processing in intermediate-density regions before entering clusters. Patton et al. (2011) use the Sloan Digital Sky Survey Data Release 7 to identify more than 20,000 pairs and com- pare them with control galaxies matched in stellar mass and redshift. They \ufb01nd a higher red fraction in paired galax- ies, which they determine is likely due to the higher density environments in which they are found. They also \ufb01nd a pop- ulation of extremely blue close pairs, indicating interaction- induced star formation in their paired galaxies (also ob- served by Alonso et al. 2006; Perez et al. 2009; Darg et al. 2010). Perez et al. (2006a,b) use GADGET-2 to study the star formation, colours, and chemical abundances of galaxies in pairs. When comparing their pairs to their control sample, they \ufb01nd strong agreement with observational trends: pairs are bluer than non-paired galaxies, which is caused by their higher star formation rate. Also, closer pairs are bluer with higher SFRs. They \ufb01nd that both pairs and control galax- ies follow the observed colour-density relation, but that the trends are stronger for close pairs. Speci\ufb01cally, Perez et al. (2006a) \ufb01nd a higher fraction of active galaxies in pairs in c \u20dd2011 RAS, MNRAS 000, 1\u201324 Galaxy Evolution: Pair Interactions versus Environment 3 all environments, but the largest di\ufb00erence when comparing the fraction of actively star-forming galaxies is in low-\u03a3 re- gions (\u03a3 < 0.8 Mpc\u22122). They claim that this indicates that galaxy-galaxy interactions help establish the colour-density relation. They also \ufb01nd that the stellar populations in paired galaxies are more metal-enriched than non-paired galaxies (Perez et al. 2006b). This is in contrast to the observations by Kewley et al. (2006; 2010), who \ufb01nd lower metallicities in interacting galaxies, possibly due to gas in\ufb02ow from the outer parts of the disc or halo (e.g. Hibbard & van Gorkom 1996; Rampazzo et al. 2005). In this paper we use a cosmological simulation to exam- ine the role of pairs and tidal interactions on galaxy colour, SFR, and gas mass. We focus on two regions within a sim- ulation with box side of 120 h\u22121 Mpc, one centred around a cluster with size 21 \u00d7 24 \u00d7 20 h\u22123 Mpc3 and the other centred around a void with size 31 \u00d7 31 \u00d7 35 h\u22123 Mpc3. This gives us a broad range of local environments to study as well as two extreme large-scale environments. We consider the galaxy populations at \ufb01ve redshifts: 0.0, 0.05, 0.1, 0.15, and 0.2. This increases our sample size, makes sure that any anomalies at a single redshift snapshot do not dominate the results, and checks to see if there is evolution in the pair population across these later redshifts. Choosing this red- shift range also allows for better comparisons with recent observational work on this topic using SDSS (e.g. Patton et al. 2011). Also, when we determine distances between galax- ies, and use a distance criteria to determine the local galaxy density, we use the physical distance rather than the comov- ing distance. Our goal in this paper is to determine under what conditions being a member of a pair or group a\ufb00ects galaxy properties. We examine this question in the context of the larger scale environment of the galaxies. After an introduction to our simulation (Section 2.1), we discuss our galaxy selection technique and our method for determining observable quantities for each galaxy in Sec- tion 2.2.1. In Section 3 we examine the reliability of obser- vational techniques used to identify pairs. We then explain our method for \ufb01nding gravitationally bound pairs in our simulation (Section 4). In Section 5 we describe the demo- graphics of bound galaxies, including where they are in re- lation to the cluster or void and their local density (\u00a75.3). We also consider the colour of galaxies in pairs (\u00a75.4). We then determine whether bound galaxies are di\ufb00erent than the general galaxy population in terms of their sSFR and gas mass in Section 6. After attempting to determine whether pair interactions have an e\ufb00ect on galaxy properties over and above any di\ufb00erences caused by the local density (Sec- tion 7), we check whether pair separation a\ufb00ects our results in Section 8. In Section 9, we synthesize our \ufb01ndings into a coherent physical scenario. Finally, we summarize our main conclusions and make some additional comparisons with ob- servations and predictions (\u00a710)."
                },
                {
                    "url": "http://arxiv.org/abs/1103.3273v1",
                    "title": "How To Light It Up: Simulating Ram-Pressure Stripped X-ray Bright Tails",
                    "abstract": "Some tails of ram-pressure stripped galaxies are detected in HI, some in\nHalpha, and some in X-ray (but never all three so far). We use numerical\nsimulations to probe the conditions for the production of X-ray bright tails,\ndemonstrating that the primary requirement is a high pressure intracluster\nmedium (ICM). This is because the stripped tail is mostly in pressure\nequilibrium with the ICM, but mixing leaves it with densities and temperatures\nintermediate between the cold gas in the disk and the hot ICM. Given a high\nenough ICM pressure, this mixed gas lies in the X-ray bright region of the\nphase diagram. We compare the simulations to observations of the ram pressure\nstripped tail of ESO 137-001, showing excellent agreement in the total measured\nX-ray and Halpha emission and non-flaring morphology of the tail, and\nconsistent HI measurements. Using these comparisons we constrain the level of\nmixing and efficiency of heat conduction in the intracluster medium (ICM)",
                    "authors": "Stephanie Tonnesen, Greg L. Bryan, Rena Chen",
                    "published": "2011-03-16",
                    "updated": "2011-03-16",
                    "primary_cat": "astro-ph.CO",
                    "cats": [
                        "astro-ph.CO"
                    ],
                    "main_content": "work investigating ram pressure stripping in general (e.g. Schulz & Struck 2001; Quilis, Bower & Moore 2000; Roediger & Br\u00a8 uggen 2008, Kronberger et al. 2008; Kapferer et al. 2009) \u2013 see Tonnesen & Bryan (2009, 2010; hereafter TB09 and TB10) for a more detailed discussion. There have also been simulations designed to predict or interpret observational characteristics of ram pressure stripped tails and the remaining disks (e.g. Vollmer et al. 2005, 2006, 2008), but detailed, quantitative predictions of all three observational probes have been missing to date (H I, diffuse H\u03b1, and X-ray emission). In our previous work (TB10), we ran a set of high resolution simulations (about 38 pc resolution, which is small enough to marginally resolve giant molecular clouds) to understand how a multiphase ISM could affect the survival and structure of ram pressure stripped gas. We focused on how density fluctuations that are observed in the multiphase ISM of galaxies can affect gas tails. Including radiative cooling allowed us to estimate the density of and emission from H I, H\u03b1, and X-ray gas separately. We found that both the morphology and velocity structure of our tails agreed with observations of long gas tails (e.g. Oosterloo & van Gorkom 2005). Our simulations also resulted in observable amounts of H I and H\u03b1 emission. However, the X-ray tail had a low surface brightness, which we attributed to the low pressure of the surrounding ICM. In this paper we will use the same method as in TB10, but have chosen ICM parameters comparable to the ICM around ESO 137-001. By focusing on the level of agreement between our simulations and the observations of ESO 137-001 we will be able to discuss the importance of physical mechanisms such as heat conduction, as well as predict the conditions under which H I, H\u03b1, and X-ray emission are produced in stripped tails. The paper is structured as follows. After a brief introduction to our methodology, we provide the characteristics of our simulations and our method of producing simulated observations (\u00a72). We then (\u00a73) present our results, specifically focusing on the comparison with ESO 137-001. In \u00a74 we discuss the broader implications of our simulation, and discuss our choice of radiative cooling floor and resolution in \u00a75.1-2. Finally, we conclude in \u00a76 with a summary of our results and predictions for observers. 2. METHODOLOGY We use the adaptive mesh refinement (AMR) code Enzo (Bryan 1999; Norman & Bryan 1999; O\u2019Shea et al. 2004). Our simulated region is 311 kpc on a side TABLE 2 Gas Disk Constants Variable Value Variable Value Mgas 1 \u00d7 1010 M\u2299 agas 7 kpc bgas 0.4 kpc with a root grid resolution of 1283 cells. We allow an additional 6 levels of refinement, for a smallest cell size of 38 pc. We refine our simulation based on the local gas mass, such that a cell was flagged for refinement whenever it contained more than about 2\u00d7104 M\u2299. We found that this refined most of the galactic disk to 38 pc resolution by the time the wind hit; dense clumps in the wake were also refined to 38 pc resolution, while more diffuse components had lower resolution. The simulation includes radiative cooling using the Sarazin & White (1987) cooling curve extended to low temperatures as described in Tasker & Bryan (2006). To mimic effects that we do not model directly (such as turbulence on scales below the grid scale, UV heating, magnetic field support, or cosmic rays), we cut off the cooling curve at a minimum temperature Tmin so that the cooling rate is zero below this temperature. In the simulations described here we use either Tmin = 8000 K, or Tmin = 300 K. Both allow gas to cool below the threshold for neutral Hydrogen formation. In TB09, we found that the minimum temperature affected the range of masses and sizes of clouds forming in the disk, and the distribution of clouds throughout the disk, although the range of gas densities was very similar. The Tmin = 300 K case resulted in a more fragmented disk whose small clouds took longer to strip. Therefore the timescales for gas stripping differed, although the total amount of gas lost was similar. In the simulations presented in this paper, we find that the cooling floor affects the amount of fragmentation in the disks, but not the mass-distribution of gas densities. The larger radii of the remaining gas disks in the two Tmin = 300 K runs are due to the survival of dense clouds in the outer disk (Figures 1, 4, and 5). In TB10, we found that the structure of the wake also depends somewhat on Tmin. Since the publication of TB10, we found and corrected an error in our implementation of the cooling rate that resulted in a slight shift in the peak of the cooling curve around 104 K, but did not significantly affect cooling at low and high temperatures (this affected only the Tmin = 300 K simulation). Tests showed that this had only a small impact on the dynamics of the flow, and on the predicted H I and X-ray measures, but did strongly affect the predicted H\u03b1 emission, which is extremely sensitive to the gas temperature around 104 K. This explains the enhanced H\u03b1 emission in this paper for the Tmin = 300 K run as compared to TB10. Our galaxy model is the same as in TB10 and TB09, which used the spiral galaxy model described in Roediger & Br\u00a8 uggen (2006). We list the model parameters for our galaxy in Tables 1 and 2. The stellar and dark matter components of the galaxy are static potentials. As in TB09 and TB10, our galaxy position and box size allows us to follow gas 200 kpc above (in the wind, or 3 TABLE 3 Runs summary Run vICM (km/s) PICM (dyne/cm2) TICM (K) Pram (dyne/cm2) tproj (Myr) T80vh 1900 4.2 \u00d7 10\u221211 8.3 \u00d7 107 11.6 \u00d7 10\u221211 85 T3vh 1900 4.2 \u00d7 10\u221211 8.3 \u00d7 107 11.6 \u00d7 10\u221211 75 T3vl 1413 2.66 \u00d7 10\u221211 7.3 \u00d7 107 5.29 \u00d7 10\u221211 110 Sun et al. 2010 1.8 \u00d7 10\u221211 \u223c7 \u00d7 107 z, direction) the galaxy. To identify gas that has been stripped from the galaxy, we also follow a passive tracer which is initially set to 1.0 inside the galaxy (de\ufb01ned as gas that is above the ICM density) and 10\u221210 outside. In the following analysis, we will use a minimum tracer fraction of 0.25 to \ufb01nd gas stripped from the galaxy (as in TB10). 2.1. Introduction to the Three Runs The galaxy initially evolves in a static, high-pressure ICM with \u03c1 = 8.7 \u00d7 10\u221228 g cm\u22123 and T = 9.069 \u00d7 106 K (\u03c1 =7.57 \u00d7 10\u221228 g cm\u22123 and T = 1.04294 \u00d7 107 K for the slower wind case), to allow cool, dense gas to form in the galaxy (each of our three runs has about 3 \u00d7 109 M\u2299of gas with densities at or above 10\u221222 g cm\u22123 when the wind hits the disk). This naturally generates a multiphase ISM (see Tasker & Bryan 2006 and TB09 for more discussion of the ISM properties). After 155 Myrs, we reset the boundary conditions to generate a constant ICM in\ufb02ow along the inner z-axis, which is always face-on to the galaxy. In Table 3 we show the details of each of the three runs. The table includes the ICM parameters and the time after the wind has hit the galaxy at which the X-ray tail is 80 kpc long (this is how we choose the outputs to compare to the observations of ESO 137-001). \u2018T80\u2019 indicates cooling to 8,000 K and \u2018T3\u2019 indicates cooling to 300 K, while \u2018vh\u2019 and \u2018vl\u2019 indicate high and low velocity wind, respectively. See TB09 for other details regarding the general numerical setup, and TB10 for a discussion of the general impact of the cooling \ufb02oor on the tail structure. In order to compare with both observations and our previous work, we use a face-on wind direction. 2.2. Projections Enzo outputs the density and temperature of the gas in each cell. To transform these values into H I column density and H\u03b1 intensity, we used Cloudy, version 08.00 of the code last described by Ferland et al. (1998). Using a table of temperatures and densities, we calculated the hydrogen neutral fraction and H\u03b1 emissivity. This table is then used to calculate the observational quantities for each cell, which are then summed to generate an image. This is described in detail in TB10, but brie\ufb02y, we included CMB radiation, the cosmic ray background, bremsstrahlung radiation from the ICM and the 2005 version of the Haardt & Madau (2001) z = 0 metagalactic continuum, as implemented by Cloudy. We chose to calculate the neutral fraction and H\u03b1 emissivity for a plane-parallel gas cloud of width 100 pc. We selected this width because it loosely corresponds to the cell size of most of the gas in the tails, and accounts approximately for attenuation of the ionizing background radiation. If we assumed the radiative thin limit (by using a very small cloud size in Cloudy), it would somewhat decrease the amount of H I we predict, and increase the H\u03b1 emission for dense, low-temperature gas. We discuss the use of di\ufb00erent cloud sizes in detail in TB10, however, in the simulations in this paper we \ufb01nd that using a 10 pc cloud does not signi\ufb01cantly change our H\u03b1 \ufb02ux nor our H I column densities because of the higher densities in our tail gas. This indicates that radiative transfer e\ufb00ects are not that important for this work. To create X-ray surface brightness projections, we use a spectral lookup table that depends on temperature and density, assuming a constant metallicity of 0.3 solar, as computed using a Raymond-Smith code (Raymond & Smith 1977), as updated in XSPEC (Arnaud 1996). The X-ray band we use is 0.5 keV to 2.0 keV, following Sun et al. (2006). 3. COMPARISON TO OBSERVATIONS In this section, we compare our simulated stripped tail to observations of ESO 137-001. We choose an output time at which the X-ray tail length is about 80 kpc in order to match the observations of Sun et al. (2010); this time is shown in Table 3. We are using this comparison with the observations of ESO 137-001 to better understand the physics at work in producing X-ray, H\u03b1, and H I tails, so we have not tuned our simulation speci\ufb01cally to \ufb01nd an exact match to the galaxy and tail of ESO 137001. While our ICM parameters are similar to those of the ICM near ESO 137-001, they are not the same. The \ufb01nal row in Table 3 displays the ICM parameters from the observations of Sun et al. (2010). We have not attempted to model the exact angle between the galaxy\u2019s disk and orbital motion (Woudt et al. (2008) \ufb01nd a position angle of 125\u25e6), and instead use a face-on wind, and we are using a larger galaxy (Initially our galaxy has a radius of 26 kpc, and in the comparison projections the radius is about 15 kpc, while the 2MASS isophotal radius for ESO 137-001 is 6.1 kpc (Skrutskie et al. 2006)). In the following comparisons we will take note of the differences between our simulations and the observations of Sun et al. (2006; 2007; 2010). We have chosen the output time at which each simulation has an X-ray tail whose length is about 80 kpc. This means that the length of time that each galaxy has been stripped in the di\ufb00erent simulations is not the same. In Table 4, we list the amount of gas in the tail in three different temperature ranges. These masses include all of the gas above 10 kpc from the disk with tracer fractions of at least 25%, so some of the gas included is at low density, as shown in Figure 2 (too low to be observable). Nevertheless, it can be very loosely stated that longer stripping times may result in more mixing of hot gas 4 Fig. 1.\u2014 X-ray surface brightness maps of our three simulated galaxies, seen side-on. From left to right, we show T3vl, T80vh, T3vh. We have chosen the outputs with tail lengths of 80 kpc for our comparison to the observations of Sun et al. (2006; 2007; 2010). See discussion in Section 3.1.1 TABLE 4 Amount of Stripped gas at Different Temperatures Run T < 104 K 104 < T < 105 K 7 \u00d7 105 < T < 4 \u00d7107 K 109 M\u2299 109 M\u2299 109 M\u2299 T80vh 1.4 1.6 6.0 T3vh 1.1 1.2 9.1 T3vl 4.2 2.9 5.9 into the ICM, and in more dense gas being stripped and condensing into clouds in the tail. This can be seen by comparing T80vh or T3vl with T3vh (of course there are also other di\ufb00erences in the simulations that in\ufb02uence the tail gas, such as cooling \ufb02oor and ICM pressure). However, we stress that in this paper we mainly focus on what causes a tail to be bright in X-ray and H\u03b1 emission, so focus more on ICM pressure than the amount of time a galaxy has been stripped (although we do consider this timescale in our discussion of heat conduction). 3.1. X-ray 3.1.1. Comparison to ESO 137-001 We \ufb01rst compare the X-ray characteristics of our simulations to observations. The X-ray surface brightness projections of our runs are shown in Figure 1. As in Sun et al. (2006; 2010), we measure the X-ray emission between 0.5-2.0 keV. The surface brightness pro\ufb01les along the tails are in rough agreement with that of ESO 137-001, which is bright near the disk and has a second bright region about 40 kpc from the disk before becoming less luminous to the end of the tail. Our model does not reproduce the exact X-ray surface brightness pro\ufb01les: we do not have a model that includes both the bright emission near the disk and a surface brightness decrease across the entire tail before the second brightness peak. To make the X-ray projections, we adopted a minimum observable surface brightness of 7.1 \u00d7 10\u22126 erg cm\u22122 s\u22121, which we estimated from the total luminosity of the observed tail and brightness pro\ufb01les in Sun et al. (2010) (our cluster background is about 3.6 \u00d7 10\u22126 erg cm\u22122 s\u22121). This results in a luminosity di\ufb00erence of an order of magnitude between the lowest and highest surface brightness features in all of our simulated tails, similar to that in the observed tail of ESO 137-001. Our tails are narrow and show a nearly constant width along the entire tail, in agreement with the X-ray morphology reported in Sun et al. (2006; 2010). This is in contrast to simulations that do not include radiative cooling and produce \ufb02ared tails (e.g. Roediger, Br\u00a8 uggen & Hoeft 2006) However, it is clear that we do not have separated X-ray tails as in the observations. This is not surprising given the explanation of Sun et al. (2010) that the two tails likely result from the stripping of two spiral arms. As we discuss in detail in TB09, our disks fragment but do not form spiral arms. In Table 5, we list some of the characteristics of our simulated X-ray tails to compare with the observed tail. To calculate the luminosity of the tail, we \ufb01nd the total energy emitted and subtract the background emission from the ICM. As the table demonstrates, the simulated tails are wider, more luminous, and have a higher average (emission-weighted) temperature than the (spectroscopic) temperature measured by Sun et al. (2010). We now address these di\ufb00erences. The tail is most likely wider because we are modeling a large spiral galaxy, while ESO 137-001 is thought to be a \u223c0.2L\u2217galaxy, with a smaller galactic radius (Sun et al. 2006 and references therein). In fact, the entire volume of the tail in any of our three runs is nearly an order of magnitude larger than the tail of ESO 137-001 (we assume that the tails are cylindrical with the heights and diameters denoted in Table 5). The other di\ufb00erence is that our ICM pressure is also somewhat larger than calculated in Sun et al. (2010) by either a factor of 1.47 (T3vl) or 2.33 (T3vh and T80vh). These di\ufb00erences in tail volume and ICM pressure impact the observables in two ways. First, as we discuss in TB10 and below, the compression of stripped gas by 5 TABLE 5 X-ray tail attributes Run or l \u00d7 w L0.5\u22122keV L0.5\u22122 corrected a T Observation (kpc \u00d7 kpc) (1040 erg s\u22121) (1040 erg s\u22121) (107 K) T80vh 80 \u00d7 26 66.3 4.8 2.5 T3vh 80 \u00d7 30 93.0 5.1 2.1 T3vl 80 \u00d7 30 41.9 3.6 1.4 Sun et al. 2010 80 \u00d7 8, 80 \u00d7 7 (8.3 \u00b1 0.4) (8.3 \u00b1 0.4) 0.93 \u00b1 0.05 aThe corrected luminosity multiplies the simulated X-ray luminosity by the ratio between the simulated and observed tail volumes and the ratio between the simulated and observed ICM thermal pressures (see text). the ICM determines the temperature and density distribution of gas in the tail. Therefore, a higher ICM pressure results in higher-density hot gas (T > 106 K), which will have a higher X-ray emissivity. As we argue in the next section, this makes the X-ray luminosity proportional to the ICM pressure. Second, if we assume that the \ufb01lling factor of X-ray emitting gas is the same in our simulations as in the tail of ESO 137-001, then the total luminosity is also directly proportional to the volume of the entire tail. The X-ray luminosity after applying these corrections is also shown in Table 5 (assuming X-ray luminosity is directly proportional to both the ICM pressure and the volume of the tail). When we account for these di\ufb00erences, our measured luminosities are within about a factor of two of the X-ray luminosity of ESO 137-001. As shown in Table 5, there is also a factor of two difference between the temperatures of the simulated and observed X-ray tails; however, this is most likely due to the di\ufb00erent ways in which this quantity is determined in simulations as compared to observations. We use luminosity-weighted temperatures, which tend to be higher than spectroscopic temperatures when there is a range of gas temperatures (see Mazzotta et al. 2004). Sun et al. (2010) discuss how the spectral \ufb01tting of the iron-L hump biases their temperatures low if there are signi\ufb01cant emission components at kT = 0.4 2 keV, which is certainly the case in our simulation and in the tail of ESO 137-001 (Sun et al. 2010; Sivanandam et al. 2009). Therefore, the agreement is probably considerably better than indicated in Table 5. 3.1.2. What Makes a Tail X-ray Bright? In this section, we examine what lights up an X-ray bright tail, and explain why some observed tails, like ESO 137-001, exhibit X-ray emission, while others do not. In Figure 2 we show the mass-weighted distribution of density and temperature of gas in the wake that originated from the galaxy from our T3vl run (left) and from the Tmin = 300 K run from TB10 using the corrected cooling curve (right). The plots include all of the gas located between 10 kpc and 240 kpc above the disk that has at least 25% of it\u2019s mass originating in the galaxy (as determined by the tracer fraction). We choose to highlight these two cases because the ICM pressure is the only di\ufb00erence between the two simulations (the thermal pressures di\ufb00er by a factor of 15). As discussed in more detail in TB10, the (T > 105 K) gas in the wake is largely in pressure equilibrium and so falls roughly along a line of constant pressure. The impact of the higher ICM pressure can be seen as a shift to higher density and temperature in the left panel. In red we also plot two contours of constant luminosity per mass (or emissivity per density). The lower contour is at 10\u22122 erg s\u22121 g\u22121. If the minimum observable X-ray surface brightness is 10\u22125 erg s\u22121 cm\u22122, then in order for X-ray emission to reach this level, there must be a su\ufb03cient amount of gas at or above the red contour. More precisely, we need a column density of hot gas of 1021 cm\u22122 in order to produce observable emission (this corresponds to about 104 M\u2299along a single line of sight through our 38 pc \u00d7 38 pc cells). In general, only the colder gas (T \u2264104 K) in the tail has these high surface densities (1021 cm\u22122), so we also plot an emissivity line which only requires a surface density of 1020 cm\u22122 in order to be observable (the upper 10\u22121 erg s\u22121 g\u22121 contour). Gas that is hot enough to emit X-rays (hotter than \u223c7 \u00d7 105 K) has this lower surface density in the tail (1020 cm\u22122). This \ufb01gure shows that gas at higher densities and lower temperatures than the ICM (but above \u223c106 K) will be emitting the most strongly in X-rays. As galactic gas is stripped it either cools into clouds (T < 105 K) or is compressed to the ICM pressure and begins to mix with ICM gas. While the tail gas is at the high ICM pressure \u2013 but before it is completely mixed with the ICM \u2013 it will be X-ray bright. The mixing occurs along the line of constant pressure seen in Figure 2. The separation between cold clouds and X-ray emitting gas is seen clearly in the left panel of Figure 3, which shows a thin slice from a detailed section above the disk. The cold clouds are black in this \ufb01gure, indicating no Xray emission, while the X-ray emitting gas is not con\ufb01ned to regions close to the dense clouds. Most of the X-ray bright cells in our simulation have between 70% and 90% of their gas originating from the galaxy. In the lower left panel of Figure 3 we show the gas temperature, which when compared with the X-ray slice again highlights that while some mixing and radiative cooling can enhance the X-ray emission, but too much lowers the density of the hot gas to the point where the X-ray emissivity is low. The X-ray bright gas may have either been stripped as hot gas from the disk and slowly mixed, or stripped from the dense clouds in the tail and mixed into the ICM. 3.2. H\u03b1 Next, we turn to H\u03b1 emission, shown in Figure 4. The minimum observable surface brightness that we adopt 6 Fig. 2.\u2014 Contour plots showing the mass in gas at di\ufb00erent densities and temperatures for the T3vl run on the left, Tmin = 300 K (from TB10) on the right. The contours are spaced by a factor of 10 in mass. For a gas cell to be included in the contour plot, it must have at least 25% of its mass originating from the galaxy (based on the tracer \ufb02uid). The two curves denote lines of constant X-ray luminosity per mass (or emissivity per density). This \ufb01gure illustrates that high ICM pressure produces an X-ray bright tail. See discussion in Section 3.1.2 for these maps is 2 \u00d7 10\u221218 erg s\u22121 cm\u22122 arcsec\u22122 (see Sun et al. (2007) and references therein). As described earlier, we use Cloudy to determine the H\u03b1 emissivity given a gas temperature and density. We \ufb01nd, as shown in Figure 4, highly structured, long tails of H\u03b1 emission. Note that we do not include UV radiation from star formation or AGN (except from the metagalactic background, as described in section 2.2). Figure 3 shows that H\u03b1 emission peaks around the edges of cold clouds, which can be seen by comparing the upper right panel of H\u03b1 emission with the lower right panel showing gas surface density. The Tmin = 8000 K and Tmin = 300 K runs show a similar amount of H\u03b1 emission. This is because, while the minimum temperature a\ufb00ects the temperature in the central regions of the clouds, it does not strongly affect the cloud edges in the simulation, whose characteristics are more determined by the interaction between the cloud and the ICM. We \ufb01nd that changing the cloud size parameter in our Cloudy run has only a small e\ufb00ect on the total H\u03b1 \ufb02ux (less than 10% in all three runs). This is because most of our emission is produced by collisional processes rather than photoionization, and so is mostly dependent on the gas temperature, not the optical depth to ionizing photons (recall that we do include star formation in the simulation and so do not model HII regions within the tail). Because we do not include star formation, we cannot compare our H\u03b1 emission to the 33 H II regions seen by Sun et al. (2007). We do compare the total \ufb02ux from our tail to the observed di\ufb00use H\u03b1 emission in Table 6. Again, the volume of our di\ufb00use tail is much larger than TABLE 6 H\u03b1 tail attributes Run or l \u00d7 w fH\u03b1/10\u221214 fH\u03b1/10\u221214 corrected a Observation (kpc \u00d7 kpc) (erg s\u22121 cm\u22122) (erg s\u22121 cm\u22122) T80vh 67 \u00d7 27 75.8 2.23 T3vh 65 \u00d7 29 75.9 2.00 T3vl 80 \u00d7 30 97.9 1.96 Sun et al. (2007) \u223c40 \u00d7 6 4.4 4.4 aThe corrected \ufb02ux multiplies the simulated H\u03b1 \ufb02ux by the ratio between the simulated and observed tail volumes. that observed by Sun et al. (2007), and we show the corrected H\u03b1 \ufb02ux by dividing by the volume ratio in the table. The di\ufb00erence in tail widths is from the di\ufb00erence in galaxy sizes, while the length of the observed tail is the minimum length of the di\ufb00use emission because there is a bright star in the \ufb01eld (Sun et al. 2007). When we take the di\ufb00erent volumes of the tail into account, our simulated H\u03b1 \ufb02ux is less than that observed from the tail of ESO 137-001, but in all three cases, the simulated H\u03b1 \ufb02ux is within a factor of 2.5 of the observed \ufb02ux. There are a number of possible explanations for our slightly lower predicted H\u03b1 \ufb02ux, including the possibility that some unresolved H II regions are counted as di\ufb00use \ufb02ux in the observations. Other heating sources such as thermal conduction \u2014 an e\ufb00ect we do not include in the simulations \u2014 could give rise to more H\u03b1 \ufb02ux than we see in our simulations. We also \ufb01nd that numerical resolution plays a role in the total H\u03b1 emission, as we 7 Fig. 3.\u2014 Projections of a very thin (0.3 kpc) slice from the T80vh run (images are 16 kpc \u00d7 19 kpc). The upper left panel shows X-ray surface brightness (red brightest), which demonstrates that X-ray emitting gas is associated with di\ufb00use, mixed gas, but not necessarily material recently stripped from dense clouds in the tail. The lower left panel (temperature) demonstrates that the brightest X-ray emitting gas is associated with intermediate temperatures. Similarly, the upper right panel shows that H\u03b1 emission is produced primarily at the edges of dense clouds. The lower right panel (gas surface density) demonstrates that the brightest H\u03b1 is produced in high surface density clouds. will discuss in Section 5.2. 3.3. H I In this section we consider H I column density, comparing projections of our simulations to observations. In Figure 5 we show the H I column density at the best resolution of our simulation. As discussed in Section 2.2, we use Cloudy to determine the neutral fraction given a temperature and density (with the assumed metagalactic UV \ufb02ux) and then apply that value in our projection routine. In Figure 6 we only show a projection comparable to the observations performed by Vollmer et al. (2001), using a resolution of 30\u201d and a minimum column density of 2 \u00d7 1020 cm\u22122. We also correct for the di\ufb00erence in disk sizes by dividing our column densities by a factor of 3 (the ratio of X-ray tail diameters). Only the tail of T3vl would have been observed by Vollmer et al. (2001). This is because in the slower velocity case there is a smaller velocity di\ufb00erence between the clouds and the ICM wind and the ICM is slighty less dense (83% of the ICM density in the higher velocity cases), which results in less cloud ablation and more high density gas (both a slightly higher maximum density of gas and slightly more gas at any particular density above n \u223c1 cm\u22123). This di\ufb00erence between the non-detection by Vollmer et 8 Fig. 4.\u2014 H\u03b1 intensity projections. These can be compared with the di\ufb00use emission observed by Sun et al. (2007). From left to right: T3vl, T80vh, T3vh. See Section 3.2 for discussion. Fig. 5.\u2014 H I column density projections at the maximum resolution of our simulation (38 pc). From left to right: T3vl, T80vh, T3vh. See Section 3.3 for discussion. al. (2001c) and our prediction that T3vl would be detected implies that ESO 137-001 is most likely moving more quickly through the ICM than 1413 km s\u22121. The H I column densities in T3vh and T80vh are within a factor of 3 and 1.3 respectively below the maximum column density as determined by the non-detection of Vollmer et al. (2001). Figure 3 clearly shows that bright H\u03b1 emission is produced only at the edges of dense neutral clouds. This spatial correspondence between neutral and H\u03b1 emitting gas agrees with the observations of Sivanandam et al. (2009), who found molecular hydrogen in the tail to the farthest distance they could search\u201320 kpc. We predict that with a deeper observation H I will be observed to at least 40 kpc (the length of the observed H\u03b1 tail), and likely even farther (our shortest H I tail is 65 kpc in T3vh), unless heat conduction is quite e\ufb03cient. 4. DISCUSSION 4.1. Which Stripped Galaxies will have X-ray Tails? In this section, we comment on the likelihood of \ufb01nding more X-ray tails. In order for a tail to have observable Xray emission, it must be in a high pressure ICM. We can estimate the pressure necessary to produce bright X-ray emission simply by shifting our mass-weighted distribution of gas until the lowest mass contour lies along the upper 10\u22121 erg s\u22121 g\u22121 contour. We choose this contour because in every simulation we have run, projections of surface density have shown that most of the tail has a column density of at least 1020 cm\u22122. Gas in the tail with higher surface densities tends to be in cold clouds (T < 104 K) (see TB10), while X-rays are emitted by hot (T > 106 K), di\ufb00use gas with lower column densities (Figure 2). This method results in a minimum ICM pressure of 9 \u00d7 10\u221212 erg cm\u22123. 9 Fig. 6.\u2014 H I column density projection smoothed to the resolution of the observations by Vollmer et al. (2001) using ATCA. The only run with observable H I in the tail using 30\u201d resolution and a minimum column density of 2 \u00d7 1020 is T3vl. See Section 3.3 for discussion. In Table 7 we show the cluster radius at which the ICM pressure falls below our minimum value. In general, we calculated the cluster radius using a \u03b2-model and constant temperature from the papers cited in column 3. There are three exceptions to this. First, the X-ray intensity contours in Figure 17 of Wang et al. (2004) denote the highest density ICM region (and are not spherically symmetric), which is the only region of A2125 with a high enough density to produce our minimum ICM pressure for X-ray bright tails. Second, we \ufb01nd the radius of Perseus with our minimum ICM pressure directly from Figure 9 in Ettori et al. (1998). Finally, we use the entropy measurements of Cavagnolo et al. (2009) to \ufb01nd that as close as 100 kpc from M87 the ICM pressure is below 9 \u00d7 10\u221212 erg cm\u22123. Note that these are \ufb01rst estimates generally using spherically symmetric cluster pro\ufb01les, which oversimplify the structure of the ICM. We can now comment on whether observed X-ray tails are in high pressure ICMs (de\ufb01ned here as at or above 9 \u00d7 10\u221212 dyn cm\u22122). The two X-ray tails in A3627, ESO 137-001 and ESO 137-002, are both within the high pressure ICM (Sun et al. 2007; Sun et al. 2010). However, Sun et al. (2010) \ufb01nd that using their spectroscopic temperatures, the tail gas is over-pressured with respect to the ICM. This might indicate that the spectroscopic temperature does not correctly model the tail temperature. We \ufb01nd that turbulent pressure is not strong enough to greatly increase the gas pressure in the tail (Figure 2 and TB10). C153 is near the X-ray peak of A2125 (Wang et al. 2004). UGC 6697 in A1367 is at least 450 kpc from the X-ray peak of the cluster, outside of our calculated high-pressure radius. However, it is near an infalling subcluster and in a higher-density ICM than predicted using the \u03b2-model centered on the X-ray peak of A1367. Using the \ufb01t to the subcluster by Donnelly et al. (1998), Sun & Vikhlinin (2005) calculated the surrounding pressure to be 7.9 \u00d7 10\u221212 dyn cm\u22122, very close to our minimum TABLE 7 Where in clusters will tails be X-ray bright? Cluster Outer radius (kpc) Reference A3627 250 h\u22121 50 Bohringer et al. (1996); Sun et al. (2010) A2125 28.5 89 h\u22121 71 Wang et al. (2004) A1367 274 h\u22121 50 Mohr et al. (1999) CL 0024+0016 250 h\u22121 70 Zhang et al. (2005) Coma 613 h\u22121 50 Briel et al. (1992) Perseus 2000 h\u22121 50 Ettori et al. (1998) Virgo (M87) < 100 h\u22121 70 Cavagnolo et al. (2009) pressure for observable X-ray emission. 4.2. E\ufb03ciency of Heat Conduction Heat conduction, which we do not include in these simulations, could be important for the survival of cool clouds in the ICM and H\u03b1 emission; however, it can be suppressed by magnetic \ufb01elds (e.g. Vollmer et al. 2001). If it is an e\ufb03cient way to transport heat from the ICM to cold, stripped gas, then the survival time of H I clouds would be less than predicted in this paper, and the length of the tails would be shorter. We can estimate the e\ufb03ciency of heat conduction by comparing an analytic calculation of the evaporation time of the most dense clouds in our simulations to the length of time we expect clouds have survived in order to produce the observations of ESO 137-001. First, we estimate the evaporation time for a typical cloud if heat conduction is not suppressed, and we will de\ufb01ne this calculated evaporation time as the time for cloud evaporation if heat conduction is 100% e\ufb03cient. We follow Cowie & McKee (1977), as in Vollmer et al. (2001). In our clouds, we \ufb01nd that the mean free path for ions is comparable to or greater than the temperature scale length, so we need to use the saturated heat \ufb02ux equations. Evaporation time is proportional to f \u22121r11/8 cloudncloud T \u22125/4 ICM n\u221211/8 ICM , where f is the conduction e\ufb03ciency relative to Spitzer. Solving for the evaporation time for each of our three runs, we \ufb01nd that using a cloud radius of 100 pc, and the maximum gas density in our tails at the time of our comparison, the evaporation times of our three runs are \u223c4 Myr for T80vh, \u223c8 Myr for T3vh, and \u223c10 Myr for T3vl. We choose to use the highest density found in our tails because we want to calculate the longest plausible evaporation time in order to \ufb01nd the most conservative estimates for the maximum e\ufb03ciency of heat conduction. The Tmin = 300 K runs have a maximum density in their tails of 2 \u00d7 10\u221223 g cm\u22123 and T80vh has a maximum density of 10\u221223 g cm\u22123. We have shown that di\ufb00use H\u03b1 emission directly traces neutral clouds (Figure 3), which means that the dense clouds must not be entirely evaporated before they reach 40 kpc above the disk. We are also able to measure the velocity of gas in our tails (see TB10 for details), so can estimate the time it would take for a cloud to reach 40 kpc above the disk. We use generous estimates of 1200 km s\u22121 for the high velocity cases and 900 km s\u22121 for the lower velocity run in order to calculate the shortest time it would take these clouds to reach 40 kpc above the disk 10 (which will maximize the value we \ufb01nd for the e\ufb03ciency of heat conduction). Therefore, the e\ufb03ciency of heat conduction must be less than 24% (T3vl and T3vh), or 12%(T80vh). Once there is a deep observation of the H I tail, we will be able to compare the length of ESO 137-001\u2019s tail to the lengths of our simulated tails to \ufb01nd a minimum e\ufb03ciency of heat conduction. To do this we will use a similar argument to the one above; namely, compare the amount of time a cloud takes to reach its height above the disk to the evaporation time, assuming that heat conduction is responsible for destroying the clouds. It is important to consider our simulations in this calculation, because they show that even without heat conduction, H I may not extend along the entire length of the X-ray tail. The simulations also show the limitations of using a simple velocity and distance argument to calculate the length of time a galaxy has been stripped\u2013using 900 km s\u22121 and the length of the H I tail we \ufb01nd that the galaxy in T3vl has been stripped for 87 Myr, while the actual time after the wind has hit the galaxy is 110 Myr. The high velocity cases have an even larger discrepancy between the actual stripping time and the time calculated using the H I tail length. Despite these caveats, we can make a very rough \ufb01rst estimate using Figure 6 (T3vl) and the non-detection result of Vollmer et al. (2001). The H I in our smoothed projection begins about 50 kpc above the disk. If the non-detection of Vollmer et al. (2001) means that there are no neutral clouds at this height above the disk, then we can calculate a minimum e\ufb03ciency for heat conduction, which is 18.5%. However, as we discussed above, we expect that a deeper observation will \ufb01nd H I beyond this height above the disk. 5. NUMERICAL CONSIDERATIONS 5.1. Radiative Cooling Floor As noted earlier, we used two di\ufb00erent values for our radiative cooling \ufb02oor (8000 K and 300 K) in order to explore in a simple way the potential impact of processes which we do not include in the simulation. We discuss the physical motivations for the two cooling \ufb02oors in TB10. We \ufb01nd that the change in the minimum temperature makes only a relatively minor change in the morphology of the \ufb02ow, and doesn\u2019t signi\ufb01cantly change the resulting length of the tail. This also translates into only a relatively small di\ufb00erence in the predicted observables, with changes of less than 30% in both X-ray and H\u03b1 luminosities.1 The biggest di\ufb00erence is in the survival of H I clouds, with Tmin = 300 K predicting longer lived clouds. Still, the impact on H I observations is quite small. The ratios of the three observables is also quite constant, generally to within 30%, as can be see from an inspection of the right two panels of Figures 1, 4, and 5, and from Tables 5 and 6. 5.2. Resolution 1 Note that this di\ufb00ers from the conclusion reached in TB10, where we found that the Tmin = 300 K run predicted lower H\u03b1 emission by more than an order of magnitude. This incorrect conclusion was reached because of the cooling curve error for that run discussed in section 2. Resolution is most likely to a\ufb00ect the survival and structure of our dense clouds in the tail. The most direct results would be di\ufb00erent amounts of neutral gas and H\u03b1 emission. A number of examinations of the survival of clouds with a variety of physics included have been performed. Mellema et al. (2002) and Yirak et al. (2009) include radiative cooling. Fragile et al. (2004) also discuss how including self-gravity increases the lifetime of clouds. Nakamura et al. (2006) discuss the impact of using smooth cloud boundaries on the growth of instabilities. They (and Yirak et al. 2009) \ufb01nd that a low density gradient results in slower growth of instabilities, which can retard cloud destruction. Our most dense clouds have an analytically calculated destruction timescale due to turbulent viscous stripping (using eq. (22) in Nulsen 1982) of more than 1 Gyr, so resolution should not have a large impact over the timescales we consider in these simulations. We use the same cloud parameters as in the evaporation time calculation, although even with an order of magnitude lower density clouds (\u223c10\u221224 g cm\u22123), the destruction timescale is still about 200 Myr, which is much longer than the time at which we make our projections. We use a relative velocity di\ufb00erence of 400 km s\u22121 (although we do not show velocity plots in this paper, see TB10 for a detailed discussion of the tail velocity). However, lower density clouds in our simulated tails cool and are compressed by the ICM, which may instead be destroyed by the ICM wind if we had better resolution that resulted in a steeper density gradient at the cloud edge. Although we do not perform a detailed resolution study of the runs in this paper, we do compare T3vl to a run with only 5 allowed levels of re\ufb01nement, to a minimum cell size of 76 pc, a factor of two worse in resolution. We compare outputs with the same amount of gas stripped from the galaxy. The total X-ray luminosity of the lower resolution tail is \u223c90% of the luminosity of T3vl (i.e. only a 10% change), while the total H\u03b1 \ufb02ux is only 28% of T3vl. The total HI \ufb02ux is also decreased by a similar amount (to 33% of the value in T3vl). For both resolutions, there is a good correspondence between the relative HI and H\u03b1 level and morphology; therefore, we argue that the ratio of HI to H\u03b1 is more robust than the absolute level of either. Both the small discrepancy in the X-ray luminosity and larger discrepancy in the H\u03b1 \ufb02ux can be explained by considering what gas is producing the emission. Xray emission is produced by gas that is mixed with the ICM and is not localized near the dense clouds in the tail, and so is not very dependent on high resolution. One explanation for the slightly lower X-ray luminosity is that mixing happens more quickly and the gas is heated out of the X-ray bright regime. Unlike the di\ufb00use nature of the X-ray emitting gas, H\u03b1 emission occurs at the edges of clouds. We \ufb01nd that in projection the range of H\u03b1 intensities is the same as T3vl, meaning that the di\ufb00erent resolution element size does not strongly a\ufb00ect the density and temperature at the edges of the dense clouds (and therefore does not strongly a\ufb00ect the H\u03b1 emission). The main di\ufb00erence is that there are fewer dense clouds in the less-resolved wind. In fact, the total H I column density in the low resolution tail is about 30% of the total H I column density in T3vl\u2013very similar to the H\u03b1 \ufb02ux fraction. In projec11 tion, there are about half as many pixels with H I column densities over 1019 cm\u22122. Since we expect the total H I column density to also depend on the number of clouds along the line of sight of the projection, we \ufb01nd that there should be roughly 26% as many clouds (by simply squaring the 51% we \ufb01nd in the projection plane). Of course, clouds are more than a single pixel, so this is a rough approximation. However, this indicates that the amount of H\u03b1 emission closely follows the amount of H I column density, and likely the number of H I clouds. There are fewer H I clouds in the low resolution run because with lower resolution the maximum density is lower and therefore the clouds are destroyed and mixed more quickly into the ICM. Deep, high resolution observations in H I will allow us to determine how many and for how long dense clouds survive, which will point to one of these mixing scenarios. 6. CONCLUSIONS We have run detailed galaxy simulations including radiative cooling and made comparisons to the observed tail of ESO 137-001 to understand the physical mechanisms at work in the ICM. We compare three cases in which we vary our cooling \ufb02oor between 8,000 K or 300 K and the ICM parameters as shown in Table 3. Our main conclusions are as follows: 1) The X-ray luminosity of our simulated tails are an excellent match to the X-ray luminosity of the tail of ESO 137-001. This suggests that we are correctly modeling the phase distribution of gas in the tail, and that the mixing of the hotter stripped ISM (T > 105 K) is being accurately modeled in the simulations. 2) We \ufb01nd that bright X-ray emission depends upon a high surrounding ICM pressure, and \ufb01nd a minimum necessary pressure of 9 \u00d7 10\u221212 erg cm\u22123. This conclusion agrees well with the local environment in clusters where bright X-ray tails are observed. 3) We compare our H\u03b1 \ufb02uxes to the total di\ufb00use H\u03b1 \ufb02ux measure by Sun et al. (2007). As in our X-ray emission, we \ufb01nd an excellent match between our simulations and observations. 4) We predict that deeper observations will \ufb01nd H I gas to at least 40 kpc above the disk, because di\ufb00use H\u03b1 emission directly traces neutral clouds (and has been observed to 40 kpc above the disk). The observations of molecular hydrogen by Sivanandam et al. (2009) strengthen this prediction. We also conclude that the mismatch between T3vl and Vollmer et al. (2001) indicates that the higher velocity cases better match the observations. 5) Using the fact that H\u03b1 traces neutral gas and calculating the evaporation times of our simulated clouds (based on their sizes and densities), we calculated a maximum e\ufb03ciency for heat conduction of 24% (T3vh and T3vl) or 12% (T80vh). By modeling a simulation using a high ICM pressure, we have shown that X-ray emission can coexist with H I and H\u03b1 emission. We have also found that H I and H\u03b1 emission spatially coincide because H\u03b1 is mostly produced at the edges of neutral clouds (Figure 3), while X-ray emission is generated in hot, di\ufb00use gas that is mixing with the ICM. This is seen by the more even distribution in the tail (Figures 1 and 3), and by the fact that the X-ray tail can be longer than the H I and H\u03b1 tails. Our excellent agreement with X-ray observations gives us con\ufb01dence that we are correctly modeling the mixing, cooling and heating rate of X-ray emitting gas. This in turn means that heat conduction is not acting strongly to heat the di\ufb00use gas in the tail, and that small scale turbulence (below our resolution scale) is not quickly mixing stripped gas. Both of these mechanisms would act to heat the gas in the tail out of the X-ray bright range and therefore lower the total luminosity, which would make our agreement to the observations worse. We cannot rule out the possibility that we have less gas mass at higher emissivities than in ESO 137-001. We also \ufb01nd excellent agreement between our simulated H\u03b1 \ufb02ux and observations of di\ufb00use H\u03b1 emission. We robustly conclude that di\ufb00use H\u03b1 emission coincides with H I gas, and we \ufb01nd that H\u03b1 emission outlines H I clouds in all of our simulations. The agreement between the total H\u03b1 emission in our cases with di\ufb00erent cooling \ufb02oors underscores the fact that the edges of clouds, which are interacting with the ICM, emit the most strongly in H\u03b1, not the central regions of the clouds, which are more likely to have radiatively cooled to the minimum allowed temperature. Although our agreement with observations indicates that we may also be correctly modeling the edges of dense clouds, we cannot dismiss the possibility that we are not fully resolving the cloud edges. In Section 5.2 we discuss how lower resolution results in fewer H I clouds, and less H\u03b1 emission. Therefore, we cannot rule out that properties of our simulations that have not converged at our current resolution\u2013the number of clouds, the rate of the decline of density at the edge of the cloud and the smallest scale of turbulent heating\u2013have combined with the lack of heat conduction in our simulations to result in an accidental, and incorrect, agreement with observations. Observations of H I in the tail will provide an important check to these results. This work highlights the importance of comparing simulations to detailed, multi-wavelength observations of individual systems. We are able to make predictions about this particular galaxy, such as the existence of H I gas in the tail and that its three-dimensional velocity relative to the ICM is probably larger than 1413 km s\u22121. However, our simulation is not able to make any prediction about why there is a separated tail in ESO 137-001. We also do not reproduce the exact surface brightness distribution along the X-ray tail. As we have discussed, our goal was not to reproduce this speci\ufb01c tail. In order to do this, we would recommend modeling a smaller galaxy and matching the inclination angle between the galaxy and the ICM wind. Using our comparison with the observations of ESO 137-001, we also draw more general conclusions about the importance of turbulence and the e\ufb03ciency of heat conduction in the ICM. We conclude that the mixing rate of the hot stripped ISM (T > 105 K) is well-modeled in our simulations using only adiabatic compression and turbulent mixing down to the resolution of our simulations (38 pc). We call upon observers to test our predictions of where in clusters tails will be X-ray bright, and to use deep observations to verify the connection between H\u03b1 and H I gas. Observations of the H I tail of ESO 137-001 can be used to test mixing of cold clouds into the ICM in our simulations. 12 We acknowledge support from NSF grants AST0547823, AST-0908390, and AST-1008134, as well as computational resources from the National Center for Supercomputing Applications, NSF Teragrid, and Columbia University\u2019s Hotfoot cluster. We thank Jacqueline van Gorkom, Je\ufb00rey Kenney and the referee Bernd Vollmer for useful discussions, as well as Elizabeth Tasker for invaluable help setting up the initial conditions.",
                    "introduction": "1. Ram pressure (and related processes) by the intraclus- ter medium (ICM) can remove a galaxy\u2019s gas (Gunn & Gott 1972). This process has been observed in var- ious stages; for example, Vollmer (2009) separates Virgo galaxies into pre-peak, peak, and post-peak ram pres- sure groups. The amount of time that a galaxy has been stripped can be estimated using the length of the observ- able tail and the velocity of the galaxy (e.g. Oosterloo & van Gorkom 2005; Sun et al. 2006). This calcula- tion is uncertain due to di\ufb03culties in determining the three dimensional galaxy velocity. Another assumption implicit in this calculation is that the observed tail pro- vides the true length of the stripped gas. In fact, tails have been observed in H I, H\u03b1, and X-ray emission, al- though never all from the same tail (e.g. Oosterloo & van Gorkom 2005; Koopmann et al. 2008; Kenney et al. 2008; Yoshida et al. 2002; Yoshida et al. 2004a,b; Sun et al. 2007; Sun et al. 2006; Sun et al. 2010; Machacek et al. 2006; Sun & Vikhlinin 2005). The lengths of tails observed in di\ufb00erent wavelengths can be quite di\ufb00erent; for example the H I tail of NGC 4388 is nearly three times as long as the observed H\u03b1 tail (Oosterloo & van Gorkom; Yoshida et al. 2002). Another method used to calculate the age of a tail is to use the estimated survival time of H\u03b1, as in Gavazzi et al. (2001). However, it is still not clear what dictates cloud survival or even what conditions are necessary to produce the various types of emission (H\u03b1, X-ray, and H I). Can all three types of emission coexist? What physical processes dominate the heating and mixing of stripped gas into the ICM? These processes include: turbulent mixing, which can generate intermediate temperature and density gas at constant pressure; shock heating, which heats the ISM; radiative cooling, which can lead to recompression of heated gas, and heat conduction, which can evaporate small clouds. In this work we focus on answering these questions by simulating gas stripping and comparing our simulated tail to a single observed stripped galaxy, ESO 137-001, which has been studied observationally in some detail. ESO 137-001 is in A3627, which is the closest massive cluster (z=0.0163, \u03c3radial = 925 km s\u22121 and kT = 6 keV), similar to Coma and Perseus in mass and galaxy content (Sun et al. 2009 and references therein). ESO 137-001 is a small (0.2L\u2217; Sun et al. 2006), blue emission- line galaxy (Woudt et al. 2004), that is \u223c200 kpc from the center of the cluster in projection. Because its radial velocity is close to the average velocity of A3627 (Woudt et al. 2004; Woudt et al. 2008), most of its motion is likely in the plane of the sky, and therefore the stripping process is seen edge-on. Sun et al. (2006) found a \u223c70 kpc X-ray tail pointing away from the cluster center us- ing Chandra and XMM-Newton data. Sun et al. (2007) then discovered a 40 kpc H\u03b1 tail with over 30 emission- line regions extending through the length of the H\u03b1 tail, and concluded that the emission-line regions are giant H II regions. In a recent follow-up paper, Sun et al. (2009) used deep Chandra data and Gemini spectra to characterize the X-ray tail and H II regions in detail. They found a narrower secondary X-ray tail with a sim- ilar length. They also con\ufb01rmed that 33 emission-line regions are H II regions, with the furthest seven regions beyond the tidally-truncated halo of 15 kpc that is cal- culated in Sun et al. (2007) using simulations by Gnedin (2003). In addition to these distinct H II regions, they \ufb01nd di\ufb00use H\u03b1 emission. Vollmer et al. (2001) searched for H I in A3627, and did not detect any H I in or around ESO 137-001 with a limiting column density of 2 \u00d7 1020 cm\u22122 and a reso- lution of 15\u201d. In fact, of the \u223c80 galaxies identi\ufb01ed by Woudt et al. (1998) in their search region, Vollmer et al. (2001) detected only 2 in H I, \ufb01nding that the H I detection rate in A3627 is similar to that in Coma. Sivanandam et al. (2009) observed ESO 137-001 with IRAC and IRS on Spitzer. The IRS data extended to 20 kpc from the galaxy along the X-ray tail, and warm (\u223c160 K) molecular Hydrogen was detected throughout the length of the observed region. The observed region contains \u223c2.5 \u00d7 107 M\u2299warm H2 gas. They also iden- tify star-forming regions using 8 \u00b5m data, which coincide with H\u03b1 emitting regions. There has been a substantial amount of theoretical arXiv:1103.3273v1  [astro-ph.CO]  16 Mar 2011 2 TABLE 1 Galaxy Stellar and Dark Matter Constants"
                },
                {
                    "url": "http://arxiv.org/abs/0909.3097v1",
                    "title": "The Tail of the Stripped Gas that Cooled: HI, Halpha and X-ray Observational Signatures of Ram Pressure Stripping",
                    "abstract": "Galaxies moving through the intracluster medium (ICM) of a cluster of\ngalaxies can lose gas via ram pressure stripping. This stripped gas forms a\ntail behind the galaxy which is potentially observable. In this paper, we carry\nout hydrodynamical simulations of a galaxy undergoing stripping with a focus on\nthe gas properties in the wake and their observational signatures. We include\nradiative cooling in an adaptive hydrocode in order to investigate the impact\nof a clumpy, multi-phase interstellar medium. We find that including cooling\nresults in a very different morphology for the gas in the tail, with a much\nwider range of temperatures and densities. The tail is significantly narrower\nin runs with radiative cooling, in agreement with observed wakes. In addition,\nwe make detailed predictions of H I, Halpha and X-ray emission for the wake,\nshowing that we generally expect detectable H I and Halpha signatures, but no\nobservable X-ray emission (at least for our chosen ram-pressure strength and\nICM conditions). We find that the relative strength of the Halpha diagnostic\ndepends somewhat on our adopted minimum temperature floor (below which we set\ncooling to zero to mimic physics processes not included in the simulation).",
                    "authors": "Stephanie Tonnesen, Greg L. Bryan",
                    "published": "2009-09-17",
                    "updated": "2009-09-17",
                    "primary_cat": "astro-ph.CO",
                    "cats": [
                        "astro-ph.CO"
                    ],
                    "main_content": "TABLE 1 Galaxy Stellar and Dark Matter Constants Variable Value 11 Variable Value M\u2217 1 \u00d7 1011 M\u2299 a\u2217 4 kpc b\u2217 0.25 kpc Mbulge 1 \u00d7 1010 M\u2299 rbulge 0.4 kpc rDM 23 kpc \u03c1DM 3.8 \u00d7 10\u221225 g cm\u22123 cooling rate is zero below this temperature. In the simulations described here we use either Tmin = 8000 K, or Tmin = 300 K. Both allow gas to cool below the threshold for neutral H formation. In TB09, we found that the minimum temperature affected the range of masses and sizes of clouds forming in the disk. This, in turn, resulted in changes in the timescale for gas loss from the disk, although the total amount of gas lost was similar. In this paper, as we will show in more detail later, we find that the structure of the wake also depends somewhat on Tmin. 2.1. The Galaxy Our galaxy is placed at a position corresponding to (155.5,155.5,68.42) kpc from the corner of our cubical 311 kpc computational volume, so that we can follow the stripped gas for more than 200 kpc. The galaxy remains stationary throughout the runs. The ICM wind flows along the z-axis in the positive direction, with the lower z boundary set for inflow and upper z boundary set as outflow. The x and y boundaries are set to outflow in all three of our high resolution cases (8000K, 300K, and no cooling) and reflecting in the lower resolution cases. The different boundary conditions in the two runs had only a very minimal impact, since the box is so wide (311 kpc wide). We chose to model a massive spiral galaxy with a flat rotation curve of 200 km s\u22121. It consists of a gas disk that is followed using the adaptive mesh refinement algorithm (including self-gravity of the gas), as well as the static potentials of the stellar disk, stellar bulge, and dark matter halo. We directly follow Roediger & Br\u00a8 uggen (2006) in our modeling of the stellar and dark matter potential and gas disk. In particular, we model the stellar disk using a Plummer-Kuzmin disk (see Miyamoto & Nagai 1975), the stellar bulge using a spherical Hernquist profile (Hernquist 1993), and the dark matter halo using the spherical model of Burkert (1995). This dark matter halo model is compatible with observed rotation curves (Burkert 1995; Trachternach et al. 2008). The equation for the analytic potential is in Mori & Burkert (2000). The gas is described as a softened exponential disk: \u03c1(R, z) = Mgas 2\u03c0a2 b s described as a softened Mgas 2\u03c0a2 gasbgas 0.52sech \ufffdR aga agas exponential  \ufffd sech \ufffd|z| bgas bgas \ufffd (1) Given this gas density distribution in the disk, the initial gas temperature and pressure are calculated to maintain the disk in hydrostatic equilibrium with the surrounding ICM in the z direction. The gas disk\u2019s rotational velocity is set so that the combination of the centrifugal force and 4 TABLE 2 Gas Disk Constants Mgas 1 \u00d7 1010 M\u2299 agas 7 kpc bgas 0.4 kpc the pressure gradient of the disk balances the radial gravitational force. We taper the gas disk smoothly by multiplying the gas density distribution by 0.5(1+cos(\u03c0(R\u221220 kpc)/26 kpc)) for 20 kpc < R \u226426 kpc. See our galaxy parameters in Tables 1 and 2. To identify gas that has been stripped from the galaxy we also follow a passive tracer which is initially set to 1.0 inside the galaxy and 10\u221210 outside. In the following analysis, we will use a minimum tracer fraction of 25% to \ufb01nd gas stripped from the galaxy (our conclusions do not change when we use 10%). 2.2. ICM Conditions The galaxy initially evolves in a static, high-pressure ICM with \u03c1 = 9.152 \u00d7 10\u221229 g cm\u22123 and T = 4.15 \u00d7 106 K, to allow cool, dense gas to form in the galaxy. This naturally generates a multiphase ISM (see Tasker & Bryan 2006 and TB09 for more discussion of the ISM properties). After 155 Myrs, we reset the boundary conditions to generate a constant ICM in\ufb02ow along the inner z-axis, which is always face-on to the galaxy. We choose to study the highest of the three ram pressure strengths examined in TB09 (this case results in the largest mass in the wake). We choose Pram = \u03c1v2 ICM = 6.4\u00d710\u221212 dynes cm\u22122. For the corresponding ICM physical conditions, \u03c1, T , and vICM, we use the results from our earlier cluster simulation to \ufb01nd the mean density, velocity, and temperature encountered by infalling galaxies for a typical cluster mass, given the ram pressures value (Tonnesen, Bryan & van Gorkom 2007). See TB09 for other details regarding the numerical setup (we use case PHRCW in TB09). Because we are interested primarily in the impact of radiative cooling on a gas stripped tail, we only consider a case with a face-on wind, again because this will result in the most gas in the tail. 2.3. Suite of Simulations We run two main simulations of a ram-pressure stripped galaxy including radiative cooling using a temperature-dependant cooling curve from Sarazin & White (1987) extended to either Tmin = 8000 K or Tmin = 300 K, as described earlier. In addition, we run a simulation without radiative cooling. In this way, we can investigate the impact of cooling to various temperature \ufb02oors. These three runs all have the highest mass resolution and provide the main results of this paper. All simulations have the same maximum re\ufb01nement level of l = 6 (i.e. the same best spatial resolution of 38 kpc), but we can compare both of our radiatively cooled runs to ones with a factor of 8 lower mass resolution (as described earlier). This allows us to investigate the e\ufb00ect of numerical resolution. A \ufb01nal comparison simulation has the same re\ufb01nement criteria as our highest mass resolution runs, but calculates cooling rates by following the non-equilibrium ionization fractions of hydrogen and helium, and directly computing their cooling rates. We do not include metals in this cooling calculation, which leads to slower cooling of hot ISM gas. This in turn results in a stripping rate which lies between our radiative cooling runs and a run without radiative cooling (largely because of the smaller amount of fragmentation in the disk). This comparison run was primarily done to allow us to check our simple calculation of H\u03b1 emission \u2013 described in the next section \u2013 by using the hydrogen ionization state as computed by the code. 2.4. Projections Enzo outputs the density and temperature of the gas in each cell. To transform these values into H I column density and H\u03b1 intensity, we used Cloudy, version 08.00 of the code last described by Ferland et al. (1998). Using a grid of temperatures and densities, we calculated the hydrogen neutral fraction and H\u03b1 emissivity. In the Cloudy calculation, we included CMB radiation, the cosmic ray background, bremsstrahlung radiation from the ICM and the 2005 version of the Haardt & Madau (2001) z = 0 metagalactic continuum, as implemented by Cloudy. We found that including the local interstellar radiation \ufb01eld emission resulted in lower amounts of neutral gas. Since much of our gas is very distant from the galaxy, we decided not to include this radiation. We also found that removing bremsstrahlung radiation did not change any of the values we considered. We chose to calculate the neutral fraction and H\u03b1 emissivity for a thin plane-parallel gas cloud of width 100 pc. We selected this width because it loosely corresponds to the cell size of most of the gas in the highly resolved tails, and accounts approximately for radiative transfer e\ufb00ects. If we assumed the radiative thin limit, it would decrease the amount of H I we predict, and increase the H\u03b1 emission for dense, low-temperature gas. Ideally, we would include the radiation \ufb01eld with radiative transfer directly in the simulation, but this is not yet feasible (and only has a mild impact on the dynamics); instead we postprocess these results to get reasonable predictions for the ionization fraction and H\u03b1 emissivity (see Furlanetto et al. 2005 for a discussion of various approaches in the context of Ly\u03b1 emission). We do compare our projections with ones made assuming clouds sizes of 10 pc and 1 kpc. To create X-ray surface brightness projections, we use a spectral lookup table for low density gas with a metallicity of 0.3 solar computed using a Raymond-Smith code (Raymond & Smith 1977), as updated in XSPEC (Arnaud 1996). The X-ray band we use is 0.5 keV to 2.0 keV, following Sun et al. (2006). 3. TAIL ATTRIBUTES In this section, we examine the physical characteristics of the wakes, focusing on the wake morphology, phase diagrams and the velocity of the stripped gas. Then, in the following section, we turn to observational diagnostics. 3.1. Morphology We \ufb01rst consider the morphological characteristics of our simulations. See Figure 1 to compare the surface 5 Fig. 1.\u2014 Surface density of all gas 500 Myr after the wind has hit the galaxy for our runs with radiative cooling to Tmin = 300 K (left), Tmin = 8000 K (center) and for the comparison run with no radiative cooling (right). The images are shown with a logarithmic stretch. Note the large amount of structure, the length, and the lack of \ufb02aring in the tail with radiative cooling, compared to the tail without radiative cooling. The radiatively cooled tails are cut o\ufb00in this projection 212 kpc from the galaxy. density of the Tmin = 300 K (left), Tmin = 8000 K (center) simulations and the run without radiative cooling (right) at a time 500 Myr after the wind has hit the galaxies. Clearly there are important di\ufb00erences in the morphology of the resulting tails, although, remarkably, the amount of mass lost by this time di\ufb00ers by only 20% between Tmin = 8000 K and the run without radiative cooling. We \ufb01nd there are three primary changes that radiative cooling makes in the tail morphology. First, because of the formation of clouds in the disk, the runs with cooling show more structure in the tail. As we will see below, there is a wide range of densities and temperatures, with lots of small pressure-con\ufb01ned clouds. This is entirely missing in the no-cooling run and makes a crucial difference in some of the observational diagnostics. This result is largely independent of Tmin, as long as cooling can generate a clumpy ISM. Second, the tails in the cooling runs are more extended at a given time, reaching more than 200 kpc past the galaxy within 500 Myr of the wind hitting the galaxy. In the run without radiative cooling, some gas has gone as far as 150 kpc, but the majority of the tail is closer than 125 kpc from the galactic disk. In all of our simulations, stripped gas begins moving away from the galaxy as a group, however, in the cases with radiative cooling, with time the material is stretched out as the velocities vary (we address the velocity distribution in more detail later). Finally, the stripped gas in the radiative cooling runs expands only slightly in the transverse direction as it moves with the ICM wind: in the Tmin = 8000 K run, 200 kpc from the disk the tail width is about 80 kpc (500 Myr after the wind has hit the galaxy). The Tmin = 300 K run is even narrower, with a tail width of 40 kpc 200 kpc downstream of the disk. This is much less \ufb02aring than seen in in our no-cooling run: 500 Myr after the wind has hit the galaxy, the tail is 85 kpc wide at distance 125 kpc downstream from the disk. Although this is total gas surface density, which cannot be observed, it is notable that most observed tails are long and narrow, and do not seem to \ufb02are (for example, see the images in Chung et al. 2007). The no-cooling results are in qualitative agreement with the simulations of Roediger & Br\u00a8 uggen (2008), who also \ufb01nd the tails to have a decreasing density pro\ufb01le with distance from the galaxy. We \ufb01nd that including radiative cooling permits higher density and lower gas 6 Fig. 2.\u2014 Contour plots showing the mass in gas at di\ufb00erent densities and temperatures for our Tmin = 300 K run on the left, Tmin = 8000 K in the middle, and the comparison run without radiative cooling on the right. The contours are log mass. For a gas cell to be included in the contour plot, it must have at least 25% of its mass originating from the galaxy. The line denotes the surrounding ICM pressure. Note that at lower temperatures the gas is below the ICM pressure due to rapid cooling (see text). Note also that the range of pressures in the simulations with cooling are much larger than the comparison run without. See section 3.2 for discussion. to form in the disk and hence to be stripped, leading to high density gas throughout the tail. Our surface density projection grossly resembles that of Kapferer et al. (2009), who also include radiative cooling in their simulations, in that we both have elongated gas clumps in the wind out to large distances above the galactic disk. However, at less than a kiloparsec in diameter, most of our clumps are much smaller (about 10% in linear size) and much less massive than the clumps in the Kapferer et al. (2009) simulation. 3.2. Gas Temperature and Density In Figure 2, we show the mass-weighted distribution of density and temperature for gas in the wake that originated from the galaxy. The plots include all of the gas located between 10 kpc and 240 kpc above the disk that has at least 25% of the gas originating in the galaxy. We show these plots for three di\ufb00erent times after the wind has hit the galaxy: 100 Myr, 250 Myr, and 500 Myr for the runs with radiative cooling to 300 K (left), with radiative cooling to 8000 K (middle) and without cooling (right). The solid line shows the background ICM pressure of 1.76 \u00d7 10\u221212 dynes cm\u22122. Once again, we see a clear di\ufb00erence between the runs with and without radiative cooling. To begin, we concentrate on a comparison between the no-cooling run and the simulation with cooling to Tmin = 8000 K. We explore three distinct changes in the phase diagram. First, there is the simple fact that gas exists at much higher density and lower temperature in the runs with cooling, even at constant pressure. This is mostly due to the formation of dense clouds in the galaxy ISM before stripping (see also TB09), but it is clear that cooling plays a role even at late times: in the no-cooling run, the 7 Fig. 3.\u2014 Zoom-in of a region of the wake from the run with cooling to 8000 K near the galactic plane 180 Myr after the wind has hit the disk. The greyscale shows temperature (lowest temperature is black), while the red contours indicate pressure. The outermost contours have the largest pressure. The slice is 6 kpc in depth, and 20 kpc \u00d7 37 kpc in size. Note that the lowest pressure contours surround the coolest gas clouds (in black). See section 3.2 for a discussion. distribution becomes narrower as time goes on, as the gas is heated and mixed, while, if anything, the cooling distributions become more extended. This higher-density gas shows up clearly in the tail morphology as shown in Figure 1. Second, the cooling runs show a wider spread of density and pressure at \ufb01xed temperature; this is true even at large temperatures, but appears to be most noticeable at lower temperatures. Turbulence can cause a spread in pressure throughout the gas in the wind, as can be seen both in the run without radiative cooling, and at higher temperatures in our radiatively cooled runs, where cooling is ine\ufb03cient. The \ufb01nal distinctive di\ufb00erence is a clear break in the distribution at T \u223c105 K, with gas below this temperature falling o\ufb00the constant pressure line. This corresponds to the peak of the cooling curve, when the cooling time becomes very short. In cooler clumps of stripped gas there is an interplay between cooling, which lowers the pressure of the gas, and adiabatic compression or shock heating from the surrounding ICM. At T \u223c105 K, radiative cooling decreases the temperature more quickly than compression can increase the pressure, resulting in most of the cool gas lying below the pressure of the ICM. The peak in the gas pressure in the Tmin = 8000 K run occurs where radiative cooling is turned o\ufb00, which suddenly allows the gas to be recompressed to the ICM pressure. To investigate this process in more detail, we look closely at a slice from our Tmin = 8000 K simulation in Figure 3, in which grayscale contours of temperature (with black being the lowest temperatures) are plotted with red contours of pressure, with the outermost contours denoting the highest pressure. This 6 kpc thick slice is 20 kpc \u00d7 37 kpc, and is taken 180 Myr after the wind has hit the galaxy. As expected from the above argument, the lowest temperature regions are also the lower pressure regions, indicating that cooling lowers pressure faster than adiabatic compression can increase it. A simple timescale argument shows that the cooling and compression times are similar. For example, at T = 105 K, the cooling time for a clump density of 0.1 cm\u22123 is about the same as the sound crossing time across the clump, given a size of 1 kpc. As we \ufb01nd that many of our clouds are smaller than this size, compression must be acting more slowly than estimated using this simple calculation. The Tmin = 300 K run is similar but shows that gas can continue to cool below 8000 K in dense regions. The return to high pressures can be seen at this lower Tmin, otherwise the gas is in a rough pressure equilibrium below T \u223c104 K, but at a pressure approximately an order of magnitude below the ICM pressure. 3.3. Velocity Distribution In this section we examine the velocity structure of the stripped gas in our three main runs, from left to right: Tmin = 300 K, Tmin = 8000 K, and the no-cooling run. Figure 4 shows the gas z-velocity, parallel to the ICM wind at times 100 Myr, 250 Myr, and 500 Myr after the wind has hit the galaxy. Again we are only considering gas that originated from the disk (a 25% minimum tracer fraction). We plot contours of gas mass as a function of velocity and distance above the disk. In our runs with radiative cooling, we \ufb01nd that the majority of stripped gas is never accelerated to the ICM wind speed of 1413 km/s. In fact, 500 Myr after the wind has hit the galaxy, the main contour of gas asymptotes at about 900 km/s from about 150 kpc above the disk in both cooling runs. Our comparison run without radiative cooling evolves very di\ufb00erently. All three cases look similar in velocity space 100 Myr after the wind has hit the galaxy, but by 250 Myr \u2013 in the no cooling case \u2013 the main mass contour of stripped gas is accelerated to very close to the ICM speed (1413 km/s) at a height 100 kpc above the disk, with a narrow velocity width of only \u03c3 \u223c250 km/s. The radiative cooling cases accelerate more slowly with distance above the disk, with none of the main contour of stripped gas at the ICM velocity at 250 Myr. By 500 Myr after the wind has hit the disk, the radiative cooling cases show a narrow range in their tail velocity distributions, but the case without cooling has a very wide range of velocities, with stripped gas moving at both the ICM velocity and falling back towards the disk (at a height of 150 kpc above the galaxy). The width of the wake in the velocity distribution is a measure of the strength of turbulence seen in the wake. At late times, the radiatively cooled cases have a characteristic width of \u03c3 \u223c700 km/s, while the no-cooling case seems to be more turbulent, with a characteristic width of \u03c3 \u223c1000 km/s. To understand this di\ufb00erence, we turn back to the different morphology of the tails. The important di\ufb00erence between our cooling and no-cooling runs is that radiative cooling forms much more structure in the tail. These dense clumps may be more di\ufb03cult to accelerate and less a\ufb00ected by turbulence, so will not shift laterally into the shadow of the disk. In the no-cooling run, the large variation in the wind velocity has to do with the large eddies that form from the interaction between the stripped gas and ICM, as seen in Roediger & Br\u00a8 uggen (2007) (their Figure 6). These eddies move the gas into the shadow of the disk, where the gas can fall back onto the galaxy. Also, both this work and Roediger & Br\u00a8 uggen (2008) \ufb01nd 8 Fig. 4.\u2014 Contour plots of gas mass at di\ufb00erent velocities parallel to the wind (perpendicular to the disk) for the Tmin = 300 K, Tmin = 8000 K, and no cooling cases (going left to right). The contours are plotted as a function of height above the disk. Again, only gas cells with at least 25% of their mass originating from the galaxy are counted. Very little of the disk gas is accelerated to the ICM wind velocity of 1413 km/s. See section 3.3 for a discussion. that some stripped gas is accelerated to the ICM velocity about 100 kpc downwind of the galaxy (this is true even though Roediger & Bruggen (2008) vary their wind velocity while ours remains constant at 1413 km/s). In addition to looking at the velocity structure of all stripped gas, we can see how di\ufb00erent density gas is affected by the ICM wind, looking for di\ufb00erential stripping and acceleration. In Figure 5, we consider in detail how the velocity in the wind direction is related to gas density. The gas in these contours is between 2 kpc and 50 kpc above the disk. The lower density gas is stripped early to a higher velocity, as shown in the top right, while higher density gas has almost no velocity parallel to the wind because the dense clouds are harder to strip and accelerate. This systematic correlation between density and velocity (di\ufb00erential stripping) has been observed in NGC 4438 with multiwavelength observations (Vollmer et al. 2009). There is a similar e\ufb00ect in the no cooling case (not shown), but it has a somewhat di\ufb00erent origin: it is caused by the exponentially declining density distribution in the disk. The gas density decreases towards the edge of the disk, which is the only part of the disk stripped by the wind. Later, as shown in the right panel of Figure 5, even higher density gas is eventually accelerated by the wind, although it does not reach the velocities of the lower density gas. This gradual acceleration of denser material with time is not seen in the no cooling run, again because only the lower density gas at the edges is ever stripped. The di\ufb00erential velocity as a function of gas density is seen throughout the tail in all of our runs. It is also notable that negative velocities, denoting gas falling back onto the disk, are more often seen in lower density gas in all of our runs. In the no cooling run, this is because 9 Fig. 5.\u2014 Contour plots of gas mass at di\ufb00erent velocities parallel to the wind (or perpendicular to the disk) for the Tmin = 8000 K case. The contours are plotted as a function of gas density. Again, only gas cells with at least 25% of their mass originating from the galaxy are counted, and we only include gas between 2 and 50 kpc above the disk. We can see di\ufb00erential stripping and acceleration. See section 3.3 for discussion. there is only low density gas in the tail. In the cooling cases, this may be because only the lower density gas can be moved into the shadow of the disk by turbulence. This result di\ufb00ers from Kapferer et al. (2009), who \ufb01nd that dense H I gas falls back onto the disk. Kapferer et al. (2009) are not the only ones to predict gas re-accretion (e.g. Vollmer et al. 2001; Roediger & Br\u00a8 uggen 2007), although it has not been clearly observed. We can now compare our simulations to observations. The stripped gas moving more slowly than the ICM wind, at 900 km/s, is marginally consistent with (although somewhat larger than) the observations of Oosterloo & van Gorkom (2005), who \ufb01nd the gas from the galaxy is only accelerated by 550 km/s, not the 1500 km/s the authors estimate as the galaxy velocity. However, if we consider the gas velocity 120 kpc above the disk, it is closer to 700 km/s. Also, recall that the contours in Figure 4 include gas at all densities. From Figure 5, we see that higher density gas moves more slowly than lower density gas. In fact, at any height above the disk, gas with densities greater than about 0.1 cm\u22123 moves more slowly than 900 km/s, and is frequently centered at about 500 km/s. This puts our results into good agreement with the observations of Oosterloo & van Gorkom (2005). 4. COMPARISON TO OBSERVATIONS 4.1. H I In this section we consider H I column density, comparing projections of our simulations to observations. We use recent deep observations (Chung et al. 2007; Oosterloo & van Gorkom 2005) to select the minimum observable column density of H I to be 1019 cm\u22122. As discussed in Section 2.4, we use Cloudy to determine the neutral fraction given a temperature and density and then apply that value in our projection routine. At the resolution of our simulation, we \ufb01nd gas with high column densities at very large distances from the galaxy, and for a long time after stripping begins (see Figure 6). The individual H I clouds frequently have a head-tail structure, indicating Kelvin-Helmholtz stripping, and indeed the gas clumps are largely shredded in the tail, losing their coherency. This di\ufb00ers from Kapferer et al. (2009), who found that Kelvin-Helmholtz stripping does not a\ufb00ect the cool clouds in their stripped tails (note that Agertz et al. (2007) have recently argued that SPH has di\ufb03culty following the Kelvin-Helmholtz and Rayleight-Taylor instabilities). There is a gap between the galaxy and region with the most H I gas at later times. Oosterloo & van Gorkom (2005) also observe a gap in H I column density in the long tail from NGC 4388. Figure 6 is the H I map from the Tmin = 8000 K run. The di\ufb00erence between the Tmin = 8000 K and Tmin = 300 K runs (not shown) is minor, similar to the density distribution (see Figure 1). The Tmin = 300 K run generally has a few more clouds, with slightly higher H I densities, where the total gas surface density is highest. The gap seen in the Tmin = 8000 K run is at the same height above the disk, but smaller in the Tmin = 300 K run. At late times (600 Myr after the wind has hit the galaxy), the width of the H I tails is about the same in the two runs, less than 40 kpc wide, and there is a paucity of high surface density clouds in both runs. The observations in Figure 6 are at unrealistically high resolution, even for H I interferometric maps. We can also \u201cobserve\u201d our simulation by smoothing to lower resolutions, like those in typical observations; this is done in Figure 7. The \ufb01rst panel has a resolution of 1.2 kpc, similar to the observations of Chung et al. 2007. The middle panel has a resolution of 1.4 kpc \u00d7 7.4 kpc (to compare with Oosterloo & van Gorkom 2005), and the right panel has a resolution of 43 kpc (to compare with Vollmer & Huchtmeier 2007). As our smoothing size increases we \ufb01nd fewer clouds because some of our high density clouds are small enough that they are smoothed below our threshold column density of 1019 cm\u22122. These three projections are all at 500 Myr after the wind has hit the galaxy, and are all from the Tmin = 8000 K run. As in Figure 6, the lowest contour is at the minimum column density of current observations, 1019 cm\u22122. We begin by comparing our left panel in Figure 7 to the results of Chung et al. (2007), \ufb01nding that our tails are generally longer. However, our tail is from a galaxy that has been stripped for 500 Myr, while the authors argue that the tails they observe are in the early stages of stripping. Indeed, about 50 Myr after the wind hits (see the left panel of Figure 6) our tail is well within 10 Fig. 6.\u2014 The column density of H I gas in the Tmin = 8000 K case shown at the 38 pc resolution of our simulation 100 Myr (left), 250 Myr (center), and 500 Myr (right) after the wind has hit the galaxy. The greyscale shows the log of the column density in units of cm\u22122. The longest tail is again cut o\ufb00at 212 kpc. See Section 4.1 for discussion. the range observed in these outer Virgo cluster galaxies. Also, by examining their Figure 2, we see that the estimated ram pressures of all but one of the observed galaxies are less than our simulated ram pressure, so the tails will lengthen more slowly. Finally, our measured tail length is the actual length, while the tails observed by Chung et al. (2007) are likely to be projected at an angle to the line of sight. Next, we compare our results to the observations of Oosterloo & van Gorkom (2005), who observe an H I tail 110 \u00d7 25 kpc in size, and estimate the tail to be a few hundred Myr old. See the central panel in Figure 7. In either of our cooling cases, we can observe tails longer than this one 500 Myr after the wind has hit the galaxy. Interestingly, in the central panel, there is a gap with no emission, just as is seen in the tail of NGC 4388. The range of surface densities in the tail in this panel are similar to those found by Oosterloo & van Gorkom (2005), although our maximum H I surface density is about a factor of two less than they observe. In the Tmin = 300 K case at this resolution, there is a clump with a surface density above 3 \u00d7 1020 cm\u22122, the starforming lower limit, 200 kpc from the disk 500 Myr after the wind has hit. This tail of H I clouds would not have been found by Vollmer & Hutchmeier (2007), as we show in the right panel of Figure 7. At this very low resolution of about 43 kpc, only the more distant gas in the tail is observable, and is more distant from the galaxy than the \u223c60 kpc search radius adopted in that paper. We \ufb01nd that the ability of the gas to radiatively cool is vital to the existence H I tails. As we discuss in Section 3.2, as long as radiative cooling in the stripped gas is more e\ufb03cient than adiabatic and turbulent heating, H I clouds will exist in our simulated tails. If heat conduction is also not e\ufb03cient enough to counteract radiative cooling, long H I tails consisting of dense clouds should be fairly common. In both of the cooling runs, the tail has clouds that are above the column density of disk gas that is associated with star formation, 3 \u00d7 1020 cm\u22122 (Schaye 2004). If these clouds could form stars, ram pressure stripped gas could result in the trails of \u201c\ufb01reballs\u201d observed by Yoshida et al. (2008) in RB 199. 4.2. H\u03b1 Next, we turn to H\u03b1 emission. The minimum observable surface brightness that we use for H\u03b1 emission is 2 \u00d7 10\u221218 erg s\u22121 cm\u22122 arcsec\u22122 (see Sun et al. (2007) and references therein). Similar to our calculation of hydrogen neutral fraction, we use Cloudy to determine the H\u03b1 emissivity given the gas temperature and density. We \ufb01nd, as shown in Figure 8, highly structured, long tails of H\u03b1 emission. Note that we do not include UV radiation from star formation or AGN (except for the metagalactic background, as described in section 2.4). The H\u03b1 emission roughly follows the H I column density, which is likely where the gas is densest and where competition between compressive and turbulent heating and radiative cooling is taking place, as discussed in Section 3.2. The Tmin = 8000 K case shows signi\ufb01cantly more H\u03b1 11 Fig. 7.\u2014 The column density of H I gas observed at a resolution of 1.2 kpc (to compare with Chung et al. 2007), 1.4 kpc \u00d7 7.4 kpc (to compare with Oosterloo & van Gorkom 2005), and 43 kpc (to compare with Vollmer & Hutchmeier 2007). These projections are 500 Myr after the wind has hit the galaxy for the standard case with cooling to 8000 K. The greyscale shows the log of the column density in units of cm\u22122. We add a red contour to the left panel, denoting a column density of 3 \u00d7 1020 cm\u22122, a lower limit for the column density of gas associated with star formation (Schaye 2004). emission than the Tmin = 300 K run, which is due to two reasons: \ufb01rst, the gas is kept close to the temperature where collisional excitation can result in emission. The other di\ufb00erence is that in the Tmin = 300 K simulation, much of the gas is at higher densities, where it is optically thick to the metagalactic ionizing background and so produces little H\u03b1 emission (and it is not hot enough to emit due to collisional excitation). Turning to observations, it is important to note that many of the observations of H\u03b1 emission are closely linked to star formation or AGN activity in a galaxy (which we do not include in the simulations). However, in the case of NGC 4438 (Kenney et al. 2008), the emission is not close to either of these ionizing sources. The brightness of the \ufb01laments matches well with the H\u03b1 emission in our simulation with radiative cooling to 8000 K, with the lowest observed surface brightness emission at the level of our third contour. The overall \ufb01lamentary structure and large gaps between emission regions in our projected H\u03b1 emission also matches the observations of Kenney et al. (2008). Gavazzi et al. (2001) see emission slightly above the brightness of our third contour, although it is di\ufb03cult to discern the structure of the observed tails. They consider it likely that the gas was ionized within the galaxy and has remained ionized in the tail, although they do not rule out heating within the tail. We believe that turbulent and adiabatic heating of stripped cool gas causes much of the emission we observe in our projections, because of the close alignment of the H I and H\u03b1 emitting gas added to our earlier discussion of di\ufb00erential acceleration (Section 3.3). As discussed in section 2.4, we computed our H I and H\u03b1 maps using Cloudy, assuming a typical cloud thickness of 100 pc, which is appropriate for our resolution. To explore our sensitivity to this assumption, we also generated maps based on cloud size of 10 pc (the \u2018thin\u2019 case), and 1000 pc (the \u2018thick\u2019 case). The thick case is very similar to our standard 100 pc cloud size, with slightly more H I in both of our cooling runs. In the Tmin = 8000 K run, the H\u03b1 emission is nearly identical, possibly because collisional excitation dominates the emission. In the Tmin = 300 K run, the thicker clouds emit a little less H\u03b1 at our lowest observable brightness \u2013 although the second contour level is nearly identical. 12 Fig. 8.\u2014 The H\u03b1 surface brightness contours that could be observed using current observational depths (Sun et al. 2007). Again, these are for 100 Myr, 250 Myr, and 500 Myr after the wind has hit the galaxy. The left column is the simulation with radiative cooling to 8,000 K and the right side has cooling to 300 K. Note that the H\u03b1 emission is \ufb01lamentary in structure and follows the H I column density. See section 4.2 for discussion. The thin cloud approximation does result in lower H I column densities, but in both of the cooling cases there are still dense clouds at star forming column densities 500 Myr after the wind hits the disk. The H\u03b1 emission is considerably brighter, by about a factor of 8 in the Tmin = 8000 K run. However, in the Tmin = 300 K run, the emission is much brighter, frequently by a factor of about 16. Another concern is that, by using Cloudy in this way to generate our emissivities, we are assuming ionization equilibrium. Given the short cooling time, it is possible to be out of equilibrium which could systematically bias the emission. To check how robust this approximation is, we used the simulation which followed the nonequilibrium ionization fractions of H and He. We computed the emissivity two ways: \ufb01rst, with our standard Cloudy procedure which uses only the total density and temperature of the gas, and second, based on the actual ionization fractions predicted in the simulations based on a set of analytic \ufb01ts to the H\u03b1 emissivity due to recombination (Spitzer 1978), and the H\u03b1 emission due to collisional excitation (Osterbrock 1989). We found that both methods produced very similar H\u03b1 maps (although note that this run did not include cooling below T = 104 K). 4.3. X-ray Finally, we turn to X-ray emission. As noted in the introduction, only a few X-ray tails are known. We show predicted X-ray images in the 0.5-2 keV band in Figure 9. None of the contours are bright enough to be observed assuming an observational limit of 5 \u00d7 10\u22126 erg s\u22121 cm\u22122 (based on the luminosity and surface area of the tail in Sun et al. 2006). A bow shock is visible early in the simulations, but most of the emission comes from gas in the wake. Lowering the radiative cooling \ufb02oor to 300 K does not e\ufb00ect the X-ray surface brightness substantially. There are a number of possible di\ufb00erence between our simulation and the X-ray observations of tails. First, since we do not include energetic feedback from supernovae, the gas in the tail that originated from the galaxy could not have been heated by supernovae explosions, as suggested by Sun & Vikhlinin (2005). However, in the case of ESO 137-001, Sun et al. (2006) conclude that the X-ray emission they observe is from mixing of the cool galactic gas with the hot ICM. This type of heating leading to X-ray emission could in fact be happening in our simulation, but just does not lead to observable emission. The ICM in our simulation is about 60% of the temperature and a third of the density of the ICM in A3627. Our galaxy velocity is 1.4 times larger than the estimated velocity of ESO 137-001, so our ram pressure is 63% as large as that experienced by the observed galaxy. However, at a distance of 200 kpc from the cluster center, a galaxy velocity of 2000 km/s is much more likely (Tonnesen & Bryan 2008), which results in our ram pressure being only 16% of that experienced by ESO 137-001. Based on their \ufb01ts, the authors predict an X-ray tail temperature of 9\u00d7106 K and a density of 10\u221226 g cm\u22123. We have no tail gas from our galaxy in any of our simulations at that temperature and density. However, if we shift our contour plots in Figure 2 by the ratio of the ICM pressure of A3627 and our simulated cluster, a small amount of gas is at the required density and temperature. This suggests that the ICM conditions may be important for producing X-ray bright tails. 5. DISCUSSION As we have demonstrated in the previous section, our stripping simulations with cooling result in very di\ufb00erent wakes than in runs without cooling. This impacts both 13 Fig. 9.\u2014 The predicted X-ray surface brightness in the 0.5-2 keV band for the Tmin = 8000 K run at 100 Myr, 250 Myr and 500 Myr after the wind has hit. Note that none of the gas in the tail is bright enough to be observed at current observational limits. the morphology of the tail, the density and temperature structure of the gas, and the observational diagnostics. In this section, we begin by discussing one point which we have noted throughout: the di\ufb00erences between the Tmin = 8000 K and Tmin = 300 K simulations. Then we investigate the e\ufb00ect of resolution and \ufb01nally turn to a discussion of the physical mechanisms which we do not include in this simulation. 5.1. Radiative Cooling Floor As noted earlier, we used two di\ufb00erent values for our radiative cooling \ufb02oor (8000 K and 300 K) in order to explore in a simple way the potential impact of processes which we do not include in the simulation. We found that most of our predictions are insensitive to this parameter, which gives us con\ufb01dence in our results. However, there were some di\ufb00erences between the runs. This included the detailed density-temperature structure of gas in the tail (at the low-T end). The biggest di\ufb00erence was the amount of H\u03b1 emission, and the survival of H I clouds, with Tmin = 300 K predicting longer lived clouds and less H\u03b1 emission. It is unclear which Tmin value is preferable. Because of the lower Jeans length in the lower temperature \ufb02oor runs, we resolve the resulting fragmentation less well in the run with a minimum temperature of 300 K. Although the Tmin = 300 K run is desirable because it allows for the existence of the low temperatures that are found in the ISM, it is not clear if this run is physically more realistic as we do not include some e\ufb00ects such as smallscale turbulence, cosmic rays and magnetic \ufb01elds, all of which may provide a source of e\ufb00ective pressure in low temperature regions. 5.2. Resolution We now discuss the impact of resolution on our results. To do this, we can compare our standard simulations with runs with lower mass resolution, resulting in less re\ufb01nement in the tail. With either re\ufb01nement criteria, the gas in the disk is mostly re\ufb01ned to a resolution of 38 pc when the winds hits the disk, but in the case of more mass re\ufb01nement, the disk fragmentation is better resolved, resulting in a larger number of lower mass clumps. This a\ufb00ects the evolution of the disk. In our radiatively cooled cases, the gas fragments from the edge inward. With lower mass resolution, the resulting clouds are more massive and can perturb the inner disk, causing fragmentation and the formation of overand underdense regions. In contrast, in the highly resolved cases that we discuss in this paper, the disk has fewer holes in the central disk, and therefore stripping does not occur in the central 7 kpc. Also, stripping occurs more slowly, although a slightly larger amount of gas is stripped from the galaxy (this is very similar to our discussion regarding the case with cooling to 300 K in TB09). With the lower mass resolution run, most of the gas in the tail is re\ufb01ned to either 304 pc or 152 pc, and none of the tail is re\ufb01ned to 38 pc. This is in contrast to the more re\ufb01ned tail, in which most of the gas is re\ufb01ned to either 152 pc or 76 pc, and there are a number of small areas re\ufb01ned to 38 pc. We go through our results discussed in this paper, highlighting the similarities and di\ufb00erences of di\ufb00erent resolution runs. The morphology of the stripped gas di\ufb00ers early in 14 the stripping process, but by 500 Myr after the wind has hit the galaxy, the stripped gas looks very similar. In Figure 10 we show the most di\ufb00erent projection of either of our comparison sets of runs (Tmin = 8000 K and Tmin = 300 K), using the Tmin = 8000 K cases at 250 Myr after the wind has hit the galaxy. The lower mass resolution case has fewer dense clouds at the edges of the disk, so most of that gas is quickly stripped. However, the higher resolution run has a slightly longer tail because the very low density gas in that run has been accelerated more quickly to larger distances. The galaxies with more re\ufb01nement have more and smaller clouds in the tail, as expected. The gas density and temperature distributions are very similar. Although the gas distribution remains similar, at late times the runs with lower resolution in the tail have less high density gas and a slightly lower maximum density. This is because clouds do not condense to as small sizes in the lower resolution tail. The tail velocity pro\ufb01les are also very similar, with similar widths and the same maximum velocities reached at the same distance from the galactic disk. All radiatively cooled runs have a consistent velocity width over time. There is also some fallback onto the disk in the lower resolution run, because larger gas clouds in the disk cause fragmentation in the central regions and therefore also result in gas stripping in those regions. This centrally stripped gas can then be protected by disk gas that is rotating or that moves to \ufb01ll the center of the disk (discussed in detail in TB09), and will be shielded from the stripping wind. This protection allows even more dense gas to have slightly negative velocities in the lower resolution cases. Thus, the gas punching through the bottom of the disk in our lower resolution runs and in the Kapferer et al. (2009) simulations may be resolution dependent. The H I maps are somewhat di\ufb00erent, again because of the increased fragmentation in our highly resolved tails. Compare the two projections in Figure 11 to the \ufb01rst panel in Figure 7. We \ufb01nd that the Tmin = 300 K run produces more H I in our maps than the Tmin = 8000 K run, a more marked di\ufb00erence than in our standard high mass resolution runs. This is because when we use the more stringent mass criterium to resolve the tail, only the lower cooling \ufb02oor creates high density clouds that are above our re\ufb01nement threshold and therefore more highly resolved. The H I tails are generally shorter, and the Tmin = 8000 K run has much less gas at large distances in the tail. Also, both cooling \ufb02oors have tails that are more connected to the disk in the lower resolution runs. This occurs for two reasons: \ufb01rst, the tail is shorter because the gas is less dense and is more easily heated by the turbulence in the tail. Second, gas can be stripped from the central region of the disk and then protected by rotating or in\ufb02owing disk gas. Therefore, gas that is immediately behind the disk may be protected from the wind and can survive there for longer. H\u03b1 emission is largely una\ufb00ected, because the same type of turbulence exists in the di\ufb00erent resolution cases despite the di\ufb00erence in size of the dense clouds. The interaction of the slower moving dense clouds with the faster low density wind still causes small scale turbulence that can heat the nearby gas. The di\ufb00erence in resolution does not change the brightness of the emission because the temperatures are the same, resulting in Fig. 10.\u2014 Contour plots of total gas surface density, comparing two Tmin = 8000 K cases with di\ufb00erent mass resolution 250 Myr after the wind has hit. The left \ufb01gure is our standard high resolution run, and the right is the lower mass resolution run. Because there is less gas clumping in the disk, especially in the outer regions, the lower resolution run has a smaller remaining disk. There is more fallback in the lower resolution run, resulting in some of the gas punching back through the disk. Although the dense clouds in either case are close to the same distance above the disk, the less dense gas has clearly been accelerated more quickly from the more highly re\ufb01ned disk. similar amounts of collisional excitation. If the di\ufb00erence in clouds sizes were enough to greatly a\ufb00ect the optical depth of the clouds, H\u03b1 emission would decrease. The main di\ufb00erence is the distribution of emission, which follows the H I clouds in the tail in any run. Therefore, as with the H I gas, the H\u03b1 emission is closer to the disk. As we discussed above, the cooling \ufb02oor has a much larger e\ufb00ect. The X-ray emission is a\ufb00ected very little. As we discussed in Section 4.3, the surrounding ICM pressure likely needs to increase for X-ray emission to be observable. In summary, the di\ufb00erent results caused by using different resolutions can be attributed to two main causes. First, and most importantly, less resolution in the tail results in less fragmentation to smaller dense clouds (although there is more fragmentation in the Tmin = 300 K run than in the Tmin = 8000 K run). Second, gas stripped from the galactic center can be protected by shadows from the wind by the remaining disk gas, and fall back towards the disk. 5.3. Heat Conduction Heat conduction could be important for the survival of cool clouds in the ICM and for H\u03b1 emission. If heat conduction is an e\ufb03cient way to transport heat from the ICM to cold, stripped gas, then the survival time of H I clouds would be less than predicted in this paper, and the length of the tails would be shorter. The fact that the length of our tails matches observations of either shorter 15 Fig. 11.\u2014 Contour plots of H I gas column density at 1.2 kpc resolution, comparing the two lower mass resolution runs with radiative cooling. These are both projected 500 Myr after the wind has hit the galaxy, and can be compared to the left panel of Figure 7. Tmin = 8000 K is on the left, and Tmin = 300 K is on the right. Notice that there is more dense gas closer to the disk. As we discuss in Section 5.2, centrally stripped gas is able to sit in the protected lee of the disk, and dense gas does not survive as far from the disk because it does not collapse into as small dense clouds. There is more dense gas in the Tmin = 300 K case because the lower cooling \ufb02oor results in smaller clouds. tails by Chung et al. (2007) for our Tmin = 8000 K case, or long tails like that observed by Oosterloo & van Gorkom (2005) using the Tmin = 300 K simulation, argues against a strong role for heat conduction, at least for the current conditions. We can perform an estimate of the evaporation time for a typical cloud if heat conduction is not suppressed. We follow Cowie & McKee (1977), as in Vollmer et al. (2001). In our clouds, we \ufb01nd that the mean free path for ions is comparable to or greater than the temperature scale length, so we need to use the saturated heat \ufb02ux equations. Solving for the evaporation time, we \ufb01nd that using a cloud radius of 100 pc, and a number density of about 0.1 cm\u22123, tevap \u223c6 \u00d7 105 years. However, this time can be lengthened if there are magnetic \ufb01elds perpendicular to the temperature gradient (Cowie & McKee 1977; Cox 1979). Vollmer et al (2001) argue that magnetic \ufb01elds could increase the evaporation time by nearly an order of magnitude, although the actual value is highly uncertain. Although McKee & Cowie (1977) predict that a cloud in our modeled ICM would be evaporated before being radiatively cooled, the cooling time for a cloud of density 0.1 cm\u22123 and temperature 105 K is 106 years. A higher density shortens the cooling time and lengthens the evaporation time, so radiative cooling may also slow down the e\ufb00ects of heat conduction. 5.4. Magnetic Fields Our simulation does not include magnetic \ufb01elds or cosmic rays. In general in the Milky Way, the magnetic \ufb01eld is measured to be about 2-3 \u00b5G (Men et al 2008). However, there are measurements of the magnetic \ufb01eld in molecular clouds (Crutcher 1991 and references therein) of up to 103 \u00b5G. If some of the denser clouds we see in the tails in our simulations had strong magnetic \ufb01elds, these \ufb01elds could protect the clouds from ablation while they move through the wind, in addition to lowering the e\ufb03ciency of heat conduction. We do not know to what extent magnetic \ufb01elds could counteract turbulent heating and ablation of stripped clouds because we do not know the amount of structural support magnetic \ufb01elds would give stripped clouds. The \ufb01rst long stripped tails were observed in radio continuum, with stretched magnetic \ufb01eld lines downstream of the galaxy (Gavazzi et al. 1995). Including magnetic \ufb01elds in our simulation would likely also result in radio continuum emission (assuming a cosmic ray population was also stripped), although because our ram pressure is less than the ram pressure estimated to be a\ufb00ecting the three galaxies in A 1367, the magnetic \ufb01elds would be stretched less. 5.5. Star Formation A molecular cloud may survive between a few and a few tens of Myr (Blitz & Shu 1980; Larson 2003; Hartmann 2003). Because we do not include star formation, our dense clouds of gas do not evolve into less dense gas that could be stripped. If our dense regions of gas could turn into low density regions through star formation (\u03c1 \u2264 10\u221223 g cm\u22123), our galaxies that include radiative cooling could be entirely stripped of gas over the lifetime of the dense clouds. This could result in a tail without a gap between the majority of the stripped gas and the galactic disk. We \ufb01nd that overdensities in the stripped tails can survive to large distances, however, our projections also show that they are being ablated by the ICM wind. Our next step is to add star formation, which could a\ufb00ect stripping in a number of ways. Ram pressure could induce star formation in the disk, using up disk gas and resulting in lower mass tails and fewer dense clouds in the tail. If there are dense clouds in the tail, we will discover whether stars can form in stripped gas, or if Kelvin16 Helmholtz stripping will destroy clouds before they can collapse. 6. CONCLUSIONS We have run detailed galaxy simulations including radiative cooling to understand the morphology of and emission from gas tails stripped by ram pressure in a cluster environment. We compare three cases: a run without cooling, one with cooling to a minimum temperature \ufb02oor of Tmin = 8000 K to approximately account for non-thermal pressure support, and one to Tmin = 300 K. Our main conclusions are as follows: 1. Including radiative cooling creates a clumpy ISM, which results in faster stripping of lower density gas, and the production of longer tails. A clumpy disk also has more holes for the ICM wind to pass through, which results in signi\ufb01cantly less \ufb02aring in the stripped material, and narrower tails in the cooling runs, in better agreement with observed tails (e.g. Chung et al. 2007). 2. We \ufb01nd that the clumpy ISM also produces a much wider range of densities and temperatures in the wake, resulting in a very di\ufb00erent morphology for the tail. Although the stripped gas is mostly at the ICM pressure, it shows a wider distribution in pressure, as well as a systematic deviation from the constant pressure line for temperatures below T = 105 K, due to radiative cooling operating more quickly than compressive heating. 3. The stripped gas in the cases with radiative cooling does not accelerate to the ICM wind speed. This is likely because the dense clumps are harder to accelerate than a smooth distribution of gas. Also, the gas is di\ufb00erentially stripped and di\ufb00erentially accelerated through the whole length of the tail for the duration of the simulation. 4. We compute realistic H I maps of our tails and compare to H I observations of stripped tails. With either a radiative cooling \ufb02oor of 8000 K or one of 300 K we \ufb01nd H I tails with long lifetimes (more than 500 Myr), and large lengths (well over 100 kpc). When we consider our run with cooling to 300 K, we \ufb01nd that the tails are longer and clouds can survive at high density for a longer time. Most tails that have been observed in Virgo have shorter lengths, like our tails at very early times, however, many of these tails seem to be in the early stages of stripping (as in Chung et al. 2007), and may have only experienced a short amount of time at large ram pressure (see the orbits in Vollmer et al. 2001). The few longer tails that have been observed are well matched by our results at late times in the cooling runs. 5. We can also map the H\u03b1 emission from our runs, and \ufb01nd \ufb01lamentary structures much like those found in deep observations of stripped tails (e.g. Sun et al. 2007). Both the Tmin = 8000 K and the Tmin = 300 K case emit in H\u03b1, but the simulation with the higher cooling \ufb02oor has more emission and a higher maximum surface brightness in the tail. The \ufb01lamentary structure in either radiative cooling run reproduces the observations of the H\u03b1 tail of NGC 4438 (Kenney et al. 2008), while the Tmin = 8000 K run has some emission that is bright enough to be observed at the Kenney et al. (2008) limit. This H\u03b1 emitting gas is near the H I gas, indicating that it is created in the tail rather than surviving as H\u03b1 emitting gas stripped from the disk. 6. None of the simulated tails have X-ray surface brightnesses high enough to match observations of X-ray tails (note that some observed H I or H\u03b1 tails also do not show X-ray emission). This may either be because we do not preheat the galactic gas with supernovae explosions, or that our ICM is not hot and dense enough for mixing to cause bright X-ray emission. It is clear from our results that adding radiative cooling greatly improves the realism of simulated tails. This is seen by comparing both the morphology and velocity structure of the simulated tails to observations. We \ufb01nd, as in observations, that there are only two types of bright emission from our tail: in our case H I and H\u03b1 emission. It remains to be discovered whether all three types of emission can be at observable levels in a single tail or if the environment necessary for X-ray emission would destroy or heat the cooler clouds. However, we can use our results and a few analytic estimates to make an initial guess: if our ICM had the same pressure as that of A3627 we would likely have some gas in our tail with the necessary density and temperature for detectable X-ray emission (see Section 4.3). At the same time, it may be that heating from compression or turbulence would still not be enough to heat clouds faster than they would be radiatively cooled, so we might still see H I in the tail. Finally, H\u03b1 emission should be present as long as there is some intermediate density gas (near T \u223c104 K), so it may not be greatly a\ufb00ected by the ICM pressure. To complete our comparison to the case of ESO 137-001, we have a lower ram pressure than that a\ufb00ecting the observed galaxy, and Sun et al. (2007) \ufb01nd that the ram pressure is likely to have triggered star formation throughout the disk. This may have heated the cool gas clouds surrounding the star forming regions so much less cool gas was left to be stripped. As we discuss in Section 5.5, we intend to add a star formation prescription to a future simulation, which will allow for a better understanding of how star formation can a\ufb00ect the gas tail. The H I column density projections indicate that higher resolution observations (similar to that of Chung et al. 2007) of cluster galaxies would \ufb01nd more massive tails. The fact that the H I tails can have large gaps between the higher column density regions means that there could be tails that would not have been found by Vollmer & Hutchmeier (2007), and points to a need for large surveys at the highest possible resolution. Our simulations predict that only slightly deeper observations of tails in H\u03b1 should reap great rewards of much more structure. It is interesting that although less dense gas moves more quickly than the dense gas throughout the tail, the emission from H\u03b1 is nearly perfectly aligned with the H I column density, indicating that gas in our simulations is heated to H\u03b1 emitting temperatures insitu, rather than being stripped while ionized and surviving for hundreds of Myr. We can consider what observational signatures of ram pressure stripping our simulations predict are likely. We \ufb01nd dense H I clouds can survive far from the disk and for a signi\ufb01cant amount of time. This means that in order to determine that any H I structure is not surviving stripped gas, other information such as kinematic data indicating rotation, is necessary (as in Haynes et al. 2007). In addition, H\u03b1 emission can be observably bright even without in-situ star formation. However, the high column densities of some of the H I clouds leads us 17 to believe that stripped gas can condense to form stars that could be formed far from the galaxy, indicating that even a stellar component in a stripped tail is not enough to prove that a gravitational interaction took place. The high resolution combined with the addition of radiative cooling in our simulation allows us to follow the interaction of dense cool clouds in the tail with the hot gas of the ICM. Unlike some previous work, we \ufb01nd ablation and destruction of the clouds are important, as they move within the wind, limiting their survival to less than found by Kapferer et al. (2009). It is important to reiterate that because it is di\ufb03cult to make a physical case for either cooling \ufb02oor, we present both 8000 K and 300 K cooling \ufb02oors. Although many of the main results about the tail attributes are very similar between the two cases, they do result in meaningfully di\ufb00erent observable pro\ufb01les in H\u03b1. Finally, although these simulations are arguably the most realistic stripping simulations performed to date, we have discussed in detail the limitations involved in our work in \u00a75. We acknowledge support from NSF grants AST-0507161, AST-05-47823, and AST-06-06959, as well as computational resources from the National Center for Supercomputing Applications. We thank Jacqueline van Gorkom, Je\ufb00Kenney and other members of the Virgo group for useful discussions, as well as Elizabeth Tasker for invaluable help setting up the initial conditions.",
                    "introduction": "1. Galaxies orbiting within a cluster may undergo a num- ber of interactions that are speci\ufb01c to dense environ- ments. These include interactions between intracluster gas and the galaxy, such as ram pressure stripping and starvation, interactions between pairs of galaxies, such as harassment, and interactions between the galaxy and the cluster gravitational potential, such as tidal strip- ping. The relative importance of these various mecha- nisms in transforming galaxy morphology, color, and gas content has been the subject of much debate, with large surveys helping to disentangle the various drivers (e.g. Moran et al 2007; van den Bosch et al. 2008). An alter- native way to gauge their relative importance, and to get a deeper understanding of the processes themselves, is to look for observational signs of the di\ufb00erent interactions. This has been attempted recently in the context of ram pressure stripping (Vollmer & Hutchmeier 2007). One di\ufb03culty with this approach is relating the speci\ufb01c ob- servations to the underlying mechanism: how long does a given signature last and what does it tell us about the physical conditions in the galaxy and cluster? In this pa- per, we will use high-resolution numerical simulations of ram pressure stripping (RPS) to better understand the properties and fate of gas stripped during the encounter, and to predict and interpret observational signatures of RPS. The ram pressure of the ICM can strip gas from a galaxy moving at typical cluster velocities (Gunn & Gott 1972), transforming a gas rich spiral to a gas poor S0. In addition, the galaxy ISM can be compressed, enhanc- ing the star formation rate (Byrd & Valtonen 1990; Fu- jita & Nagashima 1999). The ICM can also remove the loosely bound reservoir of gas that accretes onto a galaxy, thus slowly starving it of new fuel to form stars (Larson et al. 1980). In an earlier work (Tonnesen, Bryan & van Gorkom 2007), we studied cluster galaxies that had formed and evolved in a cosmological simulation, using an adaptive mesh re\ufb01nement (AMR) code to highly re- solve a single cluster. The simulation included radiative cooling and star formation, and allowed us to predict the- oretically how infalling galaxies lose their gas. We found evidence for both starvation and stripping e\ufb00ects, show- ing that most galaxies that lost their gas did so without losing stellar mass, an indication that ram pressure strip- ping was an e\ufb00ective evolutionary mechanism. Observationally, a number of studies point to ram pres- sure stripping as a common environmental interaction. Spirals in the center of the Virgo cluster have smaller H I disks than stellar disks, indicating an interaction that does not a\ufb00ect the stellar component of galaxies (Cay- atte et al. 1990; Warmels 1988). Studies of H I de\ufb01ciency have shown that galaxies in clusters have less neutral hy- drogen than their counterparts in the \ufb01eld (see the review by Haynes et al. 1984). Solanes et al. (2001) studied H I de\ufb01ciency in a sample of 18 cluster regions, and found that H I de\ufb01ciency decreases smoothly out to large pro- jected distances from cluster centers. However, the \ufb01rst sightings of head-tail structures in late-type galaxies were radio continuum observations of three galaxies in A1367 (Gavazzi & Ja\ufb00e 1987). The discovery of these tails, with a maximum length of 30 kpc, was followed up in both H I and H\u03b1 (Sullivan et al. 1981; Gavazzi 1989; Dickey & Gavazzi 1991; Gavazzi et al. 1995). Observations of dis- placed H I within the optical disk in the direction of the radio continuum tails and H II regions at the edge of the \u201chead\u201d of the galaxy supported a ram pressure stripping scenario. In a recent, more sensitive and more highly resolved H I imaging study of Virgo, Chung et al. (2007) found a number of one-sided H I tails pointing away from the cluster center (tail lengths between 13 and 32 kpc). These galaxies are likely falling in for the \ufb01rst time and gas is already being removed at large projected distances 2 from the cluster center. In addition, detailed investiga- tions of a few individual galaxies using multiple wave- lengths have begun to unravel their probable histories (e.g. Crowl et al. 2005; Chung et al. 2005). For exam- ple, observations of NGC 4522 indicate that the galaxy is undergoing ram pressure stripping, although it is out- side of the high density ICM (Kenney, van Gorkom, & Vollmer 2004). All of these observations indicate that ram pressure stripping does occur within the cluster en- vironment at a range of distances from the cluster center. Recent deep observations of clusters have revealed very long gas tails in H I (Oosterloo & van Gorkom 2005; Koopmann et al. 2008, Haynes et al. 2007). Oosterloo & van Gorkom \ufb01nd that the \u223c120 kpc tail of NGC 4388 in the Virgo cluster is well explained by ram pressure stripping. However, Koopmann et al. (2008) hesitate to attribute the tail of the Virgo pair NGC 4532/DDO 137 to ram pressure stripping because it is more than 1.5 times farther from the cluster center than any other H I tail in the Virgo cluster, and at 500 kpc is an order of magnitude longer than those found in the simulations of ram pressure stripping by Roediger & Br\u00a8 uggen (2008) and those observed by Chung et al. (2007). Haynes et al. (2007) also observed a tail that is distant from the cluster center, and used the velocity distribution of the gas in the tail to conclude that the tail associated with NGC 4254 was stripped due to galaxy harassment. The simulation by Duc & Bournaud (2008) shows that a single fast \ufb02yby could have produced the tail. There have also been an increasing number of obser- vations of gas tails in H\u03b1 (Kenney et al. 2008; Gavazzi et al 2001; Yagi et al. 2007; Yoshida et al. 2004a,b; Yoshida et al 2008; Yoshida et al 2002; Sun, Donahue & Voit 2007). The H\u03b1 tails have \ufb01lamentary structure and tend to be narrow. The suspected cause of the H\u03b1 emission varies from case to case. For example, Yoshida et al. (2004a) \ufb01nd that most of the emission near NGC 4388 is from stripped gas that has been ionized by the galaxy\u2019s AGN. Gas heating leading to H\u03b1 emission could also be caused by thermal conduction from the ICM or turbulent shock heating as suggested by both Kenney et al (2008) and Yoshida et al. (2004a,b). In a di\ufb00erent scenario, RB 199 is likely emitting in H\u03b1 due to star for- mation: it is probable that this galaxy has undergone a recent merger, making dense, star-forming gas easier to strip (Yoshida et al 2008). Tails have also been observed in X-rays, frequently op- posite a sharp edge in galactic X-ray emission or a bow shock (Sun et al. 2006; Kim et al. 2008; Irwin & Sarazin 1996; Sun & Vikhlinin 2005; Machacek et al 2006; Wang et al. 2004). Sun & Vikhlinin (2005) conclude that the tail they observe is likely galactic gas that has been heated by supernovae explosions and then removed via Kelvin-Helmholtz stripping. Sun et al. (2006) interpret the tail of the small late-type galaxy ESO 137-001 to be the cool stripped ISM mixed with the hot ICM. Wang et al. (2004) \ufb01nd a long, 88 kpc, tail from a disturbed disk-like galaxy. Like Sun et al. (2006), these authors conclude that it is a mixture of cool stripped gas from the galaxy and the ICM, largely because the X-ray emitting gas in the tail is cooler and denser than the surrounding ICM. Kim et al. (2008) \ufb01nd that the high metallicity of the tail from the large elliptical galaxy NGC 7619 indi- cates that it is gas from the galaxy, but as it is one of the dominant galaxies in its group, it is possible that the tail is actually sloshing of hot halo gas. Whether ram pressure stripping can cause these tails and how they survive in the ICM is unknown. It is un- clear how common long neutral tails are, as Vollmer & Hutchmeier (2007) examined the surrounding \u223c60 kpc around 5 H I de\ufb01cient galaxies in Virgo, and did not \ufb01nd any excess stripped gas. Also, the relationship between the gas tails of di\ufb00erent temperatures is poorly under- stood. In fact, three of the long gas tails mentioned above have been observed in multiple wavelengths. NGC 4388 has a 120 kpc H I tail (Oosterloo & van Gorkom 2005), and an extended emission line region consisting of many faint gas \ufb01laments emitting in H\u03b1 close to the galactic disk (Yoshida et al. 2002; Yoshida et al. 2004a). As dis- cussed above, although this galaxy has an AGN that is heating stripped gas (Yoshida et al. 2004), gas heating leading to H\u03b1 emission could also be caused by ther- mal conduction from the ICM or turbulent shock heat- ing. Another galaxy with multiwavelength emission is ESO 137-001 (Sun et al. 2006; Sun et al. 2007), with a tail detected in both H\u03b1 and X-ray. NGC 4438 also may have a very long tail observed in H\u03b1 (Kenney et al. 2008), while much smaller H I and CO tails have been observed (see Vollmer et. al. 2009 and references therein). Vollmer et al. (2009) found that some of the nearby H\u03b1 emitting gas is spatially coincident with CO gas, while some is not and is moving at higher velocities. There are three possible explanations for this di\ufb00erence in velocities: 1) di\ufb00erential stripping (less dense gas is stripped more e\ufb03ciently from the galactic disk); 2) dif- ferential acceleration (less dense gas is accelerated more quickly by the stripping wind); or 3) a combination of di\ufb00erential stripping and di\ufb00erential acceleration. Simulations focusing on the tails of stripped galax- ies have found somewhat di\ufb00ering results. Roediger & Br\u00a8 uggen (2008), using an adaptive mesh re\ufb01nement hy- drodynamics code, FLASH, \ufb01nd that for most ram pres- sures, observable tail lengths are about 40 kpc, with only three of their 31 tail length measurements having lengths over 80 kpc. However, these simulations did not include radiative cooling. Kapferer et al. (2009), using a smooth particle hydrodynamics code that includes radiative cool- ing and star formation, \ufb01nd that tails can survive with cool, dense clumps (T < 2 \u00d7 105 K) out to well over 100 kpc. In our previous work (Tonnesen & Bryan 2009, from now on TB09), we studied a detailed galaxy simulation that included radiative cooling in order to simulate a multiphase ISM. We found that radiative cooling led to a mixture of high and lower density gas in the disk, and the less dense gas was quickly stripped. The ICM wind was then able to stream through holes in the disk and ablate the surviving dense clouds. This is di\ufb00erent from the scenario without cooling in which galactic gas is only stripped from the edges of the disk and any gas in the shadow of the galaxy is largely protected from the ICM wind. Although we focussed on the remaining gas disk in that paper, we noticed that the stripped tail was highly structured. We found that, although the densest gas clouds, with densities of molecular clouds, were not di- rectly stripped from the galaxy, there was still a lot of structure in the stripped tail, with relatively dense clouds surviving for hundreds of Myr. 3 In this paper, we run a set of high resolution simu- lations (about 40 pc resolution, which is small enough to marginally resolve giant molecular clouds) to under- stand how a multiphase ISM could a\ufb00ect the survival and structure of ram pressure stripped gas. It is im- portant to recognize that we do not attempt to include all of the physics involved in the ISM, focusing on how density \ufb02uctuations that are observed in the multiphase ISM of galaxies can a\ufb00ect gas tails. Following Roediger & Br\u00a8 uggen (2008), we focus on the stripped tails of gas, speci\ufb01cally examining the length, width, and substruc- ture of the tails (see also Roediger, B\u00a8 ruggen & Hoeft 2006). Including radiative cooling allows us to estimate the density of the gas, and emission from H I, H\u03b1, and X- ray gas separately. The questions that we highlight are: can cool gas tails survive in the ICM with turbulence and shock heating of the stripped gas? How can bright H\u03b1 and X-ray emission be induced in a tail of gas? Finally, to what velocities is stripped gas accelerated, and does di\ufb00erential stripping occur in gas disks? The paper is structured as follows. After a brief in- troduction to our methodology, we provide the general characteristics of our simulation (\u00a72.1-3). We introduce the parameters of our speci\ufb01c simulations in \u00a72.4. We then (\u00a73) discuss our results, speci\ufb01cally focusing on the density, temperature, and velocity structure in the gas tail. In \u00a74 we compare our results to observations. We discuss our choice of radiative cooling \ufb02oor and resolu- tion in \u00a75.1-2, and the impact of additional physics to our results in \u00a75.3-5. Finally, we conclude in \u00a76 with a summary of our results and predictions for observers. 2."
                },
                {
                    "url": "http://arxiv.org/abs/0901.2115v1",
                    "title": "Gas Stripping in Simulated Galaxies with a Multiphase ISM",
                    "abstract": "Cluster galaxies moving through the intracluster medium (ICM) are expected to\nlose some of their interstellar medium (ISM) through ISM-ICM interactions. We\nperform high resolution (40 pc) three-dimensional hydrodynamical simulations of\na galaxy undergoing ram pressure stripping including radiative cooling in order\nto investigate stripping of a multiphase medium. The clumpy, multiphase ISM is\nself-consistently produced by the inclusion of radiative cooling, and spans six\norders of magnitude in gas density. We find no large variations in the amount\nof gas lost whether or not cooling is involved, although the gas in the\nmultiphase galaxy is stripped more quickly and to a smaller radius. We also see\nsignificant differences in the morphology of the stripped disks. This occurs\nbecause the multiphase medium naturally includes high density clouds set inside\nregions of lower density. We find that the lower density gas is stripped\nquickly from any radius of the galaxy, and the higher density gas can then be\nablated. If high density clouds survive, through interaction with the ICM they\nlose enough angular momentum to drift towards the center of the galaxy where\nthey are no longer stripped. Finally, we find that low ram pressure values\ncompress gas into high density clouds that could lead to enhanced star\nformation, while high ram pressure leads to a smaller amount of high-density\ngas.",
                    "authors": "Stephanie Tonnesen, Greg L. Bryan",
                    "published": "2009-01-14",
                    "updated": "2009-01-14",
                    "primary_cat": "astro-ph.GA",
                    "cats": [
                        "astro-ph.GA"
                    ],
                    "main_content": "2.1. Simulation We have simulated a galaxy using the adaptive mesh refinement (AMR) code Enzo. Although this code can follow stellar and dark matter particles, we chose to use a fixed stellar and dark matter potential for ease of computation, although the self-gravity of the gas is selfconsistently computed. To follow the gas, we employ an adaptive mesh for solving the fluid equations including gravity (Bryan 1999; Norman & Bryan 1999; O\u2019Shea et al. 2004). The code begins with a fixed, static grid and automatically adds refined grids as required in order to resolve important features in the flow as defined by enhancements in the gas density. The simulation includes radiative cooling using the Sarazin & White (1987) cooling curve. We allow cooling to 8,000 K, which results in gas with neutral hydrogen temperatures without overcooling a large fraction of our gas. With this cutoff, we find that we still can form gas clouds with densities typical of molecular clouds, although it is clear that the internal structure of such clouds is not reproduced in detail (see Figure 7 for the density mass distribution in the gas disks of our galaxies). We discuss this choice in greater detail in \u00a75.5. Our box is 311 kpc on a side. Our coarsest resolution is 2.5 kpc. We allow 6 levels of refinement for our runs that include radiative cooling, for a best resolution of 40 pc. The runs without radiative cooling have 5 levels of refinement. We refine our simulation using baryon mass, with our minimum overdensity for refinement set as 51.2, which we found immediately refined the entire galactic disk to our best resolution. We discuss resolution effects in more detail in \u00a75.4. Our galaxy is placed at (0.5,0.5,0.22) or (155.5,155.5,68.42) kpc, so that we can follow the stripped gas as far as possible. The ICM wind flows along the z-axis in the positive direction, with the lower z boundary set for inflow and higher z boundary set as outflow. The x and y boundaries are set to reflecting. 2.2. The Galaxy We model a massive spiral galaxy with a flat rotation curve of 200 km s\u22121. It consists of a gas disk that is followed using adaptive mesh refinement (including selfgravity of the gas \u2013 a crucial ingredient required to form self-gravitating molecular clouds), as well as the static potentials of a stellar disk, a stellar bulge, and a dark matter halo. We directly follow Roediger & Br\u00a8 uggen (2006) in our modeling of the stellar and dark matter potential and gas disk. Briefly, we model the stellar disk using a Plummer-Kuzmin disk (see Miyamoto & Nagai 3 TABLE 1 Galaxy Stellar and Dark Matter Constants Variable Value M\u2217 1 \u00d7 1011 M\u2299 a\u2217 4 kpc b\u2217 0.25 kpc Mbulge 1 \u00d7 1010 M\u2299 rbulge 0.4 kpc rDM 23 kpc \u03c1DM 3.8 \u00d7 10\u221225 g cm\u22123 TABLE 2 Gas Disk Constants Variable Value RC Value NC Mgas 1 \u00d7 1010 M\u22991 \u00d7 1010 M\u2299 agas 7 kpc 6.5 kpc bgas 0.4 kpc 0.4 kpc 1975), the stellar bulge using a spherical Hernquist bulge (Hernquist 1993), and the dark matter halo using the spherical model of Burkert (1995). This dark matter halo model is compatible with observed rotation curves (Burkert 1995; Trachternach et al. 2008). The equation for the analytic potential is in Mori & Burkert (2000). The gas is described as a softened exponential disk: \u03c1(R, z) = Mgas 2\u03c0a2 gasbgas 0.52sech \u0012 R agas \u0013 sech \u0012 |z| bgas \u0013 (1) Given this gas density distribution in the disk, the gas temperature and pressure are calculated to maintain the disk in hydrostatic equilibrium with the surrounding ICM in the z direction. The gas disk\u2019s rotational velocity is set so that the combination of the centrifugal force and the pressure gradient of the disk balances the radial gravitational force. We cut the gas disk smoothly by multiplying the gas density distribution by 0.5(1+cos(\u03c0(R\u221220 kpc)/26(21) kpc)) for 20 kpc < R \u226426(21) kpc. See our galaxy parameters in Tables 1 and 2. We use di\ufb00erent initial gas disk radii in order to more easily compare disks when the ICM wind hits the galaxy. We discuss this in greater detail in \u00a73. 2.3. ICM Conditions Our galaxies evolve in a pressurized ICM. Because a galaxy moving through the ICM can be more easily simulated by modeling a \ufb01xed galaxy within a moving ICM, our galaxy remains in the same place in our simulated box (at least the stars and dark matter do). The galaxy initially evolves in a static ICM, to examine the stability in the static ICM and to allow cool, dense gas to form. Later, we trigger a constant ICM in\ufb02ow along the z-axis, which is always face-on to the galaxy. See the Appendix for exactly when the wind hits each galaxy. Brie\ufb02y, the wind is triggered so that it hits the galaxy while gas is still distributed out to a large radius, but enough time has passed so that high density gas clouds have formed. The exact time was chosen to be when the galaxy in the corresponding RCNW case had gas collapsed to \u03c1 \u226510\u221220 g cm\u22123, typical of densities found in molecular clouds. Fig. 1.\u2014 The measurements of the ICM density and di\ufb00erence in velocity between the galaxies and the ICM for: the cluster in the large simulation we examined in an earlier paper (Tonnesen, Bryan & van Gorkom 2007, as blue triangles), the mean values we used for our three detailed simulations (black diamonds), and the values used by Roediger and Br\u00a8 uggen (2006) (black asterisks). To guide the eye, we also plot lines of constant ram pressure at 1 \u00d7 10\u221211 dynes cm\u22122, 1 \u00d7 10\u221212 dynes cm\u22122, and 1 \u00d7 10\u221213 dynes cm\u22122. See \u00a72.3 for discussion. We choose to study three ram pressure strengths using realistic values for the ICM density and velocity. The three ram pressure strengths we choose are Pram = \u03c1v2 ICM = 6.4 \u00d7 10\u221212 dynes cm\u22122, 1 \u00d7 10\u221212 dynes cm\u22122, and 6.4 \u00d7 10\u221213 dynes cm\u22122 (see Table 3). We choose the maximum and minimum ram pressure strengths to match two of the values used by Roediger and Br\u00a8 uggen (2006), and we pick 1 \u00d7 10\u221212 dynes cm\u22122 because it is the highest ram pressure value at the virial radius of our cluster simulation (Tonnesen et al. 2007). To choose the corresponding ICM parameters, \u03c1 and vICM, we use the results from our earlier cluster simulation to \ufb01nd the mean density, velocity, and temperature of the ICM at the three ram pressures (Tonnesen, Bryan & van Gorkom 2007). This is shown in Figure 1, where for comparison we plot the values used by Roediger & Br\u00a8 uggen (2006). As discussed earlier, we set the in\ufb02ow boundary condition in order to model the ICM wind. However, because we need to allow our galaxies to cool and evolve before the ICM wind begins to strip them, the galaxies are initialized in a static ICM and then, after a multiphase ISM has developed, the boundary values are set to generate a wind with the desired characteristics. To get the parameters for this initial ICM we backtrack from the density, temperature and velocity of the ICM wind using the Rankine-Hugoniot jump conditions, assuming a Mach number of 3.5. We choose this Mach number because it gives us a supersonic shock (which leads to cleaner behavior at the in\ufb02ow boundary), while allowing our initial static ICM to have a similar density and temperature as the ICM wind. This procedure is important because we compare the evolution of our stripped galaxy to one that only cools in a static medium that has the same density and temperature as the \ufb02owing ICM. 4 We use the same density and temperature as in the moving ICM for the cases in which the ICM always remains static, because the stripped galaxies spend more time in the simulation in the moving ICM. 2.4. Suite of Simulations We perform nine full runs because while attempting to understand how cooling a\ufb00ects galactic gas stripping, we also need to understand how cooling alone a\ufb00ects a galaxy. We examine how three di\ufb00erent ram pressure strengths a\ufb00ect galaxies that include and do not include radiative cooling. We choose a naming convention for the simulations which indicates the parameters used for that simulation (see also Table 3). The three ram pressure strengths also correspond to the three ICM thermal pressures, and are denoted PH, PM, PL for high, medium, and low. If cooling is turned on, the next identi\ufb01er is RC, if not, NC. The six runs with an ICM wind end with W. In addition to these six runs, we also study three runs of galaxies evolving with radiative cooling in a static ICM with the same temperature and density as the moving ICM. All these runs end with NW, for no wind. For details on these nine simulations, see Table 3, as well as the appendix. Because we are interested primarily in the impact of radiative cooling on gas stripping, we only consider cases with a face-on wind. These cases are likely to be the most a\ufb00ected by an ICM wind because the gas density \ufb02uctuations in the disk, caused by radiative cooling, are most apparent in a face-on view. 2.5. The Measurements We look closely at three types of measurements: 1) the total amount of gas in the galaxy, 2) the radius of the dense gas in the galaxy, and 3) the amount of gas mass at di\ufb00erent densities. We \ufb01rst measure the total amount of gas that remains in the galaxy. We measure this in two ways: the amount of gas mass in a cylinder centered on the galaxy with a height of 10 kpc and a radius of 27 kpc, and the total amount of bound gas mass in the entire box. Mass is bound if the thermal and kinetic energy are smaller than the gravitational energy from the static potential of the stars and dark matter. We can compare these values to an analytic estimate of how much gas a galaxy should lose using two analytic mass loss estimates, corresponding to two stages of gas stripping. We will follow Roediger & Br\u00a8 uggen (2007) by naming the initial stage ram pressure pushing and the later stage continuous stripping. We can predict the amount of gas loss from ram pressure pushing by measuring the amount of gas mass outside the analytic Gunn & Gott (1972) stripping radius, the radius at which the restoring force per unit area from the galaxy is equal to the ram pressure acting on the galaxy, or where \u03c1v2 = 2\u03c0G\u03a3star\u03a3gas. We calculate the radius using the initial gas distribution and measure the mass outside this radius immediately before the ICM wind hits the galaxy. Once initial gas stripping has occurred, there is a slower continuous stripping phase which is caused by the Kelvin-Helmholtz instability. Nulsen (1982) derived an equation for the mass loss rate of a spherical cloud, which Roediger & Br\u00a8 uggen (2007) adapted for a disk: \u02d9 MKH = 0.5\u03c0R2\u03c1ICMvgal. Because we use a constant density and velocity ICM wind, only the changing radius of the galaxy will change this rate of gas loss. Fig. 2.\u2014 The radii of two galaxies with no cooling and in a static ICM at two di\ufb00erent pressures. The radii \ufb02uctuate slightly at the epicyclic frequency. We believe this is because of the precipitous pressure decrease at the edge of the galaxy. We measure the stripping radius in the simulation by \ufb01nding the radius of gas with a density \u03c1 > 10\u221226 g cm\u22123 (or approximately a number density of n \u223c10\u22122 cm\u22123). To mitigate the e\ufb00ect of asymmetry on this measurement, we \ufb01nd the radius in 12 azimuthal slices around the disk and take the average. Because cooling causes both overdensities and underdensities, we measure this radius by \ufb01nding the distance to the furthest cell with gas above our threshold density. As may be expected, this increases the radius we measure for the galaxies that include cooling, and has no e\ufb00ect on the radius of the galaxies without cooling. We compare this to the analytic stripping radius. We also measure the amount of gas at di\ufb00erent densities. The gas is split into three density regimes: (1) high density: \u03c1 > 10\u221220 g cm\u22123, (2) moderate density: 10\u221220 g cm\u22123 > \u03c1 > 10\u221222 g cm\u22123, and (3) low density: 10\u221222 g cm\u22123 > \u03c1 > 10\u221226 g cm\u22123. We choose these density ranges in order to follow three di\ufb00erent types of gas: gas with high densities seen in molecular clouds (Crutcher 1991 and references therein), gas with densities that are nearly that of molecular gas, and \ufb01nally gas which is clearly not molecular, but more dense than the surrounding ICM. We use the gas that is within the cylinder centered on our galaxy for this measurement. 3. GALAXIES WITHOUT AN ICM WIND Although the stability of this galaxy model is discussed in detail in Roediger & Hensler (2005) and Roediger & Br\u00a8 uggen (2006), it is important to reiterate that using Enzo, the galaxies are stable if there is no radiative cooling and no ICM wind. Although they maintain the exact same amount of gas throughout the simulation, there is a \ufb02uctuation in the radius with the epicyclic frequency for this galaxy. This is most likely due to the rapid change in gas density, and therefore pressure, in the outer kpc (between 20-21 kpc) of the galaxy in the initial galactic pro\ufb01le. In Figure 2, we show how the radius varies with time for two of the runs in which the galaxy sits in a static environment with ICM pressure and without radiative cooling. 5 TABLE 3 ICM Data Runs \u03c1ICM TICM Pthermal Pram vICM Cooling? rinitial PHRCW 3.20 \u00d7 10\u221228 4.01 \u00d7 107 1.765 \u00d7 10\u221212 6.4 \u00d7 10\u221212 1413.5 Y 25 PHNCW 3.20 \u00d7 10\u221228 4.01 \u00d7 107 1.765 \u00d7 10\u221212 6.4 \u00d7 10\u221212 1413.5 N 21 PHRCNW 3.20 \u00d7 10\u221228 4.01 \u00d7 107 1.765 \u00d7 10\u221212 0.0 0.0 Y 25 PMRCW 9.15 \u00d7 10\u221229 2.52 \u00d7 107 3.169 \u00d7 10\u221213 1 \u00d7 10\u221212 1045.4 Y 25 PMNCW 9.15 \u00d7 10\u221229 2.52 \u00d7 107 3.169 \u00d7 10\u221213 1 \u00d7 10\u221212 1045.4 N 21 PMRCNW 9.15 \u00d7 10\u221229 2.52 \u00d7 107 3.169 \u00d7 10\u221213 0.0 0.0 Y 25 PLRCW 5.18 \u00d7 10\u221229 2.19 \u00d7 107 1.557 \u00d7 10\u221213 6.4 \u00d7 10\u221213 1111.7 Y 25 PLNCW 5.18 \u00d7 10\u221229 2.19 \u00d7 107 1.557 \u00d7 10\u221213 6.4 \u00d7 10\u221213 1111.7 N 21 PLRCNW 5.18 \u00d7 10\u221229 2.19 \u00d7 107 1.557 \u00d7 10\u221213 0.0 0.0 Y 25 In the simulations in which we include radiative cooling, at all ICM pressures, gas with a density of 10\u221220 g cm\u22123 forms. At this point, gas with the density of molecular clouds has formed, and we consider the gas disk to be a multiphase ISM. In all cases, the highest density gas (\u03c1 \u226510\u221220 g cm\u22123) only forms stably within the central 7 kpc of the disk. Also, the mass fraction of gas with densities of molecular gas (\u03c1 \u226510\u221221 g cm\u22123) is 38% 50% after evolving for \u22651 Gyr in a static ICM with radiative cooling. We closely examine three galaxies with radiative cooling in three di\ufb00erent pressure ICM\u2019s and no wind (the RCNW cases in Table 3). We \ufb01nd that \u2013 as in the galaxies without cooling \u2013 there does seem to be a radial epicyclic oscillation. However, in the higher ICM pressure cases (PHRCNW and PMRCNW), low density and low pressure regions in the disk allow non-rotating ICM gas to enter and interact with the rotating denser clouds. These clouds therefore slow and lose angular momentum, leading the disk to settle towards the center. This drop in disk radius can be seen in the bottom panels of Figure 6. It is notable that in the lowest pressure ICM there is very little entrainment of the ICM gas, and the radius of the gas is dominated by epicyclic oscillations. We also \ufb01nd evidence of this process, and how it varies with ICM pressure, by following the total amount of gas in these galaxies. For example, PHRCNW gains 3.8 \u00d7 108 M\u2299over the 950 Myr run, while PLRCNW gains 2.1 \u00d7 108 M\u2299, because of the different amounts of gas entrained through cooling of the disk. Because the radius of the gas disk decreases as the gas cools (see the bottom panels of Figure 6), we lower the gas radius of the galaxies without cooling to the radius that the radiatively cooled galaxies reach due to their entrainment of the ICM (as described in the previous paragraph). Therefore, although the radius of the galaxies with cooling begins at 25 kpc, the radius of the galaxies without cooling start at 21 kpc. Despite this di\ufb00erent initial radius, we set the radial gas scale length, agas, so that the galaxies with and without cooling have the same amount of mass. This is all done in order to ensure a fair comparison between the radiatively cooling and non-cooling runs. 4. THE EFFECTS OF RAM PRESSURE ON A MULTIPHASE ISM 4.1. Morphology of the Stripped Disk In Figures 3 and 4 we show projections along the yand zaxis towards PHRCW and PHNCW about 40 Myr, 250 Myr, 500 Myr, and 750 Myr after the wind has hit the galaxy. The projections are shaded to re\ufb02ect surface density of the gas with a logarithmic stretch, and are 103.7 kpc across. There are a number of important di\ufb00erences in the morphology of the gas disks that are re\ufb02ected in our quantitative comparisons. First, the gas in the galaxy with radiative cooling (PHRCW) forms small clouds with radii of about 100 pc near the center of the disk (within 7 kpc) that are of higher density than anywhere in the gas disk without cooling (PHNCW). Only these central clouds attain molecular densities, even in the galaxy that is never a\ufb00ected by an ICM wind. Further, at any radius of the disk in PHRCW, there is both higher and lower density gas than in the disk of PHNCW. This density structure has an important impact on the way that gas is stripped from the disk. First, it allows ICM gas to create holes in the disk, which leads to ablation of material from a wide range of radii, rather than just at the outer edge of the disk, as in the no-cooling run (PHNCW). As we will show in more detail below, this allows the gas to be stripped more quickly (see also Quilis et al 2000). In addition, the gas that is stripped tends to stream directly behind the disk, rather than \ufb02aring to the side, and therefore creates a narrower wake. We will examine the wake in more detail in a future paper. The density \ufb02uctuations in the disk in the PHRCW galaxy create a ring of higher density gas from about 10 kpc to 16 kpc. This gas never collapses to the highest densities. In fact, in the PHRCNW galaxy, gas with \u03c1 > 1022 g cm\u22123 only persists for \u223c100 Myr in the middle of the simulation. Although the vast majority of gas in this ring is always of a low enough density for direct stripping to occur, allowing the simulation to run until this ring had fully fragmented might result in a di\ufb00erent stripping scenario. It would also allow gas more time to drift towards the center of the galactic potential, making it more di\ufb03cult to strip. However, because little molecular gas is found outside the center of galaxies in both these simulations and in observations (e.g. Leroy et al. 2008), we don\u2019t expect the ring structure to make much di\ufb00erence in how much gas can be stripped. Although in this paper we will not discuss the stripped gas in any detail, it is notable that the stripped gas in PHRCW has more density substructure than that of PHNCW. Higher density gas leaves the disk in PHRCW than in PHNCW (although not gas with molecular densities), and stripped clumps survive for at least 100 kpc. 4.2. Gas Mass Loss 6 Fig. 3.\u2014 A face-on and edge-on view of gas surface density in simulation PHRCW, at 40, 250, 500, and 750 Myr after the wind has hit the galaxy. Note the substructure both in the disk and in the stripped gas. Each image side is 103.7 kpc, and the color scheme has a logarithmic stretch. We begin our quantitative analysis of the impact of cooling by comparing the amount of gas mass that is lost in the cases with and without cooling (Figure 5). In general, the amount of gas mass lost by the galaxies that include cooling is about the same as the gas mass lost by the galaxies that do not include cooling. However, the timescale for stripping is much shorter for the radiatively cooled galaxies. These di\ufb00erences are illustrated in Table Fig. 4.\u2014 A face-on and edge-on view of gas surface density simulation PHNCW, at 40, 250, 500, and 750 Myr after the wind has hit the galaxy. Note the continued smooth distribution of gas both in the disk and in the stripped gas throughout the simulation. Both the box size and color scale are the same as in Figure 3 4. Note that the last column in this table is the time from when the wind \ufb01rst hits the galaxy to when the galaxy has lost 85% of the total amount of gas lost. In the highest ram pressure runs (PHNCW and PHRCW), after the wind has been hitting the galaxy for 800 Myr, both the galaxies with and without cooling have lost similar amounts of mass: 5.845 \u00d7 109 M\u2299 and 5.86 \u00d7 109 M\u2299in the cooling and no cooling cases, 7 Fig. 5.\u2014 The mass in a cylinder with radius 27 kpc and height 10 kpc centered on the stellar disk center of the galaxy, and the mass gravitationally bound to the galaxy plotted against time for the six cases e\ufb00ected with an ICM wind. The columns are PH, PM, and PL. The top row includes radiative cooling and the bottom row has no cooling. The dash-dotted vertical line marks when the ICM wind hits each galaxy. The dash-dotted horizontal line denotes the analytic prediction for the gas mass after ram pressure pushing. respectively. We can compare these values to an analytic prediction for how much mass the galaxies should lose based on the amount of gas mass outside the analytic Gunn & Gott (1972) stripping radius measured immediately before the wind hits the galaxy. We \ufb01nd that the predictions are similar, although smaller, than the measured values: the galaxy with cooling should lose 5.46 \u00d7 109 M\u2299and the galaxy without cooling should lose 5.22 \u00d7 109 M\u2299. In the case with cooling, almost the entirety (86%) of this mass loss occurs within 150 Myr, while the same amount of mass loss takes about 650 Myr in the PHNCW case. Also, both of these galaxies have a fallback event (gas that is initially stripped from the disk region, although still gravitationally bound, falling back onto the disk) about 250 Myr after the wind hits the galaxy, although in PHNCW, the fallback is more drastic and seems to be followed by a few minor fallback events. Although the PHRCW case seems to stop losing gas despite the continued ICM wind, losing less than 5\u00d7108 M\u2299 in the \ufb01nal 300 Myr we follow the galaxy, the PHNCW case does not slow its gas loss by nearly as much, losing twice as much gas in the same amount of time. This di\ufb00erence is \ufb01t well by the di\ufb00erence in radius between the two cases and the dependence of Kelvin-Helmholtz stripping on radius squared. In PMRCW, our run with the middle ram pressure value, after 900 Myr of the wind hitting the galaxy, it has lost about 1.3 \u00d7 109 M\u2299of gas mass. In fact, it loses almost this entire amount of gas (95%) within 340 Myr of the wind \ufb01rst hitting the galaxy. On the other hand, in PMNCW, the galaxy has only lost 9.5\u00d7108 M\u2299in the 900 Myr since the ICM wind has hit the galaxy. Unlike the highest ram pressure case, the analytic prediction for the amount of gas loss is larger than the measured amount: 1.7\u00d7109 M\u2299for PMRCW and 1.6\u00d7109 M\u2299for PMNCW. Again, the \ufb02atness of the PMNCW gas mass curve and the steeper grade of the PMRCW gas mass curve may be attributed to Kelvin-Helmholtz stripping e\ufb00ecting only the galaxy without cooling. Also, there does not seem to be any steep drop in the PMNCW galaxy\u2019s gas that is the hallmark of ram pressure pushing. Even more than in the highest ram pressure case, the galaxy with cooling seems to be only instantaneously stripped, without much longer-term Kelvin-Helmholtz stripping. The lowest ram pressure runs (PLRCW and PLNCW) are very similar to the middle ram pressure runs, except that only 8.5 \u00d7 108 and 5.8 \u00d7 108M\u2299of gas are lost in the galaxies with and without cooling, respectively. Like the middle ram pressure case, the analytic prediction for the amount of gas loss is more than the amount measured, 1.0\u00d7109 (PLRCW) and 9.3\u00d7108 (PLNCW) M\u2299. Even when the ram pressure is only 6.4 \u00d7 10\u221213 dynes cm\u22122, the galaxy with radiative cooling appears to lose gas through ram pressure pushing. 8 TABLE 4 Stripping Data Runs Mlost MG&G rstrip rG&G t85% PHRCW 5.845 \u00d7 109 5.46 \u00d7 109 11 11.46 148 PHNCW 5.86 \u00d7 109 5.22 \u00d7 109 7 11.46 625 PMRCW 1.3 \u00d7 109 1.7 \u00d7 109 11 16.8 288 PMNCW 9.5 \u00d7 108 1.6 \u00d7 109 19.5 16.8 810 PLRCW 8.5 \u00d7 108 1 \u00d7 109 15 18.22 316 PLNCW 5.8 \u00d7 108 9.3 \u00d7 108 20? 18.22 754 Although similar amounts of gas mass are lost whether or not the galaxy is allowed to radiatively cool, there are a few trends. First, in the middle and low ram pressure cases, the amount of gas lost by the galaxy with radiative cooling is more than that lost by the galaxy without radiative cooling. Although this qualitatively agrees with the analytic predictions for the amount of gas mass loss indicating that the radiatively cooled galaxy will lose more gas, the di\ufb00erence in measured mass loss between the RC and NC cases is greater than the di\ufb00erence in the analytic prediction. Thus, it may be that for lower ram pressures, a multiphase ISM is easier to strip. Also, galaxies that radiatively cool lose their gas more quickly. There is slightly more mass in total outside the stripping radius in the radiatively cooling galaxies, and there is more mass at higher density. A plausible reason for the quick stripping of gas mass, then, is that a lumpy gas distribution is more quickly and easily stripped than gas with a smoother pro\ufb01le. Later continuous stripping seems to mainly a\ufb00ect the galaxies without cooling, perhaps because their larger cohesive gas disk is more affected by the Kelvin-Helmholtz instability. 4.3. Stripping Radius In general, the galaxies that include radiative cooling are stripped to a smaller radius than predicted using the Gunn & Gott (1972) analytic equation, and end at a smaller radius than stripped galaxies without cooling and at a smaller radius than galaxies with radiative cooling that are not a\ufb00ected by an ICM wind (Figure 6). Again, see Table 4 for the stripping radius values. In the highest ram pressure cases, the analytic stripping radius is 11.5 kpc, very similar to the stripping radius of the galaxy in PHNCW. The oscillations in the radius correspond to fallback episodes in Figure 5. The \ufb01nal radius of the PHRCW case is about 7 kpc. The \ufb01nal radius of the PHRCNW galaxy is just above 11 kpc. This means that including cooling without a wind causes galactic gas to spiral towards the center of the disk, most likely because the entrainment of nonrotating ICM into the disk creates drag and angular momentum loss. The entrainment of gas into the disk means that the average gas density of the resulting disk would be higher than before, making it more di\ufb03cult to strip. In fact, comparing the amount of gas at di\ufb00erent densities in PHRCW and PHNCW about 15 Myr before the ICM wind hits the galaxy, we \ufb01nd that PHRCW has more high density gas outside 10 kpc and a higher fraction of the gas in the disk region is high density than in PHNCW. Therefore, the holes in the disk must allow for easier stripping down to smaller radii. The holes may also create more drag against surviving gas, allowing it to spiral towards the center of the disk more quickly. In the middle ram pressure cases, the analytic stripping radius is 16.8 kpc. The \ufb01nal radius of the galaxy in PMNCW is between 19 and 20 kpc. However, the initial radius drop is to about 17 kpc, while a static galaxy without cooling, only undergoing epicyclic variations, has a smallest radius of about 19 kpc. The \ufb01nal average radius of the galaxy in PMRCNW is steady at 15 kpc, although it is very asymmetric. The galaxy in PMRCW is stripped down to a radius of 11 kpc. Again, a mixture of stripping and cooling results in the smallest radius. In the lowest ram pressure cases, the analytic stripping radius is 18.2 kpc. It is di\ufb03cult to say whether the galaxy in PLNCW is stripped to a smaller radius because of the large oscillation in radius over time. PLRCW is stripped to about 15 kpc. In this case more than in the previous two, it is clear that it must be the holes punched by the ICM wind in the gas disk that allow the gas to be stripped to a small galactic radius. Neither PLNCW nor PLRCNW have much change in the radius of the gas disk, so it must be a combination of the ICM wind and the clumpiness of the gas in the disk that result in the lowest gas radius. By examining the stripping radius of gas in these galaxies, we \ufb01nd that allowing radiative cooling results in a smaller radius when hit by an ICM wind. Again, the most likely explanation is that the clumpiness of the disk gas allows for stripping to a smaller radius. 4.4. Densest Gas As gas in the galaxy cools, it becomes more dense, eventually attaining densities greater than 1000 cm\u22123, certainly in the range of molecular gas. Although with a resolution of 40 pc, we only marginally resolve giant molecular clouds, we can begin to answer whether ram pressure has any e\ufb00ect on the densest gas in a galaxy (and hence on star formation). When comparing the three cases with radiative cooling and no ICM wind (bottom panels in Figure 7), it is clear that a higher pressure ICM results in a faster formation of high density gas and the formation of more high density gas. However, as we will see, including an ICM wind can either strip the surrounding lower density gas that would accrete onto clouds, or create more high density gas when the wind pressure is low. We \ufb01nd that with the highest ram pressure of 6.4 \u00d7 10\u221212 dynes cm\u22122, the amount of higher density gas (above 10\u221222 g cm\u22123) is less than if the galaxy were to radiatively cool without an ICM wind (see Figure 7). This is true even when (as in Figure 8), we shift the PHRCW line showing how much gas has cooled as a function of time by 200 Myr in order to account for the fact that the galaxy in PHRCW has been in the higher pressure ICM for almost 200 Myr less than the galaxy in PHRCNW. When the wind hits the galaxy, less dense gas throughout the disk is accelerated out of the galaxy, leaving less nearby lower density gas that would later either be accreted onto nearby clouds or cool and collapse into new clouds. However, gas with densities above 10\u221222 g cm\u22123 is never seen outside of the disk (always within 1 kpc of the disk plane), so molecular clouds are not being stripped in their entirety. Examining the snapshots indicates that higher density clouds do leave the disk, 9 Fig. 6.\u2014 The radius of gas with a density greater than 10\u221226 \u03c1 cm\u22123. The columns are PH, PM, and PL. The top row includes radiative cooling, the middle row has no cooling, and the bottom row has cooling but no ICM wind. The dash-dotted vertical line marks when the ICM wind hits each galaxy. The dash-dotted horizontal line denotes the analytic prediction for the stripping radius based on the initial gas distribution. leading us to hypothesize that dense clouds can be ablated until they are of just low enough column density to be stripped from the disk. The scenario seems less clear in the medium ram pressure case (1 \u00d7 10\u221212 dynes cm\u22122). Although the amount of higher density gas increases more slowly in PMRCW than in PMRCNW, both end their runs with similar amounts of high density gas (see Figure 8). In the lowest ram pressure case (6.4 \u00d7 10\u221213 dynes cm\u22122), the galaxy that is hit by the ICM wind has more of the highest density gas (above 10\u221220 g cm\u22123) than the galaxy that evolves in the post-shock ICM. In this case, the added ram pressure from the wind appears to compress the gas, leading to more higher density gas. In summary, molecular clouds do not get stripped, even if the ram pressure is 6.4 \u00d7 10\u221212 dynes cm\u22122. They do not grow within a high ram pressure ICM wind, however, because lower density gas is accelerated out of even the inner disk (inside the stripping radius of 7 kpc). However, with low ram pressure, 6.4\u00d710\u221213 dynes cm\u22122, more high density gas is formed, likely because the ram pressure, while not enough to strip much gas from the disk, is enough to compress gas to a higher density. 5. DISCUSSION 5.1. Comparison to Observations A galaxy is considered HI de\ufb01cient if its de\ufb01ciency value is 0.3 or greater. De\ufb01ciency is de\ufb01ned as DEF = < log X >T,D log Xobs (Giovanelli & Haynes 1985), where Xobs is the observed HI mass of the cluster galaxy and < log X >T,D is averaged over a sample of \ufb01eld galaxies of morphological type T and optical diameter D. Given this de\ufb01nition, the highest ram pressure case is almost but not quite HI de\ufb01cient. However, gas is truncated to less than half the original gas radius in the largest ram pressure case, and is down to less than 75% in the the lowest ram pressure case. If we were to roughly classify these galaxies using the scheme of Koopmann & Kenney (2004), assuming that HII regions will follow our gas distribution, all three of our runs result in truncated disks. We can also compare the amount of high density gas we \ufb01nd in our galaxies to the amount of molecular gas observed using CO. Kenney & Young (1986, 1989) found that HI de\ufb01cient galaxies in Virgo have undepleted CO, and Nakanishi et al. (2006) found that the molecular fraction in three galaxies near the center of Virgo is high. We \ufb01nd that in our high ram pressure run, the fraction of high density (i.e. molecular) gas actually remains similar to the case with no wind. On the other hand, in the low ram pressure case, the fraction of high density gas does increase as the ICM wind compresses the ISM. This case better matches the observations of high molecular gas fractions (Nakanishi et al. 2006). It is possible that galaxies will move through low ram pressure environments on their way to higher ram pressure, so the initial compression followed by strong stripping could result in HI depleted disks with una\ufb00ected, or increased, amounts of molecular gas. However, we do note that 10 Fig. 7.\u2014 The amount of mass at di\ufb00erent densities contained within the cylinder surrounding the galaxy. The columns are PH, PM, and PL. The top row includes radiative cooling and the bottom row has cooling and no wind. The dash-dotted vertical line marks when the ICM wind hits each galaxy. these results are somewhat sensitive to the resolution and details of the cooling (discussed in more detail below). We do not include star formation in our simulations, but we do have an enhanced amount of high density gas in our lowest ram pressure simulation, while our highest ram pressure simulation has less high density gas in comparison to their respective no-wind comparison runs. If we assume that higher density gas corresponds to a higher rate of star formation, the lowest ram pressure case would result in an enhanced star formation rate, while the highest ram pressure case would result in a lower star formation rate. Placing this into a cluster environment, we would expect to \ufb01nd enhanced star formation at or outside the virial radius in the lower density ICM, and post-star-forming galaxies closer to the cluster center. In Coma, Poggianti et al (2004) found that post-starburst or post-star-forming galaxies were found at the edge of ICM substructure, which seems to follow our claim that starbursts will occur outside of the densest ICM, while high ram pressure will quench star formation. We can also use morphological cues to determine how closely these simulations match observations. A perfect example of a galaxy showing both the strength and weakness of our simulations that include a multiphase medium is the Virgo spiral NGC 4402 (Crowl et al 2005). The galaxy has upturned edges in it\u2019s dust and gas distribution, similar to the earliest projection of our galaxy without cooling. However, similar to our galaxy with radiative cooling, there is evidence that two dense clouds have survived longer than the lower density ISM and are being ablated by the wind. 5.2. The Evolving ISM A molecular cloud may survive between a few and a few tens of Myr (Blitz & Shu 1980; Larson 2003; Hartmann 2003). Because we do not include star formation, our dense clouds of gas do not evolve into less dense pockets of gas that could be stripped. In the highest ram pressure case, holes are punched around the disk (as close as 6 kpc to the disk center) between 6 11 Myr after the ICM wind \ufb01rst hits the galaxy, which indicates that as long as gas stays low density for 10 Myr it can be stripped by the wind. If our dense regions of gas could turn into very low density regions through star formation (\u03c1 \u226410\u221223 g cm\u22123), our galaxies that include radiative cooling could be entirely stripped of gas in the highest ram pressure case. In the lowest ram pressure case, no gas appears to be stripped from the central region of the gas disk. 5.3. Magnetic Fields and Cosmic Rays 11 Fig. 8.\u2014 This focuses on the most dense gas in each of the radiatively cooled cases. The runs with an ICM wind have been shifted in time by the amount of time before the wind hits them (190 Myr, 274 Myr, and 271 Myr, respectively). High ram pressure results in less high density gas, while low ram pressure increases the amount of high density gas. Our simulation does not include magnetic \ufb01elds or cosmic rays. In general in the Milky Way, the magnetic \ufb01eld is measured to be about 2-3 microGauss (Men et al 2008). A \ufb01eld of this strength would not have enough magnetic pressure (2 \u22125 \u00d7 10\u221213 dynes cm\u22122) to significantly lessen the direct impact of ram pressure on the galactic gas. However, there are measurements of the magnetic \ufb01eld in molecular clouds (Crutcher 1991 and references therein) of up to 103 microGauss, which can certainly withstand ram pressures of order 10\u221212 dynes cm\u22122. These magnetic \ufb01elds could help protect molecular clouds from being ablated by the ICM wind, so could help them survive. Also, a magnetic \ufb01eld could attach a molecular cloud to less dense gas, either anchoring the surrounding gas or helping to drag out the molecular cloud. Using this simulation we cannot conjecture on the likely impact of magnetic \ufb01elds on the total amount of gas stripped. We also do not include cosmic rays in our simulation, which would add energy to the galactic gas and increase the vertical distribution (e.g. Joung & Mac Low 2006). It is also possible that the increase in gas pressure would lower the amount of entrainment into the disk from the lower pressure ICM, which would in turn lessen the number of very low density regions and make the disk more cohesive. This would make stripping more di\ufb03cult because fewer holes could be punched through the disk by the ICM wind. However, the energy input from cosmic rays would slow high density gas formation, possibly allowing for more extended stripping if the gas is not locked in very dense clouds. As with magnetic \ufb01elds, the addition of cosmic rays into our simulation does not have an easily predicted e\ufb00ect. 5.4. Resolution As has been discussed in detail in previous works (e.g. Tonnesen et al. 2007 and Roediger & Br\u00a8 uggen 2006), resolution does not have a large e\ufb00ect on our runs without radiative cooling. The runs without radiative cooling that we discuss in this paper have a cell size of 80 pc, and we ran a comparison run with a cell size of 40 pc to check this. We found very similar results in the amount of gas and the radius of the disk. In addition, our results are similar to those in Roediger & Br\u00a8 ggen (2006), where even lower resolution was used. However, including radiative cooling leads to results that are very dependent on resolution. The runs discussed in this paper have a cell size of 40 pc, which leads to gas collapsing to molecular densities. For example, the surface density in the center of the disk immediately 12 Fig. 9.\u2014 The gas mass and gas radius over time for PHRCW, PHRCW low resolution, and PHNCW. This \ufb01gure shows how the low resolution run with radiative cooling is a cross between PHRCW and PHNCW, because the gas density is smoother than PHRCW, but less smooth than PHNCW. See \u00a75.4 for discussion. before the wind hits the galaxy is 200 M\u2299kpc\u22122, with values above 10 M\u2299kpc\u22122 for much of the inner disk (this surface density corresponds to the transition between HI and molecular gas observationally found in Bigiel et al 2008). To examine the impact of resolution, we have run a comparison simulation with the same parameters as PHRCW, but with a cell size of 80 pc. We \ufb01nd that gas density does increase, but the highest density gas never forms, and there is very little gas in the middle density range. Because the lack of cloud formation results in a smoother gas distribution in the galaxy disk, the ICM wind does not have the same e\ufb00ect on this lower resolution disk as it does in the higher resolution cases. Figure 9 shows that although the low resolution disk with cooling still gets stripped slightly more quickly than the no cooling case, it does not get stripped as quickly as the higher resolution case. This occurs because the corresponding low density regions in the disk do not form, so the ICM wind does not punch holes throughout the disk. The low resolution run also has much less fallback than PHNCW, but because very dense clouds are not formed (see Figure 10), continuous stripping occurs and gas loss does not cease after a few hundred Myr. We also ran a pair of comparison runs between a galaxy with a cell size of 40 pc and one with a cell size of 20 pc. Because of the computing time needed to run the high resolution simulation, we only had output for 160 Myr of evolution. However, within this time, the maximum surface density of the higher resolution run is more than double that of the regular resolution run. Further, after 160 Myr the amount of gas with densities above 10\u221220 g cm\u22123 is already more than 25% of the total galaxy gas mass and growing at a rate of 40 M\u2299yr\u22121, while gas with those densities has not yet formed in the regular resolution run (at 160 Myr, \u03c1max \u226510\u221222 g cm\u22123). In fact, in the highest resolution run, 5 \u00d7 108 M\u2299of gas with densities above 10\u221219 g cm\u22123 (n > 105 cm\u22123) has already formed by 160 Myr into the simulation, with no sign of slowing down much higher gas density formation. A visual inspection shows that the cloud radius is set by the minimum cell size in the simulation. We conclude that there are physical processes that we do not include in the simulation, such as star formation, magnetic \ufb01elds, cosmic rays, and feedback from supernovae, that would all result in lower density gas than is found in our simulations, either by adding energy to the ISM or locking the ISM into place and hindering collapse. In this case, higher resolution is not necessarily better, because our omissions may result in unphysical gas densities. In the regular resolution run, the larger cells balance, to a certain extent, the smaller-scale physics we omit. 5.5. Radiative Cooling Floor As mentioned in \u00a72.1, we include radiative cooling using the Sarazin & White (1987) cooling curve. We allow cooling to 8,000 K, as this results in gas with neutral hydrogen temperatures without overcooling a large fraction of our gas. With this cuto\ufb00, we \ufb01nd that we form clouds with densities and sizes typical of molecular clouds, al13 Fig. 10.\u2014 The amount of mass at di\ufb00erent densities contained within the cylinder surrounding the galaxy for the strong ICM wind case at high and low resolution. The lower resolution run does not form the clouds of molecular density, so does not model the multiphase medium we attempt to study. See \u00a75.4 for discussion. though we make no attempt to reproduce the internal structure of the clouds. For a more detailed discussion of the density distribution in the ISM for similar simulations, but without a wind, see Tasker & Bryan (2006, 2008). To examine the impact of our adopted cooling \ufb02oor, we perform a run with no wind and cooling to 300 K which shows that after 800 Myr the density distribution of disk gas was nearly identical to the case with cooling to 8000 K, although the case with cooling to 300 K reached the distribution more quickly and leveled out. The highest density gas is less than a factor of three more dense in the 300 K case than in the 8000 K case. To better compare how an ICM wind would a\ufb00ect a galaxy with a lower cooling \ufb02oor, we ran a simulation which is identical to PHRCW, but with radiative cooling to 300 K. We \ufb01nd a few interesting results, shown in Figure 11. First, more gas is lost than in either PHRCW or PHNCW. Gas is initially lost more slowly than in the other two cases, but does not slow down with fallback as in PHNCW. Also, the \ufb01nal radius of the gas disk is similar to PHRCW, but it reaches this radius more slowly. Finally, the amount of gas in each of the three density ranges is similar to that in PHRCW, but the two lower density regimes have a little less gas. The highest density gas is the same in both runs throughout the simulations. We also show (Figure 12) an image of each of the two cooling cases 150 Myr after the wind has hit the galaxy. All of the di\ufb00erences in these two cases are explained by the fact that the galaxy with the lower radiative cooling \ufb02oor fragments more than our standard cooled galaxy. Because more of the gas is in dense knots, the initial onslaught of the wind does not strip gas as quickly. Further, because gas that began in the outer regions of the disk survives, we see epicyclic variation in the radius, similar to our other simulations, resulting in an increase in the radius. This is unlike PHRCW, in which all the gas that began in the outskirts is quickly stripped. Because the clouds in the 300 K cooling case move to large radii, there is more time for them to be ablated as they drift back towards the center of the galaxy. This explains why gas takes longer to be stripped, why more gas is stripped, and why the amount of mid-density gas decreases in this galaxy. In the inner region of the disk, the larger amount of fragmentation means that more gas is stripped at early times from the central regions of the disk, because the gas disk is not smooth and cannot de\ufb02ect the ICM wind. In fact, we do not see gas fallback, as in the other high ram pressure cases, presumably because the wind pushes gas at all radii. The longer period of gas stripping results both from ablation of the dense clouds in the center of the disk that are more exposed to the wind because of the larger amount of fragmentation, and because the dense clouds at large radii can be ablated more easily than their counterparts in the 8000 K case, which are closer to the galactic center. It is unclear what level of fragmentation is more realistic in observed galaxies. Because of the lower Jeans length in the lower temperature \ufb02oor runs, we resolve the resulting fragmentation less well and so prefer the runs with a higher minimum temperature. In addition, it is not clear if the lower minimum temperature runs are physically more realistic as we do not include some e\ufb00ects such as small-scale turbulence, cosmic rays and magnetic \ufb01elds, all of which may provide a source of effective pressure in low temperature regions. While our simulations represent a sizable step forward in realism, it is clear that more work is required. 6. CONCLUSIONS We have run a set of detailed galaxy simulations including radiative cooling to understand how a multiphase ISM interacts with an oncoming ICM wind. We \ufb01nd: 1. The total amount of gas mass loss is similar when comparing galaxies with and without radiative cooling. However, the time over which the gas is stripped is shorter in the galaxies with radiative cooling. The continued stripping of galaxies without radiative cooling could be Kelvin-Helmholtz stripping acting on the larger disk. 2. The stripping radius is signi\ufb01cantly smaller for the galaxy simulations with radiative cooling. This is even true when accounting for the angular momentum loss in the ISM gas due to the interaction between the ISM and ICM gas (see section 3). 3. The morphology of the stripped disks are considerably di\ufb00erent, with the cooling case producing a multiphase medium which results in many holes in the disk, while the case without cooling produces a coherent disk. These holes allow ICM gas to stream through the galaxy disk, a\ufb00ecting the evolution of the dense clouds which remain. 4. The amount of high density gas is a\ufb00ected di\ufb00erently depending on the amount of ram pressure. When the ram pressure is strong, there is less gas at all densities, including the highest density. This is because the low density gas is stripped, even from the inner regions of the galaxy, so there is less gas to feed molecular clouds. With a weaker ram pressure, there is more of the highest density gas, although there is also less of the lower density gas. A weaker wind strips less of the lower density gas, and increases the pressure on disk gas to create more high density gas. This leads us to a picture in which radiative cooling re14 Fig. 11.\u2014 Comparison between PHRCW and the case with cooling to 300 K. In both cases, the ICM wind hits the galaxies at 190 Myr. Note how extended the stripping is in the 300 K cooling case, and note that more gas is stripped. These facts are linked with the larger gas radius for much of the simulation. See \u00a75.5 for discussion. sults in both overdensities and underdensities at all radii in the galactic gas disk. The underdensities are clearly stripped quickly throughout the disk, and the overdense regions that then have the wind streaming around them through the holes in the disk are stripped more rapidly than without a multiphase medium. However, if a dense cloud is able to survive this initial onslaught, it loses angular momentum through its interaction with the nonrotating ICM wind and therefore settles toward a lower radius. This is how the runs with cooling and a wind (the RCW cases) are stripped quickly and to a small radius while not losing much more gas than the galaxies without radiative cooling. Also, the galaxies with radiative cooling seem to stop losing gas while those without cooling continue to lose gas through the entire simulation. This may be because the Kelvin-Helmholtz instability is ine\ufb03cient on small dense clouds but can a\ufb00ect the large cohesive disk in the no-cooling runs. Allowing cooling to a lower temperature supports our picture that dense clouds cannot be directly stripped but can be ablated over time. Although these simulations are arguably the most realistic stripping simulations performed to date, we have discussed in detail the limitations involved in our work in \u00a75. We acknowledge support from NSF grants AST-0507161, AST-05-47823, and AST-06-06959, as well as computational resources from the National Center for Supercomputing Applications. We thank Jacqueline van Gorkom, Je\ufb00Kenney, Hugh Crowl, Airee Chung, Tomer Tal, and Anne Abramson for useful discussions, as well as Elizabeth Tasker for invaluable help setting up the initial conditions. We would also like to thank our referee for editing and advice that greatly improved our paper.",
                    "introduction": "1. It has long been known that a galaxy\u2019s environment has an impact on its morphology: spirals dominate in the \ufb01eld, and ellipticals and S0s dominate in dense cluster environments (Hubble & Humason 1931). This has been quanti\ufb01ed in the density-morphology relation (Oemler 1974; Dressler 1980), but this relation alone does not determine whether the cluster environment a\ufb00ects the formation or the evolution of galaxies. According to the Butcher-Oemler e\ufb00ect, clusters at z \u22650.2 are bluer and contain more spirals than nearby clusters, indicating that cluster environments may be correlated with the evolu- tion of galaxies from spirals to earlier types (Butcher & Oemler 1978). More recently, by examining a speci\ufb01c merging cluster, Tran et al. (2005) presents a strong rela- tionship between the Butcher-Oemler e\ufb00ect and infalling galaxies. The environment-driven evolution of spiral galaxies into S0s is caused by mechanisms that physically remove gas and/or induce star formation until almost no gas re- mains. Galaxy-intracluster medium (ICM) interactions are ones in which the gas in a galaxy interacts with the ambient intracluster hot gas. One such process is ram pressure stripping (RPS), which removes the interstellar medium (ISM) of a galaxy as it moves through the ICM (Gunn & Gott 1972). Ram pressure could also compress the gas within a galaxy to cause a burst of star forma- tion that would consume all of the remaining gas (Fujita & Nagashima 1999). A galaxy-ICM interaction does not a\ufb00ect the stellar component of a galaxy. The cluster po- tential can also strip both gas and stars or compress gas to cause an increased star formation rate (Byrd & Valto- nen 1990). These galaxy-cluster interactions a\ufb00ect both the stellar and gas components of galaxies. There are also galaxy-galaxy interactions that can take place be- tween galaxies. These include mergers between galaxies with low relative velocities, and galaxy harassment: high- speed interactions between cluster galaxies (Hashimoto et al. 1998; Bekki 1999; Barnes & Hernquist 1991; Bekki 1998; Moore et al. 1996). These interactions can cause an increased star formation rate and will also a\ufb00ect both the stellar and gas component of galaxies. In our earlier work (Tonnesen, Bryan & van Gorkom 2007), we studied cluster galaxies that had evolved in a cosmological simulation. This simulation included dark matter and stellar particles, and followed gas through an adaptive mesh re\ufb01nement (AMR) code. It included ra- diative cooling and star formation. This work was unique because it allowed the cluster to form in a cosmological simulation, but had the resolution to follow individual galaxies (3 kpc). We found that most galaxies that lost all their gas did so without losing stellar mass, indicating that ram pressure stripping was the most e\ufb00ective evo- lutionary mechanism. This convinced us to look more closely at ram pressure stripping of galaxies. While a substantial body of literature exists on ram pressure stripping (e.g. Roediger & Hensler 2005; Roedi- ger & Br\u00a8 uggen 2006; Vollmer, Hutchmeier & van Driel 2005; see references in van Gorkom 2004), the e\ufb00ect of a multiphase ISM has only begun to be explored in simu- lations. Schulz and Struck (2001) included cooling and found that it caused a disk instability that led to an in- \ufb02ow of dense gas, and that including cooling allows the disk to remain cool and thin despite ICM heating. Strip- ping of a multiphase ISM was also studied at higher res- olution by Quilis, Moore & Bower (2000). They did not include radiative cooling, but instead randomly placed holes and overdensities in their ISM disk in an attempt to model an inhomogeneous ISM. They \ufb01nd that strip- ping is much more complete as ICM streams through the holes in their galaxy and prevents stripped material from falling back onto the galaxy as earlier simulations had shown. More recently, Kronberger et al (2008) have modeled cooling in the context of star formation. They 2 \ufb01nd increased star formation in the center of their galaxy and star formation in the stripped material (although it does not escape the galactic halo). Observations have been inconclusive about the e\ufb00ect of stripping on dense molecular clouds. In a survey of Virgo cluster galaxies, Kenney & Young (1986, 1989) found that CO remains in HI de\ufb01cient galaxies, indi- cating that molecular clouds are not being stripped en- tirely. Whether this is because molecular clouds reside in the center of galaxies where even atomic gas is rarely stripped, or because molecular clouds are too dense to be stripped is unclear. The likelihood of molecular gas being stripped varies with each individual case. Clemens et al. (2000, 2001) have examined in detail the interact- ing galaxy pair NGC 4490 and NGC 4485. They \ufb01nd evidence that in moving through the extended HI enve- lope surrounding the two galaxies, NGC 4485 has had atomic gas, molecular gas, and dust removed via ram pressure stripping. Crowl et al. (2005) have studied the Virgo cluster galaxy NGC 4402, and observe ram pressure stripping and dense cloud ablation. They \ufb01nd that it is possible to strip the lower density ISM with- out stripping dense clouds, but that the surviving clouds will eventually be ablated by the ICM wind. They also observe an HII region which has likely formed within the stripped gas, so molecular gas was either stripped or formed from stripped material. However, in NGC 4848, Vollmer et al (2001) \ufb01nd that the displaced molecular gas they observe is formed from re-accreted lower den- sity gas, and that the molecular gas was not stripped at all. NGC 4438 has been observed to have both stripped and surviving molecular gas, determined by the clouds\u2019 positions in the galaxy (Vollmer et al. 2005). Another galaxy in the Virgo cluster, NGC 4522, has no HII regions in the outer disk, but extraplanar HII regions (Kenney & Koopmann 1999; Kenney, van Gorkom & Vollmer 2004). As discussed in Kenney et al (2004), there are four pos- sibilities for stripping of molecular clouds. (1) Molecular clouds can be directly stripped from the disk, although there is probably an upper limit to the surface density for which this is possible. (2) Molecular clouds, which are thought to have a lifetime of about 107 years (Blitz & Shu 1980; Larson 2003, Hartmann 2003), can also evolve via star formation into lower density gas, which can then be stripped directly. (3) Another possibility is that the molecular clouds are not directly stripped out of the galaxy, but are instead ablated by the ICM wind on a longer timescale (Nulsen 1982). (4) Finally, dense clouds may be coupled to the rest of the ISM by mag- netic \ufb01elds or some other mechanism, so that the entire ISM is stripped out together. In this paper, we run a set of high resolution sim- ulations (40 pc resolution, which is small enough to marginally resolve Giant Molecular Clouds) to under- stand how a multiphase ISM could a\ufb00ect ram pressure stripping of a galaxy\u2019s gas. It is important to recog- nize that we do not attempt to include all of the physics involved in the ISM. We use these simulations to under- stand how the density \ufb02uctuations that are observed in the multiphase ISM of galaxies will a\ufb00ect gas loss. We vary ram pressure strength to investigate the result of di\ufb00erent wind strengths. Using our simulations, we are able to look in detail at possibilities (1) and (3). We also consider whether including molecular clouds a\ufb00ects the large scale stripping properties such as the total amount of gas stripped and the radius to which gas is stripped. In an introduction to our code, we provide the gen- eral characteristics of our simulation (\u00a72.1-3). We then discuss our suite of runs and the measurements we use to compare them (\u00a72.4-5). In \u00a73 we discuss how cooling a\ufb00ects a galaxy evolving in a static ICM. We then (\u00a74) compare our simulations. In \u00a75 we brie\ufb02y discuss the limitations and implications of our results. Finally, we conclude in \u00a76 with a summary of our results and the overall picture of ram pressure stripping of a galaxy with a multiphase ISM. 2."
                },
                {
                    "url": "http://arxiv.org/abs/0808.0007v1",
                    "title": "The Impact of ICM Substructure on Ram Pressure Stripping",
                    "abstract": "Cluster galaxies moving through the intracluster medium (ICM) are expected to\nlose some of their interstellar medium (ISM) through ram pressure stripping and\nrelated ISM-ICM interactions. Using high-resolution cosmological simulations of\na large galaxy cluster including star formation, we show that the ram pressure\na galaxy experiences at a fixed distance from the cluster center can vary by\nwell over an order of magnitude We find that this variation in ram pressure is\ndue in almost equal parts to variation in the ICM density and in the relative\nvelocity between the galaxy and the ICM. We also find that the ICM and galaxy\nvelocities are weakly correlated for in-falling galaxies.",
                    "authors": "Stephanie Tonnesen, Greg L. Bryan",
                    "published": "2008-07-31",
                    "updated": "2008-07-31",
                    "primary_cat": "astro-ph",
                    "cats": [
                        "astro-ph"
                    ],
                    "main_content": "2.1. Simulation We have simulated a massive cluster of galaxies with the adaptive mesh refinement (AMR) code Enzo. This cosmological hydrodynamics code uses particles to evolve the dark matter and stellar components, while using an adaptive mesh for solving the fluid equations including gravity (Bryan 1999; Norman & Bryan 1999; O\u2019Shea et al. 2004). The code begins with a fixed, static grid and automatically adds refined grids as required in order to resolve important features in the flow (as defined by enhanced density). An image of this cluster is shown in Figure 1 of our earlier paper (Tonnesen et al. 2007), and visualizations of these simulations can be found at http://www.astro.columbia.edu/\u02dcgbryan/ClusterMovies. We chose to examine the largest cluster (r200 is 1.8 Mpc and M200 is 6 \u00d7 1014 M\u2299) that formed within a 2 periodic simulation box which was 64 h\u22121 Mpc on a side, in a \ufb02at, cosmological-constant dominated universe with the following parameters: (\u21260, \u2126\u039b, \u2126b, h, \u03c38) = (0.3, 0.7, 0.045, 0.7, 0.9). We employ a multi-mass initialization technique in order to provide high-resolution in the region surrounding the cluster, while evolving the rest of the box at low resolution. The dark-matter particle mass is 6.4 \u00d7 108 M\u2299, with a gas mass resolution about \ufb01ve times better than this. The whole cluster has more than one million particles within the virial radius, and a typical L\u2217galaxy is resolved by several thousand particles. The adaptive mesh re\ufb01nement provides higher resolution in high density regions, giving a best cell size (resolution) of 3 kpc. The simulation includes radiative cooling using the White & Sarazin (1987) cooling curve, and an approximate form of star formation and supernovae feedback following the Cen & Ostriker (1992) model. More details can be found in our earlier paper (Tonnesen et al. 2007). 2.2. Construction of our Sample In order to accurately determine the ICM conditions a gas-rich galaxy experiences as it falls into the cluster, we identify and track a sample of galaxies which form in the simulation. This naturally gives us realistic galactic trajectories. In order to construct the sample, we \ufb01rst separate our star particles into distinct galaxies based on regions of high-density in our N-body stellar code. A visual inspection of the data shows that, as in real clusters, galaxies are easy to identify because they are highly concentrated, with relatively few stars between galaxies. We used the HOP algorithm (Eisenstein & Hut, 1998), which uses a two-step procedure to identify individual galaxies. First, the algorithm assigns a density to each star particle based on the distribution of the surrounding particles and then hops from a particle to its densest nearby neighbor until a maximum is reached. All particles (with densities above a minimum threshold, \u03b4outer) that reach the same maximum are identi\ufb01ed as one coherent group. In the second step, groups are combined if the density at the saddle point which connects them is greater than \u03b4saddle. We use HOP because of its physical basis, although we expect similar results would be found using a friends-of-friends halo \ufb01nder. We identify all such galaxies in 33 outputs over 3.5 Gyr and then form trajectories by identifying the same galaxy in all outputs. The galaxies identi\ufb01ed and followed are most often near or above the mass of the Milky Way, although we do follow a few that are about a third of the Milky Way galaxy\u2019s mass. For more details, see our earlier paper (Tonnesen et al. 2007). 2.3. Measuring Ram Pressure After identifying all of the galaxies in our cluster, we measure ram pressure only around galaxies that have cool gas (T \u226415,000 K), as these are the galaxies it will a\ufb00ect. Ram pressure is measured by using the Gunn & Gott (1972) equation Pram = \u03c1v2 \u2206, where \u03c1 is the ICM density and v\u2206is the velocity di\ufb00erence between the ICM and the galaxy (|\u20d7 vgalaxy \u2212\u20d7 vICM|). For the galaxy velocity, we adopt the mean of the the cool gas within a 26.7 kpc sphere around the center of the galaxy. As described in detail in our earlier paper (Tonnesen et al. 2007), we chose this radius because it excluded gas from nearby galaxies while containing the gas from the galaxy we followed. Gas was de\ufb01ned to be part of the ICM if it had a temperature above 107 K. A galaxy\u2019s local ICM properties were determined by averaging the density and velocity of all ICM gas within a 90 kpc sphere centered on each galaxy. We compared these ICM measurements to ones taken using a mass-weighted average and an average only in an annulus from 26.7 kpc to 90 kpc, \ufb01nding no qualitative di\ufb00erence and negligible quantitative difference in our results. 3. RESULTS 3.1. E\ufb00ect of ICM Substructure on Ram Pressure In Figure 1 (a), we show the ram pressure experienced by galaxies as a function of distance from the cluster center. Although there is a strong trend of decreasing ram pressure with cluster distance, there is also a substantial scatter at \ufb01xed radius. This suggests that the assumptions about the ICM used by observers and theorists alike to understand galaxy-ICM interactions may be too simpli\ufb01ed. To explore the origin of this scatter, we plot in Figures 1 (b) and (c) the ICM density and v2 \u2206as a function of radius. From these \ufb01gures, we see that at 1 Mpc cluster radius, the central 80% of ram pressure values range over an order of magnitude, while the ICM density and square of the velocity vary by factors of three and six, respectively. At the virial radius (1.8 Mpc) the ram pressure varies across almost two orders of magnitude and both the ICM density and v2 \u2206vary by at least an order of magnitude. In order to make this more quantitative, we measure the variance of all three values in radial bins of 250 kpc width, normalizing the standard deviation by the mean of the value measured in each bin. Bin size does not a\ufb00ect our conclusions. Our results are shown in Figure 1 (d). In this \ufb01gure the normalized standard deviation of the ram pressure is the solid black line, the ICM density is the dash-dotted red line, and v2 \u2206is the dashed blue line. We note that the sum of the variances of the two components (i.e. density and v2 \u2206) closely matches the variance in the ram pressure, indicating that the two components are uncorrelated. Within the virial radius of the cluster, the standard deviation of the ICM density and v2 \u2206are very similar. The inner region is where most ram pressure stripping is thought to take place; we also found the most ram pressure stripping in our simulated cluster within the virial radius. Even in this region, di\ufb00erent orbits of galaxies, and the resulting di\ufb00erent galaxy velocities at a \ufb01xed cluster radius, are no more important than ICM density \ufb02uctuations in determining ram pressure. Outside the virial radius of the cluster, the standard deviation of the ICM density is higher than that of v2 \u2206, and more in\ufb02uential on the variation of the ram pressure. Far from the cluster core (r \u226b4 Mpc), we see that galaxies falling into the cluster for the \ufb01rst time are distributed in regions of both high and low density. Visualizations of this simulation show that at low redshift most galaxies fall into the cluster along a wide \ufb01lament, which must also have a large scatter in density (see Dav\u00b4 e et al. (2001) 3 (a) (b) (c) (d) Fig. 1.\u2014 This \ufb01gure shows the variation in (a) ram pressure, (b) ICM density and (c) the square of the velocity di\ufb00erence between the ICM and galaxies (v2 \u2206), all as a function of distance from the cD. In panel (d) lines are the normalized standard deviation as a function of distance from the cD for each of these three measurements, while the symbols show the same quantity for galaxies experiencing ram pressure greater than 10\u221212 dynes cm\u22122 (triangles are ram pressure, squares are ICM density, and X\u2019s are v2 \u2206). See \u00a73.1 for discussion. for a detailed discussion of the density of the Warm Hot Ionized Medium). Recall that this cluster has structure not only in the ICM density, but also in the ICM velocity. To check that the ICM velocity is not reducing the standard deviation of v2 \u2206, we also extracted the normalized standard deviation of v2 galaxy. This would be v2 \u2206if the ICM velocity were zero. The scatter of this value is even smaller than the scatter of v2 \u2206, so in a static ICM the density substructure would be even more important in varying ram pressure at \ufb01xed cluster radius. The lines in Figure 1 (d) include all of our data points, including ram pressure values well below those that could strip a galaxy of its gas. To check that this does not e\ufb00ect our conclusion, we also plot the standard deviation for the three variables using only ram pressure values greater than 10\u221212 dynes cm\u22122, the Gunn & Gott (1972) limit for ram pressure stripping to e\ufb00ect a Milky Way sized galaxy, as symbols with the same color scheme as the lines. Note that when we include only these values, the ram pressure variation is still contributed equally by density and velocity variations. It is clear from these results, whether we include all of our data or only those points with high ram pressure, that it is unrealistic to assume that the scatter in ram pressure values at a \ufb01xed radius arises mainly from varying galaxy velocities using di\ufb00erent orbits. 3.2. ICM Velocity Structure Since we track galaxies moving through the ICM, we can also critically examine the motions of the ICM gas that these galaxies experience. We \ufb01nd that ICM velocity is correlated with galaxy velocity, and therefore our measured ram pressure is smaller than would be found if we assumed a static ICM. We have plotted the magnitude of v\u2206against the magnitude of the galaxy velocity 4 Fig. 2.\u2014 The correlation between v\u2206(which is vgalaxy \u2212vICM ) and the galaxy velocity for galaxies with gas. If the ICM were static, all points would lie along the solid line. Most points lie below this line, indicating that ICM and galaxy velocities are correlated. See \u00a73.2 for details. in Figure 2. To guide the eye, we have drawn a line of equality, on which the points would fall if the ICM were static. The vast majority of the velocity di\ufb00erence measurements, particularly for low galaxy velocities, are smaller than the galaxy velocity. Recall that we are only following galaxies that have cool (\u226415,000 K) gas, which are dominated by galaxies falling towards the cluster center. The ICM velocity and galaxy velocity are correlated because the ICM is also falling towards the cluster center. This is true throughout the 3.5 Gyr adopted for our analysis, during which time no major merger event occurs that would re-disturb the ICM. From the visualizations of these simulations, the last signi\ufb01cant merger occurred at a redshift of about 0.5. The sound crossing time at the virial radius (using an ICM temperature of 4 \u00d7 107 K) is less than 2 Gyr, so in simple models the ICM would equilibrate within the time we study the cluster. Again, it is clear that the most simple assumption cannot well describe the ICM or its impact on ram pressure stripping, nor does the static assumption result in a median of the measured values. 4. CONCLUSION In this paper we have presented a detailed examination of the intracluster medium with which a galaxy interacts as it falls into a simulated galaxy cluster. We \ufb01nd that substructure in the ICM is more important in varying ram pressure than is often assumed and used when modeling ram pressure stripping. Speci\ufb01cally, we highlight three main points: 1. In our simulated cluster we measure a range of ram pressure values for any given radius in the cluster. This ranges from an order of magnitude at 1 Mpc, to two orders of magnitude at the virial radius (1.8 Mpc), to even larger deviations further from the cD. Therefore, ram pressure can be e\ufb00ective at larger radii wherever there is an overdensity. 2. The scatter in ram pressure at di\ufb00erent distances from the cD is due equally to the variation in the ICM density and the relative ICM-galaxy velocity (v2 \u2206) within the virial radius. This is true even when considering only higher ram pressure values. In fact, the normalized standard deviation in galaxy velocity is smaller than that of v2 \u2206. It is therefore not only the variety of orbital velocities that causes di\ufb00erent values of ram pressure at \ufb01xed cluster radius, but also the density and velocity structure of the ICM. Further from the cD, ICM density variations dominate those of v2 \u2206. 3. The ICM velocity is correlated with galaxy velocity, resulting in a smaller v\u2206than vgalaxy. This indicates that the ICM tends to move with in-falling galaxies, which then experience somewhat less rampressure than one would expect from a static ICM (although this is less true for high-velocity galaxies that are likely near the cluster center). We emphasize that although we determine the ICM properties from a simulation, it is well-known in the X-ray cluster \ufb01eld that ICM substructure in density is common and in good agreement with simulations (Mohr, Mathiesen, & Evrard 1999; Jeltema et al. 2005; Nagai et al. 2007). Because ram pressure stripping is a fast process, even an overdensity with a relatively small extent can strip a galaxy that might otherwise retain its gas, or strip a galaxy more than predicted by its cluster position. Our results should galvanize the community currently studying galaxy evolution in clusters to look more closely at the intracluster medium. GB acknowledges support from NSF grants AST-0507161, AST-05-47823, and AST-06-06959, as well as computational resources from the National Center for Supercomputing Applications. We thank Jacqueline van Gorkom for her help with this paper.",
                    "introduction": "1. X-ray observations of clusters have shown that sub- structure in the intracluster medium (ICM) is common (e.g. Mohr, Mathiesen, & Evrard 1999; Schuecker et al 2001). In a sample of 470 clusters, Schuecker et al. (2001) measure substructure in more than 50% of their sample. Detailed examinations of nearby clusters like Perseus and Virgo have discovered substructure and/or asymmetry in both the temperature and density pro\ufb01les of these clus- ters (e.g. Bohringer et al. 1994; Shibata et al. 2001; Churazov et al. 2003; Dupke & Bregman 2001; Furusho et al 2001). Even Coma, considered a relaxed cluster, has ICM irregularities (White, Briel & Henry 1993). The im- portance of substructure on cluster mass measurements has been examined (Mohr, Mathiesen & Evrard 1999; Bohringer et al 2000), which in turn a\ufb00ects the use of cluster measurements as cosmological constraints (Jel- tema et al. 2005; Nagai et al. 2007). However, the importance of substructure in the ICM is rarely considered when studying ram pressure stripped galaxies. Common assumptions are that the ICM is static, has a smooth density pro\ufb01le, and is only dense enough very near the center of a cluster to a\ufb00ect galax- ies. Treu et al. (2003), in their evaluation of possible en- vironmental evolutionary mechanisms in Cl 0024 + 16, assume that ram pressure is only e\ufb00ective to 0.6 virial radii. Solanes et al. (2001) \ufb01nd HI de\ufb01ciency in galaxies out to two Abell radii, but only discuss the possibility that these galaxies are on highly radial orbits that have already carried them through the cluster center. Pre- vious simulations studying galaxy evolution in clusters use a static, smooth ICM pro\ufb01le when studying the or- bits of galaxies in clusters (e.g. Vollmer 2001; Roediger & Br\u00a8 uggen 2007; J\u00b4 achym et al. 2007). These authors use di\ufb00erent galaxy orbits in order to sample a variety of galaxy velocities at a \ufb01xed ICM density. Although the use of simple assumptions is widespread, there is at least one possible case in which ICM sub- structure had to be invoked to explain observations of the Virgo galaxy NGC 4522, a galaxy with a truncated gas disk (Kenney et al 2004; Vollmer et al. 2004; Vollmer et al. 2006). NGC 4522 is located at a projected distance of 1 Mpc from the center of the Virgo cluster, and as- suming a static ICM with standard density values, the ram pressure is not strong enough to cause the observed truncation. Thus, the authors propose that the nearby ICM is either moving relative to the galaxy or overdense. In a recent paper studying the environmentally-driven evolution of galaxies in clusters using a detailed cos- mological simulation (Tonnesen, Bryan & van Gorkom 2007), we examined the evolution of cool gas (i.e. ISM) in galaxies within and around the cluster, demonstrating that most gas loss from galaxies was due to ISM-ICM interactions (i.e. ram pressure and related processes), rather than galaxy-galaxy interactions or cluster tidal ef- fects. We also found that ram pressure stripping occurs out to the virial radius of the cluster (measured using r200). In this paper, we examine this result more closely and show that the ram pressure a galaxy experiences varies substantially, even at \ufb01xed distance from the cluster cen- ter. As we will see, this arises both from the density and velocity substructure of the ICM. First, we brie\ufb02y in- troduce our code in \u00a72.1 and explain how we measure ram pressure in our simulation (\u00a72.2 and \u00a72.3). We then present our results: a comparison of the standard devi- ations of ram pressure, ICM density, and velocity di\ufb00er- ence squared (\u00a73.1), followed by a more detailed look at the velocity of the ICM (\u00a73.2). 2."
                },
                {
                    "url": "http://arxiv.org/abs/0709.1720v1",
                    "title": "Environmentally-Driven Evolution of Simulated Cluster Galaxies",
                    "abstract": "Galaxies in clusters are gas-deficient and a number of possible explanations\nfor this observation have been advanced, including galaxy-cluster tidal\ninteractions, galaxy harassment, and ISM-ICM gas stripping. In this paper, we\nuse a cosmological simulation of cluster formation and evolution in order to\nexamine this issue from a theoretical standpoint. We follow a large number of\ngalaxies over time and track each galaxy's gas and stellar mass changes to\ndiscover what mechanism(s) dominate the evolution of the cluster galaxies. We\nfind that while gas is lost due to a wide variety of mechanisms, the most\ncommon way is via a gas-only stripping event, and the amount of gas lost\ncorrelates with the ram-pressure the galaxy is experiencing. Although this\ngas-stripping occurs primarily in the central region (r < 1 Mpc), it is an\nimportant mechanism out to the virial radius of the cluster. This is due to the\nwide scatter in ram-pressure strength that a galaxy experiences at fixed\nradius. We find that the timescale for complete gas removal is > 1 Gyr. In\naddition, we find that galaxies in the field and in the cluster periphery (r >\n2.4 Mpc) often accrete cool gas; the accretion stops between 1-2.4 Mpc,\npossibly indicating the onset of galaxy starvation.",
                    "authors": "Stephanie Tonnesen, Greg L. Bryan, J. H. van Gorkom",
                    "published": "2007-09-11",
                    "updated": "2007-09-11",
                    "primary_cat": "astro-ph",
                    "cats": [
                        "astro-ph"
                    ],
                    "main_content": "2.1. Simulation We have simulated a massive cluster of galaxies with the adaptive mesh refinement (AMR) code Enzo. This cosmological hydrodynamics code uses particles to evolve the dark matter and stellar components, while using an adaptive mesh for solving the fluid equations including gravity (Bryan 1999; Norman & Bryan 1999; O\u2019Shea et al. 2004). The code begins with a fixed, static grid and automatically adds refined grids as required in order to resolve important features in the flow (as defined by enhanced density). The cluster forms within a periodic simulation box which is 64 h\u22121 Mpc on a side, in a flat, cosmologicalconstant dominated universe with the following parameters: (\u21260, \u2126\u039b, \u2126b, h, \u03c38) = (0.3, 0.7, 0.045, 0.7, 0.9). We employ a multi-mass initialization technique in order to provide high-resolution in the region surrounding the cluster, while evolving the rest of the box at low resolution. Timesteps are also refined in the more dense regions to follow in detail the rapidly changing conditions. The dark-matter particle mass is 6.4\u00d7108 M\u2299, with a gas mass resolution about five times better than this. The whole cluster has about one million dark matter particles within the virial radius, and a typical L\u2217galaxy is resolved by several thousand dark matter particles. The adaptive mesh refinement provides higher resolution in high density regions, giving a best cell size (resolution) of 3 kpc. This is sufficient to resolve the large galaxies in which we are interested, and also, we believe, to approximately reproduce effects such as ram-pressure stripping (although it is clear that the internal dynamics of galaxies will not be well resolved). A study of the gasstripping properties of this code is presented in Agertz et al. (2006), which demonstrates that the resolution required to correctly reproduce stripping in grid-based codes is less stringent than in particle-based codes. We discuss our tests of different resolutions in greater detail in Appendix A. In Figure 1 we show a snapshot of the gas and stellar distribution in our cluster. This shows two features, the 3 Fig. 1.\u2014 This image shows a projection of the gas density (top) and stellar density (bottom) at z=0.23 in our simulation. A number of galaxies exhibiting tails of stripped gas can be seen in the gas distribution. The region shown is 5.1 comoving Mpc on a side, and in both cases the surface density stretch is logarithmic. \ufb01rst is that most stellar systems within the cluster show only a stellar component, and the second is several clear cases of gas being stripped from galaxies. These can be seen by the associated tail which often points away from the cluster center. The simulation includes radiative cooling using the White & Sarazin (1987) cooling curve, and an approximate form of star formation and supernovae feedback following the Cen & Ostriker (1992) model. Brie\ufb02y, the star formation method relies on identifying cold, collapsing, high-density clouds and forms stars at a rate proportional to the density of gas divided by the dynamical time, multiplied by an e\ufb03ciency factor. This e\ufb03ciency is taken to be, somewhat arbitrarily, 2%. See O\u2019Shea et al (2004) for a more complete discussion of the star formation algorithm. Stars are represented as stellar particles, and the energy from Type II SN is returned to the gas in the form of thermal energy. Although this energetic output can be important, it is known that much of this energy is deposited in high-density gas where the cooling time is short and so is radiated away. This results in an \u201covercooling\u201d problem (e.g. Balogh 2001), and manifests itself in our simulations as somewhat overly massive galaxies, as well as a higher-than-observed ratio of stars and cool gas to hot gas. In addition, we observe hot intracluster gas cooling onto the centers of a few of the most massive galaxies (and in particular the central galaxy). This cooling is not observed in real clusters, probably because of feedback from supermassive black holes, which are not included in the simulation. 2.2. Construction of the Sample Although our simulation runs from z = 40, we only wish to compare our results to nearby, virialized galaxy clusters and thus only consider our simulated cluster from z = 0.352 to the present1. We output information from the simulation at time intervals of approximately 0.122 Gyr (although the timesteps within the simulation are orders of magnitude smaller), for a total of 33 output times. The output includes (i) the position, mass, size, creation time and metallicity of each star particle, and (ii) the position, mass, cell size, temperature, metallicity, and velocity of each gas cell. In the construction of our sample, we \ufb01rst separate our star particles into distinct galaxies based on regions of high-density in our N-body stellar code. A visual inspection of the data shows that (as in real clusters), galaxies are easy to identify because they are highly concentrated, with relatively few stars between galaxies. This is unlike the case for dark matter substructure, where it can often be quite di\ufb03cult to associate a given dark matter particle with a given sub-halo. We used the HOP algorithm (Eisenstein & Hut, 1998), which uses a two-step procedure to identify individual galaxies. First, it assigns a density to each star particle based on the distribution of the surrounding particles and then hops from a particle to its densest nearby neighbor until a maximum is reached. All particles (with densities above a minimum threshold, \u03b4outer) that reach the same maximum are identi\ufb01ed as one coherent group. In the second step, groups are combined if the density at the saddle point which connects them is greater than \u03b4saddle. We chose HOP because of its physical basis, although we expect similar results would be found using a friends-of-friends halo \ufb01nder. We set \u03b4outer, the minimum density for a particle to be part of a group, to 10000; \u03b4peak, the minimum central density for a galaxy, to 30000; and \u03b4saddle, the boundary density needed to merge two groups, to 25000 (all density values are relative to the cosmic mean). We chose these values because by visual examination we found that they picked out a single galaxy as the central object; however, reasonable variations in these parameters did not make a signi\ufb01cant di\ufb00erence in the number 1 Visualizations of these simulations can be found at http://www.astro.columbia.edu/\u223cgbryan/ClusterMovies 4 of galaxies. Using this algorithm, we \ufb01nd that each output (from z = 0.35 until z = 0) has between 155 and 186 galaxies within a 123 Mpc3 box. HOP separates the cluster into a set of galaxies at each output, but we still need to identify and follow a set of individual galaxies as they move through the cluster with time. We expect that the particles with the highest density correspond to the most central particles in a galaxy. Therefore, we \ufb01rst used the density for each star particle as calculated by HOP to select the 150 densest particles in every galaxy in every output (using the 80 densest particles produced similar results). For any galaxy with less than 150 particles we used the entire set. Then, starting with each galaxy in our \ufb01rst output, we looked through the sets of densest star particles in all of the galaxies in the next output for a match between particle identi\ufb01cation numbers (which indicates the same star particle at the center of both galaxies). If there were one or more matches between galaxies in consecutive times, we concluded that we were following a single galaxy. We continued this process from one output to the next for all 33 times. Because we intend to compare our results to observations of nearby virialized clusters, we only follow galaxies that were in our box from z = 0.35 until z=0. There were 155 galaxies in our earliest output, which dictated the maximum number of galaxies we could follow. Any galaxy that had no match from one output to the next was dropped from our sample. If a galaxy was dropped at any time, no part of its evolution is reported in the statistical results given below. Of the 155 galaxies with which we began, we were able to track 133. Because one of these is the cD galaxy, we report on the evolution of 132 galaxies. Ten of these galaxies merged before z=0, so by the end of our simulation we report on 126 individual galaxies. It is notable that although we can track arbitrarily small galaxies, none of the galaxies on which we report ever have less than 150 stellar particles. In fact, 64 of the galaxies we follow always have at least 3000 particles, and using only those galaxies in the following analysis gives similar results. Our galaxies were dropped for a number of possible reasons. They may have been swallowed by the cD, ripped apart by either the cluster potential or galaxy harassment, or merged into a galaxy that we did not follow. Also, a galaxy was dropped if it left the box. HOP may erroneously group two distinct galaxies together during a close \ufb02y-by, and we dropped a galaxy if it was grouped with one that we did not follow. By examining our data on the galaxies before they were dropped, we found lower limits for three of our dropping mechanisms: 4 galaxies left the box, 4 galaxies were swallowed by the cD,while 3 galaxies were incorrectly grouped by HOP (out of a total of 22 dropped galaxies). 2.3. Galaxy De\ufb01nition By following these 132 galaxies, we are able to determine both how many galaxies in a cluster underwent environmentally-driven evolution as well as the mechanisms that were driving their evolution. To do this, we measured the gas mass and stellar mass of each galaxy through time, using any changes to identify the mechanisms at work. The mechanisms we consider fall into three broad categories: ISM-ICM, galaxy-galaxy, and galaxy-cluster. For example, an ISM-ICM interaction would not change the stellar mass of a galaxy, but would reduce the gas mass. A galaxy-galaxy or galaxy-cluster interaction would e\ufb00ect both the gas mass and stellar mass, and depending on whether the masses increased or decreased, we would label the acting mechanism either tidal accretion or stripping. Because our determination of the environmental mechanism at work depends solely on the mass evolution of a galaxy, we examined our data in detail to carefully de\ufb01ne the boundaries of each galaxy. Although we were able to use HOP to \ufb01nd our galaxies, locate their centers (de\ufb01ned as their points of maximum density), and track them through time, actually using HOP to determine the stellar mass led to substantial \ufb02uctuations in their estimated masses. To minimize this sort of noise, we de\ufb01ned our galaxies masses to include all the stars and cool gas (T \u226415,000 K) within a sphere of a uniform radius. We originally chose the largest radius as de\ufb01ned by HOP (90 kpc) and applied it to all galaxies, but found that this introduced unphysical \ufb02uctuations in both the stellar and gas mass because it tended to combine distinct galaxies that happened to have overlapping radii. Therefore we examined the radial density pro\ufb01les, and found that a radius of 26.7 kpc almost never included gas from nearby galaxies, while by this radius the gas densities had usually gone to zero. All but four galaxies were su\ufb03ciently compact that the 26.7 kpc radius included 80% or more of the mass within the larger 90 kpc sphere. 3. RESULTS 3.1. Gasless Galaxy Distribution We \ufb01rst compare the morphology distribution in the simulation and observations. Because the internal structure of our galaxies is not well-resolved, we adopt a di\ufb00erent classi\ufb01cation scheme than traditional morphological type. Instead, we relied on the amount of gas mass, dividing them into two types: those with and those without cool gas (T \u226415, 000 K). We cannot comment on the molecular gas in the simulated galaxies because gas in our simulation cannot radiatively cool to molecular cloud temperatures, and long before it collapsed to the density of molecular clouds it will have formed stars. Therefore we do not comment on molecular gas throughout this paper, although we do expect that it might be stripped more slowly than the lower density gas that we do follow. While this classi\ufb01cation scheme is overly simpli\ufb01ed, it is still instructive to consider the resulting distribution. For example, the 132 galaxies that we track through time show a clear cluster-radius and gas content relation, seen in Table 1. Gasless galaxies begin to dominate the population at 2 Mpc and galaxies with gas dominate at large radii and outside the cluster. We considered our output for the 132 galaxies at 15 equally spaced (\u22480.244 Gyr) output times, thus giving us 1,980 \u201cobservations\u201d. We treat each data point as distinct because, although every galaxy is measured 15 times, at each observation it is in a di\ufb00erent part of the cluster and therefore could be in\ufb02uenced by di\ufb00erent environmental e\ufb00ects. This is less true for galaxies far from the cluster center. Ideally, we would compare our galaxies to observations of the galaxy gas population, however, large, complete samples extending to large radius do not yet exist. Although our gasless galaxies could be either E+S0s or spi5 TABLE 1 Simulated Gasless Galaxy fraction compared to T2003 E+S0 fraction Inner 200 kpc Central Region Transition Region Periphery (0-200 kpc) (0.2-1 Mpc) (1-2.4 Mpc) (2.4-5 Mpc) Gasless Galaxy Fractiona 93.5% 66.7% 48.9% 14.5% E+S0 Fractionb 75% \u00b1 10% 50% \u00b1 7% 51% \u00b1 7% 42% \u00b1 13% aFraction of gasless galaxies whose average distance in a timestep is within the stated boundaries. bFrom T2003 and references therein rals, we expect the majority of our gasless population to be E+S0s. If we make this rough translation, we can compare our galaxy distribution to the observations of Treu et al. (2003, henceforth T2003). We choose this comparison because our simulated cluster has a virial radius (calculated as r200) similar to that of Cl 0024+16 (1.8 Mpc and 1.7 Mpc, respectively), and we can split our cluster into the same diagnostic regions as in T2003: 0-1 Mpc is the central region; 1-2.4 Mpc is the transition region; and 2.4-5 Mpc, the periphery. However, our simulation di\ufb00ers from observations in that we have the exact distance from cluster center of all our galaxies in three dimensions, so we do not have any uncertainty due to projection e\ufb00ects. In our simulation, gasless galaxies dominate the population within 200 kpc, comprising 93.5% of the galaxies. We compare our gasless fraction to the E+S0 fraction reported by T2003 in Table 1. Within 1 Mpc, our gasless galaxy fraction is larger than the E+S0 fraction of T2003. Between 1 Mpc and 2.4 Mpc the fraction of gasless galaxies in our simulation is within one sigma of the observed E+S0 fraction. In the outer region (2.4-5 Mpc) the gasless galaxy fraction is less than half of the fraction of E+S0 galaxies observed in the \ufb01eld. While this qualitative agreement is promising, we can speculate about the cause of the observed disagreement. If our simulated cluster were older than that observed by T2003, we would expect our elliptical fraction in the central regions to be larger than the value they \ufb01nd (T2003 and references therein). Also, our gasless fraction may be high because we have no dilution of our central region sample due to projection e\ufb00ects. However, one of the most important reasons for the mismatch between our gasless galaxy distribution and T2003\u2019s E+S0\u2019s is that we are comparing two di\ufb00erent populations and assuming there is signi\ufb01cant overlap. Because we are counting gasless galaxies instead of E+S0 galaxies, any gasless spirals in the inner regions of our cluster will cause our fraction to be higher than T2003\u2019s. For example, Solanes et al. (2001) have observed highly de\ufb01cient spirals in the central regions of clusters. Also, E+S0s are not necessarily gasless in the \ufb01eld (Morganti et al. 2006 and references therein). In the outer regions, the overabundance of cool gas is consistent with previous simulations of galaxy formation, a problem often referred to as the overcooling problem. One suggested solution to this problem is energetic feedback from AGN, which can heat up cool gas and eject it from the galaxy (e.g. Bower et al. 2006). Therefore, we caution that we may be overestimating the number of galaxies with gas and the amount of cool gas some galaxies contain. In addition to the overcooling problem in elliptical galaxies in general, one or two of the galaxies in the central regions of our cluster have a very large amount of cool gas (> 1011M\u2299). As noted above, the lack of AGN feedback in our simulations is one possible reason for these high gas masses. Indeed, half of the observations of galaxies with gas mass over 1011 M\u2299are of the largest galaxy we follow at di\ufb00erent times. This galaxy may be large enough that it is susceptible to the same overcooling problem as the cD galaxy. 3.2. Simulated Galaxy Evolution as a Function of Environment We will now use our simulated sample to examine how a galaxy gains and loses mass. Recall that we track the evolution of galaxies purely by following the changing gas and stellar mass of each galaxy. Using only the change in stellar mass and gas mass, we have \ufb01ve likely evolutionary tracks: (i) gas mass loss without stellar mass loss, indicative of an ISM-ICM interaction; (ii) gas mass gain without stellar mass gain, suggesting gas accretion; (iii) gas mass loss equal to stellar mass increase, implying star formation; (iv) both gas and stellar mass loss, indicative of tidal stripping or galaxy harassment; and (v) increase in both gas and stellar mass, suggesting accretion or a merger. Each of these processes is represented by a unique vector in the (\u2206Mgas, \u2206Mstar) plane, which is shown in Figure 2. From our simulated data we can compute the change in gas and stellar mass for each galaxy during each timestep (\u2206Mgas, \u2206Mstar) and plot this value for each galaxy for each time step in Fig. 2. Out of a total of 1,980 points, we only show the galaxies that may be a\ufb00ected by the cluster environment, de\ufb01ned as being closer than 5 Mpc to the cD during each 0.244 Gyr timestep. This leaves us with 1,257 observations of cluster galaxies. To make most of the points in our plot more readable we have zoomed in on the inner region of our graph. Thus two of the merger observations are outside of the range of this plot, and a few observations along the y-axis. Fewer than 2% of our observations are outside of the plot range in Figure. 2. Star formation may or may not be environmentally induced, so in this initial examination of galaxy evolution, we remove its e\ufb00ect on the gas and stellar mass. To do this, we \ufb01rst used the creation time of every star particle in our code to identify the amount of stellar mass formed during a timestep. We then transferred all of a galaxy\u2019s stellar mass that was created during that timestep to the gas mass of that galaxy. Thus, when we plot a 6 Fig. 2.\u2014 Comparison of the change in cool gas mass (T \u226415 000 K) and the change in stellar mass of all observations of galaxies within 5 Mpc of the central cD (1,275 points). The colors and shapes denote distance to the cD: blue diamonds are at 0-1 Mpc, red triangles at 1-2.4 Mpc, and green squares are at 2.4-5 Mpc. We have removed the e\ufb00ect of star formation within each galaxy in order to focus on direct environmental e\ufb00ects. galaxy that had only undergone star formation during a timestep in this \ufb01gure, we will see no change in either the stellar or gas mass. This process is done separately for each galaxy and each timestep. Our results are shown in Figure 2, with a more quantitative view of the results in Table 2. In the table, for all nine possible galaxy mass permutations (\u2206Mstar positive, zero, or negative and \u2206Mgas positive, zero, or negative), we list: the number of observations in each category, the total change in gas mass summed over all galaxy observations, and the total stellar mass change. Notice that the placement of the nine boxes visually corresponds to the nine zones in the plot. Since we have removed star formation, most of our galaxies are clustered near the origin, having no large change in mass (see also Table 2). This is the largest set of galaxies, and contains both galaxies that have no mass variation in a time-step, and those that only form stars out of their own gas (i.e. are evolving without obvious external in\ufb02uence). For the purpose of Table 2, we treat small mass changes (within \u00b13.16 \u00d7 109M\u2299of zero) as constant for both the gas and the stellar masses. We chose this value by \ufb01tting a guassian to the points near the x-axis of our plot, and adopting the 3\u03c3 value. This choice gives 729 observations in the \u201cconstant\u201d category, which is our largest group. There are also a number of galaxies \u2013 along the negative x-axis \u2013 which are undergoing gas mass loss only: it seems likely that these galaxies are a\ufb00ected by ram pressure and associated ISM-ICM stripping processes because there is gas loss and no (or very little) change in stellar mass. As can be seen in Table 2, this category represents the most frequent source of gas mass loss and also results in the highest amount of gas mass loss. We will examine these systems in more detail in section 3.3. The galaxies along the positive x-axis are accreting cool gas from their surroundings, or from a larger halo. This is also a large group of objects, and such accretion is the primary mode for the growth of gas-rich galaxies in our simulation. We will discuss them in more detail below. The galaxies that fall along the y-axis are galaxies (most often gasless galaxies with therefore exactly zero \u2206Mgas) that are either accreting or losing stars. Some of the points along the vertical axis do not represent true stellar mass gain or loss, but are instead due to doublecounting during a near collision. During close encoun7 Fig. 3.\u2014 These histograms compare of the changes in cool gas mass (T \u226415 000 K) for the galaxies that have no change in their stellar mass. The \ufb01gure on the left records gas mass loss, while the right \ufb01gure shows the gas mass gain. The colors denote distance from the cD, as in Figure 2. The central regions galaxies are denoted with a dashed line, the transition region with a dotted line, and the periphery with a solid line. Note that the central region galaxies are often gasless or undergoing gas stripping. The transition region galaxies are undergoing more gas stripping than predicted by T2003. The periphery galaxies are accreting gas as is expected outside of clusters. Because the large number of galaxies undergoing no environmentally-driven change in gas mass would dominate this histogram, we have cut out a small section surrounding zero gas mass change. ters, galaxies \ufb01rst appear to gain stars in one timestep and then lose them in the next as the other galaxy moves into and then out of the spherical galactic region. This would produce a pair of points with similar magnitudes but opposite signs. Neither of these points would represent true loss or gain (although harassment might cause some true stellar mass loss). However, we also expect to see gasless galaxies being stripped of stars by the large cluster potential and possibly by galaxy-galaxy interactions. This is observed, both in the number of galaxies a\ufb00ected and the total stellar mass gained and lost. If every instance of increased stellar mass is a product of a close \ufb02y-by and thus paired with a stellar mass decrease, we still observe at least 70 galaxies undergoing tidal stripping or harassment. Besides the axis, the other quadrants are relatively empty. The galaxies that are observed to lose stars and gain gas (in the lower right quadrant of Fig. 2) are likely to be undergoing two processes within one timestep. When we made the same graph using timesteps half as long we found only 62.5% of our observations remained in the fourth quadrant. The very small number of galaxies observed to gain stars and lose gas may also be caused by the aggregation of a few processes. Despite this, we chose not to use the smaller timestep because in most cases it splits up a single process, resulting in more smaller mass changes along the axes. The points from the central cluster region in the lower right quadrant of Figure 2 are dominated by the largest galaxy that we follow (7 of 10 points). These points may be caused by the galaxy being physically stripped by the cD while it is unphysically overcooling surrounding gas. The galaxies losing both gas and stars may be undergoing galaxy harassment or tidal stripping by either the cD or a nearby galaxy. In a parallel process, the galaxies that are gaining both gas and stars are either merging or accreting both gas and stars from their surroundings or a nearby galaxy. We found a lower limit of three mergers by counting the number of tracked pairs that merge within a radius of 5 Mpc from the cD. It is interesting that all three of these mergers involve galaxies with gas, and all three merged galaxies continue to contain cool gas throughout the simulation. The points in Figure 2 are color-coded by the galaxy\u2019s minimum distance from the central cD during each timestep; blue diamonds are within 1 Mpc, red triangles are within 2.4 Mpc, and green squares are out to 5 Mpc. It is clear from a visual inspection of the plot that many of the central galaxies are either gasless galaxies undergoing a tidal process or galaxies undergoing gas stripping. The galaxies in the periphery are the majority of the galaxies gaining gas, as spirals are conjectured to do in the \ufb01eld (Larson, Tinsley & Caldwell 1980). The transition region galaxies are not so easily categorized, and seem to consist of galaxies undergoing processes more clearly associated with one of the other two regions. On a qualitative scale, our graph compares well with T2003\u2019s Figure 10 in that we see more ISM-ICM interactions close to the cD and mergers spanning the entire 5 Mpc: three of the points in the \ufb01rst quadrant of Figure 2 are mergers between tracked galaxies, two of which are in the central region and one of which is in the periphery. In Figure 3 we look more closely at the points that lie along the positive or negative x-axis, and generate the distribution of gas mass loss and gain, again color-coded by the galaxy distance from the cD. The left histogram shows that most of the ram pressure stripping occurs in galaxies in the central region, but does also have some impact on galaxies in the transition region and, to a lesser extent, the periphery. Further, the right histogram shows that gas accretion is occuring, and occurs mostly to galaxies in the periphery. There is a signi\ufb01cant drop in the number of galaxies accreting gas in the transition region in comparison to the periphery, and we may be seeing the region where starvation begins to occur (Larson, Tinsley & Caldwell 1980). 8 Gas Mass Constant Gas Mass Loss Gas Mass Accretion Stellar Mass 5 57 26 Accretion -6.747 -0.57 56.991 4.267 49.254 62.578 Constant 84 729 169 Stellar Mass -65.834 6.977 158.785 -5.893 -27.433 -4.349 Stellar 18 125 44 Mass Loss -14.83 -0.312 54.597 -120.412 -220.414 -85.618 TABLE 2 This charts the possible changes to gas and stellar mass of the galaxies that are observed within 5 Mpc of the cD. It is a more quantitative description of the information graphed in Figures 2 and 3. Note that the organization of this chart matches the layout of Fig. 2. For each category we include three rows of information: 1) the total number of observations in that category, 2) the total amount of gas mass lost or gained in all the observations, and 3) the total stellar mass change. The total mass changes are in units of 1010M\u2299. There are a total of 1257 observations. 3.3. Ram Pressure Stripping Of the 107 observations in which a galaxy loses gas by a mechanism other than star formation, at least 84 \ufb01t our criteria for ICM-ISM interactions (refer to Table 2). In order to better examine how \u2206Mgas changes with radius, we plot \u2206Mgas against the distance from the central cD, still removing star formation. Figure 4 shows that there is an increase in both the amount of gas mass lost and the number of galaxies losing gas, with decreasing distance from the cD. This trend is strongest for r < 1 Mpc, but begins at about 2 Mpc, signi\ufb01cantly beyond the 1 Mpc radius T2003 had used as the edge of high ICM density. To clarify the reason for this trend, we calculated the ram pressure as \ufb01rst derived by Gunn and Gott (1972): \u03c1v2, where \u03c1 is the ICM density and the v is the relative velocity between the ICM and the ISM. Gas was de\ufb01ned to be part of the ICM if it had a temperature above 5 \u00d7 106 K. The density was calculated for all the hot gas in a sphere of radius 90 kpc centered on a galaxy center previously identi\ufb01ed by HOP. To \ufb01nd the velocities of the ICM and ISM we averaged the velocities of all the individual cells of gas that were included in the 90 kpc or 26.7 kpc sphere, respectively. We then took the magnitude of the velocity di\ufb00erence to use in our ram pressure calculation. Figure 5 shows how ram pressure varies with distance from the cD: there is a de\ufb01nite increase of ram pressure with decreasing distance to the cluster center beginning at about 2 Mpc. This correlates well with the increasing gas loss with decreasing distance to the cD. It is also important to note that \u03c1v2 varies by about two orders of magnitude at a given radius. This is partially due to the density and velocity structure in the ICM which is apparent in the simulations, and partially due to the wide range in galaxy velocities at a given radius. To illustrate the importance of this e\ufb00ect, we can see that, for example, at 2 Mpc from the cD, ram pressure is often below the value of 10\u221212 derived by Gunn & Gott (1972) to be the minimum ram pressure for e\ufb00ective stripping, but there are some observations of higher Fig. 4.\u2014 The change in gas mass plotted against the average distance from the cD for each timestep. The amount of gas mass loss per observation and the number of observations of gas loss begin to increase sharply at 2 Mpc, just beyond the rvir (1.8 Mpc) of the cluster. ram pressure values. Figure 6 plots the amount of gas mass loss against ram pressure. The color-codes are the same as in Figures 2 and 3, and in this \ufb01gure see a de\ufb01nite relation between gas loss and ram pressure. Although most of the points with a large amount of gas loss and high ram pressure are from galaxies within the inner 1 Mpc of the cluster, there are a few galaxies that seem to be ram pressure stripped from the transition region, consistent with our interpretation of Figures 4 and 5. While the correlation with ram pressure strength is indicative of a role for ram pressure stripping, we should note that we do not exclude viscous stripping and other mechanisms which scale in a similar way. In the following, we refer to these processes collectively as rampressure stripping. 3.4. Case Studies of Gas-stripped Galaxies To examine the stripping process in more detail, we examined the 16 galaxies that went from having a cool gas mass of more than 3.16 \u00d7 109M\u2299at z \u223c0.35 to having no cool gas by the end of the simulation. We chose this mass loss cuto\ufb00because it is the limit of our \u201cconstant\u201d category, as discussed earlier. Of the 119 observations of these 16 galaxies, 37% \ufb01t our gas loss criteria, for a total cool gas mass loss of 3.86 \u00d7 1011M\u2299, caused by all mechanisms (other than star formation). Of the observations of galaxies losing gas, 89% have no change in stellar mass, which we take to indicate ram pressure stripping (or a related mechanism). These observations are distributed among thirteen of the sixteen galaxies, for a total of 3.25 \u00d7 1011M\u2299gas mass lost by ram pressure stripping. To verify that we are not merely seeing a part of a longer episode of tidal stripping or galaxy harrassment that included only gas loss for a subset of the observations, we looked at the four observations in which both 9 Fig. 5.\u2014 Plot of \u03c1v2 against distance from the cluster center. In the inner 2 Mpc of the cluster there is an increase in ram pressure, evidence that ram pressure is indeed the cause of the increase in gas loss seen in the galaxies in the inner region of the cluster. gas and stars were lost. Only one of these was of a galaxy that also contained an observation of pure gas stripping. Even ignoring this galaxy, 88% of gas loss observations are of ram pressure stripping. To be conservative in our number of ram pressure stripped galaxies, we assumed that the galaxy that had only gas loss followed by both gas and stellar mass loss did not undergo ram pressure stripping. Thus, we only include 12 galaxies in our ram pressure stripping statistics. Next, we considered where in the cluster these galaxies were being stripped. Although most of the galaxies undergoing ram pressure stripping were in the central region of the cluster, 40% of the observations were of galaxies in the transition region. Of those in the transition region, only 13% were of galaxies that had been within 1 Mpc of the center since z\u223c0.35. Thus, most of our observations of galaxies undergoing ram pressure stripping in the transition region were beginning the ISM-ICM interaction there. We even observed a single galaxy being ram pressure stripped in the periphery for \u223c2.5 Gyr. This galaxy was also unique in that it had lost all of its gas before reaching the central region of the cluster. Finally, we can give a rough estimate (because our time resolution is 0.244 Gyr) of the length of time it took galaxies to lose their gas once gas loss began. This is a worthwhile estimate for comparison to T2003, who de\ufb01ne any ISM-ICM interaction that is longer than 1 Gyr as starvation. We \ufb01nd that 5 of the 12 galaxies ful\ufb01lling our ram pressure stripping requirement lose their gas in about 1 Gyr. However, we also \ufb01nd that 5 galaxies lose their gas in well over 1 Gyr, and only 2 galaxies lose their gas in much less than 1 Gyr. This is in tentative agreement with T2003\u2019s conclusion that galaxy transformation is generally a slow process. In order to illustrate some of the possible evolutionary paths of the galaxies that lose all their gas, we choose four galaxies to discuss in detail. In Figure 7, for each Fig. 6.\u2014 A plot of the change in cool gas against ram pressure. The color-coding is the same as in Figures 2 and 3. This also supports the claim that ram pressure stripping is the most important cause of gas loss in these cluster galaxies. We also see that ram pressure seems to be a\ufb00ecting some galaxies in the transition region (red triangles). of the galaxies, we plot four quantities as a function of time: (i) the total stellar mass of the galaxy, (ii) the total gas mass of the galaxy, (iii) the amount of mass that will form stars in the next 0.244 Gyr, and (iv) the distance from the cD. In this \ufb01gure, because we also plot the amount of star formation, we do not attempt to make any corrections to the gas or stellar mass to account for it. The galaxy in Figure 7a, galaxy A, is most representative of the 16 galaxies we examine in detail, both in terms of mass and evolution. When we begin to track this galaxy, it has more stellar mass than gas mass, although only by about a factor of three. Galaxy A\u2019s orbit is the most circular of the four chosen galaxies, and we may see most of a circuit of galaxy A around the cD. This galaxy gains gas in the \ufb01rst 0.244 Gyr of our observations. Early gas accretion is common in our sample of stripped galaxies, as 56% of the galaxies that eventually lose all their gas \ufb01rst gain gas for at least one timestep. It is also not uncommon for a galaxy to gain cool gas mass within the transition region, as this galaxy does. However, immediately after galaxy A accretes cool gas, its gas is stripped for 0.732 Gyr. This is one of the faster stripping events we observe. All the stripping occurs within the central region of the cluster, as predicted by T2003. Once the galaxy is stripped of its gas (after about 1 Gyr of observations), there are no more signi\ufb01cant changes to its mass. In Figure 7b, our observations of galaxy B begin when this galaxy has almost the same amount of gas and stellar mass. This indicates that we may be observing the \ufb01rst time this galaxy has entered the central region of the cluster. Most of the increase in stellar mass is due to star formation, and we see that it ends when there is no more gas in the galaxy. All of the small ripples in the stellar mass of the galaxy are too insigni\ufb01cant to be outside of 10 Fig. 7.\u2014 Each graph plots four items against time: 1) in blue, the total stellar mass of the galaxy (for Fig 7(a) in units of 1011M\u2299, for Fig 7(b-c) in units of 1010M\u2299, and for Fig 7(d) in units of 1012M\u2299, 2) in black, the total gas mass of the galaxy (in units of 1010M\u2299), 3) in red, the amount of mass that will form stars in the next 0.244 Gyr (in units of 1010M\u2299), and 4) in green, the distance from the cD (in Mpc). The linestyles associated with the four items are shown in the legend. In this \ufb01gure, because we also plot the amount of star formation, we do not attempt to make any corrections to the gas or stellar mass to account for it. See \u00a73.4 for discussion. our zero range of \u00b13.16 \u00d7 109M\u2299. For six of the eight timesteps that this galaxy has gas, we categorize it as undergoing ram pressure stripping. During the other two timesteps the gas mass loss is small and within our zero range. This is an interesting galaxy because it still has gas when it leaves the cluster center, perhaps because the closest approach is barely within 1 Mpc. If this galaxy is not anomalous, there should be some galaxies in clusters with displaced gas pointing towards the cD in addition to ram pressure stripped galaxies with tails pointing away from the cD. One galaxy with a tail pointing towards M86 (the central galaxy in a merging group) in the Virgo cluster has recently been observed by Oosterloo & van Gorkom (2005). Galaxy C, in Figure 7c, also begins with a similar amount of gas and stellar mass. The orbital path is consistent with a \ufb01rst entry into the cluster environment, and like galaxy B, the stellar mass increases slightly while the galaxy has gas because of star formation. As with galaxy A, this galaxy accretes gas before it starts to be stripped. This galaxy, like half of the galaxies that undergo ram pressure stripping, begins being stripped of gas in the transition region, before it enters the central region of the cluster. Galaxy C is stripped as far from the cD as 1.7 Mpc. After 1.5 Gyr this galaxy has no more gas. Nearly 2.5 Gyr after we begin observing this galaxy it is stripped of a small amount of stars. At this point the galaxy has passed its closest approach to the cD by almost 1 Gyr and 1 Mpc, so it seems unlikely that material is being stripped by the cD. Late stellar mass loss is not uncommon: 56% of the galaxies that become gasless go on to lose stars for at least one timestep. We speculate that this is due to galaxy harassment. The galaxy in Figure 7d, galaxy D, is one of the \ufb01ve most massive galaxies we observe in our simulation. We begin following this galaxy as it falls from the transition region into the central region, however, with our limited amount of orbital information, we cannot tell whether this galaxy is falling towards the central region for the \ufb01rst time. In this galaxy the amount of stellar mass is two orders of magnitude larger than the amount of gas mass. The extremely small amount of gas mass leads us to believe that this galaxy has been in\ufb02uenced by the cluster environment for some time. The gas mass lost in 11 the \ufb01rst 0.244 Gyr is almost entirely due to star formation. As galaxy D enters the central region of the cluster, a small amount of both gas and stars is lost. There is another galaxy that we follow that is less than 200 kpc from galaxy D during the second 0.244 Gyr period, and so this may be an example of a galaxy-galaxy tidal stripping event (i.e. harassment). In the third timestep, there is no change in the stellar mass of galaxy A, but the rest of the gas mass is lost. Although we measure this as ram pressure stripping, we hesitate to make a de\ufb01nitive categorization because it follows a timestep in which both gas and stars are lost. Once the gas is stripped from galaxy A, there is no signi\ufb01cant change in stellar mass until \u223c1.5 Gyr into our tracking. At this point, 43.1\u00d71010M\u2299is lost in one timestep and 9.86\u00d71010M\u2299 in the next. Again, the galaxy has passed its closest approach to the cD (by almost 0.5 Gyr and 0.5 Mpc). After this \u223c0.5 Gyr stellar stripping event, the galaxy undergoes no more signi\ufb01cant mass changes. There are a few important points that this subsample of galaxies highlights. First, approximately 75% of the galaxies that lose all their gas are a\ufb00ected by ram pressure stripping, often losing most of their gas by this mechanism. In half of the ram pressure stripped galaxies, the stripping begins in the transition region, further than assumed by T2003, although most of the gas is lost in the central region. As discussed in the introduction, there have been observations of ram pressure stripping far from the cluster center. Gas stripping tends to be a long process, generally taking at least 1 Gyr. Also, once these galaxies lose their gas, over half of them undergo a stellar stripping event that is not clearly due to the cD. 4. CONCLUSIONS In this paper we have presented a \ufb01rst examination of how the gas and stellar content of galaxies evolve within a cosmological simulation of a cluster of galaxies. We use a high resolution simulation that includes the required gas, dark matter and stellar physics in order to \ufb01nd out how and when galaxies lose their mass. Our main results are: 1. We have tracked 132 galaxies through time in a detailed simulated cluster environment. We make comparisons with recent observations, speci\ufb01cally those of Treu et al (2003). Like T2003 we split our cluster into three regions: central region (r < 1 Mpc), transitional region (1 < r < 2.4 Mpc), and the periphery (r > 2.4 Mpc). We \ufb01nd a relation between the cluster-radius and galaxy gas content that is qualitatively similar to that found by T2003 (see Table 1), although we note that a detailed comparison is di\ufb03cult by our inability to assign a reliable morphological class to our simulated galaxies. 2. Most of the gas lost from galaxies in our simulations is lost in a gas-only event (i.e. the stellar mass in unchanged). These events are preferentially found in the central region, but can occur as far out as 2 Mpc from the cluster center. We \ufb01nd that the amount of gas loss correlates with the ram-pressure experienced by the galaxy, indicative of a ram-pressure origin to the gas loss. At \ufb01xed radius from the cluster, there is a wide variation in the ram-pressure strength experienced by a given galaxy. 3. We observe mergers both in the central region of our cluster as well as in the periphery, consistent with T2003. We do not observe any dry mergers (although they might occur in the galaxies we do not follow), and none of the mergers we follow exhaust the gas supply of the participating galaxies. Further, we observe disruptions of both the gas and stellar mass in galaxies in all three regions that could be attributed to galaxy harassment or other galaxy-galaxy interactions (Figure 2 & Table 2). 4. Galaxies in the periphery and \ufb01eld (r > 2.4 Mpc) are observed to accrete cold gas; however, this accretion is largely suppressed for galaxies in the transition and central regions (r < 2.4 Mpc). We interpret this as starvation caused by the ICM. 5. By examining in detail the galaxies that lose all their gas, focusing on four di\ufb00erent cases in particular, we were able to draw more detailed conclusions about this small subset of 16 galaxies. First, ram pressure stripping, which a\ufb00ected at least 12 of these galaxies, is the dominant mechanism causing galaxies to lose their gas. Ram pressure stripping began in the transition region for half of the stripped galaxies, and in one case in the periphery. In agreement with T2003, we \ufb01nd that gas stripping tends to occur on timescales \u22651 Gyr. Although these total gas stripping events may begin as starvation, only e\ufb00ecting the outer halo gas associated with these galaxies, they clearly end by removing any gas that would have been in the galactic disk. As addressed above, we cannot make any claims about the fate of dense molecular gas. We also found that many galaxies, once they lost their gas, also lost a signi\ufb01cant amount of stellar mass. It was not clearly correlated with a galaxy\u2019s closest approach to the cD, nor was it followed by a merger. This \ufb01nding may lend tentative support to galaxy harassment as an important mass stripping mechanism. We interpret these results to mean that the decrease in gasless galaxy fraction with increasing cluster radius can be explained by environmental mechanisms out to almost 2 Mpc. This result parallels observational \ufb01ndings by, eg, Solanes et al (2001). ISM-ICM interactions are important out to this large radius, and ram pressure stripping may have a large role in transforming spirals into S0s out to this distance. The ICM in our simulation has signi\ufb01cant substructure, which can been seen in the spread of ram pressure values at any cluster radius in Figure 5. A similar range of ICM density at di\ufb00erent clustercentric radii is seen in our simulations, and density variations have also been observed (e.g. Bohringer et al. 1994). The ICM\u2019s structure could explain why it is more important than in the simple assumptions used by T2003. However, the stripping process can be very slow (\u22651 Gyr), and therefore conforms to the broad de\ufb01nition of starvation used by T2003. 12 We make clear predictions about RPS, and can compare the mass evolution caused by galaxy-galaxy and galaxy-cluster interactions with that caused by ISM-ICM interactions. However, we do not compare galaxy-galaxy and galaxy-cluster interactions. This is because these interactions can have the same signature e\ufb00ects on the gas and stellar mass of a particular galaxy. In order to make any comparisons we will have to make detailed calculations about the force over time of nearby galaxies and the cD. Also, although we see de\ufb01nite trends with radius, we have not begun to look at whether there is a relation between the local density of galaxies and evolutionary mechanism. These will wait for a future examination. We gratefully acknowledge the National Center for Supercomputing Applications, which provided computational resources for the simulation described in this paper. Greg Bryan acknowledges support from NSF grants AST-05-07161, AST-05-47823, and AST-06-06959. JvG acknowledges support from NSF grant AST-06-07643. APPENDIX RESOLUTION STUDY We have performed a set of more detailed single-galaxy simulation runs to verify that our results are resolution independent. We use the galaxy model of Roediger & Br\u00a8 uggen (2006), with the addition of radiative cooling (but no star formation). The ICM temperature and density are 4.385 \u00d7 107 K and 10\u221228 g cm\u22123, respectively. The two runs we present here have resolutions of 304 pc and 2.43 kpc. As necessitated by the di\ufb00erent resolutions, the gas disk scale height in the z direction increases from 0.4 kpc to 4.0 kpc. We perform runs with two velocities, a subsonic and supersonic case: 8.0 \u00d7 107cms\u22121 and 2.53 \u00d7 108cms\u22121. Unlike Roediger & Br\u00a8 uggen (2006), all of the ICM in our simulation instantaneously begins to move at the wind speed. As in our paper, we follow the cool (T \u226415, 000 K) gas mass within a sphere with a radius of 26.7 kpc. Although we start with no gas cooler than 15,000 K, most of the gas within the galaxy quickly cools to below our upper limit. We show our results in Figure A1. As seen in the upper panel, very little gas is lost in either of the galaxy models in the subsonic run. In the supersonic run shown in the lower panel, the galaxy with the smaller scale height and higher resolution initially loses cool gas more quickly. However, the disk with higher resolution keeps a smaller disk of cool gas, while the lower resolution disk continues to slowly be stripped of it\u2019s gas with time. Because we do not include star formation, we are missing the energy that would be input by the resulting supernovae and increase the height of the disk. We perform a simulation without radiative cooling, and therefore with a thicker disk, and \ufb01nd that the gas loss between galaxies of di\ufb00erent resolutions is more similar. We expect that including star formation results in disks with larger z scale heights, and therefore that the gas loss measured in the galaxies in the cosmological simulation is less e\ufb00ected by resolution di\ufb00erences than in the galaxies we show here (with only radiative cooling). Similar results are found when the galaxy is edge-on to the wind. As shown in Figure A1, although the gas loss history di\ufb00ers in the two models, the di\ufb00erence is never large. Based on these results we are con\ufb01dent that our resolution is high enough to measure the amount of cool gas a galaxy may lose outside of a small dense disk.",
                    "introduction": "1. It has long been known that a galaxy\u2019s environment has an impact on its morphology: spirals dominate in the \ufb01eld, and ellipticals and S0s are more prevalent in dense cluster environments (Hubble & Humason 1931). This has been quanti\ufb01ed in the density-morphology relation (Oemler 1974; Dressler 1980), but this relation alone does not determine whether the cluster environment a\ufb00ects the formation or the evolution of galaxies. According to the Butcher-Oemler e\ufb00ect, cluster galaxies at z \u22650.2 are bluer than nearby clusters (Butcher & Oemler 1978), indicating that cluster age or evolutionary status may be related to the evolution of galaxies from spirals to earlier types. It has been found that the spiral to S0 ratio increases with decreasing redshift (Dressler et al. 1997; Fasano et al. 2000). More recently, by examining a speci\ufb01c merging cluster, Tran et al. (2005) presented a strong relationship between the Butcher-Oemler e\ufb00ect and infalling galaxies. More generally it is found that galaxies evolve both morphologically and spectroscopically, where the frac- tion of early type galaxies and non-star-forming galaxies increase with time at a rate that depends on the local density (Smith et al 2005; Postman et al 2005; Poggianti et al 1999; Dressler et al 1997). The timescale for the transformation di\ufb00ers for the two processes. Spectro- scopic transformation precedes morphological transfor- mation (Dressler et al 1997, Poggianti et al 1999). A wide variety of physical processes may be respon- sible for these evolutionary trends. Galaxy-intercluster medium (ICM) interactions are ones in which the gas in a galaxy interacts with the ambient intercluster hot gas. One such process is ram pressure stripping (RPS), which removes the interstellar medium (ISM) of a galaxy as it moves through the ICM (Gunn & Gott 1972); ram pressure could also compress the gas within a galaxy to cause a burst of star formation that would consume gas that has not been stripped (Fujita & Nagashima 1999). An ISM-ICM interaction is the only type of interaction that does not e\ufb00ect the stellar component of a galaxy. Starvation, the removal of the outer gas envelope by the ICM, can result in normal star formation slowly ex- hausting the gas reservoir in the central region of the galaxy (Larson, Tinsley & Caldwell 1980). A galaxy can also interact with the cluster potential, which can strip both gas and stars, or compress the gas to cause an increased star formation rate (Byrd & Valtonen 1990). These galaxy-cluster interactions a\ufb00ect both the stellar and gas components of galaxies. There are also possible galaxy-galaxy interactions that can take place within a cluster. These include mergers between galaxies with low relative velocities, as well as galaxy harassment \u2013 high- speed interactions between cluster galaxies (Hashimoto et al. 1998; Bekki 1999; Barnes & Hernquist 1991; Bekki 1998; Moore et al. 1996). These interactions can cause an increased star formation rate and will also e\ufb00ect both the stellar and gas components of galaxies. It is likely that all of these processes occur in clusters. Attempts to di\ufb00erentiate the relative importance of these e\ufb00ects have been widespread through the years. For ex- ample, Bahcall (1977) showed that X-ray luminosity is positively correlated with the S0/spiral ratio in clusters (Bahcall 1977), and that the ratio of spirals to S0s in- creases radially (Melnick & Sargent 1977). Observational studies of HI de\ufb01ciency have shown that spirals in clus- ters have less neutral atomic hydrogen than galaxies of the same morphological type in the \ufb01eld (see the reviews by Haynes, Giovanelli, & Chincarini 1984). On the other hand the CO content does not seem to depend on envi- ronment (Stark et al 1986; Kenney and Young 1989). H I imaging of spirals in the center of Virgo shows smaller H I disks than stellar disks, pointing to an ISM-ICM in- teraction (Cayatte et al 1990; Warmels 1988). More re- cently Koopmann and Kenney 2004 have shown that in Virgo the reduced massive star formation rate is primar- ily caused by truncation of the star forming disks, thus it 2 is the removal of the lower density atomic gas that seems to control the star formation rate. Solanes et al (2001) studied HI de\ufb01ciency in a sample of 18 cluster regions, and found that HI de\ufb01ciency decreases smoothly out to large projected distances from cluster centers. In a re- cent HI imaging study of Virgo, Chung et al (2007) \ufb01nd a number of long one-sided H I tails pointing away from the cluster center. These galaxies are likely falling in for the \ufb01rst time and gas is indeed already being removed at large projected distances from the cluster center. Others have combined simple analytic models with cluster galaxy observations to determine the evolution- ary mechanism at work. For example, Treu et al (2003) use a large wide-\ufb01eld mosaic of HST images in combi- nation with a simple cluster model to identify the oper- ating environmental process. They \ufb01nd that galaxy star formation rate and morphological type have mild gradi- ents outside of the central Mpc of the cluster. This leads them to conclude that only slow (>1 Gyr) processes that can e\ufb00ect galaxies in the outer regions of clusters could be responsible, and therefore that galaxy starvation and harassment are the most likely mechanisms that evolve cluster galaxies. In addition, detailed investigations of a few individual galaxies using multiple wavelengths have begun to unravel their probable histories (e.g. Crowl et al. 2005; Chung et al. 2005). Observations of NGC 4522 indicate that the galaxy is undergoing ram pressure stripping, although it is outside of the high density ICM (Kenney, van Gorkom, & Vollmer 2004). Clearly, these varied results show the complicated nature of galaxy evo- lution in clusters. The limitation of all observations is that they are snap- shots of a long process, and cannot make detailed conclu- sions about both the history and fate of individual galax- ies. To overcome this limitation, simulations are now be- ing used to inform the debate about which morphology- changing mechanism is operating by modeling previously observed galaxies (e.g. Vollmer, Huchtmeier, & van Driel 2005). For example, Vollmer (2003) shows that one Virgo cluster galaxy in particular has both undergone ram pres- sure stripping and been involved in a gravitational inter- action. Others have studied idealized cases of galaxies in clusters (e.g., Quilis, Moore & Bower 2000; Roediger & Br\u00a8 uggen (2006)) In this paper, we take a di\ufb00erent approach and use a cosmological hydrodynamics simulation in order to track the evolution of a large number of galaxies in the close vicinity of a large galaxy cluster. The simulation is per- formed in a cosmological context and includes dark mat- ter, gas-dynamics and a treatment of star formation (see \u00a72.1). In this way, we can study the environmental im- pact of the intracluster gas, the cluster potential, as well as other galaxies in a self-consistent fashion. Although we have insu\ufb03cient resolution to determine the morpho- logical type of our galaxies with con\ufb01dence, we can com- pare the gas content of our simulated galaxies directly to observations. The advantage of using a cosmological simulation is that we do not need to guess the speci\ufb01c environmen- tal conditions of our galaxies, instead the local environ- ment is naturally modeled by the simulation. This might be important if, for example, the intracluster medium has internal motions which increase the e\ufb03ciency of ram-pressure stripping above that expected in a static medium, or if galaxies preferentially enter the cluster in groups. The output from this simulation can tell us about the evolution of a particular galaxy and give an overview of what mechanisms are at work in a cluster environment. In this paper we concentrate on the lat- ter by following the changing gas and stellar mass of 132 galaxies in our cluster. In particular, we focus on the pe- riod after the cluster has been established and ask how the gas content of infalling galaxies changes. Our data tell us how the gas content of gas-rich galaxies is a\ufb00ected by the cluster, an important part of the evolution of spi- ral galaxies to earlier types. This paper is organized in the following way. After a brief introduction to our code, we provide a comparison of the general characteristics of our simulation to cur- rent observations (\u00a72.1). We then explain the construc- tion of our sample of galaxies and simulated \u201cobserva- tions\u201d (\u00a72.2). In \u00a73 we describe our results and present an analysis of the importance of the various gas removal mechanisms in our simulation. We conclude (\u00a74) with a discussion of the limitations and implications of our results. 2."
                }
            ],
            "Paolo Serra": [
                {
                    "url": "http://arxiv.org/abs/1608.00585v2",
                    "title": "Dissecting the high-z interstellar medium through intensity mapping cross-correlations",
                    "abstract": "We explore the detection, with upcoming spectroscopic surveys, of\nthree-dimensional power spectra of emission line fluctuations produced in\ndifferent phases of the Interstellar Medium (ISM) by ionized carbon, ionized\nnitrogen and neutral oxygen at redshift z>4. The emission line [CII] from\nionized carbon at 157.7 micron, and multiple emission lines from carbon\nmonoxide, are the main targets of planned ground-based surveys, and an\nimportant foreground for future space-based surveys like the Primordial\nInflation Explorer (PIXIE). However, the oxygen [OI] (145.5 micron) line, and\nthe nitrogen [NII] (121.9 micron and 205.2 micron) lines, might be detected in\ncorrelation with [CII] with reasonable signal-to-noise ratio (SNR). These lines\nare important coolants of both the neutral and the ionized medium, and probe\nmultiple phases of the ISM. We compute predictions of the three-dimensional\npower spectra for two surveys designed to target the [CII] line, showing that\nthey have the required sensitivity to detect cross-power spectra with the [OI]\nline, and the [NII] lines with sufficient SNR. The importance of\ncross-correlating multiple lines is twofold. On the one hand, we will have\nmultiple probes of the different phases of the ISM, which is key to understand\nthe interplay between energetic sources, the gas and dust at high redshift.\nThis kind of studies will be useful for a next-generation space observatory\nsuch as the NASA Far-IR Surveyor. On the other end, emission lines from\nexternal galaxies are an important foreground when measuring spectral\ndistortions of the Cosmic Microwave Background spectrum with future space-based\nexperiments like PIXIE; measuring fluctuations in the intensity mapping regime\nwill help constraining the mean amplitude of these lines, and will allow us to\nbetter handle this important foreground.",
                    "authors": "Paolo Serra, Olivier Dor\u00e9, Guilaine Lagache",
                    "published": "2016-08-01",
                    "updated": "2017-03-24",
                    "primary_cat": "astro-ph.GA",
                    "cats": [
                        "astro-ph.GA",
                        "astro-ph.CO"
                    ],
                    "main_content": "of reionization and the physics of the ISM (Gong et al. 2011, 2012; Uzgil et al. 2014; Silva et al. 2015; Lidz & Taylor 2016; Cheng et al. 2016). Both theory and observations indicate that the atomic [CII] fine-structure is the dominant coolant of the neutral ISM (Hollenbach & Tielens 1999; Bernard-Salas et al. 2012), and one of the brightest lines in the Spectral Energy Distribution (SED) of a typical star-forming galaxy, with luminosities ranging from 0.01% to 1% of the total infrared luminosity (Stacey et al. 1991; Maiolino et al. 2005; Iono et al. 2006; Maiolino et al. 2009; Stacey et al. 2010; Ivison et al. 2010; Wagg et al. 2010; De Breuck et al. 2011). In fact, carbon is the forth most abundant element in the Universe. It has a low ionization potential, only 11.26 eV (see Table 1), below the 13.6 eV of hydrogen ionization; this ensures it is present both in the ionized and in the neutral medium. Moreover, the [CII] fine-structure transition of ionized carbon is characterized by a low temperature (91 K), and low critical density for collisions with hydrogen4. Intensity mapping from the rotational transitions of carbon monoxide, and, in particular, the lowest order transition CO(1-0) at 115 GHz, have also received increased attention in the past few years. Carbon monoxide emission lines at a given redshift act as a foreground contamination both for CMB observations (Righi et al. 2008; De Zotti et al. 2016), and for [CII] intensity mapping surveys targeting background galaxies at higher redshifts (Gong et al. 2012; Lidz & Taylor 2016; Cheng et al. 2016). Carbon monoxide molecules are easily produced from carbon and oxygen in star-forming regions, and CO intensity mapping provides information on the spatial distribution and redshift evolution of star formation in the Universe (Visbal & Loeb 2010; Carilli 2011; Lidz et al. 2011; Gong et al. 2011; Pullen et al. 2013; Breysse et al. 4 The critical density for an excited state is the density for which collisional deexcitation equals radiative deexcitation, see Draine (2011). arXiv:1608.00585v2  [astro-ph.GA]  24 Mar 2017 2 SERRA P. et al. 2014). At far-infrared (FIR) frequencies, many other lines can in principle be targeted by intensity mapping surveys, such as [OI] (63 \u00b5m and 145 \u00b5m), [NII] (122 \u00b5m and 205 \u00b5m), [OIII] (52 \u00b5m and 88 \u00b5m), and [CI] (610 \u00b5m and 371 \u00b5m), while proposed lines in other frequency bands include measurements of HeII (0.164 \u00b5m) to constrain properties of Population III stars (Visbal et al. 2015), Ly\u03b1 (0.1216 \u00b5m) to probe reionization and star formation (Pullen et al. 2014), and OII (0.3737 \u00b5m) and H\u03b1 (0.6563 \u00b5m) to study the large scale clustering at redshifts 1 < z < 4 (Fonseca et al. 2016). As emphasized in Lidz & Taylor (2016), the sensitivity of intensity mapping measurements will rapidly increase in the near future, thanks to advances in detector technology, and some surveys are already in progress, or have been planned, to perform intensity mapping of one or more emission lines from sources at multiple redshifts. The CO Power Spectrum Survey (COPPS) (Keating et al. 2015) recently published measurement of the CO abundance and power spectrum from the CO(1-0) transition in the redshift range 2.3 < z < 3.3 (Keating et al. 2016), and the Carbon Monoxide Mapping Array Path\ufb01nder (COMAP see Li et al. (2016)) has been proposed to study the CO emission at similar redshifts. Experiments targeting the [CII] emission line include the Tomographic Ionized-Carbon Mapping Experiment (TIMEPilot, Crites et al. (2014)), and CONCERTO (CarbON CII line in post-rEionization and ReionizaTiOn epoch, Lagache et al., in preparation), while the Spectrophotometer for the History of the Universe, Epoch of Reionization, and Ice Explorer (SPHEREx) will focus on Ly\u03b1, Ly\u03b2 and [OIII] (Dor\u00e9 et al. 2014, 2016). The Cryogenic-Aperture Large InfraredSubmillimeter Telescope Observatory (CALISTO) (Bradford et al. 2015) has been proposed to measure, among other things, multiple FIR \ufb01ne-structure transitions such as [NeII], [OI], [OIII] and, for z < 2, [CII]. Foregrounds are an important concern for intensity mapping surveys. Apart from the continuum emission from our Galaxy, a survey targeting an emission line observed at a given frequency \u03bdobs will also detect the sum of emissions of N atoms or molecules \u03b1i coming from redshifts zi, whose lines are redshifted to the same observed frequency, so that the measured intensity I\u03bdobs can be written as: I\u03bdobs = N X i=1 I\u03bdi em/(1+zi) i (\u03b1i, zi). (1) Different methods to overcome this dif\ufb01culty have been proposed so far. Some authors (Visbal et al. 2011; Breysse et al. 2015; Silva et al. 2015) explore the possibility of mitigating this contamination by progressively masking the brightest pixels in the observed map. However, when dealing with [CII] maps at very high redshift (e.g. z = 7), a percentage of the signal will be masked in the process, and such a loss of information translates in a underestimation of the amplitude of the measured power spectrum (Breysse et al. 2015). This is unfortunate because, while the cosmological information content of the measured power spectrum is mainly encoded in its shape (primordial non-Gaussianity, neutrino masses, modi\ufb01ed gravity can all be tested by looking at the shape of the clustering power spectrum), most of the meaningful astrophysical processes are constrained by the amplitude of the spectrum. Another method, recently discussed in Lidz & Taylor (2016); Cheng et al. (2016), exploits the fact that the interloper lines, being emitted at different redshifts respect to the targeted line, will introduce an anisotropic component in the power spectra, due to the incorrect redshift projection. A third method to mitigate contamination from different lines has been proposed by Visbal & Loeb (2010); Visbal et al. (2011), and involves the cross-correlation between maps measured at different frequencies, whose emission comes from atoms and molecules at the same redshift. Since all contaminant lines in each map will generally come from different redshifts, they will not contribute to the signal in the cross-correlation, but they will only add noise to the measurement. While cross-correlation measurements are generally more complicated to be carried out, most surveys proposed so far work in a broad frequency range, and multiple crosscorrelations produced at the same redshift among lines from different atoms and molecules might be attempted, at least in the non-linear regime. If the amplitudes of the lines to be cross-correlated is large enough, the information content from these measurements will be vast, and it will enable us to constrain various physical processes of the ISM. In this paper we propose the use of cross-correlation measurements among various emission lines from carbon, oxygen, and nitrogen to constrain the mean amplitude of each emission line at redshift z > 4. Using measurements of the Cosmic Infrared Background (CIB) angular power spectra from Herschel/SPIRE (Viero et al. 2013) and Planck (Planck Collaboration et al. 2014c), coupled to a compilation of star formation rate density (SFRD) measurements from Madau & Dickinson (2014), we constrain the galaxy FIR luminosity as a function of the halo mass at all relevant redshifts. By using scaling relations from Spinoglio et al. (2012) to link the intensity of emission lines to the constrained galaxy infrared luminosity, we compute 3D emission line power spectra for all relevant lines. Focusing on two experimental setups, corresponding to present and future ground-based surveys, we show that multiple cross-correlations with the [CII] line can constrain the mean amplitudes of all lines. This is important not only to constrain average properties of the ISM of galaxies at high redshift, but also because, as shown in Mashian et al. (2016); De Zotti et al. (2016); Carilli et al. (2016), especially the CO and [CII] line emission from galaxies across cosmic time distort the CMB spectrum at a level that must be taken into account by future space-based surveys aiming at measuring the tiny spectral distortions of the CMB, such as PIXIE. Intensity mapping, by constraining the mean amplitude of the signal, will healp dealing with this important foreground. In Sect. 2 we will derive the formalism used to compute emission line power spectra from the Halo model. We will then discuss in Sect. 3 the physics of the ISM in the context of emission lines from carbon, oxygen, and nitrogen, with particular focus on all possible cross-correlations to be performed using the experimental setups discussed in Sect. 5. Finally we will discuss our main results in Sect. 6. Throughout this paper, we adopt the standard \ufb02at \u039bCDM model as our \ufb01ducial background cosmology, with parameter values derived from the best-\ufb01t model of the CMB power spectrum as measured by Planck Collaboration et al. (2014a). 2. A HALO MODEL FOR EMISSION LINE AMPLITUDES The computation of 3D autoand cross-power spectra of intensity line emission is performed in the context of a Halo model developed in Shang et al. (2012), where the galaxy luminosity is linked to the mass of the host dark matter halo with a simple parameteric form. It has been successfully applied to the interpretation of the latest measurements of DISSECTING THE HIGH-Z INTERSTELLAR MEDIUM THROUGH INTENSITY MAPPING CROSS-CORRELATIONS 3 angular CIB power spectra from Herschel/SPIRE (Viero et al. 2013) and Planck (Planck Collaboration et al. 2014c). Using the latest measurements of CIB autoand cross-power spectra at 250, 350 and 500 \u00b5m from Viero et al. (2013), together with a compilation of measurements of SFRD in the redshift range 0 < z < 6 (Madau & Dickinson 2014), we are able to constrain the galaxy infrared luminosity as a function of halo mass and redshift. We then use known scaling relations from Spinoglio et al. (2012) to compute the amplitudes of emission lines from carbon, oxygen, and nitrogen with respect to the constrained galaxy infrared luminosity. This allows us to compute the amplitudes of 3D power spectra for all relevant emission lines at all redshifts. This approach is very similar to that discussed in Cheng et al. (2016). 2.1. The Halo model for CIB anisotropies The halo model is a phenomenological description of the galaxy clustering at all angular scales (Cooray & Sheth 2002). Assuming that all galaxies live in virialized dark matter structures, called halos, and using a recipe to populate halos with galaxies, the clustering power spectrum results from the sum of two components: a 1-halo term, related to correlations between galaxies in the same halo, and responsible for the clustering at small angular scales, and a 2-halo term, which describes the power spectrum at large angular scales, and is due to correlations between galaxies belonging to separated dark matter halos. The angular power spectrum of CIB anisotropies, observed at frequencies \u03bd and \u03bd\u2032, is de\ufb01ned as: \u27e8\u03b4 Ilm,\u03bd\u03b4 Il\u2032m\u2032,\u03bd\u2032\u27e9=Cl,\u03bd\u03bd\u2032\u03b4\u03bd\u03bd\u2032\u03b4mm\u2032 (2) where I\u03bd is the speci\ufb01c intensity at that frequency, given by: I\u03bd(z) = Z dzd\u03c7 dz aj(\u03bd, z) (3) = Z dzd\u03c7 dz \u00af j(\u03bd, z) \u0010 1 + \u03b4 j(\u03bd, z) \u00af j(\u03bd, z) \u0011 ; here \u03c7(z) denotes the comoving distance at redshift z, a(z) is the scale factor, and j(\u03bd, z) is the comoving emission coef\ufb01cient. In Limber approximation (Limber 1954), Eqs. 2 and 3 can be combined to give the clustering angular power spectrum as: C\u03bd\u03bd\u2032 clust(l) = Z dz \u03c72 d\u03c7 dz a2(z)\u00af j(\u03bd, z)\u00af j(\u03bd\u2032, z)P\u03bd\u03bd\u2032(k = l/\u03c7, z), (4) where P\u03bd\u03bd\u2032(k, z) is the 3D power spectrum of the emission coef\ufb01cient, expressed as: \u27e8\u03b4 j(\u20d7 k, \u03bd)\u03b4 j(\u20d7 k\u2032, \u03bd\u2032)\u27e9= (2\u03c0)3 \u00af j\u03bd \u00af j\u03bd\u2032P\u03bd\u03bd\u2032 j \u03b43(\u20d7 k \u2212\u20d7 k\u2032). (5) This term is composed by the mentioned 1-halo and 2-halo components. Thus, together with a scale independent shotnoise power spectrum, describing the contribution from random \ufb02uctuations due to the Poisson distribution of sources, the total CIB angular power spectrum is: C\u03bd\u03bd\u2032 tot (l) =C\u03bd\u03bd\u2032 1h (l) + C\u03bd\u03bd\u2032 2h (l) + C\u03bd\u03bd\u2032 SN(l). (6) This quantity will be computed and \ufb01t to Herschel/SPIRE measurements of CIB angular power spectra in order to constrain the galaxy infrared luminosity. Below we show how to compute the two clustering terms. This formalism will be useful in Sect. 2.3, when computing 3D power spectra of emission lines. The mean emissivity \u00af j\u03bd(z) from all galaxies is computed from the infrared galaxy luminosity function dn/dL as: \u00af j\u03bd(z) = Z dL dn dL(L, z)L(1+z)\u03bd(M, z) 4\u03c0 , (7) where the galaxy luminosity L(1+z)\u03bd is observed at the frequency \u03bd with a \ufb02ux given by: S\u03bd = L\u03bd(1+z) 4\u03c0\u03c72(z)(1 + z). (8) Neglecting any scatter between galaxy luminosity and dark matter halo mass, the luminosity of central and satellite galaxies can be expressed as Lcen,(1+z)\u03bd(MH, z) and Lsat,(1+z)\u03bd(mSH, z), where MH and mSH denote the halo and sub-halo masses, respectively. We can thus rewrite Eq. 7 as the sum of the contributions from central and satellite galaxies as: \u00af j\u03bd(z) = Z dM dN dM (z) 1 4\u03c0 n NcenLcen,(1+z)\u03bd(MH, z) (9) + Z dmSH dn dm(mSH, z)Lsat,(1+z)\u03bd(mSH, z) o ; here dN/dm (Tinker et al. 2008) and dn/dm (Tinker et al. 2010) denote the halo and sub-halo mass function respectively, while Ncen is the number of central galaxies in a halo, which will be assumed equal to zero if the mass of the host halo is lower than Mmin = 1011M\u2299, and one otherwise. Introducing f cen \u03bd and f sat \u03bd as the number of central and satellite galaxies weighted by their luminosity, as: f cen \u03bd (M, z) = Ncen Lcen,(1+z)\u03bd(MH, z) 4\u03c0 , (10) and f sat \u03bd (M, z) = Z M Mmin dm dn dm(mSH, z|M) (11) \u00d7Lsat,(1+z)\u03bd(mSH, z) 4\u03c0 , the power spectrum coef\ufb01cient of CIB anisotropies at the observed frequencies \u03bd and \u03bd\u2032 can be written as the sum of a 1-halo term and 2-halo term as, respectively: P1h,\u03bd\u03bd\u2032(k, z) = 1 \u00af j\u03bd \u00af j\u03bd\u2032 Z \u221e Mmin dM dN dM (12) \u00d7 n f cen \u03bd (M, z) f sat \u03bd\u2032 (M, z)u(k, M, z) + f cen \u03bd\u2032 (M, z) f sat \u03bd (M, z)u(k, M, z) + f sat \u03bd (M, z) f sat \u03bd\u2032 (M, z)u2(k, M, z) o , P2h,\u03bd\u03bd\u2032(k, z) = 1 \u00af j\u03bd \u00af j\u03bd\u2032 D\u03bd(k, z)D\u03bd\u2032(k, z)Plin(k, z), (13) where D\u03bd(k, z) = Z \u221e Mmin dM dN dM b(M, z)u(k, M, z) (14) \u00d7 n f cen \u03bd (M, z) + f sat \u03bd (M, z) o , 4 SERRA P. et al. and u(k, M, z) is the Fourier transform of the Navarro-FrenkWhite (NFW) density pro\ufb01le (Navarro et al. 1997), with concentration parameter from Duffy et al. (2010). The term b(M, z) denotes the halo bias (Tinker et al. 2010). The linear dark matter power spectrum Plin(k) is computed using CAMB (http://camb.info/). The \ufb01nal ingredient to be speci\ufb01ed is the link between galaxy luminosity and host dark matter halo mass. Following Shang et al. (2012), we assume a parametric function, where the dependence of the galaxy luminosity on frequency, redshift, and halo mass is factorized in three terms as: L(1+z)\u03bd(M, z) = L0\u03a6(z)\u03a3(M)\u0398[(1 + z)\u03bd]. (15) The parameter L0 is a free normalization parameter whose value is set by the amplitude of both the CIB power spectra and the SFRD. It has no physical meaning, and it will not be discussed further in the rest of the paper. A very simple functional form (see Blain et al. 2003, and reference therein) is assumed for the galaxy SED: \u0398(\u03bd) \u221d ( \u03bd\u03b2B\u03bd (Td) \u03bd < \u03bd0 ; \u03bd\u22122 \u03bd \u2265\u03bd0 , (16) where Td is the dust temperature averaged over the redshift range considered, and \u03b2 is the emissivity of the Planck function B\u03bd(Td). We note that we discarded a redshift dependence of the dust temperature, because it is not very well constrained by the data. The power-law function at frequencies \u03bd \u2265\u03bd0 has been found more in agreement with observations than the exponential Wien tail (see also Hall et al. (2010); Viero et al. (2013); Shang et al. (2012); Planck Collaboration et al. (2014c)). We also assume a redshift-dependent, global normalization of the L\u2013M relation of the form \u03a6(z) = (1 + z)\u03b4 . (17) As explained in Shang et al. (2012), a power law is motivated by the study of the star formation rate (SFR) per unit stellar mass, or speci\ufb01c star formation rate (sSFR). Assuming that the stellar mass to halo mass ratio does not evolve substantially with redshift, the ratio of galaxy infrared luminosity LIR to halo mass has an evolution similar to the sSFR, thanks to the correlation between SFR and infrared luminosity (Kennicutt 1998). Finally, following Shang et al. (2012); Viero et al. (2013); Planck Collaboration et al. (2014c) we assume a log-normal function for the L-M relation, as: \u03a3(M) = M 1 (2\u03c0\u03c32 L/M)0.5 exp h \u2212(log10M \u2212log10Me\ufb00)2 2\u03c32 L/M i ,(18) where Me\ufb00describes the most ef\ufb01cient halo mass at hosting star formation, while \u03c3L/m accounts for the range of halo masses mostly contributing to the infrared luminosity. Such a functional form captures the fact that, for halo masses much lower and much higher than Me\ufb00, various mechanisms prevent an ef\ufb01cient star formation (Benson et al. 2003; Silk 2003; Bertone et al. 2005; Croton et al. 2006; Dekel & Birnboim 2006; B\u00e9thermin et al. 2012a; Behroozi et al. 2013). 2.2. Analysis We perform a Monte Carlo Markov Chain (MCMC) analysis of the parameter space, using a modi\ufb01cation of the publicly available code CosmoMC (Lewis & Bridle 2002), and \ufb01tting to six CIB autoand cross-power spectra from Viero et al. (2013) in the multipole range 200 < l < 23000. We also add a dataset for the SFRD as a function of redshift by averaging multiple measurements, discussed in Madau & Dickinson (2014), in eleven redshift bins in the range 0 < z < 6. We vary the following set of parameters: P \u2261{Me\ufb00, Td, \u03b4, L0}, (19) and we add six free parameters Ai=1,...6 to model the amplitudes of the CIB shot-noise power spectra. All parameters have a uniform prior, and we \ufb01x the emissivity index to \u03b2 = 1.5 (Planck Collaboration 2014), and \u03c32 L/M = 0.5 (Shang et al. 2012; Planck Collaboration et al. 2014c). With a total \u03c72 value of 104.9 for 97 degrees of freedom, we obtain a very good \ufb01t to the data. In Table 3, we quote mean values and marginalized limits for all free parameters used in the \ufb01t, while in Fig. 1 we plot the Herschel/SPIRE measurements of the CIB power spectra, together with our best estimates of the 1-halo, 2-halo, shot-noise, and total power spectrum. It is important to note that there is a relevant uncertainty associated to measurements of the SFRD, especially at the high redshifts considered in this work. The compilation of measurements extrapolated from Madau & Dickinson (2014) (plotted in Fig. 2), is based on galaxy counts, and there is a number of uncertain steps in the conversion from galaxy counts and luminosities to star formation rates, mainly related to assumptions on conversion factors and dust attenuation. When considering clustering meausurements, the Planck Collaboration, using a Halo model similar to the one presented in this paper, and \ufb01tting to CIB power spectra between 217 GHz (1381 \u00b5m) and 857 GHz (350 \u00b5m) in the multipole range 50 < l < 2000, infer a much higher SFRD at high redshifts (Planck Collaboration et al. 2014c), respect to the values found here by \ufb01tting Herschel-SPIRE data and star formation rate density data from Madau & Dickinson (2014) (see also discussion in Cheng et al. (2016)). Similar results have been obtained by cross-correlating the CIB with the CMB lensing (Planck Collaboration et al. (2014b), see also Fig. 14 of Planck Collaboration et al. (2014c)). The reason for this discrepancy is mainly due to the different values inferred for the parameter \u03b4 in Eq. 17. Planck Collaboration et al. (2014c) found \u03b4 = 3.6 \u00b1 0.2 (see Table 9 of Planck Collaboration et al. (2014c)), while we \ufb01nd \u03b4 = 2.6 \u00b1 0.2, compatible with (Viero et al. 2013). We checked that the \ufb01tting to star formation rate density data from Madau & Dickinson (2014) is not responsible for such a divergence, by performing an MCMC run with only one measurement of the local SFRD at z = 0.07 from Madau & Dickinson (2014) (thus being compatible with Planck\u2019s analysis, since they use a prior on the local SFRD from Vaccari et al. (2010)). As it is clear from Fig. 2, we are not able to obtain SFRD values compatible with Planck Collaboration et al. (2014c) at high redshifts. The disagreement between our analysis and results from Planck Collaboration et al. (2014c) can be explained by a combination of multiple factors involving our ignorance of the exact values of some key parameters, such as the amplitudes of the shot noise power spectra and the redshift evolution of the galaxy luminosity, coupled to differences in the datasets considered. CIB anisotropies are mostly sourced by galaxies at redshift 1 < z < 4 and, in this range, a simple power law might not be a good description of the redshift evolution of the galaxy luminosity/halo mass relation. Some semianalytic models of galaxy formation and evolution \ufb01nd a power law slope of \u223c2.5 (De Lucia & Blaizot 2007; Neistein & Dekel DISSECTING THE HIGH-Z INTERSTELLAR MEDIUM THROUGH INTENSITY MAPPING CROSS-CORRELATIONS 5 Line A \u03c3A B \u03c3B Transition Temperature (K) [OI] 63.2 \u00b5m 0.98 0.03 2.70 0.10 3P1 \u21923 P2 228 [NII] 121.9 \u00b5m 1.01 0.04 3.54 0.11 3P2 \u21923 P1 188 [OI] 145.5 \u00b5m 0.89 0.06 3.55 0.17 3P1 \u21923 P0 327 [CII] 157.7 \u00b5m 0.89 0.03 2.44 0.07 2P3/2 \u21922 P1/2 92 [NII] 205.2 \u00b5m 1.01 0.04 4.01 0.11 3P1 \u21923 P0 70 Table 1 Main parameters to model the luminosity of all emission lines considered in this paper as a function of the total infrared luminosity, taken from Spinoglio et al. (2012). Also shown is the transition level for each line, with its associated temperature. Parameter De\ufb01nition Mean value Td SED: Redshift-averaged dust temperature 25.3 \u00b1 1.1 \u03b4 Redshift evolution of the normalization of the L \u2212M relation 2.6 \u00b1 0.2 log(Me\ufb00)[M\u2299] Halo model most ef\ufb01cient mass 12.6 \u00b1 0.1 S 250x250 Shot noise for 250x250 \u00b5m < 7237 (95 c.l.) S 250x350 Shot noise for 250x350 \u00b5m 5331 \u00b1 151 S 250x500 Shot noise for 250x500 \u00b5m 2806 \u00b1 93 S 350x350 Shot noise for 350x350 \u00b5m 4677 \u00b1 124 S 350x500 Shot noise for 350x500 \u00b5m 2659 \u00b1 80 S 500x500 Shot noise for 500x500 \u00b5m 1600 \u00b1 61 Table 2 Mean values and, where not otherwise stated, marginalized 68% c.l. for halo model parameters and shot-noise levels (in Jy2/sr) from the MCMC \ufb01t using Herschel/SPIRE measurements. 103 104 l 103 104 105 106 Cl (Jy2 / sr) 250x250 250x350 250x500 103 104 l 103 104 105 106 Cl (Jy2 / sr) 350x350 350x500 103 104 l 103 104 105 106 Cl (Jy2 / sr) 500x500 Figure 1. Angular CIB autoand cross-power spectra at 250, 350, 500 \u00b5m from Herschel/SPIRE, together with the best-\ufb01t curves for the 1-halo (Blue line), 2-halo (Green line), shot-noise (Red line) and total power spectra (Cyan line). 2008), but also a more gradual evolution, with different slopes for low redshift and high redshift sources (Wu et al. 2016). On the other end, observations are more in agreement with a steep evolution with redshift (Oliver et al. 2010), or with a steep evolution followed by a plateau for z \u223c2 (Bouch\u00e9 et al. 2010; Weinmann et al. 2011), which is also not easily explained by theoretical arguments (Bouch\u00e9 et al. 2010; Weinmann et al. 2011). Planck Collaboration et al. (2014c) is indeed able to \ufb01nd lower values for the star formation rate density at early times, more in agreement with this work, but only when they 6 SERRA P. et al. 0 1 2 3 4 5 6  z 10-3 10-2 10-1 100 \u03c8 [M\u2299yr\u22121Mpc\u22123] Herschel/SPIRE Herschel/SPIRE, no SFRD data at z>0.1 Planck Figure 2. Best \ufb01t estimates of the SFRD using Herschel/SPIRE CIB clustering measurements combined with a compilation of data extracted from Madau & Dickinson (2014) either in the range 0 < z < 6 (black line), or in 0 < z < 0.1 (one single measurement at z = 0.07, green line). Also plotted is the estimate from Planck Collaboration et al. (2014c) (red line). impose the condition \u03b4 = 0 for z \u22652 (see Fig. 14 of Planck Collaboration et al. (2014c)). The differences between the two datasets in terms of angular scales and related uncertainties can also be responsible for the difference values inferred for \u03b4. Planck data probe CIB anisotropies at large scales with very high precision. However, because of its angular resolution, Planck is not able to access multipoles higher than l \u223c2000, where the 1-halo term and the shot-noise dominate the clustering, and are degenerate. Uncertainties in the contribution of these two terms to the small-scale clustering (Planck Collaboration et al. (2014c) used free amplitudes for the shot-noise power spectra, with \ufb02at priors based on current measurements, such as, e.g., B\u00e9thermin et al. (2012b)) translates in an uncertainty in the inferred constraints on the halo model parameters. On the other end, Herschel/SPIRE data probe both large and small scales, but while adding information at small scales helps disentangling the relative contributions to the total power from the 1halo term and the shot-noise, the largest scales are measured with much larger uncertainty than Planck. Finally, Planck and Herschel probe a different frequency range, which might affects results. Thus, it is possible that the differences in the datasets used, coupled with uncertainties regarding the level of the shot-noises, and a poor description of the redshift evolution of the sources, determine different values for the parameter \u03b4. It is clear that the higher the value of the star formation rate density, the greater the value for the mean emission from all atoms and molecules. This would translate in large amplitude for the emission line power spectra. In order to be as independent as possible on the particular values of the Halo model parameters used to constrain the galaxy infrared luminosity, we compute predictions for the 3D power spectra of emission lines using both the mean values found by \ufb01tting Herschel/SPIRE data (quoted in Table 3) and the mean values quoted in Table 9 of Planck Collaboration et al. (2014c). The geometric average of these two estimates will be our best estimate of the power spectrum of the emission lines. In the rest of the paper we will focus on predictions based on these average estimates of the power spectra. In Fig. 3 we show 10-2 10-1 100 101 k [h/Mpc] 101 102 103 104 105 106 107 108 109 1010 1011 1012 k 3PCIIxCII(k)/2\u03c02 (Jy / sr)2 Herschel/SPIRE Planck Ave. CO total Figure 3. Average estimate of the [CII] auto-power spectrum at redshift z=7 (black line), together with an optimistic estimate (red line) obtained from the mean values of the Halo model parameters from Planck Collaboration et al. (2014c), and an estimate (blue line) from our analysis of Herschel/SPIRE data. Also plotted is the CO power spectrum computed as the sum of the transitions from CO(3-2) to CO(7-6). the 3D power spectrum of [CII] emission at redshift z = 7 obtained by using mean parameter values for the Halo model parameters from Planck Collaboration et al. (2014c) (optimistic scenario), mean parameter values from our analysis of Herschel/SPIRE data, and their average. The \u201caverage\u201d model considered here agrees at both large and small scales with the model prediction from Gong et al. (2012), which is based on a physical model that takes into account for the spontaneous, stimulated and collisional emission to compute the CII spin temperature. However, it predicts shot-noise amplitudes higher than what found in Silva et al. (2015); Lidz & Taylor (2016). 2.3. Intensity mapping power spectrum from the Halo model The analysis presented in the previous section has been necessary to constrain the main parameters describing the galaxy SED and its dependence on halo mass and redshift. The galaxy infrared luminosity is: LIR = Z 37.5 THz 300 GHz \u0398[(1 + z)\u03bd]d\u03bd (20) where the extremes of integration correspond to the wavelength range 8 < \u03bb < 1000 \u00b5m. We can use scaling relations provided in Spinoglio et al. (2012), to express the emission line luminosity I\u03b1 (where \u03b1 denotes emission lines from the atoms and molecules considered, such as carbon, oxygen, nitrogen) as a function of the constrained infrared luminosity, as: log10(I\u03b1) =(A \u00b1 \u03c3A)log10(LIR) \u2212(B \u00b1 \u03c3B), (21) where all luminosities are in units of 1041 erg s\u22121. These scaling relations are obtained from a sample of local galaxies compiled by Brauher et al. (2008) using all observations collected by the LWS spectrometer (Clegg et al. 1996) onboard ISO (Kessler et al. 1996). Regarding the [NII] 205 \u00b5m emission line, whose luminosity is not found in Spinoglio et al. (2012), we assume that it is three times weaker than the [NII] 122 \u00b5m; this values is in agreement with both theoretical expectations and recent measurements (Oberst et al. 2011; Zhao DISSECTING THE HIGH-Z INTERSTELLAR MEDIUM THROUGH INTENSITY MAPPING CROSS-CORRELATIONS 7 et al. 2016), although it is higher than what recently found in our Galaxy (Goldsmith et al. 2015). In Table 1 we summarize the values used for slopes, intercepts and their uncertainties, together with their associated transition, and transition temperatures from Kaufman et al. (1999); Cormier et al. (2015). The emission line luminosity at each redshift for each halo mass can now be expressed as previosly done for the galaxy luminosity (see Eq. 15) as: L\u03b1(M, z) = F(M, z)I\u03b1, (22) where the term F(M, z) contains the global dependence on redshift and halo mass as F(M, z) = L0\u03a6(z)\u03a3(M), (23) and we use the parameter values from Table 3 to compute the term F(M, z). This functional form allows us to link the emission line luminosity of a galaxy to its host halo mass, and to evolve the amplitude of all emission lines with redshifts. We note that this model assumes that the redshift evolution of all emission lines is the same, since it follows the evolution of the galaxy infrared luminosity (through the parameter \u03b4). Different emission lines might have different a evolution with redshift, and more sophisticated models could incorporate redshift-dependent scaling relations for each line. However, current data do not allow us to constrain the exact dependence on redshift of each emission lines. Thus, to keep the analysis as simple as possible, we do not consider such a scenario. It is easy to see that, assuming that each halo hosts only one galaxy (a good approximation because, at high redshift, halos are not very massive, see also Lidz et al. (2011)), and in the limit of suf\ufb01ciently large scales (so that the NFW pro\ufb01le approaches unity), the clustering auto-power spectrum of emission line \u03b1 can be written as: P\u03b1\u03b1(k, z) = K2 \u03b1(k, z)Plin(k, z), (24) where K\u03b1(k, z) = Z \u221e Mmin dM dN dM b(M, z)L\u03b1(M, z) 4\u03c0 . (25) Introducing an effective, scale independent, bias term as: be\ufb00(z) = R dM dN dMb(M, z)\u03a3(M) R dM dN dM\u03a3(M) (26) the clustering power spectrum of emission line \u03b1 can be expressed as: Pclust \u03b1\u03b1 (k, z) = b2 e\ufb00(z)\u00af I2 \u03b1(z)Plin(k, z), (27) where the average speci\ufb01c intensity \u00af I\u03b1(z) is: \u00af I\u03b1(z) = 1 4\u03c0 c H(z\u03b1) 1 \u03bd\u03b1 Z dM dN dM L\u03b1(M, z), (28) and z\u03b1 denotes the redshift of emission of the atom or molecule \u03b1. Analogously, the shot-noise power spectrum can be expressed as: PSN \u03b1\u03b1 = \u00af I2 \u03b1(z) R dM dN dM\u03a3(M)2 \u0010 R dM dN dM\u03a3(M) \u00112 . (29) 3. THE PHYSICS OF THE ISM WITH EMISSION LINES AND EMISSION LINE RATIOS Understanding the main heating and cooling processes of the ISM is a key goal of astronomy, because they play a fundamental role in the formation of stars, and thus in the galaxy evolution. Space missions such as Planck and Herschel, together with the Stratospheric Observatory for Infrared Astronomy (SOFIA) and the Atacama Large Millimeter Array (ALMA), are now giving new insights on these physical processes, providing spatially resolved maps of the interstellar dust in our Galaxy, and measuring atomic and molecular emission lines from the main phases of the ISM both in the Milky Way (Pineda et al. 2013, 2014; Goicoechea et al. 2015), and in external galaxies (see e.g. Stacey et al. (2010); Scoville et al. (2014); Capak et al. (2015); Gullberg et al. (2015); Blain (2015); B\u00e9thermin et al. (2016); Aravena et al. (2016)). The gas in the ISM of galaxies is observed in three main phases; a cold and dense neutral medium (T\u226550K) is in rough pressure equilibrium (with P/k \u223c103 \u2212104Kcm\u22123) with a hot (T\u2265106K), ionized phase, and an intermediate, warm (T\u22658000K) phase, which can be either neutral or ionized, depending on the gas density (Wol\ufb01re et al. 1995). Various mechanisms contribute to the heating and cooling of the ISM. For a gas with hydrogen density n, temperature T, cooling rate per unit volume of \u039b(T), and heating rate per unit volume of \u0393(T), the thermal balance between heating and cooling is expressed in terms of a Generalized Loss Function L: L(n, T) =\u039b(T) \u2212\u0393(T). (30) For a gas at constant thermal pressure nT, equilibrium occurs when L = 0 and the explicit form for \u039b and \u0393 depends on the heating and cooling process considered, as explained below. The investigation of the thermal balance and stability conditions of the neutral ISM started with Field et al. (1969), who \ufb01rst presented a model of the ISM based on two thermally stable neutral phases, cold and warm, heated by cosmic-rays. Subsequent analyses by many authors focused on the heating provided by the photoelectric ejection of electrons from dust grains by the interstellar radiation \ufb01eld (Draine 1978; Wol\ufb01re et al. 1995; Kaufman et al. 1999; Wol\ufb01re et al. 2003). Most of the Far-Ultraviolet (FUV) starlight impinging on the cold neutral medium is absorbed by dust and large molecules of polycyclic aromatic hydrocarbons (PAH), and then reradiated as PAH infrared lines and infrared continuum radiation. However, as pointed out by Tielens & Hollenbach (1985b), in photodissociation regions (PDRs), the photoelectric heating of dust grains provides an ef\ufb01cient mechanism (0.1% \u22121%) at converting the FUV heating into atomic and molecular gaseous line emission. The physics of heating processes in PDRs can be understood in terms of a limited set of parameters, namely the density of Hydrogen nuclei density n and the incident FUV (6eV < h\u03bd < 13.6 eV) parametrized in units of the local interstellar \ufb01eld, G0 (Tielens & Hollenbach 1985a,b; Kaufman et al. 1999), in units of the Habing \ufb01eld (1.6 \u00b7 10\u22123 ergs cm\u22122s\u22121). The basic mechanism for gas heating and cooling is the following: about 10% of incident FUV photons eject photoelectrons from dust grains and PAH molecules, which cool by continuum infrared emission. The photoelectrons (with energy of about 1 eV) heat the gas by collisions, and the gas subsequently cools via FIR \ufb01ne-structure line emission. The entire process thus results in the conversion of FUV photons to FIR continuum emission plus spectral line emis8 SERRA P. et al. sion from various atoms and molecules. As an example, the computation of the heating due to small grains is given by (Bakes & Tielens 1994): \u0393 =10\u221224\u03f5 G0nH erg cm\u22123s\u22121; (31) the radiation \ufb01eld G0 quanti\ufb01es the starlight intensity, and \u03f5 is the fraction of FUV photons absorbed by grains which is converted to gas heating (i.e. heating ef\ufb01ciency), and it depends on G0T1/2ne, where ne denotes the electron density Wol\ufb01re et al. (1995). A detailed calculation of the main heating processes in the ISM, including the effect from photoelectric heating, cosmic rays, soft X-rays, and photoionization of CI is presented in Wol\ufb01re et al. (1995); Meijerink & Spaans (2005). The cooling rate \u039b of each atom/molecule depends on both the number density and the equivalent temperature of each species. A recent estimate of the cooling rate of the [CII] line for temperatures between 20 K and 400 K is (Wiesenfeld & Goldsmith 2014): \u039bCII = 10\u221224\u0010 11.5 + 4.0e\u2212100K/Tkin\u0011 (32) e\u221291.25K/Tkinn(C+)nH2 erg cm\u22123s\u22121 where n(C+) denotes the carbon number density, and Tkin the kinetic temperature of the gas. Numerical codes compute a simultaneous solution for the chemistry, radiative transfer, and thermal balance of PDRs, providing a phenomenological description of the interplay among three main parameters n, G0 and T (see e.g. Kaufman et al. (1999)) for all emission lines. The observed intensity of line emissions can thus be compared with models to constrain these parameters. Far-infrared emission lines from forbidden atomic \ufb01nestructure transitions such as [CII] (157.7 \u00b5m), [OI] (63 \u00b5m and 145.5 \u00b5m), are the main coolants of the neutral regions of the ISM, and provide many insights on the physics of PDRs. Other lines, such as [NII] (122 \u00b5m and 205 \u00b5m), [OIII] (88 \u00b5m), and [NIII] (57 \u00b5m), being emitted only in ionized regions, complement the study of the ISM probing a different phase. For ground-based surveys such as Time-PILOT Crites et al. (2014) or CONCERTO, covering approximately the range 200 < \u03bd < 300 GHz, and targeting high redshift (5 < z < 8) galaxies, emission from [CII], [OI] (145 \u00b5m) and [NII] (122 \u00b5m and 205 \u00b5m) are accessible. A future space-based survey with characteristics similar to PIXIE will be able to detect most of the main cooling lines from both PDRs and from the ionized medium of high redshift galaxies. Below we summarize some useful diagnostics of the ISM provided by these important lines (see also Cormier et al. (2015)). \u2022 [CII] emission line: It is hard to overestimate the importance of the [CII] emission line in constraining physical properties of the interstellar medium. Because of its low ionization potential, the [CII] line arises both from ionized and neutral gas. In PDRs, the low gas critical density for collisions with Hydrogen and the low excitation temperature for the [CII] 2P3/2 \u22122 P1/2 transition (only 92 K, see Table 1), make C+ one of the major coolant of the neutral ISM. Moreover, since the [CII] line is generally one of the brightest lines in starforming galaxies, it is potentially a very strong indicator of star formation rate (SFR) (Boselli et al. 2002; De Looze et al. 2011, 2014; Herrera-Camus et al. 2015). As pointed out in De Looze et al. (2011), the tight correlation between [CII] emission and mean star formation activity is due either to emission from PDRs in the immediate surroundings of star-forming regions, or emission associated to the cold ISM, thus invoking the Schmidt law to explain the link with star formation. Intensity mapping measurements of the mean amplitude of the [CII] emission line allows us to constrain the global star formation activity of the Universe at high redshift. \u2022 [NII] (122 \u00b5m and 205 \u00b5m) emission lines: With a ionization potential of 14.53 eV, ionized Nitrogen is only found in the ionized phase of the ISM. The two infrared [NII] lines are due to the splitting of the ground state of N+ into three \ufb01ne-structure levels, which are excited mainly by collisions with free electrons in HII regions, with critical densities of 290 cm\u22123 and 44 \u22123 for [NII] (122 \u00b5m) and [NII] (205 \u00b5m) respectively, assuming Te = 8000 K, see Herrera-Camus et al. (2016); Hudson & Bell (2004). Being in the same ionization stage, their ratio directly determines the electron density of the ionized gas in HII regions. For electron densities ne larger than 10 cm\u22123, the 122/205 \u00b5m line ratio R122/205 increases as a function of ne, starting from R122/205 \u223c0.6 for ne \u223c10 cm\u22123, and reaching the value R122/205\u223c3 (the value used in this paper) for ne \u223c100 cm\u22123 (Tayal 2011; Goldsmith et al. 2015). Moreover, combined measurements of line emission from [NII] and [CII] can be used to estimate the amount of [CII] emission coming from the ionized medium (Malhotra et al. 2001; Oberst et al. 2006; Decarli et al. 2014; Hughes et al. 2016). Recently Goldsmith et al. (2015), using data from the PACS and HIFI instruments onboard Herschel, estimated that between 1/3 and 1/2 of the [CII] emission from sources in the Galactic plane arise from the ionized gas. The [NII]/[CII] ratio is also useful to estimate the metallicity of a galaxy (Nagao et al. 2012). Finally, the [NII] emission lines, arising from gas ionized by O and B type stars, directly constrains the ionizing photon rate, and thus the star formation rate (Bennett et al. 1994; McKee & Williams 1997). \u2022 Oxygen 63 \u00b5m and 145 \u00b5m lines: Oxygen has a ionization potential of 13.62 eV, just above that of hydrogen. The [OI] (63 \u00b5m) and [OI] (145 \u00b5m) line emissions come from PDRs and, together with [CII], are a major coolant of the ISM. However, because their \ufb01ne structure transitions are excited at high temperatures (228 K and 326 K respectively, against 91 K of [CII]), and their critical densities are quite high (\u223c5e5 cm\u22123 and \u223c1e5 cm\u22123 for [OI] 63 \u00b5m and [OI] 145 \u00b5m respectively) they contribute signi\ufb01cantly to the cooling of the ISM only for high FUV \ufb01elds and/or high densities. The measurement of the mean amplitude of the [OI] lines with intensity mapping would give us clues regarding the mean value of the G0 \ufb01eld and the mean density of PDRs at high redshifts (Meijerink et al. 2007). The intensity mapping technique would constrain the mean amplitude of multiple emission lines, together with their ratio, thus probing mean properties (such as mean radiation \ufb01eld, DISSECTING THE HIGH-Z INTERSTELLAR MEDIUM THROUGH INTENSITY MAPPING CROSS-CORRELATIONS 9 mean electron density in HII regions, mean density of various atoms, molecules) at high redshifts. 4. MULTIPLE CROSS-CORRELATIONS CONSTRAIN THE PHYSICS OF THE ISM As previously stated, the cross-correlation signal between different emission lines coming from the same redshift is important not only to avoid contamination from foreground lines (assuming that, at the frequencies considered in the crosscorrelation measurements, foregrounds are not correlated), but also to help constraining the mean amplitude of each signal. This is particularly true at suf\ufb01ciently small scales, where the SNR is larger. If we assume that all lines are emitted by the same objects (a reasonable assumption, especially if the emission lines are not distant from each other, as in the case of the FIR lines such as [CII], [NII] and [OI]), it will be possible to constrain the mean amplitudes of emission lines Ii=1,...N, just by looking at all cross-correlation power spectra5. For a survey working in a given frequency range where N lines are detected, there are N(N \u22121)/2 cross-correlation measurements to be performed and, assuming there is perfect correlation among lines, it is suf\ufb01cient that N \u22653 to be able to constrain the mean emission from all lines. The chances of detecting autoand cross-power spectra strongly depend on the amplitude of the spectra, which, as already seen, is very uncertain. In the following we will consider predicted measurements of multiple combinations of emission line power spectra for two different surveys. The \ufb01rst one corresponds to a survey of the [CII] emission line similar to the proposed CONCERTO. The second one, referred in literature as CII-Stage II, and described in Silva et al. (2015); Lidz & Taylor (2016), is more sensitive, and corresponds to an evolution of currently planned [CII] surveys. As already emphasized, emission line power spectra are strongly contaminated by interlopers lines emitted by molecules at different redshifts. In case of [CII], the main confusion results from foreground emission of CO molecules undergoing rotational transitions between states J and J-1. As an example, [CII] emission from z = 6 is observed at frequency \u03bdobs = 271.6 GHz, and it is mainly contaminated by CO rotational transitions J = 3 \u21922 (z = 0.27), J = 4 \u21923 (z = 0.70), J = 5 \u21924 (z = 1.12), J = 6 \u21925 (z = 1.54), and J = 7 \u21926 (z = 1.97). Emission lines beyond this transition have a negligible contribution to the total foreground due to CO molecules, and we will not consider them in the rest of the paper. Using linear scaling relations from Visbal & Loeb (2010) to express the amplitude of the various CO emission lines as a function of the infrared luminosity, it is possible to estimate the contamination due to the main CO rotational lines. In the following, when plotting the [CII] auto-power spectra at various redshits, we will also plot the CO auto-power spectrum computed as the sum of the the main CO rotational transitions involved (from 3 \u21922 to 7 \u21926), in order to highlight the amplitude of this foreground. 5. EXPERIMENTAL SETUPS AND PREDICTIONS In order to measure high-redshift \ufb02uctuations with suf\ufb01cient SNR at the scales of interest, it is important to optimize the survey area. All predictions considered in this section are 5 More generally, with enough measurements at high SNR, we could always focus on cross-correlation measurements, without even bothering with autocorrelations, which are complicated by foreground lines. based on measurements spanning a redshift range \u2206z \u223c0.6 which corresponds to a frequency range of B\u03bd \u223c20 GHz at z = 7 for the [CII] line. We follow Gong et al. (2012) to compute uncertainties on the power spectra. The primary goal of the \ufb01rst survey considered, called CONCERTO, is to detect [CII] \ufb02uctuations in the redshift range 4.5 < z < 8.5. It is based on a spectrometer working in the frequency range 200 < \u03bd < 360 GHz, with spectral resolution \u03b4\u03bd \u223c1.5 GHz. Such a frequency window imposes the use of a so-called \u201csub-millimetre\u201d telescope, with primary aperture size D = 12 m, and moderate angular resolution. The instrumental noise is thus computed for a total observing time of tsurvey = 1500 hours, and a number of spectrometers Nsp = 1500. The survey area considered here is two square degrees, and is optimized to ensure high SNR in the wavenumber range of 0.1 < k < 1 h / Mpc. Accounting for realistic observational conditions and the total atmospheric transmission, the Noise Equivalent Flux density (NEFD), computed as the sensitivity per single pixel divided by the square root of the number of spectrometers, is equal to NEFD = 155 mJy sec1/2, for a spectral resolution of \u03b4\u03bd = 1.5 GHz. The on-sky sensitivity \u03c3N can be expressed as: \u03c3N = NEFD \u2206\u2126beam (33) where \u2206\u2126beam =2\u03c0 \u0010 \u03b8beam 2.355 \u00112 (34) is the beam area (in steradians), and the beam FWHM is given by: \u03b8beam = 1.22\u03bbobs/D (35) where \u03bbobs is the observed wavelength. Values for \u03c3N at z = 5, z = 6, and z = 7 are 15, 11, and 8.3 MJy/sr \u221a(sec) respectively. The observing time per pixel is given by: tobs =tsurveyNsp \u2206\u2126pix \u2206\u2126survey , (36) where \u2206\u2126survey is the total survey area covered. Assuming a spherically averaged power spectrum measurement, and a directionally independent on sky sensitivity \u03c3N, the variance of the power spectrum is: var[ \u00af P\u03b1(k)] = [P\u03b1(k) + \u00af PN \u03b1(k)]2 Nm(k, z) , (37) where Nm(k, z) denotes the number of modes at each wavenumber: Nm(k, z) = 2\u03c0 k2\u2206k Vs (2\u03c0)3 ; (38) the term \u2206k is the Fourier bin size, and Vs(z) is the survey volume, expressed as: Vs(z) = \u03c7(z)2\u00af y\u2206\u2126surveyB\u03bd. (39) The averaged noise power spectrum in Eq. 37 is: \u00af PN \u03b1(k) = Vpix \u03c32 N tobs ; (40) where the volume surveyed by each pixel is: Vpix =\u03c7(z)2\u00af y\u03b1(z)\u2126beam\u03b4\u03bd, (41) 10 SERRA P. et al. 10-2 10-1 100 101 k [h/Mpc] 101 102 103 104 105 106 107 108 109 1010 1011 1012 k 3PCIIxCII(k)/2\u03c02 (Jy / sr)2 CIIxCII z=5.0 COxCO z=5.0 10-2 10-1 100 101 k [h/Mpc] 100 101 102 103 104 105 106 107 108 109 1010 1011 k 3PCIIxNII(k)/2\u03c02 (Jy / sr)2 CIIxNII (205 \u00b5m) z=5.0 10-2 10-1 100 101 k [h/Mpc] 101 102 103 104 105 106 107 108 109 1010 1011 k 3PCIIxOI(k)/2\u03c02 (Jy / sr)2  CIIxOI (145.5 \u00b5m) z=5.0 Figure 4. Predicted [CII] auto-power spectrum and cross-power spectra between [CII] and [NII] (205.2 \u00b5m), and [OI](145.5 \u00b5m), at z = 5 computed for the survey CONCERTO. Also plotted in the left panel (green line) is the total CO power spectrum computed as the sum of the contributions from CO(3-2) to CO(7-6). 10-2 10-1 100 101 k [h/Mpc] 101 102 103 104 105 106 107 108 109 1010 1011 1012 k 3PCIIxCII(k)/2\u03c02 (Jy / sr)2 CIIxCII z=6.0 COxCO z=6.0 10-2 10-1 100 101 k [h/Mpc] 101 102 103 104 105 106 107 108 109 1010 1011 k 3PCIIxNII(k)/2\u03c02 (Jy / sr)2 CIIxNII (122 \u00b5m) z=6.0 10-2 10-1 100 101 k [h/Mpc] 101 102 103 104 105 106 107 108 109 1010 1011 k 3PCIIxNII(k)/2\u03c02 (Jy / sr)2 CIIxNII (205 \u00b5m) z=6.0 10-2 10-1 100 101 k [h/Mpc] 100 101 102 103 104 105 106 107 108 109 1010 k 3PCIIxOI(k)/2\u03c02 (Jy / sr)2 CIIxOI (145.5 \u00b5m) z=6.0 Figure 5. Predicted [CII] and total CO (3-2 to 7-6) auto-power spectra (left panel, black and green line respectively) at redshift z = 6.0, and cross-spectra [CII]x[NII] (121.9 \u00b5m), [CII]x[NII](205.2 \u00b5m), and [CII]x[OI](145.5 \u00b5m) at z=6 for the survey CONCERTO. with \u00af y\u03b1(z) = \u03bb\u03b1(1 + z)2/H(z), (42) and \u03bb\u03b1 is the wavelength of the line \u03b1 is the rest frame. In Fig. 4 we plot measurements of the [CII] auto-power spectrum, together with [CII]x[OI] (145.5 \u00b5m), and [CII]x[NII] (205.2 \u00b5m) cross-power spectra at z = 5.0 for CONCERTO. For wavenumbers in the range 0.1 < k < 1 h / Mpc, the [CII] auto-power spectrum will be detected with high signi\ufb01cance (SNR > 50), while the [CII] cross-correlations with oxygen and nitrogen at these scales will not be very signi\ufb01cant (SNR\u223c3 and SNR\u223c0.5 respectively). However, considering smaller scales (larger wavenumbers) the SNR increases signi\ufb01cantly, and it will enable us to constrain the mean quantities I[CII], I[OI], and I[NII]. Given the CONCERTO frequency coverage, at z = 6.0 it is possible to add the cross-correlation DISSECTING THE HIGH-Z INTERSTELLAR MEDIUM THROUGH INTENSITY MAPPING CROSS-CORRELATIONS 11 10-2 10-1 100 101 k [h/Mpc] 101 102 103 104 105 106 107 108 109 1010 1011 1012 k 3PCIIxCII(k)/2\u03c02 (Jy / sr)2 CIIxCII z=6.0 COxCO z=6.0 10-2 10-1 100 101 k [h/Mpc] 100 101 102 103 104 105 106 107 108 109 1010 1011 k 3PCIIxNII(k)/2\u03c02 (Jy / sr)2 CIIxNII (205 \u00b5m) z=6.0 10-2 10-1 100 101 k [h/Mpc] 100 101 102 103 104 105 106 107 108 109 1010 1011 k 3PCIIxOI(k)/2\u03c02 (Jy / sr)2 CIIxOI (145.5 \u00b5m) z=6.0 Figure 6. Predictions for both [CII] and total CO (3-2 to 7-6) auto-power spectra (left panel, black and green line respectively), and cross-spectra [CII]x[NII](205.2 \u00b5m), and [CII]x[OI](145.5 \u00b5m) at z=6 for a CII-stage II survey. All spectra are detected with high SNR. Instrument parameters CONCERTO CII-Stage II Dish size (m) 12 10 Survey Area (deg2) 2 100 Frequency range (GHz) 200-360 200-300 Frequency resolution (GHz) 1.5 0.4 Number of spectrometers 1500 64 On-sky integration time (hr) 1500 2000 NEFD on sky (mJy \u221a(sec) 155 5 Table 3 Instrumental parameters for the two surveys, CONCERTO and CII-Stage II, considered. with [NII] (122 \u00b5m). As shown in Fig. 5, the cross-correlation of carbon with oxygen and nitrogen seems to be barely detectable at linear scales. However, in the non-linear regime, it might still be possible to measure these cross-correlations, and thus constrain the mean amplitude of these emission lines. As already described in Sect. 3, by looking at the cross-power spectra [CII]x[NII] (121.9 \u00b5)m, and [CII]x[NII] (205.2 \u00b5m), we would be able to measure the mean ratio [NII] (205.2 \u00b5m) / [NII] (121.9 \u00b5m), which is useful not only to constrain the electron density of the low-ionized gas in HII regions, but also to infer the mean emission of [CII] from PDRs, and to constrain the global star formation rate. The mean ratio between [OI] (145.5 \u00b5m) and CII is also a useful diagnostic of mean properties of properties of PDRs, such as the hydrogen density and the strength of the radiation \ufb01eld. The second experimental setup, called CII-Stage II, has been introduced in Silva et al. (2015) as an appropriate baseline to ensure detection of [CII] spectra in case of a pessimistic [CII] amplitude (see also Lidz & Taylor (2016)). It consists of a dish with diameter D = 10 m, with 16000 bolometers and Nsp = 64 beam spectrometers, observing in the frequency range 200 < \u03bd < 300 GHz, with a frequency resolution of 0.4 GHz. The total survey area is 100 deg2 for a total observing time of tsurvey = 2000 hours, and a NEFD of 5 mJy sec1/2. As it appears from Fig. 6, the cross-correlation of carbon with oxygen and nitrogen is now detectable with high SNR at z = 6. A space-based survey, being not limited by the atmosphere, would be able to perform measurements on a still wider frequency range, and thus perform measurements of high-redshift correlations with other interesting lines such as [OI] (63 \u00b5m), [OIII] (88 \u00b5m), [NIII] 57 \u00b5m, and [CI] (370 \u00b5m and 609 \u00b5m. 6. DISCUSSION We have developed a consistent framework to compute predictions of 3D power spectra of multiple FIR cooling lines of the ISM. Using measurements of CIB power spectra, together with measurements of star formation rate density from Madau & Dickinson (2014), it is possible to constrain the galaxy FIR luminosity at all redshift, which can be directly linked to emission line amplitudes through scaling relation from Spinoglio et al. (2012). Present and upcoming groundbased surveys aiming at measuring the power spectrum of the bright [CII] line, should be able to detect also the crosscorrelation between the [CII] line and other lines produced in all phases of the ISM, such as [NII] (122 \u00b5m and 205 \u00b5m), and [OI] (145.5 \u00b5m). Multiple measurements of cross-power spectra between [CII] and other emission lines will allow us to Figure 7. Amplitudes of main emission lines that can be observed in the frequency range \u03bdobs = [10 \u22121000] GHz, together with the expected spectral distortions \u00b5 and y. 12 SERRA P. et al. constrain the mean amplitude of each signal, and they will be key to gain insight into the mean properties of the ISM. Future surveys, such as PIXIE (Kogut et al. 2011, 2014), working in a broad frequency range, will detect many more atomic and molecular lines emitted from moderate to high redshift with high SNR, allowing us to obtain multiple probes of all phases of the ISM. Moreover, the cross-correlation of the target line with galaxy number densities from future surveys such as, e.g., LSST (LSST Science Collaboration et al. 2009), will be a powerful method to eliminate line foregrounds. Line emissions from multiple atoms/molecules at multiple redshifts are also an important foreground for future surveys aiming at constraining CMB spectral distortions. In Fig. 7 we plot \u00b5-type and y-type spectral distortions with \u00b5 = 5 \u00b7 10\u22128 and y = 1 \u00b7 10\u22128, corresponding to the current PIXIE 5\u03c3 sensitivity limits, together with the sum of the spectra from carbon monoxide emission lines (from J = 1 \u21920 to J = 7 \u21926), and the spectra from all emission lines considered in this work. The CO spectra have been computed using scaling relations from Visbal & Loeb (2010) to link the CO line emission to the star formation rate, and the Kennicutt relation to express the star formation rate in terms of the galaxy infrared luminosity (Kennicutt 1998). The amplitude of the global signal from CO lines is similar to what found by Mashian et al. (2016) using a radiative transfer modeling technique, even if the shape is slightly different. We note that, even if foreground lines do not have a simple spectral dependence, unlike other foregrounds that can be modeled with power law such as synchrotron or thermal dust, their shape is still monotonic in frequency, and thus very different with respect to the CMB spectral distortions. However, foreground subtraction will require a very good knowledge of the amplitude and shape of the total signal provided by the sum of these lines. The intensity mapping technique, by constraining the mean amplitude of the signal in multiple redshift bins, will help constraining the global contamination signal. Finally, it is clear that an aggressive program to model the amplitude of all emission lines at all redshifts is necessary to have a detailed interpretation of upcoming measurements. Scaling relations are useful to work with, but they provide little information on the main physical mechanisms governing the line emission. Moreover, they are based on few observations performed at some given redshift, and their redshift evolution is not very well known. Different physical conditions can dominate the line emission at different epochs, strongly affecting the amplitude of the signal. As an example, at high redshift, the CMB strongly suppresses the [CII] emission from the cold neutral medium, leaving only the emission from PDRs (Vallini et al. 2015). The redshift evolution of the galaxy infrared luminosity (which governs the evolution of the line emission in our model) is determined by the power law parameter \u03b4 (see Eq. 17), which, as stated earlier, is quite uncertain, especially at high redshifts. On the other hand, semi-analytic models of galaxy formation and evolution often involve a large number of assumptions and free parameters, and such a complexity makes them dif\ufb01cult to use. A third approach, intermediate between the two, and based on present and upcoming measurements from, e.g. ALMA and SOFIA, should be developed to model the line intensity of all relevant emission lines, together with their redshift evolution. Such a model, possibly based on the physics of photodissociation regions, ionized medium, and molecular clouds, will offer an important guidance in interpreting upcoming and future intensity mapping observations, and thus constrain the mean properties of high-redshift galaxies. We thank the anonymous referee for many useful comments and suggestions. We thank Phil Bull, Tzu-Ching Chang, Abigail Crites, Roland de Putter and Paul Goldsmith for insightful discussions, and the organizers of the stimulating workshop \u201cOpportunities and Challenges in Intensity Mapping\u201d in Stanford. We acknowledge \ufb01nancial support from \u201cProgramme National de Cosmologie and Galaxies\u201d (PNCG) of CNRS/INSU, France. PS acknowledges hospitality from the Laboratoire d\u2019Astrophysique de Marseille, where part of this work was completed. Part of the research described in this paper was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. Part of this work has been carried out thanks to the support of the OCEVU Labex (ANR-11-LABX-0060) and the A*MIDEX project (ANR11-IDEX-0001-02) funded by the \u201cInvestissements d\u2019Avenir\u201d French government program managed by the ANR.",
                    "introduction": "1. Intensity mapping, introduced in Madau et al. (1997); Sugi- nohara et al. (1999); Shaver et al. (1999), is an observational technique for measuring brightness \ufb02uctuations of emission lines produced by sources below the detection limit. Atomic and molecular emission lines, produced at a given redshift, are observed as \ufb02uctuations redshifted at a certain frequency, enabling us to map the three-dimensional structure of the Uni- verse and compute, for each redshift slice, statistical quanti- ties of interest such as the power spectrum. Intensity mapping, by measuring the aggregate radiation emitted by all galaxies in a given redshift slice, does not suffer from the incomplete- ness problem, while traditional galaxy surveys, being \ufb02ux- limited, do not detect the faintest galaxies. This can be a serious disadvantage if the galaxy luminosity function has a suf\ufb01ciently steep end, as shown in Uzgil et al. (2014). One of the \ufb01rst and main targets of intensity mapping is the 21 cm neutral hydrogen line (Battye et al. 2004; Chang et al. 2010; Bull et al. 2015), which, in principle, opens a new win- dow on both the formation of structures at high redshift and the history of reionization (Furlanetto et al. 2006). However, lines from other atoms and molecules can be used to constrain the physics of the ISM in a broad redshift range. The carbon [CII] \ufb01ne-structure line at 157.7 \u00b5m, arising from the 2P3/2 \u21922P1/2 \ufb01ne-structure transition, is one of the most promising lines not only to understand star-formation in galaxies (Boselli et al. 2002; De Looze et al. 2011, 2014; Herrera-Camus et al. 2015), but also to constrain the epoch Electronic address:"
                },
                {
                    "url": "http://arxiv.org/abs/1604.07902v1",
                    "title": "Linear relation between HI circular velocity and stellar velocity dispersion in early-type galaxies, and slope of the density profiles",
                    "abstract": "We report a tight linear relation between the HI circular velocity measured\nat 6 $R_{\\rm e}$ and the stellar velocity dispersion measured within 1 $R_{\\rm\ne}$ for a sample of 16 early-type galaxies with stellar mass between $10^{10}$\nand $10^{11}$ $\\mathrm{M}_\\odot$. The key difference from previous studies is\nthat we only use spatially resolved $v_\\mathrm{circ}$(HI) measurements obtained\nat large radius for a sizeable sample of objects. We can therefore link a\nkinematical tracer of the gravitational potential in the dark-matter dominated\nouter regions of galaxies with one in the inner regions, where baryons control\nthe distribution of mass. We find that $v_\\mathrm{circ}$(HI) = 1.33\n$\\sigma_\\mathrm{e}$ with an observed scatter of just 12 percent. This indicates\na strong coupling between luminous and dark matter from the inner- to the outer\nregions of early-type galaxies, analogous to the situation in spirals and dwarf\nirregulars. The $v_\\mathrm{circ}$(HI)-$\\sigma_\\mathrm{e}$ relation is shallower\nthan those based on $v_\\mathrm{circ}$ measurements obtained from stellar\nkinematics and modelling at smaller radius, implying that \\vcirc\\ declines with\nradius -- as in bulge-dominated spirals. Indeed, the value of\n$v_\\mathrm{circ}$(HI) is typically 25 percent lower than the maximum\n$v_\\mathrm{circ}$ derived at $\\sim0.2\\ R_\\mathrm{e}$ from dynamical models.\nUnder the assumption of power-law total density profiles $\\rho \\propto\nr^{-\\gamma}$, our data imply an average logarithmic slope\n$\\langle\\gamma\\rangle=2.18\\pm0.03$ across the sample, with a scatter of 0.11\naround this value. The average slope and scatter agree with recent results\nobtained from stellar kinematics alone for a different sample of early-type\ngalaxies.",
                    "authors": "Paolo Serra, Tom Oosterloo, Michele Cappellari, Milan den Heijer, Gyula I. G. J\u00f3zsa",
                    "published": "2016-04-27",
                    "updated": "2016-04-27",
                    "primary_cat": "astro-ph.GA",
                    "cats": [
                        "astro-ph.GA"
                    ],
                    "main_content": "We analyse a sample of 16 nearby ETGs drawn from the ATLAS3D sample (Cappellari et al. 2011). All galaxies and quantities used for this work are listed in Table 1. Galaxies are selected for hosting a regular H i disc or ring, which allows the determination of vcirc(H i) at large radius. The selection is based on a large set of interferometric H i observations and data products presented by Serra et al. (2012, 2014) for \u223c150 galaxies. This dataset was largely assembled as part of the ATLAS3D project but includes earlier data taken by Morganti et al. (2006), Weijmans et al. (2008), J\u00b4 ozsa et al. (2009) and Oosterloo et al. (2010). The H i kinematics was modelled by dH15 for all but two galaxies for which literature values were used: NGC 2685 (J\u00b4 ozsa et al. 2009) and NGC 2974 (Weijmans et al. 2008). Here we make use of the vcirc(H i) values measured at the largest possible radius RHI and listed by dH15. The RHI values fall in the range 4 to 16 Re, and their median is \u223c6 Re. All galaxies in the sample were observed with optical integral-field spectroscopy as part of the SAURON project (4 galaxies; de Zeeuw et al. 2002) or ATLAS3D (12 galaxies; Cappellari et al. 2011). Here we make use of the stellar velocity dispersion measurements \u03c3e within a 1 Re aperture given in C13. The same paper describes Jeans anisotropic modelling of the stellar kinematics of these galaxies (JAM; Cappellari 2008). Here use the maximum circular velocity vmax circ (JAM) values predicted by the JAM models at the radius Rmax. For this work we use JAM models (A), which assume that mass follows light and are appropriate for the central regions of galaxies. The values of Rmax fall in the range 0.1 to 0.4 Re (median \u223c0.2 Re). This sample does not have any strong bias on the masssize plane of ETGs, and the 16 galaxies cover a representative range of bulge-to-disc ratio (as traced by \u03c3e) in the stellar mass range 1010 1011 M\u2299(dH15). Bearing in mind the small sample size, the conclusions of this work should hold for the general early-type population within this mass range and with \u03c3e between 100 and 250 km s\u22121. 3 RESULTS 3.1 Linear relation between vcirc(H i) and \u03c3e We plot vcirc(H i) against \u03c3e in Fig. 1. The figure shows a strong correlation between these two quantities. A powerlaw fit to our data performed as a linear fit in logarithmic space with the LTS_LINEFIT software (C13) results in: log vcirc(H i) km s\u22121 vcirc(H i) km s\u22121 = (2.299 \u00b1 0.013)+ \u00b1 + (0.96 \u00b1 0.11) \u00d7 log \u03c3e 150 km \u03c3e 150 km s\u22121 , (1) \u2212 where the value 150 km s\u22121 was adopted to minimise the 25 50 100 250 \u03c3e (km/s) 25 50 100 250 500 vcirc(H i) (km/s) this work Ho (2007) Pizzella et al. (2005) vcirc(H i) = 1.33 \u03c30.96 e vcirc(H i) = 1.33 \u03c3e vcirc(H i) = 1.76 \u03c3e Figure 1. Relation between vcirc(H i) and \u03c3e. Dashed and solid lines show the best-fitting power-law and linear relation, respectively, obtained for our sample of 16 ETGs (see Sec. 3.1 and legend). The dotted line is a linear fit (with zero intercept) to the P05 data, noting that for consistency with our work we correct their \u03c3 measurements to an aperture of radius 1 Re (see Sec. 3.2 for details). We do not correct the \u03c3 values of Ho (2007) because that sample shows no correlation between vcirc(H i) and \u03c3 in the first place (Sec. 3.2), and the correction is irrelevant for the purpose of our comparison. covariance between the fit parameters (C13). The observed r.m.s. scatter around this relation is 0.049 dex (12 percent). The intrinsic scatter is 0.036 \u00b1 0.016 dex (9 \u00b1 4 percent). The value of the power-law exponent in Eq. 1 is consistent with unity. Indeed, Fig. 1 shows that, within the \u03c3e range of our sample, the best-fitting power-law is fully compatible with the linear relation: vcirc(H i) = 1.33 \u03c3e, (2) where the uncertainty on the slope is 3 percent. The scatter around this relation is 12 percent, identical to the scatter around the best-fitting power law. This is the first time that such a tight, linear relation is found using vcirc measurements obtained at such a large radius (\u223c6 Re) from the resolved H i kinematics of a sizeable sample of ETGs. In Sec. 3.2 we support this claim by performing a detailed comparison between this result and previous work. The existence of a correlation between vcirc(H i) and \u03c3e for ETGs is expected given that \u03c3 correlates with LK (Faber & Jackson 1976) and LK correlates with vcirc(H i) (dH15). However, the actual linearity, slope and scatter of the relation, which we establish here, are not trivial. In particular, its linearity implies that the LK-\u03c3 and LK-vcirc(H i) power-law relations have identical exponents, in agreement with general predictions of the Modified Newtonian Dynamics (Milgrom 1984). Importantly, the vcirc(H i)-\u03c3e relation is relatively free of systematics as both quantities involved are independent of distance and stellar mass-to-light ratio (unlike in other galaxy scaling relations), and have small errors. The main source of uncertainty on vcirc(H i) is the inclination of the MNRAS 000, 1\u20138 (2015) 4 Serra et al. 4 6 8 10 12 14 16 18 RHI/Re 0.6 0.8 1.0 1.2 1.4 1.6 vcirc(H i)/(1.33 \u03c3e) Figure 2. Deviation from the vcirc(H i)-\u03c3e relation of Eq. 2 as a function of RHI/Re. No relation is found. gas disc, which results in a typical error below 10 percent (dH15; Table 1). The uncertainty on \u03c3e is \u223c5 percent (C13). The small intrinsic scatter of the vcirc(H i)-\u03c3e relation is particularly interesting. In Secs. 3.2 and 3.3 we discuss evidence that vcirc declines with radius in ETGs, and this raises the question of whether some of this scatter is related to the relatively large range of RHI values covered by our sample. We investigate this aspect in Fig. 2. The \ufb01gure shows no clear trend between the deviation from the relation and RHI/Re: galaxies where vcirc(H i) is measured at larger (lower) radius are not systematically below (above) the relation. This suggests that other factors drive the observed scatter. An important contribution might come from the scatter in the shape of the ETG rotation curves. This can be linked to the scatter in the mass-concentration relation of dark matter halos predicted by dark-matter-only simulations (Dutton & Macci` o 2014). In the future it will be interesting to test whether the intrinsic scatter of the vcirc(H i)-\u03c3e relation is consistent with these simulations (see Dutton 2012 and Lelli et al. 2016 for a similar test based on the intrinsic scatter of the baryonic Tully-Fisher relation). The relation between vcirc(H i) and \u03c3e is remarkable as the two quantities are measured in completely independent ways and, unlike in previous work, trace the gravitational potential in two extremely di\ufb00erent regimes of the distribution of matter: \u03c3e is measured in a region where the luminous matter constitutes on average 85 percent of the mass (C13); while vcirc(H i) is measured in a region where dark matter accounts for basically all of the mass (the total dynamical mass within RHI is on average \u22733 times the total stellar mass estimated by C13). This tight correlation suggests that galaxies in our sample all have roughly the same overall distribution of mass \u2013 another manifestation of the poorly understood coupling between the distribution of luminous matter and total mass in galaxies (van Albada & Sancisi 1986; Sancisi 2004; Swaters et al. 2012; Lelli et al. 2013). We will return to this point in Sec. 3.4. 3.2 Comparison with previous vcirc-\u03c3 relations 3.2.1 vcirc from H i kinematics The only previous study of the vcirc-\u03c3 relation of ETGs entirely based on H i data is that of Ho (2007), whose sample includes \u223c100 ellipticals and lenticulars. However, that work makes use of single-dish unresolved H i data, which give no information about the dynamical state and geometry of the gas. In order to derive vcirc from unresolved spectra one must assume that i) the H i is on a rotating disc and ii) the disc has the same inclination of the stellar body. These two assumptions are in error for more than half of all H i-rich ETGs (Serra et al. 2012, 2014), resulting in inaccurate single-dish vcirc(H i) values for this type of galaxies. It is likely for this reason that vcirc(H i) and \u03c3 do not correlate signi\ufb01cantly for the ETG sample of Ho (2007), as shown in Fig. 1. We have independently obtained a Spearman correlation coe\ufb03cient of 0.41 (with p-value 0.17) for that sample, con\ufb01rming the visual impression given by the \ufb01gure. Ho (2007) \ufb01nds that vcirc(H i) and \u03c3 do correlate if they limit their analysis to a subsample of ETGs selected to follow the vcirc(H i)-LK (Tully-Fisher) relation of spirals. However, we argue that for such a subsample the vcirc(H i)-\u03c3e relation is a selection e\ufb00ect. A Tully-Fisher selection will always result in a vcirc(H i)-\u03c3 relation \u2013 even if none existed and regardless of the quality of the vcirc(H i) estimates \u2013 because of the tight \u03c3-LK (Faber-Jackson) relation of ETGs. Furthermore, the shape and scatter of the resulting vcirc(H i)-\u03c3 relation will be entirely determined by the details of the Tully-Fisher selection rather than by the properties of the galaxies being studied. Our galaxies, too, follow the TullyFisher relation (dH15), but they are not selected to do so. Therefore, the existence, shape and scatter of our vcirc(H i)\u03c3 relation fully re\ufb02ect the properties of the ETGs in our sample rather than the way they are selected. The only previous studies of the vcirc-\u03c3 relation to overcome the limitations of single-dish data and include resolved vcirc(H i) measurements for ETGs are those by P05 and, using the same H i data, C07. The main di\ufb00erence from our analysis is that the number of H i measurements used is very small \u2013 just 5. Apart from these 5 objects, those ETG samples are dominated by vcirc values obtained at a radius comparable with Re from stellar kinematics and dynamical modelling (discussed in Sec. 3.2.2), and these authors do not derive an ETG vcirc-\u03c3 relation based on H i data alone. Nevertheless, in this Section we discuss whether the tight linear relation vcirc(H i) = 1.33 \u03c3e obtained in Sec. 3.1 from our data could have been derived from the 5 ETGs with H i data included in the P05 and C07 samples. Fig. 1 shows those 5 ETGs on the vcirc(H i)-\u03c3e plane. An important detail is that P05 and C07 use \u03c3 measurements obtained within (or corrected to) an Re/8 aperture. For consistency with our work we correct those values to a 1 Re aperture multiplying them by a factor 0.872 derived from Eq. 1 of Cappellari et al. (2006). The accuracy of (and need for) this correction can be easily veri\ufb01ed considering the two ETGs in common with our sample, NGC 2974 and NGC 4278. As a whole, the 5 ETGs of P05 and C07 appear systematically o\ufb00set towards high vcirc(H i) relative to our sample in Fig. 1. Furthermore, they do not follow a linear vcirc(H i)\u03c3e relation. The best-\ufb01tting power law obtained with the MNRAS 000, 1\u20138 (2015) vcirc(H i)-\u03c3e relation and density pro\ufb01les in ETGs 5 same LTS_LINEFIT software used in Sec. 3.1 has an exponent of 0.59 \u00b1 0.17. This is signi\ufb01cantly non-linear, unlike our Eq. 1. Assuming linearity, the slope of the relation de\ufb01ned by those 5 ETGs and obtained with an orthogonal distance regression \ufb01t of a linear relation through the origin is 1.76 with a 6 percent uncertainty (Fig. 1). This is \u223c30 percent larger than the 1.33 slope of our relation. We note that, taken individually, none of the 5 ETGs studied by P05 and C07 is dramatically o\ufb00set from our sample in Fig. 1. The average \u223c30 percent o\ufb00set discussed above is most likely caused by the small number of objects combined with the large uncertainty on vcirc(H i). More in detail, P05 adopt vcirc(H i) values obtained from data with a velocity resolution of \u223c40 km s\u22121 for the two galaxies in common with our sample: NGC 2974 (Kim et al. 1988) and NGC 4278 (Lees 1994). Despite being consistent with our measurements within the large errors, the resulting vcirc(H i) values of 355 \u00b1 60 and 326 \u00b1 40 km s\u22121 obtained at \u223c4 and \u223c10Re, respectively, are 15 and 27 percent larger than those in Table 1. We also note that Lees (1994) estimate vcirc(H i) in NGC 4278 through complex modelling of the H i data cube assuming a triaxial gravitational potential at constant inclination, which may introduce systematic di\ufb00erences compared to the method used by dH15. For NGC 2865 P05 adopt the vcirc(H i) estimate at \u223c6Re from Schiminovich et al. (1995), who remark that their assumption of coplanar circular orbits for the H i gas is not necessarily supported by their data. For NGC 5266 vcirc(H i) comes from a study by Morganti et al. (1997), where again circular orbits are just assumed. These authors estimate vcirc(H i) at \u223c4Re while at larger radius the gas disc appears unsettled. Finally, for IC 2006 \u2013 the main outlier in Fig. 1 \u2013 vcirc(H i) is taken from Franx et al. (1994). Their analysis shows that the rotation curve of this galaxy is relatively \ufb02at. As we discuss below, this is not typical for ETGs. The above considerations highlight that it would have been di\ufb03cult for P05 to obtain a reliable slope of the vcirc(H i)-\u03c3e relation based on such few objects and sometimes limited data quality. The inclusion of these 5 galaxies in their sample was important at the time, and that paper clearly shows that vcirc(H i) grows with \u03c3e in ETGs. However, that sample was just too small to establish the linearity, tightness and actual slope of the vcirc(H i)-\u03c3e relation presented in Sec. 3.1. 3.2.2 vcirc from stellar kinematics at small radius Having established a precise vcirc(H i)-\u03c3e relation for ETGs based on our data, we can investigate whether such relation is identical to those obtained using kinematical data at smaller radius. This was one of the conclusions of P05: their 5 ETGs with a vcirc(H i) measurement follow the same vcirc-\u03c3 relation obtained for a larger sample consisting of 40 high-surface-brightness spirals (with vcirc from ionised gas or H i data; see references in P05) and another 19 ETGs (with vcirc measured within \u223c2 Re from the dynamical models of Kronawitter et al. 2000). Below we show that our data do not support this conclusion, and Eq. 2 is markedly shallower than relations obtained at smaller radius. First, assuming that the relation between vcirc and \u03c3 is linear, P05 \ufb01nd vcirc= (1.32\u00b10.09) \u03c3+46\u00b114. This relation is signi\ufb01cantly di\ufb00erent from our Eq. 2 for two reasons. First, it has a non-zero intercept which cannot be ignored. At the median velocity dispersion of our sample (\u223c130 km s\u22121), the intercept amounts to \u223c20 percent of the vcirc value predicted by the relation. Second, the \u03c3 values used by P05 must be corrected to the 1 Re aperture used in our work (Sec. 3.2.1). When this is done, we \ufb01nd that the best-\ufb01tting slope of a linear relation through the origin for the full P05 sample is 1.77, \u223c30 percent larger than our value of 1.33. A similar conclusion can be drawn for other samples dominated by vcirc measurements at small radius. Focusing on ETGs, C07 adds to the P05 sample \u223c50 lenticulars with vcirc measured by Bedregal et al. (2006, and references therein) based on stellar kinematics \u2013 but no new H i data. Once their \u03c3 values are corrected to an aperture of 1 Re as above, these ETGs scatter about a vcirc-\u03c3e relation of slope \u223c1.7 and are clearly inconsistent with our Eq. 2. Likewise, our slope of 1.33 is signi\ufb01cantly lower than the 1.52 value found by Gerhard et al. (2001). The comparison with the latter study is particularly useful to understand the cause of this di\ufb00erence. First, as above, we correct for the larger aperture within which we measure \u03c3 (1 Re compared to \u223c0.1 Re). We use again Eq. 1 of Cappellari et al. (2006) and \ufb01nd \u03c3e = 0.859 \u03c30.1Re. The other, crucial difference from this and all other previous studies of ETGs is that our vcirc values are obtained at a much larger radius (\u223c6 Re compared to \u223c0.3 Re in the case of Gerhard et al. 2001). This di\ufb00erence is relevant in light of the recent \ufb01ndings of C15. They show that the density pro\ufb01les of ETGs are somewhat steeper than isothermal, and that vcirc decreases slowly with radius. We discuss this aspect in more detail in Secs. 3.3 and 3.4, but for the moment it is su\ufb03cient to consider that on average vcirc \u221dr\u22120.095. Therefore, our vcirc measurements and those of Gerhard et al. (2001) are related by vcirc(6Re) = 0.752 vcirc(0.3Re). Taken together, the two corrections transform our Eq. 2 from vcirc(6Re) = 1.33 \u03c3e into vcirc(0.3Re) = 1.52 \u03c30.1Re, which is exactly the result of Gerhard et al. (2001). Finally, C13 derives the vcirc-\u03c3e relation from dynamical models of all 260 ETGs in the volume-limited, complete ATLAS3D sample. They \ufb01nd a slope of 1.76 when using the peak vcirc predicted by the models (typically at 0.2 Re). As for the study of Gerhard et al. (2001), the larger slope compared to Eq. 2 can be explained by the decline of vcirc with radius (C15 and Sec. 3.3). In summary, once aperture e\ufb00ects on the measurement of \u03c3 are taken into account, our vcirc(H i)-\u03c3e relation is shallower than all published relations based on vcirc measurements at smaller radius. This suggests that vcirc is not constant with radius and indicates the validity of the conclusions of C15 on the slow decline of vcirc. It highlights that ETG samples selected to only include objects with a \ufb02at rotation curve (as in P05) might be biased towards galaxies with a speci\ufb01c distribution of total mass, such that vcirc remains high even when it is measured at relatively large radius. We explore the variation of vcirc with radius in ETGs in the next sections. 3.3 Variation of vcirc with radius We compare vcirc(H i) with the circular velocity at small radius vmax circ (JAM) derived by C13 using dynamical models (see Sec. 2 and Table 1). Those authors \ufb01nd a tight corMNRAS 000, 1\u20138 (2015) 6 Serra et al. 200 300 400 500 vmax circ (JAM) (km/s) 100 200 300 vcirc(H i) (km/s) identity vcirc(H i) = 0.73 vmax circ (JAM) Figure 3. Relation between vcirc(H i) and vmax circ (JAM). The solid line shows the best-\ufb01tting linear relation (see Sec. 3.3 and legend). relation between vmax circ (JAM) and \u03c3e. Therefore, in light of our Fig. 1, we expect a correlation between vcirc(H i) and vmax circ (JAM). This is shown in Fig. 3. As in Sec. 3.1, we \ufb01t a power law to the data points and \ufb01nd the best \ufb01t to be relatively close to a linear relation given the error bars (the exponent is 0.79 \u00b1 0.15). Indeed, the 17 percent (0.068 dex) observed scatter around the best-\ufb01tting power law is only slightly lower than the 18 percent scatter around the linear relation: vcirc(H i) = 0.73 vmax circ (JAM). (3) The scatter of the vcirc(H i)-vmax circ (JAM) relation is considerably larger than that of the vcirc(H i)-\u03c3e relation. In particular, based on the 7 percent observed scatter of the vmax circ (JAM)-\u03c3e relation (C13), a conservative estimate of the uncertainty on vmax circ (JAM) is \u223c5 percent (as for \u03c3e). The resulting intrinsic scatter of the vcirc(H i)-vmax circ (JAM) relation is 16\u00b15 percent (it was 9\u00b14 percent for the vcirc(H i)-\u03c3e relation). This could indicate that, in the present sample, the distribution of mass is relatively homogeneous between Re and RHI, but less so between Rmax and Re. A visual inspection of the rotation curves in the Noordermeer et al. (2007) sample indicates that this is the case in early-type spirals. Our measurements show that vcirc drops on average \u223c25 percent from Rmax to RHI (the actual drop varying between 0 and 50 percent depending on the galaxy). Obvious questions are where this drop occurs within galaxies and how gradual it is with radius. Some qualitative indications come from molecular gas vcirc estimates obtained by Davis et al. (2011) at a radius intermediate between Rmax and RHI (for CO-detected galaxies in the ATLAS3D sample the molecular gas reaches a typical radius between 0.5 and 1 Re; see Davis et al. 2013). First, Davis et al. (2011) show that vcirc(CO) is on average \u223c10 percent lower than vmax circ (JAM) (with considerable scatter; see their \ufb01g. 4). Second, dH15 report an o\ufb00set between the CO and H i K-band Tully-Fisher relations of ETGs corresponding to a vcirc decrease by another \u223c10 percent. Combining these two results we conclude 0.1 0.3 1 3 10 r/Re 0.6 0.8 1.0 1.2 1.4 1.6 1.8 vcirc(r) /vcirc(Re) \u03b3 = 1.8 \u03b3 = 2.4 \u03b3 = 2.0 \u03b3 = 2.6 \u03b3 = 2.2 H i data JAM models Figure 4. Variation of vcirc with radius based on estimates at Rmax<Re from JAM models and at RHI>Re from H i data. Points and connecting solid lines are colour coded in three groups going from orange through red to magenta according to increasing RHI/Re ratio. For each galaxy, the values of vcirc at Rmax and RHI are normalised to vcirc(Re), but note that we do not make use of actual vcirc(Re) measurements. Instead, for normalisation purpose, we assume that vcirc(Re) lies on the rotation curve passing through our measurements at Rmax and RHI with logarithmic slope de\ufb01ned by Eq. 4. Blue and grey lines correspond to models with a power-law density pro\ufb01le \u03c1 \u221dr\u2212\u03b3 for the values of \u03b3 listed in the legend. that the average \u223c25 percent vcirc drop between Rmax and RHI is about equally distributed inside and outside Re. A more quantitative result would require a detailed study of the resolved rotation curve out to RHI for galaxies in this sample. However, at the typical resolution of our H i data (\u223c40 arcsec) this is possible for just a few objects. Two such galaxies are NGC 2685 (J\u00b4 ozsa et al. 2009) and NGC 2974 (Weijmans et al. 2008). Their rotation curves show indeed a clear decline out to \u223c10 and \u223c2 Re, respectively, and appear to \ufb02atten further out. This would be consistent with the situation in early-type spirals, where vcirc peaks at small radius and then drops by 10-20 percent to a \ufb02at level (Noordermeer et al. 2007). A similar study of the resolved H i rotation curve can be performed for a few more objects in our sample and will be the subject of future work. For the time being, it remains unclear whether and at what characteristic radius the H i rotation curves of ETGs become \ufb02at. Whatever results will be obtained from studying the resolved H i kinematics of more ETGs, we do know from C15 that the stellar rotation curves of most such systems decline steadily out to at least \u223c4 Re. These authors \ufb01nd that the observed decline of vcirc is well described by power-law density pro\ufb01les \u03c1 \u221dr\u2212\u03b3, and that the pro\ufb01le slopes \u03b3 cover a surprisingly narrow range centred around a mean value \u27e8\u03b3\u27e9= 2.19 \u00b1 0.03 and with an observed r.m.s. scatter \u03c3\u03b3 of just 0.11. Here we can test this result using a di\ufb00erent sample (only two galaxies are in common between our sample and that of C15) and completely di\ufb00erent observations that reach further out into the dark-matter halo. MNRAS 000, 1\u20138 (2015) vcirc(H i)-\u03c3e relation and density pro\ufb01les in ETGs 7 3.4 Average slope of the total density pro\ufb01les The analysis of C15 shows that the mass distribution of ETGs is well represented by power-law density pro\ufb01les \u03c1 \u221d r\u2212\u03b3 out to large radius. We therefore assume power law pro\ufb01les for our galaxies. It follows that vcirc \u221dr1\u2212\u03b3/2 (Binney & Tremaine 2008, Eq. 2.61). We can then use our measurements of vmax circ (JAM) and vcirc(H i) at Rmax and RHI, respectively, to measure the average logarithmic slope of the density pro\ufb01le for each galaxy: \u03b3 = 2 \u22122 log vcirc(H i) \u2212log vmax circ (JAM) log RHI \u2212log Rmax , (4) and study the distribution of \u03b3 values across the sample. Fig. 4 shows our measurements as well as model rotation curves for a range of \u03b3 values. We \ufb01nd a narrow range for \u03b3 , with all galaxies con\ufb01ned in a region of the plot corresponding to 2 < \u03b3 < 2.4. On average, galaxies in this sample appear to have pro\ufb01les somewhat steeper than isothermal. This is an important con\ufb01rmation of the result presented by C15, in particular considering the di\ufb00erent sample and type of data used here. More quantitatively, the weighted mean and the r.m.s. scatter of the 16 \u03b3 values listed in Table 1 are: \u27e8\u03b3\u27e9= 2.18 \u00b1 0.03 and \u03c3\u03b3 = 0.11 . (5) Although here we cannot check whether the assumption of power-law pro\ufb01les is correct and can only measure the average logarithmic slope, our result is in remarkable quantitative agreement with the one of C15, where the adequacy of power-law pro\ufb01les is veri\ufb01ed. Our mean slope is very close to their \u27e8\u03b3\u27e9= 2.19\u00b10.03, and the observed scatter is identical. Our result is also in relatively good agreement with that obtained at small radius from gravitational lensing, which suggests pro\ufb01le shapes only marginally closer to isothermal (Auger et al. 2010; Barnab` e et al. 2011). As discussed in Sec. 3.3, our data do not rule out that at some radius beyond Re the rotation curves of ETGs become \ufb02at. If that is the case, we would expect our measurements of \u03b3 to approach the isothermal value \u03b3 = 2 as RHI increases. Fig. 4 does not show any clear indications that this is the case. Galaxies with a vcirc(H i) measurement at \u223c10 Re or above can have a value of \u03b3 signi\ufb01cantly above 2, while galaxies with a vcirc(H i) measurement obtained below \u223c5 Re can have \u03b3 close to the isothermal value. As pointed out in the case of the vcirc(H i)-\u03c3e relation (Sec. 3.1 and Fig. 2), the scatter in the shape of the ETG rotation curves might be more important than the radius at which we measure vcirc(H i). We stress again that only the resolved study of more H i rotation curves can clarify whether and at what radius vcirc becomes \ufb02at in ETGs. The above discussion indicates that, whether or not the density pro\ufb01les of all ETGs are well approximated by single power-laws out to the radius probed by our vcirc(H i) measurements, (i) their average slopes cluster around a value of 2.2 and (ii) the small scatter of 0.11 is indicative of relatively small di\ufb00erences between galaxies, as also suggested by the scatter of the vcirc(H i)-\u03c3e relation. The origin of these di\ufb00erences is, however, unclear. Since \u03b3 measures an average property of the distribution of mass one may think that its value depends on the presence of a massive bulge and, 100 200 300 \u03c3e (km s\u22121) 1.6 1.8 2.0 2.2 2.4 2.6 2.8 \u03b3 This work Cappellari et al. (2015) Figure 5. Average logarithmic pro\ufb01le slope \u03b3 vs. stellar velocity dispersion \u03c3e for our sample and the sample of C15. No correlation is observed. therefore, on the value of \u03c3e. However, Fig. 5 shows that \u03b3 does not vary systematically with \u03c3e for our sample combined with the one of C15 (the correlation coe\ufb03cient is below 0.4). An identical conclusion is reached from dynamical modelling of ETGs within 1 Re considering only galaxies within the \u03c3e and stellar mass range covered by our sample (\ufb01g. 22 of Cappellari 2016). The same modelling shows that \u03b3 does decrease at lower \u03c3e and larger stellar masses than covered by our sample, but it is unknown whether a similar trend persists at the large, dark-matter dominated radii reached by our H i data. We have investigated possible correlations between \u03b3 and additional parameters that trace the relative importance of the bulge: the bulge-to-total ratio, the e\ufb00ective surface brightness (both total and of the bulge) and the Sersic index from Krajnovi\u00b4 c et al. (2013); the light concentration from C13; and the ratio \u03c3Re/8/\u03c3e from Cappellari et al. (2013b). In all cases we \ufb01nd correlation coe\ufb03cients below 0.4 (in absolute value). Therefore, we conclude that the current sample shows no indication of a systematic variation of \u03b3 with the optical structure of ETGs. Larger samples will be needed to establish the nature of the small scatter of the density pro\ufb01le shapes. 4 CONCLUSIONS We establish a tight linear relation between the circular velocity measured in the dark-matter dominated regions (\u223c6 Re) and the velocity dispersion measured inside 1 Re for a sizeable sample of 16 ETGs. The vcirc values are obtained from resolved H i observations and, therefore, do not su\ufb00er from the limitations of single-dish data previously used in the literature. We \ufb01nd that vcirc(H i) = 1.33 \u03c3e with an observed scatter of 12 percent. The tightness of the correlation suggests a strong coupling between luminous and dark matter from the inner regions where we measure \u03c3e to the outer regions where we measure vcirc(H i). This coupling has been long known for spirals and dwarf irregulars (van Albada & MNRAS 000, 1\u20138 (2015) 8 Serra et al. Sancisi 1986; Sancisi 2004; Swaters et al. 2012; Lelli et al. 2013) but had never been established for ETGs. Previous samples of ETGs with resolved vcirc(H i) measurements were too small to establish the tightness, linearity and actual slope of the vcirc(H i)-\u03c3e relation, and to compare it with relations obtained at smaller radius. Overall, we \ufb01nd that our relation is shallower than those based on vcirc measurements obtained from stellar kinematics and dynamical modelling at a radius comparable with Re. This indicates a decline in vcirc from Re to the outer regions where we measure vcirc(H i). Comparing our H i measurements of vcirc at \u223c6 Re with those derived from dynamical modelling of the stellar kinematics at much smaller radius (\u223c0.2 Re) we \ufb01nd that the rotation curves of ETGs drop by 0 to 50 percent towards large radius for galaxies in the sample (25 percent on average). This drop is similar to that observed in early-type spirals (Noordermeer et al. 2007). It is in excellent agreement with a recent, independent determination of the slope of the density pro\ufb01le of ETGs based on stellar kinematics and dynamical modelling of a di\ufb00erent sample (C15). It appears that the average density pro\ufb01le of ETGs in the stellar mass and \u03c3e ranges probed by our combined samples is slightly steeper than isothermal, with a logarithmic slope of 2.19 \u00b1 0.02 and a scatter of just 0.11.",
                    "introduction": "The distribution of mass in galaxies continues to be the subject of intense debate. The situation is clear at large radius: stellar kinematics, gas kinematics and gravitational lensing show that a dark matter of unknown nature domi- nates the gravitational potential of most galaxies (assuming Newtonian dynamics). In these regions the rotation curves \u22c6E-mail: paolo.serra@csiro.au are approximately \ufb02at and the total density pro\ufb01les close to isothermal (Bosma 1978, 1981; van Albada et al. 1985; Gavazzi et al. 2007; Cappellari et al. 2015, hereafter C15). Well inside galaxies\u2019 stellar body the situation is much more diverse but, in these regions, baryons and dynamics are closely connected (Sancisi 2004; Swaters et al. 2012; Lelli et al. 2013): in low-surface-brightness galaxies, rotation curves rise slowly and dark matter dominates the potential (de Blok et al. 2001); in high-surface-brightness galaxies, ro- tation curves rise fast to approximately (or slightly above) c \u20dd2015 The Authors arXiv:1604.07902v1  [astro-ph.GA]  27 Apr 2016 2 Serra et al. Table 1. H i-rich early-type galaxies Name Re \u03c3e Rmax vmax circ (JAM) RHI vcirc(H i) \u03b3 (arcsec) (km s\u22121) (arcsec) (km s\u22121) (arcsec) (km s\u22121) (1) (2) (3) (4) (5) (6) (7) (8) NGC 2685 22.1 104 4.0 163 320 144 \u00b1 10 2.06 \u00b1 0.04 NGC 2824 8.0 127 1.9 277 40 162 \u00b1 10 2.36 \u00b1 0.05 NGC 2859 27.6 163 6.6 305 115 215 \u00b1 41 2.25 \u00b1 0.14 NGC 2974 27.6 226 7.9 369 130 310 \u00b1 10 2.12 \u00b1 0.04 NGC 3522 14.0 98 2.5 187 85 121 \u00b1 8 2.25 \u00b1 0.05 NGC 3626 24.6 131 3.3 248 120 169 \u00b1 8 2.21 \u00b1 0.04 NGC 3838 9.4 133 3.5 231 150 159 \u00b1 14 2.20 \u00b1 0.05 NGC 3941 24.9 121 4.5 210 195 148 \u00b1 8 2.18 \u00b1 0.04 NGC 3945 29.7 177 9.1 342 130 237 \u00b1 13 2.28 \u00b1 0.06 NGC 3998 24.0 224 7.2 435 195 246 \u00b1 20 2.35 \u00b1 0.06 NGC 4203 38.5 129 6.2 222 195 197 \u00b1 35 2.07 \u00b1 0.11 NGC 4262 11.6 161 3.8 366 120 198 \u00b1 10 2.36 \u00b1 0.04 NGC 4278 33.4 213 11.4 364 150 256 \u00b1 26 2.27 \u00b1 0.09 NGC 5582 28.9 148 5.0 262 210 258 \u00b1 10 2.01 \u00b1 0.03 NGC 6798 12.4 130 5.0 223 150 190 \u00b1 8 2.10 \u00b1 0.04 UGC 06176 9.7 96 0.9 209 60 144 \u00b1 14 2.18 \u00b1 0.05 Column 1: galaxy name; Column 2: circularised projected half-light radius from C13; Column 3: stellar velocity dispersion measured from integral-\ufb01eld spectroscopy within the half-light ellipse (uncertainty \u223c5 percent; C13); Column 4: radius of the peak circular velocity of the JAM models (C13); Column 5: peak circular velocity of the JAM models (uncertainty \u223c5 percent; C13); Column 6: radius where dH15 measure the H i circular velocity; Column 7: H i circular velocity (dH15); Column 8: average logarithmic slope \u03b3 of the density pro\ufb01le \u03c1 \u221dr\u2212\u03b3 calculated using Eq. 4. their \ufb02at part, and baryons constitute most of the mass (van Albada et al. 1985; Kent 1987; Sackett 1997; Palunas & Williams 2000; Cappellari et al. 2006, 2013a, hereafter C13; Noordermeer et al. 2007). This situation is re\ufb02ected in the observed correlation be- tween galaxies\u2019 circular velocity vcirc measured at the largest possible radius and the stellar velocity dispersion \u03c3 mea- sured in the central regions of the stellar body (Whitmore et al. 1979; Gerhard et al. 2001; Ferrarese 2002; Baes et al. 2003; Pizzella et al. 2005, hereafter P05; Courteau et al. 2007, hereafter C07; Ho 2007; C13). In particular, the slope of this correlation depends on galaxy surface brightness in a way that, to \ufb01rst order, can be linked to the shape of the rotation curve (C07; Kormendy & Bender 2011). In simple terms, \u03c3 traces the inner gravitational potential and can be related to the circular velocity measured well within the stellar body. If the rotation curve has already reached its \ufb02at part in the regions where \u03c3 is measured (as in high- surface-brightness disc galaxies) then vcirc \u223c1.4 \u03c3, close to the theoretical expectation for an isothermal density pro- \ufb01le. However, if the rotation curve is still rising (as in low- surface-brightness galaxies) \u03c3 is lower and the vcirc-\u03c3 rela- tion is steeper, while if the rotation curve declines at large radius (as in early-type spirals) the relation should be shal- lower. Rotation curves and the correlation between vcirc and \u03c3 are powerful tools to investigate the relative distribution of baryons and dark matter in galaxies of di\ufb00erent type, pro- vided that vcirc is measured all the way to the dark-matter dominated outer regions. This is relatively straightforward for late-type galaxies, where the abundant and dynamically- cold H i traces the potential well outside the stellar body. In- deed, for such objects, resolved H i observations have been used in this \ufb01eld for decades (e.g., Bosma 1978; Begeman et al. 1991; Verheijen 2001; Martinsson et al. 2016). In contrast, in early-type galaxies (ellipticals and lentic- ulars; hereafter ETGs) H i is detected less frequently and usually other methods must be used to measure vcirc. Com- plex modelling of the stellar kinematics is generally required but this is typically limited to relatively small radius, com- parable to the half-light radius Re (Kronawitter et al. 2000; Gerhard et al. 2001; Wegner et al. 2012; C13). The resulting rotation curves and vcirc-\u03c3 relations apply therefore only to the baryon-dominated regions of these galaxies and do not cover the transition to the dark-matter dominated outskirts. As such, they provide limited information about the relation between baryons and dark matter in ETGs. Apart for a few individual objects (e.g. Napolitano et al. 2009, 2014; Wei- jmans et al. 2009; Murphy et al. 2011), the only notable exception is the study of C15, whose dynamical models of 14 ETGs reach a median radius of 4 Re. Among the above studies, only Ho (2007) provides mea- surements of vcirc for a large number of ETGs based on H i data, potentially probing the dark-matter dominated regime. However, these values are derived from unresolved H i spectra obtained with single dish telescopes, and the uncertainty on the dynamical state and geometry of the detected gas results in no signi\ufb01cant correlation between vcirc(H i) and \u03c3. More reliable, resolved vcirc(H i) measure- ments at large radius are available for a handful of ETGs included in the samples of P05 and C07. However, both sam- ples are dominated by galaxies whose vcirc is estimated from stellar kinematics and dynamical modelling at small radius. Neither P05 nor C07 derive a vcirc-\u03c3 relation for ETGs based on resolved H i data alone. We discuss these studies in more detail in Sec. 3. Here we take a step forward by using new, interfero- metric vcirc(H i) estimates obtained at a median radius of 6 Re by den Heijer et al. (2015, hereafter dH15) for a sam- ple of 16 ETGs. Thanks to the size of this sample we are MNRAS 000, 1\u20138 (2015) vcirc(H i)-\u03c3e relation and density pro\ufb01les in ETGs 3 able to establish a tight linear vcirc-\u03c3 relation for ETGs us- ing solely vcirc values derived within the dark-matter domi- nated regime from resolved H i data. We further combine our vcirc(H i) estimates with models by C13 to study the typical shape of the rotation curve in these objects, and measure the average slope of their density pro\ufb01les out to large radius."
                },
                {
                    "url": "http://arxiv.org/abs/1501.03906v1",
                    "title": "SoFiA: a flexible source finder for 3D spectral line data",
                    "abstract": "We introduce SoFiA, a flexible software application for the detection and\nparameterization of sources in 3D spectral-line datasets. SoFiA combines for\nthe first time in a single piece of software a set of new source-finding and\nparameterization algorithms developed on the way to future HI surveys with\nASKAP (WALLABY, DINGO) and APERTIF. It is designed to enable the general use of\nthese new algorithms by the community on a broad range of datasets. The key\nadvantages of SoFiA are the ability to: search for line emission on multiple\nscales to detect 3D sources in a complete and reliable way, taking into account\nnoise level variations and the presence of artefacts in a data cube; estimate\nthe reliability of individual detections; look for signal in arbitrarily large\ndata cubes using a catalogue of 3D coordinates as a prior; provide a wide range\nof source parameters and output products which facilitate further analysis by\nthe user. We highlight the modularity of SoFiA, which makes it a flexible\npackage allowing users to select and apply only the algorithms useful for their\ndata and science questions. This modularity makes it also possible to easily\nexpand SoFiA in order to include additional methods as they become available.\nThe full SoFiA distribution, including a dedicated graphical user interface, is\npublicly available for download.",
                    "authors": "Paolo Serra, Tobias Westmeier, Nadine Giese, Russell Jurek, Lars Fl\u00f6er, Attila Popping, Benjamin Winkel, Thijs van der Hulst, Martin Meyer, B\u00e4rbel S. Koribalski, Lister Staveley-Smith, H\u00e9l\u00e8ne Courtois",
                    "published": "2015-01-16",
                    "updated": "2015-01-16",
                    "primary_cat": "astro-ph.IM",
                    "cats": [
                        "astro-ph.IM",
                        "astro-ph.CO",
                        "astro-ph.GA"
                    ],
                    "main_content": "SoFiA is a modular application whose aim is to detect and parameterize sources in a data cube. The flowchart in Fig. 2 shows the various modules that users can choose to use (or not to use), in the order in which they are executed by SoFiA. Once an input data Input data cube Select sub-cube Flag bad voxels Apply weights Input weights cube 2D-1D Convolution Noise normalisation FILTERS S+C finder Threshold finder CNHI finder SOURCE FINDERS Merge detected voxels Input mask cube Reject false detections Optimize mask Parameterize Filter output Output mask cube Source catalogue Moment maps Singlesource products Figure 2. SoFiA flowchart. We highlight the \u201cFilter output\u201d module with a dashed box as this will become available in future releases of SoFiA. cube (or a sub-cube selected by the user) is loaded, these modules allow users to: \u2022 modify the input cube by applying flags, weights, or a set of filters; \u2022 detect the spectral line signal; c \u20dd2013 RAS, MNRAS 000, 1\u20139 SoFiA 3D source \ufb01nder 3 Figure 3. Screenshot of the SoFiA GUI. The GUI adopts automatically the native style of the window manager used on the system where SoFiA is installed. In this \ufb01gure we show the GUI as it appears on a Kubuntu Linux system. The GUI also offers the option of displaying the source catalogue generated by SoFiA and includes a help browser that explains the available parameter settings. \u2022 identify sources by merging detected voxels together; \u2022 reject false detections; \u2022 optimize the mask of individual sources; \u2022 measure source parameters; \u2022 \ufb01lter the output by selecting a region of interest in source parameter space; \u2022 and produce output catalogues as well as cubes, moment maps, position-velocity diagrams and integrated spectra. Individual modules are described in more detail in the rest of this Section. They are written in either Python or C++ and rely on a range of external libraries, including NumPy and SciPy (Jones et al. 2001; Walt, Colbert & Varoquaux 2011), Cython (Behnel et al. 2011), Astropy (Astropy Collaboration et al. 2013), the GNU Scienti\ufb01c Library1 and, optionally, matplotlib (Hunter 2007). Provided that these libraries are available, SoFiA can run on all machines with a Unix or Linux operating system (including, e.g., Mac OS X and Ubuntu). We refer to the SoFiA webpage for up-to-date details. SoFiA can be executed from the command line or using a dedicated graphical user interface (GUI) based on the Qt library (see Fig. 3). Both methods allow users to select which combination of the above modules and which source \ufb01nding and parameterization algorithms to use. This selection is done using either the GUI or a plain text parameter \ufb01le (if running SoFiA from the command line), allowing the source-\ufb01nding strategy and its complexity to be optimized for the type of data and sources of interest. For example, SoFiA could be asked the simple question of creating a moment-0 image of all voxels above a given threshold in a data cube \u2013 in which case most of SoFiA\u2019s functionalities would be 1 http://www.gnu.org/software/gsl/ switched off. Alternatively, it could be given a number of relatively more complex tasks such as, for example, applying a wavelet \ufb01ltering algorithm, rejecting false detections or \ufb01tting models to the spectrum of the detected sources. While SoFiA will continue to be improved, this basic principle of modularity will not change. Therefore, although this paper describes the software as it is at the time of writing and new algorithms may be introduced in the future, the main workings of SoFiA will remain as illustrated here. 2.1 Data cube, weights cube, mask cubes and \ufb01lters Four different types of input and/or output cubes are relevant at different stages of SoFiA. \u2022 Data cube, which includes signal from astronomical sources superimposed on instrumental noise (and errors). \u2022 Weights cube, which allows users to weight voxel values to take into account, e.g., noise level variations across the cube or the presence of imaging artefacts in certain regions of the data cube. \u2022 Binary mask, where detected and non-detected voxels have values of 1 and 0, respectively. \u2022 Object mask, where non-detected voxels have a value of 0 and detected voxels have an integer value corresponding to the ID of the object they belong to. All source-\ufb01nding algorithms implemented in SoFiA and described in Sec. 2.2 below assume that the noise level is uniform across the data cube. Therefore, noise variations caused by, e.g., mosaicking or frequency-dependent \ufb02agging need to be removed \ufb01rst. This can be done within SoFiA by means of a weights cube inversely proportional to the noise level. SoFiA removes noise variations by multiplying the data cube by the weights cube. Once source detection is completed, SoFiA will undo this operation before measuring source parameters. The weights cube could also be useful to down-weight regions of a data cube affected by imaging artefacts (e.g., cleaning or continuum-subtraction residuals). The weights cube can be provided by the user. Alternatively, users can provide an analytic description of the weights variation across the cube. Finally, a weights cube inversely proportional to the local noise level can be derived by SoFiA and applied to the data cube. The evaluation of the local noise level is carried out independently along any or all of the three axes of the data cube. For example, a user may wish to remove noise variations along the frequency axis alone, under the assumption that the noise does not vary within each frequency plane. We note that SoFiA measures the noise within a data cube at various other stages of the processing. Different methods of noise measurement are implemented and users can decide which one is more appropriate for their purpose. Possible choices are: i) standard deviation; ii) median absolute deviation; and iii) standard deviation of a zero-centred Gaussian \ufb01t to the negative side of the \ufb02ux histogram. The calculation and application of the inverse-noise weights cube described above is part of a more general SoFiA module which allows users to apply a \ufb01lter to the data cube before running the selected source-\ufb01nding and parameterization algorithms. As indicated in Fig. 2, this module includes two additional \ufb01ltering methods: \ufb01rstly, the convolution with a 3D kernel whose shape can be chosen among a few options and whose size can be speci\ufb01ed by the user; and secondly, the 2D-1D wavelet de-noising algorithm developed by Fl\u00a8 oer & Winkel (2012). This algorithm processes the two spatial dimensions and the spectral dimension of the data cube c \u20dd2013 RAS, MNRAS 000, 1\u20139 4 Paolo Serra et al. separately, and returns a noise-free data cube reconstructed using only wavelet coef\ufb01cients above a speci\ufb01ed threshold. Additional \ufb01ltering options may be provided in future releases. As indicated by the \ufb02owchart in Fig. 2, portions of the cube can be blanked out (\ufb02agged) prior to source \ufb01nding. This may be necessary at the location of very bright continuum sources whose spectrum was not subtracted properly from the data, or at channels dominated by line emission from the Galaxy or affected by strong radio frequency interference. Finally, mask cubes are generally calculated within SoFiA (see below) but can also be provided by the user. The latter could be desirable if a user, following an initial source-\ufb01nding run, wishes to look for additional sources with a different search algorithm or parameters. In this case the new sources are added to the initial, input mask. Alternatively, an input mask could be used if sources have already been identi\ufb01ed and only subsequent parameterization steps are required. 2.2 Detection of spectral line signal SoFiA is meant to offer a number of detection algorithms that users can choose from. A common advantage of these algorithms is the ability to look for emission on multiple scales, which is essential to detect sources in 3D (see Fig 1). An exception is the simple threshold method (see below), unless used in combination with some of the \ufb01ltering methods described above (e.g., 2D-1D wavelet denoising). The following algorithms are implemented in SoFiA. \u2022 Simple threshold. This is the simplest possible algorithm (and the only one not operating on multiple scales): only voxels whose absolute value is above a speci\ufb01ed threshold are detected. Users can specify the threshold in \ufb02ux units or relative to the noise level. \u2022 S+C. This is the smooth + clip algorithm developed by Serra et al. (2012) on the basis of techniques traditionally used within the H I community. It consists of searching for emission at multiple angular and velocity resolutions by smoothing the data cube with 3D kernels speci\ufb01ed by the user. At each resolution, voxels are detected if their absolute value is above a threshold given by the user (in noise units). The \ufb01nal mask is the union of the masks constructed at the various resolutions. \u2022 CNHI. This algorithm was developed by Jurek (2012). Individual 1D spectra (or bundles of adjacent spectra) are extracted from the data cube. For each of them, the Kuiper test is used to identify regions of the spectrum which are not consistent with containing only noise. In practice, users need to provide a probability threshold above which a spectral region is considered detected and is added to the \ufb01nal binary mask. The numerous possible combinations of these source-\ufb01nding methods together with the \ufb01ltering algorithms described in Sec. 2.1 allow users to design a number of different strategies to detect signal in their data cube. For example, the CNHI \ufb01nder could be run following convolution with a 3D kernel appropriate for the type of sources being searched. Alternatively, a simple threshold method could be used after the noise has been removed from the cube by the 2D-1D wavelet \ufb01lter. Popping et al. (2012) discuss strengths and weaknesses of these algorithms and compare their performance. An important recommendation of that work is that all source \ufb01nders should incorporate some form of 3D smoothing in order to increase completeness. In this respect, the simple threshold algorithm is of limited use unless coupled with a \ufb01ltering methods such as the 2D-1D wavelet de-noising. Popping et al. (2012) \ufb01nd this particular combination to deliver higher completeness and reliability than S+C and CNHI for sources unresolved on the sky, especially at narrow line widths. In contrast, the S+C method is by construction well suited to \ufb01nding sources on a variety of scales and Popping et al. (2012) deem it the best choice for extended objects. We note that many of the algorithms have been improved since the comparative study of Popping et al. (2012). Additional testing can now be carried out within SoFiA and will be used to investigate how to further improve their performance. Until then, we refer to the aforementioned papers for a complete discussion of these methods. All the above algorithms return a binary mask of detected voxels (and any additional source-\ufb01nding algorithm could be added to SoFiA as long as they satisfy this condition). As an example, the top panels of Fig. 4 show \ufb01ve channels extracted from the data cube in Fig. 1 and, with black contours, the regions included in the binary mask. In this case the S+C \ufb01nder was employed using 12 different smoothing kernels. The relatively low adopted threshold (3.5\u03c3) results in a number of noise peaks being included in the mask. We come back to this point in Sec. 2.4. 2.3 Merging detected voxels into sources The aforementioned binary mask is the basis for identifying individual sources or objects. In SoFiA, this computationally expensive operation is performed using the C++ implementation of the Lutz (1980) one-pass algorithm by Jurek (2012), combined with a sparse representation of 3D objects. We refer to Jurek (2012) for details on this implementation. Here it is suf\ufb01cient to say that this algorithm produces the same result as a friends-of-friends method with linking element equal to an elliptic cylinder. Users can specify the cylinder size. This step of SoFiA also returns basic source parameters such as total \ufb02ux, peak \ufb02ux (both normalised by the noise level) and size. The bottom panels of Fig. 4 show the objects created from the binary mask using a merging cylinder with a radius of 3 pixels and a height of 7 channels (we show only objects with positive total \ufb02ux). These panels show four real detections as well as a number of positive noise-peak objects. It is worth highlighting the successful detection of a faint, extended H I tail east of the brightest galaxy (second panel from the left). This detection is made possible by the fact that SoFiA looks for emission on multiple scales. Furthermore, SoFiA correctly identi\ufb01es as a single source the resolved, edge-on galaxy located in the southern part of the cube (visible in all panels but the \ufb01rst) despite the low level emission at channels close to the systemic velocity. 2.4 Reliability and rejection of false detections All detection algorithms listed above require users to specify a detection threshold. The closer this threshold is to the noise, the more noise peaks will be included in the resulting binary mask. Some of these noise peaks may be identi\ufb01ed as separate objects if they are suf\ufb01ciently far from a real object (see bottom panels of Fig. 4). SoFiA offers two ways of removing these false detections from the \ufb01nal output. The \ufb01rst method is a simple size \ufb01lter and is based on the fact that all real detections are at least as large as the data cube\u2019s resolution. In practice, users can specify the minimum acceptable source size along each axis of the cube independently. The downside of this method is that it may potentially remove relatively bright but unresolved sources from the \ufb01nal object mask. c \u20dd2013 RAS, MNRAS 000, 1\u20139 SoFiA 3D source \ufb01nder 5 +61.9\u00b0 +62.0\u00b0 +62.1\u00b0 +62.2\u00b0 +62.3\u00b0 Dec (J2000) 1110.3 km/s 1234.0 km/s 1357.7 km/s 1481.3 km/s 1605.0 km/s 180.2\u00b0 180.4\u00b0 180.6\u00b0 180.8\u00b0 RA (J2000) +61.9\u00b0 +62.0\u00b0 +62.1\u00b0 +62.2\u00b0 +62.3\u00b0 Dec (J2000) 1110.3 km/s 180.2\u00b0 180.4\u00b0 180.6\u00b0 180.8\u00b0 RA (J2000) 1234.0 km/s 180.2\u00b0 180.4\u00b0 180.6\u00b0 180.8\u00b0 RA (J2000) 1357.7 km/s 180.2\u00b0 180.4\u00b0 180.6\u00b0 180.8\u00b0 RA (J2000) 1481.3 km/s 180.2\u00b0 180.4\u00b0 180.6\u00b0 180.8\u00b0 RA (J2000) 1605.0 km/s Figure 4. Illustration of the detection of signal and identi\ufb01cation of individual sources in SoFiA. Top panels. Channel maps extracted from the data cube shown in Fig. 1. The line-of-sight velocity of each channel is indicated in the top-left corner (note that these are not adjacent channels in the original cube). The beam is shown in the bottom-left corner. Black contours show regions included in the binary mask (Sec. 2.2). Bottom panels. Same channel maps as in the top panels but now showing the individual objects formed on the basis of the binary mask (Sec. 2.3). We show only objects with positive total \ufb02ux. Each object is indicated with a different random colour. Black contours indicate the four objects whose reliability is higher than 99 per cent (Sec. 2.4). The second method is illustrated by Serra, Jurek & Fl\u00a8 oer (2012) and estimates the reliability of individual objects by comparing the distribution of positive and negative sources (i.e., sources with positive and negative total \ufb02ux, respectively) in parameter space. The simple idea is that the distribution of positive and negative noise peaks should be identical while positive, real detections should not have a negative counterpart in parameter space. It is based on the assumptions that the noise is symmetric and that real sources have positive total \ufb02ux (i.e., absorption line sources have been masked). Within SoFiA, the reliability can be calculated following the run of any source-\ufb01nding algorithm chosen by the user as long as both positive and negative noise peaks are included in the binary mask, and after the detected voxels are merged into sources (Sec. 2.3). The reliability calculation also requires that a suf\ufb01cient number of negative noise peaks is included in the mask such that their distribution in parameter space can be studied meaningfully. Users can select to produce diagnostic plots on the reliability calculation similar to those shown in Serra, Jurek & Fl\u00a8 oer (2012). The black contours in the bottom panels of Fig. 4 highlight objects whose reliability is higher than 99 per cent. In summary, users can decide to run SoFiA with a high detection threshold, resulting in a reliable but possibly incomplete catalogue of detections; but they can also decide to dig deeper into the noise using a lower threshold, and successively remove false detections. In the latter case, a reliability value can be returned for all positive detections. 2.5 Mask optimization SoFiA measures the parameters of all sources (e.g., total \ufb02ux, size, line width) considering only voxels included in the mask cube. However, experience shows that masks can miss the faint, outer edge of objects, in particular if obtained with a high detection threshold. This would introduce systematic effects in the measured parameters (e.g., the total \ufb02ux would be underestimated; see Westmeier, Popping & Serra 2012). To prevent this, SoFiA offers two mask optimization methods which modify the object mask cube by growing the masks which de\ufb01ne individual objects. In both methods, the mask is grown independently for each object. The \ufb01rst method is mostly appropriate for sources that are unresolved on the sky or, if resolved, face-on and symmetric. It starts by \ufb01tting an ellipse to the moment-0 image of the object. The ellipse is then used as a mask for all velocity channels occupied by the object \u2013 i.e., the initial mask, which generally has an arbitrary 3D shape, is converted into an elliptic cylinder. Finally, the size of the ellipse is increased until a maximum in total \ufb02ux is reached (a similar method is described by Barden et al. 2012 in the context of 2D imaging). The above method should in principle be applied only to sources which \ufb01ll most of the cylindrical mask in all channels (see above), while for objects with a more complex 3D structure it can result in a decrease of the integrated signal-to-noise ratio. For this reason we provide a second mask growth method. This consists in performing a binary dilation of the initial mask along the two spatial axes of the data cube using a 2D dilation structuring element whose shape approximates a circle. The size of the structuring element is increased iteratively until the total \ufb02ux converges (i.e., until the relative \ufb02ux growth between successive iterations is lower than a threshold speci\ufb01ed by the user). This method preserves the 3D shape of the initial mask. In addition to growth along the two spatial axes, this algorithm can also grow all masks by a \ufb01xed number of channels (selected by the user) along the frequency axis. c \u20dd2013 RAS, MNRAS 000, 1\u20139 6 Paolo Serra et al. 180.4\u00b0 180.5\u00b0 180.6\u00b0 180.7\u00b0 RA (J2000) +62.1\u00b0 +62.2\u00b0 Dec (J2000) 180.4\u00b0 180.5\u00b0 180.6\u00b0 180.7\u00b0 RA (J2000) velocity (km/s) offset (deg) \u20130.1       \u20130.05          0          0.05        0.1 1100    1200     1300     1400 1000 1100 1200 1300 1400 velocity (km/s) 0.00 0.05 0.10 0.15 0.20 F (Jy) Figure 5. Data products for the brightest galaxy in the cube shown in Fig. 1. From left to right: moment-0 image; moment-1 velocity \ufb01eld; position-velocity diagram along the morphological major axis (PA = 32\u25e6); and integrated spectrum (\ufb01lled circles) with the best-\ufb01tting busy function overlaid (solid line). In the latter panel the dotted and dashed lines indicate the line widths W50 and W20 estimated at 50 and 20 per cent of the peak \ufb02ux, respectively, on the basis of the busy function \ufb01t. 2.6 Source parameterization As mentioned in Sec. 2.3, basic source parameters are measured when detected voxels are merged into objects. These can be used to estimate the reliability of each source and reject false detections in parameter space. After mask optimization SoFiA re-computes those parameters and measures additional ones. These include: position (both geometric and centre of mass); total \ufb02ux; minimum and maximum voxel value; size and bounding region along each axis; line width measured using different methods (including the one proposed by Courtois et al. 2009); results of an ellipse \ufb01t to the moment-0 image; results of a busy function \ufb01t to the integrated spectrum (for a description of the busy function see Westmeier et al. 2014). These parameters are provided both in a \u201craw\u201d format (i.e., coordinates in pixel units, \ufb02uxes in data units, line-width in channels) as well as converted into more useful units (e.g., WCS coordinates and standard \ufb02ux and velocity units). Some of these parameterization steps are optional and implementation of additional parameters is straightforward within the code. 2.7 Output products Users can decide what output SoFiA should produce. Available output products include: \u2022 Catalog of objects and their parameters, both in ASCII and VO-compliant XML format. \u2022 Final object mask. \u2022 Moment 0 and 1 images of the sky area covered by the full data cube determined from the data within the mask. \u2022 Cut-out data cubes containing individual objects as well as their corresponding mask, moment 0, 1 and 2 images, integrated spectrum and position-velocity diagram along the morphological major axis. An example of these products is shown in Fig. 5. In future releases it will be possible to produce these products for just a subset of the detections by selecting a region of interest in source parameter space. This output is designed to not only give useful information about the detected sources but also to enable further, higher-level analysis by the user. For example, the cut-out cubes of individual objects and the corresponding masks could be used to measure additional source parameters not included in SoFiA or to produce Gauss-Hermite velocity \ufb01elds to enable kinematical studies. 2.8 Performance of SoFiA In the current implementation of SoFiA the entire input data cube (or the selected sub-cube; see Fig. 2) is loaded into memory and processed on a single core. Additional cubes will also need to be stored in memory at various stages of processing, such as the weights cube, the binary or object mask cube, and a smoothed version of the data cube if required by the source-\ufb01nding algorithm being used (e.g., S+C), plus a potentially large array of source parameters. It is therefore interesting to discuss how the memory requirement and execution time of SoFiA vary with cube size. For this purpose we make use of two cubes. The smaller cube is the one used for illustration purpose in this paper (Figs. 1 and 4). It has 360 pixels along both spatial axes and 150 channels along the frequency axis, resulting in a \ufb01le size of 78 MB. The second cube is the one used for the source-\ufb01nding tests of Serra, Jurek & Fl\u00a8 oer (2012) and Westmeier, Popping & Serra (2012). It too has 360 pixels along both spatial axes but consists of 1464 channels along the frequency axis. Therefore, its size is \u223c10 times that of the \ufb01rst cube. We process the two cubes with identical settings employing a representative combination of the algorithms described in this paper: noise normalisation along the frequency axis; S+C source \ufb01nding with 12 smoothing kernels; merging of detected voxels into sources; calculation of reliability and removal of unreliable sources; optimization of the mask of individual objects using the dilation method; source parameterization including busy function \ufb01t; creation of output products for the cubes as a whole and for the individual detections; creation of ASCII and XML catalogues. The two runs are carried out on a machine running Linux Mint 17 with a memory of 16 GB and a 2.9 GHz Intel Core processor. Figure 6 shows the memory usage of SoFiA as a function of time for the two cubes. Both axes of the plot are normalised by the cube size. The time behaviour of the two curves appears very similar, indicating that the execution time scales approximately linearly with cube size within the range explored here. The memory offset between the two curves is due to the loading into memory of a number of libraries used by SoFiA. These come with a memory overhead of the order of a few tens of megabytes, which is more noticeable in the case of a smaller data cube. For data cubes much larger than this overhead the memory usage is between 2 and 3 times the size of the cube, with occasional peaks between 3 and 4 times the cube size. Figure 6 allows us to investigate the memory and processing time taken by the various algorithms. In this case, most of the time is taken by the S+C \ufb01nder. The beginning and end of its execution are marked by open and \ufb01lled black circles for the small and large c \u20dd2013 RAS, MNRAS 000, 1\u20139 SoFiA 3D source \ufb01nder 7 0.0 0.1 0.2 0.3 0.4 0.5 0.6 time / sizecube (s/MB) 0 1 2 3 4 5 memory / sizecube sizecube = 79 MB sizecube = 759 MB Figure 6. Memory usage as a function of time for two runs of SoFiA on two cubes whose sizes differ by a factor \u223c10 (see legend). As explained in the text, both runs include the use of the S+C source \ufb01nder, and open and \ufb01lled black circles indicate the beginning and the end of the S+C execution for the two cubes, respectively. See Sec. 2.8 for a more detailed discussion of the time taken by other algorithms during the two SoFiA runs. data cube, respectively. The peaks in memory usage of S+C correspond to the smoothing operations, while the plateaus in between peaks correspond to the noise level calculation. Each additional \ufb01lter would contribute another \u223c0.05 s/MB to the execution time in this case. The noise calculation appears to be particularly time consuming. In this case, it is carried out using the aforementioned Gaussian \ufb01t to the negative side of \ufb02ux histogram (Sec. 2.1). This calculation uses the full cube, and an obvious way to increase its speed would be to calculate the noise level on a sub-cube. This option may become available in the future. The time before the beginning of the S+C \ufb01nder in Fig. 6 is taken by the noise normalisation along the frequency axis and by an initial measurement of the noise level in the normalised cube. The time after S+C is taken by all other algorithms listed above, and these are typically much faster. The memory peak right at the end of S+C corresponds to the merging of voxels into sources. The height of this peak depends on the number of sources detected. This is followed by the calculation of the reliability and the rejection of unreliable sources, which are both relatively inexpensive in terms of memory but can be time consuming. The \ufb01nal memory peaks correspond to the creation of moment images. 2.9 Source-\ufb01nding based on a catalogue of 3D coordinates The above discussion makes it clear that SoFiA is currently not able to process arbitrarily large data cubes but is limited by the memory of the system on which it is run. This problem is partially alleviated by the fact that SoFiA is able to limit the processing to a sub-cube whose boundaries are speci\ufb01ed by the user. Therefore, users could choose to run SoFiA multiple times on suf\ufb01ciently small portions of a large input cube, obtaining individual output products for each of them. They could then combine these products, creating for example a single mask or catalogue. In the future we may be able to offer such breaking up of a large input cube into sub-cubes \u2013 and the creation of \ufb01nal data products for the full cube \u2013 as a processing mode fully integrated with the other modules of SoFiA. In this context, a useful feature already available in SoFiA is that it allows users to search for emission in any number of small sub-cubes centred at a set of 3D coordinates within an arbitrarily large data cube. For example, in an era of large H I and optical redshift surveys, this mode could be used to look for emission in a large H I cube at the location of galaxies included in an optical spectroscopic catalogue. This mode is fully integrated in SoFiA and interested users need to simply provide the input data cube and a catalogue of 3D coordinates. SoFiA will process the various positions sequentially, each time loading into memory only the sub-cube of interest. The 3D size of the sub-cubes can be set by the user and is the same for all positions. Users can also request the creation of a single output catalogue of sources, which is generated by merging the catalogues obtained at each position. 2.10 Comparison to other source \ufb01nders A number of established software packages for the reduction and analysis of interferometric data allow some source \ufb01nding to be carried out on data cubes (e.g., GIPSY, Miriad). However, this approach requires users to develop custom codes which make use of (and are limited by) the tasks available within those generalpurpose packages. In contrast, the more specialised SoFiA offers a wide range of ready-to-use source-\ufb01nding algorithms, which are already integrated with one another and can be combined in a \ufb02exible way to produce a variety of output products. The other 3D application for spectral line data which shares some of these characteristics is Duchamp (Whiting 2012). This application detects sources using a simple threshold method (similar to the one described in Sec. 2.2) and then grows them using a secondary threshold. This algorithm differs from those available in SoFiA and, in this respect, the two packages could be seen as complementary (Popping et al. 2012 shows that Duchamp has the best performance for unresolved sources but does not reach the completeness of S+C for resolved sources). With respect to memory requirements, Duchamp is similar to SoFiA in that it loads and processes in one core the full input data cube. Therefore, it too is limited by the memory of the system on which it is run. c \u20dd2013 RAS, MNRAS 000, 1\u20139 8 Paolo Serra et al. A signi\ufb01cant advantage of SoFiA compared to Duchamp is that it offers a larger number of algorithms for both source \ufb01nding and parameterization. This includes the S+C and CNHI \ufb01nders, the 2D-1D wavelet de-noising (denoising is available in Duchamp but it uses isotropic wavelets, which are not ideal for spectral line sources whose size along the spectral axis is decoupled from the size along the two spatial axes), the calculation of the reliability of individual detections, the mask optimization by binary dilation, the possibility of searching for signal on the basis of an input catalogue of 3D coordinates and the busy function \ufb01t. The creation of cubelets and PV diagrams for individual detections is also not included in Duchamp but is available in Selavy, a source \ufb01nder built upon Duchamp for distributed processing of large cubes (Whiting & Humphreys 2012). While future development may reduce the difference between Duchamp/Selavy and our package, all above methods are at the moment unique to SoFiA. Finally, it is worth mentioning that SoFiA does not offer at the moment a full analysis of the sources\u2019 morphology. For example, a group of nearby detected voxels is merged into a single source regardless of the size of the source and only based on the merging element chosen by the user (Sec. 2.3). This means that no information is given about whether the source, which could be very large, is composed of distinct and easily recognisable components. Different and more specialised source \ufb01nders are able to provide such characterisation (e.g., Clumpfind by Williams, de Geus & Blitz 1994; BLOBCAT by Hales et al. 2012). We note however that the object mask cube returned by SoFiA could be used as a starting point for further morphological analysis of the detections. 3 SUMMARY We provide a high-level description of SoFiA, a \ufb02exible source \ufb01nder for 3D spectral line data. SoFiA puts together for the \ufb01rst time in a single package a number of new source-\ufb01nding and parameterization algorithms developed in preparation of upcoming H I surveys with ASKAP (WALLABY, DINGO) and APERTIF. It is, however, designed to enable the use of these new algorithms on any data cube independent of emission line or telescope used. We describe the various methods and algorithms available in SoFiA as well as planned developments. One key advantage of SoFiA is that it allows users to search for spectral line signal on multiple scales on the sky and in frequency (using. e.g., the S+C \ufb01nder or the 2D-1D wavelet \ufb01lter), which is crucial to detect and parameterize 3D sources in a complete and reliable way. Furthermore, within SoFiA it is possible to take into account noise level variations across the cube and the presence of errors and artefacts. Moreover, SoFiA is able to estimate the reliability of individual detections, which should be particularly useful for surveys expected to detect a large number of sources. It can also produce a variety of output products, including moment images, cut-out cubes and images, integrated spectra and catalogues of source parameters. Finally, SoFiA is able to search for line emission in arbitrarily large data cubes on the basis of a catalogue of 3D coordinates. Most of these methods are not available in other source \ufb01nders and are currently unique to SoFiA. We provide a few visual examples of how SoFiA works including a view of the dedicated graphical user interface. We describe the available parameterization and the wide range of output products, which include mask cubes, moment images, positionvelocity diagrams and busy function spectral \ufb01ts of individual sources. This output is designed to both provide a useful description of the sources as well as facilitate subsequent analysis. We highlight the modularity of SoFiA, which allows users to optimize the source-\ufb01nding and parameterization strategy for the data and sources of interest. This modularity also enables future expansions of SoFiA to include new source-\ufb01nding and parameterisation algorithms. SoFiA is publicly available at the website indicated in Sec. 1 together with technical information on how to use the software. Software updates, improvements and bug \ufb01xes are posted regularly at this webpage. SoFiA is registered at the Astrophysics Source Code Library with ID ascl:1412.001. ACKNOWLEDGMENTS The authors acknowledge \ufb01nancial support from a Research Collaboration Award of the University of Western Australia. TvdH and NG were supported by the European Research Council under under the European Union\u2019s Seventh Framework Programme (FP/20072013) / ERC Grant Agreement nr. 291531. LF acknowledges support by the Deutsche Forschungsgemeinschaft (DFG) under grant numbers KE757/7-1, KE757/7-2, KE757/7-3 and KE757/9-1. LF is a member of the International Max Planck Research School (IMPRS) for Astronomy and Astrophysics at the Universities of Bonn and Cologne.",
                    "introduction": "The detection of astronomical signal above instrumental noise is a crucial aspect of all astronomy observations. The techniques em- ployed to detect and characterise this signal depend on the type of data being analysed (see Masias et al. 2012 for a review). Standard methods and tools have emerged in \ufb01elds with a large community base such as 2D imaging (e.g., SExtractor; Bertin & Arnouts 1996) and 1D spectroscopy (e.g., GANDALF; Sarzi et al. 2006). In other \ufb01elds with relatively fewer users, detection algorithms vary signi\ufb01cantly between projects. This is the case for studies based on 3D spectral line data (for brevity, data cubes), where the \ufb02ux of a spectral line is mapped as a function of position on the sky and line-of-sight velocity of the emitting matter. The diversity of source \ufb01nding methods for data cubes is at least partly due to the diversity of 3D structure of the sources being \u22c6E-mail: paolo.serra@csiro.au studied. We illustrate this point in Fig. 1, where we show a data cube of the ATLAS3D H I survey (Serra et al. 2012). In this \ufb01gure, the central object is bright (and therefore easy to detect) but has a complex 3D structure, including a low surface brightness exten- sion towards large RA. On the contrary, the top object is bright and relatively simple as emission is con\ufb01ned within a small range of RA and Dec. Finally, the bottom object is the typical case of a re- solved, edge-on galaxy where the two peaks of the double-horn ve- locity pro\ufb01le are clearly visible, and detection of the faint emission between the two peaks is challenging. An ideal 3D source \ufb01nder should be able to detect and parameterize all these different sources in a complete and reliable way. Radio single dishes and interferometers have traditionally been the most common telescopes used to construct data cubes (al- though optical integral-\ufb01eld spectrographs are now also generating large numbers of such cubes \u2013 e.g., Cappellari et al. 2011; Croom et al. 2012; S\u00b4 anchez et al. 2012). The upgrade and continuing oper- ation of existing radio telescopes, as well as the construction of c \u20dd2013 RAS arXiv:1501.03906v1  [astro-ph.IM]  16 Jan 2015 2 Paolo Serra et al. Figure 1. Volume rendering of an H I data cube showing that individual sources have a complex and diverse 3D structure. This makes their detection and accurate parameterization challenging. the Square Kilometre Array and its precursors, are leading to a rapid increase in the number and size of data cubes. Standard and suf\ufb01ciently general source-\ufb01nding tools will be necessary to anal- yse these data, and recent work has started addressing this need (see, e.g., Duchamp by Whiting 2012). In this paper we introduce SoFiA, a new, \ufb02exible Source Finding Application for data cubes which combines detection algorithms and techniques from several source \ufb01nders. SoFiA is designed to work on any data cube independent of telescope or observed spectral line. However, its development is part of preparatory work for a few speci\ufb01c, upcoming H I sur- veys: WALLABY, a blind H I survey of 3/4 of the entire sky out to z \u223c0.25 to be carried out with the Australian Square Kilometre Array Path\ufb01nder (ASKAP; see Koribalski 2012a); DINGO, a deep H I survey out to z \u223c0.4 (also to be carried out with ASKAP; see Meyer 2009); and the H I surveys planned for APERTIF (Verheijen et al. 2008). This preparatory work has resulted in the development of a number of new source-\ufb01nding algorithms, which are described in a series of papers referred to in the next Section (for a summary see Koribalski 2012b). SoFiA puts these different algorithms to- gether for the \ufb01rst time in a coherent, \ufb02exible and publicly available piece of software. SoFiA can be obtained from https://github.com/ SoFiA-Admin/SoFiA . On the same webpage we provide a list of requirements, installation instructions and a user manual. The aim of this paper is to describe how SoFiA operates on data cubes and thereby provide a reference for current and future users."
                },
                {
                    "url": "http://arxiv.org/abs/1404.1933v2",
                    "title": "Cross-correlation of cosmic far-infrared background anisotropies with large scale structures",
                    "abstract": "We measure the cross-power spectra between luminous red galaxies (LRGs) from\nthe Sloan Digital Sky Survey (SDSS)-III Data Release Eight (DR8) and cosmic\ninfrared background (CIB) anisotropies from Planck and data from the Improved\nReprocessing (IRIS) of the Infrared Astronomical Satellite (IRAS) at 353, 545,\n857, and 3000 GHz, corresponding to 850, 550, 350 and 100 micron, respectively,\nin the multipole range 100<l<1000. Using approximately 6.5 10^5 photometrically\ndetermined LRGs in 7760 deg^2 of the northern hemisphere in the redshift range\n0.45 < z < 0.65, we model the far-infrared background (FIRB) anisotropies with\nan extended version of the halo model. With these methods, we confirm the basic\npicture obtained from recent analyses of FIRB anisotropies with Herschel and\nPlanck, that the most efficient halo mass at hosting star forming galaxies is\nlog(M_ eff/M_\\odot)=12.84+/-0.15. We estimate the percentage of FIRB\nanisotropies correlated with LRGs as approximately 11.8 %, 3.9 %, 1.8 %, and\n1.0 % of the total at 3000, 857, 545, and 353 GHz, respectively. At redshift\nz~0.55, the bias of FIRB galaxies with respect to the dark matter density field\nhas the value b_{FIRB}~1.45, and the mean dust temperature of FIRB galaxies is\nT_d=26 K. Finally, we discuss the impact of present and upcoming\ncross-correlations with far-infrared background anisotropies on the\ndetermination of the global star formation history and the link between\ngalaxies and dark matter.",
                    "authors": "Paolo Serra, Guilaine Lagache, Olivier Dor\u00e9, Anthony Pullen, Martin White",
                    "published": "2014-04-07",
                    "updated": "2014-09-24",
                    "primary_cat": "astro-ph.CO",
                    "cats": [
                        "astro-ph.CO"
                    ],
                    "main_content": "2.1. CMASS catalog The galaxy sample used in the cross-correlation analysis consists of LRGs selected from the publicly available SDSS-III DR8 catalog 1 (Eisenstein et al. 2011; Ross et al. 2011; Ho et al. 2012; de Putter et al. 2012), with photometric redshift in the range 0.45 < zphot < 0.65, and centered around \u00af z = 0.55 (see Fig 1). We considered the same color and magnitude cuts as the SDSSIII \u201cCMASS\u201d (constant mass) sample from BOSS (White et al. 2011; Ho et al. 2012) and, to create a galaxy map from the catalog, we used the HEALPix2 pixelization scheme of the sphere (G\u00b4 orski et al. 2005) at resolution Nside = 1024; objects are weighted with their probability of being a galaxy and pixelized as number overdensities \u03b4i with respect to the mean number of galaxies \u00af n in each pixel, as: \u03b4i \u2261(ni \u2212\u00af n)/\u00af n. (1) Complex survey geometries due to partial sky coverage and masked regions can cause numerical issues and power leakage from large to small scales when performing power spectra computations, especially when using estimators in harmonic space. Because the southern hemisphere footprint has a complicated geometry and it contributes few additional galaxies, to be as conservative as possible, we discard it and only use data in the northern hemisphere. This choice reduces the total area available of approximately 1300 deg2, leaving 7760 deg2 with approximately 650,000 galaxies, but ensures stability of results, as we will show below, where we confront error bars computed analytically with those estimated from Monte Carlo simulations. An accurate analysis of potential systematics affecting our dataset, stressing the contribution of seeing effects, sky brightness, and stellar contamination, has been performed in Ross et al. (2011) and Ho et al. (2012), and we will shape our galaxy mask according to their prescriptions to reduce these effects. As shown in Fig. 2, the computation of the LRG auto-power spectrum from these data is compatible with a non linear prescription for the dark matter power spectrum (we used the Halofit routine (Smith et al. 2003) in CAMB3), together with a scale and redshift independent galaxy bias parameter bLRG = 2.1 \u00b1 0.02 in agreement with Ross et al. (2011), and with a galaxy redshift distribution centered in \u00af z = 0.55 and with spread 1 http://portal.nersc.gov/project/boss/galaxy/ photoz/ hotoz/ 2 http://healpix.jpl.nasa.gov/ 3 http://camb.info/ 2 P. Serra et al: Cross-correlation of Cosmic Far-Infrared Background anisotropies with Large Scale Structures Fig. 1. Normalized SDSS-III DR8 LRG redshift distribution, peaked at \u00af z = 0.55. Fig. 2. Angular auto-power spectrum measured in the SDSS-III DR8 LRG survey \u03c3 = 0.07: dN dz |LRG \u221dexp(\u2212(z \u2212\u00af z)2/(2\u03c32)), (2) as shown in Fig. 1. In the rest of our analysis, we use Eq. 2 to compute the LRG redshift distribution and we \ufb01x the LRG bias to the value bLRG = 2.1. 2.2. Planck and IRIS maps We use intensity maps at 353, 545, and 857 GHz from the public data release of the \ufb01rst 15.5 months of Planck operations (Planck Collaboration I 2013), with a far-infrared map at 3000 GHz from IRAS (IRIS, Miville-Desch\u02c6 enes et al. 2002; Miville-Desch\u02c6 enes & Lagache 2005). We do not use the lower frequency Planck channels in our analysis, as they contain a large contribution from primary CMB anisotropies and, for the redshift distribution of the galaxy sample considered here, most of the cross-correlation signal comes from the higher frequency maps. Finally, the large number of point sources to be masked in the IRAS 3000 GHz map creates mask irregularities that prevent a stable computation of the cross-power spectrum for Fig. 3. Apodized mask used to cross-correlate the DR8 LRG map with the Planck temperature map at 857 GHz; the sky fraction unmasked is approximately fsky = 0.185 multipoles \u2113> 500; we thus consider only measurements at multipoles \u2113< 500 at 3000 GHz. We refer the reader to Planck Collaboration VI (2013); Planck Collaboration VII (2013); Planck Collaboration VIII (2013) for details related to the mapmaking pipeline, beam description and, in general, to the data processing for HFI data. We used two masks to exclude regions with di\ufb00use Galactic emission and extragalactic point sources. The \ufb01rst mask accounts for di\ufb00use Galactic emission as observed in the Planck data and leaves approximately 60% of the sky unmasked 4. The second mask has been created using the Planck Catalogue of Compact Sources (PCCS, Planck Collaboration XXVIII 2013) to identify point sources with signal-to-noise ratio greater or equal to \ufb01ve in the maps, and masking out a circular area of 3\u03c3 radius around each source (where \u03c3 = FWHM/2.35). The point sources to be removed have \ufb02ux densities above a given threshold, as explained in Planck Collaboration XXX (2013). At 3000 GHz, we used a more aggressive mask, which leaves 20% of the sky unmasked and covers dust contaminated regions at high latitudes more e\ufb03ciently. The \ufb01nal footprint used in our cross-correlation analysis, which is simply the product of the LRG mask with each of the four FIRB masks, has been smoothed with a Gaussian beam with full width at half maximum of ten arcminutes, to reduce possible power leakage; the mask used for the 857 GHz channel is shown in Fig. 3. 3. Cross-correlation measurement and analysis We work in harmonic space, using anafast from the HEALPix package to cross-correlate temperature and density maps and applying the pseudo-C\u2113technique described in Hivon et al. (2002) to deconvolve both mask and beam e\ufb00ects from the cross-power spectrum. A generic scalar \ufb01eld \u03b4(\u02c6 n) de\ufb01ned over the full-sky can be expressed in terms of spherical harmonics Ylm(\u02c6 n) as: \u03b4(\u02c6 n) = X \u2113,m a\u2113mY\u2113m(\u02c6 n), (3) where al,m denotes the spherical harmonic coe\ufb03cients: a\u2113m = Z Y\u2217 \u2113m(\u02c6 n)\u03b4(\u02c6 n)d\u2126 (4) 4 The mask can be found at http://pla.esac.esa.int/pla/ aio/planckResults.jsp? with CATEGORY = MASK gal \u221206 3 P. Serra et al: Cross-correlation of Cosmic Far-Infrared Background anisotropies with Large Scale Structures and, for isotropic temperature and galaxy \ufb01elds, it is possible to write their cross-power spectrum CTg \u2113 as: \u27e8aT \u2113mag \u2113\u2032m\u2032\u27e9\u2261\u27e8CTg l \u27e9\u03b4K \u2113\u2113\u2032\u03b4K mm\u2032, (5) where \u03b4K denotes the Kronecker delta function. Because of contamination or partial sky coverage, we often have access only to a given fraction of the sky. For a generic partial sky map, the resulting power spectrum (called pseudo power spectrum \u02c6 Cl) is di\ufb00erent from the full-sky power spectrum Cl, but their ensemble averages are related by: \u27e8\u02c6 Cl\u27e9= X l\u2032 Ml,l\u2032 \u27e8Cl\u2032 \u27e9. (6) The coupling matrix Ml,l\u2032, computed with the mixing matrix formalism introduced in Hivon et al. (2002), encompasses the combined e\ufb00ects of partial sky coverage, beam, and pixel respectively, and it is obtained by: Ml,l\u2032 = 2l\u2032 + 1 4\u03c0 X l3 (2l3 + 1)Wl3   l l\u2032 l3 0 0 0 !2 B2 l\u2032, (7) where we introduced the Wigner 3-j symbol (or Clebsch-Gordan coe\ufb03cient)   \u21131 \u21132 \u21133 m1 m2 m3 ! , and Bl is a window function describing the combined smoothing e\ufb00ect due to the beam and \ufb01nite pixel size. 3.1. Error bars computation Our measurements are obtained as binned power spectra with a binning \u2206\u2113= 100, and we use a Monte Carlo approach to compute the uncertainty associated with each bin. In particular, we simulate N = 500 pairs of FIRB temperature and LRG density maps, correlated as expected theoretically, adding the expected Poisson noise to both maps, in addition to an instrumental noise and a Galactic dust \u201cnoise\u2019\u201d term to the FIRB frequency maps. More speci\ufb01cally, our pipeline for the computation of error bars, also described in, e.g., Giannantonio et al. (2008), works as follows: \u2013 A simulated FIRB frequency map is created (using the program synfast from the HEALPix package) as the sum of a clustering term plus three noise contributions due to shot noise, Galactic dust contamination, and instrument noise. The total power spectrum to be used as input in synfast can be written as follows: C\u2113(\u03bd) = CTT,clust \u2113 (\u03bd) + CTT,SN \u2113 + CTT,dust \u2113 (\u03bd) + Ninstr \u2113 (\u03bd). (8) Using the Limber approximation (Limber 1953), valid on all scales considered in our analysis, the clustering term for each frequency \u03bd is simply computed as: CTT,clust \u2113 (\u03bd) = Z dz \u03c72  d\u03c7 dz !\u22121 b2 FIRB(k, z) \u0010dS dz (z, \u03bd) \u00112Pdm(k = \u2113/\u03c7, z); (9) here \u03c7(z) is the comoving angular diameter distance to redshift z, Pdm(k, z) is the dark matter power spectrum, while bFIRB(k,z) and dS dz (z, \u03bd) denote the bias of the FIRB sources and the redshift distribution of their emissivity, respectively. Values for the shot-noise power spectrum CTT,SN l are obtained from Table 9 of Planck Collaboration XXX (2013). For the dust power spectrum we use a template taken as a power law CTT,dust l \u221dKl\u03b1, where the amplitude K and the slope \u03b1 are computed by \ufb01tting the measured dust-power spectrum from our CIB maps. Finally, the Planck instrument noise power spectrum Ninstr \u2113 (\u03bd) is estimated from the jack-knife di\ufb00erence maps, using the \ufb01rst and second halves of each pointing period (see also Planck Collaboration XXX 2013). We refer to Miville-Desch\u02c6 enes et al. (2002) for the IRAS noise power spectrum computation. \u2013 A galaxy map is also created as a sum of a clustering plus a shot-noise term: Cgg \u2113= Cgg,clust \u2113 + Cgg,SN \u2113 . (10) In the Limber approximation, the clustering term can be expressed as: Cgg,clust l = Z dz b2 LRG \u03c72(z)  dN dz (z) !2 Pdm(k = l/\u03c7(z), z) , (11) and the shot noise power spectrum Cgg,SN l is directly estimated from the measured number of galaxies per pixel. The galaxy map must be correlated with the FIRB map. In general, two correlated galaxy-temperature maps are described by three power spectra, CTT l , Cgg l , and CTg l , where the last term is given by: CgT \u2113(\u03bd) = Z dz \u03c72  d\u03c7 dz !\u22121 bLRGbFIRB(k, z)dN dz (z) dS dz (z, \u03bd)Pdm(k = \u2113/\u03c7, z); (12) It is easy to correlate a galaxy map with a given FIRB map created with synfast. First, we build a FIRB map with a power spectrum CTT \u2113(\u03bd); then, we make a second map with the same synfast seed used for the clustering term CTT,clust \u2113 and with power spectrum (CTg \u2113)2/CTT \u2113 and we add this second map to a third map made with a new seed and with power spectrum CTT l \u2212(CTg \u2113)2/CTT \u2113. These two maps will have amplitudes: aTT \u2113m = \u03bea(CTT \u2113)1/2 (13) agg \u2113m = \u03beaCTg \u2113/(CTT \u2113)1/2 + \u03beb(Cgg \u2113\u2212(CTg \u2113)2/CTT \u2113)1/2, where \u03be denotes a random amplitude, which is a complex number with zero mean and unit variance (\u27e8\u03be\u03be\u2217\u27e9= 1 and \u27e8\u03be\u27e9= 0). These amplitudes yield: \u27e8aTT lm aTT\u2217 lm \u27e9= CTT l , (14) \u27e8aTT lm agg\u2217 lm \u27e9= CTg l , \u27e8agg lmagg\u2217 lm \u27e9= Cgg l . The obtained maps are then masked with the same mask as that we used to analyze the real data and the cross-power spectrum is then computed using the pseudo-power spectrum technique as in Hivon et al. (2002). The set of realizations of the cross-power spectrum provides the uncertainty in our estimate. The covariance matrix of the binned power spectrum Cb is: Cb,b\u2032 = \u27e8(Cb \u2212\u27e8Cb\u27e9MC)(Cb\u2032 \u2212\u27e8Cb\u2032\u27e9MC\u27e9MC (15) 4 P. Serra et al: Cross-correlation of Cosmic Far-Infrared Background anisotropies with Large Scale Structures with \u27e8\u00b7\u27e9standing for Monte Carlo averaging. The error bars on each binned Cb is: \u03c3Cb = (Cbb)1/2. (16) The error bars computed from simulations have been also compared with an analytic estimate of the uncertainty, given by: \u03c3Cb =   1 (2\u2113+ 1)\u2206l !1/2 h (CTg b )2 + (Cgg b )(CTT b ) i1/2 (17) where the term CTT b includes power spectra of the FIRB anisotropies, Galactic dust, shot noise, and instrument noise, as: CTT b = CTT,FIRB b + Cdust b + CSN b + Ninstr b . (18) For each frequency considered, our Monte Carlo estimates of the uncertainties are within 10% of the uncertainties derived from Eq. 17. In the \ufb01tting process, we thus conservatively increase our simulated error bars by 10%. We have also checked that cross-correlating simulated maps created from di\ufb00erent input power spectra and masked in di\ufb00erent ways, we are always able to retrieve the input spectra, within statistical uncertainties, ensuring the stability of our results. 3.2. Null tests In order to test for possible contaminants in our datasets, we also performed two null tests. In the \ufb01rst test, we cross-correlated 500 FIRB temperature random maps at 857 GHz (adding the expected level of foreground dust and instrumental noise) with the LRG map. The mean of the cross-correlation signal and its uncertainty are plotted in Fig. 4; with a \u03c72 of 6.7 for 9 degrees of freedom, our p-value is 0.67 and the null-test hypothesis of correlation consistent with zero is accepted. We also performed a rotation test (Sawangwit et al. 2010; Giannantonio et al. 2012), where one of the maps is rotated by an arbitrary angle and then cross-correlated with the other map: if the rotation angle \u2206\u03c6 is large enough, and in absence of systematics, the resulting cross-power spectrum should be compatible with zero. Keeping the FIRB map mixed, we computed N = 89 cross-power spectra with N galaxy maps, rotated by \u2206\u03c6 = 4 degrees with respect to each other and used the corresponding rotated galaxy masks; with \u03c72 = 16.5 for 9 degrees of freedom, we accept the null-test hypothesis of correlation consistent with zero. 3.3. Analysis and results In Fig. 5, we show the cross-power spectra measured for the four frequencies considered and with the uncertainty computed from Monte Carlo simulations. The statistical signi\ufb01cance of the signal is obtained by summing, for each frequency \u03bd, the signi\ufb01cance in the di\ufb00erent multipole bins i as s\u03bd = sX i=1 \u0010 Ci \u03c3Ci \u00112; (19) we obtain values of 8.7, 13.0, 12.3, and 12.6 at 3000, 857, 545, and 353 GHz, respectively. The theoretical cross-power spectrum is given by Eq. 12 and a Poisson term, because of far-infrared emission from individual galaxies, is not included, because for the LRG\u2019s number density Fig. 4. Mean cross-power spectrum of 500 FIRB random maps at 857 GHz with the LRG map; the signal is perfectly compatible with zero. and average FIR emission, it is negligible. The redshift distribution of FIRB sources at the observed frequency \u03bd is connected to the mean FIRB emissivity per comoving unit volume j\u03bd(z) through the relation dS \u03bd dz = c H(z)(1 + z) \u00af j\u03bd(z), (20) where the galaxy emissivity \u00af j\u03bd(z) can be written as \u00af j\u03bd(z) = Z dL dn dL(L, z)L(1+z)\u03bd 4\u03c0 ; (21) here L(1+z)\u03bd and dn/dL denote the infrared galaxy luminosity and luminosity function, respectively, while the term (1 + z)\u03bd denotes the rest-frame frequency. The emissivity j\u03bd(z) is modeled with a halo-model approach, introduced in Shang et al. (2012) and successfully applied in, e.g., Planck Collaboration XXX (2013); Viero et al. (2013), whose main feature is the introduction of a parametric form to describe the dependence of the galaxy luminosity on its host halo mass. This allows us to overcome the unrealistic assumption, typical of many models based on a set of infrared luminosity functions and a prescription to populate galaxies in dark matter halos using a halo occupation distribution (HOD) formalism that galaxies have all the same luminosity and contribute to the emissivity density in the same way, despite their dark matter environment. Shang et al. (2012) provide a detailed description of the theoretical motivations and limitations of the modeling. In this model, the galaxy infrared luminosity L(1+z)\u03bd is linked to the host dark matter halo mass using the following parametric form: L(1+z)\u03bd(M, z) = L0 (1 + z)3.6 \u03a3(M)\u0398[(1 + z)\u03bd] (22) where the redshift-dependent, global normalization, has been \ufb01xed to the mean value found in Planck Collaboration XXX (2013), while the term L0 is a normalization parameter constrained with the CIB mean level at the frequencies considered. We will not discuss this parameter further in the rest of our analysis. We also assume a log-normal function \u03a3(M) for the dependence of the galaxy luminosity on halo mass \u03a3(M) = M (2\u03c0\u03c32 L/M)1/2 e\u2212(log10(M)\u2212log10(Me\ufb00))2/2\u03c32 L/M (23) 5 P. Serra et al: Cross-correlation of Cosmic Far-Infrared Background anisotropies with Large Scale Structures Fig. 5. Cross-power spectra measurements among CIB maps at 3000, 857, 545, and 353 GHz, and CMASS LRGs (black points); for the IRIS 3000 GHz channel we did not use data points at multipoles l > 500. Best-\ufb01t power spectra are shown for the parametric SED functional form (red lines) and for the e\ufb00ective SED (blue dashed-dotted lines). where Me\ufb00and \u03c3L/M describe the peak of the speci\ufb01c IR emissivity and the range of halo masses which is more e\ufb03cient at producing star formation; following Shang et al. (2012); Planck Collaboration XXX (2013), we assume the condition \u03c32 L/M = 0.5 while we \ufb01x the minimum halo mass at Mmin = 1010M\u2299(compatible with Viero et al. (2013)) throughout this paper. The log-normal functional form used here describes the observation that a limited range of halo masses dominates the star formation activity. Recent cosmological simulations suggest that processes such as photoionization, supernovae heating, feedback from active galactic nuclei, and virial shocks suppress star formation at both the lowand the highmass end (Benson et al. 2003; Croton et al. 2006; Silk 2003; Bertone et al. 2005; Birnboim & Dekel 2003; Kere\u02c7 s et al. 2005; Dekel & Birnboim 2006); it is thus possible to introduce a characteristic mass scale Me\ufb00, which phenomenologically illustrates the impact of dark matter on star formation processes. In general, a modi\ufb01ed back body functional form (see Blain et al. 2003, and reference therein) can be assumed for galaxy SEDs \u0398(\u03bd, z) \u221d ( \u03bd\u03b2B\u03bd (Td) \u03bd < \u03bd0 ; \u03bd\u2212\u03b3 \u03bd \u2265\u03bd0 (24) where B\u03bd denotes the Planck function, while the emissivity index \u03b2 gives information about the physical nature of dust, in general depending on grain composition, temperature distribution of tunneling states and wavelength-dependent excitation (e.g., Meny et al. 2007). The power-law function is used to temper the exponential (Wien) tail at high frequencies and obtain a shallower SED shape, which is more in agreement with observed SEDs (see, e.g., Blain et al. 2003). The two SED functions at high and low frequencies are connected smoothly at the frequency \u03bd0 satisfying dln\u0398(\u03bd, z) dln\u03bd = \u2212\u03b3. (25) We explicitly checked that our data do not allow us to strongly constrain the emissivity index \u03b2 and the SED parameter \u03b3; thus, we \ufb01xed their values to the mean values found by Planck Collaboration XXX (2013), as \u03b2 = 1.7 and \u03b3 = 1.7. Finally, the parameter Td describes the average dust temperature of FIRB sources at z \u223c0.55. Note that, since our measurement is restricted to quite a narrow redshift bin, we do not consider a possible redshift dependence of parameters such as Me\ufb00or Td; the only redshift-dependent quantity is the global normalization term \u03a6(z). The parameter space is sampled using a Monte Carlo Markov chain analysis with a modi\ufb01ed version of the publicly available code CosmoMC (Lewis & Bridle 2002). We consider variations in the following set of three halo model parameters: P \u2261{Me\ufb00, Td, L0}; (26) 6 P. Serra et al: Cross-correlation of Cosmic Far-Infrared Background anisotropies with Large Scale Structures Fig. 6. Best-\ufb01t SEDs at z = 0.55 (both normalized to have amplitude equal to one at \u03bb=120 \u00b5m) computed with the modi\ufb01ed blackbody functional form (continuous line) and with the mean e\ufb00ective SED approach (dot-dash line), as in B\u00b4 ethermin et al. (2012a). Data points show a (normalized) estimate for the SED of FIRB \ufb02uctuations computed from the ratio of the cross-power spectra at multipole l = 450. we assume the following priors on our physical parameters: log(Me\ufb00) \u2208[11 : 13]M\u2299and Td \u2208[20 : 60]K, and we explicitly checked that our results do not depend on the priors assumed. Table 1. Mean values and marginalized 68% c.l. for halo model parameters Parameter De\ufb01nition Mean value log(Me\ufb00)[M\u2299] Halo model most e\ufb03cient mass 12.84 \u00b1 0.15 Td [K] SED: dust temperature (\u00af z=0.55) 26.0 \u00b1 1.3 In addition to \ufb01tting to the four cross-power spectra, we also use the mean level of the CIB at 3000 GHz (12.6+8.3 \u22121.7 nW m\u22122sr\u22121), 857 GHz (6.5+1.7 \u22121.6 nW m\u22122sr\u22121) and 545 GHz (2.1+0.7 \u22120.6 nW m\u22122sr\u22121) deduced from galaxy number counts as useful priors to constrain the global normalization parameter L0. Our set of three parameters allows us to obtain a very good \ufb01t to the data (Fig. 5), with a best-\ufb01t \u03c72 of 26.9 for 31 degrees of freedom. Mean values and marginalized limits on the halo-model parameters considered here are listed in Table 1. They are in good agreement with results obtained from the analysis of Planck and IRIS auto-power spectra using the same parameterization for the FIRB emissivity in Planck Collaboration XXX 2013, providing a strong con\ufb01rmation of their results. Using the values in Table 1, we also compute the approximate fraction of the total FIRB responsible for the cross-correlation with LRGs, obtaining 11.8% at 3000 GHz, 3.9% at 857 GHz, 1.8% at 545 GHz, and 1% at 353 GHz. Compatible results are obtained through the computation of the mean coherence (Kashlinsky et al. 2012; Cappelluti et al. 2013) of the signal, de\ufb01ned as the square of the ratio of the cross-power spectra to the geometric mean of the auto-power spectra: C\u03bd l = (CTg,\u03bd l )2 CT,\u03bd l CG l . (27) Finally, the mean values inferred for both the dust temperature (Td = 26.0 \u00b1 1.3 K) and the bias (bFIRB \u223c1.45) are compatible with results obtained by Planck Collaboration XXX (2013) at z \u22430.55. To test the robustness of our results, we also replaced our parametric SED functional form with the mean e\ufb00ective SED S \u03bd,e f f of all galaxies at redshift z = 0.55 from B\u00b4 ethermin et al. (2012a), and we repeated the analysis, keeping only Me\ufb00and L0 as free parameters. With a \u03c72 red of 1.0 (best-\ufb01t \u03c72 equal to 31.9 for 32 degrees of freedom) our \ufb01t is satisfying; however, the most e\ufb03cient halo mass at hosting star-forming galaxies is Me\ufb00= 12.90 \u00b1 0.14, higher than Planck Collaboration XXX (2013), and compatible at 95% c.l.. As we can see in Fig. 6, the parametric form used in this paper is similar to the mean e\ufb00ective SED for the range of wavelengths that matters in this analysis, yielding a satisfactory con\ufb01rmation of the goodness of our results. However, the \u03b3 parameter, which controls the high frequency tail of the spectrum, fails to correctly reproduce the shape of real galaxy SEDs in the midinfrared regime (from 10 to 30 \u00b5m), mainly because of broad line absorption from polycyclic aromatic hydrocarbon (PAH) molecules. In Fig. 6, we also plot the value of the FIRB SED computed from the ratio of the measured cross-power spectra at multipole l = 450 and shifted to redshift z = 0.55; our results are compatible with the best-\ufb01t SEDs used in the paper. On linear scales, the cross-power spectra considered can also be \ufb01tted by power laws. Assuming a simple, two-parameter functional form such as Cl = A  l 100 !n , (28) it is possible to obtain a very good \ufb01t at all frequencies over the multipole range 100 < l < 500. Mean values and marginalized limits on the amplitudes A\u03bd and power-law slopes n\u03bd are provided in Table 2. Table 2. Mean values and marginalized 68% c.l. for power-law parameters Frequency A n 353 0.18 \u00b1 0.07 \u22121.90 \u00b1 0.36 545 0.60 \u00b1 0.23 \u22122.08 \u00b1 0.37 857 1.72 \u00b1 0.65 \u22122.09 \u00b1 0.36 3000 2.45 \u00b1 1.33 \u22122.42 \u00b1 0.57 3.4. Discussion As mentioned earlier, the dark matter halo mass in\ufb02uences the evolution of galaxies, driving processes of gas accretion and star formation rate (SFR) (see, e.g., Rees & Ostriker 1977; Silk 1977; White & Rees 1978; Fall & Efstathiou 1980; Blumenthal et al. 1984). Numerous techniques have been considered to constrain the link between dark matter halos and their host galaxies (see discussion and references in Behroozi et al. 2010; Moster et al. 2010). From a theoretical point of view, semi analytic models and hydrodynamical simulations have been developed to study galaxy formation processes ab initio; however, they are still not able to reproduce many observational evidences and su\ufb00er from several uncertainties. A di\ufb00erent approach, which does not rely on assumptions related to poorly constrained physical processes and is based instead on a statistical description of the link between galaxies and dark matter, 7 P. Serra et al: Cross-correlation of Cosmic Far-Infrared Background anisotropies with Large Scale Structures is the basis for the HOD formalism and the abundance matching technique, which also assumes the existence of a monotonic relation between halo mass and galaxy stellar mass. Results based on abundance matching, applied to optical and infrared data (B\u00b4 ethermin et al. 2012b; Behroozi et al. 2012; Moster et al. 2010; Guo et al. 2010), constrain the characteristic halo mass at Me\ufb00\u223c1012M\u2299, with little evolution in redshift and some uncertainty, mainly due to systematics in the stellar mass estimates (Behroozi et al. 2010). The higher value obtained in this work (Me\ufb00\u223c6.9 \u00b7 1012M\u2299), can be due to the adoption of a log-normal function to model the luminosity-mass relation, while the previously mentioned analyses use a more complicated relation, to take the slow decrease of the stellar mass to halo mass ratio at the high mass end into account. However, the mean value for the most e\ufb03cient mass found here is in agreement with, or only slightly higher than, results from recent analyses of FIRB anisotropies (Shang et al. 2012; Xia et al. 2012; Viero et al. 2013; Planck Collaboration XXX 2013). We note that the narrow redshift bin involved in our analysis imposes the use of a very simple interpretative model for both the LRGs and the FIRB galaxies. In particular, both the redshift evolution of the galaxy FIR luminosity and some SED parameters are kept \ufb01xed. In an upcoming study, we will cross-correlate FIRB anisotropies with a combination of data from multiple surveys such as WISE, GALEX, and BOSS. This will allow us to probe the link between dark matter and galaxies over a wide redshift range, from low redshifts (0 < z < 1) where a steep evolution of the cosmic star formation has been measured, to high redshifts (1 < z < 3), where the SFR peaks. Introducing redshift-dependent quantities and a realistic scatter in the relation between galaxy luminosity and dark matter halo mass (that has been neglected here, see discussion in Shang et al. 2012), we will be able to study the temporal evolution of the most ef\ufb01cient halo mass at hosting star formation (possibly constraining downsizing scenarios, Cowie et al. 1996; Bundy et al. 2006; Conroy & Wechsler 2009), thus establishing cross-correlations with FIRB anisotropies as a powerful probe of the link between galaxies and dark matter and the global star formation history. 4. Conclusions We have measured the cross-correlation between LRGs from SDSS-III DR8 and CIB anisotropies from IRIS and Planck at 3000, 857, 545, and 353 GHz. Using an extended version of the halo model that connects galaxy luminosity to host halo mass with a simple parametric form, we con\ufb01rmed the basic results obtained from recent analyses of FIRB anisotropies from Planck and Herschel, with a most e\ufb03cient halo mass at hosting star-forming galaxies constrained at the value log(Me\ufb00/M\u2299) = 12.84 \u00b1 0.15, and the mean dust temperature of FIR sources at z \u223c0.55 with the value Td = 26.0 \u00b1 1.3K. The cross-correlation of FIRB sources with other tracers of the dark matter \ufb01eld now starts being successfully exploited to constrain the interplay between dark and luminous matter (see, e.g, Wang et al. 2014), and cross-correlations with data from present and upcoming surveys are particularly promising for many reasons. First of all, while the measurement of FIRB autopower spectra will not improve much in the near future, as they are limited by issues related to components separation, crosscorrelations with FIRB anisotropies are limited mostly by noise and systematics. In particular, control of the e\ufb00ects of Galactic dust will be critical to achieving a precise measurement of the cross-correlation, since it contributes signi\ufb01cantly to the total uncertainty. Dust subtraction, using ancillary data and clean regions of the sky (as done in Planck Collaboration XXX 2013) can improve the signal-to-noise ratio, provided that large enough \ufb01elds are considered. A careful analysis of systematics is also mandatory to exclude the possibility of correlated systematics between datasets; an example is stellar density a\ufb00ecting quasar catalogs and Galactic dust a\ufb00ecting FIRB anisotropies, which correlate and contaminate the cross-correlation signal. Cross-correlations with FIRB anisotropies are also important because they allow us to isolate the CIB signal in multiple redshift slices and thus constrain the link between galaxies and dark matter and global star formation as a function of redshift. These studies will be particularly interesting when performed with sources at high redshift (such as, e.g., quasars from BOSS), where the cosmic SFR peaks and current model uncertainties for DSFGs are large. Acknowledgements. The development of Planck has been supported by: ESA; CNES and CNRS/INSU-IN2P3-INP (France); ASI, CNR, and INAF (Italy); NASA and DoE (USA); STFC and UKSA (UK); CSIC, MICINN and JA (Spain); Tekes, AoF and CSC (Finland); DLR and MPG (Germany); CSA (Canada); DTU Space (Denmark); SER/SSO (Switzerland); RCN (Norway); SFI (Ireland); FCT/MCTES (Portugal); and PRACE (EU). A description of the Planck Collaboration and a list of its members, including the technical or scienti\ufb01c activities in which they have been involved, can be found at http://www.sciops.esa.int/index.php? project=planck&page=Planck_Collaboration. We would like to thank the anonymous referee for providing us with constructive comments and suggestions. P.S. would like to thank Alex Amblard and Shirley Ho for useful discussions. Part of the research described in this paper was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration.",
                    "introduction": "The cosmic infrared background (CIB), detected with both the Far Infrared Absolute Spectrophotometer (FIRAS, Puget et al. 1996; Fixsen et al. 1998; Lagache et al. 1999) and the Di\ufb00use Infrared Background Experiment (DIRBE, Hauser et al. 1998; Lagache et al. 2000), accounts for approximately half of the total energy radiated by structure formation processes throughout cosmic history since the end of the matter-radiation decoupling epoch (Dole et al. 2006). Early attempts at mea- suring CIB \ufb02uctuations at near-infrared wavelengths have been performed from degree to sub-arcminute scales using data from COBE/DIRBE (Kashlinsky & Odenwald 2000), IRTS/NIRS (Matsumoto et al. 2005), 2MASS (Kashlinsky et al. 2002), and Spitzer-IRAC (Kashlinsky et al. 2005). On the other end, \ufb02uctuations in the cosmic far-infrared background (FIRB), composed of thermal emission from warm dust en- shrouding star-forming regions in galaxies, have been reported using the ISOPHOT instrument aboard the Infrared Space Observatory (Matsuhara et al. 2000; Lagache & Puget 2000), the Spitzer Space Telescope (Lagache et al. 2007), the BLAST balloon experiment (Viero et al. 2009), and the Herschel Space Observatory (Amblard et al. 2011). In the same period, di\ufb00erent cosmic microwave background (CMB) experiments \u22c6Based on observations obtained with Planck (http://www.esa. int/Planck), an ESA science mission with instruments and contribu- tions directly funded by ESA Member States, NASA, and Canada. extended these detections to longer wavelengths (Hall et al. 2010; Dunkley et al. 2011; Reichardt et al. 2012). The Planck early results paper Planck Collaboration XVIII 2011 measured angular power spectra of CIB anisotropies from arc-minute to degree scales at 217, 353, 545, and 857 GHz and the recent paper Planck Collaboration XXX 2013 represents its extension and improvement in terms of analysis and interpretation, establishing Planck as a powerful probe of the FIRB clustering. The far-infrared component of the CIB radiation (or far-infrared background, FIRB) is primarily due to dusty, star-forming galaxies (DSFGs). The dust absorbs the optical and ultraviolet stellar radiation and re-emits in the infrared and submillimetre (submm) wavelengths. The rest frame spectral energy distri- bution (SED) of DSFGs peaks near 100\u00b5m, and it moves into the FIR/submm regime as objects at increasing redshifts are observed. Thus, a complete understanding of the star formation history (SFH) in the Universe must involve accurate observa- tions in the FIR/submm wavelength range. FIRB anisotropies are a powerful probe of the global SFH. However, because the signal is integrated over all redshifts, it prevents a detailed investigation of the temporal evolution of DSFGs over cosmic time. Cross-correlation studies are a powerful expedient to remedy this fact. Because DSFGs trace the underlying dark matter \ufb01eld, a certain degree of correlation between the CIB and any other tracer of the dark matter distribution is expected, provided that some overlap in redshifts exists between the tracers. A useful property of such 1 arXiv:1404.1933v2  [astro-ph.CO]  24 Sep 2014 P. Serra et al: Cross-correlation of Cosmic Far-Infrared Background anisotropies with Large Scale Structures cross-correlation studies is that the measurement can be used to isolate and analyze a small redshift range in one signal (e.g., the CIB) if the other population is limited in redshift (e.g., the LRGs). In addition, the measurement is not prone to systematics that are not correlated between the two datasets, giving thus a strong signal even if each dataset is contaminated by other physical e\ufb00ects. As shown in Planck Collaboration XXX (2013) for example, foreground Galactic dust severely limits CIB measurements at the high frequency channels (\u03bd \u2265545 GHz) while CMB anisotropies contaminate the CIB signal at frequen- cies \u03bd \u2264353 GHz; possible approaches to dealing with these foregrounds include their inclusion in the likelihood analysis (e.g., as a power law) or their removal using a tracer of dust and possibly selecting very clean regions of the sky. In any event, the presence of foreground and background contamination greatly complicates the analysis of CIB data. This limitation disappears when cross-correlating CIB maps with catalogs of dark matter tracers not directly correlated with Galactic dust or CMB (e.g., Planck Collaboration XVIII 2013); in this case, the presence of uncorrelated contaminants only appears in the computation of the uncertainties associated with the measurement. In this paper, we perform a measurement of the cross-correlation between FIRB maps from Planck and maps from the Improved Reprocessing (IRIS) of the Infrared Astronomical Satellite (IRAS) with a galaxy map of luminous red galaxies (LRGs) from SDSS-III Data Release 8 (DR8). By \ufb01xing both the LRGs redshift distribution and their bias with respect to the dark matter \ufb01eld, we will be able to constrain the most e\ufb03cient dark matter halo mass at hosting star formation in DSFGs, with their SED. The existence of such a characteristic halo mass has been predicted both analytically and with numerical simulations, and it constitutes a critical component that triggers the growth and assembly of stars in galaxies. After comparing our results with recent analyses in the literature, we will outline the role of upcoming cross-correlation studies with many tracers of the dark matter \ufb01eld in multiple redshift bins, in constraining the redshift evolution of the link between dark matter and star formation, thus bringing new insight into the cosmic SFH. A measurement of the cross-correlation between FIRB sources and other tracers of the dark matter \ufb01eld at high redshift can be extremely important in constraining the early star forma- tion history of the Universe and the clustering properties of high-redshift objects. In this regard, it is important to keep in mind that a good knowledge of the redshift distribution of the sources to be cross-correlated with the FIRB is mandatory in order to constrain both the FIRB emissivity and the bias of both tracers. The quasars catalog from the Wide-\ufb01eld Infrared Survey Explorer (WISE, Wright et al. 2010), whose redshift distribution can be inferred using the method developed in, e.g., M\u00b4 enard et al. (2013), and the spectroscopic quasars from the Baryon Oscillation Spectroscopic Survey (BOSS, P\u02c6 aris et al. 2013) will certainly be important for such studies. However, our very thorough attempt at computing their cross-power spectrum with the FIRB maps has shown the existence of possible systematics that have not been well understood. In particular, when cross-correlating with the spectroscopic BOSS quasar catalog, we \ufb01nd a strong anti-correlation at large angular scales whose origin, among many possibilities, has not been clearly isolated. On the other hand, the di\ufb03culty in selecting objects in the WISE dataset (beyond the approximate method based on color cuts explained in Wright et al. 2010), does not allow us to clearly interpret the results of the cross-correlation in the context of the halo model. We thus decided not to include these datasets in the present analysis and to defer this kind of study to a future publication. Throughout this paper, we adopt the standard \ufb02at \u039bCDM cosmological model as our \ufb01ducial background cos- mology, with parameter values derived from the best-\ufb01t model of the CMB power spectrum measured by Planck (Planck Collaboration XVI 2013): {\u2126m, \u2126\u039b, \u2126bh2, \u03c38, h, ns} = {0.3175, 0.6825, 0.022068, 0.8344, 0.6711, 0.9624}. We also de\ufb01ne halos as matter overdense regions with a mean density equal to 200 times the mean density of the Universe, and we assume a Navarro-Frenck-White (NFW) pro\ufb01le (Navarro et al. 1997) with a concentration parameter as in Cooray & Sheth 2002. The \ufb01tting function of Tinker et al. 2008 is used for the halo-mass function while sub-halo mass function and halo bias are taken as in Tinker et al. 2010."
                },
                {
                    "url": "http://arxiv.org/abs/1401.3180v1",
                    "title": "The Atlas3D project - XXVI. HI discs in real and simulated fast and slow rotators",
                    "abstract": "One quarter of all nearby early-type galaxies (ETGs) outside Virgo host a\ndisc/ring of HI with size from a few to tens of kpc and mass up to ~1e+9 solar\nmasses. Here we investigate whether this HI is related to the presence of a\nstellar disc within the host making use of the classification of ETGs in fast\nand slow rotators (FR/SR). We find a large diversity of HI masses and\nmorphologies within both families. Surprisingly, SRs are detected as often,\nhost as much HI and have a similar rate of HI discs/rings as FRs. Accretion of\nHI is therefore not always linked to the growth of an inner stellar disc. The\nweak relation between HI and stellar disc is confirmed by their frequent\nkinematical misalignment in FRs, including cases of polar and counterrotating\ngas. In SRs the HI is usually polar. This complex picture highlights a\ndiversity of ETG formation histories which may be lost in the relative\nsimplicity of their inner structure and emerges when studying their outer\nregions.\n  We find that LCDM hydrodynamical simulations have difficulties reproducing\nthe HI properties of ETGs. The gas discs formed in simulations are either too\nmassive or too small depending on the star formation feedback implementation.\nKinematical misalignments match the observations only qualitatively. The main\npoint of conflict is that nearly all simulated FRs and a large fraction of all\nsimulated SRs host corotating HI. This establishes the HI properties of ETGs as\na novel challenge to simulations.",
                    "authors": "Paolo Serra, Ludwig Oser, Davor Krajnovic, Thorsten Naab, Tom Oosterloo, Raffaella Morganti, Michele Cappellari, Eric Emsellem, Lisa M. Young, Leo Blitz, Timothy A. Davis, Pierre-Alain Duc, Michaela Hirschmann, Anne-Marie Weijmans, Katherine Alatalo, Estelle Bayet, Maxime Bois, Frederic Bournaud, Martin Bureau, Roger L. Davies, P. T. de Zeeuw, Sadegh Khochfar, Harald Kuntschner, Pierre-Yves Lablanche, Richard M. McDermid, Marc Sarzi, Nicholas Scott",
                    "published": "2014-01-14",
                    "updated": "2014-01-14",
                    "primary_cat": "astro-ph.GA",
                    "cats": [
                        "astro-ph.GA",
                        "astro-ph.CO"
                    ],
                    "main_content": "The ATLAS3D H I sample and the radio observations which this study is based on are described in detail in Paper XIII. Here we provide a short summary. We study a subset of the full ATLAS3D sample of ETGs (Paper I; distance < 42 Mpc, MK < \u221221.5). This subset includes all galaxies with declination \u03b4 \u2a7e10 \u25e6except the four objects closest to Virgo A, resulting in a volume-limited sample of 166 ETGs (127 outside the Virgo cluster). We obtain Westerbork Synthesis Radio Telescope H I data for most of them either as part of the ATLAS3D project or from previous projects (Morganti et al. 2006; J\u00b4 ozsa et al. 2009; Oosterloo et al. 2010). We make use of Very Large Array data for 1 galaxy with H I (Chung et al. 2009) and of Arecibo spectra for 20 galaxies (all undetected; Giovanelli et al. 2005). As mentioned in Sec. 1, our Westerbork observations allow us to detect H I down to a column density of a few times 1019 cm\u22122 and a mass of \u223c107 M\u2299. We detect H I associated with the target ETG in 53 galaxies (49 outside Virgo). In Paper XIII we classify detected ETGs in the following classes on the basis of the H I morphology: D = large discs (14 objects); R = large rings1 (10); d = small discs (10); u = unsettled distributions (14); c = gas clouds (5). Gas distributions characterized by ordered rotation (D, R and d classes) are therefore the most common ones among H I-rich ETGs, amounting to 2/3 of all detections and 1/4 of all ETGs outside Virgo. As discussed in Paper XIII, the above H I classes are a way to simplify the observed continuum of gas morphologies, with a number of objects being intermediate (or in transition) between classes. We make use of the H I classes D, R, d, u and c in the rest of this paper. In Paper XIII we show H I images of all detections. Each image is obtained after creating a mask including all emission in the corresponding H I cube. The images shown in Paper XIII are the zero-th moment of the masked cubes. In the present paper we show and analyse for the first time the H I velocity fields obtained as the first moment of the same masked cubes. 3 RELATION BETWEEN H I AND ETG INNER STRUCTURE In this section we investigate whether the H I detection rate, mass and morphology of ETGs are related to their stellar kinematics as 1 In fact, in Paper XIII we group Ds and Rs in a single class. In table 1 of that paper we indicate galaxies where the H I is distributed on a ring. Here we use that table as a basis for the division into D and R objects. c \u20dd2013 RAS, MNRAS 000, 1\u201318 4 Paolo Serra et al. Table 1. Number of galaxies in the various H I morphological classes (Paper XIII) as a function of stellar kinematics class (Paper III) and SR/FR classi\ufb01cation (Paper II) for the full ATLAS3D H I sample. Full Stellar kinematics Sample All a\u22c6 b\u22c6 c\u22c6 d\u22c6 e\u22c6 SR FR All 166 4 8 14 4 136 22 144 Undet. 113 3 5 7 4 94 13 100 Det. 53 1 3 7 0 42 9 44 H I D 14 0 1 1 0 12 2 12 R 10 0 0 2 0 8 2 8 d 10 0 0 0 0 10 0 10 u 14 1 2 2 0 9 3 11 c 5 0 0 2 0 3 2 3 well as position on the \u03bbR-\u03f5 diagram2 and mass-size plane. In particular, we make use of the kinematical classi\ufb01cation presented in Paper II. In that paper ETGs are divided in the following classes based on a quantitative analysis of their stellar velocity \ufb01eld3: a\u22c6= no rotation; b\u22c6= some rotation but with a velocity \ufb01eld not consistent with that of a rotating disc; c\u22c6= KDC; d\u22c6= two counterrotating stellar discs; e\u22c6= velocity \ufb01eld consistent with that of a rotating disc. These classes are important to understand the classi\ufb01cation of ETGs into FRs and SRs discussed in Sec. 1. In Paper III we de\ufb01ne FRs and SRs as galaxies above and below the line \u03bbR = 0.31 \u221a\u03f5 on the \u03bbR-\u03f5 diagram, respectively. Fast rotators and e\u22c6ETGs are essentially the same family and represent \u223c85 per cent of all objects. On the other hand, the SR family is very heterogeneous and includes galaxies in all other groups (a\u22c6to d\u22c6). 3.1 Fast versus slow rotators Figure 1 shows all galaxies on the \u03bbR-\u03f5 diagram. In this \ufb01gure we indicate galaxies with different stellar kinematics and H I morphology using different colours and markers, respectively. To \ufb01rst order Fig. 1 con\ufb01rms the results of Morganti et al. (2006) and Oosterloo et al. (2010): the relation between H I properties and galaxy structure is not a simple one. We detect H I in galaxies at all locations on the \u03bbR-\u03f5 diagram where there are ETGs, both FRs and SRs. Many of the H I discs and rings (D, R and d) are hosted by \ufb02at, nearly edge-on FRs (topright of the diagram) and their lower-inclination counterparts (at lower values of \u03bbR and \u03f5). This is reasonable as these galaxies have a pronounced stellar disc component and therefore must have experienced a considerable level of dissipation during their assembly. Their current H I discs/rings may be a remnant of that process. The more detailed analysis of Sec. 4 shows that this is indeed the case for about half of all gas-rich FRs, but also that in the remaining half the gas accretion episode traced by H I does not seem to be related to the formation of the current stellar disc. What might be more surprising is to \ufb01nd H I also among SRs (a\u22c6, b\u22c6and c\u22c6objects only) and that in some of them the detected H I is distributed on a large disc or ring. This indicates that SRs too can experience gas accretion and dissipative processes during their 2 We adopt the \u03bbR and \u03f5 measurements obtained within a 1 Re aperture in Paper III. Note that not all galaxies have their stellar kinematics measured out to 1 Re, as discussed in that paper. 3 Note the addition of a \u22c6subscript to the kinematical classes name to avoid confusion with the H I classes de\ufb01ned in Sec. 2. Table 2. Number of galaxies in the various H I morphological classes (Paper XIII) as a function of stellar kinematics class (Paper III) and SR/FR classi\ufb01cation (Paper II) for non-Virgo ETGs in the ATLAS3D H I sample. Outside Stellar kinematics Virgo All a\u22c6 b\u22c6 c\u22c6 d\u22c6 e\u22c6 SR FR All 127 2 7 11 1 106 16 111 Undet. 78 1 4 5 1 67 8 70 Det. 49 1 3 6 0 39 8 41 H I D 14 0 1 1 0 12 2 12 R 9 0 0 2 0 7 2 7 d 9 0 0 0 0 9 0 9 u 12 1 2 1 0 8 2 10 c 5 0 0 2 0 3 2 3 formation, and gas-poor evolutionary paths are not the only way to make a galaxy with this internal structure. A similar conclusion is reached by Paper X based on the misalignment between ionized gas and stellar kinematics in these galaxies within \u223c1 Re, by Smith et al. (2012) based on the frequent detection of cold dust in SRs, by Paper XXIII based on the existence of SRs with a cuspy nuclear light pro\ufb01le, and by both idealized and \u039bCDM hydrodynamical simulations (Paper VI; Paper XXV). Additional observations such as very deep optical imaging may provide further clues about the formation of SRs in presence of a cold gas component (Duc et al. 2011). These qualitative results are illustrated in more quantitative terms in Table 1 for the full sample and in Table 2 for non-Virgo galaxies only. Within the limited statistics available for SRs (and for classes a\u22c6to d\u22c6), their H I detection rate is the same as that of FRs (and e\u22c6objects). Namely, we detect H I in 41 \u00b1 14 per cent of all SRs and 31 \u00b1 5 per cent of all FRs, while outside Virgo the detection rate becomes 50\u00b118 per cent for SRs and 37\u00b16 per cent for FRs (error bars assume a binomial distribution). The fraction of galaxies hosting a rotating H I distribution (H I classes D, R and d) is 18 \u00b1 9 per cent for SRs and 21 \u00b1 4 per cent for FRs over the full sample, while outside Virgo it becomes 25 \u00b1 13 per cent for SRs and 25 \u00b1 5 per cent for FRs. The above paragraph describes the H I properties (detection rate and morphology) as a function of stellar kinematics. A complementary approach is to examine the stellar kinematics as a function of H I properties, but also in this case Tables 1 and 2 show that there is no clear trend. Within each H I class (including that formed by all undetected ETGs) the fraction of SRs and FRs is consistent with the global values of \u223c15 and \u223c85 per cent, respectively. The same is true considering all galaxies with a settled H I distribution together (D, R and d). We also compare the \u03bbR/(0.31 \u221a\u03f5) distribution of D + R + d ETGs to that of undetected + c objects4 and \ufb01nd that they are indistinguishable \u2013 according to a two-sample KS test the probability that the two samples are not drawn from the same parent distribution is 78 per cent, insuf\ufb01cient to claim a signi\ufb01cant difference. The only possible exception to this lack of trends is that small H I discs (d) include no SRs. This is consistent with the fact that H I in these galaxies seems to be strongly linked to the presence of molecular gas and star formation within a stellar disc (Paper XIII). 4 In this context c ETGs can be grouped together with non-detections since M(H I) is very low and the detected gas does not appear obviously associated with the host (Paper XIII). c \u20dd2013 RAS, MNRAS 000, 1\u201318 H I discs in fast and slow rotators 5 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 \u03f5Re 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 \u03bbRe N0680 N1023 N2768 N3073 N3193 N3457 N4026 N4111 N4406 N4694 N5198 N5557 N7280 N7465 N2824 N3032 N3182 N3489 N3499 N4150 N4710 N5422 N5866 U05408 N2685 N2764 N3619 N3626 N3998 N4203 N4278 N5103 N5173 N5631 N6798 U03960 U06176 U09519 N2594 N2859 N3414 N3522 N3838 N3941 N3945 N4036 N4262 N5582 H i class undet. D R d u c a\u22c6 no rotation b\u22c6 complex rotation c\u22c6 KDC d\u22c6 2\u03c3 e\u22c6 regular rotation Figure 1. H I on the \u03bbR-\u03f5 diagram. The colour scheme represents the kinematical classi\ufb01cation of ETGs presented in Paper II. The markers shape represent the H I morphology as in Paper XIII with the small modi\ufb01cation described in Sec. 2. The magenta line represents the edge-on view of anisotropic, oblate models with \u03b2 = 0.65 \u00d7 \u03f5 (Cappellari et al. 2007), and the black dashed lines represent the models with \u03f5 = 0.75 and 0.85 viewed under all possible inclinations from edge-on (top right) to face-on (bottom left). The green line represents the empirical separation between FRs and SRs \u03bbR = 0.31 \u221a\u03f5 proposed in Paper III. We indicate the name of all H I detections except that of c galaxies. However, the number of ds is low and only \u223c1 SR would be expected among them based on the global SR fraction. Better statistics would therefore be needed to con\ufb01rm this result. Another important quantity to analyse is the H I mass. Figure 2 shows the M(H I)/M\u22c6ratio plotted against the \u03bbR/(0.31 \u221a\u03f5) ratio. Here and in the rest of this paper we adopt for M\u22c6the value derived by Cappellari et al. (2013a, hereafter Paper XV) based on dynamical modelling \u2013 MJAM in that paper5. One galaxy, PGC 071531, has no reliable M\u22c6measurement and is excluded from this analysis. Figure 2 shows that H I-detected SRs are found over a wide 5 The results discussed in this section do not change if we normalize M(H I) to LK. This follows from the fact that the distribution of M\u22c6/LK ratio is very narrow for ETGs, peaking at 1.2 M\u2299/L\u2299and with an rms of 0.4 M\u2299/L\u2299. This scatter is insuf\ufb01cient to signi\ufb01cantly alter a plot like the one showed in Fig. 2, where galaxies spread over \u223c3 orders of magnitude in M(H I)/M\u22c6. range of M(H I)/M\u22c6. They seem not to reach the large M(H I)/M\u22c6 values allowed for FRs but the overall low number of SRs makes this difference statistically insigni\ufb01cant. For example, the fraction of galaxies with M(H I)/M\u22c6\u2a7e0.002 is 23 \u00b1 10 per cent within the SR family and 24\u00b14 per cent for FRs. These fractions remain comparable to one another if we consider ETGs outside Virgo only, and these (and the following) results do not change if we adopt a different M(H I)/M\u22c6threshold. Conversely, we de\ufb01ne two ETG subsamples with M(H I)/M\u22c6above and below 0.002, including 39 and 126 galaxies respectively. We \ufb01nd that they contain a similar fraction of SRs consistent with the global value of \u223c15 per cent, both considering all galaxies or non-Virgo galaxies only. Finally, according to a two-sample KS test the probability that the \u03bbR/(0.31 \u221a\u03f5) distributions of the two subsamples are not drawn from the same parent distribution is just 4 per cent. c \u20dd2013 RAS, MNRAS 000, 1\u201318 6 Paolo Serra et al. 0 1 2 3 4 5 \u03bbRe/(0.31\u221a\u03f5Re) \u22124 \u22123 \u22122 \u22121 log10 M(H\u0131)/M\u22c6 N0680 N1023 N2768 N3073 N3193 N3457 N4026 N4111 N4406 N4694 N5198 N5557 N7280 N7465 N2824 N3032 N3182 N3489 N3499 N4150 N4710 N5422 N5866 U05408 N2685 N2764 N3619 N3626 N3998 N4203 N4278 N5103 N5173 N5631 N6798 U03960 U06176 U09519 N2594 N2859 N3414 N3522 N3838 N3941 N3945 N4036 N4262 N5582 H\u0131 class undet. D R d u c a\u22c6 no rotation b\u22c6 complex rotation c\u22c6 KDC d\u22c6 2\u03c3 e\u22c6 regular rotation Figure 2. M(H I)/M\u22c6plotted against the ratio \u03bbR/(0.31 \u221a\u03f5), such that SRs and FRs are found to the left and right of the green, vertical line, respectively. Colours and markers are as in Fig. 1. 3.2 H I properties within the FR family Considering now FRs alone, we \ufb01nd no systematic variation of H I properties as a function of position on the \u03bbR-\u03f5 diagram. Specifically, we compare intrinsically \ufb02atter FRs to rounder ones. We do this by considering e\u22c6galaxies only and splitting them in two groups above and below the line of 0.75 intrinsic ellipticity, respectively (see Fig. 1; we comment below on alternative ways of de\ufb01ning \ufb02at and round galaxies). This results in 47 \u2018\ufb02at\u2019 and 89 \u2018round\u2019 e\u22c6ETGs (39 and 67 outside Virgo, respectively). We detect H I in 32 \u00b1 8 per cent of all \ufb02at objects and 30 \u00b1 6 per cent of all round ones. The detection rate of rotating H I distributions (D, R and d objects) is 26 \u00b1 7 and 20 \u00b1 5 per cent, respectively, with both \ufb02at and round ETGs exhibiting a mix of D, R and d objects. No signi\ufb01cant difference emerges if we consider non-Virgo galaxies only. Conversely, the fraction of \ufb02at and round e\u22c6ETGs does not vary signi\ufb01cantly as a function of H I class (also when grouping together all D, R and d systems). Within the error bars, we always \ufb01nd \u223c35 per cent of \ufb02at objects and \u223c65 per cent of round galaxies. Furthermore, the \u03bbR/\u03bbR,\u03f5=0.75 distribution of galaxies with an H I disc or ring (D, R and d) is statistically undistinguishable from that of galaxies with no H I (undetected and c). The two-sample KS-test probability that the two distributions are not drawn from the same parent distribution is 38 per cent. We also investigate possible variations of M(H I)/M\u22c6within the FR family. We \ufb01nd that 19 \u00b1 6 per cent of all \ufb02at galaxies have M(H I)/M\u22c6\u2a7e0.002, comparable to the 26 \u00b1 5 per cent found for round objects. Conversely, we de\ufb01ne an H I-rich and an H I-poor subsample of e\u22c6ETGs adopting the same M(H I)/M\u22c6separation as above. The two samples include 32 and 103 galaxies, respectively. The fraction of \ufb02at objects in the two groups is comparable (28 \u00b1 9 and 37 \u00b1 6 per cent, respectively). Finally, a two-sample KS test gives a probability of just 10 per cent that the \u03bbR/\u03bbR,\u03f5=0.75 distributions of the two subsamples are not drawn from the same parent distribution. The de\ufb01nition of \ufb02at and round FRs adopted above relies on a simple de-projection of galaxies\u2019 shape along model lines on the \u03bbR-\u03f5 diagram. A more accurate estimate of the intrinsic ellipticity of ETGs is derived in Paper XX based on the modelling presented in Paper XV and on the ellipticity measurement at large radius rec \u20dd2013 RAS, MNRAS 000, 1\u201318 H I discs in fast and slow rotators 7 9.5 10.0 10.5 11.0 11.5 12.0 log10 M\u22c6(M\u2299) \u22120.2 0.0 0.2 0.4 0.6 0.8 1.0 log10 Rmaj e (kpc) H\u0131 class undet. D R d u c \u22124.5 \u22124.0 \u22123.5 \u22123.0 \u22122.5 \u22122.0 \u22121.5 \u22121.0 \u22120.5 log10 M(H\u0131)/M\u22c6 Figure 3. H I properties on the mass-size plane. Different H I morphologies are indicated as in previous \ufb01gures (see legend on the bottom right) while markers are colour-coded according to the M(H I)/M\u22c6value. The velocity dispersion is constant along the blue dashed lines for galaxies following the virial relation (\u03c3e = 50, 100, 200 and 300 km s\u22121 from top-left to bottomright, respectively; see Cappellari et al. 2006). The red solid line indicates the Zone of Exclusion discussed in Paper XX. ported in Paper II. However, we have veri\ufb01ed that using these intrinsic ellipticity values does not change any of the above conclusions. Flat and round FRs keep having equal H I detection rates as well as equal fractions of H I discs and of galaxies with M(H I)/M\u22c6 \u2a7e0.002. Similarly, the distribution of FR intrinsic ellipticity does not change as a function of H I mass or morphology. 3.3 Mass-size plane Although the \u03bbR-\u03f5 diagram is very useful to separate SRs from FRs, Paper XX shows that a number of key ETG properties vary in a much clearer way on the mass-size plane instead. In particular, properties linked to the star formation history of galaxies such as their mass-to-light ratio, optical colour, H\u03b2 absorption and M(H2)/M\u22c6ratio correlate with bulge-to-disc ratio (traced by velocity dispersion) on this plane. We therefore investigate whether the ETG H I properties too exhibit any systematic variation on the mass-size plane. Figure 3 shows all galaxies on the mass size plane of Paper XX. This \ufb01gure does not show any clear trend other than the decrease of the typical M(H I) value and the prevalence of disturbed H I morphologies at high galaxy mass, already reported in Paper XIII. As with Fig. 2, the main observational result is a very large scatter of H I properties, reinforcing our conclusion that H I does not appear to be linked in any clear way to the inner galaxy structure. 3.4 Diversity of gas accretion histories The lack of a relation between ETG H I properties (detection rate, mass and morphology) and ETG structure demonstrates the importance of cold gas as an independent probe of the evolution of these objects. Neutral hydrogen observations give us clues about the diversity of ETG assembly histories which are otherwise lost in the relative simplicity of their inner shape and kinematics. Our H I survey demonstrates that there are very diverse evolutionary paths for FRs, which include the formation of both gas-poor objects (undetected in H I or with very low M(H I)/M\u22c6) as well as galaxies with a considerable mass of H I spread over a large area (and therefore with low mean column density; see Paper XIII), but that this diversity is not re\ufb02ected in the structure of ETGs within the FR family. Furthermore, we \ufb01nd that SRs too can accrete cold gas during their life and that they do so at a similar rate as FRs. It is important to realise that SRs have a fundamentally different internal structure than FRs despite having similar H I properties (in a statistical sense). This means that the accretion of cold gas has not altered their structure, which remains characterized by a relatively round shape and low speci\ufb01c angular momentum within \u223c1 Re. In other words, gas accretion has not resulted in the growth of a signi\ufb01cant stellar disc component in the central galaxy region. The same might be true for FRs: the H I discs and rings in FRs do not need to be causally related to the stellar discs revealed by integral-\ufb01eld spectroscopy inside \u223c1 Re, although they might well be in at least some cases. To investigate this aspect in more detail we now turn to the study of the kinematical misalignment between H I and stars in these objects. 4 KINEMATICAL MISALIGNMENT BETWEEN H I AND STARS In order to study the kinematical misalignment between H I and stars we de\ufb01ne a sample made of all galaxies for which we can reliably measure the position angle (PA) of the H I kinematical major axis, PA(H I). This includes all galaxies in the D, R and d classes plus two objects hosting H I on an overall unsettled con\ufb01guration (u) but where some of the gas shows ordered rotation \u2013 NGC 1023 and NGC 4026. The total sample studied in this section includes therefore 36 ETGs. 4.1 Polar, corotating, counterrotating and warped H I Figure 4 shows H I images (from Paper XIII), H I velocity \ufb01elds (shown for the \ufb01rst time here) and stellar velocity \ufb01elds (already shown in Paper II) of all D, R and u objects in this sample (26 objects in total; the 10 galaxies classi\ufb01ed as d are analysed separately below). The \ufb01gure reveals a diversity of H I-stars misalignments, including corotating, polar and counterrotating gas distributions. In a number of cases the strong variation of PA(H I) with radius indicates the warping of the gas disc. More quantitatively, we derive PA(H I) as a function of radius from the H I velocity \ufb01eld using the KINEMETRY software (Krajnovi\u00b4 c et al. 2006). In order to maximize the radius out to which PA(H I) can be measured we lower the default minimum coverage of an ellipse with data points to 30 per cent. As we are only interested in the PA values this is an acceptable choice. We compare PA(H I) to the PA of the stellar kinematical major axis, PA(stars), which is given in Paper II. Before proceeding we highlight two aspects which should be kept in mind in order to interpret the results of this analysis correctly. First, while PA(H I) is a function of radius and can be measured sometimes out to tens of Re, PA(stars) is an average value measured over an aperture of typically \u223c1 Re (see Paper II for a detailed discussion). Therefore, we are not comparing the H I kinematics to the stellar kinematics at the same radius, but the c \u20dd2013 RAS, MNRAS 000, 1\u201318 8 Paolo Serra et al. 1.7 \u00d7 1019cm\u22122 NGC 1023 (u) \u00b1210 \u00b1210 2.6 \u00d7 1019cm\u22122 NGC 2594 (R) \u00b1150 \u00b1150 1.1 \u00d7 1019cm\u22122 NGC 2685 (D) \u00b1180 \u00b1180 2.3 \u00d7 1019cm\u22122 NGC 2764 (D) \u00b1150 \u00b1150 2.9 \u00d7 1019cm\u22122 NGC 2859 (R) \u00b1180 \u00b1180 4.1 (1.4) \u00d7 1019 cm\u22122 NGC 3414 (R) \u00b1130 \u00b1130 2.2 (2.3) \u00d7 1019 cm\u22122 NGC 3522 (R) \u00b1130 \u00b1130 3.7 \u00d7 1019cm\u22122 NGC 3619 (D) \u00b1150 \u00b1150 2.0 \u00d7 1019cm\u22122 NGC 3626 (D) \u00b1210 \u00b1210 3.7 \u00d7 1019cm\u22122 NGC 3838 (R) \u00b1170 \u00b1170 2.8 \u00d7 1019cm\u22122 NGC 3941 (R) \u00b1170 \u00b1170 3.2 \u00d7 1019cm\u22122 NGC 3945 (R) \u00b1260 \u00b1260 2.7 \u00d7 1019cm\u22122 NGC 3998 (D) \u00b1240 \u00b1240 2.6 \u00d7 1019cm\u22122 NGC 4026 (u) \u00b1200 \u00b1200 -V -V/2 0 +V/2 +V Figure 4. From top to bottom (three panels per galaxy), H I images (100\u00d7100 kpc2), H I velocity \ufb01elds (50\u00d750 kpc2) and stellar velocity \ufb01elds (10\u00d710 kpc2) of all D and R ETGs, plus the two u\u2019s showing some ordered rotation (NGC 1023 and NGC 4026). The grey scale-bar represents 5 kpc in all \ufb01gures. The black ellipses overlaid on all velocity \ufb01elds have semi-major axis equal to 3 Re and ellipticity taken from Paper II. The black arrow overlaid on the H I velocity \ufb01elds indicates the PA of the stellar kinematical major axis (receding side) from Paper II and scales with the size of the ellipse. In a few cases the stellar kinematical PA could not be determined reliably and no arrow is shown (see the text). For all velocity \ufb01elds the velocity range is indicated on the top-right. This is kept \ufb01xed for the stellar and H I velocity \ufb01eld of a same galaxy in order to enable a comparison of the relative line-of-sight rotation amplitude. The colour scheme of the velocity \ufb01elds is represented by the horizontal colour bar at the bottom of the \ufb01gure. H I kinematics (out to large radius) to the inner stellar kinematics. A comparison to the stellar kinematics at larger radius would require deeper optical spectroscopy over a larger \ufb01eld (e.g., Proctor et al. 2009; Weijmans et al. 2009; Arnold et al. 2011, 2013) or the study of planetary nebulae (e.g., Romanowsky et al. 2003; Coccato et al. 2009; Cortesi et al. 2013) or globular cluster kinematics (e.g., Kartha et al. 2013; Pota et al. 2013). A comparison between gas and stellar kinematics at a common, small radius is presented in Paper X using ionized and molecular gas data. Secondly, while PA(stars) is a well de\ufb01ned quantity for FRs, where it is typically constant within the observed \ufb01eld, its interpretation may be ambiguous in SRs, where the stellar kinematics is more complex or characterized by very low-level rotation. The SRs for which we can measure PA(H I) are NGC 3414, NGC 3522, NGC 5631 (all KDCs) and UGC 03960 (b\u22c6). In the case of NGC 3414 PA(stars) re\ufb02ects the kinematics of the region outside (and counterrotating relative to) the KDC. To obtain the PA of the KDC one would have to subtract 180 \u25e6from the value given in Paper II. On the contrary, in NGC 5631 PA(stars) represents the inner (i.e., the KDC\u2019s) stellar rotation. In NGC 3522 the error on PA(stars) is very large because of the overall low-level rotation. In this case we calculate the misalignment relative to the photometc \u20dd2013 RAS, MNRAS 000, 1\u201318 H I discs in fast and slow rotators 9 3.3 \u00d7 1019cm\u22122 NGC 4036 (R) \u00b1260 \u00b1260 2.9 \u00d7 1019cm\u22122 NGC 4203 (D) \u00b1140 \u00b1140 2.5 \u00d7 1019cm\u22122 NGC 4262 (R) \u00b1180 \u00b1180 1.1 (0.9) \u00d7 1019cm\u22122 NGC 4278 (D) \u00b1220 \u00b1220 3.6 \u00d7 1019cm\u22122 NGC 5103 (D) \u00b1120 \u00b1120 3.2 \u00d7 1019cm\u22122 NGC 5173 (D) \u00b170 \u00b170 2.0 \u00d7 1019cm\u22122 NGC 5582 (R) \u00b1210 \u00b1210 3.5 \u00d7 1019cm\u22122 NGC 5631 (D) \u00b1170 \u00b1170 3.6 \u00d7 1019cm\u22122 NGC 6798 (D) \u00b1190 \u00b1190 2.6 \u00d7 1019cm\u22122 UGC 03960 (D) \u00b1110 \u00b1110 2.4 \u00d7 1019cm\u22122 UGC 06176 (D) \u00b1140 \u00b1140 2.8 \u00d7 1019cm\u22122 UGC 09519 (D) \u00b1110 \u00b1110 -V -V/2 0 +V/2 +V Figure 4. Continued ric major axis, which coincides with the (uncertain) kinematical one. Similarly, PA(stars) is unconstrained in UGC 03960 and we adopt the photometric PA as a reference. Note that using the photometric rather than kinematical PA would make no difference for NGC 3414, while NGC 5631 is nearly round on the sky and kinematics is the only possible choice. In Fig. A1 we show PA(H I) \u2212PA(stars) as a function of radius for all 26 galaxies in this subsample. This \ufb01gure and Fig. 4 show that \u223c30 per cent of the systems host corotating H I (NGC 2859, NGC 3838, NGC 3945, NGC 4026, NGC 4036, NGC 4203, NGC 5582, UGC 06176), while counterrotating and polar H I distributions account each for \u223c10 per cent of the sample (NGC 3626, NGC 3941 and NGC 6798 in the \ufb01rst group, NGC 2594, NGC 3998 and NGC 4262 in the second). Note however that the observed misalignment of polar systems depends on viewing angle and it is likely that the H I is on a polar con\ufb01guration in a larger fraction of all ETGs (e.g., NGC 3619, NGC 5103 and UGC 09519). In most of the remaining systems the misalignment angle varies signi\ufb01cantly with radius, indicating the presence of a warp. In the two most extreme cases the H I changes from polar to corotating (NGC 2685) and from counterto corotating (NGC 5173) with increasing radius. The situation is somewhat different for ds. The H I in these objects is typically very faint and extends over only a couple of Westerbork beams. For this reason instead of using KINEMETRY we assume that PA(H I) does not vary with radius and determine its value by direct analysis of the H I cubes. Position-velocity diagrams along the adopted H I kinematical major axes are published in Paper XIII (their Fig. 5). We \ufb01nd that most (8/10) of the ds are corotating. The exceptions are one counterrotator (NGC 3032) and one polar system (NGC 3499), as discussed in that paper. Considering all 36 galaxies together we \ufb01nd therefore that in \u223c45 per cent of all ETGs with an H I disc or ring the gas (which can spread out to tens of Re) is corotating with the stars inside \u223c1 Re. c \u20dd2013 RAS, MNRAS 000, 1\u201318 10 Paolo Serra et al. These galaxies are all FRs where the gas accretion episode traced by the H I might be related to the formation of the stellar disc. They are in many respects similar to spiral galaxies as they host cold gas and stars corotating on the same disc \u2013 the only difference being the absence of bright, star-forming spiral arms owing to the low H I column density (Paper XIII). The remaining 55 per cent of this sample is composed of \u223c 10 per cent of counterrotating H I systems, \u223c10 per cent of polar objects, and \u223c35 per cent of ETGs with a complex, warped H I distribution, some of which may in fact be polar. The link between H I disc and stellar disc in these objects is less obvious. These results show that the existence of multiple kinematical sub-components in ETGs, well documented in their inner region for the stellar and ionized gas phases, holds also on much larger scales. Following our results on the fraction of ETGs with a kpcscale KDC (\u223c7 per cent including counterrotating cases; Paper II) and misaligned ionized-gas kinematics (\u223c36 per cent; Paper X; see also Bureau & Chung 2006) we are now \ufb01nding misaligned H I distributions on scales from a few to tens of kpc in \u223c12 per cent of all ETGs (\u223c15 per cent outside the Virgo cluster; for previous studies of smaller samples of ETGs with misaligned H I see, e.g., van Gorkom, Schechter & Kristian 1987; Bertola, Buson & Zeilinger 1992; Bettoni et al. 2001). Whether or not associated with the presence of a stellar disc, the H I detected in ETGs provides important clues on the origin of the cold interstellar medium detected in the inner region of these objects in the form of ionized and molecular gas. This is clear in Fig. A1, where we show at R = 0 the data point corresponding to the ionized gas kinematics (when detected), which was already found to be invariably aligned with the CO kinematics (Paper X). The \ufb01gure con\ufb01rms previous claims that H I, H2 and ionized gas share the same kinematics in the region where they overlap (Morganti et al. 2006; Paper X). The few exceptions are NGC 1023, NGC 3414, NGC 4278, NGC 5103 and NGC 5631. The \ufb01rst hosts an unsettled gas distribution with very complex gas kinematics, and it is unlikely that the central value of PA(H I) derived from the velocity \ufb01eld is representative of the actual inner gas motion. Furthermore, Morganti et al. (2006) show that in both NGC 3414 and NGC 4278 the ionized gas velocity \ufb01eld twists in such a way that the outer ionized gas kinematics is aligned with the inner H I kinematics. The same occurs in NGC 5631. Therefore, these three galaxies conform to the general rule too. We do not have a good explanation for the misalignment between H I and ionized gas in NGC 5103, which represents the only genuine exception to the rule. Not shown in Fig. A1, d galaxies contribute to strengthening this result. The H I is always corotating with the CO and ionized gas, including the two cases where the H I is misaligned relative to the stars (NGC 3032 and NGC 3499). 4.2 Misalignment in fast and slow rotators Figure 5 summarizes our \ufb01ndings by showing all H I misalignments on the M(H I)/M\u22c6versus \u03bbR/(0.31 \u221a\u03f5) plane of Fig. 2. For each galaxy we adopt here the median misalignment value measured from the radial pro\ufb01le shown in Fig. A1. The median value is a fair representation of the overall misalignment for all galaxies except the heavily warped NGC 2685 and NGC 5173, which we highlight in the \ufb01gure. On the one hand Fig. 5 shows a signi\ufb01cant population of FRs where H I and stars are kinematically aligned (dark blue symbols, with the just mentioned exception of NGC 2685 and NGC 5173). In these galaxies gas and stars are just two different but coupled components of the same disc. On the other hand, as already emphasized above, the H I discs and rings detected in FRs are not always associated with the inner stellar disc, not even for the \ufb02attest and fastest rotators (see for example NGC 3626, NGC 5103 and UGC 09519). In many FRs the large scale H I kinematics is obviously not a continuation of the inner stellar kinematics to larger radius. On the contrary, counterrotating and polar H I distributions account for exactly 1/4 of all FRs analysed in this section, while another 1/4 consists of warped discs. The detected H I is therefore aligned with the inner stellar disc only in half of the cases. Neutral hydrogen observations show therefore that FRs, while being a dynamically simple and homogeneous family inside \u223c1 Re, are much more complex and diverse in their outer regions, in agreement with results obtained using other kinematical tracers at large radius (e.g., Coccato et al. 2009; Pota et al. 2013). The other clear result is that in none of the four SRs the H I kinematics is aligned with the stellar kinematics or morphology. In fact, all these systems exhibit a (close to) polar H I distribution, although PA(H I) typically varies with radius (Fig. A1). We also note that the H I morphology of these systems, although discor ring-like, appears disturbed (Fig. 4), with some cases intermediate between a D/R and a u classi\ufb01cation. The lack of very regular, settled H I discs/rings in SRs and the prevalence of polar systems may be the only difference from the FR family (H I-wise), although even among FRs many gas discs and rings appear disturbed or not perfectly settled (e.g., NGC 2764, NGC 3998, NGC 4203, NGC 4278, NGC 5103). A larger sample of H I-rich SRs would be needed to con\ufb01rm this indication. The above results, together with the established weak relation between M(H I) and ETG luminosity (e.g., Knapp, Turner & Cunniffe 1985; Wardle & Knapp 1986; Paper XIII), con\ufb01rm the severe disconnect between ETG H I properties and their stellar component. They show, as argued in Sec. 3.4, that H I provides clues about the complex evolution of ETGs which would go unnoticed using only other observables. Con\ufb01rming this complexity, we also \ufb01nd that the H I kinematical misalignment does not depend in any clear way on ETG stellar mass, environment density (quanti\ufb01ed in Paper VII) or H I mass. For example among the very H I-rich galaxies in poor environments we \ufb01nd NGC 5582 (corotating R), NGC 6798 (counterrotating D) and UGC 09519 (warped D). Low-mass, isolated galaxies include NGC 2594 (polar R), UGC 06176 (aligned D) and again UGC 09519. Among the massive ETGs we \ufb01nd relatively small, aligned H I discs/rings as in NGC 2859 and NGC 4036 but also (close to) polar H I as in NGC 3414 and NGC 5631, and the warped D NGC 4278. The only exception is that the lowest-M(H I) systems are all ds (Paper XIII) and, as illustrated above, mostly kinematically aligned to the stellar rotation. There is of course some dependence of H I properties on ETG mass and environment across the entire ATLAS3D sample. This is discussed in detail in Paper XIII, where we show that unsettled H I distributions become more common, and the typical H I mass decreases, as environment density and galaxy mass increase. Here we \ufb01nd that there is no additional trend with environment and stellar mass when studying the kinematical misalignment of settled H I discs. Ever since the work of Knapp, Turner & Cunniffe (1985) this decoupling between stars and H I in ETGs has been attributed to the external origin of the H I. The main point of this interpretation is that most of the present-day gas must be accreted once the formation of the (inner region of the) host ETG is basically complete. The accreted gas could come from the intergalactic medium or be brought in by small gas-rich satellites which individually do not contribute signi\ufb01cantly to the stellar mass of the ETG but may bring a signi\ufb01cant addition to its interstellar medium. In fact, even c \u20dd2013 RAS, MNRAS 000, 1\u201318 H I discs in fast and slow rotators 11 N2685 N5173 0 1 2 3 4 5 \u03bbRe/(0.31\u221a\u03f5Re) \u22124 \u22123 \u22122 \u22121 log10 M(H\u0131)/M\u22c6 N1023 N2764 N3619 N3626 N3998 N4203 N4278 N5103 N5631 N6798 U03960 U06176 U09519 N2594 N2859 N3414 N3522 N3838 N3941 N3945 N4026 N4036 N4262 N5582 N2824 N3032 N3182 N3489 N3499 N4150 N4710 N5422 N5866 U05408 H\u0131 class undet. D R d u c 0 45 90 135 180 H\u0131-star misalignment (deg) Figure 5. H I kinematical misalignment on the M(H I)/M\u22c6versus \u03bbR/(0.31 \u221a\u03f5) plane. This \ufb01gure is the same as Fig. 2 but here we highlight only the 36 galaxies for which we are able to study the H I kinematical misalignment (see Sec. 4 for details on this subsample; the remaining galaxies are shown with light grey markers). We colour-code them according to the median misalignment angle calculated over the full radial extent of the H I disc or ring. See Fig. A1 for the variation of the misalignment angle as a function of radius in individual galaxies. Note that NGC 2685 and NGC 5173, the two most heavily warped H I systems in the sample, have a small median misalignment angle which is not representative of their true complexity. For this reason we highlight them here with a red box. when gas is acquired at the same time as the formation of the stellar body, e.g. in gas-rich major mergers, there does not need to be a strong coupling between the stellar body of the remnant and the larger-scale H I distribution. Merging and accretion events are expected to occur in a \u039bCDM Universe, where galaxies grow hierarchically, and our results may be seen as a con\ufb01rmation of these theories. Qualitative statements of this kind have been made by previous authors and, at this stage, do not represent an advancement in our understanding of ETG formation. For this reason we attempt to take a step forward and perform a quantitative comparison to galaxy formation simulations in the next section. 5 COMPARISON TO COSMOLOGICAL SIMULATIONS We compare ETGs in the ATLAS3D sample to galaxies formed in two sets of hydrodynamical simulations performed by Oser et al. (2010) and Hirschmann et al. (2013). These are high-resolution re-simulations of \u223c50 dark-matter haloes extracted from a large, \u039bCDM, dark-matter-only simulation. In each re-simulation baryonic processes such as hydrogen and helium cooling, star formation and supernova feedback are implemented in the presence of a uniform UV background. The two sets of simulations have different implementations of supernova feedback. In the \ufb01rst set the feedback is purely thermal (hereafter, NoW simulations because they do not include galactic stellar winds). These are the simulations analysed by Paper XXV to study the generic formation paths of SRs and FRs in a cosmological context. Simulations in the second set start from identical initial conditions but include an additional empirical model for galactic out\ufb02ows driven by winds from starforming regions (Oppenheimer & Dav\u00b4 e 2006; we will refer to these as W simulations). All details on the galactic wind implementation and a comparison of galaxy properties between the two models are presented in Hirschmann et al. (2013). Here we study for the \ufb01rst c \u20dd2013 RAS, MNRAS 000, 1\u201318 12 Paolo Serra et al. time the distribution and kinematics of cold gas in the simulations. As we will show, these two sets give profoundly different predictions for galaxies\u2019 H I properties. We refer to Oser et al. (2010) and Hirschmann et al. (2013) for a full description of the simulations. For the purpose of this work it is important to \ufb01rst investigate whether the simulated galaxies are a reasonable match to the ETGs we want to compare them to. On the one hand, they cover the same M\u22c6range (from \u223c1010 to a few times 1011 M\u2299). Furthermore, the NoW simulations are in reasonable agreement with the observed mass-size relation of ETGs (Oser et al. 2012) and exhibit a diversity of stellar kinematical properties similar to that of real ETGs (Paper XXV). On the other hand, not all simulated galaxies, in particular the W sample, would necessarily meet the morphological selection of the ATLAS3D sample, which requires the absence of large-scale spiral arms in a galaxy optical image (Paper I). This is essentially a selection against strong star-formation on a disc while about half of all simulated galaxies have relatively large speci\ufb01c star formation rate (> 10\u221211 yr\u22121) at z = 0. Similar values are measured in only a handful of the observed ETGs (Davis et al., submitted). We note however that the uncertainty on the simulated star formation rate is large because of uncertainties in, e.g., star formation and feedback physics and their actual implementation. Additionally, neither of the simulated samples include AGNs, which could be an ef\ufb01cient way to suppress star formation. Therefore, we decide not to exclude star-forming galaxies from the comparison. Instead, we highlight this as a caveat of this work and stress that more sophisticated simulations would be needed to fully replicate the ATLAS3D selection. The simulations do not include a full treatment of different gas phases and the correspondence between simulated gas particles and H I is not obvious. As a \ufb01rst step we de\ufb01ne cold gas following the criterion of Hirschmann et al. (2012), which is based on a selection of gas particles on the density-temperature plane. This is preferred to a simple temperature selection since dense star-forming gas (which we want to include in the cold-gas budget) can be relatively hot in the NoW simulations. Additionally, we assume that this cold gas is made of two phases, atomic and molecular (ignoring that some of it may in fact be ionized). We separate the two phases on the gas\u2019 face-on view by applying equation 39 of Krumholz, McKee & Tumlinson (2009). In their equation s is the H I+H2 column density in M\u2299pc\u22122 (see Schruba et al. 2011 for a comparison between this theoretical relation and observations). This results in a relatively sharp transition from an atomicto a molecular dominated regime at a total gas column density of \u223c10 M\u2299pc\u22122 (Wong & Blitz 2002; Bigiel et al. 2008). The resulting face-on H I images are used to calculate H I mass and column density distribution for all simulated galaxies (at the typical gas resolution of \u22720.5 kpc). In order to study the morphology and kinematics of the H I we construct seven different projections of each simulated galaxy relative to an hypothetical observer: face on (relative to the stellar kinematics); rotated by 30, 60 and 90 \u25e6, respectively, about the stellar morphological major axis in the face-on view; and rotated by 30, 60 and 90 \u25e6, respectively, about the stellar morphological minor axis in the face-on view. When constructing these projections we do not separate H I from H2 as Krumholz\u2019s prescription is strictly valid only when the gas is seen face-on. This does not affect our conclusions since we are mainly concerned with the kinematics of the gas, which is the same for all cold-gas phases. All gas mass and surface density calculations as well the analysis of the H I and stellar kinematics presented below are performed after removal of star and gas particles associated with satellite darkmatter sub-haloes according to the SUBFIND algorithm of Springel, Yoshida & White (2001). Furthermore, we exclude from the calcu9.5 10.0 10.5 11.0 11.5 12.0 log10 M\u22c6(M\u2299) \u22124 \u22123 \u22122 \u22121 0 log10 M(H i)/M\u22c6 NoW simulations W simulations spiral M(H i)/M\u22c6 histogram H i undetected ETGs H i detected ETGs Figure 6. M(H I)/M\u22c6plotted against M\u22c6for simulated galaxies (black circles and crosses) and real ETGs from Paper XIII. For the latter, the blue area shows the kernel density estimate derived using all 53 galaxies with detected H I while the red dots indicate H I non-detections and are therefore upper limits on M(H I)/M\u22c6. The dotted histogram along the vertical axis represents the M(H I)/M\u22c6distribution of spiral galaxies derived as explained in the text. lation of gas mass and surface density the discrete cold gas clouds which are a known artefact of smoothed-particle-hydrodynamics simulations and which are not part of the gas discs we wish to study (Sijacki et al. 2012). These clouds, visible in some of the images discussed in Sec. 5.1, have a typical mass above 107 M\u2299 and may therefore have a signi\ufb01cant impact on the value of M(H I) if included in the calculation. Before showing the result of the comparison between simulated and real ETGs we note that the ATLAS3D sample is volume limited and complete down to MK = \u221221.5 mag (Paper I). On the contrary, the sample of simulated galaxies is not volume limited (it is a set of individual simulations rather than a single, large simulated volume) and does not follow the observed galaxy luminosity function. Therefore, we cannot compare the statistical distribution of real and simulated galaxy properties. Instead, we investigate whether the diversity of ETG H I properties is reproduced by the simulations. 5.1 H I mass and morphology The \ufb01rst step of our comparison is presented in Fig. 6, where we plot M(H I)/M\u22c6against M\u22c6for galaxies in the two sets of simulations. Stellar mass values are taken from Paper XXV for the NoW simulations and are measured in an identical way for the W simulations. For comparison we show the distribution of real ETGs distinguishing between H I detections (blue density \ufb01eld) and non-detections (red dots). We also show the M(H I)/M\u22c6histogram of spiral galaxies. This is obtained from the M(H I)/LK histogram shown in Paper XIII assuming that for M\u22c6> 1010 M\u2299the typical spiral has M\u22c6/LK = 0.8 M\u2299/L\u2299(Bell et al. 2003). The \ufb01gure shows that the NoW simulations produce galaxies whose H I content is to \ufb01rst order comparable to that of real ETGs and lower than that of spirals. The main discrepancy between NoW simulated and real ETGs is that extremely gas-poor galaxies with M(H I)/M\u22c6below a few times 10\u22124 are underreprec \u20dd2013 RAS, MNRAS 000, 1\u201318 H I discs in fast and slow rotators 13 3.0 \u00d7 1019 cm\u22122 \u00b1280 \u00b170 3.0 \u00d7 1019 cm\u22122 \u00b1250 \u00b150 3.0 \u00d7 1019 cm\u22122 \u00b1210 \u00b150 3.0 \u00d7 1019 cm\u22122 \u00b1330 \u00b1170 3.0 \u00d7 1019 cm\u22122 \u00b1310 \u00b150 3.0 \u00d7 1019 cm\u22122 \u00b1260 \u00b1100 velocity \ufb01eld stars velocity \ufb01eld gas gas overlay stars M0163 (NoW) M0163 (W) M0190 (NoW) M0190 (W) M0329 (NoW) M0329 (W) -V -V/2 0 +V/2 +V Figure 7. Three examples of simulated galaxies. For each galaxy we show the result of the NoW and the W simulation next to each other to highlight their differences. Each column represents one simulated object \u2013 four rows per galaxy \u2013 viewed at an inclination of 60 \u25e6. The \ufb01rst row corresponds to an extremely deep optical image (\u223c29 mag arcsec\u22122 in V band). The remaining rows are equivalent to those shown in Fig. 4 for real ETGs. Namely, the second row corresponds to a SDSS-like optical image with H I contours overlaid; the third row shows the intensity-weighted H I velocity \ufb01eld; the last row shows the intensity-weighted stellar velocity \ufb01eld. The linear scale of the various panels is the same as in Fig. 4, with the grey scale-bar representing 5 kpc. Galaxies are sorted according to decreasing dark-matter halo mass (left to right). The outer stellar isophote corresponds to a stellar mass surface density of 500 M\u2299pc\u22122. The colour scheme of the velocity \ufb01elds is represented by the horizontal colour bar at the bottom of the \ufb01gure. sented in the simulations. This results in an overall smaller range of M(H I)/M\u22c6at any given M\u22c6compared to the observations. Nevertheless, both the fact that such range is large in the simulations and that the typical M(H I)/M\u22c6decreases with M\u22c6(above a stellar mass of \u223c5 \u00d7 1010 M\u2299) are important points of agreement with the observed ETG sample. The situation is different for the W simulations. These galaxies are typically gas-richer than NoW ones (Hirschmann et al. 2013). They populate the high-M(H I)/M\u22c6end of the observed ETG distribution. At M\u22c6> 1011 M\u2299we \ufb01nd a number of objects whose H I content is too large by a factor of 10 to 100 compared to the data. We conclude that W systems are, as a family, too H I rich and that NoW galaxies are a better (albeit not perfect) match to real ETGs in terms of H I mass. Having established this we can now analyse the H I morphology of the simulated galaxies. We show three examples in Fig. 7 and another three in Fig. 8. For each galaxy we show the NoW and the W simulation next to each other. These images and velocity \ufb01elds are immediately comparable to those in Fig. 4 and are drawn adopting the same linear scale and gas contour levels. The only difference between observed and simulated galaxy \ufb01gures is that for the latter we also show the equivalent of a deep optical image (top panel, see \ufb01gure caption). Figures 7 and 8 are meant to show a few cases representative of the diversity of galaxies produced by the simulations as well as the difference between the NoW and W simulation for a same halo. Indeed, it is immediately obvious that changing the star formation feedback implementation has a strong impact on the properties of a simulated galaxy. The same object can be a FR in the NoW simulation and a SR in the W one (M0163) or vice versa (M0190, M0329). Furthermore, it can be surrounded by a large gas distribution in the W simulation but have the gas disc entirely con\ufb01ned inside the stellar body in the NoW simulation (e.g., M0190, M0721). In fact, the larger size of the H I distribution in the W simulations is a general result valid for all galaxies and a consequence of the mechanical nature of the W feedback, which pushes gas to large radius while keeping it cold. A visual comparison between Fig. 4 and Figs. 7 and 8 shows that these large W gas discs match reasonably well the size of the H I discs and rings in gas-rich ETGs. They too, like the observed systems, exhibit slight warps in the outer regions, possibly owing to their large size. The NoW gas distributions are on the contrary too small. The fact that the NoW simulations are a better match to the observed ETG M(H I) distribution (Fig. 6) but that W objects are a better match to the observed size of the H I discs may seem contradictory. In fact, this is easily understood noting that in all simuc \u20dd2013 RAS, MNRAS 000, 1\u201318 14 Paolo Serra et al. 3.0 \u00d7 1019 cm\u22122 \u00b1230 \u00b170 3.0 \u00d7 1019 cm\u22122 \u00b1170 \u00b1170 3.0 \u00d7 1019 cm\u22122 \u00b1240 \u00b190 3.0 \u00d7 1019 cm\u22122 \u00b1230 \u00b150 3.0 \u00d7 1019 cm\u22122 \u00b1240 \u00b1100 3.0 \u00d7 1019 cm\u22122 \u00b1190 \u00b1130 velocity \ufb01eld stars velocity \ufb01eld gas gas overlay stars M0549 (NoW) M0549 (W) M0721 (NoW) M0721 (W) M1196 (NoW) M1196 (W) -V -V/2 0 +V/2 +V Figure 8. Three more examples of simulated galaxies. See caption of Fig. 7. lations the H I column density is on average higher than observed. For this reason H I discs with the right mass are too small (NoW) and H I discs with the right size are too massive (W). This result, which is clear from a comparison of the H I contours in Fig. 4 with those in Figs. 7 and 8, is shown more quantitatively in Fig. 9. In this \ufb01gure the black lines represent the H I column density distribution in simulated galaxies while the red solid line shows the distribution in real galaxies (represented by the best-\ufb01tting Schechter function derived in Paper XIII). This mismatch is consistent with the fact that simulated galaxies appear to be forming stars at a rate higher than real ETGs at z = 0 (Hirschmann et al. 2013). Although not the focus of this study, it is worth noting in this context that all simulated galaxies host cold gas above a column density of 1021 cm\u22122. This gas, which we do not include in our calculation of H I mass and column density, is more centrally concentrated than the H I and can be related to the molecular gas found in the central region of ETGs (Paper IV). Its mass is typically between 5\u00d7107 and 5\u00d7109 M\u2299with a handful of exceptions at lower mass and no signi\ufb01cant difference between NoW and W simulations. Both sets of simulations miss therefore the large population of ETGs with M(H2) < 5 \u00d7 107 M\u2299reported in Paper IV while on the gas-rich side of the distribution the molecular gas masses are in reasonable agreement with the observations. We \ufb01nd that the molecular-to-total cold-gas fraction is larger in the NoW than in the W simulations. This is a consequence of their higher average coldgas column density coupled with our method for separating atomic from molecular gas. 5.2 H I discs and misalignment in simulated fast and slow rotators Figures 7 and 8 show that not only the H I mass and morphology but also the gas kinematical misalignment is affected by the feedback implementation. For example, M0549 hosts a small counterrotating gas disc in the NoW simulation and a large, corotating one in the W simulation; M0721 hosts a small corotating disc in the NoW simulation and a very large, counterrotating one in the W simulation. This kind of difference between the H I-misalignment of NoW and W galaxies is very common within the sample of simulations analysed here. It is caused by the cumulative effect of galactic stellar winds on a galaxy and the satellites which it accretes as the simulation progresses. Taken together, the NoW and the W simulations seem to reproduce qualitatively the large variety of gas morphologies and kinematics of real H I-rich ETGs. In this sense it is useful to associate some of the examples in Figs. 7 and 8 to ETGs in the ATLAS3D sample. Bearing in mind that these matches are not exact and may not hold at a more quantitative level (as we illustrate below), M0163-NoW is for example a FR with a small polar gas disc which may be related to NGC 3499. M0163-W, a bright SR with a polar gas disc slightly larger than the stellar body, could be compared to NGC 3414. M0549-NoW hosts a small, counterrotating gas disc similar to NGC 3032. M1196-NoW and many W galaxies (e.g., M0190, M1196) represent cases of large, corotating H I discs around FRs (similar for example to NGC 5582 and NGC 3838). M0329-W exhibits an H I warp and tails comparable to those of NGC 4278. Counterrotating gas discs around FRs (e.g., NGC 6798) c \u20dd2013 RAS, MNRAS 000, 1\u201318 H I discs in fast and slow rotators 15 19.5 20.0 20.5 21.0 log10 N(H i) (cm\u22122) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 normalised histogram NoW simulations W simulations H i-rich ETGs Figure 9. H I column density distribution in the simulations compared to that in real ETGs. The latter is represented by the best-\ufb01tting Schechter function derived in Paper XIII. For both NoW and W simulations we plot the median of the normalized distributions of all individual galaxies. The distributions are obtained for the cold-gas face-on view. Both median distributions and the Schechter function are scaled to intersect at N(H I) \u223c1020 cm\u22122. The peak at (and sharp drop after) N(H I) = 1021 cm\u22122 is due to our de\ufb01nition of H I in the simulations (see the text). This effect is more pronounced in the NoW case because the distribution of total gas surface density extends to larger values than in the W simulations. can be associated with M0721-W. The same galaxy simulated with the NoW feedback shows a small, corotating gas disc similar to the vast majority of the d ETGs (e.g., NGC 4710, NGC 4150). This diversity is similar to the observed one and includes also some cases of unsettled H I distributions, as observed (Paper XIII). Yet, the match between simulations and observations is far from perfect. In addition to the points of friction mentioned above with respect to mass and column density distributions, the ATLAS3D sample includes H I-rich ETGs not represented in the simulations such as SRs (NGC 3522) and FRs (NGC 2594, NGC 3998) with large polar rings. Furthermore, some simulated systems seem to have no corresponding real galaxy, such as the SRs with small, aligned gas discs (e.g., M0329-NoW). These objects may however be related to the SRs with aligned ionized-gas discs discussed in Paper X. This, together with the lack of central H I depressions (or narrow H I rings) in the simulations, is a reminder that a more sophisticated treatment of gas physics may be needed in order to relate simulated to real galaxies. We conclude this section by comparing simulated and observed misalignments on the M(H I)/M\u22c6versus \u03bbR/(0.31 \u221a\u03f5) diagram. The complexity of the observed ETG H I properties is summarized in Fig. 5. That \ufb01gure highlights that H I discs around FRs are very diverse in terms of their kinematical misalignments from the stars. Furthermore, it shows that SRs too can host an H I disc or ring and that this is typically polar relative to the stars. To investigate whether a similar picture emerges from the simulations we construct a \ufb01gure equivalent to Fig. 5. The basis of this analysis is the simulated stellar and cold-gas velocity \ufb01elds represented by the examples in Figs. 7 and 8, which are obtained on a projection such that the inclination of the stellar body is 60 \u25e6. Measurements of PA(stars) are straightforward as nearly all simulated galaxies have their kinematical major axis aligned along the X-axis. In order to measure PA(H I) as a function of radius we make use of the ROTCUR task part of the GIPSY package (van der Hulst et al. 1992). This task \ufb01ts tilted-ring models to a velocity \ufb01eld and is equivalent to the software used for the analysis of real galaxies (see Sec. 4). In this case we \ufb01x the centre of the rings to the stellar centre of mass and the H I systemic velocity to the stellar value. We then solve for PA(H I), inclination and rotation velocity of all rings. In what follows we analyse PA(H I) only. We summarize the result of this analysis in Fig. 10, where the values of \u03bbR and \u03f5 are measured on the edge-on projection. These values are taken from Paper XXV for the NoW galaxies and are measured in the same way for the W objects. Galaxies with an H I radius smaller than 3 Re are shown as diamonds. Values of Re are also taken from Paper XXV and measured in the same way for the W models. The \ufb01gure shows that, as discussed above, the simulations are able to make H I discs around both FRs and SRs, in agreement with the result of Sec. 3. As noted above, it is also important that in some of these objects the H I is misaligned (e.g., polar or counterrotating) relative to the stellar kinematics. However, the similarities between simulated and real ETGs on this diagram do not go much further than these qualitative statements. A \ufb01rst obvious difference is that, compared to Fig. 5, the vast majority of both W and NoW FRs host H I on an aligned con\ufb01guration. There are a few exceptions including some of the FRs in Figs. 7 and 8: M0163-NoW (polar) M0549-NoW (counterrotating) and M0721-W (counterrotating). However, strongly misaligned systems are con\ufb01ned to much lower levels of stellar rotation and gas content compared to some of the observed H I counterrotators (NGC 3626, NGC 3941, NGC 5103 and NGC 6798) and polar rings (NGC 2594, NGC 3998). In the W simulations the only misaligned FRs lay, in fact, close to the empirical boundary between FRs and SRs. The kinematical alignment between H I and stars in all the other, fasterrotating simulated galaxies makes them more similar to spirals than to real FRs as a family. Such stronger coupling between gas and stars compared to real ETGs may be related to the larger gas surface density and star formation rate in the simulations, as highlighted in Sec. 5.1. Rewinding the simulations reveals that the rare cases of large H I misalignment in FRs at z = 0 are usually the result of very recent events. For example, M0721-W (Fig. 8) spends most of its life as a FR with aligned H I, until a merger with a relatively small but very gas-rich satellite at z \u223c0.3 turns it into an H I counterrotator. The H I tail in Fig. 8 is a remnant of that event. Another example is M0549-NoW (also in Fig. 8). This system is surrounded by a large, warped gas disc for a large fraction of its life. Gas in the inner part of the disc is kinematically aligned with the inner stellar rotation except for some short intervals where it appears to be close to polar. The gas disc mass and size decrease as the galaxy evolves and by z \u223c0.1 the disc is so small that a relatively minor gas accretion event results in the current counterrotating H I disc. Similarly, the FR M0163-NoW (Fig. 7) has been hosting a polar gas disc only for the last \u223c2 Gyr, and in the past has been both a gas coand counterrotator. Given that the H I orbital time in ATLAS3D galaxies is at most \u223c1 Gyr it is possible that the ETGs with misaligned H I have acquired their gas relatively recently. On the contrary, FRs with an aligned (although frequently warped) gas disc at z = 0 have typically been in such a con\ufb01guration for most of their life, with occasional periods of time during which the gas is unsettled following a merger. This is true for \u223c80 per cent of all NoW FRs and \u223c70 per cent of all W FRs. Note that such a persistent alignment between stellar and gas kinematics is not the result of a lack of satellite accretion. On the contrary, these objects experience continuous merging (depending on their c \u20dd2013 RAS, MNRAS 000, 1\u201318 16 Paolo Serra et al. 0 1 2 3 4 5 \u03bbRe/(0.31p\u270fRe) \u22124 \u22123 \u22122 \u22121 log10 M(H\u0131)/M? NoW simulations 0 45 90 135 180 H\u0131-star misalignment (deg) 0 1 2 3 4 5 \u03bbRe/(0.31p\u270fRe) \u22124 \u22123 \u22122 \u22121 log10 M(H\u0131)/M? W simulations 0 45 90 135 180 H\u0131-star misalignment (deg) Figure 10. H I kinematical misalignment of the simulated galaxies on the M(H I)/M\u22c6versus \u03bbR/(0.31 \u221a\u03f5) diagram. We show NoW simulations in the left-hand panel and W simulations in the right-hand panel. The small grey crosses indicate simulations where the gas is not settled and therefore we do not measure the misalignment angle. See the caption of Fig. 5 for more details on the \ufb01gure. Note that we show these \ufb01gures with the same axes limits as in Fig. 5 to facilitate the comparison between simulated and real galaxies. halo mass), but their gas disc is probably suf\ufb01ciently massive at all times to prevent signi\ufb01cant misalignments from developing. We do not investigate this aspect in more detail since our focus here is the comparison to observed ETGs at z = 0 and not so much a detailed study of why simulated galaxies look the way they do. Slightly different paths for the formation of an aligned FR are possible (although less frequent) in the simulations. For example, M0721-NoW is a SR with very low-level rotation and a counterrotating gas disc at z \u223c1. This gas lives relatively undisturbed for the next \u223c2 Gyr and during this time forms a number of new stars suf\ufb01cient to change the direction of net rotation of the stellar body and to turn the object into a FR. So this is a case where rather than the gas disc changing its kinematics following gas accretion, it is the stellar body that changes its kinematics following star formation. Whether such evolutionary paths occur also in the real Universe remains to be established. The other, already mentioned difference between Figs. 5 and 10 is the existence of simulated gas-rich SRs where the H I is coor counterrotating relative to the stars. These SRs have no counterpart in the ATLAS3D H I sample but may be related to the ionized-gas SR corotators of Paper X. Rewinding the simulations reveals that many of the SRs with a small corotating disc at z = 0 used to have a polar disc (or sometimes a counterrotating one), which has settled only recently on an aligned con\ufb01guration. As noted above for the misaligned FRs, the H I kinematical misalignment can change very frequently in the simulations, mostly following merging with satellites. Polar gas distributions like the observed ones are found too (e.g., M0163) but they are not the rule. Their history too includes frequent changes of the kinematical misalignment as a result of mergers. The comparison presented in this section indicates that simulations are only partially successful at reproducing the observed H I properties of ETGs. A careful treatment of gas physics is essential and it appears that a better match to the observations needs to be achieved before \u039bCDM simulations can teach us why and how ETGs evolve into the diverse (H I-wise) family they are today. 6 SUMMARY In a previous ATLAS3D paper (Paper XIII) we demonstrate on a strong statistical basis that a large fraction of all ETGs outside the cluster environment host a signi\ufb01cant mass of H I gas. In particular, 1/4 of all ETGs outside the Virgo cluster host a disc or ring of low-column-density H I with size from a few to tens of kpc, and mass from \u223c107 to a few times 109 M\u2299. Here we investigate the link between the H I properties (mass and morphology) of these galaxies and their internal structure. The latter is determined on the basis of galaxies\u2019 optical morphology and stellar kinematics, leading to their classi\ufb01cation as SRs or FRs. Furthermore, we study the kinematical misalignment between H I (out to large radius) and stars (inside \u223c1 Re) in both these groups, and compare for the \ufb01rst time the H I properties of SRs and FRs to predictions from \u039bCDM hydrodynamical simulations. We \ufb01nd a large diversity of H I masses and morphologies within both the FR and SR families. Surprisingly, SRs are detected as often, host as much H I and have a similar rate of H I discs and rings as FRs. The only tentative difference between the two families is that the H I discs/rings around SRs are usually not fully settled. This comparison is mostly limited by the small number of SRs in our sample (simply because these galaxies amount to just \u223c15 per cent of the total ETG population) and a larger SR sample would be needed to improve the accuracy of some of the above conclusions. Nevertheless, our data imply that SRs can accrete a signi\ufb01cant mass of cold gas during their life, and that they may do so at a rate similar to that of FRs. This is con\ufb01rmed by the frequent detection of cold dust (Smith et al. 2012), kinematically-misaligned ionized gas (Paper X) and cuspy nuclear light pro\ufb01les (Paper XXIII) in SRs c \u20dd2013 RAS, MNRAS 000, 1\u201318 H I discs in fast and slow rotators 17 as well by simulations, which indicate that at least some SRs may have formed during gas-rich mergers (Paper VI; Paper XXV). The high detection rate of H I discs/rings in galaxies with little or no evidence of an embedded stellar disc \u2013 the SRs \u2013 indicates that the accretion of H I is not always linked to the growth of an inner stellar disc. Such weak relation between H I and stellar disc is con\ufb01rmed by the fact that in galaxies with a signi\ufb01cant stellar disc component \u2013 the FRs \u2013 the H I does not always corotate with the stars. On the contrary, we \ufb01nd corotation in just about half of all FRs with an H I disc or ring. The remaining FRs exhibit a variety of kinematical misalignments including cases of polar and counterrotating gas. The family of FRs appears therefore signi\ufb01cantly more complex and diverse at large radius than in the inner regions, as concluded also using other kinematical tracers (e.g., Coccato et al. 2009; Pota et al. 2013). The H I misalignments reveal another possible difference between FRs and SRs: in the latter the H I disc/ring is always polar (or nearly so) relative to the stars. We do not \ufb01nd any SR with a coor counterrotating H I disc or ring, although we note that such gaseous discs are detected at smaller radius in the ionized gas phase (Paper X). In Paper XIII we show that the ETG H I mass and morphology depend to some extent on galaxy stellar mass and environment density. Here we \ufb01nd no additional trends as the H I kinematical misalignment does not seem to be related to the host stellar mass or environment in any obvious way. This complex picture highlights a diversity of ETG formation histories which may be lost in the relative simplicity of their inner structure. We \ufb01nd that \u039bCDM hydrodynamical simulations (both with and without galactic stellar winds) have dif\ufb01culties reproducing the H I properties of ETGs. We develop a simple method to de\ufb01ne H I in the simulations of Oser et al. (2010) and Hirschmann et al. (2013), and \ufb01nd some clear inconsistencies with the observations. The decline of the H I column density distribution is too shallow, resulting in an average density which is larger than in real ETGs. This causes gas discs with an H I mass comparable to the observations to be too small, while discs whose size is suf\ufb01ciently large are too massive. Furthermore, none of the simulations is able to produce the many gas-poor ETGs present in the observed sample. Consistent with the observations, H I discs are found in both simulated FRs and SRs. However, their kinematical misalignment from the stars match the observations only qualitatively. On the one hand, nearly all simulated FRs host corotating H I. The few cases with polar or counterrotating gas exhibit very low levels of stellar rotation (unlike real ETGs). On the other hand, a large fraction of the simulated SRs host corotating H I while none hosts a large, (nearly) polar H I disc as in real SRs. We suggest that a more sophisticated treatment of gas physics and a better understanding of the corresponding feedback processes is needed in the simulations, and we conclude that a better match between observed and simulated galaxies should be achieved before cosmological simulations can be used to understand the origin of the complex H I properties of ETGs. ACKNOWLEDGMENTS PS acknowledges support of a NWO/Veni grant. This work is based on observations obtained with the Westerbork Synthesis Radio Telescope, which is operated by ASTRON (Netherlands Institute for Radio Astronomy) with support from the Netherlands Foundation for Scienti\ufb01c Research (NWO). MC acknowledges support from a Royal Society University Research Fellowship. This work was supported by the rolling grants Astrophysics at Oxford PP/E001114/1 and ST/H002456/1 and visitors grants PPA/V/S/2002/00553, PP/E001564/1 and ST/H504862/1 from the UK Research Councils. RLD acknowledges travel and computer grants from Christ Church, Oxford and support from the Royal Society in the form of a Wolfson Merit Award 502011.K502/jd. RLD is also grateful for support from the Australian Astronomical Observatory Distinguished Visitors programme, the ARC Centre of Excellence for All Sky Astrophysics, and the University of Sydney during a sabbatical visit. SK acknowledges support from the Royal Society Joint Projects Grant JP0869822. RMcD is supported by the Gemini Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc., on behalf of the international Gemini partnership of Argentina, Australia, Brazil, Canada, Chile, the United Kingdom, and the United States of America. TN and MBois acknowledge support from the DFG Cluster of Excellence \u2018Origin and Structure of the Universe\u2019. MS acknowledges support from a STFC Advanced Fellowship ST/F009186/1. (TAD) The research leading to these results has received funding from the European Community\u2019s Seventh Framework Programme (/FP7/2007-2013/) under grant agreement no. 229517. MBois has received, during this research, funding from the European Research Council under the Advanced Grant Program no. 267399-Momentum. LY acknowledges support from NSF grant AST-1109803. MH acknowledges \ufb01nancial support from the European Research Council under the European Communitys Seventh Framework Program (FP7/2007-2013)/ERC grant agreement no. 202781. The authors acknowledge \ufb01nancial support from ESO.",
                    "introduction": "The observation of both neutral hydrogen (H I) and molecular gas (H2, traced by CO) has shown that early-type galaxies (E/S0s, here- after ETGs), while on average gas-poorer than spirals, can in some cases host a signi\ufb01cant mass of cold gas (for early H I studies see, e.g., Gallagher, Faber & Balick 1975; Knapp et al. 1977; Bieg- ing & Biermann 1977; Knapp, Turner & Cunniffe 1985; Wardle & Knapp 1986; for CO see Wiklind & Henkel 1989; Lees et al. 1991). What has remained unclear until recently is whether gas-rich ETGs are peculiar, rare objects or represent a signi\ufb01cant fraction of the overall population (e.g., van Gorkom & Schiminovich 1997). This question has now been answered by large H I and H2 surveys of morphologically-selected ETGs carried out as part of the ATLAS3D project (Cappellari et al. 2011a, hereafter Paper I). In Serra et al. (2012, hereafter Paper XIII) we show that \u223c40 per cent of all ETGs outside the Virgo cluster and \u223c10 per cent inside Virgo host H I down to a mass of \u223c107 M\u2299and a column density of \u223c3 \u00d7 1019 cm\u22122, placing recent, previous results (Mor- ganti et al. 2006; di Serego Alighieri et al. 2007; Grossi et al. 2009; Oosterloo et al. 2010) on a strong statistical basis. We \ufb01nd that in \u223c2/3 of all detections (and 1/4 of all ETGs outside Virgo) the H I is distributed in a low-column-density disc or ring with size from a few to tens of kpc, and mass from \u223c107 to more than 109 M\u2299(see also van Driel & van Woerden 1991; Oosterloo et al. 2007). The remaining detected ETGs host H I on an unsettled con\ufb01guration which usually reveals recent dynamical interaction within a group. Concerning molecular gas, Young et al. (2011, hereafter Pa- per IV) detect CO in 22 per cent of all ETGs independent of galaxy luminosity or environment, with M(H2) between \u223c107 M\u2299(the typical sensitivity of their data) and \u223c109 M\u2299(for recent, previous surveys of smaller samples see Combes, Young & Bureau 2007; Sage, Welch & Young 2007). Follow-up interferometric observa- tions show that this gas is mostly distributed on discs and rings \u22c6E-mail:paolo.serra@csiro.au \u2020 Dunlap Fellow with typical radius \u223c1 kpc, just a fraction of the galaxy effective radius (Alatalo et al. 2013; Davis et al. 2013). Taken together, these studies establish that about half of all ETGs host between \u223c107 and \u223c109 M\u2299of cold gas (atomic and/or molecular) usually settled within the galaxy potential. Very sensi- tive observations are required to reach such a detection rate (for example, this is signi\ufb01cantly higher than in the recent surveys of massive galaxies by Catinella et al. 2010 and Saintonge et al. 2011) but when these are performed we \ufb01nd that ETGs with a signi\ufb01cant mass of cold gas are not peculiar, rare systems. The obvious im- plication is that in order to understand the assembly of ETGs as a family we need to understand how they get or retain their gas and what impact this has on the host, on its star formation history and on its structure. Here we focus on the latter aspect. In most previous studies of this kind ETGs are simply divided into ellipticals and lenticulars. When this is done, molecular gas is almost exclusively found in lenticulars (Lees et al. 1991, Welch, Sage & Young 2010, Paper IV), consistent with the fact that CO is invariably associated with dust lanes. Furthermore, H I seems to be more abundant in lenticular than in elliptical objects at a typical M(H I) sensitivity of \u223c109 M\u2299(Roberts 1975; Wardle & Knapp 1986; Bregman, Hogg & Roberts 1992; Sadler 2001) al- though more sensitive observations of smaller samples do not re- veal any signi\ufb01cant difference (Grossi et al. 2009; Oosterloo et al. 2010). One complication is that the distinction between ellipticals and lenticulars can be ambiguous and is affected by projection ef- fects (Jorgensen & Franx 1994). A more robust and physically meaningful approach is to classify ETGs on the basis of their in- ternal kinematics (e.g., Davies et al. 1983; Cappellari et al. 2007; Emsellem et al. 2007). In this context a key result of the ATLAS3D project is that the vast majority of all ETGs (\u223c85 per cent) are structurally simi- lar to spirals. They rotate like discs (Krajnovi\u00b4 c et al. 2011, here- after Paper II), can be described as a family of oblate rotators on the \u03bbR-\u03f5 diagram (Emsellem et al. 2011, hereafter Paper III), and cover the same range of intrinsic \ufb02attening and bulge-to-disc ratio of Sa to Sc spirals (Cappellari et al. 2011b, 2013b, hereafter Paper c \u20dd2013 RAS, MNRAS 000, 1\u201318 H I discs in fast and slow rotators 3 VII and Paper XX, respectively; Krajnovi\u00b4 c et al. 2013a; Weijmans et al., submitted; see also Laurikainen et al. 2011; Kormendy & Bender 2012). We call these ETGs fast rotators (FRs). In practice, FRs include nearly all classical lenticulars plus a large number of galaxies morphologically misclassi\ufb01ed as ellipticals because of un- favourable viewing angle (Paper III). The evolutionary history of most FRs must include the growth and survival of a stellar disc following accretion of cold gas from the surrounding medium as well as gas-rich minor and major mergers (Khochfar et al. 2011, hereafter Paper VIII; Naab et al. 2013, hereafter Paper XXV). The remaining \u223c15 per cent of all ETGs do not exhibit the disc-like stellar rotation observed in FRs and occupy a region of the \u03bbR-\u03f5 diagram corresponding to intrinsically lower speci\ufb01c an- gular momentum and \ufb02attening (Paper III). We call these galaxies slow rotators (SRs). We \ufb01nd that SRs form a heterogeneous family including systems with no rotation at all, non-disc-like rotation and kinematically distinct cores (KDCs). Massive SRs are thought to grow via (a small number of) major mergers at z > 1, which lower the system angular momentum and may create a KDC, followed by many minor mergers with low gas fraction, which preserve the KDC and make the stellar body rounder (Naab, Johansson & Os- triker 2009; Bois et al. 2011, hereafter Paper VI; Paper VIII; Paper XXV). This sequence of events is most likely to occur in a dense environment, in agreement with the increased fraction of SRs in the centre of the Virgo cluster (Paper VII). Within this picture one may naively think that SRs should lack a signi\ufb01cant cold-gas phase, unlike FRs. Indeed, Paper IV shows that the CO detection rate is much lower in SRs than in FRs. How- ever, the situation is not necessarily so simple. For example, the de- tection of kinematically-misaligned ionized gas (Davis et al. 2011, hereafter Paper X), cold dust (Smith et al. 2012) and stellar nuclear cusps (Krajnovi\u00b4 c et al. 2013b, hereafter Paper XXIII) in SRs sug- gests that they too can accrete some gas during their life; and sim- ulations show that at least some SRs may have formed in gas-rich mergers (Paper VI; Paper XXV). Furthermore, the mere fact that FRs are found at basically all environment densities (Paper VII) implies that there must be a large variety of evolutionary histories leading to their formation, and therefore potentially a large variety of resulting cold-gas properties. All that is required to mark the visual difference between a FR and a spiral at z = 0 is that the former should have lower star- formation-rate surface density on the stellar disc. In other words, they should be quenched owing to a lower Mgas/M\u22c6and/or star- formation ef\ufb01ciency within the stellar body. Observations indicate that such quenching may be related to the growth of the stellar bulge: the cold gas content of the stellar body decreases as the bulge becomes more dominant (Catinella et al. 2010; Saintonge et al. 2011; Paper XX) and, additionally, the bulge may stabilize the remaining gas against star formation (Kawata, Cen & Ho 2007; Martig et al. 2009; Saintonge et al. 2012; Martig et al. 2013). Yet it is still possible for a FR to host a large mass of cold gas well out- side the stellar body and at low surface density (e.g., Morganti et al. 2006; Oosterloo et al. 2007; Paper XIII). Such gas distributions are indicative that there are many ways of making a FR and that this in- formation, lost in the apparent homogeneity of their shape and stel- lar kinematics, may emerge when observing their cold-gas phase. Furthermore, these tenuous gas systems are only weakly bound to the host and hence are easily perturbed. Their actual morphology is therefore a sensitive probe of the past dynamical history of the host, and indeed in Paper XIII we show that the H I morphology varies systematically with the density of the environment. In this spirit we study here the H I properties of ETGs as a function of their structure within the context of the ATLAS3D project. The few previous attempts in this direction reveal no clear relation between H I and ETG structure but are based on signif- icantly smaller samples (Morganti et al. 2006; Oosterloo et al. 2010). Here we aim at clarifying the situation by studying the large ATLAS3D H I sample. We describe the sample and the H I data in Sec. 2, discuss H I detection rate, mass and morphology as a func- tion of galaxy structure in Sec. 3, analyse the kinematical misalign- ment between H I and stars in Sec. 4, perform for the \ufb01rst time a comparison to the predictions of \u039bCDM hydrodynamical simula- tions in Sec. 5, and summarize the results in Sec. 6."
                },
                {
                    "url": "http://arxiv.org/abs/1209.4107v1",
                    "title": "Discovery of a giant HI tail in the galaxy group HCG 44",
                    "abstract": "We report the discovery of a giant HI tail in the intra-group medium of HCG\n44 as part of the Atlas3D survey. The tail is ~300 kpc long in projection and\ncontains ~5x10^8 M_sun of HI. We detect no diffuse stellar light at the\nlocation of the tail down to ~28.5 mag/arcsec^2 in g band. We speculate that\nthe tail might have formed as gas was stripped from the outer regions of NGC\n3187 (a member of HCG 44) by the group tidal field. In this case, a simple\nmodel indicates that about 1/3 of the galaxy's HI was stripped during a time\ninterval of <1 Gyr. Alternatively, the tail may be the remnant of an\ninteraction between HCG 44 and NGC 3162, a spiral galaxy now ~650 kpc away from\nthe group. Regardless of the precise formation mechanism, the detected HI tail\nshows for the first time direct evidence of gas stripping in HCG 44. It also\nhighlights that deep HI observations over a large field are needed to gather a\ncomplete census of this kind of events in the local Universe.",
                    "authors": "Paolo Serra, Baerbel Koribalski, Pierre-Alain Duc, Tom Oosterloo, Richard M. McDermid, Leo Michel-Dansac, Eric Emsellem, Jean-Charles Cuillandre, Katherine Alatalo, Leo Blitz, Maxime Bois, Frederic Bournaud, Martin Bureau, Michele Cappellari, Alison F. Crocker, Roger L. Davies, Timothy A. Davis, P. T. de Zeeuw, Sadegh Khochfar, Davor Krajnovic, Harald Kuntschner, Pierre-Yves Lablanche, Raffaella Morganti, Thorsten Naab, Marc Sarzi, Nicholas Scott, Anne-Marie Weijmans, Lisa M. Young",
                    "published": "2012-09-18",
                    "updated": "2012-09-18",
                    "primary_cat": "astro-ph.CO",
                    "cats": [
                        "astro-ph.CO"
                    ],
                    "main_content": "HCG 44 is a compact group at a distance of \u223c25 Mpc (see below) hosting four galaxies of comparable magnitude within an area of \u223c 15\u00d715 arcmin2 (Fig. 1; Hickson 1982). The two galaxies in the centre of the figure, NGC 3187 and NGC 31901, exhibit signs of tidal interaction. The former is a blue, late-type spiral with long tails pointing \u223c90 degrees away from the plane of the galaxy. The latter is an earlier-type system with a disturbed morphology and a prominent dust lane. Vorontsov-Velyaminov (1959) groups these galaxies together in the object VV 307 (later catalogued as Arp 316), suggesting that they are interacting. The early-type galaxy to the northeast, NGC 3193, is very close in projection to these two galaxies and has regular morphology. To the south-west, NGC 3185 is a 1 Some authors refer to this galaxy as NGC 3189. According to the NASA Extra-galactic Database NGC 3189 is the south-western side of NGC 3190. c \u20dd2012 RAS, MNRAS 000, 1\u201311 A giant H I tail in HCG 44 3 Table 1. Galaxies in the HCG 44 \ufb01eld galaxy vhel distance method reference (km s\u22121) (Mpc) (1) (2) (3) (4) (5) NGC 3185 1230 20 \u00b1 5 TF a NGC 3187 1590 26 \u00b1 10 TE b NGC 3190 1300 24 \u00b1 5 SNIa c, d, e, f, g, h, i NGC 3193 1381 34 \u00b1 3 SBF j SDSS J1017 1940 29 HF this work Column 1. Galaxy name. Column 2. Heliocentric velocity measured from the H I data discussed in this article except for NGC 3193, for which we use the value given by Cappellari et al. (2011a). Column 3. Redshiftindependent distance for all galaxies except SDSS J1017, for which we assume Hubble \ufb02ow (see below). Error bars are taken from the references in column 5 except for NGC 3190, for which we give the range of distances obtained by different groups who studied the two SNIa 2002bo and 2002cv. Column 4. Method used to determine the distance: TF = TullyFisher relation corrected for Malmquist bias; TE = Tully estimate; SBF = surface brightness \ufb02uctuation corrected for Malmquist bias; HF = Hubble \ufb02ow with h = 0.73 after correction for Virgo infall by +200 km s\u22121. Column 5. References for the distance estimate: (a) Springob et al. (2009); (b) Tully (1988); (c) Reindl et al. (2005); (d) Wang et al. (2006); (e) Elias-Rosa et al. (2008); (f) Takanashi, Doi & Yasuda (2008); (g) Wood-Vasey et al. (2008); (h) Mandel et al. (2009); (i) Amanullah et al. (2010); (j) Blakeslee et al. (2001). barred galaxy with a warped, star forming outer ring. In addition to these four galaxies listed in the original Hickson (1982) catalogue, the much smaller galaxy SDSS J101723.29+214757.9 (hereafter, SDSS J1017) might be at larger distance (see below), while the small blue galaxy in the south-east corner is de\ufb01nitely a background object based on its SDSS redshift of 0.014. The group membership is not well established. Table 1 lists recessional velocity and distance estimates of the galaxies mentioned above. NGC 3185, NGC 3190 and NGC 3193 have comparable velocities. Relative to these, the velocity of NGC 3187 seems too large for such a small group. SDSS J1017 has even higher velocity, casting doubts on its membership. Redshift-independent distance estimates of individual galaxies are also puzzling. Taken at face value, the distance of NGC 3193 would put it in the background, as suggested also by Aguerri et al. (2006) based on the non-detection of planetary nebulae in this galaxy. However, error bars on individual distance measurements are large and systematic effects may be important. For example, the two SNIa in NGC 3190 (see table) are extremely obscured and dust corrections are substantial. Furthermore, NGC 3185 has a warp and this would cause a systematic error on the Tully-Fisher distance based on singe-dish H I data. In this paper we do not attempt to resolve the issue of galaxy distances and group membership. Instead, we assume that all galaxies labelled in Fig. 1 belong to the group with the exception of SDSS J1017, which we consider as a background object based on its large recessional velocity. We assume that the group is at a distance dHCG 44 = 25 Mpc. At this distance 15 arcmin correspond to \u223c110 kpc. We note that HCG 44 is part of a loose overdensity which includes 10 to 16 bright galaxies depending on the grouping criterion (see group 58 in Geller & Huchra 1983 and group 194 in Garcia 1993). Galaxies in this overdensity have recessional velocity between \u223c1100 and \u223c1500 km s\u22121 and are distributed over a sky area of about 5 \u00d7 3 deg2, which corresponds to 2.2 \u00d7 0.9 Mpc2 at the distance of HCG 44. Therefore, galaxies in this region are relatively distant from each other (each of them occupies on average 0.6 deg2 \u223c0.1 Mpc2). In comparison, the galaxy number density within HCG 44 is ten times larger, and this group stands out clearly as a strong and compact overdensity on top of the loose group. The H I properties of HCG 44 have been studied by Williams & Rood (1987) using the Arecibo telescope, Williams, McMahon & van Gorkom (1991) and Verdes-Montenegro et al. (2001) with Very Large Array (VLA) data, van Driel et al. (2001) with the Nanc \u00b8ay telescope, and Borthakur, Yun & Verdes-Montenegro (2010) using the Green Bank Telescope (GBT). These studies agree that galaxies in the group (all detected in H I except NGC 3193, which is claimed to be detected by van Driel et al. 2001 only) are gas-poor relative to similar objects in the \ufb01eld. Verdes-Montenegro et al. (2001) estimate the detected H I mass to be just \u223c40 percent of the expected value for NGC 3187 and \u223c10 percent for NGC 3185 and NGC 3190 (we revisit these estimates in Sec. 4.2). Borthakur, Yun & Verdes-Montenegro (2010) report the detection of some of the missing gas as they \ufb01nd excess H I emission in the GBT spectrum2 compared to the total VLA spectrum. Based on the strong similarity between the GBT and VLA H I pro\ufb01les they suggest that the excess gas is dynamically similar to the H I detected by the VLA within individual galaxies in the group. We observed HCG 44 in H I as part of the multi-wavelength ATLAS3D survey (Cappellari et al. 2011a). The H I observations of this survey were carried out with the Westerbork Synthesis Radio Telescope (WSRT) and presented in Serra et al. (2012). Those observations revealed a few small gas clouds around HCG 44. Serra et al. (2012) argue that the distribution of the clouds on the sky and in velocity is suggestive of a long, intra-group H I tail \u2013 the detected clouds being the densest clumps along the hypothetical tail. Here we present new, deeper WSRT observations performed as part of the ATLAS3D project to detect the H I tail itself. 3 OBSERVATIONS 3.1 H I interferometry We observed HCG 44 for 6 \u00d7 12 h with the WSRT. We pointed the telescope at \u03b1J2000 = 10 h 18 m 54.19 s, \u03b4J2000 = 21 d 59 m 30.5 s, which is a position between NGC 3193 and one of the H I clouds detected by Serra et al. (2012). We reduced the data in a standard way using the WSRT pipeline developed by Serra et al. (2012). The H I cube used for our analysis is made using robust=0 weighting and 30 arcsec FWHM tapering. This results in a beam major and minor axis of 53.0 arcsec and 32.7 arcsec, respectively (PA = 6.5 deg; the beam axes correspond to 6.4 and 4.0 kpc at the adopted distance, respectively). The cube has velocity resolution of 16 km s\u22121 after Hanning smoothing. The noise is \u03c3 = 0.22 mJy beam\u22121 in each channel, which corresponds to a formal 5\u03c3 H I column density sensitivity of 1.1 \u00d7 1019 cm\u22122 per resolution element. We use the source \ufb01nder described in Serra et al. (2012) to detect emission in the H I cube. The \ufb01nder looks for emission in the original cube and in cubes at different resolutions on the sky and/or in velocity. It \ufb02ags all voxels above +n\u03c3 and all voxels below \u2212n\u03c3 as emission and performs basic size \ufb01ltering to reduce the noise in the mask at each resolution. Here we use Gaussian \ufb01lters of FWHM 25 and 50 arcsec on the sky and top-hat \ufb01lters of width 16, 32, 64, 128, 256 and 384 km s\u22121 in velocity, and adopt n = 3. We 2 The GBT beam is \u223c9 arcmin. c \u20dd2012 RAS, MNRAS 000, 1\u201311 4 Paolo Serra et al. 10h17m 18m 19m 20m RA (J2000) +21\u25e640\u2032 50\u2032 +22\u25e600\u2032 10\u2032 20\u2032 Dec (J2000) NGC 3185 NGC 3187 NGC 3190 NGC 3193 CS TN SDSS J1017 UGC 05574 21 22 23 24 25 26 27 28 29 30 Figure 2. Constant-column-density H I contours overlaid on the g-band CFHT/MegaCam image. The colourbar on the right is in mag arcsec\u22122. Contours represent N(H I) = 1.0 \u00d7 1019 \u00d7 3n cm\u22122 (n = 0, 1, 2, 3). Contours are coloured black to red, faint to bright. The black cross indicates the pointing centre of our WSRT observation and the dotted, black circle indicates the primary beam of the WSRT. Large and small dashed, red circles indicate the location of TN and CS , respectively (see text). The beam of the H I image is shown on the bottom-left corner. Note that UGC 05574 (to the north-east) and SDSS J1017 (to the south-west) are not members of HCG 44. use the resulting mask to build the total-H I image (which we then correct for the primary beam of the WSRT) and the H I velocity \ufb01eld (intensity-weighted mean) shown in Sec. 4. All H I \ufb02ux and mass values reported in this paper are measured from the total-H I image and are therefore corrected for the primary beam. 3.2 Optical imaging Deep optical imaging of HCG 44 was obtained with the MegaCam camera mounted on the Canadian-French-Hawaiian Telescope (CFHT). These observations were taken as part of the ATLAS3D project (Cappellari et al. 2011a) with the goal of studying earlytype galaxies\u2019 morphological \ufb01ne-structure as a relic of their formation (Duc et al. 2011). We observed the HCG 44 \ufb01eld for 7\u00d7345 sec in both g and r band applying offsets of \u223c30 arcmin between consecutive exposures. The seeing was 0.9 and 1.2 arcsec in g and r band, respectively. We refer to Duc et al. (2011) for a full description of the observations and data reduction. We note here that the observing strategy and data reduction procedures (Elixir-LSB software; Cuillandre et al., in prep.) were chosen to detect stelc \u20dd2012 RAS, MNRAS 000, 1\u201311 A giant H I tail in HCG 44 5 10h17m 18m 19m 20m RA (J2000) +21\u25e640\u2032 50\u2032 +22\u25e600\u2032 10\u2032 20\u2032 Dec (J2000) NGC 3185 NGC 3187 NGC 3190 NGC 3193 CS TN SDSS J1017 UGC 05574 1000 1100 1200 1300 1400 1500 1600 1700 1800 Figure 3. Velocity \ufb01eld of the detected H I. The colourbar on the right is in km s\u22121. Large and small dashed, red circles indicate the location of TN and CS , respectively. The black open circle indicates the position of NGC 3193, whose recessional velocity from optical spectroscopy is 1381 km s\u22121. The beam of the H I image is shown on the bottom-left corner. The black solid line is the path used to draw the position-velocity diagram shown in Fig. 4. lar structures reaching \u223c28.5 mag arcsec\u22122 in g band. However, the surface brightness sensitivity may vary from \ufb01eld to \ufb01eld (and within a given \ufb01eld) and we discuss the sensitivity of our image in more detail in the following section. 4 RESULTS 4.1 H I in the intra-group medium Figure 2 shows H I constant-column-density contours overlaid on the g-band CFHT/MegaCam image of HCG 44. The main result of our new observation is the detection of a long H I tail north of NGC 3193 (hereafter TN), which is contained in the large, dashed red circle in the \ufb01gure. The tail consists of a low-column-density, \u223c20-arcmin-long component oriented north-west to south-east and a less massive, southern extension. The latter is revealed by two small clouds aligned north-east to south-west in the direction of NGC 3193. We also con\ufb01rm the Serra et al. (2012) detection of a smaller H I complex south-east of NGC 3193 (hereafter CS ), indicated by the small, dashed red circle in the \ufb01gure. The tail TN has no diffuse optical counterpart down to the surface brightness sensitivity of the deep image shown in Fig. 2 (the same result is obtained inspecting the r-band image). In Sec. 3.2 we mentioned that the generic sensitivity of the CFHT/MegaCam images taken as part of the ATLAS3D project is \u223c28.5 mag arcsec\u22122 c \u20dd2012 RAS, MNRAS 000, 1\u201311 6 Paolo Serra et al. 0 10 20 30 40 distance (arcmin) 1100 1400 1700 velocity (km s\u22121) Figure 4. Position-velocity diagram of the H I emission along the path shown by the black solid line in Fig. 3. The origin of the horizontal axis is set to be at the northern end of the path. The bright emission at distance \u223c45 arcmin is H I in NGC 3187. in g band. In this particular case TN lays on a relatively clean region of the image, which shows no large-scale noise variations or bright sources with the exception of two stars in the southern part of the tail. The noise level in this region (excluding the two stars) corresponds to a 1.5\u03c3 detection limit of 28.4 mag arcsec\u22122 within a circular aperture of radius equal to the seeing, consistent with the generic value given above. Such low detection level per resolution element is suf\ufb01cient considering that we are looking for emission over a scale of many arcminutes. Figure 3 shows the velocity \ufb01eld of the detected H I. We \ufb01nd a smooth variation of H I recessional velocity along TN. This is shown more clearly by the position-velocity diagram in Fig. 4, which is drawn along the path indicated by the black solid line in Fig. 3. The clouds detected by Serra et al. (2012) and mentioned in Sec. 1 are therefore just the tip of the iceberg of a large, coherent, gas distribution, as suggested in that article. Gas in both TN and CS is detected at velocities comparable to that of individual galaxies in HCG 44, suggesting that the tails are part of the group. TN has a total projected length of \u223c220 kpc at the assumed distance dHCG 44 = 25 Mpc . Table 2 lists the H I \ufb02ux of all detected objects shown in Fig. 2. Table 2 also shows the fractional contribution f(H I) of each object to the total H I \ufb02ux of the group. Assuming that all galaxies in HCG 44 and the intra-group gas are roughly at the same distance we conclude that H I in TN and CS amounts to \u223c20 percent of the total neutral hydrogen mass of of the compact group. This is as much H I as that found in NGC 3190 and almost half the H I mass of NGC 3187. At the assumed distance dHCG 44 we estimate an H I mass of 4.1 \u00d7 108 and 1.2 \u00d7 108 M\u2299for TN and CS , respectively. We note that TN stretches beyond the FWHM of WSRT\u2019s primary beam, which is 0.6 deg at the observing frequency of our data. Therefore, it is possible that the gaseous tail is actually longer than shown in Fig. 2 and we stop detecting H I because of a decrease in the telescope response. To check whether this is the case we make a natural-weighting H I cube from our WSRT data. This weighting scheme produces a cube with very patchy noise and poorer image quality, but the sensitivity is better than that of the main cube used in this study. Figure 5 shows a channel of the natural-weighting cube at velocity 1248 km s\u22121 suggesting indeed that some additional H I emission may exist north-west of TN. The existence of a north-western extension of TN is con\ufb01rmed 10h17m 18m 19m RA (J2000) +22\u25e605\u2032 10\u2032 15\u2032 20\u2032 25\u2032 Dec (J2000) Figure 5. Contours of the H I emission in the natural-weighting cube at a recessional velocity of 1248 km s\u22121 overlaid on a grey-scale total H I image of part of the tail TN. Grey contours are at \u22120.4 mJy beam\u22121, black contours at +0.4 and +0.8 mJy beam\u22121. The \ufb01gure shows possible additional emission north-west of TN. Note that this low-level emission was not cleaned (i.e., it was not deconvolved with the beam). by data taken as part of the H I Parkes All Sky Survey (HIPASS, Barnes et al. 2001). The HIPASS cube3 of this sky area has noise of \u223c15 mJy beam\u22121, velocity resolution 18 km s\u22121 and beam FWHM 15.5 arcmin. The formal 5\u03c3 sensitivity per resolution element is 1.7 \u00d7 1018 cm\u22122 for gas \ufb01lling the beam. We run the source \ufb01nder described in Sec. 3.1 on the cube and show contours of the detected H I in Fig. 6 overlaid on a SDSS g-band image (we also show the lowest WSRT H I contour; see Fig. 2). The \ufb01gure shows two clear HIPASS detections at the location of HCG 44 and NGC 3162 (a spiral galaxy \u223c1.5 deg north-west of HCG 44). Both detections are listed in the Northern HIPASS catalog by Wong et al. (2006) \u2013 objects HIPASS J1017+21 and HIPASS J1013+22, respectively. The main part of TN is visible only at a tentative level in HIPASS (partly because the cube contains many artefacts) and the HIPASS contours in Fig. 6 do not show it. On the other hand, the HIPASS cube reveals additional emission (not included in the catalogue of Wong et al. 2006) just north-west of TN, which was missed by our WSRT data because of its large distance from the pointing centre. The velocity of this emission is consistent with the velocity \ufb01eld shown in Fig. 3. Including this emission, the length of TN becomes \u223c300 kpc and its mass 5.2\u00d7108 M\u2299. This result is con\ufb01rmed by the newly reduced HIPASS data, which have signi\ufb01cantly lower noise level and many less artefacts (Calabretta et al., in prep.). In the new data the full tail is detected clearly (HIPASS team, priv. comm.). Another interesting aspect revealed by the HIPASS data is that the H I tail stretches towards and possibly connects with NGC 3162 (this galaxy was already detected in H I by, e.g., van Driel et al. 2001). NGC 3162, whose optical image we show in the inset of Fig. 6, has H I recessional velocity of 1300 km s\u22121, comparable to that of HCG 44 members, and is at a projected distance of \u223c650 kpc from HCG 44 assuming the distance dHCG 44 along the line of sight. We discuss this \ufb01nding in Sec. 5. 3 available at http://www.atnf.csiro.au/research/multibeam/release . c \u20dd2012 RAS, MNRAS 000, 1\u201311 A giant H I tail in HCG 44 7 10h12m 14m 16m 18m 20m RA (J2000) +21\u25e6200 400 +22\u25e6000 200 400 +23\u25e6000 Dec (J2000) HCG 44 NGC 3162 1 arcmin NGC 3162 Figure 6. HIPASS (red) and WSRT (black) H I contours on top of a SDSS g-band image. We show the HIPASS beam (15.5 arcmin) in the bottom-left corner. HIPASS contours are drawn at N(H I) = 1.0 \u00d7 1018 \u00d7 3n cm\u22122 (n = 0, 1, 2, 3). The WSRT contour is the lowest contour shown in Fig. 2: 1.0 \u00d7 1019 cm\u22122. The bottom-right inset shows the SDSS optical colour image of NGC 3162 obtained at http://skyserver.sdss3.org/dr8/en/tools/chart/chart.asp. 4.2 H I in galaxies: comparison to previous studies All gas-rich galaxies in Fig. 2 were already known to host H I. Williams, McMahon & van Gorkom (1991) observed this group with the VLA. They report H I \ufb02uxes systematically larger than those in Table 2. Namely, the \ufb02ux of NGC 3185, NGC 3187, NGC 3190 and SDSS J1017 is a factor 1.7, 1.3, 1.3 and 2.4 larger than our value, respectively4. For NGC 3185 and SDSS J1017 part 4 These factors include a correction of the VLA \ufb02uxes for the primary beam of that telescope, which was not applied by Williams, McMahon & van Gorkom (1991). The primary-beam correction is of \u223c10 percent for NGC 3185 and SDSS J1017 while it is negligible for the other two objects. Note that the VLA \ufb02ux values are consistent with those reported by Williams & Rood (1987) using Arecibo data. They are adopted by VerdesMontenegro et al. (2001) in their H I study of Hickson compact groups. They are 5 to 20 percent larger than values in van Driel et al. (2001), which have however large uncertainty. of the difference may be due to the better column density sensitivity of the VLA data relative to our WSRT data (by a factor of \u223c1.7; these galaxies are relatively far from the WSRT pointing centre as shown in Fig. 2). On the contrary, our data are slightly more sensitive at the location of NGC 3187 and NGC 3190 (10 to 20 percent) so at least some of the \ufb02ux difference must have a different cause. Flux calibration is not the reason of this discrepancy as we have veri\ufb01ed that our calibration is consistent with that of Williams, McMahon & van Gorkom (1991) within \u00b110 percent. Instead, we do \ufb01nd a relevant difference in the way we build the total-H I image. In our study we use the source \ufb01nder of Serra et al. (2012), which includes in the H I image both positive and negative noise peaks (see Sec. 3.1). On the contrary, Williams, McMahon & van Gorkom (1991) select only voxels above +1.5\u03c3. This introduces a positive bias in the total H I \ufb02ux. Indeed, if we implement their detection criterion in our source \ufb01nder we obtain \ufb02uxes a factor 1.5, 1.1, 1.2, 1.3 larger for the four galaxies mentioned above, respectively. This accounts at least partially for the difference in H I \ufb02ux. Remaining c \u20dd2012 RAS, MNRAS 000, 1\u201311 8 Paolo Serra et al. Table 2. H I detected with the WSRT in HCG 44 object F(H I) f(H I) M(H I) (Jy km s\u22121) (108 M\u2299) (1) (2) (3) (4) TN 2.79 0.15 4.1 CS 0.82 0.05 1.2 NGC 3185 2.11 0.12 3.1 NGC 3187 8.22 0.46 12.0 NGC 3190 4.00 0.22 5.8 galaxies not members of HCG 44 SDSS J1017 1.03 2.0 UGC 05574 0.84 1.1 Column 1. Object name. Column 2. Total H I \ufb02ux. Column 3. Fraction of the total H I \ufb02ux of HCG 44. Column 4. H I mass assuming a distance of dHCG 44 = 25 Mpc for galaxies in HCG 44, and Hubble \ufb02ow distance for galaxies outside HCG 44 (29 and 24 Mpc for SDSS J1017 and UGC 05574, respectively \u2013 see Table 1). differences may be explained by the better sensitivity of the VLA data at the location of NGC 3185 and SDSS J1017 (see above) and by the higher noise level of the VLA data at the location of NGC 3187 and NGC 3190, which would imply a higher level of the bias under discussion. The H I morphology of galaxies in Fig. 2 is in agreement with the image presented by Williams, McMahon & van Gorkom (1991). The main addition of our deeper image (besides the detection of TN and CS ) is a faint extension of the southern H I warp in NGC 3187. Furthermore, we set a column density limit of \u223c2\u00d71019 cm\u22122 on the H I bridge between NGC 3185 and NGC 3190, which was tentatively suggested by Williams, McMahon & van Gorkom (1991) based on the VLA data (this limit takes into account that the two galaxies lay around the half-power point of the WSRT primary beam). We note that the lower value of our M(H I) estimates compared to values in Williams, McMahon & van Gorkom (1991) would imply an even larger H I de\ufb01ciency than that derived by Verdes-Montenegro et al. (2001) (see Sec. 2). We revisit the H I de\ufb01ciency of galaxies in HCG 44 using the relation between M(H I) and optical diameter D25,r derived by Toribio et al. (2011). The isophotal major axis of NGC 3185, NGC 3187 and NGC 3190 is given in the SDSS DR7 catalogue and is 8.7, 6.5 and 13.4 kpc, respectively. Given these values, the H I mass predicted by the 1/Vmax-corrected M(H I)-D25,r relation in Toribio et al. (2011) is 7.8, 5.4 and 13.5 \u00d7 109 M\u2299, respectively. Therefore, the detected mass of H I is just 4, 22 and 4 percent of the expected value for the three galaxies (6, 3, and 6 \u03c3 below the expected H I mass, respectively, where \u03c3 = 0.23 dex is the r.m.s. residual of Toribio et al. 2011 relation). 5 DISCUSSION The detection of a 300 kpc-long tail containing 5 \u00d7 108 M\u2299of H I in a group already observed by various authors with many different radio telescopes may seem surprising (see Sec. 2 for a summary of previous H I observations of HCG 44). Our result demonstrates that signatures of on-going galaxy evolution inside groups can be truly elusive. It shows that although H I observations are unique in giving direct evidence of the fundamental role of group processes for galaxy evolution (as shown not only on individual systems but also on large, statistically representative samples; e.g., Serra et al. 2012), such observations need to be very sensitive and cover a large \ufb01eld if we want to gather a complete census of these events. This should be kept in mind when designing future H I surveys. Besides the above general conclusion, our observations reveal for the \ufb01rst time direct evidence of gas stripping in HCG 44. This is interesting because galaxies in this group have long been known to be H I de\ufb01cient and we may be unveiling the cause of at least part of the de\ufb01ciency. It is therefore interesting to speculate on how the detected H I tail may have formed. How was the gas stripped, and from what galaxy? The goal of the present section is to explore possible answers to these two questions. 5.1 Formation of the H I tail: ram pressure or tidal stripping The two possible mechanisms to form a gas tail within a group are ram pressure and tidal stripping. The former necessitates a dense medium and large relative velocity between the medium and the stripped galaxy. So far, X-ray observations have been unsuccessful in detecting the intra-group medium of HCG 44 (Mulchaey et al. 2003 using ROSAT data; Rasmussen et al. 2008 using Chandra and XMM-Newton data). Rasmussen et al. (2008) estimate that the density of the medium is n < 10\u22124 cm\u22123. Analytic calculations indicate that even at such low density some stripping might occur but they also show that this would be a fairly small effect (e.g., Rasmussen et al. 2008; Freeland, Sengupta & Croston 2010; Westmeier, Braun & Koribalski 2011). It therefore seems unlikely that ram pressure is responsible for creating such a prominent tail, longer than and as massive as tails detected in the centre of clusters (e.g., Oosterloo & van Gorkom 2005). Furthermore, no galaxy in the group shows the typical H I morphology caused by ram-pressure stripping \u2013 i.e., gas compressed against the stellar disc on one side of the galaxy and extending to larger radius on the opposite side (e.g., Kenney, van Gorkom & Vollmer 2004; Chung et al. 2007, 2009). We conclude that ram pressure is an unlikely explanation for the formation of TN. The alternative hypothesis is that TN was created by tidal interaction within the group. Tidal forces act on both stars and gas and it may therefore seem surprising that no diffuse stellar light is detected at the location of TN even in the very deep CFHT/MegaCam image shown in Fig. 2. In fact, observations (e.g., Davies et al. 2004) and simulations (e.g., Bekki et al. 2005; Duc & Bournaud 2008; Michel-Dansac et al. 2010) both show that star-less tidal tails can develop following gravitational interaction and depending on the relative distribution of gas and stars in the stripped galaxy. Therefore, tidal interaction is a viable mechanism to create the detected tail and we explore this possibility in the rest of this section. 5.2 What stripped galaxy? The \ufb01rst question we attempt to answer is what galaxy the H I was stripped from. The results described in Sec. 4 suggest two alternative hypotheses. One possibility is that the tail was stripped from NGC 3162 as it \ufb02ew by the group at high speed (see Fig. 6). This galaxy is currently at a projected distance of \u223c650 kpc from HCG 44, which it could have covered in \u223c3 Gyr if it went through the group at a velocity of 200 km/s on the plane of the sky. The optical morphology of this galaxy may support this hypothesis as the stellar disc is lopsided, indicating that it might have been perturbed recently (see inset in Fig. 6). However, lopsidedness is a relatively common phenomenon in spiral galaxies and is no de\ufb01nite proof c \u20dd2012 RAS, MNRAS 000, 1\u201311 A giant H I tail in HCG 44 9 of an interaction between NGC 3162 and HCG 44. The newly reduced HIPASS data (Calabretta et al., in prep.) hint to a possible H I bridge between TN and NGC 3162 which, if con\ufb01rmed, would be a strong clue in favour of this hypothesis. This will be explored further in a future paper presenting the new data. The other possibility is that the observed H I tail originated from one of the galaxies currently within HCG 44, and NGC 3162 played no signi\ufb01cant role. Optical imaging shows that some of the members of HCG 44 have experienced recent tidal interaction (see Fig. 1), and TN may have formed as part of the same process. The most obvious candidate for tidal stripping within the group might be NGC 3187. This galaxy exhibits a strong tidal distortion visible as an S-shaped warp and TN could be seen as an extension of the north-east side of the warp (see Fig. 2; note that any connection between TN and NGC 3187 would have to be at column density below \u223c1019 cm\u22122). This is con\ufb01rmed by the fact that the H I velocity on the south-west end of TN is similar to that on the north-east side of NGC 3187 (Figs. 3 and 4). Another interesting point is that gas in TN amounts to almost half of the total H I mass of NGC 3187. Therefore, tidal stripping would provide a possible explanation for the H I de\ufb01ciency of this galaxy (see Sec. 4.2). We speculate on the details of the stripping process below. 5.3 Tidal stripping of NGC 3187 Numerous previous authors argued that NGC 3187 might be interacting with NGC 3190. While this is possible, it is unlikely that such interaction is responsible for the formation of TN. The reason is that it would be dif\ufb01cult to explain the gap between H I in NGC 3187 and TN. Furthermore, compared to previously known cases of very long tails induced by \u223cmajor galaxy interaction and merging (e.g., Mirabel, Lutz & Maza 1991; Duc et al. 2011) the length of the tail \u2013 at least 300 kpc \u2013 seems too extreme to be caused by this particular galaxy pair. A mechanism to form very long, low-column-density H I tails (or rings) like that in HCG 44 was proposed by Bekki et al. (2005). The main ingredient of their model is the tidal interaction of a lowsurface-brightness disc (in this case, NGC 3187) with the gravitational potential of a group of galaxies. This interaction would strip the outer part of the disc (which are often observed to be essentially star-less) and distribute the stripped material on a long tail or ring. We perform a basic test of this mechanism and estimate the time-scale of the stripping process by building a three-dimensional toy model for the orbit of NGC 3187 around HCG 44 . The model is constrained by the assumed trajectory of NGC 3187 (traced by the H I tail and the current position of the galaxy) and its velocity relative to the group. In this model we assume the group potential to be \ufb01xed and Keplerian. We take the centre of the potential to be at the position of NGC 3193 and place it at coordinates [x, y, z] = [0, 0, 0] (we discuss the orientation of the sky relative to these three axes below). We further assume that NGC 3187 follows a parabolic orbit parallel to the xy plane (and therefore at constant z = z0). For z0 = 0 the orbit is determined only by the total mass of the system Mtot and the focal length of the parabola f. However, in this model we assume that the orbital plane is displaced relative to the centre of the group (z0 , 0; we show below that this is necessary for the parabola to \ufb01t the data). Under this assumption NGC 3187 should move also along the z axis but we neglect this effect. Such additional motion would be little constrained by the available data and would not in any case have a signi\ufb01cant impact on the timescale of the orbit, which is our primary goal. Therefore, the orbit remains perfectly planar (this approximation becomes increasingly -100 0 100 200 300 sky X (kpc) -100 0 100 200 300 sky Y (kpc) Figure 7. Total H I image of HCG 44 (logarithmic greyscale) with superimposed the possible orbit of NGC 3187 through the group (black line; see text). The open black circle indicates the position of NGC 3193, assumed centre of the group. Solid black circles are spaced at 0.5 Gyr time intervals. wrong as the xy distance of NGC 3187 from the group centre gets closer to the value of z0). The toy model described above has only three free parameters: Mtot, f and z0. We \ufb01x Mtot = 5 \u00d7 1012 M\u2299. We vary f between 50 and 200 kpc, and z0 between 0 and 200 kpc in an attempt to reproduce the observations. Furthermore, in order to compare the model to the data we need to project it on the sky. This introduces additional degrees of freedom. We make use of 3D visualisation to \ufb01nd a favourable projection. Figure 7 shows a possible orbit of NGC 3187, which reproduces the location of the H I tail and that of the galaxy at once. The orbit is obtained with f = 75 kpc and z0 = 100 kpc, and is viewed at an inclination of 60 deg away from face-on (note that this is not the result of a formal \ufb01t and is therefore just one possible solution of the problem). An important feature of the model is that the predicted velocity of NGC 3187 relative to the group centre (i.e., NGC 3193) is 235 km s\u22121 along the line of sight. This is a good match to the observed value of 210 km s\u22121 (see Table 1). Therefore, this simple model can explain the anomalous, high velocity of NGC 3187 relative to other members of HCG 44. Within the context of this simple model NGC 3187 passed the vertex of the orbit \u223c400 Myr ago and was at the current location of the north-west end of the H I tail (revealed by the HIPASS data shown in Fig. 6) \u223c900 Myr ago. This suggests that the galaxy may have been stripped of the H I now in TN (\u223c1/3 of its initial H I mass) within a time interval shorter than 1 Gyr. It is interesting that this timescale is consistent with the \u223c2 Gyr timescale for quenching of star formation in galaxy groups recently derived by Rasmussen et al. (2012b). There are some important differences between HCG 44 and the systems simulated by Bekki et al. (2005). Firstly, their simulations predict the existence of a leading tail which, in the case of NGC 3187, should start at the southern tip of the warp, bend towards north-west and eventually join TN to form an intra-group H I ring. This is not observed. Bekki et al.\u2019s is, however, an idealised model. In reality this process occurs in the presence of many other galaxies. It is possible that such second tail was destroyed by an inc \u20dd2012 RAS, MNRAS 000, 1\u201311 10 Paolo Serra et al. teraction with NGC 3190 (which is tidally disturbed) and gas was instead dispersed towards the location of CS . This idea is supported by both the H I and optical morphology of NGC 3187\u2019s southern tidal tail. Figure 2 shows that this tail broadens and bends towards NGC 3190, giving support to the idea that the two galaxies are interacting. Therefore, it is possible that also gas in CS once belonged to NGC 3187, and the above estimate on the amount of gas stripped from this galaxy should be regarded as a lower limit. Another difference is that in Bekki et al.\u2019s model the stripped galaxy is not tidally distorted, unlike NGC 3187. Again, interaction with NGC 3190 may explain the difference (note that, as we have argued above, this interaction is unlikely to be the formation mechanism of TN itself). We stress that we view this model as a very simple (but nevertheless useful) description of a possible formation mechanism for the detected tail. However, the system is complex: the group membership is still to be established and a number of galaxies might be playing a relevant role, including the very distant NGC 3162 (see Fig. 6 and Sec. 5.2). As a consequence, substantial differences between the data and idealised simulations like that of Bekki et al. (2005) or simple models like the parabolic trajectory presented above are not a surprise. More detailed modelling is beyond the scope of this paper (for example, a realistic mass model of the group would be needed, and the line-of-sight velocity of gas in TN should be used as a constraint for the model \u2013 taking into account also rotation within the stripped galaxy). Such modelling or the exploration of different formation mechanisms for the tail (for example interaction between NGC 3162 and a member of HCG 44 within the group potential, as in the models by Bekki, Koribalski & Kilborn 2005) would strongly bene\ufb01t from having deep H I observations over a larger \ufb01eld. 6 CONCLUSIONS We have presented deep H I and optical imaging of the galaxy group HCG 44 obtained with the WSRT and CFHT/MegaCam, respectively, as part of the ATLAS3D project. We detect a long intra-group H I tail and additional intra-group gas which, together, amount to 20 percent of the H I mass of the group. Combining these data with archive HIPASS observations we \ufb01nd that the main tail contains \u223c5\u00d7108 M\u2299of H I and is \u223c300 kpc long assuming a distance of 25 Mpc. The tail has no diffuse optical counterpart down to \u223c28.5 mag arcsec\u22122 in g band. We discuss viable formation mechanisms for the H I tail. Based on the available data (including X-ray imaging) it is unlikely that the tail is caused by ram pressure stripping. Instead, it is possible that the H I was stripped from NGC 3187, a member of HCG 44, by the group tidal \ufb01eld. We present a simple model for the orbit of the stripped galaxy through the group. Within this model, NGC 3187 has been stripped of 1/3 of its initial gas mass in less than 1 Gyr. This is consistent with recent estimates of the timescale for quenching of star formation in galaxy groups (\u223c2 Gyr). The proposed model is intentionally simple and it is possible that other processes have contributed to shaping the properties of galaxies in the group (e.g., tidal interaction between group members and, possibly, some ram-pressure stripping). Another possibility suggested by HIPASS data is that H I in the tail was stripped from NGC 3162, a spiral galaxy now 650 kpc from the group. Future work will investigate this possibility using H I data of better quality than those available at the moment. Regardless of the precise formation mechanism, the detected H I tail is the \ufb01rst, direct evidence of gas stripping in HCG 44, a group long known to be de\ufb01cient of H I. Our result highlights the importance of group processing as a driver of galaxy evolution, but also the observational challenge that has to be overcome in order to detect signatures of these processes. Sensitive H I observations over a large \ufb01eld are needed to gather a complete census of this kind of events in the local Universe. ACKNOWLEDGMENTS PS acknowledges useful discussions with T. van Albada, J. van Gorkom, R. Sancisi, S. Tonnesen and C. Toribio. MC acknowledges support from a Royal Society University Research Fellowship. This work was supported by the rolling grants \u2018Astrophysics at Oxford\u2019 PP/E001114/1 and ST/H002456/1 and visitors grants PPA/V/S/2002/00553, PP/E001564/1 and ST/H504862/1 from the UK Research Councils. RLD acknowledges travel and computer grants from Christ Church, Oxford and support from the Royal Society in the form of a Wolfson Merit Award 502011.K502/jd. RLD also acknowledges the support of the ESO Visitor Programme which funded a 3 month stay in 2010. SK acknowledges support from the the Royal Society Joint Projects Grant JP0869822. RMcD is supported by the Gemini Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc., on behalf of the international Gemini partnership of Argentina, Australia, Brazil, Canada, Chile, the United Kingdom, and the United States of America. LMD acknowledges support from the Lyon Institute of Origins under grant ANR-10-LABX-66. TN and MBois acknowledge support from the DFG Cluster of Excellence \u2018Origin and Structure of the Universe\u2019. MS acknowledges support from a STFC Advanced Fellowship ST/F009186/1. PS is a NWO/Veni fellow. (TAD) The research leading to these results has received funding from the European Community\u2019s Seventh Framework Programme (/FP7/2007-2013/) under grant agreement No 229517. MBois has received, during this research, funding from the European Research Council under the Advanced Grant Program Num 267399-Momentum. The authors acknowledge \ufb01nancial support from ESO. This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. This paper is based on observations obtained with the Westerbork Synthesis Radio Telescope, which is operated by the ASTRON (Netherlands Foundation for Research in Astronomy) with support from the Netherlands Foundation for Scienti\ufb01c Research NWO, and with MegaPrime/MegaCam, a joint project of CFHT and CEA/DAPNIA, at the CFHT, which is operated by the National Research Council (NRC) of Canada, the Institute National des Sciences de lUnivers of the Centre National de la Recherche Scienti\ufb01que of France and the University of Hawaii.",
                    "introduction": "Deep observations of neutral hydrogen (H I) around galaxies of- ten reveal faint gaseous distributions which do not trace galaxies\u2019 c \u20dd2012 RAS arXiv:1209.4107v1  [astro-ph.CO]  18 Sep 2012 2 Paolo Serra et al. stellar light. Known cases include extremely large H I discs and rings around both late-type galaxies (e.g., Krumm & Burstein 1984; Meurer et al. 1996; Koribalski & L\u00b4 opez-S\u00b4 anchez 2009) and early- type galaxies (e.g., van Driel & van Woerden 1991; Morganti et al. 2006; Oosterloo et al. 2007; Serra et al. 2012), tidal tails around merger remnants (e.g., Schiminovich et al. 1994; Koribalski, Gor- don & Jones 2003; Duc et al. 2011), tidal and ram-pressure tails in galaxy groups and clusters (e.g., Verheijen & Zwaan 2001; Davies et al. 2004; Oosterloo & van Gorkom 2005; English et al. 2010; Scott et al. 2012; Serra et al. 2012), gas accretion signatures (San- cisi et al. 2008, and references therein) and objects whose origin is still debated (e.g., Schneider et al. 1983; Thilker et al. 2009; Michel-Dansac et al. 2010). These systems carry invaluable infor- mation on the way galaxies assemble their stellar mass and accrete and lose gas in different environments. Neutral hydrogen distributions revealing on-going tidal inter- action, galaxy merging and gas stripping are particularly common in groups of galaxies (e.g., van der Hulst 1979; Verdes-Montenegro et al. 2001; Kern et al. 2008; Freeland, Stilp & Wilcots 2009; see also Hibbard et al. 2001 and references therein). The observation of these processes in action suggests that the morphology and gas con- tent of galaxies can undergo substantial evolution inside a group. In fact, group processes might be a major driver of the morphology- density relation (Dressler 1980; Postman & Geller 1984; for a dis- cussion of the role of groups in determining this relation see, e.g., Wilman et al. 2009; Bekki & Couch 2011; Cappellari et al. 2011b) and of the decrease of galaxies\u2019 H I content with increasing envi- ronment density (e.g., Verdes-Montenegro et al. 2001; Kilborn et al. 2009; Rasmussen et al. 2012a; Serra et al. 2012). Strong indications of the importance of group processes come from a combination of optical and H I results presented recently as part of the ATLAS3D survey (Cappellari et al. 2011a). Firstly, the fraction of fast rotating early-type galaxies increases (and the fraction of spiral galaxies decreases) with environment density fol- lowing a surprisingly tight log-linear relation, which is steeper and better de\ufb01ned when the density is measured on a group-like scale (de\ufb01ned by the distance from the third closest neighbour) rather than a cluster-like scale (tenth neighbour; Cappellari et al. 2011b). Secondly, the H I morphology of gas-rich early-type galaxies ap- pears to be strongly related to environment density when the latter is measured on a group-like scale (Serra et al. 2012). Large, regu- lar, settled H I distributions are typical in poor environments (where the distance from the third neighbour is larger than a few Mpc). More disturbed distributions are typical in galaxy groups and may be revealing the processes responsible for the morphology-density relation. We note that understanding group processes is important to understand galaxy properties over a broad range of large-scale en- vironment densities. On the one hand, in a \u039bCDM Universe galaxy clusters grow by accretion of groups of (rather than isolated) galax- ies, and pre-processing in groups may be important to shape the properties of galaxies living in clusters at redshift zero. On the other hand, even inside large-scale voids galaxies live clustered in small groups and their evolution is to some extent driven by tidal interac- tions and merging (Szomoru et al. 1996; Kreckel et al. 2012). Within this context, stripping of gas from galaxies in groups plays a key role. Although direct detection of stripped gas has been possible in a number of groups (see references above), in many other systems galaxies are found to be H I de\ufb01cient but no intra- group H I is detected. From an observational point of view the main challenge is that the stripped gas can diffuse quickly in the group medium (in about a group crossing time). It therefore reaches low NGC 3190 (1300) NGC 3193 (1381) NGC 3187 (1590) NGC 3185 (1230) SDSS J1017 (1940) 5 arcmin N E Figure 1. Sloan Digital Sky Survey (SDSS) optical colour image of HCG 44 (data release 8). The image covers an area of 0.4 \u00d7 0.4 deg2. We ob- tained the image at http://skyserver.sdss3.org/dr8/en/tools/chart/chart.asp. For each galaxy we indicate in parenthesis under the galaxy name the he- liocentric recessional velocity in km s\u22121 (see Table 1). column densities, requiring high sensitivity, and spreads over large areas, requiring observations over a large \ufb01eld. At the moment it is therefore unclear how ubiquitous gas stripping is in groups and, in more quantitative terms, what fraction of the original H I mass of a galaxy can be stripped and on what timescale. These esti- mates are needed to understand the importance of gas stripping rel- ative to other processes which may play a role in determining the morphology-density relation, such as the decrease of the cold-gas accretion rate in denser environments. In this article we report the discovery of a giant H I tail in the galaxy group HCG 44 as part of the ATLAS3D survey. We sum- marise the properties of the group in Sec. 2, describe radio and op- tical observations in Sec. 3, present and discuss the results in Secs. 4 and 5, and draw conclusions in Sec. 6."
                }
            ],
            "Tom Richtler": [
                {
                    "url": "http://arxiv.org/abs/1406.2868v1",
                    "title": "The globular cluster system of NGC1316. III. Kinematic complexity",
                    "abstract": "The merger remnant NGC 1316 (Fornax A) is one of the most important objects\nregarding the investigation of merger-related processes. We use kinematical\ndata of globular clusters (GCs) and the diffuse stellar light to investigate\nthe global structure of NGC 1316 and to constrain the dark matter content. We\nperform multi-object-spectroscopy with VLT/FORS2 and MXU. Out of 562 slits, we\nextract radial velocities for 177 GCs. Moreover, we measure radial velocities\nof the integrated galaxy light, using slits with a sufficiently bright \"sky\".\nTo these data, we add 20 cluster velocities from Goudfrooij et al. (2001). In\nan appendix, we identify new morphological features of NGC 1316 and its\ncompanion galaxy NGC 1317. The GC sample based on radial velocities confirms\nthe colour peaks already found in our photometric study. The bright clusters,\nwhich probably have their origin in a 2 Gyr-old starburst and younger star\nformation events, avoid the systemic velocity. A Gaussian velocity distribution\nis found only for clusters fainter than about m_R=22 mag. The velocity\ndistribution of clusters shows a pronounced peak at 1600 km/s. These clusters\npopulate a wide area in the south-western region which we suspect to be a disk\npopulation. Globular clusters or subsamples of them do not show a clear\nrotation signal. This is different from the galaxy light, where rotation along\nthe major axis is discernable out to 3 arcmin radius. A simple spherical model\nlike that suggested by dynamical analyses of planetary nebulae reproduces also\nthe velocity dispersions of the faint GCs. The central dark matter density of\nthe present model resembles a giant elliptical galaxy. This contradicts\npopulation properties which indicate spiral galaxies as pre-merger components.\nMOND would provide a solution, but the kinematical complexity of NGC 1316 does\nnot allow a really firm conclusion. (abridged)",
                    "authors": "Tom Richtler, Michael Hilker, Brijesh Kumar, Lilia P. Bassino, Matias Gomez, Boris Dirsch",
                    "published": "2014-06-11",
                    "updated": "2014-06-11",
                    "primary_cat": "astro-ph.GA",
                    "cats": [
                        "astro-ph.GA"
                    ],
                    "main_content": "2.1. Observations The observations were performed in service mode during seven nights (period November 14th to December 21th 2006) at the European Southern Observatory (ESO) Very Large Telescope (VLT) facility at Cerro Paranal, Chile (programme 078.B0856(A), PI:Richtler). The VLT Unit Telescope 4 (Yepun) was used with the FORS2 (FOcal Reducer/low dispersion Spectrograph) instrument equipped with the Mask EXchange Unit (MXU). The standard resolution collimator used for this program provided a field-of-view of 6. \u20328 \u00d7 6. \u20328. The detector system consisted of two 4096 \u00d7 2048 red optimized CCDs with a pixel size of 15\u00b5m. The grism 600B gave a spectral resolution of about 3 \u00c5. The spectral coverage was dependent on the slit position on the mask. Normally, the usable coverage was about 2000 \u00c5 with limits on the red side varying between 5500 and 6500 \u00c5. We exposed 8 spectroscopic masks, whose preparation is described in the next section. Flat fielding was done with internal flat lamps. A He-Ar lamp was used for wavelength calibration. The observations are summarized in Table 1. 2.2. Mask Preparation Preimaging of the 8 fields (see Fig. 1) was carried out in October 2006. Each field was observed in the R filter for 60 seconds. The candidate selection was based upon the photometry in the Washington system (Paper I). However, at the time of the mask design, only a preliminary version of the photometry was available. Cluster candidates had to fulfill the following criteria: the allowed color range was 0.9 < C \u2212R < 2.1, and the candidates should exhibit a star-like appearance on the pre-images to distinguish them from background galaxies. The colour interval has been defined before we became aware that NGC 1316 hosts many bluer (and younger) clusters (Paper I). We moreover avoided objects brighter than R=20 mag, only a few bright objects entered the sample in an effort to fill the mask. The ESO FORS Instrumental Mask Simulator (FIMS) software1 was then used to select the positions, widths and lengths of the slits. A slit width of 1\u2032\u2032 was chosen which tolerates also slightly worse seeing conditions. The choice of the slit lengths was determined by the fact that most targets are very faint and therefore the best strategy is to measure sky and object in the same slit. However, this severely constrains the number of observable objects per mask, especially in the more crowded fields. But in contrast to previous work, where we wanted to maximize the number of objects (compare Richtler et al. 2004; Schuberth et al. 2006) we now give more weight to the quality of the sky subtraction and choose relatively long slits of typically 5\u2032\u2032 . After the positioning of the slits for the selected GC candidates, the remaining space on the masks (especially in the outer fields) was used to include additional objects. Thus, also some background galaxies and point sources not matching the above mentioned criteria were observed. 2.3. The dataset To prevent a severe contamination from cosmic ray hits, the observation of each mask was divided into two exposures of 45 min each with the exception of Field 3 for which three science images were obtained. In all spectra, the night sky emission lines red-wards of about 5200 \u00c5 are by far the most prominent features, i.e. the spectra of the GC candidates are sky dominated. In addition to the spectroscopic observations, calibration measurements were obtained during day time. Fig. 1 shows the distribution of 562 slits, located on 8 FORS2 fields. Only a minor fraction of these slits finally provided radial velocities of GCs. In total, we determined velocities for 177 GCs and 81 stars (the velocity gap between stars and GCs is sufficiently large for safe classifications). Five GCs in our sample have been already measured by Goudfrooij et al. (2001b). We found 16 quasars, and 117 galaxies. We did not attempt to derive redshifts for all objects. The remaining spectra could not be used due to low S/N. 2.4. Remarks on the reductions and velocity measurements The reduction procedure and the measurement of radial velocities have been already described in numerous other papers, e.g. Schuberth et al. (2006); Richtler et al. (2004); Schuberth et al. (2010, 2012), so that we can be short. For basic reduction, spectrum extraction and wave-length calibration, we used the IRAF-task identify and apall. The radial velocities have been determined using the crosscorrelation IRAF-task fxcor. Due to the very different appearance and S/N of the spectra, it turned out to be impossible to establish a standard procedure, which would always use the same task parameters. Regarding the cross-correlation interval, we made good experience with the range 4700\u00c5-5400 \u00c5. Clearly defined correlation peaks are connected with uncertainties around 20-30 km/s. In the case of faint sources, more than one peak might appear, depending on the exact wavelength interval, within which the correlation is done. In these cases, we tried out what peak is the most stable against variations of the crosscorrelation interval. The uncertainty then may not be the uncertainty suggested by the broadness of the correlation peak. We 1 available from http://www.eso.org/observing/p2pp/OSS/FIMS/FIMStool.html 2 T. Richtler et al.: Globular cluster system of NGC 1316 Field Center Position Exp. Time Seeing # Slits OB Id Night UT (J 2000) (sec) (start) 1 3:23:13.0 -37:07:20 2700 0. \u2032\u20328 82 258629 2006-11-15 6:49 1 3:23:13.0 -37:07:20 2700 0. \u2032\u20328 82 258627 2006-11-15 4:53 2 3:22:58.0 -37:11:40 2700 1. \u2032\u20322 83 258618 2006-11-18 6:45 2 3:22:58.0 -37:11:40 2700 1. \u2032\u20323 83 258616 2006-11-18 7:31 3 3:23:13.0 -37:18:13 2700 1. \u2032\u20323 70 258615 2006-11-16 5:04 3 3:23:13.0 -37:18:13 2700 1. \u2032\u20320 70 258613 2006-11-16 5:59 3 3:23:13.0 -37:18:13 2700 1. \u2032\u20323 70 258615 2006-11-30 6:22 4 3:22:33.0 -37:18:39 2700 1. \u2032\u20322 64 258630 2006-11-19 5:30 4 3:22:33.0 -37:18:39 2700 1. \u2032\u20325 64 258632 2006-11-19 6:20 5 3:22:32.0 -37:15:20 2700 0. \u2032\u20329 68 258633 2006-11-19 6:53 5 3:22:32.0 -37:15:20 2700 0. \u2032\u20329 68 258625 2006-11-20 4:42 6 3:22:09.0 -37:13:52 2700 0. \u2032\u20328 66 258622 2006-11-18 5:17 6 3:22:09.0 -37:13:52 2700 0. \u2032\u20328 66 258624 2006-11-18 4:21 7 3:22:20.0 -37:08:45 2700 0. \u2032\u20329 64 258621 2006-11-20 5:47 7 3:22:20.0 -37:08:45 2700 1. \u2032\u20322 64 258619 2006-11-20 7:02 8 3:22:16.0 -37:05:36 2700 0. \u2032\u20328 65 258610 2006-12-21 3:07 8 3:22:16.0 -37:05:36 2700 1. \u2032\u20322 65 258612 2006-12-21 2:10 Table 1. Summary of observations (ESO program ID 78.B-0856(A)). The seeing values are those recorded by the ESO seeing monitor. Fig. 1. Positions of the slits overlaid on a 36\u2032 \u00d7 36\u2032 image taken with the MOSAICII camera at the 4m-Blanco telescope, Cerro Tololo (see Paper I for more details). North is up, east to the left. used as templates a high S/N spectrum of NGC 1396, obtained with the same instrumentation during an earlier run (Richtler et al. 2004) and a spectrum of one of the brightest globular clusters in NGC 4636 (Schuberth et al. 2010) (identi\ufb01cation f12-24). The globular cluster data are presented in Appendix B. 2.5. Comparison with previous measurements Because the \ufb01elds were not strongly overlapping, there are only six double measurements, i.e. the same object on two di\ufb00erent masks. In Table B.1, they have the identi\ufb01cations gc01214, 2891, 2977, 3151, 4128, 4138. The standard deviation of the velocity di\ufb00erences is 30 km/s. The small sample size probably prohibits to see more in this value than a rough approximation. However, our experience from previous work (Schuberth et al. 2010, 2012) is that the uncertainties given by fxcor normally are a good approximation of the true uncertainties. Goudfrooij et al. (2001b) measured radial velocities for a small sample of GCs. Their objects are strongly concentrated to the inner regions, so that we have only 5 objects in common. Table 2 shows the common GCs. The zeropoints agree extremely well, leaving the velocities of Goudfrooij et al. (2001b) by only a mean of 5.4 km/s higher than our velocities. This agreement can be partly coincidental, but at least it shows that the two velocity samples do not di\ufb00er greatly in their zeropoints. Table 2. Comparison of the common GCs in the sample of Goudfrooij et al. (2001b) and the present sample. The columns are: Identi\ufb01er and velocity of Goudfrooij et al., velocity as in the present paper, identi\ufb01er in Tables B.1 and B.2. IDG vr(Goud) vr(Ri) ID 123 1966\u00b11 1977\u00b110 gc03384 217 1840\u00b18 1855\u00b125 gc03318 121 1627\u00b1155 1618\u00b127 gc08412 204 1992\u00b119 1976\u00b134 gc02997 203 1639\u00b135 1610\u00b121 gc01324 Fig.2 shows the velocity uncertainties in dependence on the R-magnitude. The uncertainties are directly taken from fxcor. They cluster around 50 km/s as in previous work. The three outliers with errors around 150 km/s are the objects with the photometric identi\ufb01cation numbers (Table B.1) 341,1278, 3025. Two of them are very faint (1278,3025), and the spectrum of 341 might be badly extracted. 3. Population properties and velocities 3.1. Colour-magnitude diagram and colour distribution With the GC colours available as well as radial velocities from the present study, we show a \u201dclean\u201d CMD for con\ufb01rmed GCs in Fig.3 (upper panel). This CMD shows the same features, which have been found already in Paper I with a larger, but contami3 T. Richtler et al.: Globular cluster system of NGC 1316 Fig. 2. Uncertainties of the radial velocities in dependence from the R-magnitude. nated photometric sample. The dashed vertical line indicates the galaxy colour, as it has been measured outside the inner dust structure (Paper I). The dotted vertical line denotes the colour (C-R = 1.06) for clusters with an age of 10 Gyr and a metallicity of z=0.0002 (Marigo et al. 2008). Clusters bluer than this must be even more metal-poor (however, colour and metallicity at these low metallicity levels are not related in a simple manner, see e.g. Richtler 2013) or younger. To our sample we add 20 GCs from Goudfrooij et al. (2001b), which are coded as crosses. Their Washington colours have not been measured directly, but were transformed on the basis of Fig.1 from Paper I, using the BI colours given by Goudfrooij et al. . These objects are strongly concentrated towards small radii, thus individual reddening can be an issue. We also \ufb01nd some GCs distinctly bluer than C-R=1.0. These clusters cannot be old GCs. Note the outlying object at C-R=0.4, which has an age around 0.5 Gyr (metallicity is not anymore a critical parameter at these blue colours). As the more complete photometry of Paper I shows, such young objects are rare, but GCs as blue as C-R=0.8 are common. If these objects have their origin in star formation events which occurred later than indicated by the peak at C-R=1.4, the assumption is reasonable that they possess at least solar metallicity. As reference values we use ages for theoretical Washington colours for single stellar populations, taken from Marigo et al. (2008) and graphically displayed in Fig.1 in Paper I. Since we selected our spectroscopic sample with the help of our photometric data, but prior to the knowledge provided by Paper I, objects bluer than C-R=1.0 were only serendipitously targeted to \ufb01ll the spectroscopic masks. Clusters redder than the galaxy light must be metal-rich and quite old. The old metal-poor clusters, on the other hand, cannot be distinguished from younger, more metal-rich clusters, but, as argued in Paper I, they should not be too many. The lower panel shows the corresponding colour histogram. The striking two peaks at C-R=1.4 and C-R=1.1 match those which have been photometrically identi\ufb01ed. They are even weakly indicated in the smaller, but also clean sample of Goudfrooij et al. (2001b). In Paper I, we show that these peaks are a property of the colour distribution only for bright clusters (R<23 mag). They largely vanish if also fainter clusters are inFig. 3. Upper panel: the CMD of con\ufb01rmed globular clusters in NGC 1316 in the Washington system, marked by open circles. The photometric data are taken from Paper I. 20 objects from Goudfrooij et al. (2001b) are denoted by crosses. The dashed vertical line denotes the galaxy colour. The dotted vertical marks the colour limit for old, metal-poor globular clusters. Note the excess of clusters blueward of this limit which corresponds to ages of about 1 Gyr, if solar metallicity is assumed. Also note the object at C-R= 0.4. Lower panel: The corresponding colour histograms (solid histogram, only for our sample). The dotted histogram (scaled down for a convenient display) is the more complete photometric sample from Paper I. The two well de\ufb01ned peaks, already indicated in Goudfrooij et al. (2001a) probably mark two epochs of high star formation rates. cluded. Paper I tentatively interprets these peaks as signatures of starbursts with ages 1.8 Gyr and 0.8 Gyr, respectively. NGC 1316 has an interesting companion galaxy, NGC 1317 (see the appendix). Its systemic velocity is 1941 km/s. There is no indication for the photometric GC sample (Paper I), that GCs from NGC 1317 would be visible in the system of NGC1316. Moreover, the region of NGC 1317 is not covered by masks, but we cannot exclude that a few GCs belong to NGC 1317. None of the results of this contribution, however, depend on this possibility. 3.2. Velocities, colours, magnitudes A closer look at the relation between velocities, colours, and magnitudes reveals interesting facts. In the upper panel of Fig.4, 4 T. Richtler et al.: Globular cluster system of NGC 1316 Fig. 4. Upper panel: velocities versus colour. Open circles denote the present GC sample, crosses the objects of Goudfrooij et al. (2001b). In both panels, the systemic velocity is marked by the dotted vertical line. The bimodal colour distribution is well visible. Note that the objects belonging to the peak at C-R=1.4 avoid velocities higher than the systemic velocity. Lower panel: velocities versus R-magnitude. The brightest clusters do not show a kinematic a\ufb03nity to the bulge population. Note also the increasing velocity dispersion for clusters fainter than R= 21.5. velocities are plotted versus colours. The double peak structure in the colours is clearly discernable. A strange pattern is that the peak at C-R=1.4 is populated preferably by objects with radial velocities lower than the systemic velocity. The lower panel shows that clusters brighter than about R=21.5 avoid the systemic velocity of NGC 1316. Objects with colours 1.35< C-R <1.5 (the pronounced peak in Fig.3) are marked in red. Our GCs con\ufb01rm the trend, which is visible already in the sample of Goudfrooij et al., also for fainter clusters. One would expect that, if the majority of the bright clusters in red are clusters formed in the starburst with an age of about 2 Gyr (the dominant bulge population), they would also be kinematically connected to the bulge. However, the velocity \ufb01eld of the bulge is not known. The \ufb01eld stars related to the bright GC population should show the same kinematics, which does not \ufb01t at all to a Gaussian distribution around the systemic velocity. Relative radial velocities as high as 500 km/s and more indicate that these clusters are deep in the potential well and that their orbits are elongated. Even if these objects are now projected onto the bulge, it may be that their place of birth was not the bulge, but a star burst in one of the merger components in an early stage of the merger. The second striking observation is that the velocity distribution becomes broader with decreasing brightness. In Paper I it is shown that the bimodal colour distribution disappears if fainter clusters are included. It is therefore plausible to assume that the bright cluster population consists mainly of intermediate-age clusters belonging to a population with the complex kinematics of a merger/star burst situation still preserving, while the fainter older clusters, \ufb01lling a larger volume around NGC 1316, are progressively mixed in. 3.3. Velocity histograms The velocity histograms in several colour bins are shown in Fig.5. The colour bins refer to the bins used in Paper I to characterize the population mix of globular clusters and which appears as a reasonable binning guided by Fig.3. The interval 0.8 < C-R < 1.3 contains an unknown proportion of old, metal-poor clusters and clusters younger than about 1 Gyr. The interval 1.3 < C-R < 1.6 contains the bulk of intermediate-age clusters. In the interval 1.6 < C-R < 1.9, one expects to \ufb01nd old, metal-rich clusters. Instead of a unimodal Gaussian-like distribution, one sees in all histograms, except for the reddest clusters, two velocity peaks, which are best de\ufb01ned for the bluer clusters. The higher velocity peak agrees well with the systemic velocity of NGC 1316, but the low velocity peak at 1600 km/s indicates a peculiarity. The nature of this peculiarity can perhaps be inferred from Fig.6. The objects populating the peak are preferentially located on the western side of NGC 1316, occupying a large interval of position angles. This is suggestive of a disk-like distribution of GCs seen from face-on. Of course that does not mean that the supposed disk population is present only in the interval 1550-1650. The complete dispersion in z-direction is unknown and uncertainties in the velocities widen an intrinsically sharp distribution. 3.4. Two-dimensional distribution Fig.6 shows the two-dimensional distribution of clusters for several selection of velocities or colours/magnitudes. Because we could not achieve a complete azimuthal coverage, we have well de\ufb01ned western and eastern parts. Crosses denote velocities higher than the systemic velocity of 1760 km/s, circles lower velocities. North is up, east to the left. The upper left panel contains the full sample. The larger symbols are objects from the HST cluster sample of Goudfrooij et al. (2001b), which populate the innermost region, where we do not have objects due to the bright galaxy light. A di\ufb00erence between the western and eastern part is not discernable. This changes dramatically, if we select only the peak at 1600 km/s, which is the upper right panel with the selection indicated. These objects dominantly populate the western part and it is tempting to imagine that we are looking onto a large disk or at least a structure which is thin along the line-of-sight. A few of these objects may belong to Schweizer\u2019s L1-structure (Schweizer 1981; Richtler 2013) (see Fig.A.1), but the largest concentration is found still within the morphological bulge. The lower panels show selections according to colour and magnitude. The left panel selects the interval 1.0 <C-R<1.2, which may contain younger clusters, but also old, metal-poor objects. Here we observe that the majority of objects with veloc5 T. Richtler et al.: Globular cluster system of NGC 1316 Fig. 5. Radial velocity histograms for di\ufb00erent colour intervals, corresponding to di\ufb00erent cluster populations (see text). Typical uncertainties are of the order 50-80 km/s (compare Fig.2). The vertical dotted line indicates the systemic velocity. The dotted histogram in the left panel is the velocity histogram of Goudfrooij et al. (2001b), where the two velocity peaks already are discernable. We interpret the peak at 1800 km/s as the expected peak at the systemic velocity. The peak at 1600 km/s is caused by a dominance of clusters with this velocity in the western part of NGC 1316. ities higher than the systemic velocity are located on the eastern part. The following panel selects from this sample only objects brighter than R=21.5 mag. These bright clusters have a higher probability to be young (about 0.8 Gyr) than fainter objects. Practically all clusters are on the north-eastern side. The next panel selects 1.4<C-R<1.6, an interval which hosts the brightest clusters of intermediate age. Except for the concentration at the south-western side, there is nothing striking. Selecting only the brightest clusters (which with the highest probability are clusters of age about 2 Gyr), one recognizes the major axis of NGC 1316. Bright clusters therefore are probably connected with the bulge (we have no complete knowledge about the occurrence of bright cluster at large radii), but the population is inhomogeneous regarding colour and spatial distribution. 3.5. Velocities and radial velocity dispersions In the following, we consider only our sample and disregard the objects of Goudfrooij et al. (2001b). Fig.7 shows in its upper panel the radial velocities versus the radial distance, in its lower panel the velocity dispersions in slightly overlapping bins. The bin widths of 1\u2032 and 1.5\u2032 have been chosen to contain about 30 objects each in order to get a statistically meaningful velocity dispersion value. The velocity dispersions have been determined using the dispersion estimator of Pryor & Meylan (1993), adopting a systemic velocity of 1760 km/s. The uncertainties have been evaluated according to the quoted maximum-likelihood formalism using the individual uncertainties of the objects. Since the bins are not independent, the error bars probably overestimate the true uncertainty. However, the physical meaning of the velocity dispersion is not interpretable straightforwardly. It has a well known dynamical meaning for example in case of a nonrotating spherical or elliptical system in equilibrium, while the underlying symmetry in NGC 1316 is elliptical only in the inner region. It is clear without any test for Gaussianity that the dispersions for radii larger than 5\u2032 do not represent the dispersion of a Gaussian velocity distribution. To what extent the dominance of velocities smaller than the systemic velocity can be understood as a sample e\ufb00ect, is di\ufb03cult to evaluate, but outside the bulge are simply more clusters in the S-W-region, and it is this region which contributes with a sharp peak at about 1600 km/s. For radii smaller than 5\u2032 (which is the bulge) it is not so obvious. A Wilkinson-Shapiro test gives a p-value of 0.076, so the hypothesis that these objects follow a Gaussian distribution, is statistically valid, but not probable from other considerations. We come back to that shortly. The radial increase of the dispersion probably is real, but, as Fig.4 suggests, it may be caused by the bias towards bright clusters for smaller radii. These bright clusters show a smaller dispersion. Moreover, the relative contribution of old metal-poor clusters might be higher for larger radii, which we expect to increase the line-of-sight dispersion. Table 3 lists the values in Fig.7. It also lists the dispersion values for a subsample fainter than R=21.5, which is more appropriate for being compared to a spherical model than the full sample (see Sect.5), although the di\ufb00erence is hardly noticeable. Moreover, dispersions for an inner and an outer subsample as well as for two colour selections are given. The dispersions obviously depend in an irregular manner on the binning and sampling. The most natural assumption is that of a radially constant velocity dispersion. Table 3. Velocity dispersions for di\ufb00erent radial and magnitude/colour samples. Sample sizes are given in parentheses. Dispersion values for the fainter sample are used in Fig.12. Radius[arcmin] \u03c3[km/s] Radius[arcmin] \u03c3[km/s] no selections R> 21.5 2-3 185\u00b127 (27) 2-3.5 185\u00b128 (26) 2.5 3.5 195\u00b126 (30) 3-4.5 208\u00b131 (25) 3 4 191\u00b128 (26) 4-5.5 241\u00b137 (26) 3.5 5 204\u00b128 (29) 5-6.5 199\u00b135 (32) 4.5 6 212\u00b129 (36) 6-7.5 189\u00b132 (33) 5.5 7 145\u00b122 (33) 7-8.5 236\u00b133 (28) 6.5 8 183\u00b129 (39) 7.5 9 224\u00b132 (29) 8.5 12 220\u00b139 (19) 1.0 <C-R< 1.2 1.4 <C-R< 1.6 all 201\u00b112 (175) 182\u00b125 (45) 174\u00b126 (49) <5 194\u00b116 (79) >5 206\u00b117 (96) 6 T. Richtler et al.: Globular cluster system of NGC 1316 Fig. 6. Spatial distribution of globular clusters under various selections with the center of NGC 1316 as the origin. Crosses are clusters with velocities higher than the systemic velocity, open circles denote lower velocities. Large symbols are objects from the sample of Goudfrooij et al. (2001b). Upper left panel: Full sample, which is cleanly separated in an eastern and a western part. Upper right panel: clusters with velocities between 1550 km/s and 1650 km/s. There is an overwhelming dominance of clusters on the western side of NGC 1316, indicating that these clusters intrinsically have a disk-like distribution, seen almost face-on. Lower leftmost panel: clusters in the colour interval 1.0<C-R<1.2 (blue peak). Next panel: additional selection with only clusters brighter than R=21.5. These are bona \ufb01de younger clusters with ages around 0.8 Gyr. Almost all are located in the north-eastern bulge region. Next panel: clusters in the colour interval 1.4<C-R<1.6 (red peak). Lower rightmost panel: additional selection with only clusters brighter than R=21.5. These are bona \ufb01de younger clusters with ages around 2 Gyr and appear dominantly in the bulge region. Fig. 7. Upper panel: Radial velocities vs. galactocentric distance. Lower panel: Velocity dispersions for slightly overlapping radial bins. 3.6. Radial distribution of clusters In paper I we showed that the radial distribution of cluster candidates is quite di\ufb00erent for di\ufb00erent colour intervals. Particularly the distribution of cluster candidates with intermediate colours does not follow a uniform power-law, which means that the three-dimensionable distribution is strongly substructured. On the other hand, we want to use the GC kinematics in the frame of a spherical model to constrain the potential. The total sample is apparently not suitable, as the kinematics of the bright clusters show. Being led by Fig.4, we therefore choose all clusters fainter than mR = 21.5 to de\ufb01ne within our possibilities a sample which is the best approximation to a spherically homogeneous sample in the sense that no strong association to the inner bulge population, like the case of GC candidates of intermediate colour, is visible. For evaluating the number density pro\ufb01le, we use the photometric database from Paper I (the point-source catalog is available on-line) and select point-sources in the magnitude interval 22 < mR < 24. Fig.8 shows the resulting surface densities. The counts in the inner region become severely incomplete due to the galaxy brightness, but from 2\u2032 outwards, the counts are fairly complete. The horizontal dotted line marks the background outside of 13\u2032 . The long-dashed line represents the \u201dbeta-model\u201d n(r) = 2100 \u00b7 (1 + (r/rc)2)\u22121 (1) with n(r) as the surface density in numbers/square arcmin and rc= 8\u2032\u2032 as a scale radius. Except for the factor, which has been \ufb01tted, this is the spherical model for the galaxy light from paper I. This is a clear di\ufb00erence to giant elliptical galaxies, where at least the metal-poor GC subpopulation shows a shallower pro\ufb01le than the galaxy light. This is normally interpreted as a result of the accretion of dwarf galaxies (e.g. Richtler 2013) donating metal-poor clusters. Fig.11 in Paper I indeed shows a somewhat shallower pro\ufb01le for the blue clusters. But in NGC 1316, the blue clusters are a mix with unknown fractions of old, metalpoor and younger clusters. As the intermediate clusters from Fig.11 in Paper I demonstrate, a shallow density pro\ufb01le is probably caused by younger clusters. The fraction of old, metal-poor objects in our faint cluster sample is unknown, but it is plausi7 T. Richtler et al.: Globular cluster system of NGC 1316 ble that their number density pro\ufb01le is not signi\ufb01cantly di\ufb00erent from old, metal-rich clusters, because the pre-merger populations are expected to be dynamically well mixed. Fig. 8. The radial density pro\ufb01le for GC candidates fainter than mR = 22 mag derived with the database of Paper I. The selection of point sources has been done as described in Paper I. The horizontal dashed line denotes the background density of GC candidates. See equation 1 for more details. 4. Rotation of galaxy and clusters The bulge of NGC 1316 rotates along its major axis (D\u2019Onofrio et al. 1995; Arnaboldi et al. 1998; Bedregal et al. 2006) with an amplitude of about 100 km/s. Long-slit observations showed this rotation signal out to a radius of about 2.5\u2032 (Bedregal et al. 2006). The kinematics of globular clusters might be related to the kinematics of the stellar population, particularly for clusters of intermediate colour which show the strongest link with the bulge (Paper I). Moreover, our data provide the possibility to enlarge the radius of measured rotation and determine the kinematical axis of the galaxy light. 4.1. Galaxy velocities and rotation signal Some of our targets are so close to the galaxy\u2019s center that their \u201dsky\u201d spectra can be used to measure the radial velocity of the galaxy light at the location of the target. Since the masks were not designed for this purpose, we can use only slits where corresponding skyslits (now the real sky) can be found. In practice, we constructed average skyslits from regions of the mask with low background intensity and subtracted them from a given target background slit. O\ufb00sets along the dispersion direction obviously cause systematic errors, since the shape of the spectra without \ufb02ux calibration depends on the position within the mask. Finally, we selected 72 slits from two masks, where we measured the radial velocity by cross-correlation with NGC 1396 as the template. Fig.9 shows the resulting velocities in dependence of radius (upper panel) and position angle (lower panel). We \ufb01t the rotation signal by a sine vrot = A sin(\u03c6 + \u03c60) + v0, where A is the amplitude, \u03c60 the phase constant, and v0 the radial velocity of the center of rotation which one identi\ufb01es with the velocity of NGC 1316. In the upper panel, it is striking that the velocities higher than 1760 km/s seem to increase with radius, while the lower velocities are more or less constant. The larger velocity scatter in the two regimes of position angle do not re\ufb02ect the errors, but should be real, indicating than the rotation cannot be characterized by one amplitude only. This is strengthened by the comparison with planetary nebulae. See more remarks in Section 6.2. The resulting values of A for the entire sample and radial subsamples are given in Fig. 10. Since the subsamples do not differ signi\ufb01cantly regarding the values of \u03c60 and v0, we \ufb01x them to \u03c60=18\u25e6, the value for the innermost sample, and v0=1760 km/s, the systemic velocity. Thus a position angle of 72\u25e6marks the major axis of the rotation. Interestingly, this angle is larger by at least 10\u25e6than the position angle of the optical major axis, for which (Schweizer 1980) quotes a position angle of 50\u25e6at 1.0\u2032 and 60\u25e6at 2.5\u2032. About 10% of the ATLAS3D-galaxies show this \u201dmisalignment angle\u201d (Statler 1991; Krajnovi\u00b4 c et al. 2011). Out to a galactocentric distance of 2.5\u2032 (15.5kpc), the amplitude of the rotation signal is practically constant and very well de\ufb01ned. The outermost two bins are somewhat elevated, but whether this is due to an intrinsically higher rotation or due to a more complex velocity \ufb01eld, cannot be decided. The comparison with Bedregal et al. (2006) shows a very good agreement in the region of overlap. The comparison with McNeil-Moylan et al. (2012) reveals that the amplitude of rotation of PNe in NGC 1316 is signi\ufb01cantly smaller (85\u00b111) than our rotation amplitude of the galaxy light in the same radial regime. The PNe sample is plausibly biased towards bright PNe, stemming from younger populations, while the galaxy light samples the entire, luminosity weighted range of populations present in NGC 1316. Therefore this di\ufb00erence between PNe and galaxy light is suggestive of a kinematical di\ufb00erence between older and younger populations, as the GC kinematics re\ufb02ect it. In the projected light, the inclination of a rotating structure is not the only uncertain point. In a mix of stellar populations with di\ufb00erent kinematic properties, some substructures may contribute to a rotation signal, others not. The rotation amplitude, as observed, may also be di\ufb00erent at di\ufb00erent wavelengths, if the rotational behaviour depends on the population. 4.2. Do the clusters rotate? The comparison of the galaxy velocities with the GC velocities is interesting. The rotation signal in Fig.10 for the innermost positions is very pure. Only for radii larger than 2\u2032 one \ufb01nds velocities which do not \ufb01t into a strictly sinusoidal form. Part of the deviation might be caused by low S/N, but the velocities of the bright GCs suggest that there are parts of the galaxy moving with velocities strongly deviant from the systemic velocity or from a rotation pattern. The rotation signal of the galaxy light is fundamentally different from a rotation signal of GCs. The measured velocity of the galaxy light is the luminosity-weighted mean along the lineof-sight without a-priori knowledge of the population which is responsible for creating a rotation signal. The GCs, on the other hand, play the role of single stars without the possibility to remove the velocity dispersion, so that one does not expect such a clear rotation as measured in the galaxy. We also expect a contaminated rotation from the fact that velocities and locations can be related, e.g. in the southern L2-structure. Fig.11 shows the radial velocities vs. position angle for the entire sample and some 8 T. Richtler et al.: Globular cluster system of NGC 1316 Fig. 11. Radial velocities vs. position angle for di\ufb00erent subsamples. A clear rotation signal like that of the galaxy light is nowhere visible. The sample with r<4\u2032 and R>22 mag, i.e. the faint bulge clusters, seems to show the clearest rotation signal. Fig. 9. Upper panel: the radial distribution of galaxy velocities. Lower panel: Distribution of galaxy velocities over position angles. The displayed rotation signal (represented by a sine-curve) has an amplitude of 128 km/s, corresponding to the inner clusters, and peaks at 72\u25e6. The centre of rotation, indicated by the horizontal line, has the value 1760 km/s. subsamples, selected according magnitude, radius, and colour. The entire sample shows that intrinsically we \ufb01nd many clusters at low velocities and positions angles larger than 180\u25e6. This crowding is in part due to the objects populating the velocity peak at 1600 km/s, which seems to be related to the L1-feature of Schweizer (1980) (compare Fig.A.1 ). The clearest rotation is seen for the sample consisting of GCs fainter than 22 mag, Fig. 10. Rotation signature of the galaxy light in di\ufb00erent radial bins. The bin is indicated in arcmin, the rotation amplitude in km/s. The phase and the center of rotation has been kept at \ufb01xed values of 18\u25e6and 1760 km/s, respectively, which are excellent representations for the three innermost bins. The two outer bins start to deviate to higher values, perhaps indicating a progressive deviation from a well de\ufb01ned rotation. and closer than 4\u2032 to the centre. A \ufb01t to this sample reveals a0 = 120\u00b164 km/s and \u03c60=-1\u00b164\u25e6, demonstrating a large uncertainty. At least it is consistent with the bulge rotation. All other GC samples do not obviously rotate. 9 T. Richtler et al.: Globular cluster system of NGC 1316 5. Dynamical remarks Given the kinematic complexity, including the non-negligible rotational support, the mix of GC populations and uncertain threedimensional structure, a proper dynamical analysis presently is beyond our possibilities. However, a few remarks are adequate. The \ufb01rst remark to be made is that the kinematical data for the stellar population appear not to be entirely consistent in the literature. D\u2019Onofrio et al. (1995) measured a central velocity dispersion of 260 km/s, in good agreement with Bosma et al. (1985). The velocity dispersion then declines towards larger radii, reaching 150 km/s at 50\u2032\u2032, while in Bosma et al.\u2019s work, this decline is shallower and reaches 150 km/s at 80\u2032\u2032. Arnaboldi et al. (1998) give a central dispersion of only 200 km/s with a decline to 140 km/s at 60\u2032\u2032. There are also asymmetries with respect to the center, particularly pronounced along the minor axis. On the other hand, Bedregal et al. (2006) \ufb01nd as well a high central dispersion of about 260 km/s, but the decline is much shallower and consistent with a constant velocity dispersion of 200 km/s between 50\u2032\u2032(4.3 kpc) and 150\u2032\u2032(12.9 kpc) along the major axis. Since the VLT-data used by Bedregal et al. apparently have the highest S/N, we adopt in the following their kinematics. There is more agreement regarding the LOS velocities for which we adopt the Bedregal et al. values as well. To represent the GC velocity dispersions, we avoid to use the full sample because of the bright cluster kinematics, which apparently do not \ufb01t to a Gaussian. For a good sampling of the fainter clusters, we choose the limit R>21.5 mag to maintain a reasonable statistics and bin widths of 1.5\u2032 with an overlap of 0.5\u2032. These are the open circles in Fig.12. Looking at Fig.7, it is not surprising that deviations from a radially constant dispersion occur. The sampling of velocities is far from being ideal. 5.1. A spherical model In spite of all shortcomings, it is interesting to present spherical models. Firstly, it can be compared to the model of McNeilMoylan et al. (2012), based on PNe. Secondly, we can discuss the global characteristics of a dark halo without aiming at precision. Thirdly, we can use our new photometric surface brightness pro\ufb01le in the R-band from Paper I. Our model uses the non-rotating spherical Jeans-equation, as do McNeilMoylan et al. (2012). The Jeans-formalism was presented in many contributions, we refer the reader to Mamon & \u0141okas (2005) and Schuberth et al. (2010, 2012). The surface brightness of NGC 1316 in the spherical approximation is well represented by a \u201dbeta-model\u201d, which can be deprojected analytically (e.g. Schuberth et al. 2012). We then assign an M/L-ratio (R-band) and calculate the projected velocity dispersions, adding a dark halo to the baryonic mass. We use the formulas given by Mamon & \u0141okas (2005). We choose a logarithmic halo (hereafter log-halo) with asymptotic circular velocity v0 and core radius r0, given by vlog(r) = v0r/ q r2 0 + r2. (2) We \ufb01rst consider the simple case of isotropic models, which are shown in Fig.12 (upper panel). This maximizes the stellar M/L-value with respect to any radial anisotropy. To reproduce the central velocity dispersion of 250 km/s without dark matter, one needs an M/LR-value of 3.2, distinctly higher than the value of 2.5, we advocated in Paper I, and of course much higher than the value of McNeil-Moylan et al. (2012) (M/LR \u22481.7), whose best \ufb01t model is radially anisotropic. This high value has no support by any dynamical study (see the discussion of Richtler et al. Fig. 12. In both panels, the crosses mark velocity dispersions from Bedregal et al. (2006). The six open circles denote velocity dispersions of clusters fainter than R=21.5 mag. Upper panel: Some isotropic models. The lower short-dashed line is a model without dark matter and uses M/LR=3.5. The solid line is a log-halo with the parameters v0=300 km/s and r0=0.5 kpc and uses M/LR=1.3. The upper short-dashed line is a NFW-type halo with M/LR=2.0. See the text for its parameters. The longdashed line is a MONDian model with M/LR=2.5. Lower panel: Models with the radial anisotropy of Hansen & Moore (2006). The solid line is a log-halo with the same parameters as above, but with M/LR=2.0. The short dashed line is the same NFW halo as above to show that M/LR=2.0 results in a too high central velocity dispersion, but a stellar M/LR lower than 2.0 is di\ufb03cult to justify. 2011). Assuming solar metallicity and a Chabrier-IMF, it would correspond to an age of 5.5 Gyr as a single stellar population (Marigo et al. 2008). To minimize the dark halo, we want to keep the stellar M/L as high as possible. On the other hand, a relatively small r0 is needed to model the rapid decline of the stellar velocity dispersion. One has to lower M/LR until 1.3 to permit a log-halo with r0=0.5 kpc and v0=300 km/s. However, the central density of a log-halo is \u03c10 = 3(v0/r0)2/(4\u03c0G). (3) which means for the present halo a central density of 20 M\u2299/pc3. The \u201dsurface density\u201d (Donato et al. 2009) is \u03c10 \u00d7 r0 \u2248 104M\u2299/pc2. These values are not realistic in that they are much too high. Typical central densities of dark matter in massive elliptical galaxies are approximately 0.4M\u2299/pc3 (Richtler et al. 2011). We come back to that in the discussion. For comparison, we give a MONDian halo under isotropy with the MONDian circular velocity vM = r v2 N(r)/2 + q v4 N(r)/4 + v2 N(r)a0r, (4) 10 T. Richtler et al.: Globular cluster system of NGC 1316 where we adopt a0 = 1.35 \u00d7 10\u22128cm/sec2 (Famaey et al. 2007). Such halo needs M/LR=2.5. However, merger simulations rather indicate modest radial anisotropies. We use the \ufb01ndings of Hansen & Moore (2006) that the resulting anisotropy of stars in their merger simulations is related to the logarithmic slope of the three-dimensional stellar mass distribution by \u03b2 = 1 \u22121.15(1 + slope(r)/6). (5) For our photometric model, \u03b2 reaches a constant radial anisotropy of +0.4 at about 5 kpc. A good approximation for this relation is the anisotropy pro\ufb01le considered by Mamon & \u0141okas (2005): \u03b2 = 0.5(r/(r + ra)), ra being a scale radius with some low value. Adopting this kind of anisotropy, we can conveniently apply the formalism given by Mamon & \u0141okas (2005). A consequence of the anisotropy is to lower the stellar M/L-ratio to comply with the central velocity dispersion, which is boosted by the projected radial contributions. In the outer parts, the radial anisotropy results in a lower projected velocity dispersion. So we have to lower the M/L even more (which contradicts all existing dynamical and population evidence) or work with a more realistic value and reduce drastically the dark matter content in the inner region. The parameters M/LR=2, r0=5 kpc, and v0=300 km/s do a good job. This halo is shown in Fig.12. Its central density is 0.2M\u2299/pc3 and the surface density is 103M\u2299/pc2, which are consistent with values for massive elliptical galaxies. This is more or less a halo of the kind which McNeil-Moylan et al. (2012) derived from planetary nebulae. To enable the comparison with the dark matter densities of elliptical and spirals by Napolitano et al. (2010), we also give dark matter pro\ufb01les of the NFW-type: \u03c1 = \u03c1s r/rs(1 + r/rs)2 (6) with \u03c1s and rs being a characteristic density and a scale radius, respectively. With rs =17 kpc and \u03c1s = 0.028M\u2299/pc3 in combination with M/LR = 2.0, one has a good representation in the isotropic case (Fig.12, upper panel). For the anisotropic case (lower panel), we use the same parameters to show that the central velocity dispersion becomes too high and the M/L-value has to be lowered. The mean density within an e\ufb00ective radius of 68.9\u2032\u2032(Paper I, appendix) or 6 kpc is 0.079 M\u2299/pc3. Comparing this value with Fig.9 of Napolitano et al. (2010) shows that it is a typical value for a massive elliptical. We comment on this further in the discussion. Looking at other halo shapes is not worthwhile, given the observational constraints and model restrictions. They will di\ufb00er in details, but not in the main conclusions which we reserve for the discussion (see 6.3). 6. Discussion 6.1. The GC colour distribution within the globular cluster system It is very satisfactory that in the colour distribution of the \u201dpure\u201d GC sample, the same features appear as in the photometric sample, namely a peak at C-R\u22481.4 and a peak at C-R\u22481.1. This bimodal appearance of the colour distribution in NGC 1316 has little to do with the bimodality, which is found in the GCSs of giant ellipticals, where the blue peak (C-R \u22481.3) consists of metalpoor, probably accreted clusters and the red peak of metal-rich clusters (C-R \u22481.7) formed with the majority of the metal-rich \ufb01eld population of the host galaxy (e.g. Richtler 2013). Although ages have been spectroscopically determined only for a few of the brightest clusters (Goudfrooij et al. 2001b) of the red peak, clusters as young as 0.5 Gyr can be identi\ufb01ed by photometry alone, provided that a radial velocity is available which excludes the nature as a background galaxy or as foreground star. The detections of GCs bluer than C-R=1.0 are serendipitous and more objects remain to be discovered. The colour interval between the red peak and C-R\u22481.0 could be populated by metal-poor, old clusters, but since clusters around 0.5 Gyr de\ufb01nitely exist, we would also expect clusters with ages between 2 Gyr (the red peak) and 0.5 Gyr. The colour variation among the brightest clusters might indicate the duration of a period with a high star formation rate, but high S/N spectra are necessary to investigate this in more detail, as well as to \ufb01nd out the fraction of old, metal-poor clusters. One notes the absence of very bright clusters in the blue peak, but we designed our masks leaving out objects brighter than R=20 mag and bluer than C-R \u22481.0 (because we did not expect such bright and blue objects). 6.2. Comparison with planetary nebulae Although it is beyond our scope to discuss in detail the kinematics of PNe presented by McNeil-Moylan et al. (2012), some remarks on the comparison between GCs and PNe are appropriate. The question is to what level are the kinematic properties of PNe and GCs comparable? The youngest GC populations will have no PN counterparts and the main population of bright PNe will stem from intermediate-age populations (Buzzoni et al. 2006). The velocity dispersions of the total samples of GCs and PNe agree within the uncertainties. Fig.13 shows velocity distributions of PNe, using the list published by McNeil-Moylan et al. (2012). The upper left panel shows the total sample, which is of course also presented by McNeil-Moylan et al., but here the binning is di\ufb00erent and the peak near the systemic velocity of NGC 1317 is not visible. The PNe inside a radius of 2.5\u2032 (lower left panel) show a picture similar to the bright inner GCs. We cannot compare with the GC population within the same radius, but the comparison with GCs within 5\u2032 (which radius is needed for producing comparable numbers), shows a perplexing agreement. The GCs are depicted by the dashed histogram. The peaks at 1600 km/s and 1900 km/s are exactly reproduced. This agreement vanishes, when PNe at larger radii are included. Because of the galaxy\u2019s brightness in the central parts, one may assume that the PNe are particularly bright and belong in their majority to the 2 Gyr population. We interpreted the velocity peak of GCs at 1600 km/s as a signature of a disk-like distribution of clusters in the outer south-western part of NGC 1316, which is dominated by Schweizer\u2019s L1 structure. This view still holds, when looking at the lower right panel of Fig.13, which is the outer south-western quadrant of the PNe distribution. The shift of the distribution and the peak at 1600 km/s are clearly visible. The upper right panel for comparison shows the complementary distribution which is well centered on the systemic velocity. But then one would not expect that the inner peak at about the same velocity is due to the same feature, unless there is a disk-like distribution of PNe over the entire galaxy. This issue remains open for further investigation. A further interesting point emerges from comparison of Fig.9 with the distribution of PNe velocities. Fig.9 shows that the galaxy velocities reach quite high values for the largest distances and position angles in the range between 0\u25e6and 90\u25e6. The same can be seen in the PNe velocity distribution. The highest PNe 11 T. Richtler et al.: Globular cluster system of NGC 1316 Fig. 13. For comparison with the GCs, some PNe samples are shown. Upper left panel: Entire sample for comparison. Lower left panel: inner PNe (solid line). Note the striking similarity with the globular clusters (dashed red line). Upper right panel: outer PNe covering a position angle interval of 2700 with the exception of the south-western quadrant. Here the velocity distribution is symmetric with respect to the systemic velocity. This histogram is meant as a supplement to the lower right panel. Lower right panel: the south-western quadrant. Like in the case of globular clusters (Fig.5), the velocity distribution is shifted towards lower velocities. The peak at 1600 km/s is not as pronounced as in the case of globular clusters. velocities are found in the radial distance range 2.9\u2032<R<4.3\u2032. If we select PNe with these distances, we can plot Fig.14 which shows velocities vs. position angles. The PNe population between 0\u25e6and 90\u25e6is striking. It represents the stellar population in the lines-of-sight along which the galaxy velocities are measured. Since the galaxy velocities are luminosity-weighted mean values, their nature is di\ufb03cult to analyse without the knowledge of the full velocity \ufb01eld. But velocities as high as 2200 km/s are hardly rotation velocities and probably related to the merger history. The velocity distribution of GCs in the bulge region is very similar to the velocity distribution of PNe, but at larger radii the velocity dispersions di\ufb00er signi\ufb01cantly. The velocity dispersion of GCs is more or less constant, while that of the PNe starts to decline at a radius of 200\u2032\u2032 (about 17.3 kpc). Since both trace the same mass, any di\ufb00erence probably is due to a di\ufb00erence in the three-dimensional distribution. Again, any reasoning must remain speculative at this point due to the uncertainty regarding this distribution and the detailed population properties. The parent population of PNe is of intermediate age, while GCs cover a larger range of ages. Even if we cannot identify old clusters, one would reasonably assume their presence. Their spatial distribution will be more spherical than that of the PNe, which trace the outer stellar structures. The GC sample at larger radii will be also contain a higher proportion of old clusters compared to the bulge population. We therefore suspect that the PNe will contain a higher fraction of objects belonging to a somewhat \ufb02attened parent population, which in a radial average naturally results in a lower line-of-sight dispersion. Fig. 14. Selection of the PNe from McNeil-Moylan et al. (2012): distance between 2.9\u2032 and 4.3\u2032. This plot shall demonstrate the similarity with Fig.9 in that there is a striking population of high PNe velocities at position angles less than 60\u25e6. The velocity distribution of PNe might represent the velocity distribution along the line-of-sight, which is measured with luminosity weights by the integrated light. 6.2.1. High velocity offsets In the GC sample and even more pronounced in the PNe sample, one \ufb01nds a few objects with astonishingly large radial velocity o\ufb00sets to NGC 1316, in the case of PNe up to 1000 km/s. As McNeil-Moylan et al. (2012) suggest, some of the extreme cases may be Lyman-\u03b1 galaxies at z=3. In the Milky Way, such velocities would be labelled \u201dhypervelocities\u201d and a common interpretation is the acceleration by the supermassive black hole (SMBH) in the galactic center (e.g. Brown et al. 2012; Hills 1988). These objects are extremely rare. The SMBH in NGC 1316 is more massive and the stellar density might be higher, but one would not expect to \ufb01nd these stars in appreciable numbers in a PNe sample (in this case, the kinematics of PNe would perhaps not say much about the potential of NGC 1316). Large velocity o\ufb00sets have been found also in NGC 1399 (Richtler et al. 2004; Schuberth et al. 2010), but NGC 1399 is in the center of the Fornax cluster, while there are no such large potential di\ufb00erences near NGC 1316. The other possibility is that radial velocities near 1000 km/s are recession velocities rather than peculiar velocities. The PNe would then belong to an intergalactic population. This has been suspected before in the case of GCs around NGC 1399 (Richtler et al. 2003), but until now can be neither con\ufb01rmed nor discarded. 6.3. The dark halo of NGC 1316: Spiral galaxy or elliptical galaxy? As discussed in Paper I, all evidences point toward spiral galaxies as pre-merger components. In brief, the arguments are: the old globular cluster system, although it cannot be identi\ufb01ed cluster-by-cluster, must be quite poor, not \ufb01tting to a giant elliptical galaxy. Moreover, a simple population synthesis requires an intermediate-age population for the pre-mergers in order to reproduce the galaxy colour, not an old population. On the other hand, the dark halo does not show the characteristics of dark halos of spiral galaxies, but \ufb01ts to massive elliptical galaxies. 12 T. Richtler et al.: Globular cluster system of NGC 1316 As \ufb01rst shown by Gerhard et al. (2001), the dark halos of spiral galaxies, when represented by logarithmic halos, have central densities signi\ufb01cantly lower than those of elliptical galaxies of comparable mass. The estimated factors vary between 10 and 30. These factors appear lower in the more recent work of Napolitano et al. (2010). However, the central density of our lowdensity log-halo (0.2M\u2299/pc3) is, what we would expect for an elliptical galaxy with a stellar mass of about 2.5 \u00d7 1011M\u2299. The dark halo of McNeil-Moylan et al. (2012) has a central density of 0.12 M\u2299/pc3, but their model has a constant radial anisotropy of \u03b2=+0.4 and demands M/LB = 2.8 which corresponds to about M/LR= 1.7, a quite low value, which would correspond to a single stellar population of 1 Gyr (Marigo et al. 2008). As the authors say, these parameters may change with a more sophisticated modelling. However, one would expect that the collisionless merging of two dark matter halos would lower the characteristic densities and not enhance them. It is perhaps too early to call that a serious problem in view of the simplicity of the present approach. At least it points toward the possible existence of an inconsistency in the context of \u039bCDM and adds to the many other unsatisfactory \ufb01ndings, see the compilations of Kroupa (2012) and Famaey & McGaugh (2012). That the MONDian interpretation with M/LR=2.5 works quite well, is at least remarkable. Again, it is not necessarily a strong point for MOND, given the equilibrium assumption of an apparently quite chaotic system. However, NGC 1316 would not be the \ufb01rst galaxy outside the world of disk galaxies, where MOND works well only with an M/L, which \ufb01ts to their evolutionary history. Milgrom (2012) recently showed, that the isolated ellipticals NGC 720 and 1521 are consistent with the MONDian phenomonology. Both are late merger remnants (as it is the case with many isolated \u201dellipticals\u201d; Tal et al. 2009; Lane et al. 2013) with lower M/L-values than for old, metal-rich elliptical galaxies. So it not only seems that the MONDian phenomenology extends to elliptical galaxies (or in other words, that elliptical galaxies fall onto the same baryonic Tully-Fisher relation as disk galaxies), but that from the LCDM point of view, the dark matter content depends somehow on the M/L-values of the stellar population, which would be intriguing. 7. Summary and conclusions We present radial velocities of 177 globular clusters in NGC 1316 (Fornax A), obtained with mask spectroscopy using FORS2/MXU at the VLT. To these data, we add 20 radial velocities from Goudfrooij et al. (2001b). Moreover, we determined radial velocities for the galaxy background light at 68 locations out to a radius of 4\u2032. We discuss the kinematical structure of the globular cluster system and use existing data in combination with the globular clusters to present a spherical dynamical model, using the photometric model from Paper I. The most important \ufb01ndings are: \u2013 The colour distribution of con\ufb01rmed GCs is bimodal, showing the same peaks as in the larger, but contaminated photometric sample of GCs. To these peaks, we assign two epochs of particularly high star formation rate, one at 2 Gyr, one at 0.8 Gyr. Moreover, we con\ufb01rm that there are a few clusters as young as 0.4 Gyr. \u2013 Globular clusters brighter than about MR \u2248\u221210 mag avoid the systemic velocity, particularly so the bright clusters of the Goudfrooij et al. sample, which are constrained to the inner 5 kpc. Their \ufb01eld stellar counterpart might be an extended stream. In this case, one would expect many more bright clusters at large distances. The inner planetary nebulae show a stunningly similar pattern. \u2013 A striking peak in the velocity distribution at 1600 km/s is mainly populated by clusters outside the bulge in the southwestern region of NGC 1316. This peak may indicate a disklike distribution of star clusters. We suggest that they belong to the structure L1, which bona \ufb01de is the remnant of an infalling dwarf galaxy. \u2013 The velocity dispersion of GCs shows a clear dependence of brightness by getting higher for fainter clusters, reaching a value of about 200 km/s. \u2013 Out to 3\u2032, the galaxy light shows a clear rotation signal with a more or less constant amplitude of about 130 km/s. We do not \ufb01nd any subpopulation of GCs with a similarly clear rotation. At larger radii the velocities scatter signi\ufb01cantly, but we cannot distinguish between a chaotic velocity \ufb01eld and large errors due to low S/N-spectra. \u2013 Disregarding the question, whether spherical models are good approximations or not, we present logarithmic halos as the dark matter halos, which can reproduce quite well the kinematics of the stellar light and the globular clusters. Valid parameters are r0 = 5kpc, v0 = 320 km/s, corresponding to a central dark matter density of around 0.2 M\u2299/pc3. This halo is quite similar to the dark halo shown by McNeil-Moylan et al. (2012). Given the entire kinematic evidence, the GCS cannot be described by simple morphological parameters like it is the case with many giant ellipticals. The large variety of ages (metallicities are unknown), the uncertain three-dimensional arrangement, and the perhaps complex velocity \ufb01eld re\ufb02ect the complex history of kinematics and dynamics. The present dark halo shows high dark matter densities typical for a massive elliptical galaxy, although all indications rather point to spirals as merger progenitors. After merging activity, one would expect the pre-merger dark matter densities to be even lower. This con\ufb02ict is perhaps resolvable with MOND. Whatever the truth, NGC 1316 and its dark matter halo is probably a key object in the discussion of LCDM and alternate gravity theories.",
                    "introduction": "Globular clusters are \u201dGuides to galaxies\u201d (Richtler & Larsen 2009). The photometric and kinematic properties of a globular cluster system (GCS) permit to identify subpopulations, to con- strain scenarios of galaxy formation and star formation history, and to discover the existence and shape of dark matter halos at large galactocentric radii (see Brodie & Strader 2006 and Harris 2010 for reviews). Most kinematical studies of GCSs targeted old elliptical galaxies (e.g. Strader et al. 2011; Schuberth et al. 2010; Lee et al. 2010; Romanowsky et al. 2009; Lee et al. 2008; Schuberth et al. 2006; Richtler et al. 2004 and references therein) whose GCSs show the typical \u201dbimodality\u201d of blue and red clus- ters which also corresponds to di\ufb00erent kinematical properties (e.g. Schuberth et al. 2010). The red (bona \ufb01de metal-rich) clus- ters might have been formed in the star-burst which formed the Send o\ufb00print requests to: T. Richtler \u22c6Based on observations obtained with the VLT at ESO, Cerro Paranal, Chile under the programme 078.B-0856 main body of elliptical galaxies, while the blue (bona \ufb01de metal- poor) population might have been donated mainly by the infall of dwarf galaxies (see Richtler 2013 for an overview). The rich GCSs of giant ellipticals, which are dominated by the metal-poor cluster populations, have probably been shaped by secular evo- lution rather than by major merger events (van Dokkum et al. 2010; Genel et al. 2008). The target of the present contribution is the GCS of NGC 1316 (Fornax A). This galaxy is a well investigated merger rem- nant in the outskirts of the Fornax cluster and has been stud- ied in many wavelength domains from the X-ray to the radio. See Richtler et al. (2012b)(hereafter Paper I) for a representative summary of the work done on NGC 1316. To that we add the work on planetary nebulae by McNeil-Moylan et al. (2012) and on the mass functions of star clusters by Goudfrooij (2012). In the Washington photometry from Paper I, the GCS of NGC 1316 appears quite di\ufb00erent from that of a giant ellipti- cal galaxy. The blue and red GCs of giant ellipticals show peaks 1 arXiv:1406.2868v1  [astro-ph.GA]  11 Jun 2014 T. Richtler et al.: Globular cluster system of NGC 1316 with Washington colours at C-R=1.35 and C-R=1.75, respec- tively (Bassino et al. 2006). The colour distribution of bright clusters in the bulge region shows a clear bimodality, which, however, has a meaning di\ufb00er- ent from that in giant ellipticals. A peak at C-R=1.4 marks a star- burst with an age of about 2 Gyr, which is in agreement with the spectroscopic ages and abundances of three massive star clus- ters (Goudfrooij et al. 2001b). A bluer peak at C-R=1.1 probably corresponds to a more recent starburst 0.8 Gyr ago, but spectro- scopic con\ufb01rmation is still pending. A small sample of 22 bright GCs in the innermost region with radial velocities already ex- ists (Goudfrooij et al. 2001b). In this paper we present the radial velocities of 172 additional objects in a wide \ufb01eld. We describe the kinematics of this cluster sample and also make dynamical remarks on this complex system. This paper is the third in a series devoted to the cluster sys- tem of NGC 1316. Paper II (Richtler et al. 2012c) investigates the remarkable object SH2, perhaps a dwarf galaxy which re- cently formed a cluster population. We adopt a distance of 17.8 Mpc, quoted by Stritzinger et al. (2010) using the four type Ia supernovae which appeared so far in NGC 1316. At this distance, 1\u2032\u2032corresponds to 86.3 pc. The heliocentric systemic velocity of NGC 1316 is 1760 km/s (Longhetti et al. 1998)"
                },
                {
                    "url": "http://arxiv.org/abs/1103.3040v1",
                    "title": "Remarks on the properties of elliptical galaxies in modified Newtonian dynamics",
                    "abstract": "Two incorrect arguments against MOND in elliptical galaxies could be that the\nequivalent circular velocity curves tend to become flat at much larger\naccelerations than in spiral galaxies, and that the Newtonian dark matter halos\nare more concentrated than in spirals. Here, we compare published scaling\nrelations for the dark halos of elliptical galaxies to the scaling relations\nexpected for MONDian phantom halos. We represent the baryonic content of\ngalaxies by spherical profiles, and their corresponding MONDian phantom halos\nby logarithmic halos. We then derive the surface densities, central densities,\nand phase space densities and compare them with published scaling relations. We\nconclude that it is possible to get flat circular velocity curves at high\nacceleration in MOND, and that this happens for baryonic distributions\ndescribed by Jaffe profiles in the region where the circular velocity curve is\nflat. Moreover, the scaling relations of dark halos of ellipticals are\nremarkably similar to the scaling relations of phantom halos of MOND.",
                    "authors": "Tom Richtler, Benoit Famaey, Gianfranco Gentile, Ylva Schuberth",
                    "published": "2011-03-15",
                    "updated": "2011-03-15",
                    "primary_cat": "astro-ph.CO",
                    "cats": [
                        "astro-ph.CO",
                        "astro-ph.GA",
                        "gr-qc"
                    ],
                    "main_content": "Although it has been argued that some ellipticals do not need any dark matter or enhancement of gravity (Romanowsky et al. 2003), there are many counter-examples (Magorrian & Ballantyne 2001; Richtler et al. 2004; Schuberth et al. 2006; Kumar et al. 2007). Such a recent example is the elliptical galaxy NGC 2974 where the presence of an HI disk allowed a more or less direct measurement of circular velocities (Weijmans et al. 2008). There is also evidence that elliptical galaxies exhibit flat circular velocity curves , but that, contrary to spiral galaxies, this happens in the inner regions where g > a0 (e.g., G01, Weijmans et al. 2008). Such a flattening of circular velocities is a priori not expected in the strong to intermediate gravity regime in MOND, and poses the question of how to analytically interpret it. In the intermediate gravity regime, the transition from Newtonian to MONDian dynamics is described by the \u00b5function of MOND. Many concordant studies have recently shown that, in spiral galaxies, the \u201csimple\u201d transition of Famaey & Binney (2005) is a good representation of the data (Gentile, Famaey, & de Blok 2011, for an extensive discussion). In a spherical system, with this simple transition, the enclosed (baryonic) mass MM(r) needed to produce the same gravitational potential in MOND as the (baryonic+dark) mass MN(r) in Newtonian gravity is: MM(r) = MN(r) \u2212 \ufffd 1 MN( 1 MN(r) + G r2a r2a0 \ufffd\u22121 . (1) In a region where the circular velocity is constant vc = V (even if g > a0), one can write MN(r) = V2r/G, and thus after some algebra MM(r) = V4 a0G V4 a0G \u00b7 r r + V bly, this enc r r + V2/a0 . (2) Remarkably, this enclosed mass profile corresponds precisely to a Jaffe profile (Jaffe 1983) with scale-radius r j = V2/a0 (meaning that the acceleration is a0 at rj), and with total mass Mtot = V4/(a0G). Indeed, as the enclosed mass MM(r) = MM(r0)+4\u03c0 \ufffdr r0 \u03c1(R)R2dR, this enclosed mass profile corresponds locally to the density profile: \u03c1(r) = Mtot 4\u03c0 Mtot 4\u03c0 \u00b7 rj r2 (r + rj r2 (r + rj)2 , (3) with the characteristic surface density (see also Milgrom 1984) Mtot/r2 j = a0/G. This profile is of course not valid for the very inner parts of an elliptical galaxy, where V is not constant. Let us also note that (i) it was already known that a Jaffe profile produces a flat circular velocity curve at r \u226ar j in Newtonian gravity, which MOND generalizes to radii r \u223cr j; (ii) Mtot does not necessarily have to be the real total mass of the galaxy, as the Jaffe profile fit to the density distribution could have a cutoff in the outer parts. In that case, the constant circular velocity V would actually fall slightly above the prediction from the baryonic Tully-Fisher relation of spiral galaxies. Interestingly, this is precisely what is observed for the G01 sample of ellipticals. The fact that elliptical galaxies can exhibit (equivalent) circular velocity curves that are flat in the intermediate gravity regime is thus analytically understood in MOND by the fact that the outer regions of ellipticals can be approximated by a Jaffe profile with a large scale-radius, i.e. in regions well within the intermediate gravity regime rather than in the deep-MOND regime. These flat circular velocity curves would have been impossible with exponential density profiles (as encountered in spiral galaxies), meaning that the fact that circular velocity curves become flat quicker in ellipticals does not come as a surprise in the context of MOND. This finding looks like an interesting possibility to devise new tests of MOND based on photometry. However, in reality it might be difficult: not many spherical galaxies with a precisely measured density profile are dynamically investigated out to large radii, and have enough tracers to measure the higher order moments and constrain the anisotropy. Moreover, light might not trace the baryonic mass precisely. As an example, the circular velocity in NGC 2974, which can be traced by an HI disk, becomes constant at around 5 kpc and has the value 300 kms\u22121, which would correspond to a Jaffe scale radius of 23 kpc. Unfortunately, NGC 2974 is neither spherical nor does its photometry reach large radii so that it does not serve well as a test object. In any case, Weijmans et al. (2008, their Fig. 20) showed that the reverse procedure (going from the density to the circular velocity curve) leads to a very good fit. 3. Dark matter scaling relations for phantom halos of ellipticals We now apply the reverse procedure, and check whether the phantom halos predicted by the simple transition of MOND (Famaey & Binney 2005) comply with the observational scaling relations of dark halos of ellipticals. As stated above, Jaffe profiles are not good descriptions of the very inner parts of ellipticals. We hereafter rather choose Hernquist profiles (Hernquist 1990) to represent the baryonic content of ellipticals: these are realistic enough and allow for an exhaustive exploration of their properties without varying too many free parameters. Such a Hernquist-model is described by its total mass M and scaleradius rH. The profile of the Newtonian circular velocity curve then reads \ufffd vN(r) = ds \ufffd GMr GMr (r + rH)2 (4) where the scale-radius rH of the Hernquist-model is related to the effective (half-light) radius by Re f f = 1.815 rH. Adopting the simple transition formula between the Newtonian and the MONDian regime, one finds for the MOND circular velocity \ufffd vM = ar v \ufffd v e M \ufffd v2 N(r)/2 + \ufffd v MONDian ph \ufffd v4 N(r)/4 + v2 N(r)a0r, (5) \ufffd \ufffd and the MONDian phantom halo has the circular velocity \ufffd vphantom = ONDi \ufffd\ufffd v4 N(r)/4 + v2 N(r)a0r \u2212v2 N(r)/2 (6) T. Richtler et al.: Remarks on the properties of elliptical galaxies in modi\ufb01ed Newtonian dynamics (RN) 3 Table 1. The table shows for baryonic Hernquist pro\ufb01les with mass and e\ufb00ective radius described by the \ufb01rst two columns, the corresponding parameters of the MONDian \u201cphantom\u201d halo represented by a logarithmic potential \ufb01tted from the center to two e\ufb00ective radii of the baryonic pro\ufb01le. The columns are the baryonic mass, the luminous e\ufb00ective radius, the core radius r0 and the asymptotic velocity v0 of the log-halo, its surface density, central density and phase space density, the latter as de\ufb01ned by G01.The last column column gives the acceleration in units of a0 at a radius of 2 Re f f for each Hernquist model. The predictions for MONDian halos in the previous columns are valid only for galaxies embedded in an external \ufb01eld smaller than this value. baryonic mass [M\u2299] Ref f [kpc] r0 [kpc] v0[kms\u22121] S [M\u2299/pc2] \u03c10[M\u2299/pc3] fps acc.[a0] 1012 14.1 8.83 244 374 0.04 8.82\u00d7 10\u22129 1.53 8 \u00d7 1011 11.8 7.60 228 379 0.05 1.19 \u00d7 10\u22128 1.55 5 \u00d7 1011 8.06 5.20 193 393 0.076 3.02 \u00d7 10\u22128 1.91 2 \u00d7 1011 3.84 2.87 146 411 0.143 1.3 \u00d7 10\u22127 2.96 1011 1.47 1.24 99 438 0.35 1.02 \u00d7 10\u22126 8.44 5 \u00d7 1010 1.25 1.04 90 431 0.41 1.6 \u00d7 10\u22126 6.08 To enable the comparison with the scaling relations of G01, where the dark matter halos are adopted as logarithmic halos, we \ufb01t vphantom(r) to the circular velocity vlog(r) of a logarithmic halo with asymptotic circular velocity v0 and core radius r0: vlog(r) = v0r/ q r2 0 + r2. (7) The \ufb01ts are performed within the inner two e\ufb00ective radii 1. The \ufb01tted central dark matter density is then given by \u03c10 = 3(v0/r0)2/(4\u03c0G). (8) The characteristic central phase space density is de\ufb01ned (see G01) as fps = 33/2\u03c10/v3 0. (9) The characteristic surface density within r0 is then also de\ufb01ned as (see also Donato et al. 2009): S = \u03c10 \u00b7 r0. (10) Table 1 lists these \ufb01tted parameters for six baryonic Hernquist masses over a large mass range. The combinations of the masses and e\ufb00ective radii in Table 1 follow equation (5) of G01 (in accordance with the fundamental plane), where we transformed their luminosities into masses by using M/LB=8 for all galaxy baryonic masses. Fig.1 shows the values of the \ufb01tted dark halo parameters derived from applying MOND to the baryonic Hernquist-pro\ufb01les, together with the observational scaling relations given by G01 (dotted lines) and T09 (dashed lines). The upper panel shows the characteristic phase space density, the middle panel the central volume density, and the lower panel the characteristic surface density. Let us note that the plotted relations are indicative only, since the data (Fig.18 of G01 and Figs. 1 and 4 of T09) show a very large scatter even when logarithmically displayed. However, within this observational uncertainty, it is remarkable that some features are perfectly reproduced, particularly the slopes of the phase space density and of the central volume density as a function of baryonic mass (given the observational scatter, the almost perfect reproduction of the central volume density of G01 might of course be partly coincidental). As \ufb01rst emphasized by G01, the phase-space density values are at a given mass higher than in spirals, which means that under the \u039b Cold Dark Matter paradigm, dark halos of ellipticals 1 Let us note that these \ufb01ts are not particularly good: the circular velocity curve vc(r) = v0r/(r0 + r) would have provided better \ufb01ts, but the core radius of the corresponding halo would then be systematically smaller with respect to G01 cannot be the result of collisionless mergers of present-day spirals, but must have been assembled at a very early time, when the cosmological density was higher. In MOND this is of course not necessarily the case, as the phase-space argument does not apply to phantom halos. One also notes a remarkable exception to the scaling relations: the \ufb01tted characteristic dark matter surface density S is fully independent from the Hernquist parameters, and it is systematically lower than in G01 and T09. We emphasize that this constancy is not related to the special relation of mass and e\ufb00ective radius. Varying Re f f by a factor of two at a given mass does not change the constant surface density signi\ufb01cantly. This prediction of MOND thus brings the value closer to the (also constant) value of S observed in spiral galaxies, logS = 2.1 (Donato et al. 2009). Let us note that MOND also predicts the observed constant value of S in spirals, which is somewhat lower because (i) spirals are a bit deeper into the MOND regime (Milgrom 2009) and (ii) their \ufb02attened baryonic pro\ufb01les lead to a somewhat higher Newtonian gravity at a given mass, and in turn a somewhat lower MOND contribution to the phantom halo. On the \ufb01rst glance one might interpret this constancy and the other scaling relations as a clear signature of MOND in ellipticals: however, CDM may also predict that the surface density within the scale radius of NFW halos weakly depends on dark matter total mass (Boyarsky et al. 2010). For spiral galaxies, this is of little interest as it is known that cuspy pro\ufb01les often do not \ufb01t rotation curves (Famaey & Binney 2005; de Blok 2010; Gentile et al. 2005), the mystery then being how to erase the cusp by the feedback from the baryons while keeping the product \u03c10r0 constant. In elliptical galaxies, the situation is less clear as NFW pro\ufb01les often do \ufb01t the data equally well as cored pro\ufb01les (Schuberth et al. 2010). We thus \ufb01tted NFW pro\ufb01les to the same MONDian phantom halos and found a perfect agreement. The question remains whether these NFW-halos are \u201dcosmological\u201d or in other words, ful\ufb01ll the relation between virial mass and concentration predicted by cosmological simulations. Fig.2 displays for our Hernquist masses the resulting concentrations of the NFW-halos (open circles) corresponding to the MONDian phantom halos, while the triangles show the concentration values expected from the equation (9) of Macci` o et al. (2008), using 200 times the critical density as the mean density within the virial radius (standard cosmology: h=0.7, \u2126m = 0.3, \u2126\u039b = 0.7). One concludes that for high masses the MONDian phantom halos are not distinguishable from cosmological NFW halos, given also that the simulations predict considerable scatter. For smaller masses the di\ufb00erence between MONDian phantom halos and NFW cosmological halos is larger. 4 T. Richtler et al.: Remarks on the properties of elliptical galaxies in modi\ufb01ed Newtonian dynamics (RN) Fig. 1. The \ufb01gure shows the surface density, central density, and the central phase space density logarithmically (see the text for more explanations) of the phantom dark halos (circles) for different baryonic Hernquist masses from Table 1 together with the relations given by G01 (dotted lines) and T09 (dashed lines). Note that these parameters observationally exhibit a very large scatter around the mean relations. Note also that the relations of T09 are not given explicitly in their paper but have been constructed from their Table 3 omitting galaxies with young stellar cores. 4. External \ufb01eld effect Due to the non-linearity of MOND and its associated breaking of the Strong Equivalence Principle, a MONDian stellar system embedded in an external gravitational \ufb01eld (EF) stronger than its own internal \ufb01eld behaves in a quasi-Newtonian way, with an e\ufb00ectively higher gravitational constant (Milgrom 1983; Famaey et al. 2007). Most of the sample galaxies are located in clusters or groups where the EF might have an in\ufb02uence. Wu et al. (2010) for instance showed how the EF can lead to the lopsidedness of an originally axisymmetric non-isolated galaxy. While it is beyond the scope of this research note to evaluate in detail the EF in the present sample, a very rough estimation is presented in Fig. 3, which plots for the Virgo and the Coma cluster the accelerations based on the extrapolations of the mass models cited in the \ufb01gure caption (these extrapolations are only meant to give an order of magnitude estimate, but should not be Fig. 2. The \ufb01gure shows for our 6 Hernquist masses the concentration parameters of the associated NFW-halos, if the MONDian phantom halos are \ufb01tted by NFW pro\ufb01les (open circles). The triangles are the concentration parameters expected from the relation quoted by Macci` o et al. (2008) Fig. 3. This plot estimates the external \ufb01eld acting on Virgo (dashed) and Coma (dotted) galaxies. Abscissa is the projected distance in Mpc from M87 and NGC 4874, respectively. Ordinate is the acceleration in units of a0. Adopted distances for Virgo and Coma are 15 Mpc and 100 Mpc, respectively. The values for Virgo are generated by an extrapolation of the mass model for M87 of McLaughlin (1999). Some G01 galaxies are indicated by their NGC numbers. The values for Coma are generated by using the NFW dark halo from \u0141okas & Mamon (2003). Small open circles are the 18 T09 galaxies whose projected distances are taken from Godwin et al. (1983). The comparison with Table 1 shows that the EF is small. taken as rigorous models). This can be compared with the internal accelerations at 2 Re f f for the Hernquist models in Tab.1. Indicated are the projected distances of galaxies in the Virgo and Coma region. The positions of the Virgo galaxies correspond to the middle points of their NGC numbers, while the Coma galaxies are plotted as small open circles. One concludes that the EF should have no in\ufb02uence in the two samples at the galactocentric distances which we consider. T. Richtler et al.: Remarks on the properties of elliptical galaxies in modi\ufb01ed Newtonian dynamics (RN) 5 5. Conclusion Here we showed that (i) in MOND, galaxies exhibit a \ufb02attening of their circular velocity curve at high gravities (g > a0) if they are described by a Ja\ufb00e pro\ufb01le with characteristic surface density a0/G in the region where the circular velocity is constant (since this is not possible for exponential pro\ufb01les, it is remarkable that such \ufb02attenings of circular velocity curves at high accelerations are only observed in elliptical galaxies); (ii) the phantom halos of ellipticals predicted by MOND (i.e., the dark halos that would produce in Newtonian gravity the same additional gravity as MOND) can be \ufb01tted by logarithmic halos which perfectly reproduce the observed scaling relations of ellipticals for phase-space densities and central volume densities \u03c10; (iii) these halos have a constant characteristic surface density \u03c10r0; (iv) contrary to spirals (for which there are more data in the very central parts), the phantom halos of ellipticals can as well be \ufb01tted by cuspy NFW halos, the concentration of which is in accordance with the theoretical predictions of \u039bCDM for the highest masses, but in slight disagreement for baryonic masses smaller than 1011M\u2299: a modern, large, sample of elliptical galaxies, which are dynamically well investigated out to large radii and cover a large range of masses, will thus be required to get discriminating power. But in any case, and whatever the true physical reason for it, it is remarkable that a recipe (MOND) known to \ufb01t rotation curves of spiral galaxies with remarkable accuracy also apparently predicts the observed distribution of \u201cdark matter\u201d in elliptical galaxies. Acknowledgements. We thank an anonymous referee for a thoughtful report. TR acknowledges \ufb01nancial support from the Chilean Center for Astrophysics, FONDAP Nr. 15010003, from FONDECYT project Nr. 1100620, and from the BASAL Centro de Astro\ufb01sica y Tecnologias A\ufb01nes (CATA) PFB-06/2007. BF acknowledges the support of the Humboldt foundation. GG is a postdoctoral researcher of the FWO-Vlaanderen (Belgium).",
                    "introduction": "While data on large scale structures point towards a Universe dominated by dark matter and dark energy, e.g. Komatsu et al. (2011), the nature of these is still a deep mystery (e.g., Frieman et al. 2008; Wiltshire 2008; Bertone 2010; Kroupa et al. 2010). In this context, it is good to keep in mind that this conclusion essen- tially relies on the assumption that gravity is correctly described by Einstein\u2019s General Relativity in the extreme weak-\ufb01eld limit, a regime where the need for dark matter itself prevents the the- ory from being tested. Until this double dark mystery is solved, it is thus worth investigating alternative paradigms and their im- plications. For instance, Modi\ufb01ed Newtonian dynamics (Milgrom 1983, MOND) naturally explains various spiral galaxy scaling rela- tions (Tully & Fisher 1977; McGaugh et al. 2000; McGaugh 2004). The existence of a very tight baryonic Tully-Fisher rela- tion for disk galaxies (McGaugh 2005; Trachternach et al. 2009) is for instance one of the remarkable predictions of MOND. The corresponding relation for early-type galaxies is much more dif- \ufb01cult to investigate because they are pressure-supported systems, and the equivalent circular velocity curves determined from the velocity dispersion pro\ufb01les su\ufb00er from the well-known degen- eracy with anisotropy. However, some studies circumvented this problem: for instance, Kronawitter et al. (2000) used data on 21 elliptical galaxies to construct non-parametric models from which circular velocity curves, radial pro\ufb01les of mass-to-light ra- tio, and anisotropy pro\ufb01les as well as high-order moments could be computed. This led Gerhard et al. (2001, hereafter G01) to publish benchmark scaling relations for ellipticals. It was e.g. shown for the \ufb01rst time that circular velocity curves tend to become \ufb02at at much larger accelerations than in spiral galax- ies. This would seem to contradict the MOND prescription, for which \ufb02at circular velocities typically occur well below the ac- celeration threshold a0 \u223c10\u22128 cm s\u22122, but not at accelerations of the order of a few times a0 as in ellipticals. Also Thomas et al. (2009, hereafter T09) published scaling relations for dark matter halos of 18 Coma galaxies, using similar prescriptions as G01. We remark that G01 employed spherical models while the mod- els of T09 are axisymmetric. Not many studies have considered the predictions of MOND in elliptical galaxies. Milgrom (1984) showed that pressure- supported isothermal systems have \ufb01nite mass in MOND with the density at large radii falling approximately as r\u22124. It was also shown that there exists a mass-velocity dispersion relation of the form (M/1011M\u2299) \u2248(\u03c3r/100 kms\u22121)4 which is similar to the observed Faber-Jackson relation (Sanders 2000, 2010), and that, in order to match the fundamental plane, MOND models must deviate from being strictly isothermal and isotropic: a radial orbit anisotropy in the outer regions is needed (Sanders 2000; Cardone et al. 2011). Tiret et al. (2007) and Angus et al. (2008) also an- alyzed the distribution of velocity dispersion of PNe on scales of 20 kpc, and of satellites on very large scales of the order of 400 kpc around red isolated ellipticals, showing that MOND al- lowed to \ufb01t both scales successfully. Hereafter, we make general remarks on the properties of spherical galaxies within MOND, and their scaling relations. We \ufb01rst point out a remarkable property of elliptical galaxies ex- arXiv:1103.3040v1  [astro-ph.CO]  15 Mar 2011 2 T. Richtler et al.: Remarks on the properties of elliptical galaxies in modi\ufb01ed Newtonian dynamics (RN) hibiting a \ufb02attening of their circular velocity curve at small radii: such a \ufb02attening in the intermediate gravity regime is actually generated by a baryonic density distribution following a Ja\ufb00e pro\ufb01le in these parts of the galaxies. We then further show that the observational scaling relations for the dark halos of the ellip- tical galaxy sample by G01 are strikingly similar to the theoreti- cal \u201cphantom\u201d halos of MOND (i.e. the halo that would produce in Newtonian gravity the same additional gravity as MOND), with one remarkable exception: MOND predicts that the product of the central density with the core radius should be constant, as recently observed for spiral galaxies (Donato et al. 2009; Gentile et al. 2009)."
                }
            ],
            "Holger Baumgardt": [
                {
                    "url": "http://arxiv.org/abs/2303.01636v1",
                    "title": "Evidence for a bottom-light initial mass function in massive star clusters",
                    "abstract": "We have determined stellar mass functions of 120 Milky Way globular clusters\nand massive LMC/SMC star clusters based on a comparison of archival Hubble\nSpace Telescope photometry with a large grid of direct N-body simulations. We\nfind a strong correlation of the global mass function slopes of star clusters\nwith both their internal relaxation times as well as their lifetimes. Once\ndynamical effects are being accounted for, the mass functions of most star\nclusters are compatible with an initial mass function described by a broken\npower-law distribution $N(m) \\sim m^\\alpha$ with break masses at 0.4 M$_\\odot$\nand 1.0 M$_\\odot$ and mass function slopes of $\\alpha_{Low}=-0.3$ for stars\nwith masses $m<0.4$ M$_\\odot$, $\\alpha_{High}=-2.30$ for stars with $m>1.0$\nM$_\\odot$ and $\\alpha_{Med}=-1.65$ for intermediate-mass stars. Alternatively,\na log-normal mass function with a characteristic mass $\\log M_C = -0.36$ and\nwidth $\\sigma_C=0.28$ for low-mass stars and a power-law mass function for\nstars with $m>1$ M$_\\odot$ also fits our data. We do not find a significant\nenvironmental dependency of the initial mass function with either cluster mass,\ndensity, global velocity dispersion or metallicity. Our results lead to a\nlarger fraction of high-mass stars in globular clusters compared to canonical\nKroupa/Chabrier mass functions, increasing the efficiency of self-enrichment in\nclusters and helping to alleviate the mass budget problem of multiple stellar\npopulations in globular clusters. By comparing our results with direct N-body\nsimulations we finally find that only simulations in which most black holes are\nejected by natal birth kicks correctly reproduce the observed correlations.",
                    "authors": "Holger Baumgardt, Vincent Henault-Brunet, Nolan Dickson, Antonio Sollima",
                    "published": "2023-03-03",
                    "updated": "2023-03-03",
                    "primary_cat": "astro-ph.GA",
                    "cats": [
                        "astro-ph.GA"
                    ],
                    "main_content": "We took the input list of Milky Way globular clusters from the most recent version of the globular cluster database of Baumgardt et al. (2019), which lists 165 Galactic globular clusters. From this list we removed all clusters which either had no existing deep HST photometry reaching several magnitudes below the main sequence turn-over, were in fields of high stellar background density, or had large extinction values E(B\u2212V ) > 0.80. We also removed clusters for which the available HST photometry was not deep enough to allow us to determine the stellar mass function down to masses of at least \u223c0.50 M\u2299. In total we found 91 Galactic globular clusters which fulfilled all of the above constraints and we list these clusters in Table B1. In order to extend the measured mass functions to stars with masses above 0.8 M\u2299, which have already turned into compact remnants in \u223c12 Gyr old globular clusters, we also analysed stellar mass functions for 29 massive star clusters of the Large (LMC) and Small Magellanic Clouds (SMC) that have deep HST photometry and we list the adopted parameters and derived mass function slopes of these clusters in Table B2. For each star cluster we selected from the STSci data archive suitable HST photometry, making sure that we could get an as large as possible radial range for which we can measure the stellar mass function. Due to their proximity, this generally required us to analyse more than one HST field for Galactic globular clusters, while the more distant star clusters in the LMC and SMC usually fitted into a single HST field. Figs. A1 to A20 depict for each star cluster the location of the analysed HST fields. After downloading the HST data, we prepared the photometric images using the splitgroups and cameraspecific masking tasks as described in the DOLPHOT handbook and then performed stellar photometry on the data using DOLPHOT (Dolphin 2000, 2016). For ACS and WFC3 data, we performed the photometry on the CTE corrected flc images, while for the WFPC2 observations we used the c0m images to perform the photometry. We used the point-spread functions provided for each camera and filter combination by DOLPHOT for the photometric reductions. Photometry was done by using the drizzled drc and drz images provided by the STSci data archive as master frames, which also correct for geometric camera distortions. After obtaining the photometry, we removed detected objects that either had sharpness values |s| > 0.1 or roundness parameters r larger than r > 0.25 from the list of sources. The final magnitude and their associated errors for each star were calculated as the average and the r.m.s. of the individual magnitudes. After performing the photometry, we cross-matched the HST coordinates of bright stars with the positions of stars in the Gaia DR3 catalogue (Gaia Collaboration et al. 2022) using the Gaia proper motions to move the Gaia positions from the 2016.0 Gaia DR3 epoch to the observation epoch of the HST data. We then applied position dependent shifts to the HST coordinates to bring them into agreement with the Gaia DR3 ones. These shifts were for each star calculated by determining the median shift of the nearest 30 stars against their Gaia DR3 counterparts. For clusters with a high stellar background density, and if more than one data set in a given field was available, we performed astrometry for multiple epochs this way and then determined individual proper motions for the stars. We then fitted a Gaussian mixture model to the resulting proper motion vector point diagram, modeling both the cluster and the background stars as two-dimensional Gaussians. From the fit we then calculated membership probabilities and selected as cluster stars all stars that had a probability larger than 10% to be cluster members. We chose this relatively low limit since we can remove most of the remaining non-members by the isochrone fits described further below. For clusters with significant stellar background density but only one available epoch, proper motion cleaning is not possible. In order to remove the contribution of non-members in these clusters, we shifted the best-fitting isochrone in colour and determined stellar number counts to the left and right of the cluster main sequence and in regions that are occupied only by background stars. We then averaged the resulting stellar numbers per magnitude interval and subtracted them from the stellar number counts for the cluster main sequence. For clusters with significant and position dependent reddening we also de-reddened the final colour magnitude \u00a9 201x RAS, MNRAS 000, 1\u201316 Evidence for a bottom-light IMF in star clusters 3 diagrams (CMDs) before \ufb01tting the CMDs with stellar isochrones. Cluster de-reddening was done by \ufb01rst \ufb01tting an isochrone to the CMD of the central cluster parts. For each star we then calculated its displacement from this isochrone along the reddening vector. The coe\ufb03cients of the reddening vector were calculated based on the analytic formulae of Cardelli, Clayton & Mathis (1989) assuming R(V ) = 3.1. We also selected a magnitude interval where the CMD was dominated by cluster stars. We then corrected the CMD position of each star by calculating the mean displacement of the stars nearest to it. The number of stars used and the magnitude limits were varied for each cluster depending on the total number of cluster stars and the strength of the background contamination. Fig. 1 shows as an example the e\ufb00ects of proper motion cleaning and de-reddening for the globular cluster NGC 6558. For each analysed HST \ufb01eld we also estimated the photometric completeness using arti\ufb01cial star tests. To this end, we distributed arti\ufb01cial stars with uniform spatial density across each HST \ufb01eld. Stars were equally spread in magnitude along the location of each cluster\u2019s main sequence from the turnover down to the faintest detectable magnitudes. We created 100, 000 arti\ufb01cial stars in HST \ufb01elds that covered cluster centres and 25, 000 stars for HST \ufb01elds that covered areas outside the centre. We used a larger number of stars for central \ufb01elds since these are more a\ufb00ected by crowding and the completeness fraction will vary more quickly with radius since the stellar density varies strongly with radius in the centre. We used the DOLPHOT fakestars task to recover the magnitudes of the arti\ufb01cial stars and applied the same quality cuts to the arti\ufb01cial stars that we used to select real stars in the observed data sets. We then estimated the completeness fraction for each observed star from the ratio of successfully recovered stars to all inserted stars using the nearest 20 arti\ufb01cial stars that are within 0.2 mag of the magnitude of each observed star. In order to limit the in\ufb02uence of photometric incompleteness, we analysed mass functions only down to magnitudes where the average completeness is above 75% in each \ufb01eld. The only exception were WFPC2 observations where DOLPHOT seemed to have problems in properly aligning the individual data frames to the drizzled drz master frames and in which the photometric completeness was typically only around 75% even for bright, non-saturated stars. Since the alignment problems do not seem to depend on the stellar magnitudes and the completeness tests seem to be able to correct for their e\ufb00ect, we adopted a smaller completeness limit of 50% for WFPC2 data. 3 MASS FUNCTION DETERMINATION 3.1 Isochrone \ufb01ts We determined stellar mass functions by performing isochrone \ufb01ts to the observed CMDs. In order to determine the best-\ufb01tting isochrone, we varied the assumed cluster distances and reddenings but took the cluster ages and metallicities for which the isochrones were generated from literature data. We took the ages mainly from the compilations of De Angeli et al. (2005), Mar\u00b4 \u0131n-Franch et al. (2009), Dotter et al. (2010), VandenBerg et al. (2013) and Valcin et al. (2020). In order to account for systematic di\ufb00erences between the ages derived in these papers, we \ufb01rst averaged all ages and then calculated shifts for each individual paper against the mean ages determined this way. For the comparison we allowed the shifts to depend linearly on metallicity. This assumption is compatible with the observed age differences between di\ufb00erent studies, see e.g. Fig. 9 in (Mar\u00b4 \u0131nFranch et al. 2009). After correcting systematic di\ufb00erences in this way, we then calculated a \ufb01nal average age of each cluster. We took the cluster metallicities from the compilation of Carretta et al. (2009). We then created DSEP isochrones (Dotter et al. 2008) with these metallicities and ages and \ufb01tted the isochrones to the cluster CMDs. We used DSEP isochrones with an \u03b1 element abundance enhancement of \u03b1 = 0.2 for clusters with [Fe/H]< \u22121.0 and solar composition for clusters with metallicities larger than [Fe/H]= \u22121.0. To test the in\ufb02uence of the choice of isochrones on our results, we also \ufb01tted PARSEC isochrones (Bressan et al. 2012; Chen et al. 2014, 2015) to the clusters, but found that the derived global mass function slopes changed by less than \u2206\u03b1 = 0.20 dex. In order to \ufb01t the isochrones, we took the initial values of the cluster reddening from Harris (1996) and the cluster distances from Baumgardt & Vasiliev (2021). We then varied reddening and distance until we achieved the best \ufb01t to each observed CMD. Table B1 gives the best-\ufb01tting reddenings and distances for each cluster, averaged over all individual CMDs that we \ufb01tted for each cluster. The resulting reddening and distance values are usually within \u00b10.05 mag of the reddening given by Harris (1996) and within \u00b10.10 in distance modulus to the distances from Baumgardt & Vasiliev (2021). Once the best-\ufb01tting isochrones had been determined, we selected all stars with photometry compatible with each isochrone in radial annuli of 20\u201d width. We also calculated a best-\ufb01tting power-law mass function slope N(m) \u223cm\u03b1 for each radial annulus using the maximum likelihood method described in Clauset, Shalizi & Newman (2009) and Khalaj & Baumgardt (2013), which uses unbinned data. We note that our \ufb01nal results are rather insensitive to the assumed ages and metallicities, the measured mass function slope changes for example by only about 0.10 dex for a change in cluster age of 1 Gyr or a change in metallicity by \u2206[Fe/H]=0.20. 4 RESULTS 4.1 Initial mass function of clusters In this section we derive the mass function of star clusters that have relaxation times TRH of the order of their ages and total lifetimes at least three times larger than their ages. These clusters should have largely preserved their mass functions since they lost only a small fraction of their mass. In addition, due to their large relaxation times such clusters are also not strongly mass segregated and therefore even the small amount of mass loss they have experienced will lead to a loss of stars independent of their masses (at least as long as the clusters started without primordial mass segregation). We therefore assume that the present-day mass functions of these clusters resemble their initial mass functions. These assumptions are con\ufb01rmed by the results of the \u00a9 201x RAS, MNRAS 000, 1\u201316 4 Baumgardt et al. Figure 1. Example showing the e\ufb00ects of proper motion cleaning and di\ufb00erential reddening correction on the observed CMD of NGC 6558. Panel a) shows an mF 606W \u2212mF 814W vs. mF 606W colour-magnitude diagram of all stars that pass the sharpness and roundness criteria. Panel b) shows the proper-motion vector point diagram of these stars with the cluster centered at the origin. Stars marked in red are stars that pass the proper motion membership test. Panel c) shows the CMD after stars with membership probabilities less than 10% have been removed. Panel d) shows the CMD of the member stars after di\ufb00erential reddening correction, which leads to a further narrowing of the CMD. The arrow in the bottom right panel shows the direction of the reddening vector. N-body simulations done in sec. 4.2 of this paper as well as by the N-body simulations done by Webb & Leigh (2015). We derive the mass function for stars with masses m < 0.8 M\u2299from Milky Way globular clusters and the mass function of higher mass stars from the LMC and SMC star clusters. 4.1.1 The low-mass star IMF In this section we restrict ourselves to globular clusters that have mass function determinations both inside and outside their half-mass radii and for which the mass functions can be determined down to at least m = 0.25 M\u2299. This way we can measure the mass function directly from the observations and are independent of model \ufb01ts. These requirements restrict us to six globular clusters: IC 4499, NGC 5024, NGC 5053, NGC 5139, NGC 6101 and Ter 8. For each cluster we use the method described in Baumgardt et al. (2022) to determine the fraction fr of the cluster that is covered by our photometry at the projected distance of each star from the centre. We then assign a weighting factor w = 1/(frfp) to each star where fp is the fraction of stars of similar magnitudes and location that are recovered in our completeness tests. For NGC 5024 and NGC 5139 we are not able to apply this procedure to the innermost parts since our photometry becomes incomplete at masses m \u223c0.5 M\u2299due to crowding. The derived mass functions for these clusters could therefore be slightly skewed towards lower masses as we tend to miss preferentially higher mass \u00a9 201x RAS, MNRAS 000, 1\u201316 Evidence for a bottom-light IMF in star clusters 5 Figure 2. Global mass functions for (clockwise from top left) IC 4499, NGC 5024, NGC 5053, Ter 8, NGC 6101 and NGC 5139, the six globular clusters in our sample that have both large relaxation and lifetimes and photometry deep enough to reach down to at least 0.25 M\u2299. Filled black circles with error bars show the fraction of observed stars as a function of mass in the di\ufb00erent clusters and their 1\u03c3 errors. The orange, blue and red lines show \ufb01ts of the best-\ufb01tting single power law, two-stage power law and log-normal mass functions to the data. The parameter of the \ufb01ts are given in each panel. There is generally quite good agreement between the parameters that we \ufb01nd for each cluster, implying that all clusters have started with very similar mass functions. A two-stage power-law and a log-normal mass function provide about equally good \ufb01ts to the data, while a single power-law mass function overpredicts the number of high and low-mass stars and underpredicts the number of stars with masses around 0.4 M\u2299. The deviations are however only of order 10%. stars due to mass segregation. However the e\ufb00ect is likely only small since we are analysing clusters with large relaxation times which are not strongly mass segregated. We similarly lose a few percent of the outermost stars in all clusters since our photometry does not reach the tidal radius, however we again expect that this is not going to have a strong e\ufb00ect on our results. After deriving the individual stellar masses, we then \ufb01t a single-power mass function, a two-stage power-law mass function with a break-mass mBreak and a mass function slope \u03b1Med for stars with m > mBreak and a low-mass slope \u03b1Low for stars with m < mBreak, and a log-normal mass function \u03c6(m) \u223ce\u2212(logMC\u2212logm)2/(2\u03c32 C) with a characteristic mass MC and a width \u03c3C to the data. We derive the best-\ufb01tting parameters for each of these models using a maximum-likelihood approach, following the procedure outlined by Clauset, Shalizi & Newman (2009). Fig. 2 depicts the mass distribution of stars in each of the six clusters as well as the results of our \ufb01ts. It can be seen that single powerlaw mass functions are not accurate \ufb01ts to the data since they predict too many high and low-mass stars and too few intermediate stars with masses around 0.4 M\u2299. However, the relative deviations from the actual data are for most masses only of order 10%, so a single power-law mass function is still a useful approximation. Fig. 2 also shows that two-stage power-law mass functions and log-normal mass functions provide signi\ufb01cantly better \ufb01ts to the data. For a two-stage power-law mass function, we obtain break masses mBreak between 0.39 M\u2299to 0.44 M\u2299, mass function slopes between \u03b1M \u2248\u22121.40 to \u03b1M \u2248\u22121.90 for stars more massive than the break mass and signi\ufb01cantly \ufb02atter mass function slopes for the low-mass stars. The mass function does therefore \ufb02atten towards lower masses, a behavior qualitatively similar to that seen for Galactic disc stars (Kroupa 2001). The individual slopes are however \ufb02atter at all masses, leading again to a mass function with a smaller fraction of low-mass stars compared to what is found in the Galactic \ufb01eld. Taking the average over all six clusters we obtain for the break mass, and the high and low-mass slopes: mBreak = 0.42 \u00b1 0.02, \u03b1Med = \u22121.68 \u00b1 0.20 and \u03b1Low = \u22120.27 \u00b1 0.08. Here the error bars re\ufb02ect the standard deviation of the individual clusters around the mean. We decided to use the standard deviation as an estimate of the uncertainty since the formal error bars are usually small (typically of order 0.02) and do \u00a9 201x RAS, MNRAS 000, 1\u201316 6 Baumgardt et al. Figure 3. Mass function slopes for massive LMC and SMC star clusters. Horizontal lines depict the mass range for which the mass functions have been determined, vertical lines depict the uncertainty in the derived mass function slopes. In the left panel we show the slopes derived over the full mass range that could be \ufb01tted in each cluster, while in the right panel we have split the sample into two mass ranges for stars less and more massive than 1 M\u2299. There seems to be a clear break in mass function slope at around 1 M\u2299. not re\ufb02ect systematic errors which, under the assumption of a common initial mass function, should be better represented by the standard deviation. Fig. 2 also shows that log-normal mass functions provide acceptable \ufb01ts to the data. The values that we derive for the parameters are again similar between the di\ufb00erent clusters, making it possible that all clusters have started with the same mass function. Taking an average over all clusters, we \ufb01nd log MC = \u22120.36 \u00b1 0.03 and \u03c3C = 0.28 \u00b1 0.04. The Chabrier (2003) mass function, which \ufb01ts the distribution of stars in the Galactic disc, has a characteristic mass of log MC = \u22121.00. Hence our results again argue for a smaller fraction of low-mass stars in globular clusters compared to the Galactic disc. 4.1.2 The high-mass star IMF Since globular clusters only allow to determine the sub-solar stellar mass function, we next extend our analysis to the stellar mass functions of a number of massive star clusters in the LMC/SMC that have available deep HST photometry. The chosen clusters span a range of ages between 3 Myr and 12 Gyr and have masses from about 104 M\u2299to 7\u00b7105 M\u2299, similar to the masses of the globular clusters studied previously. We analyse each LMC/SMC star cluster in the same way as the Milky Way globular clusters by deriving their photometry from HST observations. Due to the large distances of the LMC and SMC, a single HST \ufb01eld is usually su\ufb03cient to cover most stars in a star cluster. From a comparison of the available observational data of each cluster to a grid of N-body simulations (to be described below), we then derive the physical parameters of the clusters including their mass functions. The basic data of the clusters (distances, ages, extinctions) are taken from Milone et al. (2023), or, for clusters not studied in this paper from available literature. We take the lifetimes of the clusters from Baumgardt et al. (2013), who determined lifetimes assuming that the clusters move in circular cluster orbits around the center of their parent galaxy. This seems to be a good approximation at least for the star clusters of the LMC (Bennet et al. 2022). Table B2 gives the parameters adopted in the \ufb01tting of the cluster CMDs together with the derived mass function slopes. The lifetimes and relaxation times of the LMC/SMC clusters are generally larger than their cluster ages, hence we do not expect the stellar mass function of these clusters to have signi\ufb01cantly changed since their formation. Fig. 3 shows the derived mass function slopes for the LMC/SMC star clusters. The left panel depicts the slopes derived for the full range of stellar masses that we can \ufb01t. It can be seen that there is a gradual change of the stellar mass function around 1 M\u2299. High-mass stars with masses m > 1 M\u2299have slopes close to a Salpeter mass function (\u03b1 = \u22122.3) while for low-mass stars the average power-law slope is around \u03b1 \u2248\u22121.4. The transition between both slopes happens at a mass of about m = 1 M\u2299. This conclusion is strengthened by the right panel in Fig. 3, where we have determined mass functions separately for stars with masses below and above 1 M\u2299. We have restricted the \ufb01ts in this panel to clusters where either the low-mass limit is below 0.60 M\u2299or the highmass limit is above 1.60 M\u2299. It can be seen that the derived slopes split into two well separated groups. The high-mass star function is compatible with a Salpeter slope with \u03b1 = \u22122.3 in essentially all clusters, while the low-mass stellar mass function has an average slope of \u03b1 \u2248\u22121.4, compatible with what we found for Galactic globular clusters. Combining the Milky Way and LMC/SMC results, and assuming that the Milky Way GCs had a high-mass star mass function similar to the LMC/SMC clusters, we can \u00a9 201x RAS, MNRAS 000, 1\u201316 Evidence for a bottom-light IMF in star clusters 7 Table 1. Details of the performed N-body simulations of star clusters evolving in tidal \ufb01elds. Columns 3 and 4 contain the initial cluster mass and half-mass radius. Column 5 contains the assumed black hole retention fraction. Columns 6 and 7 contain the semi-major axis and eccentricity of the cluster orbits. Column 8 contains the remaining mass fraction at T = 13.5 Gyr and column 9 the estimated lifetimes of the clusters. Model NStars MIni rh,Ini fBH aOrb eOrb MF in/MIni TDiss [M\u2299] [pc] [pc] [Gyr] 1 70,000 7.0 \u00b7 105 3.0 0.10 10000 0.00 0.197 21.7 2 70,000 7.0 \u00b7 105 3.0 0.10 5000 0.00 0.000 12.9 3 70,000 7.0 \u00b7 105 3.0 0.10 7500 0.00 0.104 16.4 4 70,000 7.0 \u00b7 105 2.0 0.10 6500 0.50 0.000 12.4 5 70,000 7.0 \u00b7 105 3.0 0.10 15000 0.00 0.294 34.4 6 70,000 7.0 \u00b7 105 5.0 0.10 15000 0.00 0.231 26.1 7 70,000 7.0 \u00b7 105 3.0 0.10 20000 0.00 0.340 48.9 8 70,000 7.0 \u00b7 105 5.0 0.10 20000 0.00 0.296 37.3 9 131,000 1.3 \u00b7 105 3.0 0.10 5000 0.00 0.159 19.0 10 131,000 1.3 \u00b7 105 2.0 0.10 6500 0.50 0.087 15.7 11 131,000 1.3 \u00b7 105 2.0 0.10 6300 0.60 0.044 14.4 12 131,000 1.3 \u00b7 105 3.0 0.10 10000 0.00 0.296 36.4 13 131,000 1.3 \u00b7 105 5.0 0.10 14000 0.44 0.219 24.7 14 131,000 1.3 \u00b7 105 3.0 0.10 3000 0.00 0.000 13.1 15 131,000 1.3 \u00b7 105 5.0 0.10 7500 0.00 0.054 14.1 16 131,000 1.3 \u00b7 105 5.0 0.10 10000 0.00 0.285 30.3 17 131,000 1.3 \u00b7 105 5.0 0.10 11250 0.33 0.245 26.5 18 131,000 1.3 \u00b7 105 5.0 0.10 20000 0.00 0.277 29.7 19 200,000 2.0 \u00b7 105 3.0 0.10 3000 0.00 0.021 13.8 20 300,000 3.0 \u00b7 105 3.0 0.10 3000 0.00 0.177 19.4 therefore describe the initial mass function of the clusters in our sample as a three-stage power-law with: \u03b1High = \u22122.30 \u00b1 0.15 for m > 1 M\u2299 \u03b1Med = \u22121.65 \u00b1 0.20 for 0.4 M\u2299< m < 1 M\u2299 \u03b1Low = \u22120.30 \u00b1 0.20 for m < 0.4 M\u2299 Alternatively, the initial mass function can also be described as a log-normal mass function with log MC = \u22120.36 and \u03c3C = 0.28 for stars with masses m < 1 M\u2299followed by a power-law mass functions for higher mass stars with a slope \u03b1 = \u22122.3. 4.2 N-body simulations of star cluster evolution Having determined the initial cluster mass function from the dynamically least evolved clusters, we now turn our attention to \ufb01tting the full cluster sample. In order to do this, we \ufb01rst ran N-body simulations of star clusters dissolving in tidal \ufb01elds starting from the three-stage power-law mass function determined in sec. 4.1. We will use these simulations in the next sections to determine the mass functions of evolved star clusters as well as to derive constraints on the black hole retention fraction of star clusters. In total we ran 20 N-body simulations of star clusters using NBODY7 (Nitadori & Aarseth 2012). The clusters contained between 70, 000 to 300, 000 stars initially and moved in either circular or elliptic orbits through an isothermal galaxy with a constant circular velocity of vc = 240 km/sec. The clusters followed King (1966) density pro\ufb01les with dimensionless concentration parameter c = 1.5 initially. We ran the simulations with an assumed neutron star and black hole retention fraction of 10%, i.e. 90% of the formed black holes and neutron stars were given large velocity kicks upon their formation so that they left their parent clusters. The retention fraction was applied to every formed neutron star and black hole independent of its mass. We took snapshots spaced by 500 Myr during the simulations and use the snapshots between 8 and 13.5 Gyr to determine the mass function of the remaining stars. By 13.5 Gyr, the studied clusters had lost between 20% to 100% of their initial stars. Table 1 gives details of the performed N-body simulations. Fig. 4 depicts the change in the mass function slopes for low, intermediate-mass and high mass stars in the N-body simulations as a function of the mass lost in the clusters. We depict only the evolution starting from the point when the clusters contain 60% of their initial mass since the mass lost up to that point is mainly due to stellar evolution within the \ufb01rst Gyr of evolution. When deriving the mass function slopes, we used for all stars their initial masses in order to remove the e\ufb00ect of stellar evolution of massive stars on the mass function. For the same reason we \ufb01t only the mass range from 1.0 to 8.0 M\u2299for the high-mass stars since most of the more massive stars were removed by natal velocity kicks, creating a discontinuity in the mass function. It can be seen that the clusters become increasingly depleted in low-mass stars as time progresses. The evolution is particularly strong for intermediate-mass stars (0.40 M\u2299< m < 1.0 M\u2299) and towards the later stages of evolution. The slower mass function evolution in the beginning is most likely due to the fact that clusters \ufb01rst need to become mass segregated before signi\ufb01cant changes occur to their internal mass functions. Overall the mass function evolution proceeds in a very similar way in the di\ufb00erent clusters despite the fact that the simulations span a wide parameter range. Hence it can be expected that the evolution of real star clusters proceeds along a similar path. The orange triangles in Fig. 4 mark the points when we determine (averaged) mass function slopes from the Nbody simulations. We list the derived mass function values in Table 2. From the initial masses of the remaining neutron \u00a9 201x RAS, MNRAS 000, 1\u201316 8 Baumgardt et al. Table 2. Power-law mass function slopes N(m) \u223cm\u03b1 and mass limits used as input values for our grid of N-body simulations. Model M(t)/M0 mLow mUp \u03b1 mLow mUp \u03b1 mLow mUp \u03b1 mLow mUp \u03b1 [M\u2299] [M\u2299] [M\u2299] [M\u2299] [M\u2299] [M\u2299] [M\u2299] [M\u2299] 1 1.00 0.10 0.40 -0.35 0.40 1.00 -1.65 1.00 6.50 -2.30 6.50 100.0 -2.30 2 0.30 0.10 0.40 -0.20 0.40 1.00 -1.35 1.00 6.50 -2.25 6.50 100.0 -2.80 3 0.22 0.10 0.40 -0.05 0.40 1.00 -1.05 1.00 6.50 -2.25 6.50 100.0 -3.15 4 0.15 0.10 0.40 0.25 0.40 1.00 -0.65 1.00 6.50 -2.20 6.50 100.0 -3.20 5 0.10 0.10 0.40 0.50 0.40 1.00 -0.05 1.00 6.50 -1.90 6.50 100.0 -3.20 6 0.05 0.10 0.40 0.80 0.40 1.00 0.30 1.00 6.50 -1.60 6.50 100.0 -3.80 Figure 4. Evolution of the mass function slopes \u03b1 of low (open circles), intermediate-mass (green triangles) and high-mass (blue squares) stars in the N-body simulations as a function of the remaining mass fraction M/MIni. For all three mass groups the mass functions evolve towards positive values due to mass segregation and the preferential loss of lower mass stars. The evolution is stronger towards the \ufb01nal stages of cluster evolution and for the intermediate-mass stars. Orange triangles mark the mass function values that are given in Table 2 and that are used for the grid of N-body simulations described in sec. 4.3. stars and black holes we also derive an additional slope for the highest mass stars. The derived values are somewhat uncertain due to the small number of remaining stars in the clusters. Nevertheless they show the strong depletion of the more massive black holes through dynamical encounters and binary formation in the cluster cores, which leads to a strong steepening of the mass function of the remaining black holes. 4.3 Derivation of the global mass function The derivation of the global mass functions for clusters that are dynamically evolved and have incomplete spatial coverage from the HST photometry was done similar to Baumgardt (2017) and Baumgardt & Hilker (2018) by \ufb01tting a large grid of N-body models to each observed cluster and \ufb01nding the model that best \ufb01ts all available data for each cluster We give a brief summary of this \ufb01tting procedure below, more details can be found in Baumgardt (2017) and Baumgardt & Hilker (2018). We \ufb01rst used the six sets of mass function values listed in Tab. 2 and ran a large grid of N-body simulations using these values. For each mass function, we used eight values for the initial half-mass radius rh, spaced roughly evenly in log rh between 2 pc and 35 pc and six values for the initial concentration index c of the initial King (1962) density pro\ufb01le between c = 0.2 to c = 2.5. All N-body simulations were isolated simulations having 105 stars initially and were run for 13.5 Gyr. Like in the simulations in the preceding section, we assumed a 10% retention fraction of black holes and neutron stars in these models. The \ufb01tting of the Galactic globular clusters and LMC/SMC star clusters was then done by selecting the snapshot closest in time to the age of an observed cluster from each N-body simulation and by then \ufb01tting these snapshots to the observational data available for each cluster. We scaled each N-body model along lines of constant relaxation time TRH to the same half-light radius of an observed cluster, using the cluster distances that were derived by Baumgardt & Vasiliev (2021) by combining a variety of individual distance determinations. We then calculated the velocity dispersion and surface density pro\ufb01les for each Nbody model from the distribution of its bright stars. We also calculated a sky projection of each N-body model centered around the position of each observed cluster and selected stars from the N-body models that are in the same region of the sky as the observed HST \ufb01elds. We then derived stellar mass function slopes for these regions and for the same radial annuli for which we have observational data. We then interpolated in our grid of models and derived the model that provides the best \ufb01t to the observed surface density pro\ufb01le from Baumgardt, Sollima & Hilker (2020), the observed velocity dispersion pro\ufb01le, and to the observed mass function slopes at di\ufb00erent radii that we calculated in this paper. We determine the best-\ufb01tting N-body model through \u03c72 minimization against the observed data and adopt as best-\ufb01tting cluster parameters the parameters of this model. From the models with \u03c72 < \u03c72 min + 1 we also obtain error bars on the cluster parameters. In order to re\ufb02ect the in\ufb02uence that e.g. uncertainties in the cluster ages have on the derived mass functions slopes, we add an uncertainty of \u2206\u03b1 = 0.10 in quadrature to the global mass function errors derived this way and adopt the resulting value as the \ufb01nal error. In order to improve the accuracy with which we can reproduce the cluster parameters, we added kinematic data published in recent years to the kinematic data from Baumgardt & Hilker (2018). Most of this data comes from large scale radial velocity surveys targeting Milky Way stars like Gaia DR3 (Gaia Collaboration et al. 2022; Katz et al. 2022), Apogee DR17 (Abdurro\u2019uf et al. 2022), Lamost DR7 (Cui \u00a9 201x RAS, MNRAS 000, 1\u201316 Evidence for a bottom-light IMF in star clusters 9 Figure 5. Comparison of the best-\ufb01tting N-body model to the observed surface density pro\ufb01le (panel a), line-of-sight velocity dispersion pro\ufb01le (panel b), proper motion velocity dispersion pro\ufb01le (panel c) velocity anisotropy pro\ufb01le (panel d), individual stellar mass functions at di\ufb00erent radii (panel e) and the slope of the mass function as a function of radius (panel f) for the globular cluster NGC 104. It can be seen that the N-body model is in general in good agreement with the observations. et al. 2012), Galah DR3 (Buder et al. 2021) and the WAGGS survey (Dalgleish et al. 2020). We list additional sources improving kinematic data for particular clusters in the Appendix. From our \ufb01ts we not only derived the stellar mass functions but also a range of other cluster parameters including total masses, core and half-mass radii and relaxation times TRH, which we will use further below. Fig. 5 shows as an example of the \ufb01tting procedure our \ufb01t for the cluster NGC 104. It can be seen that our best-\ufb01tting N-body model reproduces the surface density and velocity dispersion pro\ufb01les as well as the individual mass functions at various radii fairly well, despite the fact that our models need to \ufb01t a large amount of observational data with only few free parameters. We make the full set of comparisons as well as the derived parameters available on a dedicated website1. Finally, we also calculated the dissolution time TDiss for each cluster using the approach described in sec. 3.2 of Baumgardt et al. (2019). We present the derived mass function slopes in Tables B1 and B2. In these tables we have characterised the mass functions by both single power-law mass functions N(m) \u223cm\u03b1 over the whole observed mass range, as well as by two-stage power-law mass functions for clusters that have a su\ufb03ciently wide mass coverage to allow low-mass/high1 https://people.smp.uq.edu.au/HolgerBaumgardt/globular/ mass stars to be \ufb01tted separately. For the two-stage powerlaw mass functions we assumed \ufb01xed break masses of 0.4 M\u2299(Milky Way GCs) and 1.0 M\u2299(LMC/SMC clusters). In general two-stage power-law mass functions provide signi\ufb01cantly better \ufb01ts and we will therefore mostly use these in the rest of the paper. Fig. 6 compares the mass function slopes that we \ufb01nd in this work with mass function determinations of Galactic globular clusters by De Marchi, Paresce & Pulone (2007), Paust et al. (2010), Ebrahimi et al. (2020) and Dickson et al. (2023) for the clusters in common. The \ufb01rst three papers characterised the stellar mass function by a single power-law slope N(m) \u223cm\u03b1 over the whole range of masses \ufb01tted. We therefore also use our single power-law mass function \ufb01ts for comparison. It can be seen that the mass function slopes determined by De Marchi, Paresce & Pulone (2007) and Paust et al. (2010) span a larger range in values compared to our data and are also lower on average. This could at least partly be due to the fact that their lower-mass limits are usually higher, causing their mass functions to be more strongly dominated by stars with masses m > 0.4 M\u2299which have a steeper mass function slope. Some of the mass function slopes quoted by De Marchi, Paresce & Pulone (2007) are also locally measured ones that were not corrected for mass segregation. This will lead to an under or over estimation of the global mass function slopes if the local mass function was determined in the cluster centre or the cluster halo. We \u00a9 201x RAS, MNRAS 000, 1\u201316 10 Baumgardt et al. Figure 6. Comparison of the mass function slopes derived in this work against those derived by De Marchi, Paresce & Pulone (2007) (top left panel), Paust et al. (2010) (top right panel), Ebrahimi et al. (2020) (bottom left panel) and Dickson et al. (2023) (bottom right panel) for the clusters in common. We use single power-law slopes for the comparison with the literature papers except when comparing with Dickson et al. (2023), where we \ufb01t mass functions to stars in the low and intermediate mass regime separately. obtain excellent agreement with the mass functions derived by Ebrahimi et al. (2020) with almost all clusters being in agreement within the quoted error bars. This is despite the fact that the \ufb01tted isochrones as well as the method how the mass functions were derived are di\ufb00erent between our paper and Ebrahimi et al. (2020). The bottom right panel \ufb01nally compares our mass function slopes with the ones from Dickson et al. (2023). Here we compare the mass function slopes separately for stars with masses above and below 0.4 M\u2299. The slopes from Dickson et al. (2023) are not completely independent of ours since they also used our HST star counts. However the method to get from the star count data in different HST \ufb01elds to the global mass function is di\ufb00erent to ours. Nevertheless, the agreement between the derived mass function slopes is very good both for stars with m > 0.4 M\u2299 and for stars with m < 0.4 M\u2299. 4.4 Globular cluster mass functions We next discuss the mass function of the full sample of MW globular clusters and LMC/SMC stars clusters, derived by \ufb01tting the grid of N-body simulations calculated in the previous section against their observed mass function slopes. Fig. 7 shows the global mass function slopes of Galactic globular clusters and LMC/SMC star clusters as a function of the dynamical age (left panel) and the fractional lifetime of the clusters (right panel). We have de\ufb01ned the dynamical age as the ratio of the age of a cluster over its relaxation time and the fractional lifetime as the ratio of the cluster age to the estimated dissolution time. We \ufb01t the mass function of each cluster using either only the low mass stars m < 0.40 M\u2299(upper panels), the intermediate-mass stars with 0.40 M\u2299< m < 1.0 M\u2299(middle panels) or high mass stars with m > 1 M\u2299(lower panels). Since Galactic globular clusters do not contain high-mass main-sequence stars with m > 1 M\u2299, we have results for them only for the upper and middle panels, while for the LMC/SMC clusters we have no results for the m < 0.40 M\u2299stars since these are too faint to be observed due to the large cluster distances. It can be seen that we obtain a strong correlation between the mass function slopes and either the dynamical age or fractional dissolution time for the low and intermediate mass stars, with Spearman-rank order coe\ufb03cients equal to \u00a9 201x RAS, MNRAS 000, 1\u201316 Evidence for a bottom-light IMF in star clusters 11 Figure 7. Global mass function slopes \u03b1 as a function of the dynamical ages of globular clusters (left panel) and the ratio of their ages to their lifetimes (right panel). Globular clusters follow a narrow sequence going from clusters with negative mass function slopes (many low-mass stars) and relaxation times/lifetimes that are larger than their ages to clusters highly depleted in low-mass stars for clusters with short relaxation times/lifetimes. Clusters are also considerably more depleted in low-mass stars than canonical Kroupa/ Salpeter mass functions. r = 0.85 and r = 0.81 respectively. In particular, the mass function slopes for low and intermediate mass stars are more strongly negative for the dynamically least evolved clusters and become gradually less negative for clusters with smaller relaxation times and smaller lifetimes (relative to their ages). As will be discussed further below, the correlation of mass function slopes with dynamical ages and fractional lifetimes is likely due to the internal evolution of the clusters and not a sign of initial variations. If this is the case, the presentday mass functions of clusters on the right hand side in both diagrams should re\ufb02ect their initial mass functions, justifying the cluster selection made in sec. 4.1. There is also very good agreement between the mass functions of the Galactic globular clusters and the LMC/SMC clusters in the regions of overlap. For the high mass stars we have data only for the LMC/SMC star clusters. Since these clusters are on average more extended than Galactic globular clusters, they have large relaxation times and our data does not allow us to see an evolution of the high-mass star mass function as we can only probe the less evolved and presumably primordial distribution. The same applies to the fractional lifetime distribution, due to the young ages of the clusters and their long lifetimes times, the Age/TDiss ratio is less than 0.1 for all LMC/SMC clusters. Using only the least evolved clusters with relaxation times and lifetimes larger than a Hubble time, we \ufb01nd average mass function slopes of \u03b1Low \u2248\u22120.3 for m < 0.4 M\u2299 stars, \u03b1Low \u2248\u22121.6 for stars with 0.4 M\u2299< m < 1.0 M\u2299 and -2.3 for stars with m > 1.0 M\u2299. A Kroupa (2001) mass function has a slope of \u03b1 = \u22122.3 for stars more massive than 0.5 M\u2299and a slope of \u03b1 = \u22121.3 for less massive stars, while a Salpeter mass function has a slope of \u03b1 = \u22122.3 for all stars (see dashed and dotted lines in Fig. 7). Our results from the expanded cluster sample again argue for a low-mass star function in globular clusters with signi\ufb01cantly fewer low-mass stars compared to a Kroupa/Salpeter mass function. Our mass function below 0.8 M\u2299is in good agreement with the power-law mass function slope of \u22121.3 that Leigh et al. (2012) found from comparing the inner mass functions 27 globular clusters with the results of Monte Carlo simulations. We also con\ufb01rm earlier results by Cadelano et al. (2020) for the global mass functions of NGC 7078 and NGC 7099 as well as H\u00b4 enault-Brunet et al. (2020) for the mass function of NGC 104. \u00a9 201x RAS, MNRAS 000, 1\u201316 12 Baumgardt et al. Figure 8. Comparison of the derived mass function slopes for Galactic GCs (blue circles) with the results of N-body simulations of star clusters dissolving in tidal \ufb01elds with an assumed BH retention fraction (upon formation) of 10% (red), 30% (orange) and 100% (black). N-body models with 10% BH retention fraction follow the observed trends with dynamical age and fractional lifetime very well. 30% BH retention models reproduce the tend with dynamical age well, but reproduce the trend with fractional lifetime less well. 100% BH retention models can\u2019t reproduce these trends since they are not able to produce clusters strongly depleted in low-mass stars. 4.5 Comparison with N-body simulations We next investigate if the observed correlations of the stellar mass function with dynamical age and fractional lifetime that we \ufb01nd for Milky Way globular clusters can be explained by the dynamical cluster evolution and the constraints the results can put on the black hole retention fraction in star clusters. We again use the N-body simulations from Table 1 for 10% retention fraction. In order to test the dependence of the results on the assumed black hole retention fraction, we also re-run all simulations in Table 1 with 30% and 100% BH retention fractions. In these new simulations, we keep the neutron star retention fraction at 10%. Fig. 8 shows the comparison of the mass function slopes of observed globular clusters with the results of the N-body simulations. It can be seen that models with a 10% retention fraction of black holes reproduce the observed mass function trends with dynamical age and fractional lifetime very closely, showing that the di\ufb00erences in the stellar mass function between di\ufb00erent clusters are unlikely to arise due to initial di\ufb00erences, but can be explained by dynamical changes due to mass segregation and the preferential loss of low-mass stars. The models also show that the slope of the low-mass star mass function changes signi\ufb01cantly less over the course of evolution compared to the slope of stars in the mass range 0.4 to 1.0 M\u2299. The reason for this behavior is probably that low mass stars are pushed towards the outer parts where the relaxation time is long and there is little further mass segregation between these stars. Hence they are lost at a similar rate independent of their mass. Clusters starting with a 100% black hole retention fraction never reach a state where they are highly depleted in low-mass stars. This is because a large number of stellarmass black holes in a star cluster prevents mass segregation between the lower mass stars (e.g. L\u00a8 utzgendorf et al. 2013; Weatherford et al. 2018). As a result, clusters with many black holes are unable to reproduce the observed mass function evolution, especially for the dynamically more evolved clusters. Clusters with 30% BH retention rates can reproduce the trend with dynamical age but don\u2019t reproduce the trend with dissolution time towards the \ufb01nal stages. We therefore conclude that a high initial BH retention fraction is ruled out by our data. Given our chosen mass function, and assuming a 30% retention fraction of black holes leads to a typical ratio in the number of black holes to the total number of stars of around NBH/N\u2217\u22481.0 \u00b7 10\u22123 directly after BH formation. This ratio further decreases due to BH binary formation and subsequent hardening and ejections of the black holes from the cluster centres. Assuming a decrease by a factor of two to \ufb01ve in the number of BHs surviving up to a Hubble time, we predict between 30 to 100 (300 to 1000) remaining BHs in a 105 M\u2299(106 M\u2299) globular cluster. These estimates are in good agreement with estimates for the number of stellar-mass BHs inferred from observations of the surface density pro\ufb01les (Arca Sedda, Askar & Giersz 2018; Askar, Arca Sedda & Giersz 2018) and the internal amount of mass segregation (Weatherford et al. 2018) of Galactic globular clusters. They are also in agreement with what Dickson et al. (2023) \ufb01nd from a comparison of multimass King models with the observed kinematics of globular clusters. \u00a9 201x RAS, MNRAS 000, 1\u201316 Evidence for a bottom-light IMF in star clusters 13 Figure 9. Stellar mass function slopes as a function of (clockwise from top left) the mass of the stellar system, its stellar density, velocity dispersion and metallicity. Star clusters studied in this paper are shown by red crosses and black, open triangles. We only show clusters with relaxation times and lifetimes larger than their ages for which the present-day mass function should still be close to the initial one. In addition we also show stellar mass functions for Milky Way open clusters from Ebrahimi, Sollima & Haghi (2022) and Cordoni et al. (2023) (grey circles) as well as those for \ufb01eld stars in several nearby dwarf galaxies (blue \ufb01lled triangles). There does not seem to be a correlation of the mass function slope with any of the depicted parameters or stellar systems. The only exception seem to be open cluster mass functions, which are on average more bottom-heavy. 4.6 Environmental dependency of the stellar mass function In order to explore the in\ufb02uence of the external environment on the stellar mass function, we depict in Fig. 9 the mass-function slopes that we have derived as a function of di\ufb00erent cluster parameters. Shown are (clockwise from topleft), the cluster mass, the average density inside the halfmass radius of the cluster, the central velocity dispersion of the cluster and the cluster metallicity. We restrict our \ufb01ts to intermediate-mass stars in the range 0.4 M\u2299< m < 1.0 M\u2299since this is the mass function range for which we have the most data and the only one where LMC/SMC clusters and globular clusters overlap. We depict only clusters with remaining lifetimes several times larger than their ages since for these the present-day mass functions should still be close to the initial ones. In order to correct for mass loss due to stellar evolution, we increase the present-day cluster masses by a factor of two to get the initial masses. We also assume that stellar evolution induced mass loss leads to an adiabatic expansion of the cluster so that the initial half-mass radius was half the present-day value. Both assumptions lead to a factor 16 increase of the initial density over the present-day one and a factor two increase of the initial velocity dispersion. The true increase could be higher if the dynamical cluster evolution has led to an expansion of a cluster, how\u00a9 201x RAS, MNRAS 000, 1\u201316 14 Baumgardt et al. ever given the large relaxation times of the depicted clusters, this is likely not a large e\ufb00ect. We extend our sample beyond star clusters by adding the mass function determinations from Geha et al. (2013) and Gennaro et al. (2018) for six ultra-faint dwarf galaxies and from Kalirai et al. (2013) for \ufb01eld stars in the SMC. We also add data about the IMF of Milky Way disc stars in the solar neighborhood derived by Sollima (2019) based on Gaia DR2 parallaxes and magnitudes. These eight measurements form the galaxy sample in Fig. 9. We take the metallicities, masses, sizes and velocity dispersions of the dwarf galaxies from Simon (2019). The galaxy data covers the sub-solar mass function, making it directly comparable to the data from the cluster sample. We \ufb01nally add mass function determinations for open clusters in the solar neighborhood recently derived by Ebrahimi, Sollima & Haghi (2022) and Cordoni et al. (2023) based on Gaia DR3 data. We use only clusters with relaxation times larger than their ages from both papers in order to minimise the in\ufb02uence of dynamical evolution and use the mass function slopes for stars with m < 1 M\u2299to make the open cluster data comparable to the data of the other systems. As can be seen, most mass functions are compatible with a slope of about \u03b1 \u2248\u22121.5, without any obvious dependency of the stellar mass function slope on either the mass, the density, the metallicity or the internal velocity dispersion of the stellar system. The visual impression is con\ufb01rmed by Spearman rank order tests which do not indicate a signi\ufb01cant correlation between any of the depicted parameters and the mass function slope. Marks & Kroupa (2010) suggested a systematic change of the initial stellar mass function with the density of the star forming cloud that forms a globular cluster. However, given our data, at least the sub-solar IMF seems more or less independent on density over nearly eight orders of magnitude. We furthermore see no evidence for a metallicity dependency of the stellar IMF for globular clusters as has been argued by Zonoozi, Haghi & Kroupa (2016). In addition, as discussed in sec. 4.4, stars with masses more massive than 1.0 M\u2299seem to follow a Salpeter mass function for all studied LMC/SMC clusters, similar to the mass function seen for massive stars in a wide range of environments (Bastian, Covey & Meyer 2010), again arguing against a variation of the high-mass IMF with metallicity. The last conclusion is con\ufb01rmed by Dickson et al. (2023), who \ufb01nd that the kinematic data of globular clusters, when accounting for stars which have evolved into remnants at the present-day, is fully compatible with a Salpeter IMF above 1 M\u2299. Dickson et al. (2023) also \ufb01nd no correlation between this mass function and cluster metallicity. The only exception could be open clusters in the solar neighborhood, shown by grey circles in Fig. 9, for which we \ufb01nd an average mass function slope of \u03b1 = \u22121.9. This is about 0.4 dex steeper than the average slopes that we \ufb01nd for the other systems and could indicate a change in the IMF happening at either solar metallicity, low masses, young ages, or a combination of these parameters. The open cluster data however also shows a large scatter in the slopes for individual clusters, which range from about -1 to -3, and which seems to be much larger than what can be explained by errors in the data alone. Hence it is possible that there could still be some systematic error in the open cluster data, or that the open cluster mass functions are already in\ufb02uenced by dynamical e\ufb00ects. Detailed N-body modeling of the depicted clusters and their dynamical evolution in the Milky Way might therefore be necessary to test if the open clusters formed with their present-day mass functions. 5 CONCLUSIONS We have determined the stellar mass functions of 91 Milky Way globular clusters and 29 massive star clusters in the Large and Small Magellanic Clouds by \ufb01tting N-body models to star count data derived from over 300 individual HST \ufb01elds. We \ufb01nd that the stellar mass functions of dynamically unevolved star clusters, characterized by relaxation times TRH of the order of their ages and/or lifetimes TDiss signi\ufb01cantly larger than their ages, are well described by a multi-stage power-law mass function N(m) \u223cm\u03b1 with break masses at 0.4 M\u2299and 1 M\u2299and power lawslopes of \u03b1Low = \u22120.3 \u00b1 0.2, \u03b1Med = \u22121.65 \u00b1 0.20 and \u03b1High = \u22122.30 \u00b1 0.20 for the low-mass, intermediate-mass and high-mass stars respectively. An alternative description of the mass functions of these clusters is a log-normal mass function with characteristic mass log MC = \u22120.36 and width \u03c3C = 0.28 that transitions into a power-law mass function at 1 M\u2299. The mass function we \ufb01nd has fewer low-mass stars compared to the mass functions suggested by Kroupa (2001) or Chabrier (2003), which are measured in the solar neighborhood and are signi\ufb01cantly more bottom heavy. Our results therefore add to the increasing evidence that the stellar mass function varies across di\ufb00erent environments. We also \ufb01nd that star clusters with relaxation times or lifetimes much less than their ages are depleted in low-mass stars. The amount of depletion is in agreement with N-body simulations that model the e\ufb00ects of mass segregation and preferential depletion of low-mass stars due to the external tidal \ufb01elds on star clusters. Most investigated star clusters are therefore compatible with having formed with the same stellar mass function. By comparing the location of clusters in the dynamical age and age over lifetime vs. mass function slope planes with the results of direct N-body simulations, we also \ufb01nd that the mass function changes are best reproduced if most black holes that form in star clusters receive strong natal kicks at birth that remove them from their parent clusters. The reason for this is that clusters which retain most of their black holes do not become su\ufb03ciently depleted in low-mass stars to explain the observations. We predict a remaining black hole population in star clusters of no more than a few hundred black holes for clusters with masses up to 106 M\u2299. This estimate agrees with what has been found earlier from an analysis of the surface density pro\ufb01les of globular clusters (Askar, Arca Sedda & Giersz 2018) and their amount of mass segregation (Weatherford et al. 2018). Our data \ufb01nally argues against IMF variations with either the metallicity, mass, density or velocity dispersion of star clusters, at least among relatively old stars and for metallicities below the solar one. (Chon, Omukai & Schneider 2021) argued, based on hydrodynamical simulations of star formation, for a shift towards more bottom-heavy mass functions in higher metallicity environments. If real this shift must happen at metallicities [Fe/H] < \u22122.3 which is not probed by our data. A mass function described by our \ufb01ndings leads to an \u00a9 201x RAS, MNRAS 000, 1\u201316 Evidence for a bottom-light IMF in star clusters 15 average stellar mass at birth of \u27e8m\u27e9= 1.0 M\u2299and an about twice larger fraction of massive stars with m\u2217> 10 M\u2299that evolve into black holes and neutron stars per unit stellar mass compared to a Kroupa (2001) mass function. Furthermore, at birth such a mass function has a nearly twice as large fraction of mass in m > 10 M\u2299stars compared to m < 0.8 M\u2299stars than a Kroupa (2001) mass function. Our results therefore argue for more self-enrichment of stars in globular clusters and, if they can be generalized to \ufb01eld stars, overall more chemical enrichment in low metallicity environments. Due to the larger mass fraction in high-mass stars which can pollute lower mass stars forming in the same cluster, our mass function would also help alleviate the socalled mass budget problem in globular clusters (D\u2019Antona & Caloi 2008), according to which the observed number of chemically enriched, second population stars is far higher than expected based on standard pollution scenarios. A factor two increase in the mass ratio of massive to low-mass stars is however not enough to explain the observed number of second population stars since proposed scenarios for the origin of second generation stars fail by at least a factor of 10 to explain the current number ratios (Decressin, Charbonnel & Meynet 2007; Conroy 2012). Furthermore, these calculations assume that all of the the ejecta of massive stars are being used to enrich low-mass stars, which seems an optimistic assumption given that some of this material might escape or enrich intermediate-mass stars. A mass function described by our \ufb01ndings also increases the amount of gravitational waves created by inspiraling black holes and neutron stars compared to a standard mass function (Weatherford et al. 2021). However the number of inspiraling black holes also depends strongly on the binary and higher order multiple properties of massive stars (e.g. Belczynski et al. 2016; Antonini, Toonen & Hamers 2017) and we currently do not have good constraints on these. An independent test of our results can be obtained from stellar kinematics since the large number of compact remnants predicted by the mass function found here should lead to an increase of stellar velocities over that predicted by standard mass functions with fewer remnants. We will investigate this point for a number of well observed globular clusters in a companion paper (Dickson et al. 2023). ACKNOWLEDGMENTS We dedicate this paper to the memory of our friend and long-term collaborator Antonio Sollima who passed away prior to the publication of this paper. Antonio was a kind and humble scientist who made several key contributions to star cluster research, and he will be greatly missed. We thank Emanuele Dalessandro, Hamid Ebrahimi, Mojyaba Taheri, Andr\u00b4 es del Pino, Sven Martens and Giacomo Cordoni for sharing their kinematic and mass function data with us. We also thank an anonymous referee for comments that improved the presentation of the paper. VHB acknowledges the support of the Natural Sciences and Engineering Research Council of Canada (NSERC) through grant RGPIN-2020-05990. ND is grateful for the support of the Durland Scholarship in Graduate Research. This work is based on observations made with the NASA/ESA Hubble Space Telescope, obtained from the data archive at the Space Telescope Science Institute. STScI is operated by the Association of Universities for Research in Astronomy, Inc. under NASA contract NAS 5-26555. Part of this work was performed on the OzSTAR national facility at Swinburne University of Technology. The OzSTAR program receives funding in part from the Astronomy National Collaborative Research Infrastructure Strategy (NCRIS) allocation provided by the Australian Government. DATA AVAILABILITY Data is available upon request.",
                    "introduction": "The initial mass function (IMF) of stars is important in understanding a large number of astronomical phenomena such as the formation of the \ufb01rst stars (Bromm et al. 2009), galaxy formation and evolution (e.g Calura & Menci 2009; Abe et al. 2021), and the determination of the absolute star formation rate (Aoyama, Ouchi & Harikane 2021). It also plays a dominant role in any star formation theory as the end result of molecular cloud contraction and fragmentation (e.g. Krumholz 2014). The stellar IMF was \ufb01rst measured by Salpeter (1955), who found that the mass function of massive, m > 1 M\u2299 stars in the solar neighborhood is best described by a power- law mass function N(m) \u223cm\u03b1 with slope \u03b1 = \u22122.35. Ev- \u22c6E-mail: h.baumgardt@uq.edu.au \u2020 Deceased idence has been accumulating that the mass function for lower-mass stars in the Galactic disc increases less strongly with decreasing mass (Kroupa 2001; Chabrier 2003), but its exact form and whether it varies between individual star forming clouds is still under debate (see review by Bastian, Covey & Meyer 2010). There has also been increasing evidence that the stellar mass function is varying with galaxy environment or cosmic time. The best possible case for IMF variations are prob- ably the centers of early type galaxies, in which spectro- scopic measurements (e.g. van Dokkum & Conroy 2010) as well as measurements of the stellar kinematics (Cappellari et al. 2012) indicate that the low-mass star IMF must be bottom-heavy. It has also been suggested that, due to in- e\ufb03cient cooling, the mass function of the \ufb01rst stars in the universe must have been top-heavy (Abel, Bryan & Norman 2002; Bromm, Coppi & Larson 2002). Top-heavy IMFs for high mass stars have also been found in massive Galactic \u00a9 201x RAS arXiv:2303.01636v1  [astro-ph.GA]  3 Mar 2023 2 Baumgardt et al. molecular cloud complexes like W43 (Pouteau et al. 2022; Nony et al. 2023), which could indicate that the IMF slope depends on star formation rate and that starburst events create top-heavy IMFs. Finally, theoretical arguments and radiation-hydrodynamical simulations (e.g. Krumholz et al. 2010) indicate that radiation feedback from forming stars or cooling from dust-grains Chon, Omukai & Schneider (2021) could in\ufb02uence proto-stellar fragmentation and thereby the form of the IMF. Star clusters are one of the best environments to deter- mine the initial stellar mass functions since they o\ufb00er large, statistical signi\ufb01cant numbers of stars of similar distance, age and chemical composition. The strong crowding of stars in the cluster centres makes the detection of their lowest mass stars a challenge even when using space-based obser- vatories like the Hubble Space Telescope (HST). In addition, the large angular extent of nearby star clusters means that it is usually not possible to obtain photometry of the whole cluster with a single HST pointing. It is therefore necessary to use models like multi-mass King-Michie models (Gunn & Gri\ufb03n 1979; Sollima et al. 2017) that can correct for internal mass segregation in star clusters to correct locally measured mass functions to the global mass function. In addition, the dynamical evolution of star clusters needs to be taken into account when trying to deduce the initial mass function of a cluster from the present-day one since star clusters lose preferentially their lowest mass stars over time (Vesperini & Heggie 1997; Baumgardt & Makino 2003). In this paper we determine the stellar mass functions of 120 Galactic globular clusters and Large and Small Magel- lanic cloud clusters from archival HST photometry, obtain- ing the largest database of mass function measurements for these systems. We then use this data to determine their ini- tial mass functions and compare them to stellar mass func- tions measured for nearby galaxies. Our paper is organised as follows. In Sect. 2 we describe the selection of the clusters and the analysis of the HST data and in Sect. 3 we describe the determination of the stellar mass functions. In Sect. 4 we describe the results and we draw our conclusions in Sect. 5."
                },
                {
                    "url": "http://arxiv.org/abs/2112.04689v1",
                    "title": "Stellar mass segregation as separating classifier between globular clusters and ultra-faint dwarf galaxies",
                    "abstract": "We have determined the amount of stellar mass segregation in over 50 globular\nclusters and ultra-faint dwarf galaxy candidates based on deep HST and\nground-based photometry. We find that the amount of mass segregation in\nglobular clusters is strongly correlated with their relaxation time and that\nall clusters with relaxation times of the order of their ages or longer have\nlittle to no mass segregation. For each cluster, the amount of mass segregation\nseen is fully compatible with the amount expected by dynamical evolution from\ninitially unsegregated clusters, showing that globular clusters formed without\nprimordial mass segregation among their low-mass stars. Ultra-faint dwarf\ngalaxy candidates split into two groups, star clusters which follow the same\ntrend between relaxation time and amount of mass segregation as globular\nclusters and dark-matter dominated dwarf galaxies that are unsegregated despite\nhaving relaxation times smaller than a Hubble time. Stellar abundance and\nvelocity dispersion data, where available, confirm our classification. After\nclassification of the ultra-faint dwarf galaxy candidates, we find that outer\nhalo star clusters have average densities inside their half-light radii of 0.03\nM$_\\odot$/pc$^3 \\lesssim \\rho_h \\lesssim$ 1 M$_\\odot$/pc$^3$, while dwarf\ngalaxies have stellar densities of 0.001 M$_\\odot$/pc$^3 \\lesssim \\rho_h\n\\lesssim $ 0.03 M$_\\odot$/pc$^3$. The reason for this separation in density is\nmost likely a combination of the initial conditions by which the systems formed\nand the requirement to withstand external tidal forces.",
                    "authors": "Holger Baumgardt, Johannes Faller, Nicholas Meinhold, Chandler McGovern-Greco, Michael Hilker",
                    "published": "2021-12-09",
                    "updated": "2021-12-09",
                    "primary_cat": "astro-ph.GA",
                    "cats": [
                        "astro-ph.GA"
                    ],
                    "main_content": "We take the input list of globular clusters from Baumgardt et al. (2019), concentrating on outer halo globular clusters Table 1. Published literature photometry used in the present work Star Cluster/ Telescope/Camera/Filter Literature source UFD Balbinot 1 CFHT/MegaCam g/r Balbinot et al. (2013) Kim 1 CFHT/MegaCam g/r Mu\u02dc noz et al. (2018a) Kim 2 CFHT/MegaCam g/r Mu\u02dc noz et al. (2018a) Koposov 1 CFHT/MegaCam g/r Mu\u02dc noz et al. (2018a) Koposov 2 CFHT/MegaCam g/r Mu\u02dc noz et al. (2018a) NGC 1261 HST/ACS F606W/F814W Sarajedini et al. (2007) NGC 5053 HST/ACS F606W/F814W Sarajedini et al. (2007) HST/ACS F475W/F814W Simioni et al. (2018) NGC 5466 HST/ACS F606W/F814W Sarajedini et al. (2007) HST/ACS F475W/F814W Simioni et al. (2018) NGC 5897 HST/ACS F606W/F814W Sarajedini et al. (2007) HST/ACS F475W/F814W Simioni et al. (2018) NGC 6121 HST/ACS F606W/F814W Sarajedini et al. (2007) Ground-based V/I Stetson et al. (2019) NGC 6426 HST/ACS F606W/F814W Dotter et al. (2011) NGC 7006 HST/ACS F606W/F814W Dotter et al. (2011) NGC 7492 Ground-based V/I Stetson et al. (2019) Pal 1 HST/ACS F606W/F814W Sarajedini et al. (2007) Pal 5 Ground-based V/I Stetson et al. (2019) Pal 12 HST/ACS F606W/F814W Sarajedini et al. (2007) Pal 15 HST/ACS F606W/F814W Dotter et al. (2011) Pyxis HST/ACS F606W/F814W Dotter et al. (2011) CFHT/MegaCam g/r Mu\u02dc noz et al. (2018a) Reticulum II CFHT/MegaCam g/r Mu\u02dc noz et al. (2018a) Rup 106 HST/ACS F606W/F814W Dotter et al. (2011) Segue 3 CFHT/MegaCam g/r Mu\u02dc noz et al. (2018a) Ter 7 HST/ACS F606W/F814W Sarajedini et al. (2007) Ter 8 HST/ACS F606W/F814W Sarajedini et al. (2007) Ground-based V/I Stetson et al. (2019) Whiting 1 Ground-based V/I Valcheva et al. (2015) that cover a similar range of Galactocentric distances as the ultra-faint dwarf galaxy candidates. From the catalogue of Baumgardt et al. (2019) we exclude all clusters that lack deep enough photometry to measure the distribution of lowmass stars. We also exclude clusters like Pal 2 that have strong and variable reddening or a high stellar background density. Finally, we remove clusters with high central surface densities in which the distribution of faint stars can\u2019t be measured in the centres. This criterion excludes most highmass halo clusters like M 54. We finally require that the existing photometry must cover the cluster from the centre out to at least 2.5 half-light radii. This criterion excludes most nearby clusters for which a single HST field of view is too small to cover a large enough part of the cluster. Applying all criteria, we end up with 28 globular clusters, having relaxation times from 0.1 to 50 Gyrs and cluster masses from 7.5 \u00b7 102 M\u2299to 3.9 \u00b7 106 M\u2299. Except for M 4 and \u03c9 Cen, all clusters are at Galactocentric distances larger than 10 kpc. 17 of these clusters have published photometry and we list the clusters and the sources of their photometry in Table 1. We take the input list of dwarf galaxy candidates from Stellar mass segregation in GCs and UFDs 3 the recent overview article by Simon (2019). To this list of 54 possible dwarf galaxies, we add Eridanus III (Bechtol et al. 2015) and DES 1 (Luque et al. 2016). In addition, we investigate the star clusters Kim 1 (Kim et al. 2015), Kim 2 (Kim & Jerjen 2015a), Koposov 1 and Koposov 2 (Koposov et al. 2007), Mu\u02dc noz 1 (Mu\u02dc noz et al. 2012) and Segue 3 (Belokurov et al. 2010). We exclude from the list of Simon (2019) all systems with (stellar) relaxation times signi\ufb01cantly larger than 1010 years since these would be unsegregated even without dark matter. We also neglect systems more distant than about 120 kpc, since their main-sequence turn-o\ufb00s are so faint that only a small part of their main sequence stars can be observed, which does not allow us to detect mass segregation con\ufb01dently. In addition we neglect systems that have absolute magnitudes less than about MV \u2248\u22120.5 since these objects have less than 50 observable stars on the main sequence, which again does not allow to detect mass segregation with high enough con\ufb01dence. This leaves us with a list of 33 objects. Seven of these have published photometry and we list their names as well as the sources for their photometry in Table 1. For the remaining globular clusters and dwarf galaxies, we performed the photometric reduction ourselves. For most objects we used HST images that we downloaded from the STSci archive. We performed stellar photometry on these images using DOLPHOT (Dolphin 2000, 2016). For ACS and WFC3 observations, we performed the photometry on the CTE corrected \ufb02c images, while for the WFPC2 observations we used the c0m images to perform the photometry. We used the point-spread functions provided for each camera and \ufb01lter combination by DOLPHOT for the photometric reductions. After performing the photometry, we transformed the HST instrumental coordinates into equatorial ones by cross-matching stellar positions and magnitudes from HST with the positions of stars in the Gaia EDR3 catalogue (Gaia Collaboration et al. 2021). We list the names of all globular clusters and ultra-faint dwarf galaxies that we analysed in Table 2 together with the HST camera and \ufb01lter combinations, the HST proposal ID and the total exposure times for each cluster. The exposure times are usually several thousand sec, which allows us to measure stellar magnitudes down to about 27th or 28th magnitude in each passband. For two objects, DES 1 and Laevens 3, we performed DAOPHOT PSF photometry on deep ground-based images. Laevens 3 was observed in the g and i bands for 1440 and 2700 sec, respectively, with MegaCAM on CFHT. We used the advanced data products MegaPipe.612.210.G.MP9402 and MegaPipe.612.210.I.MP9703 from the CFHT data archive for our photometry. The photometric calibration was performed according to the prescription given in Longeard et al. (2019). DES 1 was observed in the g and r bands for 1800s each with GMOS-S on Gemini South. No advanced data products were available in the Gemini archive, so we reduced the raw data ourselves with the DRAGONS pipeline1. The photometric calibration was performed following the procedure described in Conn et al. (2018b). The instrumental coordinates of both objects were transformed to the Gaia system by cross-matching bright stars with the Gaia EDR3 catalogue (Gaia Collaboration et al. 2021). 1 https://dragons.readthedocs.io/en/release-2.1.x/ Table 2. Observing log for the ground-based and HST photometry analysed by us Star Cluster/ Telescope/Camera/Filter Proposal Exp. time UFD ID (sec) AM 1 HST/WFPC2 F555W/F814W 6512 36240 AM 4 HST/WFC3 F606W/F814W 11680 9840 Bo\u00a8 otes II HST/ACS F606W/F814W 14734 18388 Cetus II HST/ACS F606W/F814W 14734 9212 Crater HST/ACS F606W/F814W 13746 8010 DES 1 Gemini/GMOS-S g,r GS2016B 3600 Draco II HST/ACS F606W/F814W 14734 9324 Eridanus HST/WFPC2 F555W/F814W 6106 17330 Eridanus III HST/ACS F606W/F814W 14234 10340 Grus I HST/ACS F606W/F814W 14734 9532 Horologium I HST/ACS F606W/F814W 14734 9254 Horologium II HST/ACS F606W/F814W 14734 18508 Laevens 3 CFHT Megacam g/r 15AD84 4140 NGC 2419 HST/WFPC2 F606W/F814W 5481 20300 HST/ACS F814W 10815 4500 HST/WFC3 F606W/F814W 11903 2300 HST/ACS F606W/F814W 14235 10000 NGC 4147 HST/ACS F606W/F814W 10775 3500 NGC 5053 HST/WFPC2 F606W/F814W 11125 8800 HST/WFC3 F606W/F814W 14235 2120 NGC 5139 HST/ACS F435W/F625W 9442 6180 HST/ACS F606W/F814W 10252 3430 HST/ACS F606W/F814W 12193 1100 HST/ACS F435W/F606W 13066 3390 HST/ACS F606W/F814W 15594 6670 HST/ACS F606W 15764 680 NGC 5466 HST/WFPC2 F606W/F814W 11125 8800 HST/WFC3 F606W/F814W 14235 2080 NGC 5897 HST/WFPC2 F606W/F814W 11125 8800 Pal 3 HST/WFPC2 F555W/F814W 5672 14920 Pal 4 HST/WFPC2 F555W/F814W 5672 8095 Pal 13 HST/WFC3 F606W/F814W 11680 4900 Pal 14 HST/WFPC2 F555W/F814W 6512 9480 Phoenix II HST/ACS F606W/F814W 14734 9254 Pictoris I HST/ACS F606W/F814W 14734 9532 Reticulum III HST/ACS F606W/F814W 14766 54492 Segue 1 HST/ACS F606W/F814W 14734 18420 Segue 2 HST/ACS F606W/F814W 14734 9216 Sgr II HST/ACS F606W/F814W 14734 9216 Triangulum II HST/ACS F606W/F814W 14734 18384 Tucana III HST/ACS F606W/F814W 14734 18584 Tucana V HST/ACS F606W/F814W 14734 9322 Virgo I HST/ACS F606W/F814W 15332 4752 Willman 1 HST/ACS F606W/F814W 14734 9254 For each analysed cluster, we also estimated the photometric completeness using arti\ufb01cial star tests. For the clusters with HST data, we created 75,000 arti\ufb01cial stars in each cluster, equally distributed across the HST \ufb01eld. The arti\ufb01cial stars were also equally distributed in magnitude along the location of the cluster main sequence from the turnover down to the faintest detectable magnitudes. We then used 4 Baumgardt, Faller, Meinhold, McGovern-Greco, Hilker the DOLPHOT fakestars task to recover the magnitudes of the arti\ufb01cial stars and applied the same quality cuts to the arti\ufb01cial stars that we used to select bona-\ufb01de stars in the observed data set. Stars were counted as recovered if their derived magnitudes were within 0.2 mag of the input ones in both magnitude bands. We then estimated the completeness fraction for each observed star from the ratio of successfully recovered stars to all inserted stars using the nearest 20 arti\ufb01cial stars that are within 0.2 mag of the magnitude of each observed star. The incompleteness tests for the ground-based data were performed with the DAOPHOT package artdata (tasks starlist and addstars). 100 arti\ufb01cial stars with random positions and random magnitudes in the range of the main sequence were added to the images of the individual \ufb01lters, and photometry was performed in the same manner as for the true stars. The same photometric selection criteria were applied to de\ufb01ne the \ufb01nal sample of valid stars. This experiment was repeated 1000 times per image and \ufb01lter so that the \ufb01nal incompleteness values are based on the statistics of 105 arti\ufb01cial stars. Fig. 1 shows the results of our completeness tests for two representative cases, Grus I and NGC 4147. It can be seen that for Grus I our observations are more than 90% complete down to F606W=27.5 mag, well below the limit that we later use to determine mass segregation. Due to the low stellar density of Grus I, the completeness fraction is also nearly independent of the distance to the centre. We obtain similar results for the other dwarf galaxies and also most globular clusters. In NGC 4147 our observations are also more than 90% complete down to F606W=26.5, the limit of our later analysis, for radii r >30\u201d. The completeness drops below 90% only for the faintest stars and only for radii r <30\u201d. We estimated the photometric completeness for all clusters for which we performed the photometry ourselves. For the other globular clusters we used the completeness data from Sarajedini et al. (2007) for the inner \ufb01elds. When calculating cumulative pro\ufb01les, we use the inverse of the completeness fraction as a weighting factor to correct for the incompleteness, as will be explained below. 3 MASS SEGREGATION DETERMINATION In order to determine the amount of mass segregation for each cluster/dwarf galaxy, we \ufb01rst \ufb01tted the cluster colourmagnitude diagrams (CMDs) with PARSEC isochrones (Bressan et al. 2012). We took the metallicity and reddening of each globular cluster from the 2010 edition of Harris (1996), while for star clusters and UFDs we took the metallicity from published literature, or, if no metallicity determination was available, we assumed a metallicity of [Fe/H]=-2.0. We assumed cluster ages of 5 Gyr for Whiting 1 (Carraro, Zinn & Moni Bidin 2007), 8.0 Gyr for Ter 7 (Dotter et al. 2010) and 8.0 Gyr for Pal 1 (Rosenberg et al. 1998). For all other globular clusters we assumed an age of 12 Gyr, which is compatible with the published ages of these systems (e.g Dotter et al. 2010; VandenBerg et al. 2013). We then created PARSEC isochrones for each cluster for the same camera and \ufb01lter combination for which we have observed data. The isochrones were then shifted in distance modulus and reddening until we obtained the best match Figure 1. Photometric completeness as a function of F606W magnitude for four di\ufb00erent distance ranges from the centre for the ultrafaint dwarf galaxy candidate Grus I (top panel) and the globular cluster NGC 4147 (bottom panel). Due to the low stellar density of Grus I, the photometric completeness is nearly independent of distance, while the higher stellar density in the centre of NGC 4147 decreases the completeness at the faint end. with the observed color-magnitude diagram of each cluster. We then used the isochrone to select the cluster members. Cluster members were required to deviate by no more than twice their photometric error or 0.10 mag, whichever was larger, from the isochrone. Fig. 2 depicts the selection of cluster members and non-members for NGC 4147. After selecting the cluster members, we determined for each star a weight factor wi according to: wi = 1 fr,i 1 fp,i (1) where fr,i is the fraction of the cluster that is covered by our photometry at the distance of star i and fp,i is the fraction of arti\ufb01cial stars recovered in our arti\ufb01cial star tests with a magnitude and color similar to star i and at a similar spatial position. We determined the fraction covered by the photometry in steps of 1 arcsec from the cluster centre by distributing 360 points uniformly along a circle around the cluster centre. For each of these points we then determined the distance of the nearest star in our photometry from this point. If this distance was less than a critical distance (usually 1 arcsec but we chose slightly higher values for clusters with fewer member stars), we considered the point to be covered by our photometry. The spatial completeness factor fr,i for each radius is then given by the fraction of the points that were found to be covered. We stopped the analysis at a maximum radius Rmax where either the density of cluster stars becomes too low or the photometric completeness fr,i drops below 15%. The latter was done in order to avoid giving individual stars too much weight in the determination of the mass segregation pro\ufb01le. The values of Rmax are given in Stellar mass segregation in GCs and UFDs 5 [h] Figure 2. Colour magnitude diagram depicting our selection of cluster members (left panel) and the resulting cumulative distribution of stars (right panel) for NGC 4147. The green line shows the PARSEC isochrone that we used to select the cluster members. The parameters of this isochrone are given in the upper left corner of the left panel. Red and blue stars show the cluster stars selected to calculate the mass segregation pro\ufb01le. The right panel shows the cumulative pro\ufb01le after correcting for incompleteness of stars at the faint end. The solid lines depict the cumulative distribution that we derive from the data, while the shaded areas show the region containing two thirds of all curves when doing the bootstrapping. Table 3 for each system. For most systems they are at least two times the projected half-light radius of the system. The photometric completeness factor fp,i was determined from the 20 nearest arti\ufb01cial stars that were within \u00b10.20 mag of the short-wavelength (usually F606W) magnitude of each star. After the determination of the weight factors, we ordered the member stars according to their brightness and splitted the sample into two equally large groups according to stellar brightness. We then ordered the stars of each group according to their distance from the centre and determined their cumulative distribution according to \u03c6(< R) = PN(<R) i wi PNT ot i wi (2) where the sum in the numerator runs over all bright/faint stars up to a given radius R and the sum in the denominator runs over all stars of each group. For both the faint and bright sample, we then calculated the radius RH where \u03c6(< R) is equal to 0.5. We then calculated the ratio of these radii r = RH,Bright/RH,F aint and determined its error by bootstrapping. Fig. 2 shows the result of our mass segregation analysis for NGC 4147, for which we \ufb01nd RH,Bright = 30.4\u00b1 0.55 arcsec, RH,F aint = 41.9 \u00b1 0.64 arcsec and a ratio of RH,Bright/RH,F aint = 0.73 \u00b1 0.02, i.e. a highly signi\ufb01cant detection of mass segregation. As an additional measure of mass segregation, we perform a KS test on the cumulative distribution of bright and faint stars to test the signi\ufb01cance that both distributions are di\ufb00erent from each other, i.e. that the system is mass segregated. The corresponding probabilities are given in column 12 of Table 3. Since the stars carry individual weight factors, we modify the standard two-sample KS test as described by Monahan (2001) sec. 12.4 by replacing the sample sizes n1 and n2 in the e\ufb00ective sample size factor n = r n1n2 n1 + n2 (3) by n1 = \u0000P i wb,i \u00012 P i w2 b,i (4) and n2 = \u0000P i wf,i \u00012 P i w2 f,i (5) where wb,i and wf,i are the weight factors from eq. 1 for the bright and faint stars respectively. We also determine the relaxation time of each globular cluster and dwarf galaxy candidate. For the globular clusters we take the relaxation times from Baumgardt et al. (2019), updated for the new distances derived by Baumgardt & Vasiliev (2021). Baumgardt et al. (2019) \ufb01tted a large set of N-body models to the surface density, velocity dispersion pro\ufb01les and the stellar mass functions of globular clusters, thereby creating a detailed model for each individual globular cluster. For star clusters and dwarf galaxies not studied by Baumgardt et al. (2019), we estimate the relax6 Baumgardt, Faller, Meinhold, McGovern-Greco, Hilker ation times according to (Spitzer 1987): TRH = 0.138 \u221a Mr1.5 h \u221a G\u27e8m\u27e9ln \u03b3N (6) where M is the (stellar) mass of the system, rh the 3dimensional half-mass radius, \u27e8m\u27e9the average mass of stars and N = M/\u27e8m\u27e9the number of stars. \u03b3 is a constant in the Coulomb logarithm for which we assume \u03b3 = 0.11 (Giersz & Heggie 1994). We calculate the mass of the star clusters/dwarf galaxies from their V-band luminosities, assuming a mass-to-light ratio of M/LV = 1.8M\u2299/L\u2299(Baumgardt 2017). We also assume \u27e8m\u27e9= 0.35 M\u2299and rh = 0.75rhp for the conversion of projected half-light radii to 3D ones. The above formula is valid for stellar systems free of dark matter. In the presence of dark matter the relaxation times would be signi\ufb01cantly larger since ultra-faint dwarf galaxies are expected to be strongly dark matter dominated (Simon & Geha 2007). Approximating the relaxation process as dynamical friction of stars against the much lighter dark matter particles and using eq. 7-26 of Binney & Tremaine (1987), we \ufb01nd that the relaxation time should increase approximately with the square root of the ratio of dark to luminous matter TRH \u223c p MDM/M\u2217, and would therefore be a factor 30 larger for a system that has 1000 times as much dark matter than luminous matter. With the exception of the smallest systems that have relaxation times less than about 0.3 Gyr, we would therefore not expect to detect mass segregation in any system that is dark matter dominated. 4 N-BODY SIMULATIONS OF MASS SEGREGATION In order to compare the observed amount of mass segregation with theoretical expectations, we analysed the amount of mass segregation in the N-body simulations done by Baumgardt & Sollima (2017) and Baumgardt & Makino (2003). Baumgardt & Sollima (2017) performed a set of 16 N-body simulations of star clusters evolving in the tidal \ufb01eld of the Milky Way. The simulated clusters contained between 65, 536 and 200, 000 stars that followed a Kroupa (2001) mass function initially. In the simulations, the initial cluster orbits, cluster sizes and the fraction of the assumed black hole retention fraction were varied. While most simulations assumed 10% retention fraction for the black holes, \ufb01ve runs had higher black hole retention fractions up to 100%. The simulations by Baumgardt & Makino (2003) were similar in set-up and we analysed all simulations that started with N = 131, 072 stars and survived for a Hubble time from their paper. In order to also cover star clusters resembling extended halo globular clusters, we performed an additional three simulations with a set-up similar to run 4 of Baumgardt & Sollima (2017) (Kroupa mass function, N = 131, 072 stars, 10% black hole retention fraction) but orbiting at a galactocentric distance of RG = 100 kpc and starting with initial half-mass radii of 10 pc, 15 pc and 25 pc respectively. At an age of 12 Gyr the simulated clusters had typical half-mass radii of 5 to 35 pc and a remaining bound mass of between 5,000 and 30,000 M\u2299. They are therefore comparable in size to the lower-mass star clusters analysed here. In addition, their mass functions have \ufb02attened due to mass segregation and preferential mass loss of low-mass stars. When \ufb01tted by a power-law mass function, we \ufb01nd slopes between \u03b1 = \u22120.80 and \u22121.30 for most of them, in good agreement with what has been found for mass functions of globular clusters (e.g Baumgardt & Sollima 2017) and ultra-faint dwarf galaxies (e.g Geha et al. 2013; Gennaro et al. 2018). For each cluster in the N-body simulations, we analysed only the snapshots between 10 and 13 Gyrs. For each of these \u223c1,500 snapshots, we splitted the main sequence stars above a certain mass-cuto\ufb00MLow into bright and faint stars and determined the RH,Bright/RH,F aint ratio for each individual snapshot in the same way as we did for the observed globular clusters. We also determined the relaxation time and the TAge/TRH ratio of each snapshot. Since the amount of mass segregation and the mass segregation ratio will depend on the lower mass limit, we repeat the analysis for four di\ufb00erent lower mass limits of MLow,NBODY = 0.35 M\u2299, 0.45 M\u2299, 0.55 M\u2299and 0.65 M\u2299respectively. Fig. 3 depicts the resulting mass segregation ratios for the four di\ufb00erent cases. The black lines and grey shaded regions in Fig. 3 show the average ratio of RH,Bright/RH,F aint and the region containing 90% of all snapshots for the Nbody simulations. Systems that have relaxation times much longer than their ages have insu\ufb03cient time to become mass segregated and therefore still have mass segregation ratios near unity. Signi\ufb01cant mass segregation only sets in around TAge/TRH = 3 and is largely complete around TAge/TRH = 10, at which point RH,Bright/RH,F aint levels o\ufb00at values between 0.70 to 0.85 depending on the mass range of stars that are considered. The data shown in Fig. 3 is for the case that the stellar distribution is analysed out to the tidal radius of each system. Decreasing the value of RMax, we \ufb01nd that the resulting mass segregation ratio will be closer to unity. If Rmax is only twice the projected half-light radius rh,p for example we \ufb01nd that RH,Bright/RH,F aint increases by about 0.05 for the most mass segregated clusters with TAge/TRH > 10 and by about 0.10 if the stellar distribution is analysed only up to Rmax = rh,p. Changes are similar but smaller for smaller values of TAge/TRH. N-body simulations show that star clusters that start with primordial mass segregation need several relaxation times to erase the mass segregation via two-body relaxation (Pavl\u00b4 \u0131k, Kroupa & \u02c7 Subr 2019; Pavl\u00b4 \u0131k 2020). Our results therefore strongly argue against primordial mass segregation among low mass stars in globular clusters. 5 RESULTS 5.1 Globular clusters We \ufb01rst discuss our results for globular clusters. Fig. 3 depicts the RH,Bright/RH,F aint ratios as a function of the dynamical cluster ages de\ufb01ned as the ratio of the physical age TAge of a cluster over its present-day relaxation time TRH. Clusters with small values of TAge/TRH, i.e. relaxation time equal to or larger than their age should not be strongly evolved dynamically and the internal distribution of stars should still re\ufb02ect the initial distribution, while clusters with large TAge/TRH values on the other hand should be highly evolved and have developed strong mass segregation between their stars. Stellar mass segregation in GCs and UFDs 7 Table 3. Adopted parameters, relaxation times and mass segregation results for the studied clusters and ultra-faint dwarf galaxies Cluster MV RH D\u2299 Mass TRH mLow mMed mUp Rmax NStar PMseg RBright/RF aint Ref. [\u201d] [kpc] [M\u2299] [Gyr] [M\u2299] [M\u2299] [M\u2299] [\u201d] [%] Globular clusters AM 1 -6.11 25.8 118.9 4.0 \u00b7 104 4.68 0.64 0.74 0.80 82 2190 100.0 0.87 \u00b1 0.03 1,2,3 AM 4 -0.97 45.4 29.0 7.5 \u00b7 102 1.51 0.27 0.50 0.88 97 558 98.6 0.84 \u00b1 0.06 1,2,3 Crater -5.10 27.1 147.2 1.1 \u00b7 104 5.75 0.60 0.75 0.92 115 2976 100.0 0.86 \u00b1 0.03 1,2,3 Eridanus -5.43 33.5 84.7 1.2 \u00b7 104 2.75 0.54 0.69 0.81 95 1513 100.0 0.87 \u00b1 0.05 1,2,3 Laevens 3 -2.85 23.8 61.8 2.1 \u00b7 103 0.78 0.70 0.74 0.78 70 197 96.6 0.74 \u00b1 0.12 1,3,4 NGC 1261 -7.80 40.9 16.4 1.8 \u00b7 105 1.91 0.49 0.65 0.80 130 44171 100.0 0.77 \u00b1 0.01 1,2,3 NGC 2419 -9.17 45.8 88.5 9.8 \u00b7 105 48.98 0.67 0.74 0.80 160 51855 99.0 0.99 \u00b1 0.01 1,2,3 NGC 4147 -6.11 28.1 18.5 3.8 \u00b7 104 0.37 0.40 0.61 0.78 139 12214 100.0 0.69 \u00b1 0.02 1,2,3 NGC 5053 -6.33 145.5 17.5 7.4 \u00b7 104 9.12 0.48 0.68 0.78 442 8327 99.9 0.96 \u00b1 0.03 1,2,3 NGC 5139 -10.17 286.8 5.43 3.9 \u00b7 106 26.91 0.52 0.64 0.78 474 327420 100.0 0.97 \u00b1 0.00 1,2,3 NGC 5466 -6.72 122.1 16.1 6.0 \u00b7 104 6.46 0.46 0.60 0.79 434 12055 98.4 0.91 \u00b1 0.02 1,2,3 NGC 5897 -7.29 124.6 12.6 1.5 \u00b7 105 5.37 0.44 0.60 0.79 408 27076 100.0 0.89 \u00b1 0.02 1,2,3 NGC 6121 -6.77 277.6 1.85 8.8 \u00b7 104 0.78 0.46 0.66 0.82 600 23449 100.0 0.75 \u00b1 0.01 1,2,3 NGC 6426 -6.57 51.9 20.7 7.0 \u00b7 104 2.45 0.41 0.56 0.79 130 29678 100.0 0.85 \u00b1 0.01 1,2,3 NGC 7006 -7.50 22.6 39.3 1.3 \u00b7 105 2.34 0.49 0.65 0.80 113 41596 100.0 0.83 \u00b1 0.01 1,2,3 NGC 7492 -5.80 63.9 24.4 2.7 \u00b7 104 1.95 0.55 0.69 0.80 200 4544 100.0 0.80 \u00b1 0.02 1,2,3 Pal 1 -1.76 33.2 11.2 1.0 \u00b7 103 0.08 0.42 0.62 0.91 124 446 100.0 0.62 \u00b1 0.09 1,2,3 Pal 3 -5.49 44.0 94.8 1.4 \u00b7 104 7.94 0.54 0.66 0.79 79 3547 99.6 0.90 \u00b1 0.02 1,2,3 Pal 4 -5.86 32.2 101.4 2.6 \u00b7 104 8.71 0.58 0.70 0.82 136 2491 79.9 0.97 \u00b1 0.03 1,2,3 Pal 5 -4.94 21.9 21.9 1.0 \u00b7 104 7.41 0.58 0.70 0.80 300 2221 97.2 0.96 \u00b1 0.03 1,2,3 Pal 12 -4.41 18.5 76.7 6.3 \u00b7 103 1.29 0.54 0.69 0.88 300 2020 100.0 0.74 \u00b1 0.04 1,2,3 Pal 13 -3.15 113.0 23.5 3.0 \u00b7 103 1.82 0.51 0.66 0.77 250 584 100.0 0.72 \u00b1 0.09 1,2,3 Pal 14 -5.30 77.0 73.6 1.9 \u00b7 104 13.80 0.53 0.68 0.82 112 2217 68.6 0.95 \u00b1 0.03 1,2,3 Pal 15 -5.72 94.0 44.1 5.0 \u00b7 104 12.02 0.55 0.68 0.79 134 6634 37.8 0.99 \u00b1 0.02 1,2,3 Pyxis -5.49 96.2 36.5 2.5 \u00b7 104 7.76 0.60 0.71 0.82 250 4566 100.0 0.94 \u00b1 0.02 1,2,3 Rup 106 -6.15 75.7 20.7 4.2 \u00b7 104 2.67 0.47 0.63 0.81 133 9111 100.0 0.94 \u00b1 0.02 1,2,3 Ter 7 -5.28 54.5 24.3 2.1 \u00b7 104 3.72 0.49 0.65 0.94 128 6752 100.0 0.85 \u00b1 0.02 1,2,3 Ter 8 -6.52 27.5 113.7 6.1 \u00b7 104 10.72 0.62 0.70 0.79 220 7434 78.4 1.00 \u00b1 0.02 1,2,3 Whiting 1 -4.17 64.1 30.6 2.0 \u00b7 103 1.51 0.66 0.85 1.04 200 333 100.0 0.69 \u00b1 0.10 1,2,3 Ultra-faint dwarf galaxies/Star clusters Balbinot 1 -1.21 52.2 31.9 4.7 \u00b7 102 0.82 0.55 0.63 0.78 80 141 99.8 0.65 \u00b1 0.10 5,6 Bo\u00a8 otes II -2.94 190.2 42.0 1.4 \u00b7 103 5.63 0.41 0.54 0.78 225 285 54.0 0.95 \u00b1 0.07 5,7 Cetus II 0.00 114.0 26.3 1.5 \u00b7 102 1.47 0.31 0.49 0.79 140 111 26.0 1.12 \u00b1 0.20 5,8 DES 1 -1.42 14.7 76.0 5.7 \u00b7 102 0.47 0.68 0.74 0.78 40 56 95.3 0.69 \u00b1 0.21 9 Draco II -2.90 162.0 20.0 2.2 \u00b7 103 3.17 0.25 0.43 0.78 170 150 88.4 0.78 \u00b1 0.07 10 Eridanus III -2.37 18.0 87.0 1.4 \u00b7 103 1.05 0.53 0.65 0.78 130 440 91.7 0.84 \u00b1 0.09 5 Grus I -3.40 106.6 120.0 3.5 \u00b7 103 26.92 0.58 0.67 0.79 130 531 75.7 0.89 \u00b1 0.09 11 Grus II -3.90 360.0 55.0 5.6 \u00b7 103 74.35 0.42 0.56 0.79 135 291 8.9 1.00 \u00b1 0.07 12,13 Horologium I -3.40 69.8 68.0 3.5 \u00b7 103 7.60 0.50 0.62 0.79 140 1099 9.4 0.99 \u00b1 0.06 14 Horologium II -1.56 116.4 78.0 6.5 \u00b7 102 4.84 0.54 0.64 0.79 220 352 29.1 1.06 \u00b1 0.12 5,15 Kim 2 -1.50 28.8 100.0 6.1 \u00b7 102 1.77 0.63 0.73 0.79 75 65 70.3 0.81 \u00b1 0.14 5,16 Koposov 1 -1.04 37.2 48.3 4.0 \u00b7 102 0.88 0.55 0.70 0.78 100 60 74.4 0.70 \u00b1 0.16 5 Koposov 2 -0.92 26.4 34.7 3.6 \u00b7 102 0.31 0.48 0.60 0.79 130 114 89.5 0.73 \u00b1 0.17 5 Pegasus III -2.95 51.0 174.0 2.3 \u00b7 103 16.86 0.69 0.74 0.79 145 605 44.3 1.04 \u00b1 0.06 17,18 Phoenix II -2.80 65.4 83.0 2.0 \u00b7 103 7.69 0.55 0.64 0.78 135 491 19.5 1.07 \u00b1 0.07 5,19 Pictoris I -3.45 52.8 110.0 3.7 \u00b7 103 10.52 0.63 0.70 0.78 125 585 7.4 1.02 \u00b1 0.08 5,13 Reticulum II -3.88 331.2 31.4 5.1 \u00b7 103 28.23 0.44 0.57 0.78 550 1953 25.6 1.03 \u00b1 0.05 5,20 Reticulum III -3.30 159.0 92.0 3.2 \u00b7 103 34.27 0.55 0.66 0.79 130 450 92.5 1.20 \u00b1 0.10 11 Segue 1 -1.30 217.2 23.0 5.1 \u00b7 102 4.84 0.27 0.47 0.78 240 292 40.6 0.93 \u00b1 0.06 5 Segue 2 -1.86 225.6 35.0 8.5 \u00b7 102 9.65 0.32 0.49 0.78 155 336 4.5 1.02 \u00b1 0.06 5 Segue 3 -0.87 29.4 27.0 3.4 \u00b7 102 0.24 0.42 0.61 0.79 100 100 75.9 0.73 \u00b1 0.17 5 Sagittarius II -5.41 89.9 66.4 2.3 \u00b7 104 8.37 0.57 0.67 0.78 200 5171 97.5 0.96 \u00b1 0.02 1,2,3 Triangulum II -1.60 119.4 30.0 6.7 \u00b7 102 2.89 0.36 0.52 0.79 215 320 14.4 0.99 \u00b1 0.09 5 Tucana III -1.30 306.0 22.9 5.1 \u00b7 102 7.25 0.25 0.46 0.78 240 157 42.8 0.95 \u00b1 0.07 20 Tucana V -1.60 60.0 55.0 6.7 \u00b7 102 2.55 0.48 0.61 0.79 140 227 1.3 1.00 \u00b1 0.12 11 Virgo I -0.80 90.0 87.0 3.2 \u00b7 102 7.50 0.61 0.68 0.79 135 74 28.5 0.80 \u00b1 0.17 21 Willman 1 -2.53 150.6 38.0 1.6 \u00b7 103 7.77 0.36 0.55 0.79 135 420 29.7 1.04 \u00b1 0.10 5 References for distances, structural and photometric parameters: 1) Baumgardt et al. (2019), 2) Baumgardt, Sollima & Hilker (2020), 3) Baumgardt & Vasiliev (2021), 4) Longeard et al. (2019), 5) Mu\u02dc noz et al. (2018b), 6) Balbinot et al. (2013), 7) Walsh et al. (2008), 8) Conn et al. (2018b), 9) Conn et al. (2018a), 10) Laevens et al. (2015), 11) Koposov et al. (2015a), 12) Drlica-Wagner et al. (2015), 13) Mart\u00b4 \u0131nez-V\u00b4 azquez et al. (2019), 14) Jerjen et al. (2018), 15) Kim & Jerjen (2015b), 16) Kim et al. (2015), 17) Kim et al. (2016), 18) Garofalo et al. (2021), 19) Bechtol et al. (2015), 20) Mutlu-Pakdil et al. (2018), 21) Homma et al. (2016) 8 Baumgardt, Faller, Meinhold, McGovern-Greco, Hilker Figure 3. Ratio of the radius containing half the bright stars, RH,Bright, over the radius containing half the faint stars, RH,F aint, as a function of the dynamical age TAge/TRH for Milky Way globular clusters. The globular sample is split into four di\ufb00erent groups depending on the mass MLow,Obs of the lowest-mass star that was analysed in each cluster. The lowest mass star analysed in the N-body simulations MLow,NBODY is varied accordingly and is indicated in each panel. Observed globular clusters are shown by red circles with error bars, while the results of the N-body simulations are shown as a black line and grey shaded region. Observed globular clusters with young dynamical ages TAge/TRH \u22641 are almost completely unsegregated with RH,Bright only a few percent smaller than RH,F aint. The amount of mass segregation increases with increasing dynamical age and the range of values seen for each TAge/TRH is in good agreement with N-body simulations of initially unsegregated clusters, showing that the observed mass segregation is not primordial but a result of two-body relaxation driven dynamical evolution. The red circles in Fig. 3 show the distribution of observed Milky Way globular clusters. It can be seen that all systems with large relaxation times have RH,Bright/RH,F aint ratios very close to unity, showing that these clusters are (nearly) unsegregated. For increasing TAge/TRH the amount of mass segregation increases and the most dynamically evolved clusters in our sample have TAge/TRH ratios around 0.7. These clusters also have P values from the KS test that are close to 100%, showing a very secure detection of mass segregation in these clusters. The grey shaded region and black line in Fig. 3 depict the mass segregation results that we get from an analysis of the Nbody simulations. It can be seen that the amount of mass segregation in observed globular clusters is in full agreement with the observed amount of mass segregation in the simulated clusters. Since the simulated clusters started without Stellar mass segregation in GCs and UFDs 9 mass segregation, we take this as clear evidence that the globular clusters that we have analysed here also started without primordial mass segregation among their low-mass stars. Given that the clusters analysed span about two orders of magnitude in mass and a factor 30 in Galactocentric distance, there is no reason to assume that our results can not be generalised to the other globular clusters as well. 5.2 Star clusters/Ultra-faint dwarf galaxies We next analyse the ultra-faint dwarf galaxy candidates. The determination of mass segregation for them is done in exactly the same way as for the globular clusters. Fig. 4 and Table 3 show the distribution of RH,Bright/RH,F aint ratios that we obtain this way. Since the ultra-faint dwarf galaxy candidates have generally fewer stars than globular clusters, we obtain larger error bars on these ratios. Hence the RH,Bright/RH,F aint ratios alone are not always su\ufb03cient to safely classify an object, so our \ufb01nal classi\ufb01cation also includes literature data whenever available. Before studying the full distribution, we therefore \ufb01rst discuss the available observational data of each individual object to derive a \ufb01nal classi\ufb01cation. 5.2.1 Balbinot 1 Balbinot et al. (2013) discovered Balbinot 1 in Sloan Digital Sky Survey (SDSS) data and studied the system in more detail using CFHT/MegaCam data. They found a half-light radius of rh = 7.2 pc, an age of about 11.7 Gyr and an absolute luminosity of MV = \u22121.21 \u00b1 0.66. The latter quantity is within the range of values measured for Galactic open clusters. Not much else is known about the system. Using the CFHT/MegaCam from Balbinot et al. (2013), we obtain RH,Bright/RH,F aint = 0.68 \u00b1 0.18 for Balbinot 1 and a highly signi\ufb01cant detection of mass segregation with PMseg = 99.8%. We therefore conclude that Balbinot 1 is a star cluster. 5.2.2 Bo\u00a8 otes II Bo\u00a8 otes II was discovered in SDSS data by Walsh, Jerjen & Willman (2007), who speculated that it was a dwarf galaxy based on its large half-light radius (about 70 pc). Spectroscopic observations by Koch & Rich (2014) and Ji et al. (2016) later found a very low metal abundance and a low fraction of neutron capture elements, in agreement with the assumption that Bo\u00a8 otes II is a dwarf galaxy. Our results are also compatible with this assumption since we \ufb01nd RH,Bright/RH,F aint = 0.95 \u00b1 0.07, i.e. no signi\ufb01cant detection of mass segregation. We conclude that Bo\u00a8 otes II is a dwarf galaxy. 5.2.3 Cetus II Cetus II was discovered by Drlica-Wagner et al. (2015) who determined a heliocentric distance of 30 kpc and a compact size of rh = 17 pc. The parameters of Cetus II were later revised by Conn et al. (2018b) using deep Gemini GMOS-S g, r photometry, who failed to \ufb01nd a stellar overdensity in Cetus II and, given the similarity in distance and metallicity, suggested that Cetus II is made up of stars from the Sagittarius dwarf galaxy. We also see no density concentration in our data, however the HST photometry we use covers a too small \ufb01eld of view to be conclusive. We obtain RH,Bright/RH,F aint = 1.12 \u00b1 0.20 for Cetus II, compatible with no mass segregation and the system being either a dwarf galaxy or a tidal stream. We can rule out a star cluster nature of Cetus II since the expected value of RH,Bright/RH,F aint would then be about 0.70 to 0.80, depending on the fraction of the system that is covered by our photometry. We classify the nature of Cetus II as inconclusive. Radial velocities for some of the member stars might help to decide if Cetus II is a tidal tail of the Sagittarius galaxy or a separate stellar system. 5.2.4 DES 1 DES 1 might be a satellite of the Small Magellanic Cloud (Conn et al. 2018b) but its status as a dwarf galaxy or star cluster has so far not been established. Conn et al. (2018b) found a PMseg = 14.8% chance that the DES 1 is not mass segregated. From our analysis of the stellar distribution in their ground-based Gemini/GMOS-S g, r data we \ufb01nd a similar, albeit somewhat lower chance of PMseg = 4.7% that the bright and faint stars follow the same distribution. The low probabilites together with the compact size of DES 1 therefore argue for the system being a star cluster. 5.2.5 Draco II Draco II was discovered by Laevens et al. (2015) in the PanSTARRS1 3\u03c0 survey. According to Longeard et al. (2018) it is an old, metal-poor stellar system at a distance of about 21 kpc. Martin et al. (2016a) and Longeard et al. (2018) carried out spectroscopic observations of Draco II but obtained only upper limits on the velocity dispersion. Longeard et al. (2018) also failed to \ufb01nd signi\ufb01cant mass segregation in the analysis of their CFHT/MegaCam data. We obtain RH,Bright/RH,F aint = 0.78 \u00b1 0.07, clearly indicating mass segregation and in full agreement with the expected value for a dark matter free star cluster of the mass and size of Draco II. The di\ufb00erence to Longeard et al. (2018) could be due to our deeper HST photometry which reaches nearly 2 magnitudes further below the main-sequence turnover than their data. We conclude that Draco II is star cluster. 5.2.6 Eridanus III Eridanus III was discovered along with 8 other Milky Way satellite candidates by Koposov et al. (2015a) in Dark Energy Survey (DES) data. Conn et al. (2018b) obtained Gemini/GMOS-S g, r photometry and derived a Galactocentric distance of 91 \u00b1 4 kpc and an absolute luminosity of MV = \u22122.07 \u00b1 0.50 for Eridanus III. From their data they did not \ufb01nd evidence for mass segregation in the system. Nevertheless, they classi\ufb01ed Eridanus III as a star cluster mostly due to its compact size and low luminosity, which are similar to that of other known halo star clusters. Our results support this conclusion since we obtain a signi\ufb01cant detection of mass segregation and a mass segregation ratio 10 Baumgardt, Faller, Meinhold, McGovern-Greco, Hilker of 0.84 \u00b1 0.09 in full agreement with the expected one for a star cluster with the relaxation time of Eridanus III. The di\ufb00erence between their results and ours could again be due to the fainter magnitudes that we reach with our HST data, which allow us to probe less massive stars that show a larger degree of mass segregation. 5.2.7 Grus I Like Eridanus III, Grus I was discovered by Koposov et al. (2015a) in Dark Energy Survey (DES) data. Walker et al. (2016) obtained Magellan/M2FS spectra of 7 likely members but failed to \ufb01nd a velocity or metallicity spread among them. Ji et al. (2019) obtained high-resolution spectra for two member stars which still showed no metallicity di\ufb00erence but revealed that both stars were de\ufb01cient in neutroncapture elements. Since such an abundance pattern is rare among globular cluster stars, they concluded that Grus I is a dwarf galaxy. Further evidence for a dwarf galaxy nature of Grus I was presented by Cantu et al. (2021), who derived a half-mass radius of 150 pc for Grus I, much larger than expected for a star cluster. Furthermore Jerjen et al. (2018) identi\ufb01ed two stellar overdensities in Grus I, one of which is covered by our HST photometry. We derive mass segregation parameters of 0.87 \u00b1 0.08 for Grus I using the centre position given by Jerjen et al. (2018) which is mid-way between the two density peaks they identi\ufb01ed. Adopting the density peak covered by the HST photometry as centre of Grus I, this value changes to 0.91 \u00b1 0.08. Both values could indicate that Grus I is mass segregated, something that is at variance with the large relaxation time of the system, which is larger than a Hubble time even if Grus I would be free of dark matter. A possible explanation could be that Grus I is a dwarf galaxy with one or two small star clusters orbiting inside it. 5.2.8 Grus II Grus II was discovered by Drlica-Wagner et al. (2015) in second year DES data. They estimated a half-light radius of 6 arcmin and a distance of 55 kpc to the system. The halflight radius would correspond to a physical size of about 95 pc, making it unlikely that Grus II is a star cluster. For the stars in our HST \ufb01eld, we \ufb01nd a half-number radius of 96 arcsec, corresponding to a lower limit of 25 pc on the half-light radius, in agreement with the size estimated by Drlica-Wagner et al. (2015). We also do not \ufb01nd signi\ufb01cant mass segregation among the member stars (PMseg = 8.9%). Grus II is therefore most likely a dwarf galaxy. We \ufb01nally note that Simon et al. (2020) recently obtained spectroscopy for three member stars but failed to \ufb01nd a signi\ufb01cant velocity dispersion or metallicity spread for them. Additional radial velocities might be necessary to \ufb01nally settle the nature of Grus II. 5.2.9 Horologium I Not much is known about the nature of Horologium I. Based on \ufb01ve member stars, Koposov et al. (2015b) measured a velocity dispersion of 4.9+2.8 \u22120.9 km/sec for Horologium I. From the velocity dispersion they also derived a mass-to-light ratio of M/L \u223c600. However, given the small number of stars and the fact that the radial velocities were taken at a single epoch, there is the possibility that their velocity dispersion is in\ufb02uenced by binary stars or non-members. Nagasawa et al. (2018) measured the abundances of three stars in the system and found a mean metallicity of [Fe/H]=-2.6 and very similar abundance patters between these stars. The low metallicity is more compatible with a dwarf galaxy but would not exclude a star cluster either. We \ufb01nd no signi\ufb01cant mass segregation between the stars (PMseg = 9.4%) and therefore conclude that Horologium I is most likely a dwarf galaxy. 5.2.10 Horologium II There is some confusion about the correct density centre of Horologium II. Kim & Jerjen (2015b) give the position of the density centre as RA=49.13375, DEC=-50.01806, while Mu\u02dc noz et al. (2018b) \ufb01nd RA=49.1077, DEC=-50.0486 with signi\ufb01cant errors in both right ascension and declination. The stars selected as members in our HST data show a clear concentration around RA=49.138, DEC=-50.008 and we therefore adopt this position as the centre of Horologium II. With that position, we obtain RH,Bright/RH,F aint = 1.05 \u00b1 0.11, i.e. no evidence for mass segregation. No further information is available for the system, however given the lack of mass segregation we conclude that Horologium II is most likely a dwarf galaxy. 5.2.11 Kim 2, Koposov 1, Koposov 2 Our analysis of these three systems is based on the groundbased CFHT/Megacam data of Mu\u02dc noz et al. (2018b). Since this data is less deep than the HST data that we use for most of the other star clusters and dwarf galaxies, we can only analyse about \u223c100 stars in each system. Nevertheless we get relatively strong detections of mass segregation for each system. Our detection of mass segregation in Kim 2 agrees with the results of Kim et al. (2015). Since the compact sizes of these systems also argue in favour of them being star clusters, we conclude that the three systems are most likely star clusters. 5.2.12 Pegasus III The most detailed study of Pegasus III was done by Kim et al. (2016), who obtained Keck/DEIMOS spectroscopy and Magellan/IMACS photometry of Pegasus III. They derived a large half-light radius of 54 pc and a signi\ufb01cant elongation of the system, something that we also see in our HST photometry. Based on eight stars, they also determined a low metallicity and a stellar velocity dispersion of \u03c3 = 5.4+3.0 \u22122.5 km/sec, indicating a strongly dark matter dominated system. However, Kim et al. (2016) also noticed that their solution for the velocity dispersion would drop to zero with the exclusion of the star with the most discrepant radial velocity. Garofalo et al. (2021) obtained B, V time series photometry of Pegasus III and derived a 20% smaller distance to the system. Their photometry also indicated a signi\ufb01cant metallicity spread in the system, which again would speak for a Stellar mass segregation in GCs and UFDs 11 dwarf galaxy nature of Pegasus III. Our results are compatible with this conclusion since we \ufb01nd no evidence for mass segregation of Pegasus III. Taking all evidence together, it seems most likely that Pegasus III is a dwarf galaxy, although a tidally disrupted star cluster might still be a possible solution. Additional spectroscopy should help settle the question. 5.2.13 Phoenix II and Pictoris I Phoenix II and Pictoris I were discovered by Bechtol et al. (2015) and Koposov et al. (2015a) in Dark Energy Survey (DES) data. No velocity or metallicity information is available for these systems. The structural parameters that have been determined for both systems by Mutlu-Pakdil et al. (2018) and Mu\u02dc noz et al. (2018b) make them larger than normal star clusters and are more typical for dwarf galaxies. Since we also do not detect signi\ufb01cant mass segregation in both systems we conclude that they are most likely dwarf galaxies, although given the large relaxation times, a star cluster nature is not completely ruled out either by our data. 5.2.14 Reticulum II A dwarf galaxy nature of Reticulum II seems \ufb01rmly established by its large velocity dispersion, which is far larger than expected for a purely stellar system (Walker et al. 2015; Simon et al. 2015; Minor et al. 2019) as well as the chemical abundance patterns found in its member stars by Roederer et al. (2016), which closely resemble those of other con\ufb01rmed dwarf galaxies. Our mass segregation data is compatible with this conclusion, although, due to the large relaxation time which is larger than a Hubble time even in case of a purely stellar system, we would not be able to distinguish between a star cluster or a dwarf galaxy. 5.2.15 Reticulum III No velocity or metallicity data is available for Reticulum III which would allow a classi\ufb01cation of the system. We obtain a mass segregation ratio of RH,Bright/RH,F aint = 1.20 \u00b1 0.10, which is compatible with no mass segregation. Given the lar lack of mass segregation and the large size of the system, we conclude that Reticulum III is a dwarf galaxy. 5.2.16 Sagittarius II Sagittarius II was discovered as a stellar overdensity by Laevens et al. (2015) in Pan-STARRS 1 data. Longeard et al. (2020) and Longeard et al. (2021) obtained stellar radial velocities and metallicity estimates for about 25 member stars of Sagittarius II from which Longeard et al. (2021) determined a velocity dispersion of about 1.7 \u00b1 0.5 km/sec. Such a velocity dispersion would be signi\ufb01cantly higher than the one expected for a stellar system with the size and mass of Sagittarius II, since, using the N-body models of Baumgardt (2017), we predict a velocity dispersion of only about 0.5 km/sec for Sagittarius II. The measured velocity dispersion of Sagittarius II might however be in\ufb02ated by binaries. From our mass segregation test we obtain a mass segregation parameter of 0.96\u00b10.02, in full agreement with the expected value for a star cluster. We therefore conclude that Sagittarius II is a star cluster. This classi\ufb01cation is in agreement with the fact that Longeard et al. (2021) \ufb01nd no metallicity spread among the member stars of Sagittarius II. 5.2.17 Segue 1 Segue 1 seems almost certainly a dwarf galaxy based on its large velocity dispersion (Simon et al. 2011) as well as the large metallicity spread seen among its giant stars (Frebel, Simon & Kirby 2014). We obtain a mass segregation ratio of 0.93 \u00b1 0.06, fully compatible with an unsegregated dwarf galaxy and signi\ufb01cantly higher than expected for a star cluster of the size of Segue 1 (about 0.80). We therefore conclude that Segue 1 is a dwarf galaxy. 5.2.18 Segue 2 Kirby et al. (2013) identi\ufb01ed Segue 2 as a dwarf galaxy based on the wide spread in metallicity that they found among the member stars, even though they were not able to resolve its velocity dispersion. Our mass segregation data is compatible with this assumption since we do not detect signi\ufb01cant mass segregation among the member stars (PMseg = 4.5%). We therefore classify Segue 2 as a dwarf galaxy. 5.2.19 Segue 3 Fadely et al. (2011) performed the \ufb01rst detailed kinematic and photometric study of Segue 3. They derived an age of 12 Gyr and found no signi\ufb01cant metallicity spread among the member stars. Since they were also not able to resolve the velocity dispersion, they concluded that Segue 3 is an old star cluster. The age of Segue 3 was later revised downwards to 3.2 Gyr by Ortolani, Bica & Barbuy (2013) and 2.5 Gyr by Hughes et al. (2017). We \ufb01nd a moderately signi\ufb01cant detection of mass segregation in Segue 3 (PMseg = 75.9%). Together with the young age and its location in a mass vs. size relation we therefore conclude that Segue 3 is a star cluster. 5.2.20 Triangulum II Martin et al. (2016b) obtained Keck/DEIMOS spectroscopy for 13 member stars of Triangulum II and found a high central velocity dispersion of \u03c3 = 4.4+2.8 \u22122.0 km/sec. They also found that the velocity dispersion increased further outwards, indicating either a strongly dark matter dominated system or the ongoing tidal disruption of the system. Kirby et al. (2015) con\ufb01rmed the high central velocity dispersion, and also found a metallicity spread of \u2206[Fe/H]=0.8 dex among the member stars. However Kirby et al. (2017) obtained additional velocities for 13 member stars and obtained only an upper limit of 3.4 km/sec for the velocity dispersion. In addition, they also noted that the metallicity spread detected among the member stars hinges on the membership of the two most metal-rich stars, leaving open the possibility that Triangulum II is a star cluster. We obtain a mass segregation parameter RH,Bright/RH,F aint = 0.99 \u00b1 0.09, in good agreement with the assumption that Triangulum II is unsegregated. As a star cluster we would 12 Baumgardt, Faller, Meinhold, McGovern-Greco, Hilker expect to \ufb01nd a value around 0.80 due to the low relaxation time of Triangulum II. We therefore conclude that the system is a dwarf galaxy. 5.2.21 Tucana III Tucana III is unique among the known ultra-faint dwarf galaxy candidates of the Milky Way since it has con\ufb01rmed tidal tails (Li et al. 2018) indicating ongoing tidal disruption of the system. However the nature of Tucana III is still not certain. Simon et al. (2017) presented radial velocities for 26 member stars of Tucana III, from which they were only able to derive an upper limit of 1.5 km/sec for the velocity dispersion. They also did not detect a signi\ufb01cant metallicity spread among those stars. Marshall et al. (2019) presented high-resolution spectroscopy for four member stars and found a moderate enrichment in r-process elements. They argued that the abundance pattern suggest a dwarf galaxy nature for Tucana III. Our data is inconclusive, since we \ufb01nd a mass segregation ratio of 0.95 \u00b1 0.07, compatible with both a mass segregated star cluster or a dwarf galaxy without mass segregation. However, based on the results of Marshall et al. (2019), we assume that Tucana III is more likely a dwarf galaxy. 5.2.22 Tucana V Simon et al. (2020) obtained Magellan/IMACS spectroscopy for 3 stars in Tucana V but found neither a signi\ufb01cant metallicity spread nor a velocity dispersion of the system. The photometry by Conn et al. (2018b) was equally inconclusive since they found that Tucana V is compatible with the location of dwarf galaxies in a luminosity-metallicity plane, but compatible with a star cluster in a size-luminosity plane. We \ufb01nd no signi\ufb01cant mass segregation for Tucana V (PMseg = 1.3%) while as star cluster it should be strongly mass segregated and therefore conclude that Tucana V is a dwarf galaxy. 5.2.23 Virgo I Virgo I was discovered by Homma et al. (2016) in data from the Subaru/Hyper Suprime-Cam survey. Nothing much is known about the system. Our HST photometry shows a clear concentration of member stars around RA=180.035, DEC=-0.690, slightly di\ufb00erent to the centre position given by Homma et al. (2016). Adopting this position as density centre, we \ufb01nd a mass segregation parameter 0.80 \u00b1 0.17, compatible with either a mass segregated or an unsegregated system. We notice however that the spatial distribution of stars in our HST \ufb01eld appears very elongated. Furthermore the absolute luminosity and distance given by Homma et al. (2016) would result in a tidal radius for Virgo I of about 45 pc, not much larger than the quoted half-mass radius of 38 pc. Virgo I might therefore not be a bound system, although with the data at hand we can\u2019t distinguish between a tidal tail of a dwarf galaxy or that of a star cluster. 5.2.24 Willman 1 Willman 1 was discovered by Willman et al. (2005) in SDSS data. Willman et al. (2011) obtained Keck/DEIMOS spectroscopy for 45 likely member stars, and, while they were not able to detect a velocity dispersion for the system, they found a signi\ufb01cant metallicity spread between two member stars. They therefore concluded that Willman 1 is a dwarf galaxy. We \ufb01nd RH,Bright/RH,F aint = 1.05 \u00b1 0.08, indicating that Willman 1 is unsegregated. The expected value for a star cluster would only be around 0.90, which is signi\ufb01cantly below the observed ratio. We therefore conclude that Willman 1 is a dwarf galaxy. 5.3 Final results Fig. 4 depicts the \ufb01nal distribution of the mass segregation ratios as a function of the relaxation time for all dwarf galaxy candidates. Objects that we classify as star clusters are shown in red, dwarf galaxies are shown in blue and objects with an unclear status in yellow. The only two objects that we cannot classify are Cetus II and Virgo I, which are most likely tidal streams. Our \ufb01nal classi\ufb01cation takes the observed mass segregation ratios as well as literature results on metallicity and velocity dispersion into account. In order to allow a comparison of our classi\ufb01cation with existing literature, we show with triangles objects that have either a resolved velocity dispersion, a signi\ufb01cant abundance spread among the member stars or an heavy element abundance pattern that makes them likely dwarf galaxies. Objects without such signs are shown by circles. It can be seen that our mass segregation results provide a clear separation between dwarf galaxies and star clusters since most objects either have no obvious mass segregation or are clearly mass segregated. In addition the classi\ufb01cation based on our mass segregation ratio generally agrees with the literature classi\ufb01cation based on metallicity or velocity dispersion (blue and red triangles). The only exception is Grus I, where our mass segregation classi\ufb01cation could be in\ufb02uenced by the substructure found by Jerjen et al. (2018). Fig. 5 \ufb01nally shows the distribution of known Galactic globular clusters and dwarf galaxies in a mass vs. size plane. Globular clusters studied in this paper are marked by yellow triangles, star clusters by red squares and dwarf galaxies are shown as blue squares and objects without a classi\ufb01cation as black circles. For systems not studied in this work we have searched the literature to classify them into dwarf galaxies or star clusters. For most objects this classi\ufb01cation was relatively straightforward since they are relatively large objects with sizes of 100 pc or more that show clear evidence of being dwarf galaxies. There is a relatively clear division between dwarf galaxies and star clusters in Fig. 5. All known systems with sizes rh > 20 pc are dwarf galaxies, with the exception of a few globular clusters. These are however signi\ufb01cantly more luminous than the dwarf galaxies of the same size and occupy a region in parameter space quite distinct from the dwarf galaxies. The possible unbound systems Cetus II and Virgo I are signi\ufb01cantly less luminous than dwarf galaxies of comparable size, which again shows that they could be di\ufb00erent from the other dwarf galaxies. Interestingly there is no con\ufb01rmed dwarf galaxy with size of less than 20 pc. This could Stellar mass segregation in GCs and UFDs 13 Figure 4. Same as Fig. 3 for the dwarf galaxies and star clusters. Red, blue and yellow symbols show our \ufb01nal classi\ufb01cation based on the measured RH,Bright/RH,F aint ratios as well as literature data on metallicities and velocity dispersions. Circles/triangles mark star clusters and dwarf galaxies without/with literature information on their nature. There is a clear dichotomy in the mass segregation distribution. Star clusters follow the same trend between mass segregation and their relaxation times as seen for globular clusters and simulated star clusters while the dwarf galaxies are all compatible with no mass segregation. be a true limit meaning lower mass halos don\u2019t exist or were not able to form any stars. Alternatively, given that about half of all compact and low-mass objects in Fig. 5 have no classi\ufb01cation yet, we might have simply not found more compact dwarf galaxies. Fig. 6 compares the location of all systems in a size vs. luminosity plane with the tidal radius of the systems due to the gravitational \ufb01eld of the Milky Way added. For a system of mass M in circular orbit with radius RG in a logarithmic potential with circular velocity VC, the tidal radius is given by RT ide = \u0012 M 2V 2 C \u00131/3 R2/3 G (7) The tidal radius describes the maximum radius out to which a system can keep stars bound. Tides will start to remove the outer stars well before the half-mass radius of a system equals its tidal radius, leading to mass loss and a further shrinking of the tidal radius. Dissolution should therefore already set in well before the half-mass radius of a dwarf galaxy or star cluster approaches its tidal radius. Assuming a maximum ratio RH/RT ide = 0.33 necessary for stability 14 Baumgardt, Faller, Meinhold, McGovern-Greco, Hilker Figure 5. Half-mass radius vs. absolute magnitude for all dwarf galaxy candidates and globular clusters. Systems studied in this work are marked by their names. Systems classi\ufb01ed as star clusters are shown by red squares, those classi\ufb01ed as dwarf galaxies by blue squares and those without a \ufb01nal classi\ufb01cation by green squares. We also performed a literature search to classify the systems that were not studied in detail in this paper. Systems that have no classi\ufb01cation in the literature are shown by black circles. and that the projected half-light radius that observers measure is 0.75 times the 3D one, we obtain RLim = 0.25 RT ide as the maximum radius that any system can have before tidal disruption happens. The two dashed lines in Fig. 6 show this relation for the case of a pure stellar system with MT ot = MLum and a dark matter dominated system with MT ot = 100MLum. For both lines we assume a Galactocentric distance of 80 kpc and a circular velocity of 170 km/sec (Deason et al. 2021) at this distance. We restrict ourselves to objects with RGC > 30 kpc in this plot, and show globular clusters at smaller distances with a di\ufb00erent symbol. It can be seen that all objects classi\ufb01ed as star/globular clusters stay to the left of the tidal limit line for purely stellar systems and should therefore be stable to tidal forces even in the absence of dark matter, con\ufb01rming our classi\ufb01cation. Objects that have no classi\ufb01cation so far occupy either side of the RLim,Star line. As star clusters with rh,p > RLim,Star should undergo quick dissolution, the unclassi\ufb01ed objects with rh,p > RLim,Star are most likely dark matter dominated dwarf galaxies or star clusters in the process of disruption. Given that we \ufb01nd only very few con\ufb01rmed dwarf galaxies with rh,p < RLim,Star, it seems likely that the unclassi\ufb01ed objects with rh < 10 pc are star clusters. Most dwarf galaxies have rh,p < RLim,DM, meaning they should be stable as long as they are strongly dark matter dominated. The only systems to the right of this line are Antila 2 and Crater II, for which Ji et al. (2021) detected signs of ongoing tidal disruption, and Bo\u00a8 otes IV for which Homma et al. (2019) found a large intrinsic ellipticity of \u03f5 = 0.64 which could indicate tidal interaction and distortion. Furthermore Bo\u00a8 otes IV is at a Galactocentric distance of \u223c210 kpc and has a relatively large error bar on its half-mass radius. Hence it might have rh,p < RLim,DM and be bound. Since the tidal radius of a system increases with its mass to the power of 1/3, the derived limits can be turned into densities. We \ufb01nd that star clusters in the outer halo have densities (within their half-light radii) between 3\u00b710\u22122 M\u2299< \u03c1h < 1 M\u2299while dwarf galaxies have (stellar) densities of 10\u22123 M\u2299< \u03c1h < 3 \u00b7 10\u22122 M\u2299, about a factor 30 smaller than star clusters. Adding the dark matter to these numbers would make the densities of the dwarf galaxies roughly comparable to those of the star clusters. Dwarf galaxies and star clusters in the halo of the Milky Way are subject to tidal forces from the Milky Way, which can remove mass from the system. If the mass loss is strong enough this could change the expected mass segregation signal and therefore in\ufb02uence our classi\ufb01cations. However, our classi\ufb01cations are unlikely to be strongly in\ufb02uenced by tidal e\ufb00ects since, with a few exceptions like Tuc III, most dwarf galaxies do not show obvious tidal tails (Simon 2019). In addition, Hammer et al. (2021) recently found from an analysis of the orbital motions of dwarf galaxies that most of them are probably on their \ufb01rst passage of the Milky Way, again arguing against signi\ufb01cant tidal stripping of most them. Finally the lifetimes calculated by Baumgardt et al. (2019) signi\ufb01cantly exceed a Hubble time for most globular clusStellar mass segregation in GCs and UFDs 15 Figure 6. Similar to Fig. 5 but now also showing limits where a stellar system should be tidally disrupted by the gravitational \ufb01eld of the Milky Way. The line RLim,Star shows the tidal limit for a purely stellar systems while the line RLim,DM is for a system with 100\u00d7 as much dark matter as luminous matter. Both lines are for a Galactocentric distance of 80 kpc. All star clusters are to the left of the RH = RLim,Star line and most dwarf galaxies are to the left of the RH = RLim,DM line, implying that most are bound systems. Unclassi\ufb01ed systems with RH > RLim,Star can\u2019t be bound star clusters and are likely dwarf galaxies or undergoing tidal disruption. ters studied in our paper, again arguing against strong mass loss. 6 CONCLUSIONS We have derived the amount of mass segregation in over 50 globular clusters and dwarf galaxy candidates by analysing their colour-magnitude diagrams based on deep HST and ground-based photometry. We \ufb01nd that dynamically young globular clusters (i.e. clusters with relaxation times of the order of or larger than their ages) have little to no mass segregation and that the amount of mass segregation increases with increasing dynamical age. At each dynamical age the amount of mass segregation is fully compatible with the one found in N-body simulations of initially unsegregated clusters. Our results therefore strongly indicate that globular clusters form without primordial mass segregation between their low-mass stars. This conclusion is strengthened by the fact that the investigated globular clusters cover the full mass range seen for globular clusters (from 3 \u00b7 102 M\u2299to 3 \u00b7 106 M\u2299), and nearly the full metallicity range and range of Galactocentric radii (6.7 kpc to 147 kpc). The only alternative explanation would be if globular clusters form segregated but the initial mass segregation is erased by the primordial gas expulsion process (e.g. Marks, Kroupa & Baumgardt 2008; Haghi et al. 2015). However it is di\ufb03cult to see how this process could almost completely erase the initial mass segregation signature, so the assumption of no initial mass segregation is by far the more natural assumption. The lack of mass segregation that we \ufb01nd in the least evolved clusters is in agreement with observations of young open clusters which also \ufb01nd the low-mass stars to be unsegregated (e.g Parker, Maschberger & Alves de Oliveira 2012; Parker & Alves de Oliveira 2017). Our study leaves open the question of primordial mass segregation of the more massive stars, for which both hydrodynamical simulations and observations show that they form preferentially in the highest density regions of a star forming molecular cloud (e.g Bonnell & Davies 1998; Maschberger & Clarke 2011; Dib & Henning 2019). We \ufb01nd that the dwarf galaxy candidates fall mostly into two groups, star clusters that are mass segregated in the same way as globular clusters of the same dynamical age and unsegregated systems. Most unsegregated systems have dynamical ages larger than unity, so some additional process must be invoked to prevent mass segregation in these systems. The most natural mechanism is a signi\ufb01cant amount of dark matter. This is corroborated by the fact that many unsegregated dwarf galaxy candidates also have either large velocity dispersions, a signi\ufb01cant spread in [Fe/H] or r-process metal abundances typical of dwarf galaxies. Combining our mass segregation data with published literature data, we are thus able to classify almost all investigated dwarf galaxy candidates as either star clusters or dwarf galaxies. The only exceptions are Cetus II and Virgo I, which could be tidally disrupting systems, but is not clear if they are former star clusters or dwarf galaxies. 16 Baumgardt, Faller, Meinhold, McGovern-Greco, Hilker We \ufb01nally \ufb01nd that star clusters and dwarf galaxies occupy narrow strips in the size vs. mass plane. Star clusters in the outer halo have densities (within their half-light radii) between 0.03 M\u2299/pc3 \u2272\u03c1h \u22721 M\u2299/pc3 while dwarf galaxies have (stellar) densities of 0.001 M\u2299/pc3 \u2272\u03c1h \u2272 0.03 M\u2299/pc3, about a factor 30 smaller than the star clusters. The dividing line between both populations roughly corresponds to the limit where star clusters would be tidally disrupted by the tidal \ufb01eld of the Milky Way. Dwarf galaxies seem to be limited in the same way if their dark matter is taken into account and all systems with stellar densities \u03c1h < 3 \u00b7 10\u22124 M\u2299/pc3 show signs of ongoing tidal disruption. van den Bergh (2008) suggested a division corresponding to M \u223cR5.7 H (for constant mass-to-light ratio) between globular clusters and dwarf galaxies, which seems too steep since many of the con\ufb01rmed ultra-faint dwarf galaxies would end up on the star cluster side of this relation. Also the commonly used division based on surface brightness (corresponding to a M \u223cR2 H relation for constant mass-to-light ratio) seems to work less well since many star clusters would lie on the dwarf galaxy side. ACKNOWLEDGMENTS We thank an anonymous referee who helped improve the presentation of the paper. This work is based on observations made with the NASA/ESA Hubble Space Telescope, obtained from the data archive at the Space Telescope Science Institute. STScI is operated by the Association of Universities for Research in Astronomy, Inc. under NASA contract NAS 5-26555. DATA AVAILABILITY Data is available upon request.",
                    "introduction": "Dwarf galaxies have in recent years become useful probes to test the properties of dark matter. Determining their ab- solute numbers and mass function is an important test for our understanding of galaxy formation on small scales and allows to put constraints on the mass of the dark matter particle (Bode, Ostriker & Turok 2001; Jethwa, Erkal & Be- lokurov 2018). Furthermore their central densities can pro- vide clues to the behavior of the dark matter particle on small scales (e.g. Safarzadeh & Spergel 2020; Hayashi, Fer- reira & Chan 2021). Dwarf galaxies are also useful tools to enhance our understanding of galaxy formation. Especially the faintest dwarf galaxies provide vital insights into the star formation process in the early universe, since their low stel- lar masses and low metallicities mean that they formed at high redshift and have likely the simplest enrichment history of all galaxies. This makes them pristine relics of the early \u22c6E-mail: h.baumgardt@uq.edu.au universe (Bland-Hawthorn, Sutherland & Webster 2015; Ro- mano et al. 2019). The number of known dwarf galaxy candidates has in- creased dramatically in the last \ufb01fteen years thanks in large part to wide area digital sky surveys (see e.g. Fig. 1 in Simon 2019). Most of the newly discovered dwarf galaxies are ultra- faint dwarf galaxies (UFDs) with luminosities MV > \u22127 and sizes of a few tens of pc. The location of these UFDs in a size vs. mass plane overlaps with that of faint globular clusters. It is therefore important to obtain additional information to be able to separate UFDs from halo star clusters. Two common ways to identify UFDs are either through their kinematics or by measuring the stellar abundances of their member stars. While the kinematics of globular clusters can be well ex- plained based on the visible stars alone (e.g. Baumgardt & Hilker 2018), UFDs are found to have velocity dispersions signi\ufb01cantly larger than those expected based solely on their visible stars. The measured velocity dispersions of UFDs are so large that their total masses must be orders of magni- tude higher than their stellar masses (e.g. Simon & Geha 2007). Furthermore the faintest dwarf galaxies have gener- arXiv:2112.04689v1  [astro-ph.GA]  9 Dec 2021 2 Baumgardt, Faller, Meinhold, McGovern-Greco, Hilker ally low iron abundances (down to about [Fe/H]\u223c\u22123.0), while the more massive dwarf galaxies show large abun- dance spreads between their member stars, indicating pro- longed star formation histories. In addition, low-mass UFDs have been found to be enriched in r-process elements (Ji et al. 2016), indicating that their stars were enriched by sin- gle core-collapse supernova events. Globular clusters on the other hand have a large range of metallicities, their internal iron abundance spreads are small and limited to the most massive clusters, and abundance spreads in other elements occur mainly among the light elements (Gratton, Sneden & Carretta 2004; Carretta et al. 2010; Roediger et al. 2014). Both the abundance as well as the velocity dispersion test become increasingly harder to apply for fainter UFDs since the faintest detected UFDs contain few if any giant stars for which high-resolution spectra can be obtained. Measuring velocity dispersions from only a few stars is how- ever subject to signi\ufb01cant uncertainties: Apart from the fact that the error bars reach a sizeable fraction of the measured dispersion itself, the measured dispersion also su\ufb00ers from contamination by \ufb01eld stars and stellar binaries (e.g. Kirby et al. 2015, 2017). Furthermore a low metallicity alone is not a proof for a stellar system being a dwarf galaxy, since glob- ular clusters with metallicities as low as [Fe/H]=-2.5 and [Fe/H]=-2.9 have been found in the Milky Way and M31 respectively (Simpson 2018; Larsen et al. 2020). Such metal- licities are similar to the ones found for the most metal-poor dwarf galaxies like Bo\u00a8 otes II (Koch & Rich 2014). It is therefore important to obtain further information that can help to distinguish dwarf galaxies from star clus- ters among the known ultra-faint dwarf galaxy candidates in the halo of the Milky Way. One such possibility is to look for stellar mass segregation (e.g. Longeard et al. 2018; Conn et al. 2018a): Due to energy equipartition, high mass stars are expected to sink into the centers of star clusters while low-mass stars are pushed towards the outskirts of the clusters. Energy equipartition takes typically a few re- laxation times to be established, old halo star clusters and globular clusters with relaxation times less than a few Gyr should therefore be mass segregated. The presence of a sig- ni\ufb01cant amount of dark matter prolongs the timescale for mass segregation signi\ufb01cantly, hence most low-mass dwarf galaxy candidates are predicted to be mass segregated only if free of dark matter, i.e. if they are star clusters. If they contain signi\ufb01cant amounts of dark matter, their relaxation times are larger than a Hubble time and they should not be mass segregated. Our paper is organized as follows: In sec. 2 we discuss the analysis of the HST and ground based photometry and in sec. 3 we present our determination of the amount of mass segregation. In sec. 4 we discuss the determination of mass segregation in a number of N-body simulations that we use to test the origin of the observed mass segregation. In sec. 5 we discuss our results of the amount of mass segregation in the di\ufb00erent systems and in sec. 6 we present our conclu- sions."
                },
                {
                    "url": "http://arxiv.org/abs/2105.09526v2",
                    "title": "Accurate distances to Galactic globular clusters through a combination of Gaia EDR3, HST and literature data",
                    "abstract": "We have derived accurate distances to Galactic globular clusters by combining\ndata from the Gaia Early Data Release 3 with distances based on Hubble Space\ntelescope HST data and literature based distances. We determine distances\neither directly from the Gaia EDR3 parallaxes, or kinematically by combining\nline-of-sight velocity dispersion profiles with Gaia EDR3 and HST based proper\nmotion velocity dispersion profiles. We furthermore calculate cluster distances\nfrom fitting nearby subdwarfs, whose absolute luminosities we determine from\ntheir Gaia EDR3 parallaxes, to globular cluster main-sequences. We finally use\nHST based stellar number counts to determine distances. We find good agreement\nin the average distances derived from the different methods down to a level of\nabout 2%. Combining all available data, we are able to derive distances to 162\nGalactic globular clusters, with the distances to about 20 nearby globular\nclusters determined with an accuracy of 1% or better. We finally discuss the\nimplications of our distances for the value of the local Hubble constant.",
                    "authors": "Holger Baumgardt, Eugene Vasiliev",
                    "published": "2021-05-20",
                    "updated": "2021-05-21",
                    "primary_cat": "astro-ph.GA",
                    "cats": [
                        "astro-ph.GA"
                    ],
                    "main_content": "2.1 Cluster sample and selection of member stars We take our target list of globular clusters from Baumgardt et al. (2019b). To this sample we add six additional Milky Way globular clusters that have been found in recent years: VVV-CL001 (Minniti et al. 2011; Fern\u00b4 andez-Trincado et al. 2021), BH 140 and FSR 1758 (Cantat-Gaudin et al. 2018), Sagittarius II (Laevens et al. 2015; Mutlu-Pakdil et al. 2018), RLGC 1 and RLGC 2 (Ryu & Lee 2018), and Laevens 3 (Longeard et al. 2019). The status of Sagittarius II is still debated, while Mutlu-Pakdil et al. (2018) argue for it to be a star cluster based on its location in a size vs. luminosity plane, Longeard et al. (2020) argue, based on a small spread in [Fe/H] that they find among the cluster stars, for it to be a dwarf galaxy. We tentatively include the object in our list of clusters. The other systems are most likely globular clusters based on their color-magnitude diagrams, kinematics and location in the Milky Way. Together with the 158 GCs studied in Baumgardt et al. (2019b), we therefore have a sample of 162 globular clusters. 2.2 Cluster parallax distances Determining distances to globular clusters via the parallaxes of individual stars has the advantage that the distances are determined directly, without having to rely on another distance method as an intermediate step in the distance ladder. In addition, parallaxes are not influenced by the reddening of the clusters. In this paper, we take the cluster parallaxes from Vasiliev & Baumgardt (2021) (hereafter VB21). VB21 determined mean parallaxes for 170 globular and outer halo star clusters by averaging the cluster parallaxes of individual member stars from the Gaia EDR3 catalogue. Cluster members were selected based on the Gaia EDR3 proper motions and parallaxes. VB21 also applied multi-gaussian mixture modeling to classify stars into cluster members and background stars and determined the mean cluster parameters and their errors over multiple realizations of statistically created member catalogues. In order to account for possible magnitude, color and position dependent biases in the Gaia catalogue, VB21 applied the parallax corrections of Lindegren et al. (2020) to the individual stellar parallaxes. However when testing the derived cluster parallaxes against the literature distances that we derive further below, VB21 found that even after applying the Lindegren et al. corrections, there is still a mean offset in the Gaia parallaxes. In particular, they found that the parallax corrections suggested by Lindegren et al. (2020) might have been overcorrecting the Gaia EDR3 parallaxes by \u2206\u03d6 \u223c0.007 mas. VB21 also found evidence for spatially correlated small scale systematic errors of order \u03f5\u03d6 \u223c0.01 mas. We therefore subtract \u2206\u03d6 = 0.007 mas from the derived mean parallaxes to correct for the parallax bias. The small-scale correlated errors were already taken into account by the parallax averaging procedure of VB21. We list the median distances D = 1/\u03d6 for clusters with \u03d6/\u03c3\u03d6 > 10 in Table 2 to allow a comparison of the Gaia EDR3 parallax distances with the other distances that we derive. When calculating mean cluster distances we use the data for all clusters and the parallax values directly as will be described further below. 2.3 Kinematic distances For clusters with accurately measured line-of-sight and proper motion velocity dispersion profiles one can determine cluster distances kinematically by varying the cluster distance until the velocity dispersions are the same or a best match to a theoretical model of the cluster is achieved (e.g. H\u00b4 enault-Brunet et al. 2019). The advantage of such kinematic distances is that, like parallaxes, the kinematic distance method is a direct method which does not rely on other, more nearby methods in the distance ladder. Similar to parallax distances, kinematic distances are also not affected by cluster reddening, allowing in principle to derive accurate distances for highly reddened clusters. In order to calculate kinematic distances, one either needs to know the anisotropy profile of the internal velocity dispersion of a cluster, or assume that the cluster is isotropic. The latter is most often assumed since observed velocity dispersion profiles usually show that globular clusters are isotropic, at least in their inner parts (van Leeuwen et al. 2000; Watkins et al. 2015a; Raso et al. 2020; Cohen et al. 2021), N-body simulations of star clusters also show that most globular clusters should have isotropic velocity dispersion profiles (Baumgardt & Makino 2003; L\u00a8 utzgendorf et al. 2011; Tiongco, Vesperini & Varri 2016). We take the line-of-sight velocity dispersion profiles for the kinematic distance fitting from Baumgardt & Hilker (2018), Baumgardt et al. (2019a) and Baumgardt et al. Accurate distances to Galactic globular clusters 3 Figure 1. Illustration of the kinematic distance determination for the globular clusters NGC 6624 (left panel) and NGC 6656 (middle panel). Shown are the \u03c72 values from the \ufb01t of our N-body models to the velocity dispersion pro\ufb01les as a function of distance for the HST proper motions (red circles) and Gaia EDR3 proper motions (blue triangles). Solid lines show a quadratic \ufb01t to the \u03c72 values of each data set and the dashed lines and shaded areas mark the best-\ufb01tting distances and their 1\u03c3 error. The literature distances are D = 8020 pc (NGC 6624) and D = 3330 pc (NGC 6656) and are in agreement with the kinematic ones. The right panel compare the error weighted distance di\ufb00erences from Gaia and HST data for clusters which have proper motion velocity dispersion pro\ufb01les from both satellites. The resulting distribution is compatible with a normal distribution (shown by a blue solid line). (2019b). Baumgardt & Hilker (2018) calculated line-of-sight velocity dispersion pro\ufb01les by combining literature velocities with line-of-sight velocities derived from archival spectra from the ESO and Keck data archives. Baumgardt et al. (2019a) and Baumgardt et al. (2019b) added line-of-sight velocities from Gaia DR2 and the Anglo-Australian Observatory (AAO) data archive to these pro\ufb01les. In addition we use the line-of-sight velocity dispersion pro\ufb01les published by Kamann et al. (2018) based on MUSE data. We take the proper motion dispersion pro\ufb01les either from VB21 based on Gaia EDR3 data, or from published pro\ufb01les based on multiepoch HST measurements. Table 1 lists the HST proper motion velocity dispersion pro\ufb01les that we use in this paper together with the distances that we derive from these pro\ufb01les. Unfortunately we could not use the recently published proper motion dispersion pro\ufb01les for nine inner Milky Way globular clusters by Cohen et al. (2021) since no accurate line-of-sight velocity dispersion pro\ufb01les are available for these clusters. We determine a kinematic distance independently for each proper motion velocity dispersion pro\ufb01le that we have from either Gaia EDR3 or HST data. The best-\ufb01tting distance is determined by \ufb01tting each cluster with the grid of N-body models calculated by Baumgardt (2017) and Baumgardt & Hilker (2018). Their grid contains several thousand N-body models of star clusters, varying the size, initial density pro\ufb01le, metallicity and stellar mass function of each cluster. We interpolate within this grid and determine for each cluster the N-body model that simultaneously provides the best \ufb01t to the internal mass function, velocity dispersion and surface density pro\ufb01le. More details about the N-body models can be found in Baumgardt (2017) and Baumgardt & Hilker (2018) and we refer the reader to these papers for a full description of the \ufb01tting procedure. We restrict the radial extent of the line-of-sight velocity dispersion pro\ufb01les to the same range for which we have proper motion dispersions in order to avoid a possible bias due to the N-body models not providing a match to the Table 1. Kinematic distances based on HST proper motion velocity dispersion pro\ufb01les. The second last panel gives the kinematic distance derived by the authors of the original HST data set, the last column gives our distances for the same data set. Cluster HST Data set Lit. Dist. Our Dist. [kpc] [kpc] NGC 104 Watkins et al. (2015a) 4.45 \u00b1 0.50 4.545 \u00b1 0.047 Heyl et al. (2017) 4.29 \u00b1 0.47 4.347 \u00b1 0.236 NGC 288 Watkins et al. (2015a) 9.98 \u00b1 0.37 9.098 \u00b1 0.291 NGC 362 Watkins et al. (2015a) 9.37 \u00b1 0.18 9.202 \u00b1 0.280 NGC 1261 Raso et al. (2020) \u2212 16.775 \u00b1 0.824 NGC 1851 Watkins et al. (2015a) 11.41 \u00b1 0.20 11.440 \u00b1 0.254 NGC 2808 Watkins et al. (2015a) 10.18 \u00b1 0.12 9.837 \u00b1 0.122 NGC 5139 Watkins et al. (2015a) 5.22 \u00b1 0.05 5.264 \u00b1 0.082 NGC 5904 Watkins et al. (2015a) 8.77 \u00b1 0.15 7.456 \u00b1 0.146 NGC 6266 Watkins et al. (2015a) 5.67 \u00b1 0.07 6.354 \u00b1 0.128 McNamara et al. (2012) \u2212 6.945 \u00b1 0.264 NGC 6341 Watkins et al. (2015a) 8.43 \u00b1 0.34 8.231 \u00b1 0.347 NGC 6352 Libralato et al. (2019) \u2212 6.260 \u00b1 0.762 NGC 6362 Watkins et al. (2015a) 7.34 \u00b1 0.24 7.720 \u00b1 0.315 NGC 6388 Watkins et al. (2015a) 10.44 \u00b1 0.12 10.894 \u00b1 0.137 NGC 6397 Watkins et al. (2015a) 2.54 \u00b1 0.05 2.332 \u00b1 0.057 Heyl et al. (2012) 2.20 \u00b1 0.60 2.416 \u00b1 0.062 NGC 6441 Watkins et al. (2015a) 11.77 \u00b1 0.20 12.059 \u00b1 0.172 H\u00a8 aberle et al. (2021) 12.74 \u00b1 0.16 12.364 \u00b1 0.226 NGC 6624 Watkins et al. (2015a) 6.69 \u00b1 0.36 7.972 \u00b1 0.277 NGC 6656 Watkins et al. (2015a) 3.18 \u00b1 0.07 3.161 \u00b1 0.070 NGC 6681 Watkins et al. (2015a) 9.33 \u00b1 0.14 9.260 \u00b1 0.165 NGC 6715 Watkins et al. (2015a) 23.79 \u00b1 0.33 25.019 \u00b1 0.646 NGC 6752 Watkins et al. (2015a) 4.28 \u00b1 0.03 4.005 \u00b1 0.130 NGC 7078 Watkins et al. (2015a) 10.23 \u00b1 0.13 10.375 \u00b1 0.237 full pro\ufb01le. In the N-body models we measure the line-ofsight velocity dispersion pro\ufb01le for stars brighter than the main-sequence turno\ufb00. The magnitude limit for the proper motion velocity dispersion pro\ufb01les was varied for each data set independently so we match the magnitude limit of the 4 Baumgardt & Vasiliev observed data. Hence, except for the nearest clusters like NGC 6121, we chose a magnitude limit equal to the mainsequence turno\ufb00for \ufb01ts to the Gaia EDR3 proper motions, while we choose deeper limits for the HST data. The left and middle panels of Fig. 1 show the resulting \ufb01ts to two clusters that have both Gaia and HST data and Table 1 gives the derived distances from the HST data together with the kinematic distances derived by the authors of the original papers. There is usually good agreement between the distances derived by us and the original kinematic distances. The only exceptions are NGC 5904 and NGC 6266. At least for NGC 5904, one the reason for di\ufb00erent distances could be the lack of a radial overlap between the line-of-sight and proper motion velocity dispersion pro\ufb01les used by Watkins et al. (2015a), which makes the derived distance strongly dependent on the dynamical model used for the cluster. We give the full set of distances including the Gaia ED3 kinematic distances in the Appendix. The right panel of Fig. 1 shows the error weighted distribution of di\ufb00erences in the kinematic distances for the Gaia EDR3 and HST data. It can be seen that they roughly follow a normal distribution, indicating good agreement between the HST and Gaia distances. 2.4 Subdwarf distances The main idea of our subdwarf distances is to make use of the excellent accuracy of Gaia EDR3 parallaxes for nearby stars. As discussed in sec. 2.2, Gaia EDR3 parallaxes have small-scale, systematic uncertainties of \u223c0.01 mas that can\u2019t be removed through calibration of the parallaxes against objects with known parallaxes. This means that even the distances to the nearest globular clusters cannot be determined directly with an accuracy better than a few percent. The accuracy of parallax distances also quickly deteriorates with increasing distance and drops below the accuracy of CMD \ufb01tting distances beyond distances of about 5 kpc. In contrast, the distance to a nearby star at d = 100 pc has a relative uncertainty of only 0.1% using Gaia EDR3 parallaxes. Our basic approach for deriving subdwarf distances is the same as the one used by Cohen & Sarajedini (2012), except that we replace the Hipparcos parallaxes by Gaia EDR3 ones. We start using the compilation of precise Johnson-Cousins UBVRI photometry of nearby subdwarfs by Casagrande et al. (2010) and identify the counter-parts of these stars in the Gaia EDR3 catalogue. We then apply the Lindegren et al. (2020) parallax corrections to the stars as well as the additional shift of \u2206\u03d6 = 0.007 mas found by VB21. Using only stars which have published V and I band photometry by Casagrande et al. (2010), a reddening E(B \u2212V ) < 0.02 and Gaia EDR3 parallaxes with a relative precision \u03d6/\u03f5\u03d6 > 20 leaves us with a sample of 206 stars. Despite our more stringent limit on the parallax accuracy, our sample is almost a factor 10 larger than the one used by Cohen & Sarajedini (2012). Thanks to the superior accuracy of the Gaia EDR3 parallaxes, our sample also contains about 20 stars with metallicities [Fe/H] < \u22122.0, while no accurate Hipparcos parallaxes were available for any of these stars. We \ufb01nally use the SIMBAD astronomical data base to exclude known binaries from this sample, leaving us with a sample of 185 stars. Our source for the globular cluster photometry is the compilation of HST photometry published by Sarajedini et al. (2007) based on observations made with the Advanced Camera for Surveys (ACS) onboard HST. Their survey contains deep photometry in the ACS/WFC F606W and F814W bands for 67 globular clusters. In addition to the photometry for 67 globular clusters from Sarajedini et al. (2007), we also use the ACS/WFC photometry published by Dotter, Sarajedini & Anderson (2011) for 6 globular clusters as well as the photometry for NGC 6528 from Lagioia et al. (2014) that was kindly provided to us by the authors. We \ufb01nally use the photometry from Baumgardt et al. (2019b) for an additional 6 globular clusters (NGC 6325, NGC 6342, NGC 6355, NGC 6380, NGC 6401 and NGC 6558). We skipped Pal 2 due to signi\ufb01cant di\ufb00erential reddening and E 3 since the cluster has such a low mass that the location of its main sequence cannot be accurately determined. This leaves us with a sample of 79 globular clusters with accurate, deep ACS/WFC photometry in the F606W and F814W bands. We dereddened the photometry of each globular cluster using the reddening values given by Dotter et al. (2010) together with the extinction coe\ufb03cients from Sirianni et al. (2005). We then transformed the subdwarf photometry, from the Johnson-Cousins UBVRI system to the ACS/WFC \ufb01lter system using eqn. 12 of Sirianni et al. (2005) together with the transformation coe\ufb03cients given in Table 18 of their paper. We then \ufb01tted PARSEC isochrones (Bressan et al. 2012) to the color-magnitude diagram of each cluster, and used the isochrone to select the cluster members. We then calculated the average color of the cluster stars as a function of magnitude and de\ufb01ne a main-sequence ridge line by cubic spline interpolation between the data points. In order to compare the subdwarf photometry with the globular cluster photometry and derive the cluster distances, we select for each globular cluster all subdwarfs with metallicities |[Fe/H]SD-[Fe/H]GC| <0.2. We took the metallicities of the subdwarfs from Casagrande et al. (2010) and the metallicities of the globular clusters from Carretta et al. (2009). In order to correct the colors of the subdwarfs to the color they would have at the metallicity of the globular cluster, we created a set of PARSEC isochrones equally spaced in metallicity by \u2206[Fe/H] = 0.5 and calculate the colors of zero-age main sequence stars as a function of their absolute V -band luminosity. We then use this grid of isochrones and the absolute magnitudes of the subdwarfs which we calculate using their Gaia EDR3 parallaxes to correct the subdwarf colors for the di\ufb00erence in metallicity. Due to the proximity of the subdwarf metallicities to the metallicity of the clusters, the resulting shifts are always below 0.02 mag. After transforming the subdwarf photometry to the ACS/WFC system and correcting the subdwarf metallicities, we \ufb01tted the cluster main sequences in a F814W0 vs. (F606W-F814W)0 CMD with the subdwarfs. To this end, we vary the assumed cluster distance modulus until the errorweighted di\ufb00erence between the subdwarfs and the previously determined main-sequence ridgeline are minimal. Due to the steepness of the cluster ridgelines and the accurate Gaia parallax distances, this essentially results in minimizing the error weighted color di\ufb00erences between the subdwarfs and the main sequence ridge lines. We exclude subdwarfs with M814 < 4 from the \ufb01ts since these could already Accurate distances to Galactic globular clusters 5 Figure 2. Illustration of the subdwarf distance determination for four globular clusters with a range of metallicity and reddening values. Grey points mark stars considered to be background stars, black points are cluster members. The green line shows our \ufb01tted ridge line for each cluster. Subdwarfs used in the distance \ufb01tting are shown by red circles, subdwarfs not used are shown by blue circles. Photometric error bars are also shown. Note that the error in absolute magnitude due to the Gaia EDR3 parallax error is shown but usually too small to be seen. have evolved away from the main sequence. We also exclude subdwarfs with discrepant photometry since these could be undetected binaries. Fig. 2 shows examples of our subdwarf \ufb01ts for four globular clusters. The clusters shown are the same as the ones depicted in Fig. 2 of Cohen & Sarajedini (2012). We will derive an error bar for the subdwarf distance moduli in sec. 3 when we compare the subdwarf distance moduli against literature data. 2.5 Star count distances For a given velocity dispersion pro\ufb01le, the derived mass of a cluster increases (decreases) with increasing (decreasing) cluster distance. If the velocity dispersion pro\ufb01le is based entirely on line-of-sight velocities, the total cluster mass changes linearly with distance, while for a cluster with a velocity dispersion pro\ufb01le based only on proper motions, the mass changes with the distance to the third power. For a cluster with measured line-of-sight and proper motion ve6 Baumgardt & Vasiliev Figure 3. Illustration of the \ufb01t of our N-body models to the globular cluster NGC 104. The left panel shows all \ufb01elds in NGC 104 with available HST photometry. The di\ufb00erent \ufb01elds are labeled by the name of the Principal Investigator of the HST observations and the white circle marks the observed half-light radius of NGC 104. The middle panel shows the \ufb01t of a PARSEC isochrone (shown in red) to the combined photometry of the four HST/WFPC2 \ufb01elds of Rhoads (HST Proposal ID: 9634) from the left panel. The parameters of the isochrone are given in the \ufb01gure. Grey circles mark all stars in the \ufb01eld and black stars are the stars used for the determination of the stellar mass function of NGC 104. The group of stars visible in the lower left part of the middle panel is the SMC. The right panel compares the derived mass functions as a function of radius against the mass function of the best-\ufb01tting N-body model (shown by solid lines). There is a clear change in the derived mass function slope from increasing towards higher masses in the centre to increasing towards lower masses in the outermost parts, indicating that NGC 104 is mass segregated. This trend is reproduced by the best-\ufb01tting N-body model. locities, the scaling will be in between these limits. Since the predicted number of main-sequence stars changes linearly with the cluster mass (for a given mass function), one can use the observed number of cluster stars in a given magnitude interval and a given \ufb01eld, together with the measured cluster kinematics and a theoretical model for the cluster, to determine the cluster distance. We use as source for the globular cluster photometry the compilation of ACS/WFC F606W/F814W photometry published by Sarajedini et al. (2007) as well the HST photometry that was derived in Baumgardt et al. (2019b), Baumgardt, Sollima & Hilker (2020) and Ebrahimi et al. (2020). We also use the photometry published by Kerber et al. (2018) for NGC 6626 as input photometry. We exclude NGC 5139 from this list due to the signi\ufb01cant metallicity spread among the cluster stars. For each HST observation, we again \ufb01t PARSEC isochrones (Bressan et al. 2012) to the cluster color-magnitude diagrams. To create the isochrones, we use the cluster ages derived by VandenBerg et al. (2013), or, for clusters not studied by them, from available literature sources, and take the cluster metallicities and reddenings from Harris (1996). From the isochrones we then derive individual stellar masses for the main-sequence stars in the clusters. We \ufb01t the N-body models of Baumgardt (2017) and Baumgardt & Hilker (2018) to the observed surface density, velocity dispersion pro\ufb01les and the observed mass function of main sequence stars in the HST \ufb01elds and determine the best-\ufb01tting N-body model from the \ufb01t. For each HST observation, we \ufb01t a power-law mass function N(m) \u223cm\u03b1 to the observed stellar mass distribution as well as the masses of stars in the N-body models in the same \ufb01eld. We use the mass function slopes \u03b1 as \ufb01t parameters but not the absolute number of stars. Fig. 3 shows as an example the distribution of HST \ufb01elds with measured photometry (left panel), the derived color-magnitude diagram (middle panel), and the measured stellar mass functions at di\ufb00erent distances from the centre (right panel) for the globular cluster NGC 104. Varying the cluster distance, we then determine the distance that gives the best match between the number of main-sequence stars in the best-\ufb01tting N-body model and the observed number of main sequence stars in the di\ufb00erent HST \ufb01elds. We restrict ourselves to well observed clusters in which the errors of the total mass (based on the cluster kinematics) are less than 5%. Fig. 4 depicts the ratio between the best-\ufb01tting cluster distances based on the star count method against the mean cluster distances that we derive from the other methods. We split the cluster sample into two groups, clusters with 10 or more distance determinations from the other methods and clusters with less than 10 measurements. We expect that the distances of clusters in the \ufb01rst group are well determined so that any deviation is mainly due to errors in the star count distances. It can be seen that the average distance ratio is well below unity. The reason is probably that the N-body models that we use to \ufb01t the clusters do not contain primordial binaries. Since the average mass of binaries is larger than that of single stars, real globular clusters contain fewer stellar systems than models with only single stars for the same total mass, leading to an underprediction of the cluster distances with our method. The size of this underprediction is also in rough agreement with the observed binary fractions, which are around 10% (Sollima et al. 2007; Milone et al. 2012; Giesers et al. 2019). Fig. 4 also indicates that the star count distances contain additional errors that are not accounted for by the uncertainties in the cluster kinematics, since even when applying a constant shift, the deviations between the star count distances and the mean distances of the other methods are larger than what can be accounted for by the errors in either method. These additional errors could arise due to for example mismatches between the choAccurate distances to Galactic globular clusters 7 Figure 4. Ratio of the best-\ufb01tting distance based on star counts to the average distance from the other methods as a function of the global mass function slope \u03b1 of the clusters. The cluster sample is split into clusters with 10 or more distance measurements (blue circles) and those with less than 10 individual measurements (red triangles). The dashed line shows the average DStarCount/DMean ratio for the former group which has more secure distance determinations. It can be seen that the average ratio is well below unity. sen mass functions of the N-body models and those of the real clusters or errors in the conversion from luminosity to mass from the isochrones. We will \ufb01t for an additional shift in the star count distances as well as additional errors in sec. 4 when we compare all distances. 2.6 Moving group distances Stars in star clusters move on very similar trajectories through the Milky Way since the internal motion of stars in the cluster is usually two orders of magnitudes smaller than the velocity with which the cluster moves around the Galactic centre. As the distance and viewing angle to the stars changes along the orbit, the proper motion and lineof-sight velocity of the stars will change as well and one can use this variation to measure the distance to the cluster. This is the so-called moving group or convergent point method (Brown 1950; de Bruijne 1999). To \ufb01rst order, the change in proper motion \u00b5 due to these perspective e\ufb00ects can be approximated by \u00b5 = \u2212vLos\u03b1 DA mas yr\u22121 (1) where vLos is the line-of-sight velocity of the cluster in km/sec, \u03b1 the distance from the cluster centre in the direction of motion in radians, D the distance of the cluster from the Sun in kpc, and A = 4.74 (Brown 1950; van de Ven et al. 2006). Using the above equation, VB21 determined moving group distances to about 40 globular clusters based on Gaia EDR3 proper motions and the average lineof-sight velocities of the clusters from Baumgardt & Hilker (2018). Here we use the two most precisely determined distances D = 4.62\u00b10.28 kpc (NGC 3201) and D = 5.34\u00b10.55 kpc (NGC 5139). For all other clusters the derived distances have too large error bars to be useful. 3 LITERATURE SURVEY OF GLOBULAR CLUSTER DISTANCES In addition to our own distance determinations, we also performed a literature search of globular cluster distances. Limiting our search to the last 20 to 25 years, we were able to \ufb01nd about 1300 distance determinations in total, with each globular cluster having between 1 to 35 individual measurements. Whenever a paper gave multiple measurements for the same cluster, we averaged these and took the scatter between the individual values as an indication of the uncertainty. When we had multiple distance determinations from the same research group which were based on the same method and similar input data, we included only the newest value since we expect the di\ufb00erent distances to not be independent from each other and the newest measurement to be the most accurate one. When a paper gave both a distance and a distance modulus to a cluster, we used the distance modulus since we expect the errors to be Gaussian only in distance modulus. The resulting list of distance moduli and distances can be found in the Appendix. In order to calculate a mean distance modulus for each cluster, we de-reddened distance moduli using the reddening values given in the papers, or, if no value was available, given in the 2010 edition of Harris (1996). We also transformed linear distances into distance moduli for those papers which did not give distance moduli. For distance moduli without an error bar, we assumed an error equal to the mean error of the other distance determinations for the same cluster, with a minimum of 0.10 mag. A comparison of distance moduli for a few well observed clusters shows that even in clusters with low reddening, individual distance moduli show a scatter of around 0.07 to 0.10 mag around the mean. This scatter is independent of the chosen method, with only eclipsing binary and RR Lyrae distances based on infrared P/L relations showing smaller scatter. We therefore set the minimum error of any measurement except for EB or infrared RR Lyrae distances, for which we use the quoted errors, to 0.07 mag. We neglected distances that deviate strongly from the other measurements. In total we had to exclude about 25 measurements out of the 1300 measurements we found this way. Most of the excluded measurements were for highly reddened clusters with E(B \u2212V ) > 1.0 where the individual measurements also often show a larger scatter. This scatter probably re\ufb02ects an uncertainty in the exact amount of reddening and the proper selection of cluster and background stars. We also found that the subdwarf distance moduli of Cohen & Sarajedini (2012) were systematically smaller than the other literature values for low-metallicity clusters with [Fe/H] < \u22121.2. The average di\ufb00erence increased with decreasing metallicity and reached about 0.30 mag for the lowest-metallicity clusters. In order to correct this bias, we \ufb01tted a linear relation between the di\ufb00erence in distance modulus and metallicity to the data and shifted the Cohen & Sarajedini (2012) distance moduli upwards to bring them 8 Baumgardt & Vasiliev \u03f5CMD = 0. 023+0. 011 \u22120. 012 0.02 0.04 0.06 0.08 0.10 \u03f5RRL \u03f5RRL = 0. 024+0. 015 \u22120. 014 0.025 0.000 0.025 0.050 \u2206RRL \u2206RRL = \u22120. 021+0. 010 \u22120. 010 0.02 0.04 0.06 0.08 0.10 \u03f5EB \u03f5EB = 0. 038+0. 019 \u22120. 018 0.025 0.000 0.025 0.050 \u2206EB \u2206EB = 0. 002+0. 015 \u22120. 015 0.02 0.04 0.06 0.08 0.10 \u03f5Oth \u03f5Oth = 0. 012+0. 011 \u22120. 008 0.025 0.000 0.025 0.050 \u2206Oth \u2206Oth = \u22120. 007+0. 009 \u22120. 009 0.02 0.04 0.06 0.08 0.10 \u03f5SD \u03f5SD = 0. 077+0. 009 \u22120. 007 0.02 0.04 0.06 0.08 0.10 \u03f5CMD 0.025 0.000 0.025 0.050 \u2206SD 0.02 0.04 0.06 0.08 0.10 \u03f5RRL 0.025 0.000 0.025 0.050 \u2206RRL 0.02 0.04 0.06 0.08 0.10 \u03f5EB 0.025 0.000 0.025 0.050 \u2206EB 0.02 0.04 0.06 0.08 0.10 \u03f5Oth 0.025 0.000 0.025 0.050 \u2206Oth 0.02 0.04 0.06 0.08 0.10 \u03f5SD 0.025 0.000 0.025 0.050 \u2206SD \u2206SD = \u22120. 025+0. 011 \u22120. 011 11 12 13 14 15 16 17 18 19 20 \u00b5CMD 0.4 0.3 0.2 0.1 0.0 0.1 0.2 0.3 0.4 \u00b5RRL \u2212\u00b5CMD 11 12 13 14 15 16 17 18 19 20 \u00b5CMD 0.4 0.3 0.2 0.1 0.0 0.1 0.2 0.3 0.4 \u00b5EB \u2212\u00b5CMD 11 12 13 14 15 16 17 18 19 20 \u00b5CMD 0.4 0.3 0.2 0.1 0.0 0.1 0.2 0.3 0.4 \u00b5other \u2212\u00b5CMD Figure 5. Comparison of the distance moduli derived from isochrone \ufb01tting of CMDs (CMD), optical RR Lyrae P/L relations (RRL), eclipsing binaries and infrared RR Lyrae P/L relations (EB), and a combination of all other literature methods (OTH) and our subdwarf distance moduli (SD). For each of the methods shown we use Monte Carlo Markov chain (MCMC) sampling to determine a maximum likelihood solution, solving for a constant shift \u2206in distance modulus of each method against the CMD isochrone \ufb01tting distances as well as additional systematic errors \u03f5 of each method. The RR Lyrae distance moduli are on average about \u2206RRL = 0.021 mag smaller than the CMD \ufb01tting and our subdwarf distance moduli are smaller by about 0.025 mag. The MCMC sampling also indicates additional errors of order 0.02 mag for the CMD and RR Lyrae distance moduli and 0.04 mag for the eclipsing binary ones. It \ufb01nally \ufb01nds an error of 0.08 mag for our subdwarf distance moduli. The insets compare the distance moduli for individual clusters. Clusters with E(B \u2212V ) < 0.40 that are used for the comparison are shown in blue, clusters with E(B \u2212V ) > 0.40 are shown in grey. into agreement with the other literature data. We \ufb01nally shifted the distances that Recio-Blanco et al. (2005) derived from CMD \ufb01tting down by 0.10 mag since we found a systematic bias of this size when comparing their distances with other literature distances. In order to assess the accuracy of the derived distances and the reliability of the quoted errors, we compare in Fig. 5 the mean distance moduli calculated from various methods (isochrone \ufb01tting of CMDs, visible light RR Lyrae P/L relations, eclipsing binaries and infrared RR Lyrae P/L relations Accurate distances to Galactic globular clusters 9 and a combination of all other literature methods) plus the distance moduli we derived from subdwarfs with each other. For each cluster we take a weighted average of all individual measurements of a given type. We split the RR Lyrae distances into distances derived from visible or infrared P/L relations, since infrared P/L relations are usually thought to be more accurate (e.g. Bono et al. 2016). We also group the infrared P/L distances together with the EB distances to have a larger sample of clusters with very accurate distances. For each cluster we calculate average distance moduli for each method separately and then use Monte Carlo Markov chain (MCMC) sampling and maximum likelihood optimisation to determine possible shifts \u2206between the CMD distance moduli and the other distance moduli, as well as additional systematic errors \u03f5 that could still be present in the data. We use only clusters with E(B \u2212V ) < 0.4 mag for the comparison since more strongly reddened clusters show larger deviations between the individual measurements, and would therefore require a separate treatment. We compare all distance moduli against the CMD \ufb01tting ones since these are available for the largest number of clusters. It can be seen that the RR Lyrae distance moduli are smaller by \u2206RRL = \u22120.021 mag compared to the CMD \ufb01tting ones, which is signi\ufb01cant at the 2\u03c3 level. Our subdwarf distance moduli are also smaller, while the other methods show no statistically signi\ufb01cant o\ufb00set to the CMD distances. Since, without independent information, it is not possible to determine which of these distance scales is closer to the true distances, we do not apply shifts to any individual method and perform a straight averaging of the individual measurements instead. Our MCMC sampling also \ufb01nds evidence for additional systematic errors of \u03f5 \u22480.023 in the CMD \ufb01tting and RR Lyrae distance moduli and additional systematic errors of \u03f5EB \u22480.038 mag in the eclipsing binary/IR RR Lyrae distance moduli. The MCMC sampling \ufb01nally shows that our subdwarf distance moduli have errors of about \u03f5SD = 0.077 mag, which we use when calculating the mean distance moduli. Adding the above systematic errors in quadrature to the individual errors for the CMD, RR Lyrae and eclipsing binary distances, we then calculate a mean literature distance modulus and its formal error for each cluster from the mean distance moduli of each individual method. We also calculated a reduced \u03c72 r value of all distance determinations according to \u03c72 r = 1 N \u22121 X i (< \u00b5Lit > \u2212\u00b5i)2/\u03c32 i (2) where < \u00b5Lit > and \u00b5i are the average distance modulus and the individual distance moduli respectively and \u03c3i is the error of the individual measurements. For clusters with \u03c72 r > 1, i.e. a larger than expected scatter of the individual measurements, we increase the \ufb01nal distance error by the square root of \u03c72 r. Table 2 gives the average distance and its 1\u03c3 upper and lower error that we obtain after averaging the literature distances for each cluster in this way. For easier comparison with the other methods, we give the literature data in linear distances, however when calculating a \ufb01nal value for the distance we use the distance modulus as explained below. Plots depicting the individual measurements for each cluster can be found in the Appendix. 4 RESULTS 4.1 Calculation of \ufb01nal distances Fig. 6 compares the distances that we derive from the Gaia EDR3 data (separated into parallax and kinematic distances), the HST kinematic distances and the star count distances with the mean literature distances determined in the previous section. We again use MCMC sampling and determine o\ufb00sets between the distances as well as additional unaccounted for errors. We restrict ourselves again to clusters with E(B-V)< 0.4 mag for which the distances should be least in\ufb02uenced by reddening uncertainties. We \ufb01nd a constant shift of the Gaia parallax distances of \u2206\u03d6 = 0.007 mas, con\ufb01rming the results of VB21. There is no evidence for a signi\ufb01cant shift of the CMD distances against the other methods. However, given that the error bar on \u2206CMD is about 0.04, the RR Lyrae distances would also be in statistical agreement with the distances that we determined from the Gaia EDR3 data. The MCMC sampling \ufb01nds \u2206DGaia = \u22120.016\u00b10.020, implying that the Gaia kinematic distances are in statistical agreement with the other methods. However the HST kinematic distances are smaller by about 3.0%. There is also some evidence for signi\ufb01cant, additional unaccounted for errors in the HST kinematic distances. We therefore add an error equal to 0.017 times the distance in quadrature to the formal distance error of the HST distances for each cluster. We do not apply a shift to the HST kinematic distances since it is \ufb01rst not clear which method gives the correct distance, and also because we found the HST and Gaia kinematic distances to be in agreement with each other, meaning that the error might well be with the CMD distances. The MCMC analysis \ufb01nally shows that the star count distances need to be increased by a factor 1/0.93 = 1.075 and that their uncertainties have an additional systematic contribution of 4.4% of the cluster distances. After increasing the star count distances and adding additional errors to the HST kinematic and star count distances, we determine the \ufb01nal distance for each cluster by minimizing the combined likelihood of all measurements according to: ln L = \u22121 2 \u0000\u03d6G \u2212 1 < D > \u00012 \u03f52 \u03d6 \u22121 2 X i (Di\u2212<D>)2 \u03c32 i \u22121 2 X j (\u00b5j \u22125 log <D> + 5)2 \u03c32 j (3) Here \u03d6G and \u03f5\u03d6 are the cluster parallaxes and their 1\u03c3 errors, Di and \u03c3i are the cluster distances and associated 1\u03c3 errors of the kinematic, star count and moving group distances. \u00b5j and \u03c3j are the distance moduli and error bars that we obtain from the averaging of the literature data and our subdwarf \ufb01ts. < D > is the mean cluster distance that we want to determine. We use the Gaia parallaxes here instead of the distances that can be calculated from them since errors on the parallax distance are Gaussian only in parallax space. For the same reason we use distance moduli for the literature and subdwarf distances. We calculate the mean distance from the point where ln L has a maximum and calculate the associated upper and lower distance errors from the condition that \u2206ln L = 1.0. The resulting mean 10 Baumgardt & Vasiliev \u2206CMD = 0. 003+0. 036 \u22120. 040 0.0075 0.0090 0.0105 0.0120 \u03f5 \u03f5  = 0. 010+0. 001 \u22120. 001 0.003 0.006 0.009 0.012 0.015 \u2206 \u2206 = 0. 007+0. 002 \u22120. 002 0.015 0.030 0.045 0.060 \u03f5Gaia \u03f5Gaia = 0. 009+0. 010 \u22120. 006 0.050 0.025 0.000 0.025 \u2206DGaia \u2206DGaia = \u22120. 016+0. 019 \u22120. 021 0.015 0.030 0.045 0.060 \u03f5HST \u03f5HST = 0. 017+0. 010 \u22120. 009 0.050 0.025 0.000 0.025 \u2206DHST \u2206DHST = \u22120. 030+0. 018 \u22120. 018 0.015 0.030 0.045 0.060 \u03f5SC \u03f5SC = 0. 044+0. 008 \u22120. 007 0.05 0.00 0.05 0.10 \u2206CMD 0.100 0.075 0.050 \u2206DSC 0.0075 0.0090 0.0105 0.0120 \u03f5 0.003 0.006 0.009 0.012 0.015 \u2206 0.015 0.030 0.045 0.060 \u03f5Gaia 0.050 0.025 0.000 0.025 \u2206DGaia 0.015 0.030 0.045 0.060 \u03f5HST 0.050 0.025 0.000 0.025 \u2206DHST 0.015 0.030 0.045 0.060 \u03f5SC 0.100 0.075 0.050 \u2206DSC \u2206DSC = \u22120. 070+0. 020 \u22120. 021 11 12 13 14 15 16 17 18 19 20 \u00b5CMD 0.20 0.15 0.10 0.05 0.00 0.05 0.10 0.15 0.20 Dkin, Gaia/DCMD \u22121 11 12 13 14 15 16 17 18 19 20 \u00b5CMD 0.20 0.15 0.10 0.05 0.00 0.05 0.10 0.15 0.20 Dkin, HST/DCMD \u22121 11 12 13 14 15 16 17 18 19 20 \u00b5SC 0.25 0.20 0.15 0.10 0.05 0.00 0.05 0.10 Dkin, SC/DCMD \u22121 Figure 6. Comparison of the CMD \ufb01tting distances with the Gaia parallax and kinematic distances and the HST kinematic distances. We again use MCMC sampling and solve for constant scale factors \u2206D in the distance scales of the various methods as well as additional systematic errors \u03f5. \u2206DGaia and \u2206DHST are relative shifts in the kinematic distances of the Gaia and HST kinematic distances and \u2206\u03d6 is a shift in the Gaia parallaxes. We obtain a signi\ufb01cant shift in the Gaia parallaxes of \u2206\u03d6 \u22480.007 mas, in agreement with VB21. The HST kinematic distances are on average also smaller than the literature distances by about 3.0%, while the Gaia kinematic distance shift \u2206DGaia is compatible with zero. The HST kinematic distances also show evidence of additional relative distance errors of about 1.7%. The inset compares the kinematic and star count distances with the distances from isochrone \ufb01tting of the cluster CMDs. distances along with the individual values from the various methods are given in Table 2. All data has been transformed to linear distances to make the di\ufb00erent measurements easier comparable with each other. Fig.7 depicts the relative distance accuracy that we achieve by combining all data as a function of the cluster reddening. It can be seen that for clusters with low reddening values E(B \u2212V ) < 0.3 we achieve relative accuracies of about 1%. For larger reddening values E(B \u2212V ) > 0.3 there is a continuous rise of the distance errors and we achieve only 20% accuracy for the most highly reddened clusters. This rise could partly be driven by the fact that heavily reddened clusters have often only few individual distance determinations. Accurate distances to Galactic globular clusters 11 Figure 7. Final distance error \u03c3D/D as a function of the cluster reddening E(B \u2212V ). Clusters with reddening values E(B \u2212V ) < 0.20 have an average distance error of about 1%. More reddened clusters show a continuous increase of the distance error with reddening. The location of three of the clusters discussed in the text is marked in the plot. 4.2 Individual clusters 4.2.1 47 Tuc We derive a distance of D = 4.52 \u00b1 0.03 kpc to 47 Tuc (NGC 104). For 47 Tuc, both literature distances and kinematic distances have small formal errors and are fully consistent with each other (see Fig. 8). Our mean distance also agrees very well with the value of D = 4.53 \u00b1 0.06 kpc that Ma\u00b4 \u0131z Apell\u00b4 aniz, Pantaleoni Gonz\u00b4 alez & Barb\u00b4 a (2021) determined from the Gaia EDR3 parallaxes, correcting for the small scale angular covariances in the Gaia data by comparing the parallaxes of 47 Tuc stars with those of background SMC stars. It also agrees very well with the distance of D = 4.45 \u00b1 0.12 kpc that Chen et al. (2018) derived with the same method from Gaia DR2 data as well as the distance of D = 4.53 \u00b1 0.05 kpc that Thompson et al. (2020) found from the analysis of two detached eclipsing binaries in the cluster. The distance to 47 Tuc therefore seems to be established with an accuracy of better than 1%. 4.2.2 NGC 362 We correct the Gaia EDR3 parallaxes in the same way done by Ma\u00b4 \u0131z Apell\u00b4 aniz, Pantaleoni Gonz\u00b4 alez & Barb\u00b4 a (2021) for NGC 104 and Chen et al. (2018) for NGC 104 and NGC 362. We again use SMC \ufb01eld stars in the direction of NGC 362 as reference, assuming a distance of D = 62.1 \u00b1 1.9 kpc as distance to the SMC (Cioni et al. 2000; Graczyk et al. 2014). The resulting cluster parallax is \u03d6 = 109.9 \u00b1 3.7\u00b5as, corresponding to a distance of 9.10+0.32 \u22120.30 kpc. This distance is in agreement with the earlier value of Chen et al. (2018) (D = 8.54\u00b10.48 kpc) as well as the distance we derive from an averaging of literature values (8.80 \u00b1 0.11 kpc) and our own kinematic distance determinations (see Fig. 8). 4.2.3 \u03c9 Cen There is also good agreement in our distance determinations for \u03c9 Cen. The literature distances lead to an average distance of D = 5.47 \u00b1 0.06 kpc (see Fig. 8). The Gaia kinematic distance is in good agreement with the literature distance, however the HST kinematic distance (5.26 \u00b1 0.12 kpc) is about 200 pc shorter. One possible reason for the mismatch could be the intrinsic \ufb02attening of \u03c9 Cen. Mackey & Gilmore (2004) \ufb01nd an ellipticity of \u03f5 = 0.17 for \u03c9 Cen based on its projected isophotes. The true \ufb02attening is likely even larger, with the exact value depending on the cluster inclination. van de Ven et al. (2006) found through axisymmetric Schwarzschild modeling that the resulting \ufb02attening of the velocity ellipsoid can decrease the kinematic cluster distance to \u03c9 Cen by several hundred pc if the \ufb02attening is not taken into account in the modeling. Since the N-body models that we use to derive the kinematic distances are spherically symmetric, there is a chance that our kinematic distances underestimate the true distance to \u03c9 Cen. This e\ufb00ect is much less likely for most other clusters which have much smaller relaxation times and should therefore be closer to being spherically symmetric. This is indeed also seen in observations (e.g. White & Shawl 1987). We therefore regard the literature distance as more reliable for \u03c9 Cen. The Gaia EDR3 parallaxes after application of the systematic parallax o\ufb00set also favor a longer distance, however the error bar is too large to be decide between the two possibilities. 4.2.4 NGC 6121 We derive a distance of D = 1.851 \u00b1 0.015 kpc to M4 (NGC 6121). This distance is slightly larger than the distance of D = 1.82\u00b10.04 kpc found by Kaluzny et al. (2013) based on three eclipsing binary stars as well as recent results from RR Lyrae stars (e.g Braga et al. 2015; Neeley et al. 2019; Bhardwaj et al. 2020b) (see Fig. 8). Nevertheless their distances are compatible with our distance within the error bars. The true distance to NGC 6121 is therefore likely somewhere in the range 1.83 to 1.85 kpc, making M4 another cluster whose distance is determined with an accuracy of about 1%. 4.2.5 NGC 6397 and NGC 6656 NGC 6397 and NGC 6656 (M 22) are among the closest globular clusters to the Sun. Their small distances together with their low reddening make them ideal targets for globular cluster studies, so a large amount of observational data exists for both clusters. For NGC 6397 we \ufb01nd a total of 27 individual distance determinations in the literature, from which we derive a mean cluster distance of 2.521 \u00b1 0.025 kpc. Despite a relative distance error of only about 1%f or the literature distance and similarly small errors for most of the other methods, most distances are in good statistical agreement with each other, with the exception of the HST kinematic distances that are too short by about 100 pc. Taking the average over all methods, we derive a distance 12 Baumgardt & Vasiliev of 2.488 \u00b1 0.019 kpc for NGC 6397, making this cluster the second closest cluster to the Sun. There is a similar good agreement in the individual distances values for NGC 6656, for which we derive a mean distance of D = 3.307 \u00b1 0.037 kpc. 4.3 Absolute luminosity of the TRGB and the value of H0 Globular clusters can be used to determine the absolute luminosity of the tip of the red giant branch (TRGB), which in turn can be used to measure the distance to nearby galaxies. Using Gaia EDR3 parallaxes, Soltis, Casertano & Riess (2021) recently derived a distance of 5.24 \u00b1 0.11 kpc to \u03c9 Cen. Using this distance, they derived an absolute I-band magnitude of the TRGB of MI,T RGB = \u22123.97 \u00b1 0.06, from which they deduced a value of the local Hubble constant of H0 = 71.2 \u00b1 2.0 km/sec. In contrast, Freedman et al. (2020) used stars in the LMC to derive an an absolute TRGB magnitude of MI,T RGB = \u22124.05 \u00b1 0.06, using eclipsing binaries in 47 Tuc and the SMC to calibrate the LMC distance. The \u03c9 Cen distance of Soltis, Casertano & Riess (2021) was based on a direct averaging of the Gaia EDR3 parallaxes of individual member stars, applying only the Lindegren et al. (2020) parallax corrections. Their parallax value did not take systematic biases in the Gaia parallaxes or small scale correlated errors into account. Accounting for both, we derived a parallax of \u03d6 = 182.3\u00b19.5\u00b5as for \u03c9 Cen (Vasiliev & Baumgardt 2021), corresponding to a distance D = 5.48 \u00b1 0.24 kpc, slightly larger than Soltis, Casertano & Riess (2021) and also with a larger formal error than found by them. Combining this data with the other distances, we then derive a distance of D = 5.43 \u00b1 0.05 to \u03c9 Cen. A similar analysis as the one done by Soltis, Casertano & Riess (2021) leads to an absolute TRGB magnitude of MI,T RGB = \u22124.06 \u00b1 0.06, con\ufb01rming the value found by Freedman et al. (2020). In addition, our results also con\ufb01rm their adopted distance to NGC 104. The resulting value of the local Hubble constant of H0 = 69.4 \u00b1 2.0 km/sec would be in better agreement with the expected value based on the Planck data of 67.4 \u00b1 0.5 km/sec (Verde, Treu & Riess 2019). 5 CONCLUSIONS We have derived mean distances to globular clusters using a combination of our own measurements based on Gaia EDR3 data and published literature distances. We derived our own distances using six di\ufb00erent methods: Gaia ED3 parallaxes, kinematic distances using proper motion velocity dispersion pro\ufb01les based on Gaia EDR3 proper motions, \ufb01tting nearby subdwarfs to the globular cluster main sequences where the distances and absolute luminosities of the subdwarfs are calculated from their Gaia parallaxes and moving group distances based on Gaia ED3 proper motions. In addition, we also derive kinematic distances from HST proper motion velocity dispersion pro\ufb01les and distances using HST star counts in combination with the cluster kinematics. Apart from a bias in the Gaia EDR3 parallaxes, we \ufb01nd good internal agreement among the distances calculated with the di\ufb00erent methods and also with published distances in the literature down to a level of about 2%. There is a possibility that our HST kinematic distances could slightly underestimate the distances to globular clusters, however the di\ufb00erence that we see could also signify a problem in the isochrone \ufb01tting distances. We also \ufb01nd some evidence that isochrone based distance moduli are larger than RR Lyrae based ones by about 0.02 mag. Averaging over the various distance determinations, we are able to determine distances to a number of nearby globular clusters with an accuracy of 1%, making these clusters valuable objects for the establishment of a cosmic distance ladder. In particular, our results for the distances to 47 Tuc and \u03c9 Cen argue for an absolute TRGB magnitude of MI,T RGB = \u22124.05 leading to a value of the local Hubble constant that is in agreement with the expected value based on Planck data. They however do not remove the tension between the Cepheid based value of H0 and the Planck data, which is currently signi\ufb01cant at about the 4\u03c3 level (Riess et al. 2019). Given that we \ufb01nd that the di\ufb00erent literature distances to globular clusters are consistent down to a level of about 1-2%, it is also unlikely that our results would lead to a signi\ufb01cant revision of the distance modulus to nearby galaxies like the LMC, and therefore a reduction of the tension in H0. Future releases of the Gaia catalogue will further increase the sample of globular clusters with highly accurate distances by reducing the random and systematic errors in the parallaxes and proper motions of stars. There is currently also still a substantial uncertainty in the distances of highly reddened clusters, where individual distances can deviate from each other by up to a factor of two. At least for the more nearby clusters, Gaia parallaxes and proper motion velocity dispersion pro\ufb01les based on future Gaia data releases should bring a signi\ufb01cant improvement to the distances to these clusters. ACKNOWLEDGMENTS EV acknowledges support from STFC via the Consolidated grant to the Institute of Astronomy. We thank Domenico Nardiello for providing us with the HST photometry for NGC 6626. This work presents results from the European Space Agency (ESA) space mission Gaia . Gaia data are being processed by the Gaia Data Processing and Analysis Consortium (DPAC). Funding for the DPAC is provided by national institutions, in particular the institutions participating in the Gaia MultiLateral Agreement (MLA). This work is also based on observations made with the NASA/ESA Hubble Space Telescope, obtained from the data archive at the Space Telescope Science Institute. STScI is operated by the Association of Universities for Research in Astronomy, Inc. under NASA contract NAS 5-26555. DATA AVAILABILITY The distances and the \ufb01t results of our N-body models to Galactic globular clusters using these distances can be obtained from the following webpage: https://people.smp.uq.edu.au/HolgerBaumgardt/globular/ Accurate distances to Galactic globular clusters 13",
                    "introduction": "Galactic globular clusters constitute an important rung on the extragalactic distance ladder. They are nearby enough to be resolved into individual stars, making them ideal objects to calibrate the brightnesses of physically interesting stars like RR Lyrae or Type II Cepheids. In addition they are also massive enough to contain statistically signi\ufb01cant samples of these stars. Hence globular clusters are useful to determine the slopes and zero-points of RR Lyrae period-luminosity (P/L) relations (e.g. Bono, Caputo & Di Criscienzo 2007; Dambis et al. 2014) as well as a possible metallicity depen- dence of the zero points (e.g Sollima, Cacciari & Valenti 2006). Globular clusters can also be used as calibrators for other distance methods, like the tip of the red giant branch distance method (TRGB), which allows to determine dis- tances to external galaxies without having to rely on P/L relations of variable stars (e.g Cerny et al. 2020; Freedman et al. 2020; Soltis, Casertano & Riess 2021). Distances to globular clusters are determined either through \ufb01ts of their color-magnitude diagrams (CMDs) with theoretical isochrones (e.g Ferraro et al. 1999; Dotter et al. 2010; Gontcharov, Mosenkov & Khovritchev 2019; Valcin \u22c6E-mail: h.baumgardt@uq.edu.au et al. 2020), or by using variable stars that follow known re- lations between their periods and absolute luminosities like RR Lyrae stars (e.g Bono, Caputo & Di Criscienzo 2007; Hernitschek et al. 2019), Type II Cepheids (Matsunaga et al. 2006) or Mira type variables (Feast, Whitelock & Menzies 2002). In order to avoid circularity, the absolute luminosi- ties of these stars need to be determined independently from globular cluster distances by using for example theoreti- cal models (e.g Catelan, Pritzl & Smith 2004) or Hippar- cos or Gaia parallaxes (Fernley et al. 1998; Neeley et al. 2019; Ripepi et al. 2019). Accurate distances have also been obtained for globular clusters by using eclipsing binaries (Kaluzny et al. 2007; Thompson et al. 2020), however the faintness and scarcity of suitable binaries means that obser- vations have so far been limited to a few globular clusters. Finally it is possible to determine distances by comparing the magnitudes of main-sequence stars with stars of similar metallicity in the solar neighborhood, the so-called subdwarf method (e.g Reid & Gizis 1998; Cohen & Sarajedini 2012) or kinematically by comparing line-of-sight and proper motion velocity dispersion pro\ufb01les in globular clusters (e.g. McNa- mara, Harrison & Baumgardt 2004; van de Ven et al. 2006; Watkins et al. 2015b). The latter method has the advantage that the derived distance is not in\ufb02uenced by the reddening of the cluster. arXiv:2105.09526v2  [astro-ph.GA]  21 May 2021 2 Baumgardt & Vasiliev Typical uncertainties in the zero points of the P/L re- lations of RR Lyrae stars are thought to be of order 0.05 mag (Bhardwaj 2020) and other methods like CMD \ufb01t- ting have similar uncertainties. In addition, the reddening of many clusters presents an additional challenge for the de- termination of accurate distances since it can be variable even across small, arcminute size \ufb01elds (Bonatto, Campos & Kepler 2013; Pallanca et al. 2019). Furthermore there is evidence for non-standard reddening laws in the directions of several globular clusters like for example M4 (Dixon & Longmore 1993; Hendricks et al. 2012). It is therefore important to use independent methods to verify ine distances to globular clusters, especially methods which are not e\ufb00ected by the reddening of stars. In this paper we use data from the Gaia EDR3 catalogue (Gaia Collabo- ration et al. 2016, 2020) to determine distances to Galactic globular clusters. In addition to using the Gaia EDR3 par- allaxes directly, we also determine moving group distances and kinematic distances derived by comparing proper mo- tion velocity dispersion pro\ufb01les with line-of-sight velocity dispersion ones. We \ufb01nally use the Gaia EDR3 parallaxes of nearby subdwarfs as well as Hubble Space Telescope (HST) star counts together with kinematic information to deter- mine distances. Our paper is organised as follows: In sec. 2 we present our derivation of cluster distances using the methods men- tioned above. In sec. 3 we describe our survey of literature distances. We compare the distances that we derive from the di\ufb00erent methods and derive the average distance to each globular cluster in sec. 4. We \ufb01nally draw our conclusions in sec. 5."
                },
                {
                    "url": "http://arxiv.org/abs/1907.10845v1",
                    "title": "No evidence for intermediate-mass black holes in the globular clusters $\u03c9$ Cen and NGC 6624",
                    "abstract": "We compare the results of a large grid of N-body simulations with the surface\nbrightness and velocity dispersion profiles of the globular clusters $\\omega$\nCen and NGC 6624. Our models include clusters with varying stellar-mass black\nhole retention fractions and varying masses of a central intermediate-mass\nblack hole (IMBH). We find that an $\\sim 45,000$ M$_\\odot$ IMBH, whose presence\nhas been suggested based on the measured velocity dispersion profile of\n$\\omega$ Cen, predicts the existence of about 20 fast-moving, $m>0.5$ M$_\\odot$\nmain-sequence stars with a (1D) velocity $v>60$ km/sec in the central 20 arcsec\nof $\\omega$ Cen. However no such star is present in the HST/ACS proper motion\ncatalogue of Bellini et al. (2017), strongly ruling out the presence of a\nmassive IMBH in the core of $\\omega$ Cen. Instead, we find that all available\ndata can be fitted by a model that contains 4.6% of the mass of $\\omega$ Cen in\na centrally concentrated cluster of stellar-mass black holes. We show that this\nmass fraction in stellar-mass BHs is compatible with the predictions of stellar\nevolution models of massive stars.\n  We also compare our grid of $N$-body simulations with NGC 6624, a cluster\nrecently claimed to harbor a 20,000 M$_\\odot$ black hole based on timing\nobservations of millisecond pulsars. However, we find that models with\n$M_{IMBH}>1,000$ M$_\\odot$ IMBHs are incompatible with the observed velocity\ndispersion and surface brightness profile of NGC 6624,ruling out the presence\nof a massive IMBH in this cluster. Models without an IMBH provide again an\nexcellent fit to NGC 6624.",
                    "authors": "Holger Baumgardt, Chenyu He, Sarah M. Sweet, Michael Drinkwater, Antonio Sollima, Jarrod Hurley, Christopher Usher, Sebastian Kamann, Hannah S. Dalgleish, Stefan Dreizler, Tim-Oliver Husser",
                    "published": "2019-07-25",
                    "updated": "2019-07-25",
                    "primary_cat": "astro-ph.GA",
                    "cats": [
                        "astro-ph.GA"
                    ],
                    "main_content": "2.1 \u03c9 Cen Our main source for the kinematic data on \u03c9 Cen are the radial velocity dispersion profiles recently published by Baumgardt (2017) and Baumgardt & Hilker (2018). Baumgardt (2017) calculated the velocity dispersion based on \u223c4, 500 individual stellar radial velocities from published literature data, while Baumgardt & Hilker (2018) determined the radial velocities of an additional 1,000 cluster stars from unpublished ESO/FLAMES spectra. In order to improve the coverage of the outer regions of \u03c9 Cen, we added to this data a set of 10 AAOmega/2dF observations of \u03c9 Cen made between July 2007 and May 2011, that we downloaded from the AAT Data Archive. We restricted ourselves to AAOmega spectra taken with the 1700D grating which have a spectral resolution of R = 10, 000, the highest of all available AAOmega gratings. The basic data reduction of these spectra was done with the program 2dfdr, which also performed the heliocentric correction of the spectra. We calculated radial velocities from the reduced spectra with the help of the IRAF task fxcor, which is based on the Fourier crosscorrelation method developed by Tonry & Davis (1979). For the cross-correlation, we used as template the spectrum of a cool giant star that we created with the help of the stellar synthesis program SPECTRUM (Gray & Corbally 1994) using ATLAS9 stellar model atmospheres (Castelli & Kurucz 2004) with a metallicity of [Fe/H] = \u22121.50 as input. In total we obtained 6,500 radial velocities of stars in the field of \u03c9 Cen, from which we calculated the velocity dispersion profile of \u03c9 Cen using a maximum-likelihood approach: We first cross-correlated the different data sets against each other to bring them to a common mean radial velocity and cross-matched the stellar positions against the Gaia DR2 catalogue. We next removed all stars that have proper motions incompatible with the mean cluster motion determined by Baumgardt et al. (2019). The mean cluster velocity and velocity dispersion profile were then determined using all remaining stars and the membership probability of each star was determined based on the velocity dispersion of the cluster. We then removed stars with radial velocities differing by more then 3\u03c3 from the cluster mean from the sample and calculated a new mean cluster velocity and velocity dispersion profile. This procedure was repeated until a stable solution for the list of cluster members and the velocity dispersion profile was found and we reached this convergence within two or three steps. In order to increase the coverage of the central cluster region, we also use the velocity dispersion profile published by Kamann et al. (2018) based on VLT/MUSE observations in our modeling. We accompany the line-of-sight No evidence of IMBHs in \u03c9 Cen and NGC 6624 3 radial velocity data with the HST based proper motion dispersion pro\ufb01le of Watkins et al. (2015) in the inner cluster parts and the Gaia DR2 proper motion dispersion pro\ufb01le from Baumgardt et al. (2019). Finally, we use the catalogue of 240, 000 stars with measured HST proper motions and photometry derived by Bellini et al. (2014) and Bellini et al. (2017). When transforming the proper motions into velocities, we assume a distance of d = 5.24 kpc to \u03c9 Cen (Baumgardt et al. 2019). The resulting velocity dispersion pro\ufb01le of \u03c9 Cen is shown in Fig. 1. It can be seen that the velocity dispersion is roughly constant in the central 100\u201d, and decreases further out before leveling o\ufb00beyond about 1000\u201d. There is generally very good agreement between the HST proper motion based velocity dispersion pro\ufb01le and the line-of-sight radial velocities. Inside 10\u201d both the line-ofsight radial velocity dispersion pro\ufb01le as well as the proper motion dispersion pro\ufb01le show some larger scatter due to a lack of stars with measured kinematics. In addition to the velocity dispersion pro\ufb01le, we also \ufb01t the observed surface brightness pro\ufb01les with our N-body models. For both \u03c9 Cen and NGC 6624, we create surface brightness pro\ufb01les by combing the HST based surface brightness pro\ufb01le of Noyola & Gebhardt (2006) in the inner cluster parts with the ground-based data of Trager, King & Djorgovski (1995) at larger radii. The mass function of \u03c9 Cen has been measured by Sollima, Ferraro & Bellazzini (2007), who found a steep, Salpeter-like increase of the mass function between 0.5 M\u2299< m < 0.8 M\u2299, a break in the mass function at m = 0.5 M\u2299and a \ufb02atter increase below this mass. Since this mass function is close to a Kroupa initial mass function, we use N-body models with a Kroupa mass function to model \u03c9 Cen. A mass function rich in low-mass stars is also reasonable given the high mass and long relaxation time of \u03c9 Cen, which means that only little mass segregation and little dynamical mass loss have occurred over a Hubble time. 2.2 NGC 6624 Radial velocities for 19 stars in the centre of NGC 6624 were determined by Pryor et al. (1991). In addition, Baumgardt & Hilker (2018) determined the radial velocities of 125 stars in the \ufb01eld of NGC 6624 based on archival VLT/FLAMES observations (proposal ID 083.D0798(D), PI B. Lanzoni) and another 8 cluster stars from Keck/NIRSPEC observations (Keck proposal ID U17NS, PI: M. Rich). We add to this data set, 58 stars in the central region with measured radial velocities from the WAGGS survey (Usher et al. 2017). The observations were made using the WiFeS integral \ufb01eld spectrograph (Dopita et al. 2007, 2010) and the basic data reduction was done as described in (Usher et al. 2017). Using PampelMuse (Kamann, Wisotzki & Roth 2013), stellar spectra were extracted from the WAGGS datacubes and radial velocities were determined with the IRAF task fxcor. Further details will be described in a forthcoming paper (Dalgleish et al. in prep). We furthermore added radial velocities based on MUSE observations of NGC 6624 that were taken during the nights of 2015-05-11 and 2017-10-17, as part of observing programmes 095.D-0629 and 0100.D-0161 (PI: Dreizler). The reduction and analysis of the data were performed as described in Kamann et al. (2018). In particular, we used PampelMuse to extract stellar spectra from the reduced data cubes, while the derivation of the \ufb01nal radial velocities was done with spexxy (see Husser et al. 2016). For the present study, we selected a high-quality sample of 241 stars with V < 17 and radial velocity uncertainties < 1.5 km s\u22121 from the full MUSE sample for NGC 6624. In order to increase the number of stars with measured radial velocities in the outer cluster parts, we also observed NGC 6624 for one half-night using the DEIMOS spectograph (Faber et al. 2003) on the Keck II telescope (Programm ID: Z252, PI M. Drinkwater). Observations were performed on 19 July 2017 with 0.6\u201d seeing and some thin cirrus, using the 1200G grating with a central wavelength of 8000 \u02da A and the OG550 order-blocking \ufb01lter. Four slitmasks were observed at position angles (PAs) of 0, 90, 270 and 315 degrees, in order to maximise the number of stars near the centre of the cluster, where the proportion of member stars is expected to be higher, and to maximise the spatial coverage of the outer regions. Slits were placed on a total of 685 unique targets, comprised of 545 stars with 2MASS coordinates and 140 with positions derived from HST imaging. Each mask had seven stars in common with the VLT/FLAMES data set to assist in radial velocity calibration. Exposure times were 3 x 800 seconds for the mask with PA = 0, 3 x 850 s for PA = 270, and 3 x 900 s for the masks with PA = 90 and 315. The DEIMOS spectra were reduced with the help of the DEEP2 data reduction pipeline developed by the DEEP2 survey team (Cooper et al. 2012; Newman et al. 2013). Individual stellar radial velocities were again determined from the reduced spectra with the help of the IRAF fxcor task. To correct for residual systematic errors in the absolute wavelength calibration of the DEIMOS spectra, we cross-correlated them against a telluric template spectrum that was kindly provided to us by Tony Sohn and Emily Cunningham. Since the telluric lines should be at zero radial velocity, wavelength calibration errors can be corrected from the radial velocity of these lines. Final radial velocities for each star were then calculated according to vr = vobs \u2212vtel \u2212vhel, where vobs is the radial velocity derived from the stellar template, vtel the radial velocity from the telluric spectrum and vhel the heliocentric correction. In total we were able to determine the radial velocities of 264 stars from the DEIMOS spectra. Table A1 gives the individual radial velocities that we have derived from the DEIMOS spectra. The membership probabilities in Table A1 are calculated as described in Baumgardt & Hilker (2018). Our \ufb01nal data set consists of about 600 stars with measured radial velocities in the \ufb01eld of NGC 6624, out of which about 200 stars are cluster members. 35 stars have measured radial velocities from both the VLT/FLAMES observations and our DEIMOS observations and 31 stars are in common between the MUSE data and the combined VLT/FLAMES and Keck/DEIMOS data set. Virtually all the stars measured by Pryor et al. as well as the stars measured by the WAGGS survey are also in the MUSE sample. The good overlap between the di\ufb00erent data sets allows us to bring them to within 0.3 km/sec of each other. Since the remaining uncertainty adds quadratically to the true velocity dispersion pro\ufb01le, it does not signi\ufb01cantly in\ufb02uence our measurement of the \ufb01nal velocity dispersion pro\ufb01le. In order to calculate the velocity dispersion pro\ufb01le of NGC 6624 from the individual stellar radial velocities, we 4 Baumgardt, He, Sweet, Drinkwater, Sollima, Hurley, Usher, Kamann, Dalgleish, Dreizler & Husser Table 1. Observed line-of sight velocity dispersion pro\ufb01les of \u03c9 Cen and NGC 6624. For each bin, the table gives the name of the cluster, the number of stars used to calculate the radial velocity dispersion, the average distance of stars from the cluster centre, and the velocity dispersion together with the 1\u03c3 upper and lower error bars. Cluster NRV r \u03c3 \u2206\u03c3u \u2206\u03c3l [arcsec] [km/sec] [km/sec] [km/sec] \u03c9 Cen 95 44.10 19.09 1.46 1.29 \u03c9 Cen 100 75.11 19.00 1.44 1.29 \u03c9 Cen 195 101.14 15.72 0.84 0.77 \u03c9 Cen 195 126.99 17.94 0.95 0.87 \u03c9 Cen 195 148.85 15.89 0.85 0.78 \u03c9 Cen 195 171.92 14.63 0.78 0.71 \u03c9 Cen 195 198.68 15.39 0.82 0.76 \u03c9 Cen 195 222.19 14.44 0.77 0.70 \u03c9 Cen 195 244.66 14.30 0.76 0.70 \u03c9 Cen 195 266.18 12.84 0.68 0.63 \u03c9 Cen 195 288.99 13.83 0.73 0.68 \u03c9 Cen 195 315.19 12.89 0.69 0.63 \u03c9 Cen 195 341.95 13.27 0.70 0.65 \u03c9 Cen 195 378.73 11.72 0.62 0.58 \u03c9 Cen 195 426.96 11.96 0.64 0.59 \u03c9 Cen 195 480.76 12.66 0.67 0.62 \u03c9 Cen 195 536.14 11.22 0.60 0.55 \u03c9 Cen 195 590.69 10.86 0.58 0.54 \u03c9 Cen 195 681.63 9.58 0.51 0.47 \u03c9 Cen 195 943.29 9.52 0.51 0.47 \u03c9 Cen 195 1279.52 8.32 0.45 0.41 \u03c9 Cen 120 1898.97 6.77 0.47 0.42 NGC 6624 46 4.33 6.41 0.75 0.63 NGC 6624 46 9.93 7.13 0.83 0.71 NGC 6624 46 15.15 6.15 0.72 0.61 NGC 6624 46 20.27 6.04 0.71 0.60 NGC 6624 46 26.54 5.11 0.60 0.51 NGC 6624 46 40.96 5.15 0.61 0.52 NGC 6624 50 95.83 3.25 0.39 0.32 again cross-correlated the di\ufb00erent data sets against each other to bring them to a common mean radial velocity and then selected as possible cluster members all stars with radial velocities between 30 km/sec < v < 80 km/sec and Gaia DR2 proper motions that match the mean cluster proper motion determined by Baumgardt et al. (2019). Due to the signi\ufb01cant stellar background density, we restricted the member search to distances less than 200\u201d from the cluster centre, since outside this radius a reliable membership determination was not possible. The calculation of the velocity dispersion pro\ufb01le was again done via a maximum-likelihood approach, following the procedure described above for \u03c9 Cen. The resulting velocity dispersion pro\ufb01le is presented in Table 1. We also used the proper motion velocity dispersion pro\ufb01le of Watkins et al. (2015) who determined the velocity dispersion pro\ufb01le inside 80\u201d based on \u223c1, 800 stars with magnitudes brighter than about 1.5 mag below the mainsequence turn-o\ufb00. We \ufb01nally used the stellar mass function of NGC 6624 measured by Saracino et al. (2016) in the central 40\u201d from ultra-deep, adaptive optics assisted J and KS band Gemini/GSAOI images to constrain the mass function of the best-\ufb01tting N-body models. 3 N-BODY MODELS We used the grid of N-body simulations presented by Baumgardt (2017) and Baumgardt & Hilker (2018) to model \u03c9 Cen and NGC 6624 and to derive limits on the presence of intermediate-mass black holes in these clusters. Baumgardt (2017) and Baumgardt & Hilker (2018) have run a grid of 1400 N-body simulations of star clusters containing N = 100, 000 or N = 200, 000 stars using NBODY6 (Aarseth 1999; Nitadori & Aarseth 2012), varying the initial density pro\ufb01le and half-mass radius, the initial mass function, the cluster metallicity and the mass fraction of an intermediate mass black hole in the clusters. All models consisted initially only of single stars and formed binaries only through encounters of stars in the cluster centres. Given the low observed binary fraction in globular clusters (only of order 10% see e.g. Milone et al. (2012) and Ji & Bregman (2013)) we do not think that our results would signi\ufb01cantly change with the inclusion of primordial binaries. The basic strategy that we use to compare the N-body models with the observed surface brightness and velocity dispersion pro\ufb01le of a globular cluster is the same as in these two papers and we refer the reader to these papers for a detailed description. In short, the N-body simulations were run up to an age of T = 13.5 Gyr and \ufb01nal cluster models were calculated by taking 10 snapshots from the simulations centered around the age of each globular cluster. The combined snapshots of the N-body clusters were then scaled in mass and radius to match the density and velocity dispersion pro\ufb01les of the observed globular clusters and the best-\ufb01tting model was determined from an interpolation in the grid of N-body models. When comparing with the N-body data, we assume an age of T = 11.25 Gyr for NGC 6624 (VandenBerg et al. 2013) while for \u03c9 Cen we assume an age of T = 12.0 Gyr. Our results are however not very sensitive to the adopted cluster age. In order to model \u03c9 Cen, we ran an additional grid of models in which we varied the retention fraction of stellarmass black holes. The simulations by Baumgardt (2017) and Baumgardt & Hilker (2018) assume a retention fraction of 10% for the black holes that form in the simulations, with the remaining black holes given such high kick velocities upon formation that they immediately leave the star clusters. Such a retention fraction could be too small for \u03c9 Cen, since the models by Baumgardt & Hilker (2018) predict a central escape velocity of vesc = 63 km/sec for \u03c9 Cen, which is one of the highest central escape velocities of all Galactic globular clusters. Given that the initial escape velocity was probably even higher due to stellar evolution driven mass loss and cluster expansion, a signi\ufb01cant fraction of black holes could have been retained in \u03c9 Cen. In this paper we therefore ran additional simulations of star clusters without IMBHs, but with stellar-mass black hole retention fractions of 30%, 50% and 100%. The initial mass function of stars in these simulations was also assumed to be a Kroupa (2001) mass function initially. We also ran additional simulations for NGC 6624 since the IMBH models of Baumgardt (2017) only contain IMBHs with up to 2% of the cluster mass at T = 12 Gyr, while the 20, 000 M\u2299IMBH inferred by Perera et al. (2017a,b) implies a much larger mass fraction. We therefore extended the grid No evidence of IMBHs in \u03c9 Cen and NGC 6624 5 of IMBH models of Baumgardt (2017) to also contain IMBH masses of 5% and 10% of the \ufb01nal cluster mass. 4 RESULTS 4.1 \u03c9 Cen We start our discussion of \u03c9 Cen by comparing the best\ufb01tting N-body models with and without an IMBH to the observed surface brightness and velocity dispersion pro\ufb01le of \u03c9 Cen. Three sets of models were calculated. In the \ufb01rst set of models, we kept the black hole retention fraction \ufb01xed at 10% and varied only the initial cluster radius and the initial surface brightness pro\ufb01le, quanti\ufb01ed by the King concentration parameter c. This was done until we found the best-\ufb01tting model to the observed surface brightness and velocity dispersion pro\ufb01le. These models are the same models as the N-body models used by Baumgardt (2017) and Baumgardt & Hilker (2018). When scaled to \u03c9 Cen, these models produce about 34,000 M\u2299in stellar mass black holes after stellar evolution and velocity kicks have been applied, out of which 14, 000 M\u2299remain in the cluster by T = 12 Gyr. In the second set of models we varied the assumed black hole retention fraction in addition to the the initial cluster radius rh and initial surface density pro\ufb01le. In the third set of models we \ufb01xed the retention fraction of stellarmass black holes to 10%, but varied the mass fraction of a central IMBH from 0.5% to 2% of the \ufb01nal cluster mass, corresponding in the case of \u03c9 Cen to IMBHs with masses between about 12,000 to 50,000 M\u2299, to \ufb01nd the best \ufb01t to the observed surface brightness and velocity dispersion pro\ufb01le. Panel a) of Fig. 1 shows the resulting \ufb01ts of the surface brightness and velocity dispersion pro\ufb01le of \u03c9 Cen. Based on the di\ufb00erences between the polynomial \ufb01t of the surface brightness pro\ufb01le by Trager, King & Djorgovski (1995) and the actual surface brightness measurements, we estimate a typical uncertainty of the observed surface brightness of \u03c9 Cen of \u2206\u03a3 = 0.1 mag. This uncertainty is shown in the lower left of panel a) in Fig. 1. It can be seen that all models provide \ufb01ts of similar accuracy to the surface brightness pro\ufb01le of \u03c9 Cen, at least outside the central 10\u201d. Inside this radius the IMBH model provides a better \ufb01t to the weak cusp which Noyola & Gebhardt (2006) found in the surface brightness pro\ufb01le. We note however that several determinations of the centre of \u03c9 Cen exist and that Anderson & van der Marel (2010) did not \ufb01nd a rise in the surface brightness pro\ufb01le of \u03c9 Cen around their centre. We conclude that the surface brightness pro\ufb01le alone cannot be used to discriminate between the di\ufb00erent models. The main reason for this is the low central concentration and long relaxation time of \u03c9 Cen, which means that the cluster is still far from core collapse and has not undergone much dynamical evolution. Such evolution would be necessary to establish a weak cusp pro\ufb01le in the surface brightness pro\ufb01le, which would separate models with and without IMBHs from each other (see discussion in Baumgardt, Makino & Hut 2005). Panels c) and d) of Fig. 1 compare the velocity dispersion pro\ufb01les predicted by the di\ufb00erent models against the proper motion and radial velocity dispersion pro\ufb01le of \u03c9 Cen. It can be seen that the model with an initial retention fraction of stellar mass black holes of 10% (about 14,000 M\u2299in stellar mass black holes after T = 12 Gyr) underestimates the velocity dispersion in the central 100\u201d by about 2 km/sec. It also overpredicts the velocity dispersion pro\ufb01le beyond 200\u201d and can therefore be rejected. The best-\ufb01tting model in which the black hole retention fraction and the total mass in stellar mass black holes was left as a free parameter is shown by a solid, red line in Fig. 1. For an initial retention fraction of stellar-mass black holes of 75% \u00b1 8%, (corresponding to 165,000 M\u2299or about 4.6% \u00b1 0.5% of the cluster mass in stellar-mass black holes at T = 12 Gyr), this model provides a signi\ufb01cantly better \ufb01t to the velocity dispersion pro\ufb01le, especially in the inner cluster parts. Due to mass segregation of the stellar mass black holes into the centre, the mass in the centre is increased compared to the model with a low retention fraction and this increases the velocity dispersion of the stars. Similarly, a model with a MIMBH = 47, 500 M\u2299IMBH provides a good \ufb01t to the velocity dispersion pro\ufb01le. Our results con\ufb01rm the models of Zocchi, Gieles & H\u00b4 enault-Brunet (2019) who already found that a dense cluster of stellar-mass black holes containing 5% of the total cluster mass can mimic the in\ufb02uence of an intermediate-mass black hole. 4.1.1 Central velocity distribution Fig. 2 shows the 1D velocity distribution in the centre of \u03c9 Cen for the di\ufb00erent N-body models and compares them with the observed velocity distribution which we calculated from the proper motion data published by Bellini et al. (2017). For the observed pro\ufb01le, we used all stars within a projected radius of 20 arcsec of the cluster centre as determined by Goldsbury, Heyl & Richer (2013). This area is large enough to encompass the cluster centres of Noyola & Gebhardt (2006) and van der Marel & Anderson (2010) as well, which are about 12\u201d and 0.5\u201d respectively away from the Goldsbury et al. cluster centre. We restrict ourselves to stars that have reduced \u03c72 r values of less than 1.5, have a NUsed/Nfound ratio between the number of data points used for PM \ufb01ts NUsed to the number of data points available Nfound of larger than 0.85, proper motion errors of less than 5 km/sec, and have velocities within 100 km/sec of the mean cluster velocity. For the N-body models we use all main-sequence and giant stars that are more massive than 0.5 M\u2299to roughly cover the same mass range as the stars with observed proper motions in the Bellini et al. sample. We scale all theoretical distributions to contain the same number of stars as are in the observed sample. We also add random velocity errors that follow a Gaussian with a width of 3 km/sec to the stars from the N-body simulations to mimic the in\ufb02uence of velocity errors in the observations. It can be seen that the model without an IMBH but a high black hole retention fraction matches the observed velocity distribution very well. In both data sets the fastest star is moving with about 62 km/sec and the overall shape of the observed velocity distribution is also matched very well. A Kolmogorov-Smirnov (KS) test between the theoretical and observed data gives a 15% chance that both distributions are drawn from the same underlying distribution. Given the considerable uncertainties in e.g. the mass distribution of formed black holes, and the large number of observed stars in Fig. 1, which makes modeling their exact distribution challenging, we consider the black hole models 6 Baumgardt, He, Sweet, Drinkwater, Sollima, Hurley, Usher, Kamann, Dalgleish, Dreizler & Husser Figure 1. Fit of the surface brightness pro\ufb01le (panel a) and the velocity dispersion pro\ufb01le (panels c and d) of \u03c9 Cen for the best-\ufb01tting N-body models. Upper panels show the actual pro\ufb01les, lower panels show the di\ufb00erences between the observed and modeled pro\ufb01les. The surface brightness pro\ufb01le from Trager, King & Djorgovski (1995) is shown by solid circles while open circles show the data from Noyola & Gebhardt (2006). The errorbar in the lower left of panel a) depicts an uncertainty of 0.1 mag. In panels c) and d), the observed velocity dispersions are from Watkins et al. (2015) (circles), Kamann et al. (2018) (squares) and this work (triangles). Shown are the best-\ufb01tting IMBH model (blue dashed lines) and the best \ufb01tting no IMBH model with a retention fraction of stellar-mass black holes of 75% (red solid lines). Also shown is the best-\ufb01tting model with a 10% retention fraction of black holes (black dotted lines). All three models \ufb01t the surface brightness pro\ufb01le within the observational uncertainties outside the central 10\u201d. The model with a low assumed retention fraction of stellar-mass black holes has too little mass in the centre and underpredicts the observed velocity dispersion in the centre and overpredicts it at larger radii. The model with a high stellar-mass black hole retention fraction provides a signi\ufb01cantly better \ufb01t. Panel b) compares the anisotropy pro\ufb01le of \u03c9 Cen with all three models. The models are in agreement with the observed pro\ufb01le out to several hundred arcsec. to be in very good agreement with the observations. In contrast, the best-\ufb01tting IMBH model leads to a signi\ufb01cantly less satisfactory \ufb01t of the velocity distribution. The stellar distribution extends to too high velocities, the IMBH model predicts 20 stars with velocity v > 62 km/sec while none is seen in the observations. The reason for the larger number of stars with very high velocities is the lowering of the central potential well due to the IMBH, which is more e\ufb00ective than that caused by a more widely distributed population of stellar-mass black holes. The absence of fast moving stars in the observations cannot be a selection e\ufb00ect since such stars are present outside the central 20\u201d and are most likely nonmembers which move with a large velocity relative to the cluster. The velocity distribution for a central IMBH also clearly deviates from the observed distribution at smaller velocities, and a KS test gives a less than 10\u22127 chance that both distributions are drawn from the same underlying distribution. The model with a low black hole retention fraction No evidence of IMBHs in \u03c9 Cen and NGC 6624 7 Figure 2. Velocity distribution of stars within 20\u201d of the centre of \u03c9 Cen. Shown is the 1D velocity distribution for the stars with measured proper motions by Bellini et al. (2017) (black dots) and the best-\ufb01tting N-body model with an IMBH (blue dashed line) and with 10% and 75% BH retention fractions (black dotted and red solid lines). The model with a high retention fraction of stellar-mass black holes provides the best \ufb01t to the observed distribution. The IMBH model predicts about 20 high-velocity stars with v > 62 km/sec while none is seen in the observations. The velocity distribution of the IMBH and low black hole retention fraction models also have the wrong shape for stars moving with less than 60 km/sec. also does not match the observed distribution of slow moving stars. We therefore conclude that \u03c9 Cen does not contain an IMBH, or at least, if the cluster contains an IMBH, then its mass must be signi\ufb01cantly less than the 47, 500 M\u2299needed to explain the velocity dispersion pro\ufb01le. Additional simulations with lower IMBH mass fractions and varying stellarmass black hole fractions would be needed to determine the upper mass limit of an IMBH. 4.1.2 The role of anisotropy and rotation Zocchi, Gieles & H\u00b4 enault-Brunet (2017) investigated the in\ufb02uence of orbital anisotropy on the velocity dispersion pro\ufb01le of \u03c9 Cen by \ufb01tting limepy models (Gieles & Zocchi 2015) with varying degrees of radial anisotropy to the surface and velocity dispersion pro\ufb01le of the cluster. They found that the central velocity dispersion increases with increasing orbital radial anisotropy and that limepy models could be constructed that reproduced the proper motion dispersion pro\ufb01le of \u03c9 Cen without the need to invoke an IMBH in the centre of the cluster. While a massive IMBH is already ruled out by the velocity distribution of stars in the centre, orbital anisotropy might still have an in\ufb02uence on the parameters of the best-\ufb01tting models, especially the amount of stellar mass black holes needed to reproduce the velocity dispersion pro\ufb01le. Panel b) of Fig. 1 compares the orbital anisotropy pro\ufb01le of \u03c9 Cen with the velocity dispersion pro\ufb01le for the best\ufb01tting model with a 10% retention fraction of black holes, the best-\ufb01tting model with a higher black hole retention fraction and a model with a central IMBH. We de\ufb01ne as orbital anisotropy the ratio of the tangential to the radial velocity dispersion component of the proper motions \u03b2 = \u03c3t/\u03c3r. The observed anisotropy \u03b2 is taken from the measurements of Watkins et al. (2015) and van Leeuwen et al. (2000). In addition, we determine the velocity anisotropy in the outer parts of \u03c9 Cen from the Gaia DR2 proper motions. The velocity distribution of stars in \u03c9 Cen is isotropic in the centre out to about 100\u201d, slightly radially anisotropic with \u03b2 = 0.9 at intermediate radii, before becoming more or less isotropic again in the outermost parts. The amount of anisotropy is overall rather small, with the tangential velocity dispersion \u03c3t never di\ufb00ering by more than 10% from the radial velocity dispersion \u03c3r. In the simulated clusters the velocity pro\ufb01le is also isotropic in the centre before becoming increasingly anisotropic beyond 100\u201d due to stars being scattered out of the centre onto radial orbits. The simulated clusters provide an acceptable \ufb01t to the anisotropy pro\ufb01le in the inner parts but, except for the IMBH model which is isotropic out to about 1000\u201d, are too anisotropic beyond about 400\u201d. The increasing anisotropy is most likely due to the fact that the simulated clusters are isolated, while the Galactic tidal \ufb01eld de\ufb02ects stars on their orbits inside \u03c9 Cen and keeps the cluster isotropic. This mismatch could be the reason why the velocity dispersion in the simulated clusters is below the observed velocity dispersion in the outermost parts of \u03c9 Cen. However, given the good match in the centre, it seems quite unlikely that velocity anisotropy has a signi\ufb01cant e\ufb00ect on our results. In addition to anisotropy, rotation could also in\ufb02uence the results of our \ufb01tting since it re-distributes kinetic energy between di\ufb00erent spatial directions while the models that we \ufb01t to \u03c9 Cen are non-rotating. Kamann et al. (2018) found a rotation amplitude of about 4 km/sec in the central parts of \u03c9 Cen from MUSE spectroscopy. Similarly, Sollima, Baumgardt & Hilker (2019) found a rotational amplitude of A = 4.27 \u00b1 0.52 km/sec and a 100% probability that \u03c9 Cen is rotating by analysing the Gaia DR2 proper motions and stellar radial velocities of Baumgardt et al. (2019). Both values are signi\ufb01cantly smaller than the central velocity dispersion, meaning that the in\ufb02uence of rotation is small in the centre It is therefore also unlikely that rotation has a signi\ufb01cant in\ufb02uence on the derived black hole mass fraction and the possible presence of an IMBH. Finally, stellar binaries could also a\ufb00ect our velocity dispersion estimates. However the binary fraction in \u03c9 Cen is small, only about 13% (Sollima, Ferraro & Bellazzini 2007) and, according to the simulations by Ibata et al. (2011), the velocity shift of most of these binaries will be close to zero with only few systems producing velocity shifts larger than 20 km/sec. 4.1.3 Implication for the initial stellar-mass black hole retention fraction In this section we compare the 4.6% mass fraction in stellarmass black holes that produced the best \ufb01t to the observational data of \u03c9 Cen with the estimated BH mass fraction predicted by stellar evolution theory. To this end, we set up an initial model of \u03c9 Cen assuming the cluster stars follow a Plummer model with an initial total cluster mass of M = 7 \u00b7 106 M\u2299and initial half-mass radius of rh = 5 pc, a Kroupa (2001) initial mass function between mass limits of 0.1 and 120 M\u2299for the cluster stars and no primordial mass segregation between high and low-mass stars. We then apply the e\ufb00ect of stellar evolution to this model by decreasing 8 Baumgardt, He, Sweet, Drinkwater, Sollima, Hurley, Usher, Kamann, Dalgleish, Dreizler & Husser Figure 3. Final mass of a black hole as a function of the initial stellar mass for the stellar evolution models of Belczinski et al. (2010) (B10), Fryer et al. (2012) (F12), Spera et al. (2015) (S15) and Spera et al. (2017) (S17). It can be seen that there is a significant variation between the four models especially for stars with mass m > 30 M\u2299. the masses of the stars and turning the more massive stars into compact remnants and evolve all stars to T = 12 Gyrs. We also apply velocity kicks to the stars that turn into black holes. We assume that stars with masses less than 0.8 M\u2299do not undergo stellar evolution and keep their initial masses. Stars with initial masses between 0.8 < m < 8 M\u2299are assumed to be transformed into white dwarfs and we use the initial-\ufb01nal mass function of Kalirai et al. (2008) to predict their masses. For the neutron stars we assume that 90% are removed due to natal kicks, in agreement with the assumption in the N-body models and that the mass of each neutron star is mNS = 1.3 M\u2299. For stellar-mass black holes, we test four di\ufb00erent initial-\ufb01nal mass relations from the literature: Belczynski et al. (2010, B10), Fryer et al. (2012, F12), Spera, Mapelli & Bressan (2015, S15) and Spera & Mapelli (2017, S17). For the S15 and S17 models we assume a cluster metallicity of Z = 0.0005, close to the average metallicity of \u03c9 Cen according to Harris (1996) and Johnson & Pilachowski (2010), while for the B10 and F12 models we assume a metallicity of Z = 0.0002, which is the metallicity closest to the metallicity of \u03c9 Cen that was studied in detail in these papers. Fig. 3 depicts the \ufb01nal mass of a black hole vs. the initial mass of a star for the four stellar evolution models and the metallicities chosen. We note that the initial-\ufb01nal mass relation for black holes in our N-body simulations is given by Belczynski, Kalogera & Bulik (2002), which is similar to the B10 and (for low stellar masses) F12 models, so these models can most easily be compared with the results of our simulations. We also apply velocity kicks to the black holes. Following Fryer et al. (2012), we assume that the 1D kick velocity vkick is given by the following formula: Figure 4. Black hole mass fraction after T=12 Gyr as a function of the kick velocities \u03c3 for the four stellar evolution models depicted in Fig. 3. The grey shaded area shows the predicted black hole mass fraction in \u03c9 Cen from our N-body models. The current BH mass fraction is compatible with the Fryer et al. (2012) (F12) stellar evolution models and a 1D kick velocity of 270 km/sec as found by Repetto, Davies & Sigurdsson (2012) or the Belczinski et al. (2010) (B10) models for low kick velocities. vkick = (1 \u2212ffb) \u03c3 . (1) Here ffb is the mass fraction of the stellar envelope falling back onto the black hole (Fryer et al. 2012). We assume that \u03c3, the 1D kick velocity in case of no mass fallback, follows a Gaussian distribution and we vary it between 0 < \u03c3 < 400 km/sec to explore the in\ufb02uence of \u03c3 on our results. We calculate three kick velocities for each spatial direction and add them to the velocity of the progenitor star upon formation of a black hole. Black holes are assumed to escape if their total energy is larger than zero and we sum up the masses of all remaining black holes to obtain the number and mass fraction of all black holes after their formation. Since the best-\ufb01tting N-body model of \u03c9 Cen loses about 1/3 of all black holes between the time of their formation and T=12 Gyr due to dynamical encounters between single black holes and black hole binaries in the core of the cluster, we \ufb01nally reduce the mass in stellar-mass black holes that we derive from the di\ufb00erent stellar-evolution models by 1/3 in order to account for the dynamical mass loss. Fig. 4 depicts the mass fraction in stellar-mass black holes after 12 Gyr for the four di\ufb00erent stellar evolution models. The black hole mass fraction decreases with increasing kick velocity but becomes roughly constant beyond 300 km/sec due to black holes forming from stars with ffb \u22481 which receive only small kicks. The grey shaded area shows the observed fraction of 4.6 \u00b1 0.5%. It can be seen that the observed mass fraction is compatible with the Belczinski et al. (2010) models for kick velocities up to about 80 km/sec and with the Fryer et al. (2012) models for larger kick velocities. The Fryer et al. (2012) models produce the right black hole mass fraction for the 1D kick velocity of \u03c3 = 270 km/sec found by Repetto, Davies & Sigurdsson (2012) from observations of No evidence of IMBHs in \u03c9 Cen and NGC 6624 9 Galactic black holes. The Spera, Mapelli & Bressan (2015) and Spera & Mapelli (2017) models overpredict the mass fraction of black holes due to the fact that more massive black holes form in these models, especially for high mass stars. There are however several ways which could also bring these models into agreement with the observations, for example a steepening of the high mass end of the initial mass function. In addition, the larger number of massive black holes that are produced in these models could lead to a more e\ufb03cient dynamical ejection of stellar-mass black holes, which could help to bring these models into better agreement with the observations. We therefore conclude that the mass fraction of stellar-mass black holes that we found from the N-body models is, within the model uncertainties, in agreement with the expected fraction based on recent models for the evolution of massive stars. 4.2 NGC 6624 Peuten et al. (2014) analyzed 16 years of timing data of the low-mass X-ray binary (LMXB) 4U 1820-30 that is located close to the centre of NGC 6624 and found that this LMXB has a strongly negative period derivative. They suggested that an acceleration of the star along the line-of-sight due to either a dark concentration of remnants or an intermediatemass black hole could be responsible for creating this period change. Furthermore, Perera et al. (2017a) analysed timing observations of the three innermost pulsars in NGC 6624 and concluded that a 60,000 M\u2299IMBH (later revised down to 20,000 M\u2299by Perera et al. (2017b)) is required if their period changes are due to a central intermediate mass black hole. Gieles et al. (2018) on the other hand noticed that the strong negative period derivative of 4U 1820-30 is not exceptional when compared to \ufb01eld LMXBs, making it likely that other explanations like mass-loss from the companion star or spin-orbit coupling can also explain the period change. They also showed through \ufb01tting of the observed surface brightness and velocity dispersion pro\ufb01le of NGC 6624 by multi-mass models that models without an IMBH are suf\ufb01cient to explain the observed acceleration of pulsar A in NGC 6624. For a total cluster mass of 55, 400 \u00b1 1, 500 M\u2299 (Baumgardt & Hilker 2018; Baumgardt et al. 2019) even the lower IMBH mass of 20,000 M\u2299of Perera et al. (2017b) would still imply that the IMBH would contain more than 1/3 of the total mass of NGC 6624, making NGC 6624 one of the most black hole dominated stellar systems known. We therefore also \ufb01tted our grid of N-body simulations to NGC 6624. Fig. 5 depicts cluster \ufb01ts with various IMBH mass fractions to the observed velocity dispersion and surface brightness pro\ufb01le of NGC 6624. We performed one set of simulations of clusters without a central black hole, and three sets of simulations of star clusters containing central black holes containing 2%, 5% and 10% of the total cluster mass. For each IMBH mass fraction, we searched for the model that produced the best \ufb01t to the observed surface brightness and velocity dispersion pro\ufb01le of NGC 6624. It can be seen that the model without an IMBH is in excellent agreement with the observations since it \ufb01ts the observed surface brightness and velocity dispersion pro\ufb01le. There is a slight discrepancy with the observed surface density pro\ufb01le in the innermost few arcsec, however this discrepancy is nowhere larger than a factor of two and is probably within the uncertainties with which the density pro\ufb01le can be determined in the center. Our N-body simulations therefore con\ufb01rm earlier results by Gieles et al. (2018) who also found that no IMBH is required to explain the observed surface brightness and velocity dispersion pro\ufb01le of NGC 6624. Models with IMBHs containing less than 5% of the cluster mass in the form of an IMBH also provide acceptable \ufb01ts to the velocity dispersion pro\ufb01le. However, more massive IMBH models start to overpredict the central velocity dispersion. Although we were not able to run models with IMBHs containing more than 10% of the cluster mass in the form of an IMBH due to stability issues in the simulation, it is clear from Fig. 5 that such models would be excluded even more strongly. In addition all IMBH models produce weak cusps in the cluster centre which are in disagreement with the observed surface brightness pro\ufb01le. Finally, the IMBH models produce a smaller amount of mass segregation among the cluster stars than the no-IMBH model, which is unable to reproduce the strong change of the observed mass function with radius (see panel c). This reduced amount of mass segregation is in agreement with theoretical expectations (Baumgardt, Makino & Ebisuzaki 2004; Gill et al. 2008) and further argues against the presence of an IMBH in NGC 6624. We derive an upper limit for an IMBH in NGC 6624 of at most a few percent (i.e. about 3,000 M\u2299) if only the cluster kinematics is taken into account. This value drops to around 1,000 M\u2299if the \ufb01t of the surface brightness pro\ufb01le is also taken into account. Table 2 presents the derived parameters for NGC 6624 from our best-\ufb01tting no-IMBH model. The cluster distance was determined by a simultaneous \ufb01t of the radial velocity dispersion and proper motion dispersion pro\ufb01les. The global mass function slope \u03b1 (de\ufb01ned as the best-\ufb01tting powerlaw slope N(m) \u223cm\u03b1) was derived for main-sequence stars between 0.2 and 0.8 M\u2299. It\u2019s strongly positive value shows that the number of stars is decreasing towards lower masses, meaning that NGC 6624 is highly depleted in low-mass stars. For the best-\ufb01tting cluster distance, the mass-to-light ratio of NGC 6624 is around 1.4, somewhat below the expected M/L ratio of a cluster with a Kroupa IMF (around 1.7 given the age and metallicity of NGC 6624). This can be explained by the highly depleted mass function of NGC 6624. Our values for the total cluster mass, mass-to-light ratio and halfmass radius are in good agreement with those derived by Gieles et al. (2018). Table 2 also presents the maximum accelerations for the LMXB and the three pulsars with measured period derivatives that are possible in the best-\ufb01tting model. The maximum accelerations were determined for stars at the same projected distance as each of the observed pulsars by varying the distance along the line of sight until the maximum lineof-sight acceleration was found. The central density of our best-\ufb01tting no-IMBH model is lower than the one found by Gieles et al. (2018). As a result, the observed period changes of the pulsars and the LMXB cannot be explained by our N-body model through an acceleration due to the smooth background cluster potential. Instead, they have to be either due to nearby stars or an internal spin-down of the pulsars. Indeed, the period derivative, \u02d9 P, values of pulsars B and C are comparable with observed \u02d9 P values of \ufb01eld pulsars of similar period. These pulsars were also not considered 10 Baumgardt, He, Sweet, Drinkwater, Sollima, Hurley, Usher, Kamann, Dalgleish, Dreizler & Husser Figure 5. Surface density pro\ufb01les (panel a), velocity dispersion pro\ufb01les (panel b) and stellar mass functions (panel c) of the best-\ufb01tting cluster models with and without an intermediate-mass black hole (blue lines) and the observed pro\ufb01les of NGC 6624. Panel c) shows the measured mass functions at three di\ufb00erent radii. Only the comparison with the no-IMBH model is shown here for clarity. Panel d) depicts the reduced \u03c72 r values for the \ufb01ts of the di\ufb00erent models against surface brightness and velocity dispersion pro\ufb01les. While the cluster model without an IMBH is in good agreement with the observed cluster, none of the IMBH models provides a simultaneous \ufb01t of the observed surface brightness and velocity dispersion pro\ufb01le. by Perera et al. (2017b) for the determination of the cluster potential and IMBH mass. Pulsar A is the most luminous \u03b3-ray pulsar known and the observed \u03b3-ray luminosity requires an intrinsic period derivative that is comparable to the observed value (Freire et al. 2011). A \ufb01nal caveat to note is that the results of our N-body \ufb01tting show that NGC 6624 has a half-mass relaxation time of around 108 yrs, much smaller than its age, making it likely that NGC 6624 has gone through core-collapse. Clusters in core-collapse go through core oscillations during which the core continuously collapses and re-expands due to dynamical heating of the core due to binaries formed during the dense collapse phases (Bettwieser & Sugimoto 1984). This could signi\ufb01cantly change the central density without affecting the outer density pro\ufb01le much, i.e. such density \ufb02uctuations might not be visible observationally. We therefore No evidence of IMBHs in \u03c9 Cen and NGC 6624 11 [t] Table 2. Properties of NGC 6624 and observed and predicted accelerations of the milli-second pulsars from our best-\ufb01tting noIMBH model. Distance 7425 \u00b1 273 pc Mass 9.40 \u00b1 0.23 \u00b7 104 M\u2299 M/L ratio 1.37 \u00b1 0.17 M\u2299/L\u2299 Mass function slope \u03b1 +1.5 Relaxation time TRH 3.0 \u00b7 108 yrs Core radius 0.25 pc Half-mass radius 2.50 pc Central velocity dispersion 7.1 km/sec Half-mass density 7.3 \u00b7 102 M\u2299/pc3 Central density 6.1 \u00b7 105 M\u2299/pc3 Observed period derivatives \u02d9 P/P PSR B1820-30A1 6.22 \u00b7 10\u221216 s\u22121 PSR B1820-30B1 8.32 \u00b7 10\u221217 s\u22121 PSR J1823-3021C1 5.51 \u00b7 10\u221216 s\u22121 4U 1820-302 \u22121.7 \u00b7 10\u221215 s\u22121 Maximum accelerations PSR B1820-30A 1.03 \u00b7 10\u221216 s\u22121 PSR B1820-30B 1.21 \u00b7 10\u221217 s\u22121 PSR J1823-3021C 2.19 \u00b7 10\u221217 s\u22121 4U 1820-30 8.79 \u00b7 10\u221217 s\u22121 Notes: 1: from http://www.naic.edu/~pfreire/GCpsr.html, 2: from Peuten et al. (2014) investigate how the previous results change over time. Fig. 6 shows the variation of the core radius, central density and maximum acceleration of pulsar A in an N-body simulations that uses our best-\ufb01tting no-IMBH model as a starting point. This run was done without stellar evolution, however we do not expect that stellar evolution will change the results signi\ufb01cantly over the 500 Myr timescale depicted in Fig. 6. The core radius and central density are calculated according to eq. 2 of Baumgardt, Hut & Heggie (2002). The model cluster quickly collapses and reaches a central density of around 109 M\u2299/pc3, three orders of magnitudes larger than the initial density of the best-\ufb01tting Nbody model, after about T = 130 Myr of evolution. We note that the best \ufb01t to the surface density pro\ufb01le of NGC 6624 determined by Trager, King & Djorgovski (1995), which we use in this paper, is reached at about T = 50 Myr in this simulation, while the surface density pro\ufb01le determined by Gieles et al. (2018) corresponds to the density pro\ufb01le reached in the deepest collapse phases. After the initial collapse, core oscillations are clearly visible in the evolution of the core density and the central density can \ufb02uctuate by about two orders of magnitude within a few 10s of Myr. However while the core can reach extremely high central densities, it contains only of order 30 stars during the densest collapse phases. As a result the maximum acceleration of a pulsar seen in projection at the same distance as pulsar A \ufb02uctuates much less and is always a factor two to three below the observed acceleration. We therefore conclude that the observed period change of pulsar A must at least in part be due to an internal period change or a nearby companion. It cannot solely be explained by an acceleration due to the general cluster potential, making this pulsar and also the other two pulsars unsuitable for the determination of the Figure 6. Core radius (bottom panel), central density (middle panel) and maximum acceleration of pulsar A (top panel) as a function of time in an N-body simulation that uses our best\ufb01tting no-IMBH model as a starting point. Since NGC 6624 is in core collapse, the core radius and the central density show large \ufb02uctuations as the core contracts and re-expands due to the formation of binaries followed by heating due to encounters between cluster stars and these binaries. However even during the strongest contraction phases the maximum \u02d9 P/P value of pulsar A is well below the observed value (shown by a blue line in the top panel). This implies that most of the observed period change of this pulsar is due to internal processes or a nearby companion, not the background cluster potential. cluster potential and the presence of an IMBH in NGC 6624. 5 CONCLUSIONS We have \ufb01tted results of dynamical N-body simulations to the surface brightness and velocity dispersion pro\ufb01les of \u03c9 Cen and NGC 6624, two Galactic globular clusters that have been claimed to harbor intermediate-mass black holes (IMBHs). Our results show that, while IMBH models can be constructed that produce a simultaneous \ufb01t to the velocity and surface brightness pro\ufb01le of \u03c9 Cen, these models predict too many fast moving stars within the central 20\u201d of the cluster and can therefore be rejected. Instead, we \ufb01nd that a model containing 4.6% of the cluster mass in a centrally concentrated cluster of stellar mass black holes is a viable alternative to an IMBH model. This con\ufb01rms earlier results by Zocchi, Gieles & H\u00b4 enault-Brunet (2019). Such a model not only provides a very good \ufb01t to the velocity dispersion pro\ufb01le of \u03c9 Cen, but also correctly predicts the velocity distribution of stars in the central 20\u201d of \u03c9 Cen in the HST proper motion survey of Bellini et al. (2017). We \ufb01nd that a mass fraction of 4.6% in stellar mass black hole is compatible with the expected mass fraction due to stellar evolution of massive stars. Our N-body simulations show that this centrally concentrated cluster of black holes can have formed due to 12 Baumgardt, He, Sweet, Drinkwater, Sollima, Hurley, Usher, Kamann, Dalgleish, Dreizler & Husser dynamical mass segregation and energy partition from an initially unsegregated distribution of stars. For NGC 6624 we \ufb01nd that a model without an IMBH produces an excellent \ufb01t to the observed surface brightness and velocity dispersion pro\ufb01le as well as the stellar mass function of the cluster, corroborating earlier results by Gieles et al. (2018). If an IMBH is present at all in this cluster, it must be less massive than 1,000 M\u2299since more massive IMBHs produce clusters that are in con\ufb02ict with the observed surface brightness and velocity dispersion pro\ufb01le as well as the amount of mass segregation of NGC 6624. In particular IMBHs with more than 5% of the cluster mass (corresponding to more than about 3,000 M\u2299), produce a strong central rise in velocity dispersion which is neither seen in the HST proper motion dispersion pro\ufb01le of Watkins et al. (2015) nor our radial velocity dispersion pro\ufb01le. Hence, the observed period derivatives of the millisecond pulsars in the centre of NGC 6624 cannot be due to an acceleration produced by the smooth background potential of the cluster. Our results therefore show that caution has to be applied when using millisecond pulsars as probes of globular cluster potentials. ACKNOWLEDGMENTS We thank Andrea Bellini for useful discussions concerning the analysis of the HST proper motions of \u03c9 Cen. We also thank Mark Gieles and an anonymous referee for comments that helped improve the presentation of the paper. C.U. and S.K. gratefully acknowledge \ufb01nancial support from the European Research Council (ERC-CoG-646928, Multi-Pop). This paper includes data that has been provided by AAO Data Central (datacentral.org.au). Part of this work is based on data acquired through the Australian Astronomical Observatory, [under program A/2013B/012]. Parts of this research were supported by the Australian Research Council Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), through project number CE170100013 . Some of the data presented herein were obtained at the W. M. Keck Observatory, which is operated as a scienti\ufb01c partnership among the California Institute of Technology, the University of California and the National Aeronautics and Space Administration. The Observatory was made possible by the generous \ufb01nancial support of the W. M. Keck Foundation. The authors wish to recognize and acknowledge the very signi\ufb01cant cultural role and reverence that the summit of Maunakea has always had within the indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this mountain.",
                    "introduction": "Black holes were long considered to be a mathematical cu- riosity, but nowadays their existence has \ufb01rm observational support. Until recently, observational evidence for black holes has mainly been gathered in two distinct mass ranges: stellar mass black holes, which are produced as the end prod- uct of the stellar evolution of massive stars (Fryer 1999), and supermassive black holes with masses 106-1010 M\u2299, which are found in the centres of galaxies (Gebhardt et al. 2000; G\u00a8 ultekin et al. 2009). In recent years, evidence has also been accumulating \u22c6E-mail: h.baumgardt@uq.edu.au for the existence of intermediate-mass black holes (IMBHs) with masses in the range 103-105 M\u2299. First, some IMBHs have been found in the centres of dwarf galaxies. Barth et al. (2004) for example found a 105 M\u2299black hole at the cen- tre of the Seyfert 1 galaxy POX 52 through optical imag- ing and stellar radial velocity measurements. Farrell et al. (2009) found evidence that the ultraluminous X-ray source in the galaxy ESO243-49 is powered by an accreting black hole with mass 102 to 105 M\u2299. Further evidence for an IMBH nature of the accreting black hole was later found by Webb et al. (2010) and Servillat et al. (2011). Accret- ing IMBH candidates were also found at the centres of the galaxies NGC 404 (Nyland et al. 2012) and NGC 3319 (Jiang et al. 2018), making it plausible that IMBHs could 2 Baumgardt, He, Sweet, Drinkwater, Sollima, Hurley, Usher, Kamann, Dalgleish, Dreizler & Husser be intermediate steps in the formation of supermassive black holes. Most recently Lin et al. (2018) found that a luminous X-ray outburst in a massive star cluster near the lenticular galaxy 6dFGS gJ215022.2-055059 was most likely powered by the tidal disruption of a star by a 50,000 M\u2299IMBH. IMBHs might also exist in globular clusters, cre- ated through either the formation of a central clus- ter of compact remnants which later merge due to the emission of gravitational waves (Miller & Hamilton 2002; Mouri & Taniguchi 2002), run-away merging of massive main sequence stars within the \ufb01rst few Myrs after clus- ter formation (Portegies Zwart et al. 2004), or the repeated formation of tight binaries between a stellar mass black hole and main sequence stars followed by mass accretion onto the black hole and subsequent growth of the black hole over longer timescales (Giersz et al. 2015). IMBHs might also be the remnants of \u223c104 M\u2299supermassive stars that have been suggested as the sources of the observed abundance anomalies in globular clusters (Denissenkov & Hartwick 2014). Observational evidence for the existence of IMBHs has been reported in about 20 Galactic globular clusters based on either stellar kinematics (e.g. Gerssen et al. 2002), X-ray or radio signals from accretion of interstellar gas (Ulvestad, Greene & Ho 2007) or the acceleration of pulsars (K\u0131z\u0131ltan, Baumgardt & Loeb 2017; Perera et al. 2017a). In particular, Noyola, Gebhardt & Bergmann (2008), Jalali et al. (2012) and Baumgardt (2017) found evidence for a 40, 000 M\u2299IMBH in the centre of \u03c9 Cen based on the velocity dispersion and surface brightness pro\ufb01le of this cluster. Since \u03c9 Cen is thought to be the nuclear cluster of a tidally disrupted dwarf galaxy (e.g. Bekki & Norris 2006), such a discovery could provide a link between IMBHs and supermassive black holes. However the presence of an IMBH in \u03c9 Cen was challenged by van der Marel & Anderson (2010), who created models of \u03c9 Cen that \ufb01tted the velocity dispersion pro\ufb01le of the cluster without the need for an IMBH, and Zocchi, Gieles & H\u00b4 enault-Brunet (2019) who \ufb01tted the velocity dispersion pro\ufb01le of \u03c9 Cen by a model that contained a centrally concentrated cluster of stellar-mass black holes. Furthermore, Haggard et al. (2013) found no evidence of radio signals from gas accretion onto a central black hole in \u03c9 Cen. In addition, Perera et al. (2017a) and Perera et al. (2017b) found evidence for a massive IMBH in NGC 6624 based on timing observations of several pulsars close to the cluster centre. However Gieles et al. (2018) were able to ex- plain the observed period changes by a cluster model that did not contain an IMBH. In summary, there is currently no undisputed case for an IMBH in any Galactic globular clus- ter. If IMBHs exist in globular clusters, most of them must have masses of less than a few thousand M\u2299, otherwise their in\ufb02uence on the velocity dispersion pro\ufb01les (Baumgardt 2017) or radio emission from the accretion of interstellar gas (Strader et al. 2012; Tremou et al. 2018) should have been detected. In the present paper we use theoretical models to inves- tigate whether the surface brightness and velocity dispersion pro\ufb01les of the globular clusters \u03c9 Cen and NGC 6624 require the presence of IMBHs in these clusters. Our models are based on direct N-body simulations, which follow the evolu- tion of both clusters under the combined in\ufb02uence of stellar evolution and two-body relaxation. For \u03c9 Cen we also inves- tigate a centrally concentrated cluster of stellar mass black holes as an alternative to an IMBH. Our paper is organ- ised as follows: In Section 2 we describe the observational data used in this work. In Section 3 we describe the grid of N-body simulations used to \ufb01t the velocity and surface brightness pro\ufb01les and the stellar mass functions of globular clusters. In Section 4 we compare the N-body models with the observations and we draw our conclusions in Section 5."
                },
                {
                    "url": "http://arxiv.org/abs/1708.09530v2",
                    "title": "The Global Mass Functions of 35 Galactic globular clusters: II. Clues on the Initial Mass Function and Black Hole Retention Fraction",
                    "abstract": "In this paper we compare the mass function slopes of Galactic globular\nclusters recently determined by Sollima & Baumgardt (2017) with a set of\ndedicated N-body simulations of star clusters containing between 65,000 to\n200,000 stars. We study clusters starting with a range of initial mass\nfunctions (IMFs), black hole retention fractions and orbital parameters in the\nparent galaxy. We find that the present-day mass functions of globular clusters\nagree well with those expected for star clusters starting with Kroupa or\nChabrier IMFs, and are incompatible with clusters starting with single\npower-law mass functions for the low-mass stars. The amount of mass segregation\nseen in the globular clusters studied by Sollima & Baumgardt (2017) can be\nfully explained by two-body relaxation driven mass segregation from initially\nunsegregated star clusters. Based on the present-day global mass functions, we\nexpect that a typical globular cluster in our sample has lost about 75% of its\nmass since formation, while the most evolved clusters have already lost more\nthan 90% of their initial mass and should dissolve within the next 1 to 2 Gyr.\nMost clusters studied by Sollima & Baumgardt also show a large difference\nbetween their central and global MF slopes, implying that the majority of\nGalactic globular clusters is either near or already past core collapse. The\nstrong mass segregation seen in most clusters also implies that only a small\nfraction of all black holes formed in globular clusters still reside in them.",
                    "authors": "Holger Baumgardt, Antonio Sollima",
                    "published": "2017-08-31",
                    "updated": "2017-10-26",
                    "primary_cat": "astro-ph.GA",
                    "cats": [
                        "astro-ph.GA"
                    ],
                    "main_content": "The simulations in this paper were made using the GPUenabled version of the collisional N-body code NBODY6 (Aarseth 1999; Nitadori & Aarseth 2012). Clusters started with particle numbers between N = 65, 536 to N = 200, 000 stars. The initial mass functions (IMFs) of the clusters were given by either Kroupa (2001), Chabrier (2003) or Salpeter (1955) mass functions. In all simulations, stars were distributed between mass limits 0.1 < m < 100 M\u2299and stellar evolution was modeled by the stellar evolution routines of Hurley, Pols & Tout (2000), assuming a metallicity of [Fe/H] = \u22121.30. This metallicity is close to the average metallicity of Galactic globular clusters. We assumed a retention fraction of neutron stars of 10% in our simulations. Neutron stars not retained in the simulation were given large enough kick velocities upon formation so that they leave the clusters. In most simulations we also assumed a retention fraction of 10% for the black holes, however we also made simulations of star clusters with either 30%, 50% or 100% black hole retention fractions to test the influence of the black hole retention fraction on the cluster evolution. The initial half-mass radii of the clusters were equal to either rh = 1 pc, 2 pc or 4 pc to simulate the evolution of star clusters starting with different initial relaxation times. All clusters followed King (1966) density profiles initially with a dimensionless central potential W0 = 5.0. The simulated clusters were moving on circular orbits through an external galaxy which was modeled as an isothermal sphere with constant rotational velocity of VG = 220 km/sec. The distances of the clusters from the centers were chosen such that most clusters had lifetimes of between 13 to 30 Gyr so that they are dynamically evolved to various degrees when they reach globular cluster ages. This resulted in initial Galactocentric distances of between 3.5 kpc to 8.5 kpc. Most clusters did not contain primordial binaries, however we also made one simulation of a star cluster starting with a primordial binary fraction of 10% to see how binaries influence our results. The binary stars in this cluster were set up as described in L\u00a8 utzgendorf, Baumgardt & Kruijssen (2013), with a flat period distribution between 1 and 106 days and a thermal eccentricity distribution. In addition to the N-body runs described above, we also used the best-fitting N-body models of individual globular clusters derived from the simulations of Baumgardt (2017). These models are based on N-body simulations of isolated star clusters starting with N = 100, 000 stars initially, which are scaled in mass and radius to match the velocity dispersion and surface density profiles of Galactic globular clusters. The stars in these simulations followed a Kroupa (2001) IMF between mass limits 0.1 < m < 100 M\u2299and a 10% retention fraction was applied to all neutron stars and black holes formed in the simulations. In this paper we only use the noIMBH models of Baumgardt (2017). Table 1 presents an overview of the performed N-body simulations. It gives for each simulation the number of cluster stars, the chosen initial mass function, the Galactocentric distance of the cluster, the initial cluster mass, the primordial binary fraction, the assumed retention fraction of black holes, the initial half-mass radius of the cluster, the initial tidal radius, the initial relaxation time and lifetime of the cluster (defined by the time a cluster has lost 99% of its initial mass) and the best-fitting power-law slopes \u03b1 of the global and central mass function at T = 12 Gyr. 3 RESULTS 3.1 Initial mass function We first compare the global cluster mass functions determined by Sollima & Baumgardt (2017) with the evolution of clusters starting with different initial mass functions in order to determine the initial mass function of Galactic globular clusters. For star clusters evolving in a tidal field, the shape of the global mass function changes as a result of the preferential loss of low-mass stars due to mass segregation and the removal of outer cluster stars (Vesperini & Heggie 1997; Baumgardt & Makino 2003). If the cluster mass function is described by a power-law N(m) \u223cm\u03b1, the preferential loss of low-mass stars leads to an increase of the slope \u03b1.1 Fig. 1 depicts the mass distribution of main sequence stars in globular cluster as determined by Sollima & Baumgardt (2017). Shown are the global mass functions which Sollima & Baumgardt (2017) determined by fitting multimass King-Michie models to the observed mass functions. We have split the cluster sample of Sollima & Baumgardt (2017) into six different groups depending on the best-fitting power-law slopes \u03b1G of the global mass functions and show the average number of stars over all clusters in each group with solid circles. The mass functions of globular clusters flatten due to the preferential loss of low-mass stars, from mass functions strongly increasing towards low-mass stars in the lower left panel to flat mass functions in the upper right panel. In addition, the stellar mass function of the clusters in the three left panels also show a flattening towards low-mass stars. Fitting a powerlaw only to the low-mass stars with m < 0.40 in the lower left panel for example gives a best-fitting slope \u03b1 \u2248\u22121, while the higher-mass stars with m > 0.40 are best fit by \u03b1 \u2248\u22121.4. The solid lines in Fig. 1 depict the stellar mass distribution of clusters 4 to 6 from Table 1. The cluster starting with a Kroupa mass function is shown by blue lines, while the clusters with Chabrier and Salpeter IMFs are shown by red and green lines respectively. All depicted clusters started with N = 131, 072 stars and had circular orbits at a Galactocentric distance of 5 kpc. For each cluster we calculate the global mass function slope \u03b1G for each snapshot during the evolution and split the snapshots into the same six groups as the globular clusters. It can be seen that the stellar mass distribution in star clusters which start with either 1 In the following we will therefore speak of globular clusters with more negative values of \u03b1 as being dynamically less evolved than clusters with larger values of \u03b1. The mass function of 35 Galactic GCs 3 Table 1. Details of the performed N-body runs. Model N Mass RG M0 rh fBin BH ret. rt trh TDiss \u03b1g \u03b1i Nr. Function [pc] [M\u2299] [pc] [pc] [MYR] [MYR] 1 65536 Kroupa 8500 40815 2.0 0 10 50.79 219.0 20520 \u22120.52 \u00b1 0.01 0.13 \u00b1 0.02 2 65536 Chabrier 8500 42710 2.0 0 10 51.56 206.8 20110 \u22120.50 \u00b1 0.02 0.26 \u00b1 0.03 3 65536 Salpeter 8500 25021 2.0 0 10 43.14 353.1 16450 \u22120.63 \u00b1 0.02 0.37 \u00b1 0.04 4 131072 Kroupa 5000 83853 2.0 0 10 45.33 282.2 20750 \u22120.56 \u00b1 0.01 0.09 \u00b1 0.03 5 131072 Chabrier 5000 89355 2.0 0 10 46.30 270.1 20540 \u22120.91 \u00b1 0.01 0.15 \u00b1 0.03 6 131072 Salpeter 5000 49569 2.0 0 10 38.04 364.5 16510 \u22120.85 \u00b1 0.01 0.30 \u00b1 0.04 7 131072 Kroupa 3500 83853 2.0 0 10 32.24 282.2 13420 0.51 \u00b1 0.02 1.35 \u00b1 0.04 8 131072 Kroupa 8500 83438 1.0 0 10 64.57 100.9 30020 \u22121.02 \u00b1 0.01 \u22120.30 \u00b1 0.03 9 131072 Kroupa 8500 82777 1.0 10 10 64.41 112.0 29525 \u22120.99 \u00b1 0.01 \u22120.36 \u00b1 0.01 10 200000 Kroupa 3500 127642 2.0 0 10 37.09 336.6 17950 \u22120.41 \u00b1 0.01 0.43 \u00b1 0.03 11 200000 Kroupa 5000 127523 4.0 0 10 52.14 937.9 31240 \u22120.78 \u00b1 0.01 \u22120.47 \u00b1 0.02 12 131072 Kroupa 5000 83281 2.0 0 30 45.24 276.9 21750 \u22121.16 \u00b1 0.01 \u22120.36 \u00b1 0.01 13 131072 Kroupa 5000 83281 2.0 0 50 45.24 276.9 22850 \u22121.16 \u00b1 0.01 \u22120.36 \u00b1 0.01 14 131072 Kroupa 5000 83853 2.0 0 100 45.33 281.5 14450 \u22121.07 \u00b1 0.01 \u22121.16 \u00b1 0.01 15 131072 Kroupa 8500 83575 1.0 0 50 45.29 101.0 32400 \u22121.13 \u00b1 0.01 \u22120.45 \u00b1 0.03 16 131072 Kroupa 8500 83438 1.0 0 100 64.57 101.0 33150 \u22121.18 \u00b1 0.01 \u22120.69 \u00b1 0.01 Figure 1. Mass distribution of main sequence stars in globular clusters (circles) and simulations 4 to 6 from Table 1 (solid lines). Globular clusters are split into 6 di\ufb00erent groups depending on the power-law slope \u03b1G of their global mass functions and the number of stars is averaged over all clusters in each group. The number of globular clusters used is shown in the upper left corner of each panel. Solid lines show the corresponding mass distributions of simulated star clusters starting with either a Kroupa (blue), Chabrier (red) or Salpeter mass function (green). Clusters starting with Kroupa or Chabrier mass functions provide a very good \ufb01t to the stellar mass distribution of globular clusters at each evolutionary stage, while the cluster starting with a Salpeter mass function provides a signi\ufb01cantly worse \ufb01t to the observed mass distribution. a Kroupa or Chabrier IMF is in very good agreement with the observed stellar mass distribution of globular clusters in each panel. In contrast, the cluster which starts with a (single power-law) Salpeter IMF overpredicts the number of low-mass stars with log m < \u22120.6 and underpredicts the number of stars with log m \u2248\u22120.4. These deviations are present for the least evolved clusters in the lower left panel and are also present for the more evolved clusters. We obtain similar results for models 1 to 3 which start with N = 65536 stars, as well as for clusters that start with a Kroupa IMF and N = 200, 000 stars and take this as strong evidence that the mass function of globular clusters was not a single power-law at the low-mass end, but had a steeper slope for high-mass stars than for lower-mass stars, with a break or turnover at around m \u22480.4 M\u2299, in good agreement to what is expected for either a Kroupa or Chabrier IMF. In order to further explore the initial distribution of cluster stars, we depict in Fig. 2 the observed mass function slope as a function of distance from the cluster centre for the six least evolved clusters from Sollima & Baumgardt (2017), (excluding NGC 6304 where the mass function is probably in\ufb02uenced by background contamination, see discussion in Sollima & Baumgardt 2017, and NGC 5024 where the mass function cannot be reliably determined in the centre due to incompleteness). We concentrate on the least evolved clusters since in the dynamically more evolved clusters the initial stellar distribution has been strongly modi\ufb01ed by the cluster evolution and ongoing dissolution and cannot be easily compared with the simulations of Baumgardt (2017). The observed mass functions are shown by red \ufb01lled circles and lines in Fig. 2. It can be seen that all depicted clusters are mass segregated to various degrees since the mass function slopes decrease towards larger radii, implying a larger fraction of low-mass stars at larger radii. Also shown are the mass function slopes of the best-\ufb01tting N-body models from Baumgardt (2017) over the same radial range for each cluster. The clusters in the simulations by Baumgardt (2017) are isolated clusters, hence the global mass functions in these clusters do not evolve with time, unlike the mass functions in the observed clusters which change due to the prefer4 Baumgardt & Sollima ential loss of low-mass stars. In order to account for this preferential loss of low-mass stars, we shift the mass function slopes of each N-body model up until we obtain the best \ufb01t to the observed mass function slope for each cluster. Except for this o\ufb00set in the MF slope \u03b1, the radial variation of the mass function is the same in the theoretical models and the observed clusters. Since the clusters in the N-body simulations started unsegregated, the six depicted clusters must have also started without primordial mass segregation and the radial variation of the mass function seen in each cluster is only due to energy equipartition driven by two-body relaxation. Given the good agreement for the six depicted clusters, which span a large range of cluster masses and sizes, we conclude that most Galactic globular clusters started unsegregated. The only exception could be low-mass and low-density halo clusters like Pal 4, which are highly mass segregated despite having long relaxation times and for which N-body simulations have shown that the amount of mass segregation seen cannot be explained by dynamical evolution (Zonoozi et al. 2014, 2017). 3.2 Constraints on the cluster evolution Sollima & Baumgardt (2017) found a tight anti-correlation between the half-mass relaxation time of globular clusters and their global mass function slopes. Fig. 3 compares the location of the Galactic globular clusters in the relaxation time vs. mass function slope plane which they found with results of three N-body simulations that start with a Kroupa (2001) IMF. Half-mass relaxation times trh for the clusters in the N-body simulations were calculated from eq. 2-62 of Spitzer (1987) using all stars still bound to the clusters at any given time. We show the evolution of three N-body simulations starting with di\ufb00erent particle numbers, half-mass radii and Galactocentric distances but all having a low retention fraction of black holes. The evolution of the clusters in the simulations can be divided into two phases, in the initial phase the clusters expand due to stellar evolution mass loss and also heating due to binary stars in the core until they \ufb01ll their Roche lobes. In this phase the relaxation times increase but there is no strong evolution in the global mass function since the clusters are not yet mass segregated, so clusters move to the right in the relaxation time vs. global MF slope plane. In the second phase, the clusters have become mass segregated and their mass functions become depleted in low-mass stars due to mass loss, so the MF slopes evolve towards more positive values. This two stage behavior in the mass function evolution of star clusters was also found by Lamers, Baumgardt & Gieles (2013) and Webb & Vesperini (2016). At the same time, the clusters lose mass and shrink due to mass loss and a decreasing tidal radius, hence their relaxation times decrease as well. As a result, the simulated clusters move from the lower right corner to the upper left in the relaxation time vs. global MF slope plane. Since the clusters in the N-body simulations are about a factor 10 less massive and also on average about 30% more compact than observed globular clusters by the time they are 12 Gyr old, we increase the relaxation times of the star clusters in the N-body simulations by a factor 5 to match the relaxation times of globular clusters and show these scaled curves by dashed lines in Fig. 3. The scaled N-body clusters will probably not correctly capture the initial phases of cluster evolution, in particular the timescale for mass segregation and cluster expansion, but should describe the evolution of star clusters once they have become mass segregated and \ufb01ll their Roche lobes since then the evolution is driven mainly by a single process: mass loss. It can be seen that the location of the observed globular clusters agrees very well with that of the clusters in the N-body simulations when corrected for the di\ufb00erences in the relaxation times, indicating that the anti-correlation between mass function slope and relaxation time found by Sollima & Baumgardt (2017) could be due to the ongoing dissolution of globular clusters. If correct, Fig. 3 also implies that most globular clusters studied by Sollima & Baumgardt (2017) are tidally \ufb01lling and their sizes start to shrink as they lose more and more of their stars. Such an evolution seems reasonable for many of the depicted clusters: A globular cluster with a mass of M = 3 \u00b7 105 M\u2299orbiting at a distance of 4 kpc from the Galactic centre for example would have a Jacobi radius of rJ = 60 pc, and, assuming that rh/rJ \u22480.10 in the tidally \ufb01lling phase (K\u00a8 upper, Kroupa & Baumgardt 2008), would have a half-mass radius of rh = 6 pc when tidally \ufb01lling. Our simulated clusters moving at RG = 8.5 kpc reach similar half-mass radii within a few Gyr, meaning that many globular clusters, especially those in the inner parts of the Milky Way should also become tidally \ufb01lling within a Hubble time. In addition, using the formula for globular cluster lifetimes derived by Baumgardt & Makino (2003), we would expect the globular cluster described above to have undergone a signi\ufb01cant amount of mass loss within 12 Gyr and have experienced signi\ufb01cant changes to its initial mass function, similar to the observed globular clusters. Figs. 4 and 5 depict the location of the Galactic globular clusters in a global MF slope vs. inner MF slope plane. Inner mass function slopes are derived from all stars located between projected radii of 0.15 rhp \u2a7dr \u2a7d0.25 rhp, where rhp is the projected half-light radius of a cluster. This radial range was chosen since in most clusters this is the innermost region where the completeness fraction is still higher than 80% even for the faintest stars in the HST/ACS images. For comparison, we also depict the evolution of the mass function slope for several N-body simulations. In Fig. 4 we show simulations with a 10% retention fraction of stellar-mass black holes, while in Fig. 5 we depict clusters with higher retention fractions. The evolution of the clusters in the N-body simulations also falls into two phases. The clusters start with global and inner MF slopes around \u03b1g = \u03b1i \u2248\u22121.5 since they start from Kroupa IMFs without primordial mass segregation. Before core-collapse, clusters are not strongly mass segregated, therefore the global mass function changes only slowly, while the inner mass function evolves rapidly as the clusters become mass segregated. This near constancy of the global mass function before core collapse was also found by Lamers, Baumgardt & Gieles (2013) in N-body simulations. After core collapse there is a strong evolution in both the inner and global mass function slope. Depending on the initial relaxation time of the clusters, core-collapse happens at slightly di\ufb00erent points in the global vs. inner MF plane. Clusters with an initial relaxation time of TRH,0 = 100 Myr are already mass segregated before any mass loss has set in, while in clusters with TRH,0 = 900 Myr core collapse takes nearly as long as the dissolution of the clusters. Both The mass function of 35 Galactic GCs 5 Figure 2. Mass function slopes in projection as a function of distance from the cluster centre for the six least evolved clusters from Sollima & Baumgardt (2017). Red, solid lines and circles show the observed MF slopes, blue solid lines and triangles show the best-\ufb01tting N-body models from Baumgardt (2017) for each cluster. Dashed lines show the MF slopes from the N-body simulations shifted to correct for mass loss. The variation of the mass function slope with radius seen in the globular clusters can be entirely explained by two-body relaxation, indicating that the clusters started without primordial mass segregation. curves seem incompatible with the location of the observed globular clusters. The best agreement with the location of observed globular cluster is achieved for an initial relaxation time of TRH,0 \u2248300 Myr, implying an initial half-mass radius of rh = 1 pc for a MC = 3 \u00b7 105 M\u2299cluster. Addition of 10% primordial binaries leads only to a small change in the cluster evolution when all other parameters are kept the same (see the evolution of model 8 vs. model 9). The mass function slopes of globular clusters also fall into two phases similar to the N-body clusters: a strong evolution in the inner MF slope together with a near constant global MF slope until \u03b1i \u22480, followed by a rapid evolution in both inner and global MF slope. In the latter phase the di\ufb00erence between inner and global MF slope is nearly constant at \u03b1i \u2212\u03b1g \u22481.1 as clusters evolve towards dissolution. Given the agreement between simulations and observations, we conclude that globular cluster mass functions are shaped by the same interplay of mass segregation and dissolution as the clusters in the N-body simulations. If correct, Fig. 4 indicates that about 80% of the clusters in the sample of Sollima & Baumgardt (2017) have already undergone core collapse or are at least close to core collapse. In addition, globular clusters must have undergone a signi\ufb01cant amount of mass-loss, since clusters in the N-body simulations which have lost half their initial cluster stars have a global MF slope of \u03b1g = \u22121.0. Clusters in the simulations with \u03b1g = \u22120.5, which is a typical slope for the observed globular clusters, have already lost 75% of their stars. Judging from Fig. 4, the most evolved globular clusters should already have lost 90% of their initial cluster stars, and, for a constant mass loss rate, should therefore dissolve within the next 1 to 2 Gyr. These estimates agree with the mass loss estimates obtained by Webb & Leigh (2015), who also concluded that globular clusters must have undergone a strong mass loss based on their present-day mass function slopes. Fig. 5 shows the evolution of star clusters with high BH retention fractions of 30% to 100%. Due to the high fraction of stellar-mass black holes, mass segregation is strongly suppressed in these clusters and none of them shows strong mass segregation for most of its evolution. This is also depicted in Fig. 6, which compares the di\ufb00erence between the global and the inner mass function slope for our Nbody simulations with the observed di\ufb00erences for Galactic globular clusters. Galactic globular clusters have an average \u03b1g \u2212\u03b1i \u2248\u22121.13 \u00b1 0.32. The average \u03b1g \u2212\u03b1i and its 1\u03c3 deviation are shown by the blue dashed-dotted line and the shaded area in Fig. 6. The di\ufb00erent curves in Fig. 6 show the evolution of the di\ufb00erence of \u03b1g \u2212\u03b1i for six of the N = 131, 072 and N = 200, 000 star simulations from Table 1 which start with a Kroupa IMF. In most models a decrease in the number of black holes is accompanied by an increase in the amount of mass segregation. Regardless of the assumed initial retention fraction of black holes, the observed amount of mass segregation can only be reached 6 Baumgardt & Sollima Figure 3. Global mass function slopes as a function of relaxation time for observed globular clusters (red circles) and three large Nbody simulations of dissolving star clusters. Solid lines show the relaxation times of the simulated clusters, dashed lines show the simulated clusters after their relaxation times were multiplied by a factor 5 to account for the fact that galactic globular clusters are more massive and more extended than the clusters studied in the N-body simulations. After scaling there is a good overlap between both, indicating that Galactic globular clusters are tidally limited. when the fraction of black holes still retained in the clusters NBH/NBHKroupa is only a few percent of the fraction of all black holes that formed in the clusters. This poses a problem for the models which start with high initial retention fractions of either 50% or 100%. The only models which can reach large enough values \u03b1g \u2212\u03b1i are those that start with small initial relaxation times of TRH = 100 Myrs (e.g. model 16) and even in this model the black holes are exhausted only very close to the end of the lifetime of the cluster. For larger initial relaxation times the clusters dissolve before all black holes are ejected, hence mass segregation is either too slow (model 12) or no mass segregation is happening at all (model 14). We conclude that the current number of black holes in globular clusters must be rather small, if clusters formed with a Kroupa IMF then at most a few percent of the initially formed black holes still remain in the clusters. For a typical globular cluster forming with M = 3 \u00b7 105 M\u2299, this implies that no more than 50 stellar mass black holes currently reside in the cluster. Given their masses, globular clusters probably started with relaxation times of several hundred Myr, more similar to our clusters starting with rh = 2 pc or rh = 4 pc initial half-mass radius than the rh = 1 pc clusters. In addition, as we have seen before, most globular clusters have probably already lost a sizeable fraction of their initial cluster mass, meaning that their lifetimes are of the order of 20 Gyr. A quick cluster dissolution together with the long initial relaxation times and the small current black hole fraction is incompatible with a large initial black hole retention fraction. We therefore conclude that the initial black hole retention Figure 4. Global vs. inner mass function slope for observed globular clusters (red circles) and four di\ufb00erent N-body simulations starting with a BH retention fraction of 10% and di\ufb00erent initial relaxation times. The evolution of the simulated clusters falls into two categories, before core collapse when only the inner slope changes and the global slope stays nearly constant, and after core collapse when low-mass stars are preferentially lost and both slopes evolve. Observed globular clusters follow a very similar trend. The best match between observations and simulations is achieved for an initial relaxation time around 300 Myr. Figure 5. Same as Fig. 4 for clusters with a high initial BH retention fraction. It seems impossible to reproduce the strong mass segregation seen in globular clusters with N-body models that have high stellar-mass BH retention fractions since the stellarmass black holes suppress mass segregation among the low-mass stars. The mass function of 35 Galactic GCs 7 Figure 6. The di\ufb00erence between the global and the inner mass function slope for N-body simulations starting with di\ufb00erent initial black hole retention fractions. All simulations shown start with a Kroupa mass functions and N = 131, 072 or N = 200, 000 stars. The mean di\ufb00erence for galactic globular cluster and its scatter are shown by the blue, dot-dashed line and the shaded area. Clusters in the N-body simulations reach a di\ufb00erence of \u03b1g \u2212\u03b1i \u2248\u22121.1 only after nearly all black holes have been removed from the clusters. fraction in globular clusters was at most 50%, otherwise it is impossible to explain the large amount of mass segregation seen in the clusters today. 4 DISCUSSION We have compared the observed stellar mass functions of 35 Galactic globular clusters recently determined by Sollima & Baumgardt (2017) from HST/ACS data with a set of large N-body simulations of star clusters dissolving in external tidal \ufb01elds. We \ufb01nd that the observed mass functions are compatible with globular clusters having started from either Kroupa (2001) or Chabrier (2003) mass functions but are incompatible with Salpeter (1955) mass functions at the low mass end. Despite a di\ufb00erence of up to 103 in cluster mass, the IMF of globular clusters is therefore almost the same as that seen for stars in open clusters and \ufb01eld stars in the Milky Way (Bastian, Covey & Meyer 2010). This is in agreement with theoretical star formation simulations which predict only a weak dependence of the shape of the stellar mass function with environment (Myers et al. 2011; Hennebelle 2012). The amount of mass segregation seen in the least evolved globular clusters can be completely explained by two body relaxation driven mass segregation. It therefore seems likely that globular clusters formed without primordial mass segregation at least among the low-mass stars with m < 0.8 M\u2299. The observations of Sollima & Baumgardt (2017) have shown that the average global mass function slope of globular clusters for stars with masses in the range 0.2 < m/M\u2299< 0.8 is around \u03b1g = \u22120.5, higher by 1 than the slope of the best-\ufb01tting power-law MF for a Kroupa mass function slope over the same mass range. According to our simulations, clusters that have global mass function slopes \u03b1g = \u22120.5 after a Hubble time have typical lifetimes of about 20 Gyr. Hence, for a constant mass loss rate, more than half of all globular clusters should dissolve within the next 10 Gyr. From our simulations we also estimate that a typical globular cluster should have lost about 75% of its initial stars and about 2/3 of its initial mass since formation. If globular clusters underwent an even more dramatic mass loss, as some scenarios used to explain the large fraction of 2nd generation stars in globular clusters imply (e.g D\u2019Antona & Caloi 2008; D\u2019Ercole et al. 2008), then this mass loss must have happened early on before globular clusters were signi\ufb01cantly mass segregated. We also \ufb01nd a strong amount of mass segregation within globular clusters, the average di\ufb00erence between the global mass function slope to the inner mass function slope (which we de\ufb01ne as the mass function slope of stars around 20% of the projected half-light radius) is about \u03b1g \u2212\u03b1i = -1.1. Our simulations show that due to the e\ufb00ective suppression of mass segregation by stellar mass black holes, such a large amount of mass segregation is only possible if the number of stellar mass black holes currently residing in the clusters is only a few percent of the initial number of black holes formed (for a Kroupa IMF). A decrease in the amount of mass segregation or complete suppression of mass segregation due to stellar mass black holes has also been found previously by Webb & Vesperini (2016) and Alessandrini et al. (2016). Our simulations show that clusters with black hole retention fractions equal to or higher than 50% are not able to reach the low required black hole numbers before \ufb01nal cluster dissolution unless their initial relaxation times would have been of order 100 Myrs or less. Such small relaxation times seem di\ufb03cult to achieve for star clusters starting with several 105 M\u2299. We therefore conclude that the initial stellar mass black hole retention fractions were 50% or less. This result is in agreement with Sippel & Hurley (2013), who found that the current number of BHs observed to be in binary systems with a main-sequence companion as well as the estimated total number of BHs in M22 can be matched with a low initial BH retention fraction of 10%. Recently Peuten et al. (2016) showed that the absence of mass segregation in NGC 6101 found by Dalessandro et al. (2015) can be explained by a high stellar-mass BH retention fraction. However, as Fig. 2 shows, the HST/ACS data actually shows NGC 6101 to be mass segregated, so there is currently no need to assume a high BH retention fraction in NGC 6101. The clusters studied here only contain up to 200,000 stars initially and even though we do not \ufb01nd signi\ufb01cant di\ufb00erences between the clusters with di\ufb00erent initial particle numbers studied here, it is not clear how our results scale to globular clusters which typically formed with a 5 to 10 times larger number of stars. For globular clusters in the inner parts of the Milky Way, where the tidal \ufb01eld is strong, it seems possible that they could have expanded from small initial sizes to become tidally \ufb01lling within a few Gyr and then undergo signi\ufb01cant mass loss, e.g. undergo a similar evolution as the clusters in our simulations. Problems could arise for clusters in the outer parts of the Milky Way, where the 8 Baumgardt & Sollima tidal \ufb01eld is too weak to allow expansion up to the tidal radius and signi\ufb01cant mass loss (Zonoozi et al. 2011). For such clusters additional mass loss mechanisms, due to e.g. formation and evolution in a dwarf galaxy (Webb et al. 2017) or highly elliptic orbits (Zonoozi et al. 2017) might be necessary to create su\ufb03cient mass loss to explain their presentday mass functions. Alternatively, we cannot completely rule out variations in the global mass functions or primordial mass segregation in some globular clusters. Simulations of individual globular clusters on their exact orbits through the Milky Way would help to further constrain their starting conditions, but are challenging since only low-mass or very extended globular clusters can be simulated with direct N-body simulations at the moment (Zonoozi et al. 2011; Heggie 2014; Wang et al. 2016), while Monte Carlo codes can currently only handle constant tidal \ufb01eld strengths. ACKNOWLEDGMENTS We thank Elham Hasani Zonoozi and an anonymous referee for comments which helped improve the paper.",
                    "introduction": "This is the second of two papers in which we explore the present-day stellar mass functions of Galactic globu- lar clusters. In the \ufb01rst paper (Sollima & Baumgardt 2017) we derived completeness corrected stellar mass functions within the central 1.6\u2019 of 35 Galactic globular clusters based on HST/ACS data obtained as part of the Globu- lar Cluster ACS Treasury Project (Sarajedini et al. 2007). We also derived the global mass functions, structural pa- rameters and dark remnant fractions of the studied clus- ters by modeling their observed mass functions, veloc- ity dispersion pro\ufb01les and surface density pro\ufb01les with isotropic, multi-mass King-Michie models (Gunn & Gri\ufb03n 1979; Sollima, Bellazzini & Lee 2012). Our results showed that the derived global mass functions could generally be \u22c6E-mail: h.baumgardt@uq.edu.au well described by single power-law mass functions in the mass range 0.2 < m/M\u2299< 0.8 except for the least evolved clusters. We also found a tight anti-correlation between the present-day mass functions slope and the half-mass relax- ation time of the clusters. In addition, we found that the mass fraction of dark remnants in a cluster correlates with the mass function slope of the cluster, in the sense that clusters with \ufb02atter mass functions have a higher remnant fraction. In the present paper we investigate what the results ob- tained in Sollima & Baumgardt (2017) imply for the stellar mass function with which globular clusters were born and for their subsequent evolution. To this end we compare the ob- servational data with a set of 16 N-body simulations of star clusters starting with di\ufb00erent initial mass functions, parti- cle numbers, half-mass radii, orbits in their parent galaxy, and black hole (BH) retention fractions. In addition, we also use data from the large grid of 900 N-body simulations re- 2 Baumgardt & Sollima cently published by Baumgardt (2017). Our paper is organ- ised as follows: In sec. 2 we describe our N-body simulations in greater detail. In sec. 3 we compare the mass functions of the simulated clusters with the observed mass functions of Galactic globular clusters and in sec. 4 we draw our conclu- sions."
                },
                {
                    "url": "http://arxiv.org/abs/1701.03818v3",
                    "title": "The distribution of stars around the Milky Way's black hole III: Comparison with simulations",
                    "abstract": "The distribution of stars around a massive black hole (MBH) has been\naddressed in stellar dynamics for the last four decades by a number of authors.\nBecause of its proximity, the centre of the Milky Way is the only observational\ntest case where the stellar distribution can be accurately tested. Past\nobservational work indicated that the brightest giants in the Galactic Centre\n(GC) may show a density deficit around the central black hole, not a cusp-like\ndistribution, while we theoretically expect the presence of a stellar cusp. We\nhere present a solution to this long-standing problem. We performed\ndirect-summation $N-$body simulations of star clusters around massive black\nholes and compared the results of our simulations with new observational data\nof the GC's nuclear cluster. We find that after a Hubble time, the distribution\nof bright stars as well as the diffuse light follow power-law distributions in\nprojection with slopes of $\\Gamma \\approx 0.3$ in our simulations. This is in\nexcellent agreement with what is seen in star counts and in the distribution of\nthe diffuse stellar light extracted from adaptive-optics (AO) assisted\nnear-infrared observations of the GC. Our simulations also confirm that there\nexists a missing giant star population within a projected radius of a few\narcsec around Sgr A*. Such a depletion of giant stars in the innermost 0.1 pc\ncould be explained by a previously present gaseous disc and collisions, which\nmeans that a stellar cusp would also be present at the innermost radii, but in\nthe form of degenerate compact cores.",
                    "authors": "Holger Baumgardt, Pau Amaro-Seoane, Rainer Sch\u00f6del",
                    "published": "2017-01-13",
                    "updated": "2017-12-07",
                    "primary_cat": "astro-ph.GA",
                    "cats": [
                        "astro-ph.GA"
                    ],
                    "main_content": "We have run N\u2212body simulations of star clusters containing massive central black holes using the GPU enabled version of the collisional N-body code NBODY6 (Aarseth 1999; Nitadori Article number, page 2 of 6 H. Baumgardt et al.: The distribution of stars around the Milky Way\u2019s black hole & Aarseth 2012), and we followed the evolution of the star clusters under the combined in\ufb02uence of star formation, stellar evolution, and two-body relaxation. The mass distribution of stars in our simulations was given by a Kroupa (2001) mass function with lower and upper mass limits of 0.1 and 100 M\u2299, respectively. This mass function is compatible with observations of the mass-to-light ratio of the nuclear cluster and the temperature and luminosity distribution of individual giant stars in the nuclear cluster (L\u00f6ckmann et al. 2010; Pfuhl et al. 2015). Owing to the high escape velocity from the nuclear cluster, we assumed a 100% retention fraction for stellar-mass black holes and neutron stars upon their formation. We also assumed solar metallicity for the stars in our simulation, which is compatible with the average metallicity of stars in the GC (Ryde & Schultheis 2015; Do et al. 2015). Because of the high computational cost of N-body simulations, we simulated clusters with smaller particle numbers but larger half-mass radius so that the relaxation time of the simulated clusters is the same as the relaxation time of the nuclear cluster in the GC. This approach is similar to the approach used by Baumgardt et al. (2003) to model the globular cluster G1 and Baumgardt (2017) to model Galactic globular clusters. It allows us to correctly model the e\ufb00ects of two-body relaxation, which is the main focus in this paper, but processes that do not occur on relaxation timescales like tidal disruption of stars cannot be modelled easily in scaled simulations. The nuclear cluster in the GC has a projected half-light radius of RhNC = 4.2 \u00b1 0.4 pc and a mass of MNC = 2.5 \u00b1 0.4 \u00b7 107 M\u2299(Sch\u00f6del et al. 2014). Using the de\ufb01nition of the half-mass relaxation time as given by Spitzer (1987) and assuming the 2D half-light radius to be 75% of the 3D half-light radius, this results in a half-light relaxation time of TRH \u224814 Gyr. We therefore used an initial projected half-mass radius of our simulated clusters of Rh = RhNC \u00b7 (MNC/MC)1/3 = 26.9 pc, so that our simulated clusters have the same half-mass relaxation time as the nuclear cluster and evolve dynamically with the same rate per physical time. At the end of the simulations, we scaled our clusters down to a projected half-light radius of RhNC = 4.2 pc, so that we were able to directly compare with observational data. In total we performed three realisations using di\ufb00erent random number seeds for each density pro\ufb01le and overlaid the results of \ufb01ve snapshots of each realisation centred on the MBH after scaling each cluster to the same half-mass radius. Pfuhl et al. (2011) found that most stars in the nuclear cluster are old, with about 80% of them having been born more than 5 Gyr ago. They also found that an exponentially decreasing star formation rate according to S FR(t) = e\u2212t/\u03c4S FR (1) with a characteristic timescale \u03c4S FR = 5.5 Gyr matches the age distribution of old stars in the nuclear cluster. We therefore started our simulations with a star cluster containing N = 50, 000 stars and an MBH that contained 15% of the cluster mass, similar to the mass ratio seen for the GC SMBH (see e.g. Genzel et al. 2010, and references therein). We then simulated the evolution of this cluster for 1 Gyr and added new stars to it after 1 Gyr with a rate given by Eq. 1. We evolved the new cluster for another Gyr before adding the next generation of stars and repeated this process until the cluster reached an age of T = 13 Gyr. Throughout the evolution, the mass ratio between the cluster and the central MBH was kept constant at 15%, that is, we assumed that the MBH grows at the same rate as the nuclear cluster. The new stars added to the simulation following a King (1966) model with dimensionless central potential of W0 = 5.0 initially. In order to Fig. 1. J \u2212KS CMD of the simulated nuclear clusters after 13 Gyr of evolution for a distance of 8 kpc to the GC and and an average reddening of AKs = 2.54 mag. The di\ufb00erent stellar generations that were added to the simulations can clearly be distinguished in the CMD. Stars marked in red have KS < 18.5 and are used for comparison with the density pro\ufb01le of resolved stars from Gallego Cano et al. (2017). The remaining stars are used to create the di\ufb00use light pro\ufb01le of the simulated clusters. study the in\ufb02uence of the initial density pro\ufb01le on the \ufb01nal results, we also ran simulations in which the initial density pro\ufb01les had central potentials of W0 = 3.0 and W0 = 7.0, but found that the \ufb01nal slopes of the power-law pro\ufb01les do not change by more than \u2206\u0393 = \u00b10.1 in surface density, con\ufb01rming that the GC nuclear star cluster is dynamically relaxed in its centre. When setting up the King (1966) models, we took the potential of the central black hole into account when calculating the stellar velocities. After 13 Gyr, we ended up with star clusters containing about \u223c255, 000 stars and a \ufb01nal mass of MC = 9.5 \u00b7 104 M\u2299. Figure 1 depicts a J-KS vs KS colour-magnitude diagram (CMD) of the stars in our simulation after T = 13 Gyr, calculated using the PARSEC isochrones (Bressan et al. 2012). In order to calculate the apparent KS band magnitudes, we assumed a distance of 8 kpc to the GC and a KS -band extinction of AKs = 2.54 mag (Sch\u00f6del et al. 2010) for all stars. The di\ufb00erent generations of stars that were added to the star cluster during the simulation can clearly be distinguished in the CMD. In the following, we use stars with KS < 18.5 mag (shown in red) for the comparison with the number density pro\ufb01le of resolved stars from Gallego Cano et al. (2017). For the comparison with the di\ufb00use light pro\ufb01le of Sch\u00f6del et al. (2017), we used all stars fainter than this limit and summed their KS -band luminosities. With these limits, resolved stars have masses in the range 0.86 < m < 2.31 M\u2299 , while 90% of the di\ufb00use light is created by stars with masses 0.78 < m < 1.76 M\u2299. On average, the resolved stars are about 0.25 M\u2299more massive than the brightest stars that contribute to the unresolved light. Article number, page 3 of 6 A&A proofs: manuscript no. 30462corr Fig. 2. Spatial density of di\ufb00erent stellar components at the end of our simulations. From top to bottom, we show the density distribution of black holes and neutron stars (green), giant stars with apparent magnitudes KS < 18.5 (red), upper main-sequence stars with masses 0.6 M\u2299 and 0.8 M\u2299(blue), and low-mass main-sequence stars with masses 0.1 and 0.3 M\u2299(orange). For clarity, curves are shifted vertically. Dashed lines show power-law density distributions \u03c1(r) \u223cr\u03b3 \ufb01tted to the density distribution inside the in\ufb02uence radius of the black hole (rBH = 2.8 pc). Because of mass segregation, the slope steepens from \u03b3 = 1.04 for the lowest-mass main-sequence stars to \u03b3 = 1.55 for black holes. 3. Results Figure 2 shows the density distribution of di\ufb00erent types of stars after 13 Gyr of evolution. Shown are the density distributions of stellar mass black holes; giant stars, which we assume to be all stars with K-band luminosities KS < 18.5; upper main-sequence stars with masses between 0.6 M\u2299and 0.8 M\u2299; and lower mainsequence stars with masses between 0.1 and 0.3 M\u2299. For clarity we have shifted all curves vertically to separate the di\ufb00erent curves from each other. We also scaled the \ufb01nal cluster to have a projected half-light radius of 4.2 pc to match the GC nuclear cluster. For this half-light radius, the in\ufb02uence radius of the central black hole, that is, the radius where the cumulated mass in stars becomes equal to the central black hole mass, is rBH = 2.8 pc. This value is close to the break radius seen in the surface density distributions of resolved stars and di\ufb00use light as found by Gallego Cano et al. (2017) and Sch\u00f6del et al. (2017) and depicted in Figs. 3 and 4. Inside the in\ufb02uence radius, the density distribution of the different stellar components can be well described by single-powerlaw distributions. Black holes and neutron stars follow a powerlaw distribution with the steepest slope of \u03b3 = 1.55, close to the theoretically predicted slope of \u03b3 = 1.75 for a single-mass stellar population around a massive black hole (Bahcall & Wolf 1976). Owing to mass segregation, all other components follow \ufb02atter density distributions. The slopes vary by only \u2206\u03b3 = 0.16 between giant stars and the lowest-mass main-sequence stars, however. Overall, the power-law slopes of the di\ufb00erent stellar mass groups are \ufb02atter than what Baumgardt et al. (2004) found for a single-age stellar cluster with the same initial mass function Fig. 3. Surface density \u03a3(R) of old giant stars in the GC for three di\ufb00erent KS -band intervals. The observed surface densities and associated error bars are taken from Gallego Cano et al. (2017) and are shown by circles for the di\ufb00erent magnitude intervals. Black dashed lines and triangles show the pro\ufb01le that we obtain for giant stars at the end of our simulations. The pro\ufb01les are in excellent agreement with each other in the di\ufb00erent magnitude intervals, with the exception of the innermost density pro\ufb01le of stars in the magnitude interval 12.5 < KS < 16. after T = 12 Gyr of evolution (see their Fig. 7). This indicates that the GC star cluster is dynamically not yet completely relaxed because of its relatively long relaxation time (T \u223c14 Gyr). In addition, the continuous star formation reduces mass segregation between the di\ufb00erent stellar components. Because of the small amount of mass segregation, low-mass stars dominate the stellar mass pro\ufb01le for all radii outside 0.01 pc and the luminosity pro\ufb01le closely follows the mass pro\ufb01le in the nuclear cluster, that is, we do not predict a strong variation of the M/L pro\ufb01le of the nuclear cluster with radius. When scaled to the GC, our simulations predict about \u223c300 stellar-mass black holes and a total mass of 7000 M\u2299in stars inside the central 0.1 pc. Our mass estimate is in good agreement with the approximate 104 M\u2299of total mass within this region that can be calculated with the Nuker model and the mass normalisations of Sch\u00f6del et al. (2017), and it is also consistent with the upper limit of 1.3\u00b7105 M\u2299recently derived by Boehle et al. (2016). We note that these mass limits have been derived assuming a mass-to-light ratio that is independent of radius for the nuclear star cluster. Figure 3 depicts the distribution of bright stars in the central parsec and compares it with the observed distribution of latetype giant stars within three di\ufb00erent KS -band intervals as determined by Gallego Cano et al. (2017). In order to avoid uncertainties and systematic biases in mixing di\ufb00erent observational data sets, we only depict the NACO data, that is, data in the radial range from 0.011 pc to 1 pc in Fig. 3. In order to increase the statistical signi\ufb01cance of our results, we use all stars with KS < 18.5 in the simulations for the comparison with the observed distribution in the three magnitude intervals. This is justi\ufb01ed since the observed stars are giant stars, which show Article number, page 4 of 6 H. Baumgardt et al.: The distribution of stars around the Milky Way\u2019s black hole Fig. 4. KS -band surface luminosity pro\ufb01le \u03a3(R) of the di\ufb00use light of the GC star cluster. The data points show the results of Sch\u00f6del et al. (2017) corrected for di\ufb00erential extinction. Red line and data points show the surface luminosity pro\ufb01le of the simulated cluster, determined from all main-sequence stars fainter than KS > 18.5. Theoretical and observational pro\ufb01les are in excellent agreement with each other outside the innermost few arcsec. only a small dependence of average mass and age with luminosity. Hence we expect the stars in the di\ufb00erent magnitude bands to follow similar density distributions in our simulations. The observed and simulated density pro\ufb01les agree very well with each other, the di\ufb00erences between the two pro\ufb01les are usually less than 10% for all three magnitude intervals and are of the same order as the uncertainties of the observed pro\ufb01les. The combined surface density distribution of the three simulations we have performed can be \ufb01tted by a power-law distribution \u03a3(R) \u223cR\u2212\u0393 with a slope \u0393 \u223c0.46 in the range 0.04 pc < R < 1.0 pc. This is in excellent agreement with the observed density distributions of bright stars, which have best-\ufb01tting slopes of \u0393 = 0.45 \u00b1 0.01 for stars with 12.5 < KS < 16, \u0393 = 0.47 for stars with 16.5 < KS < 17.5 and \u0393 = 0.47 \u00b1 0.02 for stars with 17.5 < KS < 18.5 over the same radial range (Gallego Cano et al. 2017). The observed data have almost the same slopes in the di\ufb00erent bands, as expected from our simulations. While we compared our results only to the most recent results, we note that previous determinations of the surface density distribution of late-type giant stars (e.g. Sch\u00f6del et al. 2007; Buchholz et al. 2009) are also compatible with our results, at least outside the central few arcsec. Stars with 12.5 < Ks < 16 display a density de\ufb01cit inside the innermost few arcsec, while their distribution at larger radii agrees with our simulations. This could indicate that some depletion process like giant star collisions or disc passages has altered their apparent distribution at the very centre. Figure 4 compares the surface density pro\ufb01le of di\ufb00use light in the GC from Sch\u00f6del et al. (2017) with the results of our simulations. The black data points depict the KS -band surface luminosity derived by Sch\u00f6del et al. (2017) after correction for differential extinction and combining their data inside 1.5 pc with the azimuthally averaged extinction-corrected near-infrared data by Fritz et al. (2016). The red line shows the surface luminosity density of faint stars in our simulations. The simulated surface light distribution is well described by a single power-law pro\ufb01le with \u03a3(R) \u223cR\u22120.37 inside 1.0 pc. This is close to the observed pro\ufb01le, which has \u0393 = 0.26 \u00b1 0.02stat \u00b1 0.05sys (Sch\u00f6del et al. 2017). The slope predicted from our simulations is nearly the same as in the case of the resolved stars, again indicating that there was insu\ufb03cient time for the nuclear cluster to develop signi\ufb01cant mass segregation between main-sequence stars of di\ufb00erent masses. The observed pro\ufb01le is slightly below our predicted data in the innermost few arcsec, but the di\ufb00erences are within the uncertainty with which we can determine the surface luminosity pro\ufb01le from our simulations and might therefore not be signi\ufb01cant. In addition, the surface density of the di\ufb00use light may show some systematic uncertainties at radii R = 1-2\u201d because of the presence of very bright stars and the related di\ufb03culty of accurate PSF subtraction in this region (see discussion in Sch\u00f6del et al. 2017). We also see that our model somewhat over-predicts the surface density of di\ufb00use light at radii R < 2\u201d. However, the qualitative agreement, in particular the slope of the power-law at larger radii, is very good. There is a clear steepening of both the observed and simulated pro\ufb01les beyond 20 arcsec, that is, outside the in\ufb02uence radius of the central black hole. We conclude that the simulated and observed data agree excellently well with each other. In particular, the inferred powerlaw indices of the surface densities as well as the corresponding 3D power-law slopes (see caption of Fig. 2) agree well with the values estimated by Gallego Cano et al. (2017) and Sch\u00f6del et al. (2017). The surface density pro\ufb01le of both resolved stars and diffuse light of the nuclear cluster are therefore entirely compatible with what we expect for a star cluster around a massive black hole that is evolving under the combined in\ufb02uence of dynamical relaxation and continuous star formation given the age and star formation history of the nuclear cluster. Conclusions The existence of stellar cusps in relaxed clusters around massive black holes is a long-standing prediction of theoretical stellar dynamics, but it has escaped con\ufb01rmation for decades for several reasons, some observational and some theoretical. On the observational side, there is only a single target where the cusp theory can be tested with current instrumentation: the Galactic centre. Extragalactic nuclei are too far away for current instrumentation, and the existence of (intermediate-mass) massive black holes in globular clusters is still debated. However, the GC is not an easy target, and number counts and stellar classi\ufb01cation both su\ufb00er from the very high and spatially highly variable interstellar extinction as well as from the extreme source crowding. Observational evidence has therefore been ambiguous for a long time. Recent new analyses, however, have found a stellar cusp around Sgr A*, with very consistent morphologies for di\ufb00erent tracer populations that di\ufb00er by several magnitudes in brightness. While the distribution of resolved giant stars with KS = 18 might be contaminated by young stars that formed within the last few 100 Myr, the contribution of such stars is much smaller for brighter giant stars with KS < 16 and the di\ufb00use stellar light (Gallego Cano et al. 2017). The observations therefore imply the existence of a stellar cusp among the old and dynamically relaxed giant stars. This cusp has been found to be rather shallow, which is one of the reasons why it has so successfully escaped detection over a long time. Article number, page 5 of 6 A&A proofs: manuscript no. 30462corr On the theoretical side, the main limitation was probably that the systems that were analysed were too simple. As we now know, the nuclear cluster around the SMBH at the GC is a highly complex system and has experienced many episodes of repeated star formation and/or cluster infall. As a result of the di\ufb00erent physical and dynamical ages, stars that formed at di\ufb00erent epochs will follow di\ufb00erent radial distributions even if their masses are the same (Aharon & Perets 2015). This work presents an attempt to take the complex star formation history of the Milky Way\u2019s NSC into account. As we have shown, twobody relaxation and repeated star formation across the lifetime of the Galaxy indeed results in a rather weak stellar cusp, consistent with the observations. It appears that this is the \ufb01rst time that theory and observations reach convergence on the question of the stellar cusp. Because we can be sure now that there is a powerlaw cusp around Sagittarius A*, the apparent de\ufb01cit of giants within the innermost few arcsec of the central black hole also indicates that the latter do not trace the overall cluster structure. Either they do not have the same age structure as the fainter stars, or some process such as a destruction of their envelopes via interactions with a fragmenting gaseous disc (the idea of AmaroSeoane & Chen 2014) has altered their apparent distribution. The existence of a stellar cusp at the heart of the Milky Way implies that density cusps might also exist in many other galactic nuclei, especially smaller nuclei with relaxation times shorter than a Hubble time. This is of importance for gravitational wave astronomy because it means that Extreme-Mass Ratio Inspirals (EMRIs) may be observed with signi\ufb01cant frequency. Acknowledgements. The research leading to these results has received funding from the European Research Council under the European Union\u2019s Seventh Framework Programme (FP7/2007-2013) / ERC grant agreement n\u25e6[614922]. PAS acknowledges support from the Ram\u00f3n y Cajal Programme of the Ministry of Economy, Industry and Competitiveness of Spain. This work has been partially supported by the CAS President\u2019s International Fellowship Initiative.",
                    "introduction": "The Galactic centre (GC) is the nucleus closest to us, o\ufb00ering the unique possibility of studying the interaction between a su- permassive black hole (SMBH) and its surrounding star clus- ter using individual resolved stars. Adaptive-optics (AO) as- sisted near-infrared photometric and spectroscopic studies of the stars within about 1 pc of the SMBH have shown that the surface density of massive early-type stars is rising steeply to- wards Sagittarius A* (Sgr A*, the electromagnetic manifestation of the SMBH), while the density distribution of bright late-type stars down to the apparent median luminosity of the Red Clump (Ks \u224815.5) \u2013 and therefore mostly old and lower mass stars \u2013 rises much more slowly and may even be \ufb02at within a few 0.1 pc of the black hole (Sch\u00f6del et al. 2007; Do et al. 2009). Typically, the projected stellar surface number density (and equivalently the 3D density) is described by a power law of the form \u03a3(R) \u221dR\u0393, where R is the distance from Sgr A*. Buchholz et al. (2009) for example found that the surface density distribu- tion within a projected radius R = 6\u201d of Sgr A* can be described with an exponent \u0393 = 0.2 \u00b1 0.1, which would correspond to a decreasing density within the innermost few arcseconds (one arcscond corresponds to approximately 0.04 pc at the distance of the GC). Since the relaxation time at the GC is of order of a Hub- ble time, old stars should have had enough time to settle into an equilibrium distribution around the black hole. Bahcall & Wolf (1976) found that a single-mass stellar population should settle into a power-law cusp \u03c1(r) \u223cr\u2212\u03b3 with a slope of \u03b3 = 1.75 within the in\ufb02uence radius of the central supermassive black hole, much steeper than what is observed. This has led to the so-called \u2019miss- ing giant star\u2019 problem. Moreover, the impact goes beyond stel- lar dynamics and the GC because these massive stars close to the MBH are the precursors of compact objects, which might even- tually become a source of gravitational waves for a space-borne observatory such as LISA or Taiji (Amaro-Seoane et al. 2013, 2012; Gong et al. 2015). The gradual inspiral of a stellar-mass black hole has been coined an \u201cextreme-mass ratio inspiral\u201d, and it accumulates hundreds of thousands of cycles in the detector band, with impressive implications in fundamental physics and astrophysics (Amaro-Seoane et al. 2007; Amaro-Seoane 2012; Amaro-Seoane et al. 2015). A number of works have tried to explain this conundrum with di\ufb00erent ideas, which follow one of three possibilities. When Genzel et al. (1996) \ufb01rst discovered missing RGB stars, they proposed that this might be due to stellar collisions deplet- ing giant stars in the innermost parts through the high stellar densities that are reached near the SMBH. Later, Davies et al. (1998), Alexander (1999), Bailey & Davies (1999), and Dale Article number, page 1 of 6 arXiv:1701.03818v3  [astro-ph.GA]  7 Dec 2017 A&A proofs: manuscript no. 30462corr et al. (2009) addressed this idea in detail and came to the conclu- sion that it can only explain the absence of the brightest and most extended giant stars. A di\ufb00erent suggested possibility to explain the missing stars is that our GC does not only have one, but a bi- nary of two massive black holes. This hypothesised binary could indeed carve a core into the stellar distribution through three- body interactions, as shown by a number of authors (Baum- gardt et al. 2006; Portegies Zwart et al. 2006; Matsubayashi et al. 2007; L\u00f6ckmann & Baumgardt 2008; Gualandris & Merritt 2012). Nonetheless, the mass of the secondary needs to be of the order of \u223c105 M\u2299to explain the observed core. Such a massive secondary black hole would require the Milky Way to have expe- rienced a major merger relatively recently, which is excluded by observations (see Hansen & Milosavljevi\u00b4 c 2003; Yu & Tremaine 2003; Chen & Liu 2013). Moreover, the existence of such a mas- sive secondary black hole is largely ruled out from a number of other considerations, for instance, constraints on the proper mo- tion of Sgr A* from radio interferometry (see Gualandris & Mer- ritt 2009). A number of inspiraling smaller-mass black holes can also create a shallow stellar density pro\ufb01le in the centre, which would relax the major merger requirement, as has been shown by Mastrobuono-Battisti et al. (2014). It has also been put for- ward that a star cluster falling towards the GC could increase the density pro\ufb01le outside of 10\u2032\u2032, so that within this distance the pro\ufb01le would be like a core (Kim & Morris 2003; Ernst et al. 2009; Antonini et al. 2012; Antonini 2014). However, mass seg- regation would rebuild a steeper pro\ufb01le in as fast as a quarter of the relaxation time (as shown by Preto & Amaro-Seoane 2010a; Amaro-Seoane & Preto 2011). This requirement would hence need a steady in\ufb02ow of clusters to maintain a weak cusp pro\ufb01le in the centre. Finally, Merritt (2010) and Antonini (2014) found that if the nuclear cluster in the GC formed with an extended enough initial core pro\ufb01le, the current stellar distribution would still not be dynamically relaxed. While this solution is possi- ble, it requires \ufb01ne-tuning in the initial conditions to produce the density distribution seen in the GC. Amaro-Seoane & Chen (2014) proposed that the discs of young stars observed at the GC (Paumard et al. 2006) are connected to the missing bright giants: the precursor gaseous disc must have gone through a fragmen- tation phase that produced dense enough clumps to ensure an e\ufb03cient removal of the outer layers of the giants through colli- sions, rendering them invisible to observations. Their degenerate cores would nonetheless populate the same area of phase space where the missing bright giants should be. Kie\ufb00er & Bogdanovi\u00b4 c (2016) recently showed that in order to be viable, this scenario requires the total mass of the fragmenting disc to have been sev- eral orders of magnitude higher than that of the early-type stars in the stellar discs in the GC. Owing to the extreme extinction and source crowding to- wards the GC, observational studies are complex, even with the power of AO assisted 10m class telescopes. In particular, the spectroscopic identi\ufb01cation of stars is limited to bright giants and massive young stars, while the crowding makes it almost impossible to detect main-sequence stars lower than two solar masses. Gallego Cano et al. (2017) and Sch\u00f6del et al. (2017) have revisited the observational data with improved methods. On the one hand, they were able to push the completeness of the star counts one magnitude deeper than in previous studies. This means that not only bright giants down to the Red Clump (RC), but also fainter giants and sub-giants are included in the star counts. Thus we now have access to two stellar tracer pop- ulations, with di\ufb00erent luminosities but similar masses, that can provide us with information on the structure of the nuclear star cluster (NSC). Furthermore, the authors also succeeded in de- riving the surface brightness pro\ufb01le of the di\ufb00use stellar light, which traces even fainter stars, probably sub-giants and main- sequence stars of \u22721.5 M \u2299. The two new analyses provide fully consistent results. The spatial stellar density can be described by a power law with exponents between \u03b31.15 to 1.40 inside 0.5 pc for three di\ufb00erent tracers: resolved giant and sub-giant stars in the magnitude ranges 12.5 \u2264Ks \u226416.0 and 17.5 \u2264Ks \u226418.5 and the di\ufb00use light, which is created mainly by sub-giants and main-sequence stars. After combining the data on the central 1- 2 pc with other measurements of the stellar distribution on scales 2-10 pc, the authors de-projected the surface density and deter- mined a 3D power-law index \u03b3 between 1.15 to 1.40. For RC stars and brighter giants, Sch\u00f6del et al. (2017) reproduced the \ufb01ndings of previous work, that is, a \ufb02attening of the stellar den- sity distribution in the innermost 0.1 to 0.3 pc. The authors con- cluded that outside of this projected radius, the distribution of these stars is consistent with a stellar cusp, but that some process has probably altered the giant star distributions at smaller radii. The masses of all tracer populations are very similar, be- tween 1 \u22122 M\u2299. These stars can live for several Gyr and thus be old enough to be dynamically relaxed. If the faint stars and di\ufb00use stellar light at the GC indeed trace an underlying old stel- lar population (of age \u223c109 to \u223c1010 years), then the stellar cusp is surprisingly shallow. Here it becomes important to look at the theory in more detail. The steep power-law cusp solution found by Bahcall & Wolf (1976) only holds for a single-mass stellar population. If stars follow a distribution of masses, mass segregation causes stars of di\ufb00erent masses to follow di\ufb00erent density distributions with more massive components that have steeper central slopes (Bahcall & Wolf 1977; Baumgardt et al. 2004; Amaro-Seoane et al. 2004; Freitag et al. 2006). In partic- ular, Alexander & Hopman (2009) and Preto & Amaro-Seoane (2010a) independently derived the so-called \u201cstrong-mass seg- regation\u201d solution for two stellar mass groups, which is more e\ufb03cient than the solution expected from the theory of Bahcall & Wolf (1977), which is mathematically correct but physically inappropriate because of the number fractions they used. Baumgardt et al. (2005) showed that in globular clusters con- taining intermediate-mass black holes, the surface density dis- tribution of luminous stars can be described by a weak power- law cusp distribution, o\ufb00ering a new way to explain the missing- mass problem seen in the GC. However, their results cannot be directly applied to it, since in their simulations all stars formed at the same time, which is a valid assumption for a globular clus- ter, but not for the nuclear cluster at the centre of the Milky Way, where stars have formed continuously over a Hubble time (Pfuhl et al. 2011). In addition, while the GC has a relaxation time of the same order as its age, the star clusters in their simulations were simulated for about ten relaxation times. In this paper we present results of direct N-body simula- tions aimed at studying the dynamics of the nuclear cluster in the Milky Way. In our simulations, we evolve a star cluster sur- rounding a central massive black hole over a Hubble time under the combined in\ufb02uence of two-body relaxation and continuous star formation. Our paper is organised as follows: In section 2 we discuss our simulations and in section 3 we compare the re- sulting distribution of stars with observations of the nuclear star cluster in the Galactic centre. Section 4 presents our conclusions."
                },
                {
                    "url": "http://arxiv.org/abs/1609.08794v1",
                    "title": "N-body modeling of globular clusters: Masses, mass-to-light ratios and intermediate-mass black holes",
                    "abstract": "We have determined the masses and mass-to-light ratios of 50 Galactic\nglobular clusters by comparing their velocity dispersion and surface brightness\nprofiles against a large grid of 900 N-body simulations of star clusters of\nvarying initial concentration, size and central black hole mass fraction. Our\nmodels follow the evolution of the clusters under the combined effects of\nstellar evolution and two-body relaxation allowing us to take the effects of\nmass segregation and energy equipartition between stars self-consistently into\naccount. For a subset of 16 well observed clusters we also derive their\nkinematic distances. We find an average mass-to-light ratio of Galactic\nglobular clusters of $<M/L_V>=1.98 \\pm 0.03$, which agrees very well with the\nexpected M/L ratio if the initial mass function of the clusters was a standard\nKroupa or Chabrier mass function. We do not find evidence for a decrease of the\naverage mass-to-light ratio with metallicity. The surface brightness and\nvelocity dispersion profiles of most globular clusters are incompatible with\nthe presence of intermediate-mass black holes (IMBHs) with more than a few\nthousand $M_\\odot$ in them. The only clear exception is $\\omega$ Cen, where the\nvelocity dispersion profile provides strong evidence for the presence of a\n$\\sim$40,000 $M_\\odot$ IMBH in the centre of the cluster.",
                    "authors": "Holger Baumgardt",
                    "published": "2016-09-28",
                    "updated": "2016-09-28",
                    "primary_cat": "astro-ph.GA",
                    "cats": [
                        "astro-ph.GA"
                    ],
                    "main_content": "In total we calculated a grid of \u223c900 N-body simulations, varying the initial density profile, half-mass radius rh, cluster metallicity [Fe/H] and the mass fraction MBH/MGC of a central IMBH between the different simulations. Our clusters did not contain primordial binaries, however binaries could form dynamically during the simulations. All simulations were made using the GPU-enabled version of the collisional N-body code NBODY6 (Aarseth 1999; Nitadori & Aarseth 2012). Clusters without IMBHs and clusters with IMBH mass fractions of MBH/MGC = 0.01 and MBH/MGC = 0.02 started with N = 100, 000 stars, while clusters with an IMBH mass fraction of MBH/MGC = 0.005 were run with N = 200, 000 stars initially. In total we performed 720 simulations with N = 100, 000 stars and 48 simulations with N = 200, 000 stars. We also performed test simulations with N = 50, 000 stars to test the dependency of our results on the initial number of cluster stars, but found that the initial particle number has a negligible influence on the results. The initial density profiles of our clusters were given by King (1962) models with initial dimensionless central concentrations c = log rc/rt of c =0.2, 0.5, 1.0, 1.5, 2.0 and 2.5 respectively. We also simulated clusters starting with King (1966) density profiles, but found that these led to clusters with a too small variation in the final density profile which cannot fit observed surface density profiles for a significant fraction of globular clusters. Initial cluster models were set up using the method described in ?, by first deprojecting the density profile, then calculating the distribution function f(E) and finally choosing particle positions and velocities. We used 8 grid points for the initial half-mass radius rh given by rh = 2, 3, 5, 7, 10, 15, 25 and 35 pc for the N = 50, 000 star clusters. For the N = 100, 000 and N = 200, 000 star clusters, the initial half-mass radii were reduced by factors of 0.836 and 0.696 respectively so that these clusters have the same initial relaxation time than the corresponding N = 50, 000 star models. For each value of rh and c we ran three simulations starting from different random number seeds to increase the statistical significance of our results. Stellar evolution was modeled according to the stellar evolution routines of Hurley, Pols & Tout (2000), assuming black hole and neutron star retention fractions of 10%. All clusters started with stars distributed according to a Kroupa (2001) mass function with lower and upper mass limits of 0.1 M\u2299and 100 M\u2299respectively. For clusters without IMBHs, we ran simulations at three different metallicities given by [Fe/H]=-1.8, -1.3 and -0.7 respectively. For the later comparison with observed clusters we always use those clusters from our grid that are closest in metallicity to the metallicity of the observed clusters. This should be accurate enough since metallicity dependent effects on the internal cluster evolution are largely removed due to our scaling procedure described below so that the influence of cluster metallicity on our results (e.g. cluster mass) is small. Simulations were run up to an age of T = 13.5 Gyrs, and we stored data spaced by T = 50 Myrs for all times between T = 10.5 and T = 13.5 Gyr. In order to compare our grid of simulations to observed clusters, we combined 10 snapshots spanning a T = 500 Myr time span centered around the age of each cluster. Since we ran three different realizations for each grid point, our final models after combining the individual snapshots contained roughly 3 \u00b7 106 stars per grid point, which is larger than the actual number of stars in most observed clusters. For [Fe/H]=-1.3 we also ran simulations with central IMBHs, choosing the IMBH masses such that the mass ratio of the IMBH to the total cluster mass at the end of our simulations (T = 13.5 Gyr) was equal to MIMBH/MGC=0.005, 0.01 and 0.02 respectively. The initial concentrations and half-mass radii of these models were varied in the same way as for the no-IMBH models described above. All clusters in this paper were isolated, however we plan to add external tidal fields in subsequent papers when we compare the internal mass function of stars at different radii with observations. Since our simulations contain fewer stars than the acN-body models of GCs: Masses, M/L ratios and IMBHs 3 tual globular clusters and have di\ufb00erent half-mass radii at the end of the simulations, we need to scale our simulations to match the masses and sizes of observed globular clusters. Our scaling procedure is the same as that used by Baumgardt et al. (2003b) who \ufb01tted the massive globular cluster G1 in M31 by a set of N-body simulations, and Jalali et al. (2012) who \ufb01tted \u03c9 Cen by a set of N-body models. The basic assumption of the scaling is that since the simulated star clusters are isolated, they evolve only due to stellar evolution and two-body relaxation. Hence the simulations can be scaled to star clusters of di\ufb00erent mass or radius as long as the scaling is done in such a way that the overall relaxation time remains constant. Using the de\ufb01nition of the half-mass relaxation time given by Spitzer (1987), this implies rNB rGC = \u0010 MGC MNB \u00111/3 \u0012 ln\u03b3NNB ln\u03b3NGC \u00132/3 (1) where M is the mass of a cluster, r its half-mass radius, N = M/ < m > the number of cluster stars, and the subscripts NB and GC refer respectively to a star cluster from our grid of N-body simulations and an observed globular cluster that we want to model. \u03b3 is a constant in the Coulomb logarithm which we assume to be equal to 0.11 (Giersz & Heggie 1994). We determine the projected half-light radius of a globular cluster by integrating the observed surface density pro\ufb01le up to the outermost radius for which data is available. For each simulated cluster, we then determine iteratively the scaling factor fr = rNB/rGC that is necessary so that the cluster from the N-body simulation has the same projected half-light radius inside the same limiting radius as the observed globular cluster if put at the same distance as the observed globular cluster. For the calculation of the surface brightness pro\ufb01les of the simulated clusters, we converted the bolometric luminosities of NBODY6 to V -band luminosities using the conversion formulae given by Eggleton, Fitchett & Tout (1989). After determining the radial scaling factor fr, we determine the corresponding mass scaling factor from eq. 1 and then multiply the velocities of the stars in the N-body simulation by a factor fv = \u0010rNB rGC \u00111/2 \u0010 MGC MNB \u00111/2 , (2) where the \ufb01rst term on the right-hand side is due to the change in radius and the second term is due to the change in cluster mass. After scaling the velocities, we calculate the surface density, and line-of-sight and proper motion velocity dispersion pro\ufb01les for the simulated clusters. In order to improve the statistical signi\ufb01cance of our results in the cluster centers, we use the in\ufb01nite projection method of Mashchenko & Sills (2005) when calculating surface density and velocity dispersion pro\ufb01les. For the velocity dispersion pro\ufb01les we mimic the magnitude limits of the observations by using only stars brighter than the main-sequence turno\ufb00to determine the line-of-sight velocity dispersion pro\ufb01le. To compare with the proper motion data of Watkins et al. (2015a) we use all stars brighter than 1 mag below the turno\ufb00magnitude. The resulting velocity dispersion pro\ufb01les di\ufb00er due to mass segregation, however the di\ufb00erences are typically less than 5%. In order to increase the number of models that can be compared with each globular cluster, we assume that the Figure 1. Location of the best-\ufb01tting no-IMBH model for each globular cluster within the simulated grid of models. Individual globular clusters are marked by their NGC numbers. Small halfmass radii imply small initial relaxation times and therefore dynamically more advanced globular clusters. Most globular clusters can be \ufb01tted by models starting from initial half-mass radii between 3 to 7 pc corresponding to initial relaxation times between 0.5 to 2 Gyr. properties of the \ufb01nal cluster change linearly with the initial concentration c, the logarithm of the initial half-mass radius log rh and the IMBH mass fraction MBH/MGC and interpolate between our grid points. In total we use 300 interpolation values for each grid dimension and determine the best-\ufb01tting model to the observed surface brightness and velocity dispersion pro\ufb01le by means of a \u03c72 test. Fig. 1 shows the location of the best-\ufb01tting no-IMBH model for each globular cluster within the simulated grid of models. In this \ufb01gure a small initial half-mass radius rh implies a small initial relaxation time and therefore a more dynamically advanced globular cluster. It does not necessarily imply that a cluster actually started with a small half-mass radius, although relaxation time and half-mass radius are correlated with each other. Most clusters can be \ufb01tted with clusters starting with half-mass radii around 5 pc, implying initial relaxation times of TRH \u22481 Gyr. The best-\ufb01tting models of most globular clusters are located within our grid boundaries, however for nine globular clusters we need models with the lowest modeled King concentration parameter of c = 0.2 to \ufb01t their surface density pro\ufb01les. A look at Figs. 9 to 21 shows that we nevertheless usually obtain very good \ufb01ts to their surface density and velocity dispersion pro\ufb01les, so the low initial concentrations are not of immediate concern. They might however be an indication that either the surface density pro\ufb01les of these clusters are in\ufb02uenced by the tidal \ufb01eld of the Milky Way or ongoing mass loss, processes which are not included in our simulations. Indeed most of these clusters have small galactocentric radii (RG < 5 kpc) where tidal e\ufb00ects should be most important. Alternatively, a compact cluster of stellar mass black holes might prevent 4 Baumgardt the cores of these clusters from collapsing (Morscher et al. 2013; L\u00a8 utzgendorf, Baumgardt & Kruijssen 2013). Indeed, this possibility has been suggested by Mackey et al. (2007) to explain the large core radii of young star clusters in the LMC and more recently by Peuten et al. (2016) to explain the absence of mass segregation in NGC 6101. Additional simulations will be necessary to distinguish between these possibilities. 2.1 Validation In order to test how well our \ufb01tting method can reproduce star cluster masses from their surface density and velocity dispersion pro\ufb01les we apply our models to the N-body simulations uf13 and uf14 from Lamers, Baumgardt & Gieles (2013) and models D1 and D2 from the DRAGON simulation (Wang et al. 2016a). We use four snapshots of simulations uf13 and uf14 between T = 11.5 and T = 12.5 Gyr and one snapshot of models D1 and D2 at T = 12 Gyr and calculate the surface density and velocity dispersion pro\ufb01le using all stars that are still bound to the clusters at these times. We then apply our \ufb01tting method to the four clusters. Fig. 2 compares the derived masses with the true masses of the simulated clusters (red circles). By the time the snapshots are created, the simulated clusters have lost between 12% to 75% of their initial mass and for some of the clusters the mass function has already evolved signi\ufb01cantly away from a Kroupa mass function. Nevertheless our \ufb01tting method reproduces the cluster masses to within 10%. It performs slightly better for the dynamically less evolved clusters of the DRAGON simulation and less well for the highly evolved clusters from Lamers, Baumgardt & Gieles (2013). As a second check, we compare results of our \ufb01tting method with the results of Monte-Carlo simulations aimed to reproduce the luminosity and velocity dispersion pro\ufb01les and the luminosity function of stars in a number of globular clusters. The Monte Carlo results were published by Giersz & Heggie (2011) (for NGC 104), Heggie & Giersz (2008) (NGC 6121), Giersz & Heggie (2009) (NGC6397) and Heggie & Giersz (2014) (NGC 6656). For all clusters we adopt the same distances as assumed by Giersz & Heggie and use only the velocity dispersion data which Giersz & Heggie used for each cluster. Fig. 2 compares the masses which we derive from N-body models with those found in the Monte-Carlo simulations. We can reproduce the masses from the Monte-Carlo simulations to within \u223c20%. The deviations are again larger for the dynamically more evolved clusters NGC 6121 and NGC 6397 and better for the more massive clusters NGC 104 and NGC 6656. The reason for the larger deviation of the Monte Carlo models compared to the N-body simulations is probably the small number of radial velocity data points of the observed clusters, which leave large freedom in the mass pro\ufb01les and total cluster masses. We conclude that our models can reproduce cluster masses to within 10% for clusters that have a well determined radial velocity dispersion pro\ufb01le. Better mass estimates will probably require knowledge of the internal mass function of the cluster stars in addition to the clusters\u2019 velocity dispersion and surface density pro\ufb01le. Figure 2. Comparison of the masses derived from our grid of Nbody simulations with the true masses of star clusters in N-body simulations (red circles) and the masses of Galactic globular clusters derived by \ufb01tting results of Monte-Carlo simulations (blue crosses). Our mass estimates reproduce the true masses of star clusters in N-body simulations to within 10% and are within 20% of the masses of Galactic globular clusters derived from MonteCarlo simulations. 3 GLOBULAR CLUSTER DATA We \ufb01rst determined the radial velocity dispersion pro\ufb01les of Galactic globular clusters from individual radial velocity measurements of their member stars published in the literature. To this end, we searched the astronomical literature for published radial velocity measurements, excluding small data sets with less than \u224820 stars. In total we found 95 publications containing about 25500 individual radial velocities of stars in 45 clusters. About one third of the radial velocity measurements were from the three, recent large-scale surveys of Lane et al. (2011), Lardo et al. (2015) and Kimmig et al. (2015), which each contain radial velocity information for several thousand stars. The rest of the data comes from smaller data sets. For nine globular clusters we also included radial velocities from the APOGEE survey (Majewski et al. 2015), which has measured abundances and radial velocities for over 150,000 red giants, including several hundred stars in globular clusters. Information on the papers used as input for calculating the radial velocity dispersion pro\ufb01les can be found in Table 31. For each individual set of radial velocities, we \ufb01rst calculated the average cluster velocity using the method of Pryor & Meylan (1993) and using all stars which roughly fall within the radial velocity range of the cluster. We then subtracted the average cluster velocity from the individual measurements and merged all radial velocity data sets into a master catalogue for each cluster, containing the positions, radial velocities and radial velocity errors of all stars. We 1 The radial velocity dispersion pro\ufb01les can be downloaded from https://people.smp.uq.edu.au/HolgerBaumgardt/globular/ N-body models of GCs: Masses, M/L ratios and IMBHs 5 Table 1. Input parameters for the studied globular clusters. The sources for the distances are: F99: Ferraro et al. (1999), V07: Valenti, Ferraro & Origlia (2007), D11: Di Criscienzo et al. (2011), Z98: Zinn & Barnes (1998), H96: Harris (1996, 2010 edition), tw: This work Name Alt. V \u2206V Age Dist. Dist. name [mag] [mag] [Gyr] [kpc] Source NGC 104 47 Tuc 4.07 0.11 11.75 3.95 tw NGC 288 8.16 0.07 11.50 8.80 tw NGC 362 6.55 0.16 10.75 8.85 tw NGC 1851 7.24 0.09 11.00 10.40 tw NGC 1904 M 79 7.99 0.19 11.70 13.27 F99 NGC 2419 10.48 0.15 12.75 87.50 D11 NGC 2808 6.33 0.09 11.00 9.50 tw NGC 3201 6.88 0.20 11.50 4.90 F99 NGC 4147 10.38 0.11 12.25 18.20 F99 NGC 4372 7.23 0.01 12.00 6.30 F99 NGC 4590 M 68 8.15 0.22 12.00 10.59 F99 NGC 4833 6.91 0.20 12.50 6.76 F99 NGC 5024 M 53 7.71 0.10 12.25 17.90 H96 NGC 5053 7.71 0.10 12.25 17.20 F99 NGC 5139 \u03c9 Cen 3.53 0.11 12.00 5.00 tw NGC 5272 M 3 6.40 0.16 11.75 10.06 F99 NGC 5286 7.20 0.12 12.50 11.70 H96 NGC 5466 9.46 0.30 12.50 16.90 F99 NGC 5694 10.02 0.14 12.75 37.33 F99 NGC 5824 8.83 0.19 13.00 31.80 F99 NGC 5904 M 5 5.83 0.16 11.50 6.40 tw NGC 5927 7.74 0.39 10.75 8.00 tw NGC 6093 M 80 7.35 0.13 11.40 9.73 F99 NGC 6121 M 4 5.63 0.09 11.50 2.14 F99 NGC 6139 8.95 0.13 12.00 10.40 Z98 NGC 6171 M 107 8.18 0.31 12.00 6.09 F99 NGC 6205 M 13 5.80 0.10 12.00 7.60 F99 NGC 6218 M 12 6.92 0.28 13.00 5.22 F99 NGC 6254 M 10 6.42 0.38 11.75 4.71 F99 NGC 6266 M 62 6.45 0.12 11.40 6.55 tw NGC 6273 M 19 6.80 0.05 12.75 8.24 V07 NGC 6341 M 92 6.51 0.06 12.75 8.10 tw NGC 6362 7.67 0.10 12.50 7.60 H96 NGC 6388 6.76 0.13 11.75 11.00 tw NGC 6397 5.77 0.18 13.00 2.40 tw NGC 6402 M 14 7.66 0.08 11.50 9.30 H96 NGC 6441 7.16 0.11 11.00 13.49 V07 NGC 6535 11.14 0.57 12.75 7.28 H96 NGC 6624 7.78 0.13 11.25 8.43 V07 NGC 6656 M 22 5.07 0.07 12.50 2.66 tw NGC 6681 M 70 7.98 0.15 12.75 9.89 F99 NGC 6715 M 54 7.47 0.10 11.75 23.50 tw NGC 6723 7.11 0.17 12.50 8.20 V07 NGC 6752 5.52 0.17 12.50 3.90 tw NGC 6809 M 55 6.63 0.24 13.00 5.75 F99 NGC 6838 M 71 7.84 0.49 11.00 3.86 F99 NGC 7078 M 15 6.13 0.10 12.75 9.90 tw NGC 7089 M 2 6.43 0.03 11.75 11.50 H96 NGC 7099 M 30 7.25 0.24 13.00 8.67 F99 Terzan 8 12.11 0.32 13.00 26.73 F99 then use the stellar positions to identify stars with multiple measurements and calculate a weighted mean radial velocity and corresponding error for each star with multiple measurements. Stars for which the individual radial velocity measurements show a too strong deviation from the mean were rejected as binaries. After removing binary stars, we put the stars into radial bins and calculated the radial velocity dispersion \u03c3bin by determining the maximum of the likelihood function log L = \u22121 2 N X i=1 ln \u0000\u03c32 bin + e2 i \u0001 + N X i=1 v2 i \u03c32 bin + e2 i . (3) based on all stars in a bin. Here vi and ei are the radial velocity and its respective error of each individual star. The 1\u03c3 lower and upper uncertainties of the velocity dispersion were calculated by determining the velocity dispersion where the likelihood is less than 0.5 the maximum value in each direction. After the velocity dispersion of a radial bin was determined, we calculated the deviation of each star from the cluster mean according to \u03c72 = v2 i \u03c32 + e2 i (4) and rejected all stars as binaries or background stars that deviated more than three standard deviations from the mean. We repeated the above procedure for each bin until we found a stable value for the velocity dispersion and the list of member stars. Depending on the number of radial velocity measurements available for a cluster, we used between 20 to 250 stars per bin to calculate the radial velocity dispersion. In order to calculate the radial velocity dispersion pro\ufb01le, we used the positions determined by Goldsbury, Heyl & Richer (2013) as cluster centers, except for NGC 1904, NGC 5694, NGC 5824 and NGC 6266 where we used the centers determined by L\u00a8 utzgendorf et al. (2013). This was necessary in order to get a radial velocity dispersion pro\ufb01le centered on the same position as the IFU data published by L\u00a8 utzgendorf et al. (2013). For clusters that contain a signi\ufb01cant number of stars at large distances from the cluster center, we used proper motions from the PPMXL catalogue (Roeser, Demleitner & Schilbach 2010) to help separate cluster members from non-members. PPMXL data was only used to separate members from non-members for stars more than a few hundred arcsec away from the cluster center since for stars closer to the center PPMXL proper motions were either not available or were found to be unreliable, presumably due to the strong crowding of stars towards the cluster centers. In addition to radial velocity dispersion data, we also used velocity dispersion data based on individual stellar proper motions to constrain the cluster kinematics. Most of the proper motion dispersion pro\ufb01les were taken from Watkins et al. (2015a), who published velocity dispersion pro\ufb01les for 21 clusters. We excluded NGC 7099 since the proper motion dispersion pro\ufb01le from Watkins et al. (2015a) disagrees signi\ufb01cantly from the radial velocity dispersion pro\ufb01le calculated in this paper for any reasonable cluster distance. As discussed by Watkins et al. (2015a) this might be due to the small number of stars which have measured proper motions in this cluster. We \ufb01nally used velocity dispersion measurements based on integral-\ufb01eld unit (IFU) spectroscopy. IFU spectroscopy was available for 9 clusters (NGC 1851, 1904, 2808, 5286, 5694, 5824, 6093, 6266 and NGC 6388). The surface brightness pro\ufb01les were taken mainly from Trager, King & Djorgovski (1995). If available for a cluster, we replaced the Trager et al. pro\ufb01le in the 6 Baumgardt cluster center with HST surface brightness pro\ufb01les published by Noyola & Gebhardt (2006). For a few clusters we took the surface density pro\ufb01les from other literature sources. These cases are listed in Tab. 3 in the Appendix. For NGC 5927 the surface density pro\ufb01le calculated by Trager, King & Djorgovski (1995) has a bump in the center that is impossible to reproduce by our modeling. Since no other cluster shows such a feature, the surface density pro\ufb01le might be in\ufb02uenced by a few bright stars in the center. We therefore calculated a surface brightness pro\ufb01le based on the number counts of bright stars published by the ACS Survey of Galactic Globular Clusters (Sarajedini et al. 2007). The same was done for NGC 4833 where we combined data published by Melbourne et al. (2000) with the ACS data to calculate the surface density pro\ufb01le. 16 clusters from our list have accurate proper motion dispersion pro\ufb01les and also accurate enough radial velocity dispersion pro\ufb01les so that their distances can be determined by \u03c72 minimization of a simultaneous \ufb01t of our models to both pro\ufb01les. From the \ufb01ts we are able to measure their distances to an accuracy of between 50 to 450 pc and the distances are given in Table 2. For the remaining clusters, the distances were taken mainly from Ferraro et al. (1999), who determined globular cluster distance moduli by CMD \ufb01tting. For clusters not studied by Ferraro et al. (1999), we took the distances from recent literature values. The adopted distances are listed in Table 1 together with the cluster ages and the calculated V -band magnitudes. The apparent V -band magnitudes and errors are calculated by taking the average of the apparent magnitudes given in Harris (1996), McLaughlin & van der Marel (2005), Dalessandro et al. (2012) and the integrated magnitudes determined in this work from the \ufb01t of our models to the surface brightness pro\ufb01les. Cluster ages were taken from VandenBerg et al. (2013), or, if not available, from literature data. We \ufb01nally took the cluster metallicities from the recent compilation by Carretta et al. (2009a) and the cluster reddenings from Harris (1996). 4 RESULTS Figs. 9 to 21 compare our best-\ufb01tting pro\ufb01les with the observed velocity dispersion and surface density pro\ufb01les of globular clusters. Except for \u03c9 Cen and NGC 6715 all pro\ufb01les shown are the no-IMBH models. As can be seen we usually obtain very good \ufb01ts to the observed pro\ufb01les. The surface brightness pro\ufb01les of our best-\ufb01tting clusters are generally within 20% of the observed surface brightness, despite the fact that the observed surface brightness pro\ufb01les vary by up to 6 orders of magnitude in some clusters. Only beyond several hundred arcsec, some clusters show larger di\ufb00erences in their surface density pro\ufb01les. This could be due to the in\ufb02uence of the Galactic tidal \ufb01eld which was not taken into account in our simulations, but might also be a result of observational uncertainties since a few hundred arcsec from the cluster center the surface density of many globular clusters is already signi\ufb01cantly below the background density of stars, making the determination of the outer surface density pro\ufb01les uncertain. The di\ufb00erences with the measured velocity dispersion pro\ufb01les are also usually less than 1 km/sec and for most clusters within the observational uncertainties. The Table 2. Derived parameters of the studied globular clusters Name \u03c72 red Mass M/L ratio Distance [M\u2299] [pc] NGC 104 2.01 7.00 \u00b1 0.06 \u00b7 105 1.99 \u00b1 0.20 3950 \u00b1 50 NGC 288 1.43 8.76 \u00b1 0.26 \u00b7 104 2.23 \u00b1 0.15 8800 \u00b1 400 NGC 362 0.76 3.21 \u00b1 0.06 \u00b7 105 1.73 \u00b1 0.26 8850 \u00b1 300 NGC 1851 1.81 2.99 \u00b1 0.05 \u00b7 105 2.40 \u00b1 0.20 10400 \u00b1 200 NGC 1904 1.95 2.20 \u00b1 0.18 \u00b7 105 2.23 \u00b1 0.43 NGC 2419 2.60 8.15 \u00b1 1.19 \u00b7 105 1.54 \u00b1 0.22 NGC 2808 2.13 8.29 \u00b1 0.06 \u00b7 105 1.96 \u00b1 0.16 9500 \u00b1 150 NGC 3201 1.51 1.58 \u00b1 0.11 \u00b7 105 2.20 \u00b1 0.43 NGC 4147 1.60 5.32 \u00b1 1.71 \u00b7 104 2.45 \u00b1 0.32 NGC 4372 0.32 2.20 \u00b1 0.25 \u00b7 105 1.67 \u00b1 0.19 NGC 4590 0.95 8.45 \u00b1 1.71 \u00b7 104 1.39 \u00b1 0.65 NGC 4833 0.74 2.66 \u00b1 0.39 \u00b7 105 1.59 \u00b1 0.33 NGC 5024 0.61 3.83 \u00b1 0.51 \u00b7 105 1.60 \u00b1 0.84 NGC 5053 0.54 5.37 \u00b1 1.32 \u00b7 104 1.58 \u00b1 0.54 NGC 5139 2.56 2.95 \u00b1 0.02 \u00b7 106 2.54 \u00b1 0.26 5000 \u00b1 50 NGC 5272 1.85 5.00 \u00b1 0.43 \u00b7 105 1.98 \u00b1 0.37 NGC 5286 1.09 4.61 \u00b1 0.23 \u00b7 105 1.51 \u00b1 0.18 NGC 5466 0.92 6.43 \u00b1 1.47 \u00b7 104 1.60 \u00b1 0.56 NGC 5694 0.97 4.22 \u00b1 0.45 \u00b7 105 2.79 \u00b1 0.42 NGC 5824 0.32 8.28 \u00b1 0.55 \u00b7 105 2.25 \u00b1 0.42 NGC 5904 1.08 3.08 \u00b1 0.04 \u00b7 105 1.74 \u00b1 0.26 6400 \u00b1 200 NGC 5927 1.96 3.45 \u00b1 0.03 \u00b7 105 2.19 \u00b1 0.42 8000 \u00b1 400 NGC 6093 1.46 3.37 \u00b1 0.16 \u00b7 105 2.18 \u00b1 0.28 NGC 6121 0.89 1.01 \u00b1 0.03 \u00b7 105 1.70 \u00b1 0.15 NGC 6139 0.55 5.31 \u00b1 1.22 \u00b7 105 2.59 \u00b1 0.61 NGC 6171 0.96 9.62 \u00b1 1.04 \u00b7 104 2.22 \u00b1 0.69 NGC 6205 2.03 5.00 \u00b1 0.42 \u00b7 105 2.06 \u00b1 0.33 NGC 6218 0.70 1.03 \u00b1 0.12 \u00b7 105 1.51 \u00b1 0.40 NGC 6254 1.05 2.26 \u00b1 0.29 \u00b7 105 1.99 \u00b1 0.72 NGC 6266 1.58 9.31 \u00b1 0.09 \u00b7 105 2.54 \u00b1 0.28 6550 \u00b1 140 NGC 6273 0.08 9.21 \u00b1 1.62 \u00b7 105 2.83 \u00b1 0.45 NGC 6341 0.74 3.05 \u00b1 0.04 \u00b7 105 2.06 \u00b1 0.12 8100 \u00b1 150 NGC 6362 1.26 1.44 \u00b1 0.05 \u00b7 105 2.64 \u00b1 0.26 NGC 6388 1.11 1.24 \u00b1 0.01 \u00b7 106 2.11 \u00b1 0.26 11000 \u00b1 450 NGC 6397 1.09 9.40 \u00b1 0.32 \u00b7 104 2.33 \u00b1 0.39 2400 \u00b1 60 NGC 6402 1.43 7.63 \u00b1 1.19 \u00b7 105 2.17 \u00b1 0.37 NGC 6441 1.55 1.86 \u00b1 0.02 \u00b7 106 2.30 \u00b1 0.24 NGC 6535 2.28 5.96 \u00b1 0.59 \u00b7 104 14.29 \u00b1 7.93 NGC 6624 1.70 2.42 \u00b1 0.07 \u00b7 105 2.33 \u00b1 0.29 NGC 6656 0.93 3.21 \u00b1 0.04 \u00b7 105 2.15 \u00b1 0.14 2660 \u00b1 100 NGC 6681 1.31 1.72 \u00b1 0.04 \u00b7 105 2.62 \u00b1 0.36 NGC 6715 5.07 1.62 \u00b1 0.03 \u00b7 106 2.18 \u00b1 0.20 23500 \u00b1 300 NGC 6723 0.26 1.96 \u00b1 0.40 \u00b7 105 2.06 \u00b1 0.41 NGC 6752 0.71 2.34 \u00b1 0.04 \u00b7 105 2.60 \u00b1 0.41 3900 \u00b1 100 NGC 6809 3.34 1.78 \u00b1 0.15 \u00b7 105 2.25 \u00b1 0.52 NGC 6838 1.43 4.60 \u00b1 0.61 \u00b7 104 2.43 \u00b1 1.18 NGC 7078 1.72 5.01 \u00b1 0.06 \u00b7 105 1.27 \u00b1 0.12 9900 \u00b1 200 NGC 7089 0.46 7.64 \u00b1 0.51 \u00b7 105 2.13 \u00b1 0.15 NGC 7099 0.58 1.21 \u00b1 0.10 \u00b7 105 1.37 \u00b1 0.32 Terzan 8 0.49 5.37 \u00b1 2.34 \u00b7 104 4.36 \u00b1 2.96 only clusters which cannot be well modeled by the no-IMBH models are \u03c9 Cen and M54 (NGC 6715). For these clusters the observed velocity dispersion pro\ufb01le is signi\ufb01cantly above our predictions in the center and below in the outer parts. This could be due to an unseen mass concentration in the center and we will discuss these clusters in greater detail in sec. 4.1 when we investigate the possible presence of IMBHs in globular clusters. Fig. 3 depicts the V-band mass-to-light ratio pro\ufb01les which we derive from our \ufb01ts. The average mass-to-light raN-body models of GCs: Masses, M/L ratios and IMBHs 7 Figure 3. Local V band mass-to-light ratios as a function of the distance to the cluster center expressed in units of the halfmass radius. The average M/L ratio of all 50 clusters is shown by a solid line. Dark blue and light blue shaded regions mark the values of the M/L ratio which contain 68% and 95% of all clusters. The M/L ratio pro\ufb01les of the clusters follow a U-shaped curve due to mass segregation, which concentrates high-mass compact remnants and giant stars in the cluster center and pushes lowmass main sequence stars towards the cluster outskirts. tio of all 50 clusters as a function of distance to the cluster center is shown by a solid line and the regions in M/L ratio that contain 68% and 95% of all clusters are shown by dark and light blue areas respectively. In order to better compare individual clusters, we have divided the distances to the cluster centers by the half-mass radius of each cluster. It can be seen that the M/L ratios have a minimum between 0.1 to 0.2 half-mass radii. This minimum is due to the mass segregation of giant stars and high-mass main sequence stars towards the cluster center. Since giant stars dominate the cluster light but contain only a small fraction of the cluster mass, the M/L ratio decreases in the center. Inside of 0.1 half-mass radii the M/L ratios rise again since compact remnants like high-mass white dwarfs, neutron stars and black holes have masses even higher than the giant stars and are therefore more strongly concentrated towards the cluster center. The M/L ratios also increase towards the outer cluster parts since low-mass main sequence stars are pushed out of the cluster due to mass segregation. We also \ufb01nd that the importance of mass segregation depends on the relaxation time of a cluster. In clusters with very large relaxation times like NGC 2419, the M/L ratio changes by less than 30% between the center and the cluster halo. In contrast, for strongly mass segregated clusters the variation of the M/L ratio can reach a factor of 4 between the core region and the cluster outskirts. This agrees with recent results of Monte Carlo simulations by Bianchini et al. (2016), who found that the amount of mass segregation tightly correlates with the dynamical state of the cluster. Table 2 presents a summary of our results. It gives the name of the cluster, the reduced \u03c72 value from \ufb01tting the velocity dispersion and surface brightness pro\ufb01les, the derived cluster mass and its error, the global M/L ratio and its error, and the best-\ufb01tting cluster distance and its error for those clusters where we derived cluster distances ourselves. Errors in the M/L ratio were calculated from the errors in cluster mass and cluster luminosity but do not include uncertainties in the cluster distances. The average V-band M/LV ratio for our whole cluster sample is M/LV = 1.98\u00b10.03 M\u2299/L\u2299 and M/LV = 1.98 \u00b1 0.04 M\u2299/L\u2299if we restrict ourselves to clusters that have more than 200 radial velocity measurements and mass-to-light ratios with relative errors less than 30%. If we split the more accurate cluster sample into two sub-samples depending on cluster metallicity, we derive a mean V-band mass-to-light ratio of M/LV = 1.88 \u00b1 0.06 M\u2299/L\u2299for the metal-poor clusters with [Fe/H]< \u22121.5 and M/LV = 2.07 \u00b1 0.06 M\u2299/L\u2299for the metal-rich clusters. This increase of the average mass-to-light ratio with metallicity is in general agreement with predictions from stellar evolution theory. Fig. 4 compares the global M/L ratios derived here with the predictions of stellar evolution models. Shown are predicted M/L ratios from PARSEC (Bressan et al. 2012), \u03b1 enhanced BaSTI (Pietrinferni et al. 2006) and \u03b1 enhanced Dartmouth isochrones (Dotter et al. 2008). The theoretical M/LV values were calculated assuming a Kroupa (2001) IMF with mass limits of 0.1 and 100 M\u2299, the Kalirai et al. (2008) initial-\ufb01nal mass ratio for white dwarfs and a 10% retention fraction of neutron stars and black holes in the clusters. For the PARSEC isochrones, we also calculated M/LV ratios for stars distributed according to a Chabrier (2003) IMF between mass limits of 0.1 and 100 M\u2299. Since the BaSTI isochrones only give luminosities for stars with masses larger than 0.5 M\u2299, we used PARSEC luminosities for less massive stars. For clarity, we show only clusters with more than 200 radial velocity measurements and mass-tolight ratios with relative errors less than 30% in Fig. 4, however the full cluster sample has a very similar distribution. It can be seen that the derived mass-to-light ratios are in general agreement with the PARSEC and BaSTI isochrones, especially at low metallicity. The agreement is less good for the Dartmouth isochrones, however these isochrones have a less detailed treatment of giant star evolution than either the BaSTI or PARSEC isochrones. Since giant stars dominate the cluster light we regard the predictions of the BaSTI or PARSEC isochrones as more reliable. Strader, Caldwell & Seth (2011) found a decrease of the M/L ratio down to about M/LV \u22481 M\u2299/L\u2299for solar metallicity for globular clusters in M31, which they attributed to a systematic change of the IMF with metallicity. We do not see a decrease of the M/L ratio with increasing metallicity. A possible reason could be that Strader, Caldwell & Seth (2011) \ufb01tted single-mass King models to derive the global velocity dispersion from the measured central one. This will produce a bias in the derived masses if clusters are mass segregated. In order to better compare the derived M/L ratios with predictions of stellar evolution models, we depict in Fig. 5 the ratio of the observed M/L ratio \u03a5Obs = M/LV to \u03a5Kroupa, the M/LV ratio predicted by the PARSEC isochrones for clusters with a Kroupa IMF at the measured age of each individual cluster. The average \u03a5Obs/\u03a5Kroupa 8 Baumgardt Figure 4. V band mass-to-light ratios derived in this work as a function of metallicity. Solid lines show the predicted mass-tolight ratios for a Kroupa IMF according to the PARSEC (blue), BaSTI (green), and Dartmouth (red) isochrones for an age of T = 12.5 Gyr. The dashed blue line shows the predicted M/L ratio from the PARSEC isochrones for a Chabrier IMF. Except for the Dartmouth isochrones, our derived M/L ratios agree well with the theoretical predictions for either a Kroupa or Chabrier IMF. ratio for all clusters shown in Fig. 5 is <\u03a5Obs/\u03a5Kroupa >= 0.97 \u00b1 0.03, compatible with unity. In particular the metalpoor clusters have M/L ratios in good agreement with a Kroupa IMF. Kruijssen & Mieske (2009) and Kimmig et al. (2015) found that the dynamical mass-to-light M/L ratios of globular clusters are systematically lower than expected from canonical stellar population models. This was interpreted by Kruijssen & Mieske (2009) as due to ongoing cluster dissolution. We cannot con\ufb01rm their results for the majority of globular clusters. The only clusters which are systematically below unity are the metal-rich clusters with [Fe/H]> \u22121. This could indicate a di\ufb00erent presentday mass function, possible due to either a di\ufb00erent IMF or ongoing dissolution. However we have only \ufb01ve clusters with [Fe/H]> \u22121 in our sample and their \u03a5Obs/\u03a5Kroupa ratios are within the range of values seen for the low-metallicity clusters. It therefore remains an open question if the mass function of the high metallicity clusters is really di\ufb00erent from that of the low-metallicity ones and, if true, where this di\ufb00erence is coming from. 4.1 Intermediate-mass black holes Intermediate-mass black holes (IMBHs) are black holes in the mass range 102 105 M\u2299. They might provide the missing link between stellar mass black holes formed as the endproduct of stellar evolution and the supermassive black holes found in the centers of galaxies. In the last few years, evidence for the existence of IMBHs has been accumulating. Barth et al. (2004) for example found a 105 M\u2299black hole Figure 5. Ratio of the measured M/L ratios to the M/L ratios predicted by the PARSEC isochrones for clusters with a Kroupa IMF at the measured ages of the clusters as a function of cluster metallicity. Blue triangles mark clusters for which the distances were determined in this work. The average \u03a5Obs/\u03a5Kroupa ratio is close to unity, indicating that most clusters have mass functions compatible with a Kroupa IMF. at the center of the Seyfert 1 galaxy POX 52 based on the broadness of the H\u03b2 pro\ufb01le. Farrell et al. (2009) found evidence that the ultraluminous X-ray source in the galaxy ESO243-49 is powered by an accreting black hole with a mass between 102 and 105 M\u2299. The IMBH nature of the accreting black hole was later con\ufb01rmed by Webb et al. (2010) and Servillat et al. (2011). Evidence for the existence of IMBHs in globular clusters is more controversial, mainly due to the fact that a centrally concentrated cluster of compact remnants can produce a rise in the velocity dispersion pro\ufb01le similar to an IMBH. Gerssen et al. (2002) found evidence for the existence of a 4000 M\u2299IMBH in the Galactic globular cluster M15 based on radial velocity measurements of individual stars near the cluster center. However, Baumgardt et al. (2003a) performed N-body simulations of star clusters without IMBHs and found that they could reproduce the radial velocity and surface density pro\ufb01le of M15 without the need for a central IMBH. Noyola et al. (2010) and Jalali et al. (2012) reported evidence for a 50000 M\u2299IMBH in the globular cluster \u03c9 Cen based on VLT-FLAMES integrated spectra of the central parts of the cluster and detailed N-body models. In contrast, van der Marel & Anderson (2010) found that the velocity dispersion increase in the center can be explained by a radially anisotropic velocity dispersion pro\ufb01le and derived a 1\u03c3 upper limit of only 12000 M\u2299for any possible IMBH. L\u00a8 utzgendorf et al. (2011) presented results from ground based VLT/FLAMES spectroscopy in combination with HST data for the globular cluster NGC 6388 and found a very large central velocity dispersion of 25 km/sec in this cluster, which they could only explain by an IMBH N-body models of GCs: Masses, M/L ratios and IMBHs 9 with a mass of 1.7 \u00b1 0.9 \u00b7 104 M\u2299. Lanzoni et al. (2013) and Lapenna et al. (2015) on the other hand obtained VLT FLAMES and KMOS spectra of 52 and 82 giant stars near the cluster center and found a low central velocity dispersion of about 13 km/sec, which limited the mass of any central black hole to less than 2000 M\u2299. In a re-analysis of all existing data, L\u00a8 utzgendorf et al. (2015) found that individual radial velocities in the core of NGC 6388 are systematically biased towards the mean cluster velocity due to the blending of stars as a result of the high central density. By simulating this e\ufb00ect using arti\ufb01cially created IFU data cubes, they con\ufb01rmed their initial high value for the velocity dispersion and derived an IMBH mass of 2.8 \u00b1 0.4 \u00b7 104 M\u2299. IMBH detections were furthermore reported by L\u00a8 utzgendorf et al. (2013) for NGC 1904 (MBH = 3000 \u00b1 1000 M\u2299) and NGC 6266 (MBH = 2000 \u00b1 1000 M\u2299), Feldmeier et al. (2013) for NGC 5286 (MBH = 1500 \u00b1 1000 M\u2299), Ibata et al. (2009) for NGC 6715 (MBH \u22489400 M\u2299) and most recently by Kamann et al. (2016) for NGC 6397 (MBH \u2248600 M\u2299). Figs. 6 and 7 depict the surface density pro\ufb01les of the above mentioned eight clusters and compare the observed pro\ufb01les with the best-\ufb01tting no-IMBH models and the best\ufb01tting IMBH models from our grid of N-body simulations. The best-\ufb01tting IMBH models were obtained by interpolating only among models with IMBHs. Since we calculated models containing IMBHs with masses of 0.5%, 1% and 2% of the \ufb01nal cluster mass, the IMBH models are restricted to IMBH mass fractions between 0.5% to 2% of the cluster mass. In NGC 1904, the best-\ufb01tting IMBH model does signi\ufb01cantly worse than the best-\ufb01tting no-IMBH model, the reduced \u03c72 value for the IMBH model is 2.36 as opposed to 1.12 for the best-\ufb01tting IMBH model. The reason is the poor \ufb01t of the observed surface density pro\ufb01le in the innermost 30 arcsec, for the velocity dispersion data alone both IMBH and no-IMBH model do about equally well. The reason for the bad \ufb01t of the surface density pro\ufb01le is the fact that star clusters with IMBHs have a weak cusp in surface density as a result of mass segregation and energy equipartition (Baumgardt, Makino & Hut 2005). This together with the fact that NGC 1904 has a relatively small relaxation time (T \u22483 Gyrs) means that no IMBH model is able to reproduce the observed surface density pro\ufb01le after a Hubble time, independent of the starting density pro\ufb01le. We conclude that NGC 1904 does not contain an IMBH. A similar problem exists for NGC 6266 (lowest panels of Fig. 6). The problem is even more apparent for NGC 6397 and NGC 7078 (M15), both clusters with very steeply rising central density pro\ufb01les which are in complete disagreement to how IMBH models at the same dynamical age look like (see Fig. 7). In NGC 5286, the IMBH model \ufb01ts the observed pro\ufb01les marginally better than the best-\ufb01tting no-IMBH model. However, since the best-\ufb01tting no-IMBH model has a reduced \u03c72 value near one, the IMBH detection is not significant. This con\ufb01rms the results of Feldmeier et al. (2013). In NGC 6388 the best-\ufb01tting no-IMBH model \ufb01ts the surface density pro\ufb01le better than the best-\ufb01tting IMBH model. Unfortunately the velocity dispersion pro\ufb01le in the central few arcsec is highly controversial in this cluster. If the central velocity dispersion is as low as 13 km/sec as found by Lanzoni et al. (2013) the cluster de\ufb01nitely does not contain an IMBH, while if the velocity dispersion pro\ufb01le is rising as found by L\u00a8 utzgendorf et al. (2015) an IMBH could be present. Interestingly, we have di\ufb03culties reproducing both the low velocity dispersion from Lanzoni et al. (2013) with a no IMBH model as well as the high velocity dispersion found by L\u00a8 utzgendorf et al. (2015) with our best-\ufb01tting IMBH model, which could be an indication that both values are biased to too low/high values. A \ufb01nal decision on whether an IMBH is present in NGC 6388 or not can only be made once the velocity dispersion pro\ufb01le in the center of the cluster is known. The cluster with the strongest evidence for an IMBH is \u03c9 Cen. Our best-\ufb01tting no-IMBH model provides a very poor \ufb01t to the velocity dispersion pro\ufb01le. It has a reduced \u03c72 r value of 2.72, the second highest \u03c72 r value of all clusters in our sample after NGC 6715. An unsegregated, isotropic star cluster without an IMBH can therefore be safely excluded as the starting condition for \u03c9 Cen. In contrast an IMBH model with an IMBH of 40,000 M\u2299has a reduced \u03c72 value of only 1.71. Fig. 6 shows that this models provides a much better \ufb01t than the no-IMBH model, the \u03c72 r value is larger than one mainly because the measured data points have very small error bars of only a few hundred m/s. Given the limited range of models which we can explore, it is di\ufb03cult to reproduce any velocity dispersion pro\ufb01le to such a level of precision. Zocchi, Gieles & H\u00b4 enault-Brunet (2016) have argued that radially anisotropic velocity dispersion pro\ufb01les could create a similar increase in the velocity dispersion pro\ufb01le as a central IMBH. In addition, van der Marel & Anderson (2010) found that anisotropic models provided a better \ufb01t to the velocity dispersion pro\ufb01le of \u03c9 Cen than isotropic models with central IMBHs. While the models of van der Marel & Anderson (2010) took mass segregation of stars into account, it is not clear how realistic their approach was. A look at their Fig. 7 for example shows that their isotropic no-IMBH model is already in very good agreement with the observed velocity dispersion pro\ufb01le, while it provides a very poor \ufb01t in our case. It is therefore not clear if the inclusion of radial anisotropy would change the velocity dispersion pro\ufb01le by a large enough amount to bring our models without IMBHs into agreement with the observations, especially since van der Marel & Anderson (2010) and the proper motion data of Watkins et al. show that \u03c9 Cen is essentially isotropic in its center and only mildly radially anisotropic beyond 200 arcsec. It seems more likely that \u03c9 Cen contains either a dark cluster of compact remnants or a population of low-mass stars in its center on top of what mass segregation is already producing in our models, or a \u223c 40,000 M\u2299IMBH. Comparison of the observed stellar mass function of stars at di\ufb00erent radii will help to further re\ufb01ne our models and should hopefully clarify the situation. In NGC 6715 a model with an IMBH of MIMBH = 11, 000 M\u2299provides a slightly better \ufb01t to the velocity dispersion pro\ufb01le of the cluster but \ufb01ts the central surface density pro\ufb01le less well. NGC 6715 (M54) has however the added complication that the cluster is the center of the Sagittarius dwarf galaxy so that at each radius stars that are part of the nucleus of Sagittarius contribute to the surface density and velocity dispersion pro\ufb01le (Bellazzini et al. 2008). An increase in the fraction of Sagittarius stars is almost certainly responsible for the rise in the velocity dispersion pro\ufb01le seen beyond 200\u201d. There is also still a signi\ufb01cant discrepancy between the best-\ufb01tting IMBH model and the ob10 Baumgardt Figure 6. Fit of the surface density pro\ufb01les (left panels) and velocity dispersion pro\ufb01les (right panels) of the globular clusters NGC 1904, NGC 5139, NGC 5286 and NGC 6266 for which previous literature work found evidence for the presence of IMBHs. For each cluster we show the best-\ufb01tting N-body models with (red lines) and without (blue lines) IMBHs. The IMBH models were obtained by interpolating between the grid of models containing IMBHs between 0.5% to 2% of the total cluster mass. The best-\ufb01tting IMBH models \ufb01t the observed surface density pro\ufb01les worse for NGC 1904 and NGC 6266 and do not improve the \ufb01ts of the velocity dispersion pro\ufb01les, indicating that the clusters do not contain IMBHs. For NGC 5286 both no-IMBH and IMBH models provide a a good \ufb01t. In NGC 5139 a model with an IMBH of 4.1 \u00b7 104 M\u2299provides a signi\ufb01cantly better \ufb01t of the surface density and velocity dispersion pro\ufb01le than a no-IMBH model, making this cluster the cluster which shows the strongest evidence for an IMBH. N-body models of GCs: Masses, M/L ratios and IMBHs 11 Figure 7. Same as Fig. 6 for the globular clusters NGC 6388, NGC 6397, NGC 6715 and NGC 7078. IMBHs are excluded for NGC 6397 and 7078 due to the very poor \ufb01t of the surface density pro\ufb01les. In NGC 6388, IMBH models provide a less good \ufb01t to the surface density pro\ufb01le than the no IMBH model, however the uncertainty about the central velocity dispersion pro\ufb01le prevents us from drawing any \ufb01rm conclusions. In NGC 6715 a model with a 11, 000 M\u2299IMBH provides a better \ufb01t to the velocity dispersion pro\ufb01le than a no IMBH model, but \ufb01ts the surface density pro\ufb01le less well. 12 Baumgardt Figure 8. Ratio of the cluster distances derived in this work to the distances found by Watkins et al. (2015b) (left panel) and cluster distances compiled from the literature (right panel) for the clusters for which we have determined distances. Dashed lines show the average distance ratio in each panel. Our distances agree very well with the distances of Watkins et al. (2015b), but are on average about 8% smaller than the literature distances. served velocity dispersion pro\ufb01le of NGC 6715. Although an IMBH might be present in NGC 6715 as well, we regard the evidence for an IMBH in NGC 6715 as weaker than in \u03c9 Cen. 4.2 Cluster distances Fig. 8 compares the cluster distances derived in this work with the distances derived by Watkins et al. (2015b) (left panel) and cluster distances from the literature (right panel). In order to derive the distances, we \ufb01tted our models to the surface density, radial velocity and proper motion dispersion pro\ufb01les of the clusters and varied the distance until the combined \u03c72 was minimal. Our distances are on average 2% \u00b1 3% smaller than those of Watkins et al. (2015b) and hence in excellent agreement with their distances. The discrepancy is larger when we compare with literature distances which are mainly obtained from CMD \ufb01tting since our distances are on average 8% smaller. The literature distances were taken mostly from Ferraro et al. (1999), however we obtain a similar di\ufb00erence when using the Harris (1996) distances. We \ufb01nd no obvious correlation between the distance ratio DT W /DLit and any other cluster parameter like metallicity, total mass or cluster distance (see Fig. 8). It therefore remains unclear where the discrepancy between our distances and the literature values is coming from. Parallax data from the GAIA satellite should help to settle the globular cluster distance scale. 4.3 Deviations from Newtonian dynamics? Scarpa et al. (2007a) and Scarpa et al. (2011) reported evidence for a \ufb02attening of the velocity dispersion pro\ufb01le in the outermost parts of a number of globular clusters including NGC 288, NGC 1851, NGC 1904 and NGC 7099, which they attributed to a deviation from Newtonian dynamics. Our models give us a chance to verify their claims. As can be seen from Figs. 9, 10 and 20, the measured velocity dispersion pro\ufb01les of the four clusters studied by Scarpa et al. are compatible with predictions of our N-body models out to the outermost data points with no evidence for a breakdown of Newtonian mechanics. The same is the case for most other clusters. We attribute the di\ufb00erence to Scarpa et al. to the fact that we calculate velocity dispersion pro\ufb01les based on a larger number of radial velocities, which allows us to more e\ufb03ciently identify binaries and non-members. In addition we apply a \u03c72 test based on the local velocity dispersion to separate members from non-members, while Scarpa et al. include all stars as members that have radial velocities within certain velocity limits. In the outer parts of globular clusters, where a larger fraction of stars are nonmembers, the approach used by Scarpa et al. is likely to overestimate the velocity dispersion. The agreement with our models could probably be improved further since the simulations presented here do not include tidal \ufb01elds, which increase the velocity dispersion of stars near the tidal radius (K\u00a8 upper et al. 2010; Claydon, Gieles & Zocchi 2015). The only cluster which deviates signi\ufb01cantly from our predictions is NGC 6715 (M54), where the velocity dispersion pro\ufb01le rises in the outermost few 100\u201d. As discussed by Bellazzini et al. (2008), this is most likely due to the fact that the sample includes stars from the Sagittarius dwarf galaxy, which follow a di\ufb00erent kinematical pro\ufb01le and whose relative contribution increases in the outermost cluster parts. We have therefore neglected all data points beyond 200\u201d in the dynamical analysis of this cluster. Apart from NGC 6715, the globular cluster velocity dispersion pro\ufb01les do not show any evidence for deviations from Newtonian dynamics out to distances of several 100 arcsec, corresponding to a physical distance of \u223c10 pc. 5 CONCLUSIONS AND OUTLOOK We have run a large grid of 900 N-body simulations of star clusters, varying the initial half-mass radius, density pro\ufb01le, cluster metallicity, and the mass fraction of a central IMBH. We have also determined new radial velocity dispersion pro\ufb01les of 50 Galactic globular clusters from about 25,000 published line-of-sight radial velocity measurements of stars in globular clusters, and combined these pro\ufb01les with velocity dispersion data based on proper motions and published surface density pro\ufb01les. By comparing the N-body data with the observed data and selecting the best-\ufb01tting model for each cluster, we were then able to derive absolute masses, mass-to-light ratios and limits on the possible presence of IMBH in the centers of all clusters. For a subset of 16 clusters for which both good proper motion and radial velocity information is available we also determined the cluster distances. We \ufb01nd that the average mass-to-light ratio of Galactic globular clusters is < M/LV >= 1.98 \u00b1 0.03 which agrees very well with the expected M/LV ratio for stars that formed with a standard Kroupa or Chabrier initial mass function. The mass-to-light ratios of high metallicity clusters with [Fe/H]> \u22121 could be slightly lower then predicted by standard stellar mass functions. The number of highmetallicity clusters in our sample is however small and the variation seen for them is within the variation found for lowmetallicity clusters. Given the good agreement between the derived and the theoretically expected M/L ratios, there is no evidence that globular cluster M/L ratios are signi\ufb01cantly e\ufb00ected by ongoing cluster dissolution. More accurate N-body models of GCs: Masses, M/L ratios and IMBHs 13 M/L ratios, or M/L ratios for a wider range of cluster parameters will be necessary to determine what role dissolution has played for globular clusters. We \ufb01nd strong evidence that \u03c9 Cen hosts an intermediate-mass black hole (IMBH) of \u223c40, 000 M\u2299in its center since the velocity dispersion pro\ufb01le of the cluster is in strong disagreement to N-body models without an IMBH. A compact cluster of stellar remnants in the center or a cluster that starts with a radially anisotropic velocity dispersion pro\ufb01le might be alternatives to an IMBH, however these possibilities seem unlikely given how well our isotropic, non mass-segregated models \ufb01t all other clusters. Given the absence of radio and X-ray emission from the center of \u03c9 Cen (Maccarone, Fender & Tzioumis 2005; Haggard et al. 2013), this result implies that if an IMBH exists in the center, it must accrete very little or with very low e\ufb03ciency (\u03b7 < 10\u22129). Evidence for the presence of an IMBH is also found in NGC 6715 (M54), however in NGC 6715 the best\ufb01tting IMBH model is still in signi\ufb01cant disagreement with the velocity dispersion pro\ufb01le. We can strongly exclude the presence of IMBHs in NGC 6397 and M15 and \ufb01nd that they are also unlikely to be present in most other clusters since IMBH models provide signi\ufb01cantly less good \ufb01ts to the surface density pro\ufb01les than no-IMBH models. We therefore conclude that if IMBHs exist in globular clusters, they can only exist in a small fraction of them. In the present work we only compared the observed velocity dispersion and surface density pro\ufb01les with results from our N-body simulations. The next step is to also compare the mass function of stars at di\ufb00erent radii with our predictions by performing simulations of star clusters which start with a range of initial mass functions and performing simulations that include cluster dissolution due to external tidal \ufb01elds. Mass functions of stars have been observed for about half of all globular clusters from our sample by De Marchi, Paresce & Pulone (2007); Paust et al. (2010), and Sollima, Bellazzini & Lee (2012). Comparison of the stellar mass functions will allow to accurately predict the structural parameter of the clusters like core and half-mass radii and the corresponding densities and relaxation times. It will also allow to determine the starting conditions of globular clusters in terms of initial radii, initial mass functions and the amount of primordial mass segregation and thereby gain a much better understanding of their formation and evolution. ACKNOWLEDGMENTS We thank Karl Gebhardt, Georges Meylan, Ben MacLean and Sandro Villanova for sharing unpublished data with us. We are also grateful to Long Wang for sending us data from his simulations. We \ufb01nally thank Pouria Khalaj and two anonymous referees for comments that helped improve the presentation of the paper. This work has made use of BaSTI web tools.",
                    "introduction": "Globular clusters are among the oldest structures in the uni- verse, having formed within 1 to 2 Gyr after the Big Bang (Kravtsov & Gnedin 2005). Studying their origin and evo- lution has therefore important implications for our under- standing of star formation and the growth of structure in the early universe. In addition, due to their high central den- sities and high stellar encounter rates, globular clusters are also unique environments for the creation of exotic stars like blue stragglers (Bailyn 1995; Davies, Piotto & de Angeli 2004), low-mass X-ray binaries (Verbunt 1993; Pooley et al. 2003) and millisecond pulsars (Manchester et al. 1991). The high stellar densities in globular cluster could also give rise to the creation of intermediate-mass black holes (Portegies Zwart & McMillan 2002; Portegies Zwart et al. 2004; Giersz et al. 2015), which might be the progenitors of supermassive black holes in Galactic centers. Globular clusters are \ufb01nally important environments for the creation of tight black hole binaries which merge through the emis- sion of gravitational waves (Banerjee, Baumgardt & Kroupa \u22c6E-mail: h.baumgardt@uq.edu.au 2010; Downing et al. 2011; Rodriguez, Chatterjee & Rasio 2016; Rodriguez et al. 2016; Askar et al. 2016). In order to understand the rate of creation of exotic stars, it is important to know the mass density pro\ufb01le of globular clusters and how di\ufb00erent types of stars are distributed within a globular cluster. This is possible by a detailed modeling of the internal kinematics of globular clusters. Several methods have been suggested in the literature to derive cluster masses from observed density pro\ufb01les: One can either using analytic formulas which relate a cluster\u2019s mass to its radius and velocity dispersion inside some radius (e.g. Mandushev, Staneva & Spasova 1991; Strader, Caldwell & Seth 2011), or \ufb01t analytic density pro\ufb01les like Plummer or King models to the observed velocity and surface density pro\ufb01les of globular clusters (e.g. McLaughlin & van der Marel 2005; Kimmig et al. 2015). Finally it is possible to deproject the observed surface density pro\ufb01le and then derive the cluster mass through Jeans modeling and a \ufb01t of the observed ve- locity dispersion pro\ufb01le (e.g. van de Ven et al. 2006; Noyola, Gebhardt & Bergmann 2008; L\u00a8 utzgendorf et al. 2012, 2013). Most approaches assume a constant mass-to-light ra- 2 Baumgardt tio inside globular clusters. However, since the relaxation times of globular clusters are generally much smaller than their ages, high-mass stars like compact remnants and gi- ant stars are concentrated towards the cluster centers while low-mass stars are pushed towards the outer cluster parts (Baumgardt & Makino 2003). Hence the assumption of a constant mass-to-light ratio is not valid for globular clus- ters. In addition, due to energy equipartition, massive stars move more slowly at a given radius compared to average cluster stars (Trenti & van der Marel 2013; Bianchini et al. 2016). As a result, the velocity dispersion derived from gi- ant stars will underestimate the true velocity dispersion, which leads to an underestimation of the total cluster mass if mass segregation is not properly taken into account (Shanahan & Gieles 2015). It is possible to account for mass segregation by e.g. using multi-mass King-Michie models (Michie 1963; Gunn & Gri\ufb03n 1979) or the more recently suggested LIMEPY models (Gieles & Zocchi 2015; Zocchi et al. 2016). Multi- mass models have however additional degrees of freedom since the amount of mass segregation between di\ufb00erent mass components can in principle be freely chosen in the models. In the present paper we follow a di\ufb00erent approach to derive the absolute masses and mass-to-light ratios of globu- lar clusters from their surface density and velocity dispersion pro\ufb01les. We perform a large grid of N-body simulations and scale each model so that it has the same half-light radius as the observed clusters. Scaling is done in such a way that the relaxation time is kept constant, thereby making sure that mass segregation of stars and (partial) energy equipartition between them are taken into account in a self consistent way in the scaled models, i.e. each model has the exact amount of mass segregation which a real globular cluster would have if it started from the same initial condition. We then deter- mine the model which best \ufb01ts the observed density and velocity dispersion pro\ufb01le for each globular cluster and de- termine the total mass, mass-to-light ratio and the possible presence of an intermediate mass black hole in the observed clusters from the best-\ufb01tting model. Our paper is organised as follows: In section 2 we describe the grid of N-body mod- els that we have performed, and in section 3 we describe the selection of the observational data. Section 4 presents our results and we draw our conclusions in section 5."
                },
                {
                    "url": "http://arxiv.org/abs/1207.5576v2",
                    "title": "The star cluster formation history of the LMC",
                    "abstract": "The Large Magellanic Cloud is one of the nearest galaxies to us and is one of\nonly few galaxies where the star formation history can be determined from\nstudying resolved stellar populations. We have compiled a new catalogue of\nages, luminosities and masses of LMC star clusters and used it to determine the\nage distribution and dissolution rate of LMC star clusters. We find that the\nfrequency of massive clusters with masses M>5000 Msun is almost constant\nbetween 10 and 200 Myr, showing that the influence of residual gas expulsion is\nlimited to the first 10 Myr of cluster evolution or clusters less massive than\n5000 Msun. Comparing the cluster frequency in that interval with the absolute\nstar formation rate, we find that about 15% of all stars in the LMC were formed\nin long-lived star clusters that survive for more than 10 Myr. We also find\nthat the mass function of LMC clusters younger than 1 Gyr can be fitted by a\npower-law mass function with slope \\alpha=-2.3, while older clusters follow a\nsignificantly shallower slope and interpret this is a sign of the ongoing\ndissolution of low-mass clusters. Our data shows that for ages older than 200\nMyr, about 90% of all clusters are lost per dex of lifetime. The implied\ncluster dissolution rate is significantly faster than that based on analytic\nestimates and N-body simulations. Our cluster age data finally shows evidence\nfor a burst in cluster formation about 1 Gyr ago, but little evidence for\nbursts at other ages.",
                    "authors": "Holger Baumgardt, Genevieve Parmentier, Peter Anders, Eva K. Grebel",
                    "published": "2012-07-24",
                    "updated": "2012-12-20",
                    "primary_cat": "astro-ph.GA",
                    "cats": [
                        "astro-ph.GA"
                    ],
                    "main_content": "We use four recent compilations of LMC star cluster parameters to derive a combined catalogue for LMC clusters. Our first catalogue is the recent work of Glatt, Grebel & Koch (2010), who used data from the Magellanic Cloud Photometric Surveys together with isochrone fitting to derive ages and luminosities for 1193 populous star clusters in a 64 deg2 area of the LMC. The cluster identifications, sizes, and positions were taken from the catalogue of Bica et al. (2008). Since the MCPS becomes highly incomplete below V = 24, the Glatt et al. data become incomplete for ages larger than 500 Myr and do not contain any clusters older than T = 1 Gyr. Glatt et al. also did not determine ages for clusters younger than about 10 Myr to avoid confusion between star clusters and unbound stellar associations. The second data set that we use is the catalogue of Pietrzynski & Udalski (2000), who used BVI data from the OGLE II microlensing experiment (Udalski et al. 1998) together with isochrone fitting to derive ages of about 600 star The star cluster formation history of the LMC 3 clusters which are located in the central parts of the LMC and are younger than 1.2 Gyr. Since Pietrzynski & Udalski did not derive cluster luminosities or cluster masses, we could only use their data if luminosity information was available from another source. Our third catalogue is the cluster catalogue presented by Hunter et al. (2003). The Hunter et al. catalogue contains data for about 746 di\ufb00erent LMC clusters, limited to the inner regions of the LMC and to absolute luminosities brighter than MV = \u22123.5. New age determinations for the cluster in the Hunter et al. catalogue were presented by de Grijs & Anders (2006) from broadband spectral energy distribution \ufb01tting of the integrated UBVR photometry given by Hunter et al. (2003) and recently also Popescu, Hanson & Elmegreen (2012). Popescu et al. use the stellar cluster analysis package MASSCLEANage to derive new ages and masses for the Hunter et al. cluster sample. The advantage of MASSCLEANage is that it allows to take into account stochastic \ufb02uctuations in cluster colors and magnitudes which arise from the \ufb01nite number of stars present in clusters. We average the ages for clusters which appear multiple times in the Popescu et al. sample and are left with a list of 746 unique clusters which are almost identical to those analysed by de Grijs & Anders. In order to increase the accuracy of the age and mass determinations especially for bright clusters, we also include age determinations from the literature. In particular, we use the ages recently derived by Milone et al. (2009) for massive intermediate-age star clusters from colour-magnitude \ufb01tting and the age data compiled by Mackey & Gilmore (2003) for 53 massive LMC clusters. Many of the ages in these papers are derived from HST data reaching several magnitudes below the turnover and are therefore signi\ufb01cantly more accurate than the ages derived in the above surveys. Fig. 1 depicts the positions of all clusters from the above catalogues. Since the list of clusters in de Grijs & Anders is nearly identical to that of Popescu et al., we do not show them separately. It can be seen that the Glatt et al. data covers most of the LMC, while de Grijs & Anders (2006), Popescu, Hanson & Elmegreen (2012) and Pietrzynski & Udalski (2000) catalogues are restricted to varying parts of the LMC. Since the LMC shows evidence for di\ufb00erent regions having undergone di\ufb00erent star formation histories (Glatt, Grebel & Koch 2010), it is clear that only a combination of all catalogues can give a complete picture of the LMC cluster population. Fig. 2 and Table 1 compare the ages of star clusters derived in the studies by Pietrzynski & Udalski, de Grijs & Anders, Glatt et al., and Popescu et al. with one another for the clusters common to the di\ufb00erent studies. The de Grijs & Anders ages are in good agreement with the OGLE II ages but disagree signi\ufb01cantly with the Glatt et al. and Popescu et al. ages, since clusters with T < 108 yrs in de Grijs & Anders tend on average to be younger than found by the other authors, while clusters with T > 108 yrs are on average older in de Grijs & Anders than in the other catalogues. As noted by Popescu et al., this di\ufb00erence could be due to the absence of single red giants or supergiants in young clusters, which make the cluster appear bluer and therefore younger. The Glatt et al. data shows fairly good agreement with Popescu et al. It is also in rough agreement with the OGLE II data, however the number of clusters in common is too small to make a meaningful comparison. The OGLE II ages have a small o\ufb00set by about log T = 0.2 dex compared with the de Grijs & Anders ages, which might also be present in the comparison with the Popescu et al. data. As noted by de Grijs & Anders, this can be explained by the smaller LMC distance modulus of (m \u2212M) = 18.23 adopted by Pietrzynski & Udalski, compared to the value of (m\u2212M) = 18.50 used by most other authors. Placing the LMC at a smaller distance decreases the absolute luminosities of the stars and the turn-over region in the CMD, and therefore makes the clusters appear older. In order to correct for this bias, we increase the OGLE II ages by 0.2 dex. From the comparison of the cluster ages shown in Fig. 2, we calculate Pearson r coe\ufb03cients and best-\ufb01tting linear relations log age1 = \u03b1 log age2 + \u03b2 and the standard deviation in log T about this best-\ufb01tting relation. The results are shown in Table 1, which also includes a comparison with the literature data. The relatively large discrepancy between the de Grijs & Anders data on the one hand and Glatt et al. and Popescu et al. on the other is again apparent. Since Glatt et al. use CMD \ufb01tting while Popescu et al. work with integrated colors, the di\ufb00erence cannot result from the method used and is more likely due to stochastic e\ufb00ects in\ufb02uencing the integrated colors. Given the Pearson r coe\ufb03cients, the ages from OGLE II seem to better agree with de Grijs & Anders ages than with either Glatt et al. or Popescu et al. However the slope \u03b1 of the best-\ufb01tting relation for OGLE II is in all cases compatible with unity. The literature sample has only few clusters in common with the other studies, so it is hard to make a meaningful comparison, but the Pearson r coe\ufb03cients as well as the slopes \u03b1 are mostly compatible with unity within the error bars, indicating good agreement. The \ufb01nal column of Table 1 shows that the RMS deviation in log t between the di\ufb00erent catalogues is typically around 0.20 to 0.30, a value that also agrees with the age uncertainties of individual clusters (see Table 2). To obtain a complete catalogue of LMC clusters, we combine the clusters from the above data sets, excluding duplicate entries through a coordinate based search with a search radius of 20\u201d, which corresponds to a distance of 5 pc at an assumed LMC distance of 50 kpc. When assigning ages to the clusters, we give the highest priority to the ages given in Milone et al. (2009) and Mackey & Gilmore (2003), followed by Glatt et al. (2010), the OGLE II data, and \ufb01nally Popescu et al. (2012). We ignore the de Grijs & Anders dataset due to its signi\ufb01cant deviation against the Glatt et al. and Popescu et al. ages. Since we need cluster luminosities to calculate cluster masses and OGLE II has only age information, we include clusters from OGLE II only if information on the total cluster luminosity is available from Popescu et al. (2012). Cluster masses are then derived from the MV luminosities by calculating M/LV values using the Padova isochrones for Z = 0.008. These isochrones are based on the Marigo et al. (2008) stellar evolution tracks with corrections from case A in Girardi et al. (2010), assuming a Kroupa (1998) stellar mass function corrected for binaries. The resulting cluster masses show good agreement with the cluster masses calculated by Popescu et al. for the clusters which we take from their catalogue. As shown by Anders et al. (2009), cluster dissolution can a\ufb00ect the cluster M/L ratios since lowmass stars are lost preferentially, however the resulting e\ufb00ect 4 Baumgardt et al. Figure 2. Comparison of age determinations from Pietrzynski & Udalski (2000) (OGLE II), de Grijs & Anders (2006), Glatt et al. (2010) and Popescu et al. (2012). Crosses denote the positions of individual clusters. Solid lines show lines of equal ages, while dashed lines give the best-\ufb01tting linear relation. Shown are also the Pearson r coe\ufb03cients and the slope \u03b1 of the best \ufb01tting relation for the di\ufb00erent comparisons. on the M/L ratios is less than 50% until the cluster is close to dissolution. Fig. 3 depicts the location of all clusters from the combined data set in a mass vs. age diagram. The dotted line shows the 50% completeness limit of MV = \u22123.5 from Hunter et al. (2003). The majority of clusters have ages between 107 to 109 yrs and masses of a few hundred to a few thousand M\u2299. The lack of clusters younger than 107 yrs is due to the fact that such clusters are often obscured by dust clouds and are also easy to confuse with unbound associations and were therefore not analysed by Glatt et al. and OGLE II. The Glatt et al. and OGLE II samples also do not contain clusters older than \u2248109 yrs, since neither the OGLE nor the MCPS photometry is deep enough to permit age dating such clusters from resolved CMDs. This could in part explain the absence of clusters above 109 yrs. In addition, the 50% completeness limit of the Hunter et al. sample reaches several thousand M\u2299for ages larger than 109 yrs. In order to work with a sample that is as complete as possible, we therefore restrict our analysis to clusters older than 107 yrs and brighter than MV = \u22123.5. For clusters of a few thousand stars, a single giant star can have a luminosity exceeding that of the rest of the cluster, leading to large \ufb02uctuations in the clusters\u2019 M/L ratio (Piskunov et al. 2011). This makes mass estimates based on cluster luminosity highly uncertain. We therefore also restrict our analysis to clusters more massive than 5000 M\u2299. For clusters of this mass and ages larger than 107 yrs, Fig. 11 in Piskunov et al. (2011) The star cluster formation history of the LMC 5 Table 1. Number of clusters NCl in common between di\ufb00erent catalogues, Pearson r coe\ufb03cient, slope of best-\ufb01tting relation \u03b1 in an log(age) vs. log(age) diagram, and the residual scatter log T about this best-\ufb01tting relation for all data sets. Data set 1 Data set 2 NCl Pearson Slope Scatter Data set 1 Data set 2 NCl Pearson Slope Scatter r \u03b1 <\u2206log T > r \u03b1 <\u2206log T > OGLE II de Grijs&Anders 198 0.75 0.95 \u00b1 0.19 0.28 de Grijs&Anders OGLE II 198 0.75 1.05 \u00b1 0.21 0.28 OGLE II Glatt et al. 29 0.44 0.75 \u00b1 1.38 0.26 de Grijs&Anders Glatt et al. 294 0.46 0.38 \u00b1 0.11 0.33 OGLE II Popescu et al. 191 0.54 0.84 \u00b1 0.22 0.37 de Grijs&Anders Popescu et al. 745 0.68 0.73 \u00b1 0.07 0.62 OGLE II Literature val. 11 0.96 2.07 \u00b1 1.40 0.13 de Grijs&Anders Literature val. 18 0.91 1.60 \u00b1 0.67 0.27 Glatt et al. OGLE II 29 0.44 1.33 \u00b1 1.81 0.26 Popescu et al. OGLE II 191 0.54 1.19 \u00b1 0.31 0.37 Glatt et al. de Grijs&Anders 294 0.46 2.61 \u00b1 0.83 0.33 Popescu et al. Glatt et al. 293 0.77 0.74 \u00b1 0.16 0.20 Glatt et al. Popescu et al. 293 0.77 1.35 \u00b1 0.30 0.20 Popescu et al. de Grijs&Anders 745 0.68 1.37 \u00b1 0.13 0.62 Glatt et al. Literature val. 18 0.70 1.71 \u00b1 1.56 0.30 Popescu et al. Literature val. 18 0.07 3.99 \u00b1 0.67 0.82 shows that stochastic e\ufb00ects due to bright giants change the M/L ratio in the V band by less than 20% compared to a model with a continuous IMF. Comparable mass uncertainties are also found by Popescu et al. for clusters more massive than a few thousand solar masses. The resulting selection limit is shown in Fig. 3 by dashed lines. Out of a total number of 1649 unique clusters in the four data sets, 322 clusters pass our selection criteria. Their basic parameters (names, positions, total MV luminosities, ages, age uncertainties and masses) are listed in Table 2. Although containing only the brightest and most massive clusters in the LMC, none of the individual catalogues is complete within our age and mass ranges: Of the 322 clusters in our \ufb01nal sample, only 86 were listed in OGLE II, 85 in Glatt et al. and 194 in Popescu et al. In the following analysis, we restrict ourselves to the area of the LMC covered by Glatt et al., which is roughly located between 4.7 and 6.1 hours in right ascension and -65 and -72.5 degrees in declination. This region contains 294 clusters of our \ufb01nal sample and is identical to the region for which Harris & Zaritsky (2009) determined the \ufb01eld star formation rate, which we will compare to the cluster formation rate in the next section. 3 RESULTS Fig. 4 depicts the cluster frequency dN/dt, de\ufb01ned as the number of clusters per time unit, as a function of age for clusters with present masses MC > 5000 M\u2299and magnitudes brighter than MV = \u22123.5. It can be seen that the observed frequency drops steadily as a function of age. The drop is relatively small during the \ufb01rst 100 Myr since the data point at T=150 Myr is only a factor of two lower than the one at the youngest age. The data show clear evidence for a peak in cluster frequency at T = 1.5 \u00b7 109 yrs. Other peaks are more ambiguous, but could be present between 20 to 30 Myr and around 100 Myr. The peak at ages between 20 to 30 Myr, might however simply be due to cluster incompleteness at ages T < 20 Myr. Also visible is the wellknown absence of star clusters between 3 and 8 Gyr, where the cluster frequency is at least a factor of 10 lower than at older and younger ages. In order to disentangle true variations in cluster frequency from star formation variations, we divide the cluster frequency by the total star formation rate in each age bin according to Harris & Zaritsky (2009) and show the result Figure 3. Location of all clusters in a mass vs. age diagram. The dotted line shows the location of the 50% completeness limit of MV = \u22123.5 for the Popescu et al. (2012) data. The dashed line shows the location of clusters used for our analysis, which are con\ufb01ned to ages larger than 107 yrs, masses larger than 5000 M\u2299 and total luminosities brighter than MV = \u22123.5. in the bottom panel of Fig. 4. As can be seen, the cluster to star ratio is now nearly constant for ages from 10 Myr to 200 Myr. Primordial gas expulsion does therefore either have only a moderate e\ufb00ect on star clusters or its observable e\ufb00ects must be limited to either the \ufb01rst 10 Myr of cluster evolution or low-mass clusters with MC < 5000 M\u2299since no strong drop in cluster frequency is visible in the \ufb01rst 100 Myr. After 200 Myr, the frequency of clusters drops significantly, at T = 1 Gyr it is roughly only 1/10th of that at T < 200 Myr, and at T = 10 Gyr it is lower by an additional factor of 10. We note that at T = 10 Gyr, the 50% completeness limit of Hunter et al. (2003) is almost a factor of 4 more massive than our mass-cut at 5000 M\u2299(see Fig. 4). This, however, does not explain the low number of clusters at T = 10 Gyr, since all of them are more massive than 105 M\u2299. 6 Baumgardt et al. Figure 4. Upper panel: Cluster frequency dN/dt as a function of age. Solid points show the observed LMC data for clusters with masses MC > 5000 M\u2299. Lower panel: Cluster frequency divided by the average star formation rate in each age bin. The number of clusters formed per unit stellar mass is constant up to an age of 200 Myr and drops sharply for larger ages, indicating the onset of cluster dissolution for ages T > 200 Myr. A nearly constant cluster frequency at young ages followed by a strong decrease at later ages was also found by Lamers et al. (2005) for the open clusters in the solar neighborhood. In the solar neighborhood the break occurs at around log t/yr = 8.6, equivalent to 400 Myr. It is also visible in the distribution of massive star clusters with M > 103 M\u2299in the SMC resented by Chandar, Fall & Whitmore (2006) (see their Fig. 1). Boutloukos & Lamers (2003) showed that this behavior is due to cluster dissolution: For ages t < tbreak, where tbreak is a characteristic time related to the dissolution time, only a small number of low-mass clusters fall below the detection threshold, so the cluster frequency drops only slowly, while for ages t > tbreak signi\ufb01cant dissolution of clusters causes a strong decrease in cluster frequency. From Fig. 4, we can therefore conclude that a) if residual gas expulsion has an in\ufb02uence on star clusters, its e\ufb00ects must be limited to either the \ufb01rst 10 Myr of evolution or low-mass clusters with MC < 5000 M\u2299b) the characteristic lifetime of a \u223c104 M\u2299star cluster (which make up the majority of our clusters in our sample) in the LMC is a few hundred Myr and roughly the same as in the solar neighborhood (Lamers et al. 2005); c) for ages > 200 Myr about 90% of clusters are destroyed per 1 dex in log t. The data shown in Fig. 4 con\ufb01rm the absence of star clusters in the LMC in the age range 4 Gyr < T < 10 Gyr, which was \ufb01rst noticed by Bertelli et al. (1992). A similar gap is not seen in the \ufb01eld star formation rate, as found by Harris & Zaritsky (2009) from an analysis of the MCPS data and Holtzman et al. (1999) from an analysis of HST color-magnitude diagrams of three \ufb01elds in the LMC. If the star formation rate derived by Harris & Zaritsky (2009) is correct, then the ratio of the number of clusters formed to the absolute star formation rate was at least a factor 5 to 10 lower in this age range then at both earlier ages T > 10 Gyr and later ages T < 3 Gyr. Alternatively, only lowmass clusters with M < 5000 M\u2299may have been formed in this age range. Fig. 5 \ufb01nally depicts the mass distribution of clusters, split into four age groups. In most age bins, the mass function of clusters can be approximated well by a power-law mass function N(m) \u223cm\u2212\u03b1. Applying a maximum likelihood estimator to the cluster mass distribution as described in Clauset, Rohilla Shalizi & Newman (2009), gives as best-\ufb01tting slope \u03b1 = 2.32 \u00b1 0.11 for the youngest age bin. This is in good agreement with the slope found by Hunter et al. (2003) and only slightly steeper than the slope of \u03b1 = 1.8\u00b10.2 found by Chandar, Fall & Whitmore (2010) for clusters more massive than 103 M\u2299. In our sample, clusters up to 1 Gyr can be \ufb01tted by a slope similar to that for clusters in the youngest age bin, con\ufb01rming results by Chandar, Fall & Whitmore (2010) that the dissolution of clusters up to 1 Gyr is mass independent, at least for the mass range considered here. Clusters between 1 and 4 Gyr have a signi\ufb01cantly \ufb02atter best-\ufb01tting slope of \u03b1 = 1.67 \u00b1 0.08. This could be due to either incompleteness of the sample at the low-mass end or be a sign of ongoing cluster dissolution, since low-mass clusters are more easily destroyed by two-body relaxation than high-mass ones (Baumgardt & Makino 2003). If the \ufb02attening were due to incompleteness and the true mass function still a power-law with slope \u03b1 = 2.3, then about 400 clusters with masses between 5000 M\u2299and 105 M\u2299would be missing from our sample. This seems highly unlikely, given the relatively faint 50% completeness limit of the Hunter et al. sample (about 5000 M\u2299at T = 2 Gyr). We therefore conclude that the observed \ufb02attening of the mass function for clusters with ages 1 < T < 4 Gyr is due to ongoing cluster dissolution. Interestingly, clusters with ages 1 < T < 4 Gyr and masses larger than 105 M\u2299can still be \ufb01tted with a slope \u03b1 \u22482.3, the slope \ufb02attens only for lower-mass clusters, which is also in agreement with ongoing dissolution of low-mass clusters (see sec. 5). The mass-function slope is even \ufb02atter for clusters in the oldest age bin (bottom panel of Fig. 5), however for these a power-law mass function provides a rather poor \ufb01t and their mass function is much better described by e.g. a log-normal distribution, similar to what is seen for globular clusters in other galaxies. From Figs. 4 and 5, we can also deduce the ratio of stars born in clusters that survive gas expulsion and infant mortality to the total number of stars born. Our sample contains 87 clusters with ages 10 Myr < T < 100 Myr and masses MC > 5000 M\u2299, which have a total mass of 1.3 \u00b7 106 M\u2299. If we assume that clusters follow a powerlaw mass function with exponent \u03b1 = 2.3 and extend the cluster mass function down to clusters of 102 M\u2299, the total mass in clusters is about a factor 3 higher. Integrating the Harris & Zaritsky (2009) star formation rate, we \ufb01nd that over the same time span 2.6\u00b7107 M\u2299were born in \ufb01eld stars. Hence about 15% of all stars with T < 100 Myr formed in clusters that survive for at least 10 Myr. This is within the The star cluster formation history of the LMC 7 Figure 5. Mass distribution of star clusters for four di\ufb00erent age bins. The dashed lines show best-\ufb01tting power-law mass functions. The power-law slopes \u03b1 and their errors are also given in the di\ufb00erent panels. Clusters in the two youngest age bins follow power-law mass functions with slope \u03b1 \u22482.35. Clusters older than 1 Gyr follow a signi\ufb01cantly \ufb02atter distribution, which is most likely a result of ongoing cluster dissolution. For clusters with T > 4 Gyr, a power-law mass function does not give a good description of their mass function. range of ratios seen in other nearby galaxies as determined by Goddard, Bastian & Kennicutt (2010). 4 THEORETICAL ESTIMATES FOR THE DISSOLUTION OF STAR CLUSTERS Star clusters are destroyed through a number of mechanisms, including residual gas expulsion (Hills 1980; Goodwin 1997; Baumgardt & Kroupa 2007), two-body relaxation and external tidal \ufb01elds (Vesperini & Heggie 1997; Baumgardt & Makino 2003) and tidal shocks from disc or bulge passages or passing giant molecular clouds (Spitzer 1958; Ostriker et al. 1972; Wielen 1985; Gnedin & Ostriker 1997; Gieles et al. 2006a). In the following, we discuss each of these dissolution mechanisms in more detail. 4.1 Gas expulsion Clusters typically form at the centres of dense molecular clouds with star formation e\ufb03ciencies of about 30%. When the residual gas that is not converted into stars is removed by winds from young O and B type stars, the gravitational potential is lowered and some clusters can become unbound. Baumgardt & Kroupa (2007) showed that the impact of gas expulsion depends on the star formation e\ufb03ciency \u01eb, the timescale over which the gas is removed compared to the clusters crossing time \u03c4gas/tcross, and the strength of the external tidal \ufb01eld which can be quanti\ufb01ed through the ratio of the clusters half-mass radius prior to gas expulsion to its tidal radius rh/rt. Although gas expulsion is thought to happen within the \ufb01rst few Myr after cluster formation, and therefore does not directly a\ufb00ect clusters with ages \u226510 Myr, clusters need several initial crossing times to dissolve into the \ufb01eld. While dissolving, they could still be visible as clusters and would therefore in\ufb02uence our sample at the youngest ages (see e.g. Parmentier & Baumgardt 2012). The absence of any decrease of cluster frequency between 10 and 200 Myr (see Fig. 4), argues against the presence of dissolving clusters in our sample. We therefore assume that the observed cluster response to gas expulsion is over by an age of 10 Myr and neglect the in\ufb02uence of residual gas expulsion. 4.2 Stellar evolution Stellar evolution reduces the masses of star clusters by about 45% during a Hubble time if stars follow a Kroupa (2001) IMF. Low-mass clusters with masses M < 104 M\u2299 will therefore fall below our adopted lower mass limit of M = 5000 M\u2299even without any dynamical mass loss. In order to model stellar evolution, we assume for the mass lost by stellar evolution: dM dt = \u2212(MC \u2212MDyn(t)) d\u00b5ev dt (1) where MC is the initial cluster mass, MDyn(t) is the accumulated mass lost by the dynamical e\ufb00ects described below and \u00b5ev is calculated as described in Lamers et al. (2010), assuming a metallicity of Z = 0.0080. Apart from mass loss, stellar evolution also causes the clusters to expand and very extended clusters could su\ufb00er additional dynamical mass loss due to this expansion and the related tidal over\ufb02ow. However we neglected the in\ufb02uence of this process since it is most e\ufb00ective in the \ufb01rst few 100 Myr of cluster evolution, where we see little evidence for cluster dissolution (see Sec. 3). 4.3 Two-body relaxation and external tidal \ufb01elds The e\ufb00ects of two-body relaxation and a spherical external tidal \ufb01eld were modeled according to the results of Baumgardt & Makino (2003), who performed simulations of multi-mass clusters moving through spherically symmetric, isothermal galaxies. According to Baumgardt & Makino (2003), the lifetime tDis|Rel of a star cluster moving through an external galaxy with circular velocity VC on an orbit with distance R from the centre of the galaxy is given by tDis|Rel [Gyr] = k \u0012 N ln(0.02 N) \u0013x R [kpc] \u0012 VC 220km/s \u0013\u22121 . (2) Here N is the initial number of cluster stars, which can be calculated from the initial cluster mass and the mean mass of the cluster stars as N = MC/< m >. A Kroupa (2001) IMF between mass limits of 0.1 and 100 M\u2299has < m >= 0.64 M\u2299. x and k are constants describing the dissolution process and are given by x = 0.75 and k = 1.91 \u00b7 10\u22123 (Baumgardt & Makino 2003). Kinematic studies of various population tracer populations show that the LMC has near-solid body rotation in its inner parts 8 Baumgardt et al. (Meatheringham et al. 1988; Hughes, Wood & Reid 1991, e.g.). van der Marel et al. (2002) found that the LMC shows solid body rotation out to a radius of about 4 kpc and an approximately \ufb02at rotation curve for larger radii. The rotation velocity of the LMC is however rather uncertain and depends on the tracer population that is used. Olsen & Massey (2007) \ufb01nd values of VC = 61 km/sec for carbon stars, VC = 80 km/sec for H I gas and VC = 107 km/sec for red supergiants and speculate that the di\ufb00erences could be a sign of the ongoing tidal perturbation of the LMC. If we assume a maximum circular rotation speed of the LMC of 80 km/sec, similar to what Olsen & Massey (2007) found for the rotation velocity of the H I gas, eq. 2 becomes tDis|Rel [Gyr] = 3.92 \u0012 MC 104M\u2299 \u00130.75 (3) for radii R < 4 kpc. We do not consider larger radii since observed LMC clusters mostly have R < 4 kpc. Note that, as a result of the solid body rotation, tDis|Rel does not depend on galactocentric distance. We \ufb01nally note that Gieles & Baumgardt (2008) have shown that compact clusters dissolve faster than the tidally \ufb01lling clusters simulated by Baumgardt & Makino (2003) due to their smaller relaxation times. However we neglect this e\ufb00ect since it only becomes important for rh/rJ < 0.05, where rh is the half-mass radius and rJ is the Jacobi radius of the cluster. A cluster starting with an initial mass of 104 M\u2299at a typical distance of 1 kpc from the centre of the LMC has a Jacobi radius rJ = 20 pc, so this e\ufb00ect would only be important if clusters start with radii rh \u226a1 pc. 4.4 Disc shocks Clusters passing through galactic discs experience tidal heating due to the di\ufb00erence in acceleration for stars in di\ufb00erent parts of the cluster (Ostriker et al. 1972). The dissolution time against disc shocking is given by (Binney & Tremaine 1987, eq. 7-72): tDis|Shock = T\u03c8\u03c32 \u2217V 2 z 8 \u00af z2 \u00af g2 z (4) where T\u03c8 is the orbital time of the cluster, \u03c3\u2217the 1D velocity dispersion of stars in the cluster, Vz the velocity with which the cluster passes the disc, \u00af z2 = r2 h/3 the root-mean square z distance of stars in the cluster and gz the gravitational acceleration of stars due to the disc. Using the virial theorem, we \ufb01nd 3 2MC\u03c32 \u2217= \u03b7GM 2 C rh (5) where \u03b7 \u22480.4 for most density pro\ufb01les. For a typical halfmass radius of rh = 4 pc, this gives \u03c3\u2217 km/sec = 1.7 r MC 104M\u2299. (6) The LMC is classi\ufb01ed as a SBm galaxy (de Vaucouleurs & Freeman 1972) and contains a relatively thick disc with an out-of-plane axial ratio of \u223c0.3 or larger (van der Marel et al. 2002). The velocity dispersion of stars perpendicular to the LMC disc depends on their age and increases for older stars, similar to the situation in the Milky Way (van der Marel et al. 2009). We adopt a velocity dispersion of Vz = 10 km/sec, which is intermediate between the velocity dispersion found for red supergiants and that of the H I gas (van der Marel et al. 2009). If we also assume a circular velocity of V = 20 km/sec at a distance of R=1 kpc from the centre of the LMC, we \ufb01nd T\u03c8 = 312 Myr. For an in\ufb01nitely thin disc with radial scale length of RD = 1.42 kpc (Weinberg & Nikolaev 2001) and a total mass in stars and gas of MD = 3.2 \u00b7 109 M\u2299 (van der Marel et al. 2002), the acceleration in z direction is gz = 4.3 pc/Myr2 at R = 1 kpc. Inserting all the values in eq. 4 gives a dissolution time of roughly 110 Myr for a 104 M\u2299cluster. Eq. 4 is however only valid for impulsive encounters in which the time scale for shocking is much smaller than the orbital time for stars in the cluster. Slower encounters have a reduced e\ufb00ect since stars with orbital times torb \u226atshock can adiabatically adjust to the shocking. Gnedin & Ostriker (1997) give various forms for the adiabatic correction factor. If we use their eq. 11, then A(x) = \u00001 + x2/4\u0001\u22123/2 (7) where x is the ratio of the angular velocity of stars in the cluster to the crossing timescale of the cluster through the disc and is given by x = \u03c3\u2217 rh 2z0 Vz (8) For a vertical scale height of z0 = 270 pc (van der Marel et al. 2002) and a cluster mass of 104 M\u2299, x \u224820, and A(x) \u22481/1500. Disc shocks therefore seem to have a negligible in\ufb02uence on the evolution of star clusters in the LMC. Even if we set Vz = 50 km/sec, corresponding to a cluster moving on a highly inclined orbit through the disc and assume a smaller scale height of z0 = 100 pc in the past, the lifetime of a 104 M\u2299cluster against disc shocks is still larger than that against two-body relaxation. We therefore neglect the in\ufb02uence of disc shocks on the cluster evolution. 4.5 GMC encounters Similar to galactic discs, passing giant molecular clouds create transient tidal forces on a star cluster, which increases the internal energy of a cluster and leads to cluster dissolution (Spitzer 1958). Wielen (1985) found that giant molecular clouds dominate the dissolution of star clusters in the solar neighborhood. The most thorough calculation of the in\ufb02uence of GMC encounters has been given by Gieles et al. (2006), who showed that considering only the total energy gain can overestimate the e\ufb00ect of GMC encounters since much of the energy gained by the cluster is carried away by escapers and that considering the mass loss of a cluster leads to a better description of the dissolution process. Gieles et al. (2006) also showed that GMCs cannot destroy clusters with more than \u223c104 M\u2299in a single disruptive encounter if one takes the \ufb01nite size of the GMCs into account. For the cumulative e\ufb00ect of many distant encounters, they derived the following expression for the lifetime of a star cluster of mass MC and half-mass radius rh: tdis|GMC = \u0012 3\u03c3cn\u03b7 8\u03c03/2gfG r2 h \u00af r2 \u0013 \u0012 MC r3 h \u0013 1 \u03a3n\u03c1n (9) The star cluster formation history of the LMC 9 where \u03c1n = MGMC nGMC is the mass density of GMCs in a galaxy, \u03a3n the typical surface density of a single GMC, f is the ratio of relative mass loss to the relative energy gain of a cluster during an encounter, g a numerical correction factor for close encounters, \u03c3cn is the typical relative velocity between a star cluster and a GMC, \u00af r the root-mean square radius of the cluster, and \u03b7 a constant which depends on the density pro\ufb01le of the cluster. A King (1966) model with W0=5.0 has \u03b7 \u22480.4 and (r2 h/\u00af r2) = 0.50. The typical velocity dispersion of stars in the LMC is \u03c3 = 20 km/sec (van der Marel et al. 2002). Fig. 12 in Gieles et al. shows that for a typical cluster mass of 104 M\u2299and a typical GMC mass of 105 M\u2299, the correction factor g is slightly larger than unity, so we adopt g = 1.5. We also assume f = 0.25 as found by Gieles et al. through direct N-body simulations and an average cluster radius of rh = 4 pc. The mass density \u03c1n and the surface density \u03a3n of the GMCs are taken from the results of the NANTEN LMC molecular cloud survey (Fukui et al. 2008). Fukui et al. found 270 molecular clouds with masses MCO > 2 \u00b7 104 M\u2299within a survey area of 30 deg2. Inside 2 kpc from the center of the LMC, they found a surface mass density of GMCs of 2 M\u2299/pc2. Assuming a disc scale height of 180 pc (Padoan et al. 2001) for the gas and that all GMCs are located within \u00b11 scale height of the plane of the disc, gives a space density \u03c1n = 0.0056 M\u2299/pc3. Hughes et al. (2010) found an average surface density of \u03a3n = 50 M\u2299/pc2 for individual GMCs in the LMC. Inserting all values, we \ufb01nd for the lifetime of star clusters in the LMC: tdis|GMC [Gyr] = 93.0 \u0012 MC 104M\u2299 \u0013 (10) Unlike in the Milky Way, GMC encounters do not seem to be a dominant dissolution process for star clusters in the LMC, the main reason being their lower space density as a result of the large disc scale height and their smaller surface density (\u03a3n = 50 M\u2299/pc2 for clouds in the LMC vs. \u03a3n = 170 M\u2299/pc2 in the Milky Way, see Solomon et al. 1987). N-body simulations by Weinberg (2000) suggest that the large scale height of the LMC disc could be a result of the interaction with the Milky Way. Hence the importance of GMC encounters might have been higher in the past when the LMC disc had a smaller scale height. It is however unlikely that the lifetime would drop below a Hubble time even for the smallest clusters in our sample, and we therefore also neglect GMC encounters. We are therefore left with two-body relaxation driven evaporation as the only dissolution process which seems to have a signi\ufb01cant in\ufb02uence on the LMC cluster system. In order to model relaxation driven evaporation, we assume that the dynamical mass loss is linear in time, so the dynamically lost mass is given by: dM dt = \u2212(MC \u2212Mev(t)) /tDis|Rel , (11) where Mev(t) is the total mass lost by stellar evolution up to time t. We assume that clusters form with the same rate as the \ufb01eld stars and use the star formation history of LMC \ufb01eld stars as derived by Harris & Zaritsky (2009) to form clusters. We assume that clusters form with a power-law mass function dN(m) \u223cm\u2212\u03b1dm and adjust the exponent such that the mass function of clusters in the youngest age bin in Fig. 5 is \ufb01tted. We also assume that clusters follow an exponential density distribution in the LMC with scale length R = 1.42 kpc, similar to what is seen for the \ufb01eld stars, and that clusters move on circular orbits. Clusters are then evolved according to the description presented in this section up to the present time. The mass and age distribution of the surviving clusters with MC > 5000 M\u2299and absolute luminosities MV > \u22123.5 mag is then compared with the observational data for LMC clusters and we discuss the results in the next section. 5 COMPARISON WITH THEORY The left panel of Fig. 6 shows a comparison between the predicted and observed cluster frequency as a function of time, assuming that star clusters form with a power-law mass function N(m) \u223cm\u2212\u03b1 and with a rate similar to the star formation rate determined by Harris & Zaritsky (2009) for LMC \ufb01eld stars. Clusters are distributed in the LMC following an exponential density distribution up to a maximum radius of R = 4 kpc, similar to the largest distances from the centre of the LMC for clusters in our sample. The black, solid line depicts the expected cluster frequency distribution if dissolution mechanisms are applied to star clusters exactly as described in the previous section. It can be seen that the frequency of the predicted clusters decreases significantly slower with time than the cluster frequency of the observed clusters for ages T > 200 Myr, and the black solid line predicts about a factor 10 more clusters than observed for ages of several Gyr. If due to incompleteness, several hundred unstudied clusters with ages 1 < T < 4 Gyr would still exist in the LMC. While new clusters in this age range are still being found (e.g. Piatti 2011), it seems rather unlikely that so many clusters are missing from our sample. It is therefore much more likely that the theoretical estimates from sec. 4 underestimate the true rate of cluster dissolution. The red (short dashed), blue (dotted) and green (long dashed) lines show the predicted cluster distribution if we reduce the cluster lifetimes by factors of 5, 10 and 20 respectively. It can be seen that lifetimes need to be reduced by about a factor of at least 10 to 20 to give an agreement between predicted and observed cluster frequency. The right panel of Fig. 6 depicts the mass distribution of star clusters as a function of their age. If we apply the various dissolution mechanisms as described in the previous section (solid lines), the mass distribution of star clusters up to 1 Gyr is in good agreement with the observational data since the predicted mass function can be \ufb01tted by the same slope for all ages, similar to what was found for the observed cluster distribution in sec. 3. The reason is that in this case the turnover carved into the cluster mass function remains at masses lower than our mass-cut, and is therefore not seen in our cluster sample. As a result, at masses higher than 5000 M\u2299, the slope of the cluster mass function is preserved during the \ufb01rst Gyr. For ages larger than 109 yrs, dissolution of clusters more massive than 5000 M\u2299becomes important and the slope starts to \ufb02atten at the low-mass end of our sample. For clusters that are more than 4 Gyr old and standard dissolution, the power-law mass function develops a turn-over at a few thousand solar masses. The location 10 Baumgardt et al. Figure 6. Frequency of clusters as a function of time (left panel) and mass distribution of star clusters for di\ufb00erent age bins (right panel). Black dots in both panels depict the observed distribution of LMC clusters. The solid lines in both panels show the theoretical prediction if clusters form with the same star formation rate as the \ufb01eld stars and the cluster dissolution due to relaxation is applied as described in sec. 4. Red (short dashed), blue (dotted) and green (long dashed) lines show predicted distributions if the cluster lifetimes are reduced by factors of 5, 10 and 20 respectively. In order to \ufb01t the data, cluster dissolution has to be signi\ufb01cantly faster than predicted by theory. of this turn-over is at signi\ufb01cantly smaller masses than the observed one, since the observed one is around 2 \u00b7 105 M\u2299. In order to bring the mass function of predicted clusters in the oldest age bin into better agreement with observations a reduction in the lifetimes by about a factor 20 is needed (see green, long-dashed curve). In the age bin from 109 yrs and 4 \u00b7 109 yrs, lifetimes reduced by a factor 20 produce a mass function that also has a turnover, which is not present in the observed data. A reduction by a factor of 5 to 10 is here in much better agreement with the observations. The comparison with observations indicates that cluster lifetimes are shorter by about a factor 10 to 20 than given by the theoretical estimates of sec. 4. Given that most of the results in that section were derived based on N-body simulations, which are to a large degree free of underlying assumptions, such a reduction seems to be outside the uncertainties of the theoretical estimates. It also does not seem possible to achieve such a reduction in lifetime by changing the adopted LMC parameters, like the rotational velocity or the velocity dispersion, within the uncertainties quoted in the literature. Either the mode of star formation and the properties of LMC clusters were drastically di\ufb00erent at ages of 200 Myr and larger, or our knowledge of star formation in the LMC and the star clusters which were formed at these ages is still incomplete. For example, if the star formation rate at ages T > 1 Gyr was smaller than estimated by Harris & Zaritsky (2009), the di\ufb00erence in frequency between the predicted and observed curves would be smaller and the reduction in lifetime necessary to \ufb01t the observed cluster frequencies would be smaller. In addition, the globular cluster system of the LMC might have formed with a log-normal distribution instead of a power-law (Vesperini 1998; Parmentier & Gilmore 2007), alleviating the need to drastically modify cluster lifetimes in order to predict the cluster mass distribution in the oldest age bin. 6 CONCLUSIONS We have compiled a new catalogue of ages and masses of LMC star clusters by combining results from four di\ufb00erent surveys. Our catalogue covers the whole LMC and contains data for 307 clusters with masses M > 5000 M\u2299, ages T > 107 yrs and absolute magnitudes MV < \u22123.5. We \ufb01nd no signi\ufb01cant in\ufb02uence of cluster dissolution for clusters younger than about 200 Myr, since both the ratio of the number of clusters divided by the absolute star formation rate as well as the mass function of clusters is independent of time for these clusters. If residual gas expulsion is an important dissolution mechanism for star clusters, its in\ufb02uence must be restricted to the \ufb01rst 10 Myr of cluster evolution or low-mass clusters with masses M < 5000 M\u2299. Young star clusters in the LMC form with a power-law mass function with slope \u03b1 = 2.3. If we extrapolate this mass function down to 102 M\u2299, then about 15% of all stars in the LMC form in bound star clusters that survive for at least 10 Myr. For ages larger than T = 200 Myr, the cluster frequency starts to drop and the ratio of cluster frequency to star formation rate is about a factor 40 smaller at T = 4 Gyr than what it was at T = 200 Myr. In addition, the mass function of clusters \ufb02attens for clusters older than T = 1 Gyr. The number of missing clusters in our catalogue needed to explain this \ufb02attening seems to be too large to be explained by incompleteness and we therefore conclude that most of the \ufb02attening is due to cluster dissolution. The amount of cluster The star cluster formation history of the LMC 11 dissolution necessary to \ufb01t the observed cluster distribution is about a factor 10 higher than predicted by theory, indicating either that the e\ufb00ectiveness of the considered processes was signi\ufb01cantly underestimated or that older star cluster formed with a mass distribution signi\ufb01cantly di\ufb00erent from their younger counterparts. ACKNOWLEDGMENTS HB is supported by the Australian Research Council through Future Fellowship grant FT0991052. EKG wishes to acknowledge support from the Sonderforschungsbereich \u201dThe Milky Way System\u201d (SFB 881) of the German Research Foundation (DFG), especially via subproject B5. PA acknowledges funding by the National Natural Science Foundation of China (NSFC, grant number 11073001). GP acknowledges support from the Max-Planck-Institut f\u00a8 ur Radioastronomie (Bonn) in the form of a Research Fellowship.",
                    "introduction": "Open clusters are important test beds for star formation and stellar evolution theories since they provide statistically sig- ni\ufb01cant samples of stars of known distance, age and metallic- ity. Especially useful are star clusters in Local Group galax- ies, which are close enough so that they can be resolved into individual stars and therefore allow their age and mass to be determined more accurately than based on integrated photometry as is done for more distant clusters. The Large Magellanic Cloud (LMC) is one of the near- est galaxies to the Milky Way and contains several thousand star clusters (Bica et al. 2008) with ages ranging from a few Myr to a Hubble time. The large cluster system together with its proximity and the low extinction due to the low in- clination of the LMC disc make the LMC cluster system an ideal test case to study the relation between star formation and cluster formation and the dissolution of star clusters. \u22c6E-mail: h.baumgardt@uq.edu.au Two main epochs of cluster formation have been found in the LMC, separated by an age gap of several Gyr (Bertelli et al. 1992; Girardi et al. 1995; Olszewski et al. 1996). The \ufb01rst star formation episode led to the formation of globular clusters and ended about 10 Gyr ago, while the second epoch started about 4 Gyr ago and is still ongoing. Within the last few Gyrs, several short peaks of star forma- tion have been found (e.g. Harris & Zaritsky 2009), which might have been triggered by close encounters between the Large and Small Magellanic Cloud or between the LMC and the Milky Way (Pietrzynski & Udalski 2000; Chiosi et al. 2006). Similar peaks have also been found in the cluster formation rate and at least during the last Gyr, peaks in star cluster formation correspond to similar peaks that are seen in the \ufb01eld star formation rate (Maschberger & Kroupa 2011). The mass function of star clusters in the LMC is gener- ally found to follow a power-law N(m) \u223cM \u2212\u03b1, although the value of the power-law exponent \u03b1 varies considerably be- tween di\ufb00erent authors. Chandar, Fall & Whitmore (2010) 2 Baumgardt et al. found that the mass function of LMC clusters more mas- sive than 103 M\u2299can be \ufb01tted with a power-law slope \u03b1 = 1.8 \u00b1 0.2 without any evidence for a change of this value with cluster age up to 109 yrs. de Grijs & Anders (2006) found that cluster older than 100 Myr can be \ufb01t- ted by a power-law mass function with slope \u03b1 = 2, while younger clusters follow signi\ufb01cantly \ufb02atter mass functions. A slope between 2 and 2.4 was also found by Hunter et al. (2003) for clusters more massive than a few times 103 M\u2299 at T = 1 Gyr and a few times 102 M\u2299at T < 10 Myr in the combined cluster sample of the LMC and SMC. On the other hand, from their reanalysis of the Hunter et al. cluster sample, Popescu et al. (2012) found a relatively small value of only \u03b1 = 1.5 to 1.6 as the average slope for all clusters that are more massive than 103 M\u2299and less than a few Gyr old. Star clusters are prone to a number of dissolution mechanisms, including two-body relaxation and an external tidal \ufb01eld (Vesperini & Heggie 1997; Baumgardt & Makino 2003), disc and bulge shocking (Ostriker et al. 1972; Gnedin & Ostriker 1997) and encounters with giant molec- ular clouds (Spitzer 1958; Wielen 1985; Gieles et al. 2006a). Boutloukos & Lamers (2002) found evidence for ongoing dis- solution of star clusters in the LMC with a characteris- tic lifetime of log(tdis 4 /yr)=9.7 \u00b1 0.3 for a 104 M\u2299cluster, signi\ufb01cantly longer than the corresponding value found by Lamers et al. (2005) for a sample of nearby galaxies. The long characteristic timescale implies that the high mass end of the cluster mass function in the LMC has stayed virtually unchanged since the time of its formation. Using the same data but a more careful treatment of the incompleteness limit, Parmentier & de Grijs (2008) showed that the cluster disruption time scale is actually highly uncertain and only a lower limit of tdis 4 = 1 Gyr can be given, since clusters at the low-mass end fall below the completeness limit of Hunter et al. (2003) before they are destroyed. Apart from the absolute time scale of cluster dissolu- tion, another important question is whether the timescale for cluster dissolution depends on the cluster mass. Using the cluster sample of Hunter et al. (2003) and based on the observed relation between the mass of the most massive cluster and the sampled age range, Gieles & Bastian (2008) found evidence for mass dependent cluster dissolution for ages larger than 108 yrs, but mass independent dissolution for smaller ages. Chandar, Fall & Whitmore (2010) on the other hand found no evidence for mass dependent cluster dissolution up to 109 yrs when looking at the evolution of the mass function of LMC and SMC star clusters. Most of the above papers are based on data from the cluster catalogue of Hunter et al. (2003), who de- termined properties of 939 clusters in the SMC and LMC based on ground-based CCD photometry. Re- cently a wealth of new data has been obtained for LMC star clusters by Glatt, Grebel & Koch (2010) and Popescu, Hanson & Elmegreen (2012). Glatt et al. have pre- sented ages and luminosities of almost 1200 star clusters in the LMC using data from the Magellanic Cloud Photo- metric Surveys (Zaritsky et al. 2002, 2004, MCPS). In ad- dition, Popescu et al. (2012) have presented new age and mass estimates based on integrated colors for the clusters of Hunter et al. (2003) taking into account random sampling of the IMF and stochastic e\ufb00ects due to bright stars. Figure 1. Position of star clusters in the LMC from recent large surveys plus a few additional clusters from the literature. Only Glatt et al. (2010) and Mackey & Gilmore (2003) cover the whole LMC, while all other surveys are restricted to certain parts of the LMC. In this paper, we present a new derivation of the mass and age distribution of LMC clusters and use it to study the relation between star and star cluster formation and di\ufb00erent cluster dissolution models. Our paper is organised as follows: In Sec. 2 we present the observational data for LMC clusters and derive a combined catalogue of ages and masses for massive LMC clusters. We use this catalogue in Sec. 3 to calculate the age distribution and mass function of LMC clusters. In Sec. 4 we present a discussion of the vari- ous cluster dissolution mechanisms and compare predictions with the observational data in Sec. 5. Our conclusions are \ufb01nally presented in Sec. 6."
                },
                {
                    "url": "http://arxiv.org/abs/0909.5696v1",
                    "title": "Evidence for two populations of Galactic globular clusters from the ratio of their half-mass to Jacobi radii",
                    "abstract": "We investigate the ratio between the half-mass radii r_h of Galactic globular\nclusters and their Jacobi radii r_J given by the potential of the Milky Way and\nshow that clusters with galactocentric distances R_{GC}>8 kpc fall into two\ndistinct groups: one group of compact, tidally-underfilling clusters with\nr_h/r_J<0.05 and another group of tidally filling clusters which have 0.1 <\nr_h/r_J<0.3. We find no correlation between the membership of a particular\ncluster to one of these groups and its membership in the old or younger halo\npopulation. Based on the relaxation times and orbits of the clusters, we argue\nthat compact clusters and most clusters in the inner Milky Way were born\ncompact with half-mass radii r_h < 1 pc. Some of the tidally-filling clusters\nmight have formed compact as well, but the majority likely formed with large\nhalf-mass radii. Galactic globular clusters therefore show a similar dichotomy\nas was recently found for globular clusters in dwarf galaxies and for young\nstar clusters in the Milky Way. It seems likely that some of the\ntidally-filling clusters are evolving along the main sequence line of clusters\nrecently discovered by Kuepper et al. (2008) and are in the process of\ndissolution.",
                    "authors": "Holger Baumgardt, Genevieve Parmentier, Mark Gieles, Enrico Vesperini",
                    "published": "2009-09-30",
                    "updated": "2009-09-30",
                    "primary_cat": "astro-ph.GA",
                    "cats": [
                        "astro-ph.GA"
                    ],
                    "main_content": "In order to investigate the degree of tidal filling, one has to obtain an estimate of the Jacobi radius of a cluster. Most investigations so far used the tidal radius rt obtained by fitting the observed surface density profile with an empirical profile like King (1962) or a theoretical one like King (1966) as an estimate of the Jacobi radius. Surface density data for most globular clusters is however either not available near the Jacobi radius or becomes unreliable in the outer parts due to the low number of cluster stars and the uncertain density of background stars. In addition, due to the high number of stars, surface densities can be much better determined in the inner cluster parts, so that the published tidal radii rt of globular clusters are determined more by the density profile inside a few half-mass radii and might not reflect the true tidal radius of a cluster. Baumgardt et al. (2009) for example found that in case of NGC 2419, the best-fitting King model has a nominal tidal radius of 150 pc, while they estimated that the Jacobi radius rJ of the cluster is around 800 pc. An additional problem of fitting King models to determine Jacobi radii is depicted in Fig. 1. This figure shows the ratio between the projected half-mass radius and the tidal radius rhp/rt for King (1962) and King (1966) models of various concentrations c = log10 rt/rc. It can be seen that with both families of models only a limited range of rhp/rt values can be reached. King (1962) models are restricted to values between 0.028 \u2a7drhp/rt \u2a7d0.29 while King (1966) models are restricted to the even smaller range 0.074 \u2a7drhp/rt \u2a7d0.23. A typical globular cluster with a mass of Mc = 2\u00b7105 M\u2299and a projected half-mass radius of rhp = 3 pc has rhp/rJ = 0.029 at a galactocentric distance of RGC = 10 kpc and rhp/rJ = 0.018 at RGC = 20 kpc. Hence King models cannot accurately describe the density profile of such a cluster and one would have to use models allowing for more extended envelopes like those described by Wilson (1975) to fit the outer surface density profile. This was also noted by McLaughlin & van der Marel (2005), who found that Wilson models provide equally good or significantly better fits than King (1966) models for about 90% of their sample of young massive clusters and old globular clusters. In the present paper we use the ratio of the half-mass radius to the Jacobi radius rJ as a measure for the degree of tidal filling that a globular cluster experiences in the tidal field of the Galaxy. The Jacobi radius can be determined if the cluster mass, galactocentric distance and the underlying Galactic potential is known. For typical globular clusters, Figure 1. Ratio of projected half-mass radius rhp to tidal radius rt as a function of the concentration index c = log10 rt/rc for King (1962) and King (1966) models. The dotted lines mark expected ratios of rhp/rJ for a typical globular cluster with Mc = 2 \u00b7 105 M\u2299and rhp = 3 pc at RGC = 10 kpc and RGC = 20 kpc galactocentric distance. The rhp/rJ ratio of such a cluster cannot be reproduced by any King model, showing that fitting King models to observed density profiles in order to derive the Jacobi radius can lead to a significant bias towards a too small value. masses and galactocentric distances should have typical errors of less than 20%, hence Jacobi radii can for many clusters be determined with higher accuracy than their tidal radii rt. The main disadvantage is that the Jacobi radius varies along the orbit of a cluster, so for highly eccentric orbits, the current radius might not be a good measure for the average Jacobi radius which a cluster experiences and which determines its mass loss rate. We will discuss the influence of eccentric orbits on our results further below. In order to calculate the ratio rh/rJ of Galactic globular clusters, we calculated 3D half-mass radii rh from the projected half-light radii rhp under the assumption that mass follows light and by assuming rh = 1.33rhp. This relation is correct to within 5% for most King (1962) or King (1966) density profiles. We note that half-light radii can be different from half-mass radii for highly evolved clusters that have undergone core-collapse (Baumgardt & Makino 2003; Balbinot et al. 2009). However, correcting for this effect would require detailed observational data for each cluster which is not available at the moment. Jacobi radii were calculated according to King (1962) (see also Innanen, Harris & Webbink 1983 who added a factor of 2/3 to correct for the elongation in the direction along the line connecting the Lagrangian points): rJ = \u201eG Mc 2 V 2 G 2 V 2 G \u00ab1/3 R2/3 GC . (1) Here Mc is the mass of the cluster, VG the circular velocity of the galaxy and RGC the distance of the cluster from the Half-mass to Jacobi radii of Galactic globular clusters 3 galactic centre. We assumed a spherically symmetric density distribution for the Milky Way with a constant circular velocity of VG = 220 km/sec. Cluster masses were calculated from the absolute luminosities of the clusters and an assumed V-band mass-to-light ratio of M/LV = 2.0. The cluster data (projected half-light radii, total luminosities, galactocentric distances) was taken from the 2003 version of the Globular Cluster database of Harris (1996), supplemented by additional data for a few clusters from Bonatto & Bica (2008). We exclude Omega Cen, M54 and NGC 2419 from our analysis since these clusters might be stripped nuclei of dwarf galaxies rather than genuine globular clusters. Fig. 2 depicts the ratio of 3D half-mass radius rh to Jacobi radius rJ as a function of galactocentric distance. It can be seen that the distribution of Galactic globular clusters is not uniform in this plane. First, clusters with large values of rh/rJ > 0.5 are basically absent. Since such clusters would be subject to strong tidal forces and have consequently small dissolution times, if they ever existed they should be quickly destroyed and not be present any more after 10 Gyr of evolution. The absence of such clusters in our distribution therefore serves as a sanity check of our method. Second, most clusters inside \u223c8 kpc exhibit a relatively broad distribution of rh/rJ values between 0.02 < rh/rJ < 0.2 without any noticeable separation. Outside about 8 kpc, the Galactic globular clusters can be split into two groups, one group of clusters with rh/rJ < 0.05 and a second group of clusters with 0.08 < rh/rJ < 0.3. A KS test gives only an 14% chance that clusters beyond 8 kpc follow a log-normal distribution in log rh/rJ. In addition, the average mass of extended clusters in the outer Milky Way is signi\ufb01cantly lower than the mass of the more compact clusters (see Fig. 4), the mean mass of compact clusters is log Mc = 5.44\u00b10.11 while the extended group has a mean mass of only log Mc = 4.38 \u00b1 0.06. Both results indicate that two distinct groups of globular clusters exist in the Milky Way. The dividing line between both groups seems to be around rh/rJ = 0.07 and Table 1 lists the basic parameters of clusters having rh/rJ ratios smaller or larger than this value. Di\ufb00erent orbits seem unlikely to be an explanation for this dichotomy since clusters of both groups are located within the same interval of galactocentric distances and, at least for those clusters with orbital information, the average ratios of RGC/RP eri are similar. The dashed line in Fig. 2 depicts the position which a Mc = 105 M\u2299with rh = 3 pc would have in the rh/rJ vs. RGC plot at di\ufb00erent galactocentric distances. It can be seen that clusters in the lower group outside 8 kpc and most clusters inside this radius fall onto this line. Most clusters in the lower group are therefore relatively massive and compact, something which can also be seen in Table 1. Clusters in the upper group strongly feel the tidal \ufb01eld of the Galaxy. It can be seen that this group is more diverse since it is made up of massive and extended as well as low-mass compact clusters. In the following, we will discuss possible reasons for the origin of both groups. Figure 2. Ratio of half-mass radius rh to Jacobi radius rJ as a function of galactocentric distance RGC for Galactic globular clusters. It can be seen that clusters outside RGC \u22488 kpc fall into two distinct groups, clusters with rh/rJ < 0.05 and clusters with 0.07 < rh/rJ < 0.3. The dashed line depicts the position that a Mc = 105 M\u2299with rh = 3 pc would have at di\ufb00erent galactocentric distances. Compact clusters outside 8 kpc and most clusters inside this radius fall onto this line. 3 DISCUSSION 3.1 Correlation with old and younger halo membership The Galactic Globular cluster system consists of di\ufb00erent subsystems. While bulge/disc GCs di\ufb00er from halo clusters with respect to their metallicity ([Fe/H] \u2a7e\u22120.8 and [Fe/H] < \u22120.8, respectively), the halo subsystem itself is made of clusters with more than one origin. It is traditionally splitted up into two groups, referred to as the Old Halo and the Younger Halo (Zinn 1993, van den Bergh 1993, Mackey & Gilmore 2004), based on di\ufb00erences in horizontal branch (HB) morphology, age, kinematics, spatial distribution (see Parmentier et al. 2000, their Section 2, for a review). Because of their predominant location beyond the Solar Circle, YH clusters are assumed to have been accreted \u2013 along with the dwarf galaxies which used to host them \u2013 after the main body of the Galaxy was built up. Depending on how late they were accreted into the Galactic halo, their evolutionary history may be di\ufb00erent from what in-situ OH clusters have experienced in the Milky Way tidal \ufb01eld. The current accretion of the Sagittarius dwarf galaxy and of its small globular cluster system is the smoking gun of this process (Ibata, Gilmore & Irwin 1994). In Fig. 3, data points are symbol-coded to highlight these di\ufb00erent cluster origins. Filled circles depict disc GCs ([Fe/H] \u2a7e\u22120.8), open triangles show GCs associated to the merging dwarf galaxy Sagittarius (Ter7, Arp2, Ter8, Pal12, NGC4147; see Da Costa & Armandro\ufb001995, MartinezDelgado et al. 2002 and Bellazzini et al. 2003 for cluster 4 Baumgardt et al. Table 1. Basic data for Galactic globular clusters with RGC > 8 kpc belonging to both groups Name rh rh/rJ log MC log TRH RGC RP eri Name rh rh/rJ log MC log TRH RGC RP eri [pc] [M\u2299] [yr] [kpc] [kpc] [pc] [M\u2299] [yr] [kpc] [kpc] Compact group Tidally \ufb01lling group NGC 362 2.67 0.023 5.60 9.09 9.4 0.8 NGC 288 7.58 0.093 4.93 9.50 12.0 5.3 NGC 1261 4.77 0.032 5.36 9.37 18.2 Pal 1 2.87 0.104 3.22 8.23 17.0 Pal 2 7.17 0.029 5.44 9.67 35.4 AM 1 23.64 0.114 4.12 9.92 123.2 NGC 1851 2.44 0.015 5.57 9.02 16.7 5.7 Eridanus 13.99 0.070 4.29 9.65 95.2 NGC 1904 4.00 0.026 5.38 9.27 18.8 4.2 Pyxis 20.79 0.150 4.53 10.00 41.7 NGC 2298 3.24 0.038 4.75 8.87 15.7 1.9 Pal 3 23.73 0.100 4.51 10.08 95.9 82.5 NGC 2808 2.83 0.016 5.99 9.29 11.1 2.6 Pal 4 22.87 0.079 4.64 10.10 111.8 NGC 3201 5.20 0.062 5.22 9.37 8.9 9.0 Rup 106 9.04 0.094 4.77 9.55 18.5 NGC 4147 3.22 0.032 4.70 8.85 21.3 4.1 NGC 5053 22.26 0.218 4.92 10.20 16.9 NGC 4590 6.13 0.070 5.17 9.46 10.1 8.6 AM 4 4.87 0.175 2.87 8.46 25.5 NGC 5024 7.66 0.039 5.71 9.83 18.3 15.5 NGC 5466 13.87 0.130 5.02 9.93 16.2 5.4 NGC 5272 4.52 0.028 5.81 9.52 12.2 5.5 IC 4499 11.00 0.094 5.17 9.84 15.7 NGC 5286 2.94 0.026 5.68 9.19 8.4 Pal 5 26.63 0.395 4.30 10.07 18.6 6.1 NGC 5634 5.28 0.033 5.31 9.42 21.2 Pal 14 32.96 0.233 4.13 10.14 69.0 NGC 5694 4.44 0.022 5.36 9.32 29.1 NGC 6101 10.15 0.124 5.00 9.72 11.1 NGC 5824 4.47 0.017 5.77 9.50 25.8 Pal 15 20.93 0.175 4.43 9.96 37.9 NGC 6205 4.45 0.037 5.71 9.47 8.7 5.0 NGC 6426 7.71 0.084 4.91 9.50 14.6 NGC 6229 4.36 0.020 5.45 9.35 29.7 Ter 7 8.73 0.148 4.25 9.33 16.0 NGC 6341 3.47 0.031 5.51 9.23 9.6 1.4 Arp 2 21.19 0.276 4.35 9.94 21.4 NGC 6779 4.54 0.053 5.19 9.27 9.7 0.9 Ter 8 10.08 0.152 4.25 9.42 19.1 NGC 6864 3.77 0.023 5.65 9.34 14.6 Pal 12 9.48 0.193 4.03 9.29 15.9 NGC 6934 3.65 0.034 5.22 9.14 12.8 6.0 Pal 13 4.60 0.083 3.73 8.71 26.7 NGC 6981 5.80 0.062 5.05 9.37 12.9 NGC 7492 12.21 0.124 4.54 9.66 24.9 NGC 7006 6.12 0.026 5.31 9.51 38.8 18.2 IC 1257 13.57 0.149 4.69 9.79 18.5 NGC 7078 4.23 0.027 5.90 9.52 10.4 5.4 BH 176 4.84 0.138 3.97 8.84 10.2 NGC 7089 4.15 0.028 5.84 9.48 10.4 6.4 ESO 280 8.42 0.156 4.19 9.28 15.0 membership). Plus-signs stand for GCs with no HB morphology index. A list of OH clusters (\ufb01lled squares) is provided in Parmentier & Grebel (2005, their Table 1). Other clusters are sorted in the YH group (open squares). Mackey & Gilmore (2004) emphasize that accreted clusters could also contribute a small fraction of the OH component. Based on either large core radius reminiscent of those observed for GCs in satellite galaxies (their \ufb01g. 16) or spatial motions more typical of YH objects (see also Dinescu et al. 1999), they identify 11 OH GCs which might have been accreted (NGC 6809, 6101, 7492, 5897 and Pal 15 in the \ufb01rst category and NGC 1904, 2298, 5024, 5904, 6205, 7089 in the second category). These ill-de\ufb01ned status clusters are shown as \ufb01lled squares with open circles in Fig. 3. Clusters from Bonatto & Bica (2008) \ufb01nally are shown as \ufb01lled triangles. It can be seen that there is no correlation among the classi\ufb01cation of a cluster to either younger or old halo group and its rh/rJ value. The compact cluster group contains 11 younger halo clusters and 10 old halo clusters unsuspected of having been accreted. They represent each \u223c40 % of the total number of clusters (26) in the compact cluster group. The tidally \ufb01lling cluster group contains 10 younger halo clusters and 5 old halo clusters unsuspected of having been accreted. The higher fraction of younger halo clusters, however, is mostly driven by the 4 clusters with RGC \u223c100 kpc. Considering the same radial extent as for the compact group, that is, RGC = 8 \u221250 kpc, younger and old halo clusters contribute similarly to the tidally \ufb01lling group, with 6 and 5 clusters, respectively, out of 22 clusters. Corresponding  0.01  0.1  1  1  10  100 rh/rJ RGC[kpc] OH Accr. OH? YH Sgr Disc no HB Index BB08 Figure 3. Ratio of rh/rJ vs. galactocentric distance for Galactic globular clusters. Di\ufb00erent symbols indicate to which subsystem a cluster belongs, old halo clusters are marked by \ufb01lled squares, younger halo clusters by open squares, disc globular clusters by \ufb01lled circles and clusters accreted from the Sagittarius dwarf galaxy by open triangles. There is no correlation between the classi\ufb01cation of a globular cluster and its rh/rJ value. number fractions (\u223c25 %) agree with previous ones within the statistical uncertainties. Moreover, both compact and tidally \ufb01lling groups are characterized by the same number fraction of clusters accreted or suspected of having been accreted (i.e. younger halo clusters or Sagittarius clusters Half-mass to Jacobi radii of Galactic globular clusters 5 or old halo clusters suspected of having been accreted see above), namely, \u223c60%. We therefore conclude that the rh/rJ dichotomy is not due to a di\ufb00erent origin of the two cluster populations 3.2 Origin of the compact cluster group Tab. 1 lists the basic parameters of clusters belonging to either group, including the 3D half-mass radius, current mass and galactocentric distance. It also shows the current relaxation time, calculated according to Spitzer (1987): TRH = 0.138 \u221aMcr3/2 h \u221a G <m> ln 0.11Mc/ <m> (2) where <m>= 0.4M\u2299is the average mass of stars and G the gravitational constant. It can be seen that the compact clusters mostly have very large relaxation times. The average relaxation time for a cluster in this group is about 2.8 Gyr, and nearly all clusters have relaxation times larger than 1 Gyr. According to G\u00a8 urkan et al. (2004), it takes about 7 to 10 initial half-mass relaxation times until star clusters with a narrow mass spectrum where the massive stars are about twice as massive as the average cluster star, which is typical for globular clusters, have gone into core collapse. The compact clusters should therefore still be mostly in their pre-core collapse phase and should not have started postcore collapse expansion. Tab. 1 also lists the perigalactic distances of the globular clusters as determined by Dinescu et al. (1999), Allen, Moreno & Pichardo (2006) and Casetti-Dinescu et al. (2007). Although there are clusters which have perigalactic distances of less than 2 kpc, for the majority of the compact group clusters, the perigalactic distances are within a factor of 3 of the current galactocentric distance. The estimates of rJ would therefore decrease by no more than a factor of 2 if we used the perigalactic distance to calculate rJ. Most compact clusters therefore have rh/rJ < 0.1 also at perigalacticon and are at most moderately in\ufb02uenced by the Galactic tidal \ufb01eld. Hence, their small half-mass radii are likely not due to tidal stripping at perigalacticon but must have been the result of the formation process. We conclude that clusters in the compact group also formed very compact. N-body simulations show that the expansion factor due to gas expulsion is typically a factor 2 to 3 for moderate star formation e\ufb03ciencies of 30% to 40% (Baumgardt & Kroupa 2007) and stellar evolution will increase this value by another factor 2 if mass is lost adiabatically. Hence the initial half-mass radius of clusters in the compact group must have been around 1 pc or less. Since most star clusters inside 8 kpc have half-mass radii very similar to compact group star clusters, it seems likely that most globular clusters in the Milky Way formed compact and with half-mass radii of 1 pc or less, which is comparable to the half-mass radius of embedded star clusters in the Milky Way (Lada & Lada 2003). 3.3 Origin of the tidally \ufb01lling cluster group Fig. 4 depicts the position of inner clusters (green triangles) and of clusters with rh/rJ < 0.07 (red crosses) and clusters with rh/rJ > 0.07 (blue dots) in a half-mass radius vs. mass diagram. It can be seen that clusters with rh/rJ < 0.07 are mostly massive clusters with half-mass radii of a few pc, while clusters with rh/rJ > 0.07 have larger radii and also smaller masses. Due to the smaller masses, clusters in the tidally \ufb01lling group should on average be closer to dissolution. This is con\ufb01rmed by observational data for a few clusters like Pal 5, which has very pronounced tidal tails and might be on its \ufb01nal orbit before dissolution (Odenkirchen et al. 2001; Dehnen et al. 2004). Clusters in the inner Milky Way also have smaller masses than compact outer clusters which might be due to stronger cluster dissolution in the inner Milky Way as a result of the stronger tidal \ufb01eld (Vesperini & Heggie 1997; Baumgardt & Makino 2003). One way to explain the large radii of the tidally \ufb01lling clusters would be that they also formed extended. Indeed, Elmegreen (2008) has recently discussed di\ufb00erent modes of star formation and attributed the di\ufb00erence between star formation in bound clusters and loose groupings to a difference in cloud pressure and di\ufb00erent background tidal forces. This could explain why clusters with low densities are only found far away from the centers of major galaxies or in dwarf galaxies. The fact that Milky Way globular clusters are clearly separated in rh/rJ is however more di\ufb03cult to understand if cluster radii are set at formation time. An alternative viewpoint would be that the tidally \ufb01lling clusters expanded from smaller radii, possible e.g. through post-collapse expansion driven by a population of stellar binaries in the cluster core. Goodman (1984) and Baumgardt, Hut & Heggie (2002) (their Eq. 4) estimated that during post-core collapse expansion, the half-mass radius of an isolated cluster satis\ufb01es rh(t) = rh0 (t/tcc)(2+\u03bd)/3 (3) where rh0 is the initial half-mass radius, tcc the time of core collapse and \u03bd \u22480.1 a constant related to the cluster mass loss. Gieles & Baumgardt (2008) found that the above relation also holds for clusters in a tidal \ufb01eld as long as rh/rJ < 0.05. For clusters with a narrow mass spectrum, core collapse happens after 7 to 10 initial half-mass relaxation times (G\u00a8 urkan et al. 2004), in which case the above relation would predict that expanding clusters should have relaxation times which are roughly 1/10th of their current age, i.e. of order TRH \u2248109 yrs. The majority of clusters in the tidally \ufb01lling group however have relaxation times TRH > 3 \u00b7 109 yrs, which is too large to be explained by binary driven expansion from small radii. Also the fact that tidally \ufb01lling clusters have on average larger relaxation times than compact clusters argues against post-collapse expansion from smaller radii. Merritt et al. (2004) and Mackey et al. (2007) have shown that stellar mass black holes, if present in su\ufb03cient numbers, can cause strong cluster expansion. For clusters retaining all the black holes formed in them, Mackey et al. (2008) found that the core radius can reach values up to 8 pc after 10 Gyr of evolution and is almost as large as the halfmass radius. This value is large enough to explain the halfmass radii of a signi\ufb01cant fraction of clusters in the tidally \ufb01lling group (see Fig. 4). Interestingly, in such a case clusters of the tidally \ufb01lling group would have been the most com6 Baumgardt et al. pact clusters initially such as to be able to retain their BHs. However, some clusters in the tidally-\ufb01lling group have halfmass radii too large to be explained by BH-driven expansion and there is no signi\ufb01cant di\ufb00erence in metallicity between compact and tidally \ufb01lling clusters, as might be expected if BH kick velocities depend on metallicity, which both argue against BH driven expansion. Central intermediate-mass black holes can also act as an e\ufb03cient heat source, but judging from the results of Baumgardt, Makino & Ebisuzaki (2004), the half-mass radii of most clusters in the tidally \ufb01lling group are too large to be explained by intermediate-mass black hole driven expansion. Strong expansion is also possible by stellar evolution if star clusters are initially mass segregated since the fractional loss of potential energy can in such a case be much larger than the mass fraction lost by stellar evolution (Vesperini et al. 2009). The question of whether clusters in the tidally \ufb01lling group were born compact and later expanded or already formed with the large half-mass radii we see today therefore remains open. If they formed with large half-mass radii, their initial relaxation times were also quite large and the clusters should be dynamically less evolved. In this case they would not be mass segregated, so measuring stellar mass functions at di\ufb00erent radii might be one way to test the formation scenario. In this context it is interesting to note that Jordi et al. (2009) recently found that the stellar mass function of Pal 14, which is one of the clusters with the longest relaxation time in our sample, di\ufb00ers from a Kroupa IMF inside the clusters half-mass radius. Unfortunately no information on the stellar mass function in the outer cluster parts is available at the moment to test whether this is due to dynamical cluster evolution. We note that the tidally \ufb01lling clusters, due to the large half-mass radii and galactocentric distances of many of them, are partly responsible for driving the correlation between rh and RGC found by Mackey & van den Bergh (2005). A linear least-square \ufb01t gives a relation between half-mass radius and galactocentric distance log rh = 0.50 \u00b7 log RGC + 0.27 for all Galactic GCs. This relation \ufb02attens to log rh = 0.25\u00b7log RGC +0.38 if we exclude the tidally \ufb01lling clusters, indicating that globular clusters in the compact group formed with similar parameters nearly everywhere in the Galaxy. 4 CONCLUSIONS We have studied the distribution of the ratio of half-mass radius rh to Jacobi radius rJ for Galactic globular clusters and have shown that clusters with distances larger than \u223c 8 kpc fall into two distinct groups: One group of compact clusters with rh/rJ < 0.05 and a group of more extended clusters with 0.08 < rh/rJ < 0.30. Compact clusters are mainly massive clusters with half-mass radii of a few pc. The half-mass radius and density of the compact clusters in the outer halo seems not to be adjusted to the Jacobi radius, so they were probably also born compact with halfmass radii rh < 1 pc, comparable to the half-mass radii of embedded clusters and young open clusters in the Milky Way. Tidal radii derived from \ufb01tting King pro\ufb01les to the surface density pro\ufb01les of these clusters can be signi\ufb01cantly smaller than their Jacoby radii since the rh/rJ ratios of these Figure 4. Half-mass radius rh vs. cluster mass for globular clusters with RGC < 8 kpc (green triangles) and for clusters RGC > 8 kpc that are weakly in\ufb02uenced by the Galactic tidal \ufb01eld (rh/rJ < 0.07, red crosses) and for strongly tidally in\ufb02uenced clusters (0.07 < rh/rJ < 0.3, blue dots). Clusters weakly in\ufb02uenced by the tidal \ufb01eld are all massive and compact while strongly tidally in\ufb02uenced clusters have signi\ufb01cantly smaller masses. Inner clusters also have smaller masses on average, which might be a result of their stronger dissolution. Dashed lines show where clusters with a given half-mass relaxation time are located in this plot. clusters are smaller than what can be reached with any King pro\ufb01le. Some of the tidally \ufb01lling clusters might also have formed compact and could have expanded later due to dynamical heating by binary stars, stellar-mass black holes or intermediate-mass black holes, although it is unclear if this holds for all clusters in this group since about half of the tidally \ufb01lling clusters have relaxation times of the order of a Hubble time or larger. Da Costa et al. (2009) have recently found a bimodality of the globular cluster size distribution in dwarf galaxies. The average radii of clusters in both of their groups agree quite well with the radii of Milky Way globular clusters in our compact and tidally \ufb01lling group, showing that globular clusters formed under similar conditions in di\ufb00erent galaxies. Furthermore, Pfalzner (2009) has recently shown that open clusters in the Milky Way evolve along two sequences in the age vs. radius plane, one group of clusters starting compact with half-mass radii rh < 1 pc and reaching sizes of a few pc after 20 Myr of evolution and a second group of clusters starting with half-mass radii larger than a few pc and reaching \u223c20 pc after 20 Myr. The latter value agrees quite well with the sizes of most clusters in the tidally \ufb01lling group. Galactic globular clusters therefore show the same dichotomy seen for globular clusters in dwarf galaxies and for young star clusters in the Milky Way. Extended star clusters appear therefore as an ubiquitous feature of star Half-mass to Jacobi radii of Galactic globular clusters 7 cluster systems hosted by a variety of galaxies. It would be interesting to see how the extended globular clusters of the Milky Way relate to other star clusters with large rh values, like the Faint Fuzzy star clusters in lenticular galaxies (Larsen & Brodie 2000), the di\ufb00use star clusters found by Peng et al. (2006) in early-type galaxies of the Virgo cluster and those hosted by dwarf galaxies (Da Costa et al. 2009). K\u00a8 upper, Kroupa & Baumgardt (2008) found that initially compact star clusters in a tidal \ufb01eld expand after core collapse until they reach a mass-dependent rh/rJ value and then evolve along a common sequence towards dissolution. They dubbed the latter phase the main sequence evolution of star clusters. During the main sequence phase, the rh/rJ values increase slowly with decreasing cluster mass. Extrapolating from the results of K\u00a8 upper, Kroupa & Baumgardt (2008) to Mc = 105 M\u2299, we expect that globular clusters should have approximately rh/rJ \u22480.1 when on the main sequence, which \ufb01ts observed rh/rJ of clusters in the tidally \ufb01lling group rather well. It is therefore likely that part of the clusters in the tidally \ufb01lling group, especially those with small relaxation times, have reached the mainsequence stage of their evolution and are evolving towards dissolution. As for those with long relaxation times, however, whether their large half-mass radius is an imprint of their formation process or a result of cluster expansion remains an open question. We \ufb01nally note that it is possible that the extended clusters were initially much more numerous, since due to their large sizes, they are e\ufb00ectively destroyed by the Galactic tidal \ufb01eld, especially in the inner part of the Milky Way. ACKNOWLEDGEMENTS We thank the referee for comments which improved the presentation of the paper. HB acknowledges support from the German Science Foundation through a Heisenberg fellowship. GP acknowledges support from the Belgian Science Policy O\ufb03ce in the form of a Return Grant and from the Alexander von Humboldt Foundation in the form of a Research Fellowship. EV was supported in part by NASA grant NNX08AH15G. We acknowledge the support of the KITP during the program \u2019Formation and Evolution of Globular Clusters\u2019, which was supported in part by the United States National Science Foundation under Grant No. PHY05-51164.",
                    "introduction": "It is well known that most, if not all, stars form in star clus- ters. Star clusters are therefore important probes of the star formation process (Kroupa 2005; Parmentier 2009). This is especially the case for globular clusters which, due to their large ages and low metallicities, are relics of star formation processes in the early universe. Observations show that in nearby galaxies star clus- ters form compact, with half-mass radii of rh < 1 pc, at the centres of giant molecular cloud cores (Lada & Lada 2003). They then undergo a signi\ufb01cant expansion as a re- sult of gas expulsion driven by stellar winds and UV ra- diation from bright stars and supernovae explosions (Hills 1980; Bastian & Goodwin 2006; Baumgardt & Kroupa 2007) and later also by mass loss from stellar evolu- tion (Cherno\ufb00& Weinberg 1990; Fukushige & Heggie 1995; Vesperini & Zepf 2003). As a result, the radii of star clusters show a steady increase with cluster age within the \ufb01rst 20 Myrs (Bastian et al. 2008; Pfalzner 2009). Globular clusters are dynamically evolved systems, so in addition to the early evolution due to gas ex- pulsion and stellar evolution, cluster radii are also sub- ject to dynamical cluster evolution due to two-body re- laxation. As a result of mass segregation and core col- lapse, the core radius shrinks while the half mass ra- dius stays roughly constant before core collapse. After core collapse, stellar binaries provide a central heat source and the cluster expands self-similarly (Goodman 1984; McMillan et al. 1990; Gao et al. 1991; Giersz & Heggie 1994; Baumgardt, Hut & Heggie 2002; Heggie et al. 2006). This process continues until the cluster runs into the ex- ternal tidal \ufb01eld, at which point cluster expansion is bal- anced by the loss of outer stars over the tidal boundary. As a result, the ratio of half-mass radius to Jacobi ra- dius1 evolves along a common sequence which, at least for single-mass clusters, only depends on current cluster mass (K\u00a8 upper, Kroupa & Baumgardt 2008). The ratio of the half- mass to Jacobi radius for individual clusters therefore con- tains important information on the dynamical state of a star cluster. In the current paper we examine the distribution of half- 1 Throughout the paper we will denote the distance from the centre of a star cluster to the \ufb01rst Lagrangian point as the Jacobi radius rJ, while the term tidal radius rt refers to the limiting radius of King (1962) or King (1966) models. 2 Baumgardt et al. mass to Jacobi radii of Galactic globular clusters in order to better understand the formation and evolution of Galactic globular clusters. The paper is organised as follows: In Sec. 2 we present the data and show that outer globular clusters fall into two distinct groups. In Sec. 3 we discuss the relation of these groups to di\ufb00erent subsamples of Galactic globular clusters like old and younger halo clusters or globular clus- ters believed to be accreted from dwarf galaxies and use additional information like half-mass relaxation times and cluster orbits to determine the degree of dynamical cluster evolution. In Sec. 4 we \ufb01nally draw our conclusions."
                },
                {
                    "url": "http://arxiv.org/abs/0809.2783v1",
                    "title": "High mass-to-light ratios of UCDs - Evidence for dark matter ?",
                    "abstract": "Ultra-compact dwarf galaxies (UCDs) are stellar systems with masses of around\n10^7 to 10^8 Msun and half mass radii of 10-100 pc. They have some properties\nin common with massive globular clusters, however dynamical mass estimates have\nshown that UCDs have mass-to-light ratios which are on average about twice as\nlarge than those of globular clusters at comparable metallicity, and tend to be\nlarger than what one would expect for old stellar systems with standard mass\nfunctions.\n  One possible explanation for elevated high mass-to-light ratios in UCDs is\nthe existence of a substantial amount of dark matter, which could have ended up\nin UCDs if they are the remnant nuclei of tidally stripped dwarf galaxies.\nTidal stripping of dwarf galaxies has also been suggested has the origin of\nseveral massive globular clusters like Omega Cen, in which case globular\nclusters could have also formed with substantial amounts of dark matter.\n  In this paper, we present collisional N-body simulations which study the\nco-evolution of a system composed out of stars and dark matter. We find that\nthe dark matter gets removed from the central regions of such systems due to\ndynamical friction and mass segregation of stars. The friction timescale is\nsignificantly shorter than a Hubble time for typical globular clusters, while\nmost UCDs have friction times much longer than a Hubble time. Therefore, a\nsignificant dark matter fraction remains within the half-mass radius of\npresent-day UCDs, making dark matter a viable explanation for the elevated M/L\nratios of UCDs. If at least some globular clusters formed in a way similar to\nUCDs, we predict a substantial amount of dark matter in their outer parts.",
                    "authors": "Holger Baumgardt, Steffen Mieske",
                    "published": "2008-09-17",
                    "updated": "2008-09-17",
                    "primary_cat": "astro-ph",
                    "cats": [
                        "astro-ph"
                    ],
                    "main_content": "In our simulations, we assume that stars and dark matter particles follow the same density distribution initially, which was given by a Plummer (1911) model. Determinations of mass-to-light ratios of globular clusters or UCDs rely mainly on stars located inside the half-mass radius (Hilker et al. 2007; Mieske et al. 2008) or even closer within (McLaughlin & van der Marel 2005). Tidal effects are therefore not likely to have a strong influence on determined massto-light ratios. Also, due to their high mass and corresponding large dissolution times, tidal interactions probably play only a minor role for UCDs. In our simulations we therefore neglect the influence of an external tidal field. We assume that the stars initially follow a Kroupa (2001) mass function with lower and upper mass limits of 0.1 and 100 M\u2299. Stellar evolution changes the mass function of stars, however most of this change happens within the first 109 yrs (see e.g. the grid of models by Baumgardt & Makino (2003)), i.e. on a timescale short against the lifetime of globular clusters or UCDs. We therefore also neglect stellar evolution and immediately transform stars to the assumed age of GCs and UCDs, T=12 Gyrs. For the transformation, we assume that stars with mass larger than 25 M\u2299form black holes and assume that the black hole mass is 10% of the mass of the initial star. This way, black hole masses in our models are compatible with observed masses for stellar mass black holes (e.g. Casares (2006)). Stars with masses between 8 M\u2299and 25 M\u2299are assumed to form neutron stars with a mass of m = 1.3 M\u2299(Thorsett & Chakrabarty 1999). Stars between 0.8 M\u2299and 8 M\u2299are assumed to form white dwarfs due to stellar evolution. The masses of the white dwarfs are obtained from Kalirai et al. (2008), who found, based on observations of white dwarfs in star clusters, the following relation between the initial and final mass of white dwarfs: mwd = 0.109m + 0.394M\u2299. Stars less massive than 0.8 M\u2299 are still on the main sequence and we assume that they have not yet lost any mass. The following table summarises our initial-to-final mass relation: mrem = 8 > > > > > < > > > > > < > > > > > : tro m, m < 0.8M\u2299 0.109 m M\u2299 m M\u2299+ 0.394, 0.8M\u2299< m < 8M\u2299 1.35, 8M\u2299< m < 25M\u2299 0.1m, 25M\u2299< m (1) > : Neutron stars and probably also black holes receive kicks at the time of their birth due to asymmetric supernova explosions. The size of these kicks is a few hundred km/sec (Lyne & Lorimer 1994), which is large enough that most will be lost from globular clusters or UCDs (Pfahl et al. 2002). We therefore assume only a small neutron star and black hole retention fraction of 20% in our simulations. With Evidence for dark matter in UCDs 3 these assumptions, the mean mass of stars in our models is 0.344 M\u2299. The dark matter is also modeled as point mass particles. In our reference simulation we assume a mass of 0.03 M\u2299for the dark matter particles, but we also make simulations with masses of 0.15 M\u2299and 0.01 M\u2299to study the in\ufb02uence of the adopted particle mass on our results. Theoretically, the dynamical friction of stars should not depend on the mass of the dark matter particles as long as the mass ratio between stars and dark matter is high enough (Binney & Tremaine 1987). Also, with the adopted masses, the self-interaction of the dark matter particles is still unimportant over the timescales studied here. We will further investigate the in\ufb02uence of the mass of the dark matter particles in sec. 3.4. All runs are performed with the collisional N-body code NBODY4 (Aarseth 1999) on the GRAPE6 computers (Makino et al. 2003) of Bonn University and the results are expressed in N-body units (Heggie & Hut 2002), in which the constant of gravity and total cluster mass are equal to 1 and the total potential energy is equal to -0.5. Table 1 gives an overview of the runs performed. 3 RESULTS 3.1 Mass segregation timescale: analytical estimate In the following we derive an analytical estimate of the mass segregation time scale in compact stellar systems. Massive stars will segregate against dark matter particles and lighter stars as a result of dynamical friction and energy equipartition. Since the masses of stars are much higher than the mass of the dark matter particles, the frictional drag on the stars is given by (see Binney & Tremaine (1987) Eq. 7-18): d\u20d7 v dt = \u2212\u22124\u03c0 ln \u039bG2\u03c1(r)m v3 \u00bb erf(X) \u22122X \u221a\u03c0 e\u2212X2\u2013 \u20d7 v (2) where \u03c1(r) is the background density of dark matter and stars, m the mass of an inspiraling star, ln \u039b the Coulomb logarithm, and X = \u20d7 v/( \u221a 2\u03c3) is the ratio between the velocity of a star and the (1D) stellar velocity dispersion \u03c3. If we assume v \u2248\u03c3, it follows that X = 1/ \u221a 2. Setting ln \u039b = 12 for globular clusters (Binney & Tremaine (1987) Tab. 7-1), the eq. 2 can be rewritten as: dv dt = \u221229.96G2\u03c1(r)m v2 . (3) The resulting energy change is dE dt = d dt( 1 2mv2) = mv dv dt . For a distribution of stars in virial equilibrium, an energy change dE corresponds to a change in potential energy md\u03a6 = 2dE. Hence d\u03a6 dt = \u221259.93G2\u03c1(r)m v . (4) For a Plummer model, the density \u03c1, circular velocity vc and speci\ufb01c potential \u03a6 at point r are given by: \u03c1(r) = 3MT ota2 4\u03c0 ` a2 + r2\u00b4\u22125/2 \u03a6(r) = \u2212 GMT ot (a2 + r2)1/2 (5) vc(r) = \u221a GMT otr2 (a2 + r2)3/4 where MT ot is the total cluster mass and a is the scale radius of the Plummer model. With these equations, the above relation can be rewritten as: dr dt = \u221214.31 \u221a Ga2m \u221aMT otr2 (a2 + r2)1/4 (6) For an order of magnitude estimate of the inspiral time scale, one can approximate ` a2 + r2\u00b41/4 \u2248a1/2. One can then solve the above relation and obtains as time which a star starting at radius R0 needs to reach the centre: TFric = 0.023 \u221a MT ot \u221a Ga3/2m R3 0 (7) For a Plummer model, a = 0.766RH, so the inspiral time for stars near the half-mass radius is given by: TFric = 0.035 \u221aMT otR3/2 H \u221a Gm (8) For a globular cluster or UCD we thus obtain: TFric = 5.86 \u201e MT ot 106M\u2299 \u00ab1/2 \u201eRH 5pc \u00ab3/2 \u201e m M\u2299 \u00ab\u22121 Gyr (9) The resulting dynamical friction time agrees to within 20% with what Binney & Tremaine found for the inspiral time of an isothermal sphere (their eq. 7-26). Eq. 9 predicts a dynamical friction time scale of 4-5 Gyr for a typical GC (3\u00d7105M\u2299, rh = 3pc), and about 400 Gyr for a typical UCD (107M\u2299, rh = 20pc). That is, after a Hubble time most of the dark matter in globular clusters should have been pushed out of the centre, while in UCDs the inspiral of stars should be far from complete and a signi\ufb01cant fraction of DM should still reside in their centres, leading to high mass-to-light ratios. 3.2 N-body results Fig. 2 shows the evolution of Lagrangian (lag.) radii, i.e. radii which contain a certain fraction of the total mass, of stars and dark matter particles in our \ufb01rst simulation, which had a dark matter particle mass of m = 0.03 M\u2299and an equal amount of mass in stars and dark matter. The e\ufb00ect of dynamical friction and mass segregation is clearly visible since the lag. radii of dark matter particles increase with time while those of the stars shrink. In N-body units, the total cluster mass and constant of gravity are both unity. With a mean stellar mass of m = 6.0 \u00b7 10\u22125, we predict a dynamical friction timescale of TFric = 391 in N-body units according to eq. 8. It can be seen that by this time the cluster center is indeed nearly free of dark matter: inside the lag. radius of 10% of the stars, only 1% of the dark matter particles are located. At the end of the simulation, the 10% lag. radius of the dark matter particles is almost equal to the half-mass radius of the stars, i.e. only 20% of the cluster mass is still made up of dark matter inside the (visible) half-mass radius of the cluster. The core of the cluster is even stronger depleted and is nearly free of dark matter by the end of the simulations. It would therefore be di\ufb03cult to detect the remaining dark matter by its e\ufb00ect on stellar velocities if mainly stars from the cluster center or inside 4 H. Baumgardt and S. Mieske Figure 2. Evolution of Lagrangian radii, i.e. radii which contain a certain fraction of the total mass, of stars (red solid lines) and dark matter particles (blue dashed lines) in the \ufb01rst run from Table 1. The left panel depicts the evolution as a function of Nbody time, the right panel as a function of current relaxation time, where the relaxation time is calculated based on the distribution of stars only. Inside the half-mass radius of the cluster, less than 20% of the total mass is made up out of dark matter after the clusters are ten apparent relaxation times old. the half-mass radius are used to determine the line-of-sight velocity dispersion. The right panel of Fig. 2 depicts the evolution of lag. radii as a function of the ratio of cluster age to the actual relaxation time. In order to allow for a better comparison with observations, the relaxation time is calculated from the stellar component according to (Spitzer 1987): TRH = 0.138 \u221aM\u2217R3/2 H\u2217 \u221a Gm\u2217ln \u03b3N\u2217 (10) where M\u2217is the total stellar mass of the cluster, RH\u2217 the half-mass radius of the stellar distribution, m\u2217and N\u2217are the mass and number of stars and \u03b3 a constant in the Coulomb logarithm which is taken to be \u03b3 = 0.11 (Giersz & Heggie 1994). Eq. 10 would be the relaxation time inferred by an observer who can only determine the stellar distribution and does not know about the dark matter. It has the same dependence on cluster mass and radius as the friction timescale and can therefore also be used to judge the dynamical state of a cluster. The right panel of Fig. 2 shows that once a cluster is two to three apparent relaxation times old, the centre is free of dark matter and by the time the cluster has become ten relaxation times old, there is little dark matter left inside the half-mass radius. Since most globular clusters have relaxation times of only a few Gyr, their mass-to-light ratios should be within 20% of those of pure stellar populations if mainly stars inside the clusters half-mass radius are used to determine the velocity dispersion. Since this is within the uncertainty of measured mass-to-light ratios and current stellar population models, such a small dark matter cannot be detected kinematically in globular clusters. UCDs on the other hand have relaxation times signi\ufb01cantly larger than a Hubble time and should therefore still have large mass-to-light ratios if they formed as a mix of dark matter and stars. This is con\ufb01rmed by the upper panel of Fig. 3, which depicts the dark matter fraction inside the cluster core (assumed to be the region inside the 5% lag. radius of the stars) Figure 3. Dark matter fraction (upper panel) and average mass of stars (bottom panel) as a function of time. Core values are shown by solid lines, values inside the half-mass radius by dashed lines. The core radius is assumed to be equal to the 5% lag. radius of the stellar distribution. The dark matter is depleted from the centre within 1 to 2 friction times. At the same time, heavy mass stars segregate against the light mass stars and the average mass of stars increases in the centre. Clusters where the centers are depleted of dark matter should therefore also be mass segregated in their centre. and inside the half-mass radius of the cluster stars. It can be seen that after about 1.5 to 2 friction times, the cluster core is almost completely free of dark matter. Within the half-mass radius, only about 30% of the initial dark matter amount remains after this time. The lower panel of Fig. 3 depicts the evolution of the average mass of stars in the core and inside the half-mass radius. At both radii, the average mass of stars is increasing since, while stars segregate against the dark matter particles, heavy-mass stars also segregate against the lighter ones. After about 2 dynamical friction timescales, the mass of stars has reached a near constant value of about 0.65 M\u2299, which is signi\ufb01cantly higher than the average mass of stars. Clusters which have expelled dark matter out of their centres should therefore also be mass segregated. 3.3 Comparison with observations Fig. 4 shows the e\ufb00ect which the decreasing dark matter fraction in the center has on the projected velocity dispersion of stars. In order to determine this e\ufb00ect, we \ufb01rst calculate the velocity dispersion pro\ufb01le \u03c3Obs(r) of bright stars with masses in the range 0.6 < m < 0.9 M\u2299as a function of projected radius. We restrict ourselves to this mass range since in a globular cluster or UCD, these would be the stars which dominate the cluster light. After determing the velocity dispersion pro\ufb01le of bright stars, we calculate Evidence for dark matter in UCDs 5 the expected velocity dispersion pro\ufb01le based on the stellar density distribution according to (Binney & Tremaine 1987, eq. 4-54): \u03c32(r) = \u22121 \u03c1(r) Z \u03c1(r\u2032) d\u03a6 dr \u02db \u02db \u02db \u02db r=r\u2032 dr\u2032 (11) where \u03c1(r) is the (3D) density distribution of bright stars and \u03a6(r) is the potential coming from the stars alone. Eq. 11 assumes a spherical cluster potential and an isotropic velocity dispersion of stars. After projecting \u03c3(r) we can calculate the correction factor f needed so that the predicted velocity dispersion matches the true velocity dispersion of the clusters in the N-body simulations, i.e. f(r) = \u03c3Obs(r)/\u03c3P red(r). The resulting correction factor is plotted in Fig. 4 for the \ufb01rst run from Table 1. Initially, dark matter and stars follow the same density distribution, so the velocity dispersion is a factor f(r) = p (MDM + M\u2217)/M\u2217= 1.41 higher than predicted by eq. 11. As the cluster evolves, dark matter is removed from the center, so the velocities of stars in the center are determined more and more by the stars alone and f approaches unity. After 3 relaxation times, the central velocity dispersion is only 10% higher than what one would expect based on the stars alone and after 10 relaxation times the di\ufb00erence is less than 1%. Most globular clusters should therefore have central M/L ratios which are close to those predicted by stellar population models. Beyond 10 half-mass radii, f remains close to the initial value even after 10 relaxation times. As long as dark matter is not removed by tidal e\ufb00ects (Mashchenko & Sills 2005), it should therefore be detectable in globular clusters through the observation of stellar velocities in the outer cluster parts. We \ufb01nally discuss the in\ufb02uence of the dark matter on the global mass-to-light ratios. In order to compare our simulations with observed clusters, we again calculate true and expected velocity dispersions of stars with masses in the range 0.6 < m < 0.9 M\u2299. Since mass-to-light ratios of UCDs are determined from stellar velocities covering a signi\ufb01cant fraction of the cluster area (see e.g. discussion in Hilker et al. (2007)) and measured mass-to-light ratios of globular clusters are based mainly on stars in the inner cluster parts (McLaughlin & van der Marel 2005), we determine global velocity dispersions in the simulations for all stars located inside the projected half-light radius. The resulting mass-tolight ratios of our model clusters are then given by M/L = f 2M/L|\u2217 (12) where M/L|\u2217is the mass-to-light ratio which a pure stellar population would have and f is again f = \u03c3Obs/\u03c3P red. Fig. 5 depicts the evolution of M/L with cluster age for runs 1 and 2 of Table 1, and compares it with observed M/L ratios of UCDs and GCs from Mieske et al. (2008). Note that the literature M/L estimates are normalised to the same (solar) metallicity, to allow direct intercomparison. Time is again expressed in terms of age divided by the relaxation time as determined from the stars alone. The observed normalised M/L ratios show a clear trend in the sense that dynamically more evolved systems have on average lower M/L values. The mass-to-light ratios in our simulations also decrease as the dynamic age increases, since, as the dark matter is depleted from the cluster centers, the velocity dispersion is determined more and more by Figure 4. Evolution of the ratio f of observed velocity dispersion to predicted one based on the stellar distribution alone for 4 different ratios of cluster age to apparent relaxation time calculated according to eq. 10. Initially, dark matter and stars follow the same distribution and there is an equal amount of mass in dark matter and stars, so \u03c3Obs = \u221a 2\u03c3P red independent of radius. As the dark matter is expelled from the centre, stellar velocities in the inner parts are increasingly determined by the stars alone and f drops towards unity in the cluster centre. Globular clusters should therefore have central mass-to-light ratios in agreement with stellar population models. the stars alone, so M/L approaches M/L|\u2217. Depending on whether a stellar M/L|\u2217of 2.5 or 2.0 is assumed, a run with a primordial dark matter content equal to or twice as high as the stellar mass provides an acceptable \ufb01t to the data, making dark matter a viable alternative to explain the elevated mass-to-light ratios of UCDs. We note that if the observed decrease of M/L with dynamical age is due to the dynamical depletion of non-luminous particles from the cluster centers, the dark matter particles have to be of lower mass than the stars, ruling out e.g. a central concentration of black holes in UCDs as the explanation for their high M/L ratios. The stellar mass-to-light ratios we have to assume in order to \ufb01t the data for GCs are marginally lower than predicted by simple stellar population models for 12 Gyr old, solar-metallicity star clusters. For example, the Bruzual & Charlot (2003) models predict an M/L of 2.5 for a 8-9 Gyr old stellar population. The di\ufb00erence to a 12 Gyr old population (M/L=3.5) is still within individual error bars for the literature estimates, and there is also some uncertainty in the underlying stellar mass functions and stellar population models. Nevertheless, we note that the slightly too low M/L ratios may also be interpreted as signs of preferential loss of low-mass stars in the Galactic tidal \ufb01eld (Baumgardt & Makino 2003; Kruijssen 2008). If this was the case, then less dark matter would be needed to explain the elevated mass-to-light ratios of UCDs, implying a DM mass of \u223c50-80% of the stellar mass. However, it is unclear whether the actual dissolution times of the GCs 6 H. Baumgardt and S. Mieske Figure 5. Mass-to-light ratios of UCDs (circles) and globular clusters (triangles) as a function of their age divided by their relaxation time. There is a clear trend towards lower M/L values for dynamically more evolved systems. The red solid and blue dashed curves show predicted M/L values for two of our runs calculated from the velocity dispersion of bright stars inside the clusters half-mass radius, assuming stellar mass-to-light ratios of M/L|\u2217= 2.0 and M/L|\u2217= 2.5 for the two runs. It can be seen that the resulting theoretical curves provide a good \ufb01t to the combined globular cluster/UCD sample. with available M/L measurements are short enough to have experienced signi\ufb01cant evaporation (Mieske et al. 2008). A case-by-case analysis for Galactic GCs will be necessary to assess this, based on measured absolute proper motions and orbital parameters (Allen et al. 2006). 3.4 Scaling issues We \ufb01nally discuss a possible biasing of our results due to the \ufb01nite mass of the dark matter particles. Fig. 6 depicts the evolution of Lagrangian radii in simulations with di\ufb00erent dark matter particle masses. All simulations had an equal amount of mass in stars and dark matter and the mass of the dark matter particles was set to be m = 0.1 M\u2299(blue lines), m = 0.03 M\u2299(red lines) and m = 0.01 M\u2299(green lines). Since the mass of heavy stars which drive the inspiral is in all cases much higher than the mass of the dark matter particles, eq. 8 should still apply for the inspiral timescale. In all three simulations, the mass of individual stars if expressed in N-body units was the same, so according to eq. 8, the inspiral timescale of the stars should be the same in the three simulations. It can be seen that the inspiral of stars and the ejection of dark matter particles happens in all three clusters in a very similar way. The agreement is especially good between the two simulations with the lightest dark matter particles. We therefore conclude that the adopted mass m = 0.03 M\u2299 for the dark matter particle does not in\ufb02uence the results Figure 6. Evolution of Lagrangian radii of stars (left panel) and dark matter particles (right panel) in simulations which assume dark matter particle masses of m = 0.1 M\u2299(blue lines), m = 0.03 M\u2299(red lines, the default mass for the simulations presented in Figs. 2 to 5) and m = 0.015 M\u2299(green lines). The agreement between the di\ufb00erent curves, especially for light dark matter particles is very good, showing that the adopted mass m = 0.03 M\u2299 of the dark matter particle should not in\ufb02uence our results. presented in Figs. 2 to 5. Our simulations should therefore give a correct picture of the dynamical ejection of dark matter from the centers of globular clusters and UCDs. 4 CONCLUSIONS We have performed collisional N-body simulations of the evolution of compact systems composed out of a mix of stars and dark matter particles. Our simulations show that dark matter is depleted from the centers of these systems due to dynamical friction and energy equipartition between stars and dark matter particles. The inspiral time of stars is short enough that only 20% of the original dark matter would remain within the half-mass radius in typical globular clusters. If mainly stars from the inner cluster parts are used to determine mass-to-light ratios, the resulting increase in the mass-to-light ratio is within the errors with which massto-light ratios are typically determined for globular clusters and would therefore be di\ufb03cult to detect. If not tidally stripped, dark matter should also reside in the outer parts of globular clusters. For a number of globular clusters, Scarpa et al. (2007) have indeed reported a \ufb02attening of the velocity disperion in the outer cluster parts. This could however be due to a number of reasons like contamination of the sample by background stars or the tidal interaction of a star cluster with the gravitational \ufb01eld of the Milky Way (Drukier et al. 1998; Capuzzo Dolcetta et al. 2005). Detailed simulations would be necessary to exclude these possibilities and con\ufb01rm that the observed \ufb02attening is due to a dark matter halo. UCDs on the other hand have inspiral times signi\ufb01cantly longer than a Hubble time and therefore still contain most of the dark matter in their centers. Dark matter therefore seems a viable explanation for the elevated M/L ratios of UCDs, provided that UCDs originate from the centers of dark matter halos and have seen their dark matter content being increased by dark matter funneling, through e.g. adiabatic gas infall (Goerdt et al. 2008). A prediction of our simulations, which can in principle Evidence for dark matter in UCDs 7 be tested by observations, is that globular clusters which have expelled the dark matter from their centers should also be mass segregated. Non-mass segregated clusters with velocity dispersions and mass-to-light ratios in agreement with simple stellar population models, would therefore have formed without signi\ufb01cant amounts of dark matter in their centers. Also, if dark matter existed in a globular cluster at the time of its formation, it should still reside in its outer parts, especially if tidal stripping due to external tidal forces from the host galaxy (Mashchenko & Sills 2005) and relaxation driven internal mass loss was not important for the cluster evolution. In this case, the measured mass-to-light ratio should increase towards the outer cluster parts, which can in principle be detected with dedicated radial velocity or proper motion surveys. The future astrometric satellite GAIA would be an excellent tool for such a search since it will provide accurate proper motions for thousands of stars in the halos of nearby globular clusters. ACKNOWLEDGEMENTS",
                    "introduction": "Ultra-compact dwarf galaxies (UCDs) were discovered in the late 1990s in spectroscopic surveys of the Fornax galaxy cluster (Hilker et al. 1999; Drinkwater et al. 2000) and have since then been found in other nearby galaxy clusters as well (Hasegan et al. 2005; Mieske et al. 2005, 2007; Jones et al. 2006; Firth et al. 2007; Rejkuba et al. 2007). They are bright (\u221211 < MV < \u221213.5) and compact (7 < rh < 100 pc) stellar systems which have ages of at least several Gyr and possibly up to 10 Gyr (Mieske et al. 2006; Evstigneeva et al. 2007). The masses and sizes of UCDs are larger than those of Galactic globular clusters, but similar to those of nuclei in dwarf elliptical galaxies (Drinkwater et al. 2003, Bekki et al. 2003). One of the most remarkable properties of UCDs is that their dynamical mass-to-light ratios are on average about twice as large than those of globular clusters of comparable metallicity, and also tend to be larger than what one would expect based on simple stellar evolu- tion models that assume a standard stellar initial mass function, like e.g. Kroupa (2001) (Hasegan et al. 2005; Dabringhausen, Hilker & Kroupa 2008; Mieske et al. 2008). If not due to a failure of stellar evolution models, this points either to unusual stellar mass functions (Mieske & Kroupa 2008; Dabringhausen, Baumgardt & Kroupa 2008) or possi- bly to the presence of a signi\ufb01cant amount of dark matter in UCDs. We note that most methods used to determine M/L ratios for UCDs rely on the assumptions that mass follows light and isotropic velocity dispersions. How well these as- sumptions are ful\ufb01lled is currently not known. Also due to the large distances of UCDs, only integrated velocity disper- sions can be obtained, which in most cases are intermediate between the central and the global velocity dispersions. In 2 H. Baumgardt and S. Mieske Figure 1. The mean mass density within the half-mass radius of the joint sample of GCs and UCDs from Fig. 5 is plotted vs. their relaxation time (Mieske et al. 2008). The dotted line indicates the approximate central (r \u227210pc) dark matter densities expected for cuspy dwarf galaxy CDM halos (Gilmore et al. 2007). order to determine the mass-to-light ratio, the mass mod- eling has to take the density pro\ufb01les of the UCDs as well as the e\ufb00ects of seeing and a \ufb01nite slit size into account, as done for example in Hilker et al. (2007). Several formation scenarios have been discussed for UCDs, like e.g. that UCDs are simply massive globular clusters and form in the same way (Hilker et al. 1999; Evstigneeva et al. 2007; Forbes et al. 2008), that they are the nuclei of tidally stripped, originally much more extended galaxies (Bekki, Couch & Drinkwater 2001; Bekki et al. 2003; Thomas, Drinkwater & Evstigneeva 2008; Goerdt et al. 2008), or that they are merged glob- ular clusters (Oh & Lin 2000; Fellhauer & Kroupa 2002). Goerdt et al. (2008) have shown that funneling of dark matter to the central region of a disk galaxy, due to gas-infall, can signi\ufb01cantly increase the M/L ratios in the nuclear region, and hence may explain the elevated M/L ratios of UCDs, provided that UCDs formed by tidal stripping. Indeed, it has been suggested that also GCs may have originated as centers of individual primordial dark matter halos (e.g. Carraro & Lia 2000, Lee et al. 2007, Bekki et al. 2007). If dark matter funneling is an e\ufb03cient mechanism (Goerdt et al. 2008), one may therefore expect both UCDs and GCs to be formed with a signi\ufb01cant fraction of dark matter. It is important to note that such an increase of dark matter density by some kind of funneling mechanism is necessary to explain a signi\ufb01cant amount of dark matter in UCDs or GCs, since their present-day stellar (and hence implied dark matter) densities are up to 2-3 orders of magnitude higher than expected for cuspy dark matter halos of dwarf galaxy mass (Gilmore et al. 2007). This is shown in Fig. 1. In this paper, we start from the working hypothesis that both GCs and UCDs are formed with the same non-zero dark-to-stellar-mass-fraction. We then investigate how the dynamical co-evolution of dark matter and stars changes the observed dark matter fraction as a function of time. We assess whether the observed rise of M/L ratios from the regime of GCs to that of UCDs can be explained by our working hypothesis and the subsequent dynamical evolution."
                },
                {
                    "url": "http://arxiv.org/abs/0806.0622v1",
                    "title": "Evidence for primordial mass segregation in globular clusters",
                    "abstract": "We have studied the dissolution of initially mass segregated and unsegregated\nstar clusters due to two-body relaxation in external tidal fields, using\nAarseth's collisional N-body code NBODY4 on GRAPE6 special-purpose computers.\nWhen extrapolating results of initially not mass segregated models to globular\nclusters, we obtain a correlation between the time until destruction and the\nslope of the mass function, in the sense that globular clusters which are\ncloser to dissolution are more strongly depleted in low-mass stars. This\ncorrelation fits observed mass functions of most globular clusters. The mass\nfunctions of several globular clusters are however more strongly depleted in\nlow-mass stars than suggested by these models. Such strongly depleted mass\nfunctions can be explained if globular clusters started initially mass\nsegregated. Primordial mass segregation also explains the correlation between\nthe slope of the stellar mass function and the cluster concentration which was\nrecently discovered by De Marchi et al. (2007). In this case, it is possible\nthat all globular clusters started with a mass function similar to that seen in\nyoung open clusters in the present-day universe, at least for stars below m=0.8\nMsun. This argues for a near universality of the mass function for different\nstar formation environments and metallicities in the range -2 < [Fe/H] < 0. We\nfinally describe a novel algorithm which can initialise stationary mass\nsegregated clusters with arbitrary density profile and amount of mass\nsegregation.",
                    "authors": "Holger Baumgardt, Guido de Marchi, Pavel Kroupa",
                    "published": "2008-06-04",
                    "updated": "2008-06-04",
                    "primary_cat": "astro-ph",
                    "cats": [
                        "astro-ph"
                    ],
                    "main_content": "BM03 performed a large set of N-body simulations of multi-mass star clusters moving in external tidal fields and evolving under the combined influence of two-body relaxation, an external tidal field and stellar evolution. All models contained between 8.192 to 131.072 stars and started with a canonical mass function that consisted of two power-laws with slope \u03b1 = 1.3 for stars between 0.08 and 0.5 M\u2299and slope \u03b1 = 2.3 for more massive stars (Kroupa 2001). The clusters moved on circular or eccentric orbits through an isothermal galaxy with circular velocity VC = 220 km/sec. BM03 obtained the following expression for the lifetime TDiss of a star cluster: TDiss TDiss [Myr] = \u03b2 \ufffd N ln(\u03b3 ln(\u03b3 N) \ufffdx RG [kpc [kpc] \ufffd VG 220 km 220 km/sec \ufffd\u22121 (1 \u2212\u01eb) , (1) where N is the number of cluster stars, \u03b3 = 0.02 a constant in the Coulomb logarithm and RG and \u01eb the apocenter distance and eccentricity of the cluster orbit, respectively. The constants \u03b2 and x were found to depend on the density profile. For King W0 = 7 models, x and \u03b2 are given by x = 0.82 and \u03b2 = 1.03. BM03 found that mass is lost more or less linearly with time from a star cluster, except for the mass lost due to stellar evolution, which decreases the initial mass by about 30% within the first Gyr. The mass left at a time T < TDiss can therefore be approximated by M(T) = 0.70 M0 (1 \u2212T/TDiss) . (2) BM03 also found that, while the clusters are dissolving, mass segregation causes massive stars to sink into the cluster center and low-mass stars to move to the outer parts, where they are easily removed by the tidal field, so that the global mass function of stars gets depleted in low-mass stars. By fitting power-law mass functions dN/dm \u223cm\u2212\u03b1 to the mass \u2013 4 \u2013 function of stars with m < 0.5 M\u2299, BM03 derived the following expression for the change in the slope of the mass function: \u03b1 = 1.3 \u22121.51 \u0012 T TDiss \u00132 + 1.69 \u0012 T TDiss \u00133 \u22121.50 \u0012 T TDiss \u00134 . (3) They found that this expression gave a good \ufb01t to the change of the mass function for a wide range of initial cluster orbits and cluster masses. Since observed mass function slopes of the clusters in De Marchi et al. (2007) are determined mainly from stars with masses 0.3 M\u2299< m < 0.8 M\u2299, we have re-analysed the data by BM03 and \ufb01nd that the following formula \ufb01ts the change of the mass function in this range: \u03b1 = 1.74 \u22120.34 T TDiss + 4.52 \u0012 T TDiss \u00132 \u22127.59 \u0012 T TDiss \u00133 + 5.86 \u0012 T TDiss \u00134 . (4) The runs by BM03 also indicated that the mass-to-light ratio drops as a cluster evolves and loses preferentially low-mass stars which do not contribute much to the overall cluster light. The results of BM03 (their Fig. 14) can be \ufb01tted by the relation M/L = 1.5 \u22120.5 T TDiss . (5) Using the above equations 1, 2 and 5, we can calculate the initial mass of individual globular clusters, provided their orbits and present-day luminosities are known. One way to do this is to \ufb01rst guess two initial masses MLow and MUp which lead to too small and too large present-day masses, and then iterate to the correct initial mass by interval-halving. Once the initial masses and dissolution times are known, the expected present-day mass function slopes of low-mass stars can be calculated from eq. 4. Table 1 and Fig. 1 compare our predictions with the observed slopes from De Marchi et al. (2007). We have taken the pericenter and apocenter distances from Dinescu et al. (1999), except for NGC 6496 for which a circular orbit at the current Galactocentric distance was assumed since its proper motion is not known. The integrated luminosities were taken from Harris (1996). We assumed an age of T = 12 Gyr for the Galactic globular cluster system. Fig. 1 compares the predicted mass function slopes with the observations. It can be seen that all clusters with remaining lifetimes larger than T = 20 Gyr have nearly identical slopes with \u03b1 \u22481.5. This value is close to the expected slope for stars with 0.3 < m < 0.8 M\u2299drawn from a canonical IMF, \u03b1 = 1.7. Globular clusters have therefore started with a mass function slope at the low mass end which is similar to that seen for open clusters in the present-day universe. Fig. 1 also shows that, in agreement with the theoretical results from the N-body simulations, the mass functions of clusters close to dissolution become \u2013 5 \u2013 Fig. 1.\u2014 Observed mass function slope vs. lifetime remaining to dissolution as determined from the current mass of each cluster and eqs. 1 and 2. The errorbar in the lower left corner shows typical uncertainties of the observed slopes which are around 0.2. The observed mass function slopes show a clear correlation in the sense that clusters closer to dissolution are on average more strongly depleted in low-mass stars. The dashed line shows the expected mass function slope for clusters without primordial mass segregation, determined from the models of Baumgardt & Makino (2003) (eq. 4). It provides a good \ufb01t for most clusters, however a number of clusters close to dissolution are much more strongly depleted in low-mass stars. \u2013 6 \u2013 depleted in low-mass stars. While some clusters lie close to the predictions from the models of BM03 (dashed line), a number of clusters are signi\ufb01cantly stronger depleted in low-mass stars. In the N-body models, slopes with \u03b1 < 0 are hardly reached since the clusters \ufb01rst have to go into core-collapse to become mass segregated and then dissolve before reaching a strong enough depletion of low-mass stars. Hence, these clusters cannot be explained with the type of initial conditions used by Baumgardt & Makino (2003), i.e. clusters that form in dynamical equilibrium, \ufb01lling their tidal radii and start without primordial mass segregation. In addition, the correlation of mass function slope and cluster concentration noted by De Marchi et al. (2007) is di\ufb03cult to understand with non-mass-segregated clusters (see Fig. 3, left panel). As explained in the Introduction, several lines of evidence indicate that star clusters form mass segregated, in which case the depletion of low-mass stars could happen much quicker than in the models by Baumgardt & Makino (2003). This o\ufb00ers a possible way how to explain the observations. We will therefore explore the in\ufb02uence of primordial mass segregation in the next sections. 3. N-body models of mass segregated clusters In order to understand if primordial mass segregation helps reconciling the discrepancy between observations and simulations, we calculated a number of models starting with primordial mass segregation. All runs were performed with the collisional N-body code NBODY4 (Aarseth 1999) on the GRAPE6 computers of Bonn University. The modeled clusters contained between 10.000 to 90.000 stars initially. Since these numbers are rather small compared to particle numbers in globular clusters, we decided to omit stellar evolution and start all runs with a power-law mass function with slope \u03b1 = 1.3 between lower and upper mass limits of m = 0.1 and m = 1.2 M\u2299. This should capture the essential physics of the collisional evolution of globular clusters. In order to account for the break in slope of the canonical IMF at 0.5 M\u2299, we assume that for stars more massive than 0.5 M\u2299, only a fraction 0.5M\u2299/m of stars are main-sequence stars while the other are compact remnants which are not taken into account when mass function slopes are determined. All clusters started from King W0 = 3.0 density pro\ufb01les and moved on circular orbits through an isothermal Galaxy. In order to study the in\ufb02uence of the initial cluster size, we calculated two sets of models, one in which the tidal radius of the external tidal \ufb01eld, rJ, was equal to the tidal radius of the King model, rJ/rt = 1, and one set of tidally under\ufb01lling models with rJ/rt = 3. The algorithm for creating mass segregated clusters in virial equilibrium is described in the Appendix. In our models, we studied the evolution of unsegregated clusters and clusters in \u2013 7 \u2013 which the mass and energy arrays are completely ordered before stars are assigned positions and velocities. These models therefore show the maximum in\ufb02uence mass segregation can have and realistic clusters should lie between the two extremes covered by our simulations. Table 2 summarises the runs performed. 4. Results for mass segregated clusters Fig. 2 depicts the evolution of the mass function of initially mass segregated clusters starting from various initial conditions and compares it with the evolution of non-segregated clusters and observations of Galactic globular clusters. Final mass functions were determined from a \ufb01t to the distribution of stars in the mass range 0.3M\u2299< m < 0.8M\u2299, similar to the mass range for which observed mass functions are determined for most star clusters. It can be seen that in tidally under\ufb01lling models (upper panels with rJ/rt = 3.0), the evolution does not depend much on whether the cluster initially starts mass segregated or not. This is probably due to the short core collapse times of strongly concentrated clusters compared with their dissolution times (see Table 2). Since the starting condition has largely been erased by the time a cluster goes into core collapse, and since the pre-core collapse evolution typically lasts only about 20% of the total lifetime for these models, the starting condition should not strongly in\ufb02uence the overall evolution. The lower panels in Fig. 2 depict the evolution of tidally \ufb01lling clusters with rJ/rt = 1.0. While non-segregated clusters still evolve close to the prediction of Baumgardt & Makino (2003) (dotted lines), the evolution of mass segregated clusters is now markedly di\ufb00erent: Since in mass segregated clusters, low-mass stars start close to the tidal radius, they are being depleted right from the start of the simulations, leading to \ufb01nal mass functions much more strongly depleted in low-mass stars. The amount of depletion is strong enough to explain most observed mass functions. Hence, the range of slopes seen for Galactic globular clusters can, at least in principle, be explained if some started mass segregated while others didn\u2019t, or all of them started mass segregated but with a range of tidal \ufb01lling factors. We also note that the expulsion of residual gas within the \ufb01rst Myr can enhance the depletion of low-mass stars if the clusters start mass segregated (Marks, Kroupa & Baumgardt 2008). Fig. 3 \ufb01nally depicts the evolution of star clusters in the concentration vs. mass function slope plane. In order to determine the concentration, King models were \ufb01tted to the surface density distribution of stars with masses in the range 0.6 \u2264m \u22640.8 M\u2299and the concentration c was chosen from the King model which gave the best \ufb01t to the simulated clusters. The restriction to stars in the mass range 0.6 \u2264m \u22640.8 M\u2299was done since in globular clusters these would be the stars which create most of the cluster light. As can be seen, the cluster \u2013 8 \u2013 Fig. 2.\u2014 Same as Fig. 1, but now for mass segregated and not mass segregated clusters. The upper panels depict the evolution of tidally under\ufb01lling clusters with rJ/rt = 3.0, the lower panels that of clusters with rJ/rt = 1.0. The left panels depict the evolution of non-segregated clusters, the right panels that of mass segregated clusters. Mass segregated clusters in strong tidal \ufb01elds lose low-mass stars right from the start of the simulations, leading to more strongly depleted mass functions by the time the clusters are close to dissolution. This can explain the mass function slopes of strongly depleted globular clusters. In most cases, mass functions evolve nearly independently of the initial number of stars. \u2013 9 \u2013 concentration \ufb01rst increases in all models as the clusters go into core collapse and then decreases again in post-collapse due to core expansion driven by binaries in the cluster centre. In post-collapse, all models reach a stable value of c = 1.6 nearly independent of the initial concentration. Clusters also move upward in Fig. 3 as the mass function becomes depleted in low-mass stars. For initially non-segregated clusters (left panel), core collapse is fast enough that they are always in post-collapse by the time they have become strongly depleted in low-mass stars. Especially concentrated clusters hardly lose any stars in the pre-collapse phase. Since our clusters started from already very low-concentration, King W0 = 3.0 models, it seems impossible to delay core collapse much further by doing simulations of even lower concentration models. Hence, as was already noted by De Marchi et al. (2007), one cannot explain low-concentration clusters which are strongly depleted in low-mass stars by non-segregated models assuming that the IMF of stars is universal. The right panel of Fig. 3 depicts the evolution of initially mass segregated clusters. For tidally under\ufb01lling clusters with rJ/rt = 3.0, the evolution is virtually indistinguishable from the evolution of non-segregated clusters with rJ/rt = 3.0. Clusters with rJ/rt = 1.0 on the other hand lose low-mass stars much quicker and go into core collapse only after their mass function has become signi\ufb01cantly depleted in low-mass stars. Primordial mass segregation would therefore also provide an explanation for low concentration globular clusters which are strongly depleted in low-mass stars. 5. Conclusions We have followed the dynamical evolution of star clusters in tidal \ufb01elds starting with and without primordial mass segregation. We \ufb01nd that clusters with primordial mass segregation lose their low-mass stars more rapidly than non-segregated ones if being immersed in a strong external tidal \ufb01eld, due to the fact that low-mass stars start their lifes in the outer cluster parts where they can easily be removed by the tidal \ufb01eld. For clusters in weaker tidal \ufb01elds, primordial mass segregation makes only a small di\ufb00erence to the cluster evolution since strong mass loss starts only after core collapse, by which time cluster evolution has largely erased the initial conditions. For all studied models, the absolute values of the core collapse time and the lifetime decrease by no more than 10% due to the introduction of primordial mass segregation. The di\ufb00erence could be larger for simulations which also include the e\ufb00ects of stellar evolution, although e.g. Ardi, Baumgardt & Mineshige (2008) found only a slight increase in core-collapse time for mass segregated clusters compared to non-segregated ones. Our simulations show that primordial mass segregation is a way to explain the strong depletion of low-mass stars seen in some globular clusters as well as the correlation between \u2013 10 \u2013 Fig. 3.\u2014 Evolution of initially non-mass-segregated (left panel) and mass segregated (right panel) clusters in the concentration vs. mass function slope plane. The arrows mark the direction in which the clusters are evolving. The cluster concentration \ufb01rst increases as the clusters go into core collapse and then decreases again in post-collapse evolution. Initially not mass segregated clusters are always in post-collapse by the time they have become signi\ufb01cantly depleted in low-mass stars, making it impossible to explain clusters with both low concentration and strongly depleted mass functions. In contrast, clusters \ufb01lling their tidal boundary (rJ/rt = 1.0) and with primordial mass segregation become signi\ufb01cantly depleted in low-mass stars before going into core collapse. \u2013 11 \u2013 mass function slope and cluster concentration recently found by De Marchi et al. (2007). Given the strong observational evidence for primordial mass segregation in young star clusters, we conclude that at least some, but possibly all, globular clusters started mass segregated. The range of mass function slopes seen for Galactic globular clusters can then be explained if they started with a range of tidal \ufb01lling factors but all of them had the same initial mass function slope. Also, the clusters in the De Marchi et al. (2007) sample span a range of metallicities \u22122.2 < [Fe/H] < \u22120.6 and formed at high redshifts, while current (z \u223c0) star formation with [Fe/H] \u22480.0 produces an indistinguishable IMF. Our results therefore indicate that the initial mass function of low-mass stars has been more or less universal for a large range of star formation environments, redshifts and cluster metallicities. The e\ufb00ect of primordial mass segregation on the mass function is enhanced if residual gas removal is taken into account, since due to the sudden drop of the cluster potential as a result of gas expulsion, stars at large radii are preferentially lost from star clusters. Gas expulsion also naturally leads to tidally \ufb01lling clusters. The in\ufb02uence of this e\ufb00ect together with the e\ufb00ect of unresolved binaries on the observed mass functions is discussed in Marks, Kroupa & Baumgardt (2008). Their study shows that the e\ufb00ect of gas expulsion depends on several parameters, like the amount of gas removed (i.e. the star-formation e\ufb03ciency), the timescale over which gas expulsion happens and how strongly the proto-globular cluster is immersed in an external tidal \ufb01eld (see the grid of models run by Baumgardt & Kroupa 2007). Due to their high masses, embedded globular clusters must have started with ratios of half-mass radius to tidal radius, rh/rt, signi\ufb01cantly smaller than 0.1. Also, the crossing time of a rh = 1 pc, 106 M\u2299proto-globular cluster is only 20.000 yr, while e.g. Baumgardt, Kroupa & Parmentier (2008) found that gas expulsion from globular clusters should take several 105 to 106 yr. Hence the primordial gas was probably removed adiabatically (i.e. on a timescale much longer than the crossing time of the cluster) from globular clusters. As can be seen from \ufb01g. 3 of Marks et al. (2008), clusters with rh/rt values smaller than 0.06 and adiabatic gas removal mostly preserve their IMF or receive only small changes to it, even when ending up with low concentrations. Hence, while primordial gas expulsion might contribute to the change in the IMF, gas expulsion alone is not likely to explain strongly depleted mass functions in globular clusters. Primordial binaries also in\ufb02uence measured mass function slopes because a fraction of low-mass stars is hidden in binaries with more massive primaries and because cluster evolution, especially the evolution after core-collapse, is di\ufb00erent if primordial binaries are present. The in\ufb02uence of hidden low-mass stars on the mass function slope is also discussed in Marks, Kroupa & Baumgardt (2008). The in\ufb02uence of primordial binaries on cluster evolution is less clear since for example the simulations by Fregeau & Rasio (2007) show that clusters with primordial binaries reach concentrations around c \u22482 in the post-collapse \u2013 12 \u2013 phase, which is close to the values found here for clusters without primordial binaries. Also, in mass segregated, multi-mass clusters, primordial binaries are likely to have a smaller e\ufb00ect on the evolution, since the cluster evolution is driven by only few active binaries. If massive stars start their life in the core, they quickly form binaries and the later cluster evolution becomes indistinguishable from clusters with primordial binaries. It therefore remains to be seen how results change for models which self-consistently include the e\ufb00ects of gas expulsion, two-body relaxation and primordial binaries. We plan to carry out such studies in the future. We \ufb01nally suggest a new method for setting-up mass segregated clusters, which has the advantage that it always creates clusters which are in virial equilibrium since the mass density pro\ufb01le is not changed due to the introduction of mass segregation. It is also \ufb02exible and can work with any given mass density pro\ufb01le, initial mass function of stars and can be combined with any scheme for setting up mass segregation. Acknowledgments The authors would like to thank Sverre Aarseth for his constant help with the NBODY4 code and Eliani Ardi for useful discussions.",
                    "introduction": "In recent years, stellar mass functions have been obtained for an increasing number of globular clusters by deep HST and VLT measurements (see DeMarchi et al. 2007 and 1 Argelander-Institute for Astronomy, University of Bonn, Auf dem H\u00a8 ugel 71, 53121 Bonn, Germany 2 European Space Agency, Space Science Department, Noordwijk, Netherlands \u2013 2 \u2013 references therein). These observations have shown that there is a considerable spread in the present-day mass functions of individual clusters, and that a number of star clusters are strongly depleted in low-mass stars. If one expresses the mass function of a cluster as a power-law1 by dN/dm \u223cm\u2212\u03b1, where N is the number of stars per unit mass m, the observed slopes range from between \u03b1 = 1.9 to \u03b1 = \u22120.9 for stars with masses in the range 0.3 < m < 0.8 M\u2299. For clusters where information from di\ufb00erent radii is available, the data point to a global decrease of the number of low-mass stars in the clusters, rather than a local e\ufb00ect due to mass segregation. The depletion of low-mass stars can in principle be understood by mass segregation and the preferential loss of low-mass stars as a result of the dynamical evolution of star clusters. Indeed, using direct N-body simulations, Baumgardt & Makino (2003) found a correlation between the observed and expected slopes for the then available sample of star clusters. However, for a number of clusters, the di\ufb00erence between theoretical and expected slope is far too large to be explained just by observational uncertainties. This is emphasised by De Marchi et al. (2007), who found a correlation between the mass function slope \u03b1 and the concentration parameter c = log10(rt/rc) for globular clusters, where rt and rc are the tidal and core radius of the cluster as determined from the projected light density pro\ufb01le. The correlation found by De Marchi et al. (2007) is in the sense that clusters with small values of c are depleted in low-mass stars, while clusters with large values of c have mass functions still rising towards small masses. Since simulations show that mass segregation and the preferential loss of low-mass stars should only happen after a cluster has gone into core-collapse, and since core-collapse is connected to the shrinkage of the core size rc, the observed correlation is the exact opposite of the theoretically expected one. One possible interpretation of this \ufb01nding would be that star clusters that formed more concentrated have a bottom-heavy IMF, which would be a challenge to star formation theo- ries and dispose the universality of the IMF. However this conclusion needs to be tested by taking into account the stellar-dynamical evolution of the clusters. In the present paper we compare the observational results with theoretical predictions by Baumgardt & Makino (2003) (BM03), who have performed a large parameter study of ini- tially not mass segregated multi-mass clusters evolving under the combined in\ufb02uence of relax- ation, stellar evolution and an external tidal \ufb01eld. We also report results of new simulations of multi-mass star clusters which start initially mass segregated. Initial mass segregation is expected to occur in star clusters as a result of star formation feedback in dense gas clouds (Murray & Lin 1996) and due to competitive gas accretion and mutual mergers between 1Note that De Marchi et al. (2007) used dN/dm \u223cm\u03b1 in their paper. \u2013 3 \u2013 protostars (Bonnell & Bate 2002). Numerous studies have also found observational evidence for it in young star clusters of the Milky Way and the Magellanic Clouds (Bonnell & Davies 1998; Gouliermis et al. 2004; Chen et al. 2007), so that it is certainly possible that globular clusters started mass segregated. The paper is organised as follows: In \u00a72 we compare the results of simulations of non- mass-segregated clusters done by Baumgardt & Makino (2003) with the observed mass func- tion slopes of globular clusters. In \u00a73 we describe the numerical simulations of star clusters with primordial mass segregation and in \u00a74 we compare the results of these runs with the observations. We brie\ufb02y summarize in \u00a75."
                }
            ],
            "Antonio Sollima": [
                {
                    "url": "http://arxiv.org/abs/1708.09529v1",
                    "title": "The global mass functions of 35 Galactic globular clusters: I. Observational data and correlations with cluster parameters",
                    "abstract": "We have derived the global mass functions of a sample of 35 Galactic globular\nclusters by comparing deep Hubble Space Telescope photometry with suitable\nmultimass dynamical models. For a subset of 29 clusters with available radial\nvelocity information we were also able to determine dynamical parameters,\nmass-to-light ratios and the mass fraction of dark remnants. The derived global\nmass functions are well described by single power-laws in the mass range $0.2 <\nm/M_\\odot < 0.8$ with mass function slopes $\\alpha>-1$. Less evolved clusters\nshow deviations from a single-power law, indicating that the original shape of\ntheir mass distribution was not a power-law. We find a tight anticorrelation\nbetween the present-day mass function slopes and the half-mass relaxation\ntimes, which can be understood if clusters started from the same universal IMF\nand internal dynamical evolution is the main driver in shaping the present-day\nmass functions. Alternatively, IMF differences correlated with the present-day\nhalf-mass relaxation time are needed to explain the observed correlation. The\nlarge range of mass function slopes seen for our clusters implies that most\nglobular clusters are dynamically highly evolved, a fact that seems difficult\nto reconcile with standard estimates for the dynamical evolution of clusters.\nThe mass function slopes also correlate with the dark remnant fractions\nindicating a preferential retention of massive remnants in clusters subject to\nhigh mass-loss rates.",
                    "authors": "Antonio Sollima, Holger Baumgardt",
                    "published": "2017-08-31",
                    "updated": "2017-08-31",
                    "primary_cat": "astro-ph.GA",
                    "cats": [
                        "astro-ph.GA"
                    ],
                    "main_content": "The derivation of the global MFs and the cluster parameters has been performed through the analysis of three different kinds of datasets: photometry, surface brightness profiles and individual stellar radial velocities. The photometric data consists of high-resolution HST observations of a sample of 66 Galactic GCs obtained as part of the Globular Cluster ACS Treasury Project (Sarajedini et al. 2007). The data has been obtained using deep images obtained with the Advanced Camera for Surveys (ACS) Wide Field Channel through the F606W and F814W filters. The field of view of the camera (202\u201d \u00d7 202\u201d) was centered on the cluster centres with a dithering pattern to cover the gap between the two chips, allowing a full coverage of the core of all the GCs considered in our analysis. This survey provides deep colour-magnitude diagrams (CMDs) providing photometry of main sequence stars down to the hydrogen burning limit (at MV \u223c10.7) with a signal-to-noise ratio c \u20dd2017 RAS, MNRAS 000, 1\u201314 The mass function of 35 Galactic GCs 3 Table 1. Parameters of the best-\ufb01t models. NGC \u03b1 log(Mlum/M\u2299) log(Mdyn/M\u2299) rh fremn log (trh/yr) Mdyn/LV log \u03c10 log \u03c1h pc M\u2299/L\u2299 M\u2299/pc3 M\u2299/pc3 288 -0.66 \u00b1 0.04 4.67 \u00b1 0.04 4.96 \u00b1 0.03 9.12 0.50 \u00b1 0.05 9.60 1.89 \u00b1 0.49 1.92 1.16 1261 -0.65 \u00b1 0.03 4.93 \u00b1 0.10 5.23 \u00b1 0.05 5.70 0.50 \u00b1 0.11 9.39 1.51 \u00b1 0.53 3.26 2.04 1851 -0.69 \u00b1 0.03 5.14 \u00b1 0.07 5.51 \u00b1 0.04 5.14 0.57 \u00b1 0.08 9.43 1.64 \u00b1 0.49 4.49 2.45 2298 0.11 \u00b1 0.03 4.18 \u00b1 0.12 3.19 3201 -1.26 \u00b1 0.09 4.81 \u00b1 0.03 5.08 \u00b1 0.03 6.41 0.47 \u00b1 0.05 9.46 1.95 \u00b1 0.50 3.05 1.74 4147 0.03 \u00b1 0.05 4.21 \u00b1 0.13 4.81 \u00b1 0.22 5.22 0.75 \u00b1 0.26 9.12 2.13 \u00b1 1.36 3.83 1.73 4590 -1.27 \u00b1 0.07 4.87 \u00b1 0.06 5.29 \u00b1 0.06 8.60 0.62 \u00b1 0.09 9.74 2.91 \u00b1 0.89 3.12 1.56 4833 -0.69 \u00b1 0.08 5.10 \u00b1 0.03 5.35 \u00b1 0.07 8.60 0.43 \u00b1 0.08 9.71 1.32 \u00b1 0.39 3.21 1.62 5024 -1.41 \u00b1 0.11 5.53 \u00b1 0.05 5.82 \u00b1 0.06 15.12 0.49 \u00b1 0.08 10.34 1.95 \u00b1 0.56 3.09 1.36 5053 -1.29 \u00b1 0.03 4.62 \u00b1 0.03 4.78 \u00b1 0.11 19.30 0.32 \u00b1 0.11 10.11 1.64 \u00b1 0.57 0.59 0.00 5272 -0.95 \u00b1 0.08 5.35 \u00b1 0.05 5.61 \u00b1 0.04 7.29 0.45 \u00b1 0.07 9.73 1.68 \u00b1 0.46 3.76 2.10 5286 -0.61 \u00b1 0.03 5.29 \u00b1 0.07 5.71 \u00b1 0.08 4.43 0.61 \u00b1 0.11 9.43 1.30 \u00b1 0.45 4.28 2.85 5466 -1.68 \u00b1 0.09 4.82 \u00b1 0.03 4.77 \u00b1 0.11 24.64 -0.12 \u00b1 0.12 10.25 1.25 \u00b1 0.45 0.98 -0.33 5904 -0.88 \u00b1 0.10 5.27 \u00b1 0.04 5.58 \u00b1 0.04 7.66 0.51 \u00b1 0.06 9.73 1.99 \u00b1 0.53 3.86 2.00 5986 -0.65 \u00b1 0.07 5.20 \u00b1 0.07 5.48 \u00b1 0.05 5.47 0.48 \u00b1 0.09 9.46 1.43 \u00b1 0.44 3.53 2.34 6093 -0.14 \u00b1 0.04 5.10 \u00b1 0.08 5.58 \u00b1 0.07 3.39 0.67 \u00b1 0.11 9.16 1.54 \u00b1 0.52 4.97 3.07 6101 -1.60 \u00b1 0.15 5.11 \u00b1 0.03 18.75 6144 -0.15 \u00b1 0.06 4.42 \u00b1 0.06 5.82 6205 -0.60 \u00b1 0.08 5.34 \u00b1 0.04 5.77 \u00b1 0.03 6.87 0.63 \u00b1 0.06 9.71 2.01 \u00b1 0.53 3.43 2.34 6218 -0.32 \u00b1 0.04 4.60 \u00b1 0.06 4.95 \u00b1 0.03 4.09 0.55 \u00b1 0.06 9.01 1.50 \u00b1 0.41 3.38 2.19 6254 -0.48 \u00b1 0.09 4.94 \u00b1 0.05 5.33 \u00b1 0.05 5.21 0.59 \u00b1 0.07 9.34 1.93 \u00b1 0.55 3.79 2.26 6304 -1.89 \u00b1 0.19 5.17 \u00b1 0.05 5.27 \u00b1 0.05 5.69 0.20 \u00b1 0.07 9.57 3.05 \u00b1 0.86 4.13 2.08 6341 -0.75 \u00b1 0.05 5.15 \u00b1 0.06 5.48 \u00b1 0.03 5.39 0.53 \u00b1 0.07 9.47 1.56 \u00b1 0.44 4.47 2.36 6397 -0.40 \u00b1 0.03 4.61 \u00b1 0.02 4.96 \u00b1 0.02 4.60 0.56 \u00b1 0.03 9.14 1.09 \u00b1 0.26 5.65 2.05 6541 -0.49 \u00b1 0.05 5.09 \u00b1 0.06 5.41 \u00b1 0.05 4.64 0.53 \u00b1 0.08 9.32 1.64 \u00b1 0.49 4.85 2.49 6584 -0.53 \u00b1 0.02 4.62 \u00b1 0.13 4.67 6656 -0.98 \u00b1 0.13 5.42 \u00b1 0.02 5.69 \u00b1 0.03 6.25 0.46 \u00b1 0.04 9.70 1.86 \u00b1 0.46 3.88 2.38 6723 -0.24 \u00b1 0.05 4.84 \u00b1 0.07 5.23 \u00b1 0.11 5.04 0.59 \u00b1 0.13 9.28 1.91 \u00b1 0.71 3.37 2.20 6752 -0.49 \u00b1 0.07 4.97 \u00b1 0.03 5.38 \u00b1 0.02 5.68 0.60 \u00b1 0.04 9.44 1.94 \u00b1 0.48 5.03 2.19 6779 -0.55 \u00b1 0.03 4.79 \u00b1 0.09 4.92 6809 -0.89 \u00b1 0.05 4.90 \u00b1 0.03 5.29 \u00b1 0.03 6.31 0.59 \u00b1 0.04 9.50 1.83 \u00b1 0.45 2.81 1.97 6934 -0.77 \u00b1 0.04 4.84 \u00b1 0.10 5.98 7078 -1.16 \u00b1 0.07 5.54 \u00b1 0.05 5.81 \u00b1 0.03 7.71 0.47 \u00b1 0.06 9.89 1.79 \u00b1 0.48 4.16 2.23 7089 -0.83 \u00b1 0.07 5.53 \u00b1 0.05 5.89 \u00b1 0.06 7.87 0.56 \u00b1 0.08 9.88 1.98 \u00b1 0.57 4.11 2.28 7099 -0.72 \u00b1 0.02 4.82 \u00b1 0.07 5.16 \u00b1 0.05 5.53 0.54 \u00b1 0.08 9.37 1.48 \u00b1 0.44 5.04 2.01 S/N > 10 for all target clusters. The results of arti\ufb01cial star experiments are also available to allow an accurate estimate of the completeness level and photometric errors. A detailed description of the photometric reduction, astrometry, and arti\ufb01cial star experiments can be found in Anderson et al. (2008). Within this database we excluded from our analysis all GCs with i) evidence of large (\u2206Y > 0.1) helium variation (\u03c9 Cen, NGC 2808, NGC 6388, NGC 6441), ii) signi\ufb01cant contamination by either bulge (NGC 6624, NGC 6637) or Sagittarius dwarf galaxy stars (M54), or iii) a completeness level estimated in the innermost arcminute at the hydrogen-burning limit smaller than \u03c8 < 10%. Thirty-\ufb01ve GCs passed the above selection criteria (see Table 1). The surface brightness pro\ufb01les for most GCs of our sample were taken from Trager, King & Djorgovski (1995). They were constructed from generally inhomogeneous data based mainly on the Berkeley Globular Cluster Survey (Djorgovski & King 1984). The surface brightness pro\ufb01le of each cluster has been derived by matching several sets of data obtained with di\ufb00erent techniques (aperture photometry on CCD images and photographic plates, photoelectric observations, star counts, etc.). Moreover, the pro\ufb01les of the more distant and/or faint GCs are often noisy and do not extend beyond a few core radii. For this reason we adopted, where available, the number density pro\ufb01les calculated by Miocchi et al. (2013) from wide \ufb01eld photometry. Finally, the density pro\ufb01le calculated by Melbourne et al. (2000) and AlonsoGarc\u00b4 \u0131a et al. (2012) have been adopted for NGC 4833 and NGC 6144, respectively. Because of the better angular resolution of HST data, ACS observations sample the innermost portion of our clusters much more accurately than any other previous ground based analysis. For this reason, the surface brightness pro\ufb01le of the innermost 1.6\u2032 has been calculated directly from ACS data by summing completeness-corrected F606W \ufb02uxes \u00b5 = \u22122.5log  X i 10\u22120.4F 606Wi ci ! in annuli of 0.1\u2032 width and matched to the adopted external pro\ufb01le using the overlap region. The completeness factors ci have been calculated for all stars as the fraction of recovered objects1 in the arti\ufb01cial star catalog among all stars within 1 An arti\ufb01cial star has been considered recovered if its input and output magnitudes di\ufb00er by less than 2.5 log(2) (\u223c0.75) mag in both F606W and F814W magnitudes. c \u20dd2017 RAS, MNRAS 000, 1\u201314 4 Sollima et al. 0.\u203205 from the position of each individual star and within 0.25 mag of the F606W and F814W magnitudes of each individual star. Among the 35 GCs of our sample we found large sets (>50) of available radial velocities in the literature for 29 of them (see Table A1 of Baumgardt 2017 for the references for each cluster). Radial velocities from di\ufb00erent sources were corrected for systematic shifts using the stars in common. Additional radial velocities for clusters NGC 1261, NGC 5986, NGC 6304 and NGC 6541 were derived from archival FLAMES@VLT spectra collected under the observing programmes 193.D-0232 (PI Ferraro) and 093.D-0628 (PI Zocchi). For this task, pipeline-reduced spectra were cross-correlated with the solar spectrum observed with the same setups as the science observations using the task fxcor within the IRAF package2. 3 MODELS As explained in Sec. 1, in dynamically evolved stellar systems like GCs, the distribution of stars depends on their mass. Hence, in order to derive the global MF of our target clusters, their MFs measured in the ACS \ufb01eld of view need to be corrected using the prescriptions of a dynamical model. The structure and kinematics of our clusters have been modelled with a set of isotropic multimass King-Michie models (Gunn & Gri\ufb03n 1979). According to this model, the distribution function is given by the sum of the contribution of several mass groups f(E, L) = H X j=1 kj \u0014 exp \u0012 \u2212AjE \u03c32 K \u0013 \u22121 \u0015 H X j=1 fj(mj, r, v) = H X i=1 kj \u0014 exp \u0012 \u2212Aj(v2 + 2\u03c8) 2\u03c32 K \u0013 \u22121 \u0015 (1) where E is the energy per unit mass, mj is the mass of the stars in the j-th component, H is the number of mass components, kj are coe\ufb03cients determining the relative fraction of stars in the j-th mass group, \u03c32 K is an energy normalization constant, r and v are the 3D distance from the cluster centre and velocity, and Ai are coe\ufb03cients governing the kinetic energy balance among di\ufb00erent mass groups. In the original formulation by Gunn & Gri\ufb03n (1979) Aj \u221dmj. Although this last assumption is arbitrary, it has been shown that it reproduces the structure and the degree of mass segregation of both N-body simulations during most of their evolution and real GCs (Sollima et al. 2015, 2017). In principle, a degree of radial anisotropy can be included by multiplying the distribution function of eq. 1 by a term dependent on the angular momentum. However, because of the lack of accurate proper motion determinations for the GCs analysed here, no stringent constraints on the degree of anisotropy can be put. Moreover, the recent analysis by Watkins et al. (2015) based on accurate HST proper motions 2 IRAF is distributed by the National Optical Astronomy Observatories, which are operated by the Association of Universities for Research in Astronomy, Inc., under cooperative agreement with the National Science Foundation. in 22 Galactic GCs showed that they appear to be isotropic across the \ufb01eld of view analysed by these authors. For the above reasons, we prefer to consider only isotropic models to limit the number of free parameters. We adopted 23 mass groups: 8 evenly spaced bins comprised between 0.1 M\u2299and the mass at the tip of the Red Giant Branch (Mtip) and 15 evenly spaced bins between Mtip and 2.6 M\u2299(i.e. the largest mass allowed in our synthetic population; see Sec. 4). The distribution function in eq. 1 can be integrated over the velocity domain to obtain the 3D density and velocity dispersion of each mass group. \u03bdj(r) = Z \u221a \u22122\u03c8(r) 0 4\u03c0v2kjfj(v, r, mj)dv \u03c32 v,j(r) = R \u221a \u22122\u03c8(r) 0 4\u03c0kjv4fj(v, r, mj)dv \u03bdj(r) (2) while the potential at any radius is determined by the Poisson equation \u22072\u03c8 = 4\u03c0G\u03c1 (3) where \u03c1(r) = H X j=1 mj\u03bdj(r) Equations 1 to 3 have been integrated after assuming, as a boundary condition, a value of the potential and its derivative at the centre (\u03c80; d\u03c8/dr(0) = 0) outward till the radius rt at which both density and potential vanish. Observational quantities (global MF, surface brightness and line-of-sight velocity dispersion pro\ufb01les) can be obtained through the relations Nj = 4\u03c0 Z rt 0 r2\u03bdj dr \u00b5(R) = \u22122.5log  H X j=1 \u0393j\u03a5j ! \u03c32 LOS,j(R) = 2 3\u0393j(R) Z rt R \u03bdj\u03c32 v,jr \u221a r2 \u2212R2 dr (4) where \u0393j(R) = 2 Z rt R \u03bdjr \u221a r2 \u2212R2 dr is the projected number density and \u03a5j is the average Vband \ufb02ux of stars in the j-th component. These models are completely de\ufb01ned by the free parameters W0 \u2261\u2212\u03c80/\u03c32 K, kj (unequivocally de\ufb01ning the shape of all pro\ufb01les), rc \u2261 p 9\u03c32 K/4\u03c0G\u03c1(0) (de\ufb01ning the size of the model), and \u03c32 K (determining the normalization in mass and velocity dispersion). The total mass and luminosity of the model can \ufb01nally be calculated as c \u20dd2017 RAS, MNRAS 000, 1\u201314 The mass function of 35 Galactic GCs 5 Figure 1. Selection boxes adopted for the population of single stars (m1 to m8) and binaries (bin) of NGC 288. The observed CMD is overplotted. The 50% completeness limit is marked by the dashed line. M = H X j=1 Njmj LV = H X j=1 Nj\u03a5j 4 METHOD The algorithm adopted to determine the global MF of each GC is similar to that described in Sollima, Bellazzini & Lee (2012) and Sollima et al. (2017) and can be schematically described as follows: (i) As a \ufb01rst step, a synthetic stellar population has been constructed by randomly extracting N = 106 stars from a Kroupa (2001) IMF between 0.1 and 8 M\u2299. A fraction fb of binaries has also been simulated by randomly pairing Nb = 2Nfb synthetic stars. All single stars and stars in binaries with masses m > Mtip have been turned into compact remnants following the prescription mW D = 0.109m + 0.428 (Kalirai et al. 2009) Due to the adopted upper limit of the IMF, only white dwarfs are created in this process. This is consistent with the assumption that all neutron stars and black holes are ejected in the early stage of cluster evolution because of the e\ufb00ect of natal kicks and/or Spitzer instability (Krujissen 2009). (ii) The corresponding synthetic CMD has been constructed by interpolating the masses of visible stars with the mass-luminosity relation of a suitable isochrone from the Dotter et al. (2007) database. For each cluster, the isochrone metallicity, age and \u03b1-enhancement as well as the reddening and distance modulus listed in Dotter et al. (2010), providing an excellent \ufb01t to the ACS data, have been adopted A synthetic horizontal branch (HB) has been simulated for each cluster using the tracks by Dotter et al. (2007), tuning the mean mass and mass dispersion along the HB to reproduce the observed HB morphology. The magnitude and colours of binary systems have been calculated by summing the \ufb02uxes of the two components in both passbands. We do not account for the negligible contamination of fore/background Galactic \ufb01eld interlopers possibly present in the ACS \ufb01eld of view. Indeed, the Galactic model of Robin et al. (2003) predicts <50 \ufb01eld stars, corresponding to a fraction <0.1%, contained in the selection box (see below) and within the innermost 1.6\u2032even in the low-latitude GCs of our sample. (iii) The synthetic stars (singles, binaries and remnants) have been binned in mass (see Sec. 3) and for each bin a fraction 1\u2212Xj of particles has been randomly rejected. The average F606W \ufb02uxes (\u03a5j) of the remaining stars in each mass group have also been calculated; (iv) A dynamical model is constructed tuning the parameters W0 and rc in order to obtain the best \ufb01t of the surface brightness pro\ufb01le and the kj coe\ufb03cients are modi\ufb01ed to reproduce the MF of the mock catalog (see eq. 4); (v) The distribution in phase-space (3D position and velocity) of synthetic stars was then extracted from the modelled distribution function using the von Neumann rejection technique: for each star a random position in phase-space (r, v) is extracted and assigned to the star only if a random number between 0 and 1 turns out to be smaller than f(mi, r, v)/f(mi, 0, 0). Projected distance and LOS velocities have then been calculated assuming an isotropic distribution; (vi) For each synthetic star, a particle from the arti\ufb01cial star catalog with distance from the cluster centre within 0.\u203205 and magnitudes within 0.25 mag with respect to the same quantities of the given star, has been extracted and, if recovered, the magnitude and colour shift with respect to its input quantities have been added to those of the corresponding star. In this way, a mock CMD accounting for photometric errors and incompleteness has been obtained; (vii) The number of stars within 1.\u20326 from the cluster centre (i.e. the extent of the ACS \ufb01eld of view) and contained in 9 regions of both the observed and the mock CMD have been counted (see Fig. 1). In particular, we de\ufb01ned \u2022 eight F606W magnitude intervals corresponding to the \ufb01rst 8 mass intervals and including all stars with colours within three times the photometric error corresponding to their magnitudes; \u2022 a region including the bulk of the binary population with high mass ratios (q > 0.5). This last region is delimited in magnitude by the loci of binaries with primary star mass m1 = 0.45M\u2299(faint boundary) and m1 = 0.75M\u2299 (bright boundary), and in colour by the MS ridge line (blue boundary) and the equal-mass binary sequence (red boundary), both redshifted by three times the photometric error. (viii) The retention fractions (Xj) of stars in the eight mass bins and the global binary fraction fb are adjusted by multiplying them for corrective terms which are proportional to the ratio between the relative number counts in each bin c \u20dd2017 RAS, MNRAS 000, 1\u201314 6 Sollima et al. Figure 2. Comparison between three observables of NGC 288 and the corresponding model prediction (red lines; grey in the printed version of the paper). Bottom-left panels: surface brightness pro\ufb01le; bottom-right panel: velocity dispersion pro\ufb01le; upper-left panels: CMDs; upper-right panels: F606W luminosity function. The predicted \u00b1\u03c3LOS range is indicated in the bottom-right panel. of the observed sample and the corresponding model prediction X\u2032 j = Xj   Qobs j Qmock 8 Qobs 8 Qmock j !\u03b7 f \u2032 b = fb   Qobs bin Qmock bin P8 j=1 Qmock j P8 j=1 Qobs j !\u03b7 where Qj and Qbin are the number of stars observed in the j-th single and in the binary selection boxes respectively, the superscripts obs and mock indicate counts measured either in the observed or in the mock catalog respectively, and \u03b7 is a softening parameter, set to 0.5, used to avoid divergence. All the coe\ufb03cients Xj with j > 8 have been set equal to 1. Steps from (iii) to (viii) have been repeated until convengerce. For the \ufb01rst step we adopted Xj = 1 for all j and fb = 5%. The above described procedure converged after \u223c20 iterations for all the considered clusters. The global MF of single stars can therefore be calculated directly from the mock catalog simulated in the last iteration. A \ufb01nal step is constituted by the mass normalization of the model. This can be done by best \ufb01tting two independent quantities: i) the actual number of stars in the observed (Qobs) and in the mock (Qmock) CMDs, and ii) the amplitude of the velocity dispersion pro\ufb01le. The former way allows to estimate the mass in luminous stars as Mlum = Qobs Qmock Nsin+Nbin X i=1 mi where the sum is extended to all single and binary stars in the \ufb01nal mock catalog excluding remnants. For clusters with available radial velocities, the latter way provides an estimate of the dynamical mass (Mdyn). The best \ufb01t value of Mdyn has been chosen as the one minimizing the penalty function c \u20dd2017 RAS, MNRAS 000, 1\u201314 The mass function of 35 Galactic GCs 7 Figure 3. Global MFs of NGC 288, NGC 1261, NGC 1851, NGC 2298, NGC 3201, NGC 4147 and NGC 4590. An arbitrary shift has been added to each MF for clarity. L = N X i=1   (vi \u2212v)2 \u03c32 LOS,8(Ri) + \u01eb2 i + ln(\u03c32 LOS,8(Ri) + \u01eb2 i ) ! where vi is the radial velocity of the i-th star, v is the systemic velocity of the cluster, \u01ebi is the individual uncertainty on the radial velocity and \u03c3LOS,8(Ri) is the line-ofsight velocity dispersion predicted by the best \ufb01t model at the projected distance Ri of the i-th star for the 8-th mass group. The choice of the 8-th mass bin is because radial velocities are available only for stars along the Red Giant Branch which cover a restricted range of masses. Because of the dependence of kinematics on mass, it is therefore necessary to compare the observed velocity dispersion pro\ufb01le with that of the corresponding mass bin to avoid bias in the mass estimate. Once luminous and dynamical masses are determined the fraction of dark mass can be calculated as fremn = 1 \u2212Mlum Mdyn Finally, the central density \u03c10, the half-mass radius rh, the Mdyn/LV ratio of the best \ufb01t model are computed as well as the half-mass relaxation time as trh = 0.138 M 1/2 dynr3/2 h G1/2m ln(\u03b3 Mdyn/m) (Spitzer 1987) (5) with \u03b3 = 0.11 (Giersz & Heggie 1996). The outcome of the application of the above thechnique for NGC 288 is shown in Fig. 2, as an example. 5 RESULTS The global MFs of the 35 GCs analysed in this work are shown in Figs. 3 to 7 and the derived dynamical parameters Figure 4. Same as Fig. 3 but for NGC 4833, NGC 5024, NGC 5053, NGC 5272, NGC 5286, NGC 5466 and NGC 5904. Figure 5. Same as Fig. 3 but for NGC 5986, NGC 6093, NGC 6101, NGC 6144, NGC 6205, NGC 6218 and NGC 6254. are listed in Table 1. Among the various parameters, the power-law index \u03b1 of the MF has been calculated for stars more massive than 0.2 M\u2299since stars below this limit often show relatively low levels of completeness (\u03c8 < 50%) and their relative fraction is subject to large errors. For testing purpose, we also calculate \u03b1 adopting a high mass cut at m> 0.3 M\u2299. In the scale adopted here a Salpeter (1955) MF has \u03b1 = \u22122.35 and a Kroupa (2001) MF would have a best \ufb01tting slope of \u03b1 \u223c\u22121.64. c \u20dd2017 RAS, MNRAS 000, 1\u201314 8 Sollima et al. Figure 6. Same as Fig. 3 but for NGC 6304, NGC 6341, NGC 6397, NGC 6541, NGC 6584, NGC 6656 and NGC 6723. Figure 7. Same as Fig. 3 but for NGC 6752, NGC 6779, NGC 6809, NGC 6934, NGC 7078, NGC 7089 and NGC 7099. The estimated slopes cover a wide range from \u03b1 = \u22121.89 (NGC 6304) to \u03b1 = 0.11 (NGC 2298). Thirteen GCs are in common with the work by Paust et al. (2010), who estimated MFs using the same photometric dataset and also used multimass dynamical models. We show the comparison between the two works in Fig. 8. The mean di\ufb00erence between the two studies is \u2206\u03b1(this work\u2212Paust) = 0.16\u00b10.13 consistent with only a small (if any) systematic shift. However the dispersion about the mean (\u03c3 = 0.47) is not comFigure 8. Comparison between the MF slopes derived in this work and those determined by Paust et al. (2010) for the 13 GCs in common. The one-to-one relation is marked by the dashed line. The location of NGC5466 and NGC6093 is shown. patible with the combined errors of the two works. In this context, it should be noted that the formal error quoted by Paust et al. (2010) as well as those listed in Table 1 are errors on the MF \ufb01t and do not re\ufb02ect the actual error budget (due to incomplete radial sampling, errors of the estimated completeness factor, isochrone/dynamical model inadequacy, etc.). Given the above considerations, we believe that a more realistic uncertainty of the MF slopes of both works is of the order of \u03c3\u03b1 \u223c0.3. It is worth noting that for NGC 6093 the di\ufb00erence between the two estimates exceeds \u2206\u03b1 >1.2. Moreover, for NGC 5466 we \ufb01nd an unphysical solution with Mlum > Mdyn. Among the GCs in common, these are those with the smallest fraction of stars contained within the ACS \ufb01eld of view. In this situation, even a small di\ufb00erence in the \ufb01tting process can produce large extrapolation errors. For comparison, a similar analysis of NGC 5466 performed in Sollima et al. (2017) using MF constraints in the outer portion of this cluster leads to a signi\ufb01cantly \ufb02atter MF slope (\u03b1 = \u22120.97). The mean difference between the MF slopes derived adopting di\ufb00erent low-mass cuts is \u2206\u03b10.3\u22120.2 = \u22120.05\u00b10.01, indicating only a small dependence of the estimated MF slopes on the adopted lower mass limit. An inspection of the MFs reveals that while some of them are well \ufb01tted by single power-laws, others show strong deviations from a power-law MF. To investigate this issue further, we correlated the \u03c72 value of the power-law \ufb01t with various cluster parameters. A single signi\ufb01cant correlation has been found with the MF slope itself, in the sense that \ufb02atter MFs present better power-law \ufb01ts. To highlight this result, we plot in Fig. 9 the residuals of the power-law \ufb01t for clusters with \u03b1 \u2277\u22121. It is apparent that while clusters with a relatively \ufb02at MF (\u03b1 > \u22121) show no signi\ufb01cant deviation from the best-\ufb01tting power-law, clusters with steep c \u20dd2017 RAS, MNRAS 000, 1\u201314 The mass function of 35 Galactic GCs 9 Figure 9. Residuals of the power-law \ufb01t for clusters with \u03b1 < \u22121 (left panel) and \u03b1 > \u22121 (right panel). The average residuals and their standard deviations for all mass bin are marked with red dots and errorbars (grey in the printed version of the paper). The Kroupa (2001; blue line) and Chabrier (2003; green line) IMFs are also marked with dotted lines. MFs have a convex shape. In particular, a point of maximum curvature is apparent at log(m/M\u2299) \u223c\u22120.4 (corresponding to a mass m \u223c0.4 M\u2299). The same evidence remains apparent even using the \u03b1 values calculated adopting a high mass cut at m > 0.3 M\u2299, indicating a negligible e\ufb00ect of the uncertainties of the MF estimate at very low masses. 6 ANALYSIS OF CORRELATIONS The MF slopes derived here constitute the largest available database and can be therefore used to search for correlations with other structural and general parameters. We considered the following parameters to look for possible correlations with the MF slope: Position in the Galaxy (RGC, Z from the Harris catalog; Harris 1996, 2010 edition), destruction rates (\u03bd; from Allen, Moreno & Pichardo 2006, 2008), concentration (c; from McLaughlin & van der Marel 2005), age and metallicity (t9, [Fe/H]; from Dotter et al. 2010), central V-band surface brightness, mass-to-light ratio, central and half-mass density, half-mass relaxation time and remnant mass fraction (\u00b5V,0, Mdyn/LV , \u03c10, \u03c1h, trh, fremn; from the best \ufb01t multimass model adopted in this analysis). As a \ufb01rst step, we analysed univariate correlations between \u03b1 and the other parameters. For this purpose a Monte Carlo procedure has been applied to estimate the signi\ufb01cance of the obtained correlations. For each of the considered parameters, we performed an error-weighted least-square \ufb01t and calculated the \u03c72 values. Then, the same analysis has been performed on one-thousand realizations simulated by randomly swapping the values of the independent variable among the GCs of the sample. The probability that the observed correlation is signi\ufb01cant is therefore given by the fraction of realizations with a \u03c72 larger than the observed value. From this approach we found three signi\ufb01cant (P > 99.7%) correlations with log trh, fremn and log \u03c1h, and a marginally signi\ufb01cant correlation (95% < P < 99.7%) with the central density, while no signi\ufb01cant correlations have been found with other parameters suggested by previous works (see Sec. 1). The entire set of correlations and their associated probabilities are shown in Fig. 10. We note that, the correlation between \u03b1 and log trh has a surprisingly small dispersion (\u03c3 = 0.29 i.e. compatible with the actual \u03b1 uncertainties; see Sec. 5). The only cluster straying from the observed trend is NGC 6304 with a MF slope \u03b1 = \u22121.89 \u00b1 0.19 steeper than those of the other GCs of our sample. It should be noted however that this cluster is close to the Galactic bulge whose MF is known to be bottom-heavy (Zoccali et al. 2000; Calamida et al. 2015). We therefore cannot exclude the possibility that the peculiar MF measured in this GC is due to a signi\ufb01cant contamination from the bulge. Another way to visualize the above correlation is shown in Fig. 11 where the MF slope \u03b1 is plotted against the ratio of age to present-day half-mass relaxation time tage/trh. Again, GCs de\ufb01ne a very tight correlation in this plot, indicating an evolutionary sequence. In other words, after the same number of present-day half-mass relaxation times clusters have similar MF slopes regardless of their orbits and chemical compositions. Another investigation can be made based on the location of clusters in the tage/trh \u2212\u03b1 plane as shown in Fig. 11: while GCs with tage/trh < 1 have MF slopes \u03b1 \u223c\u22121.5 similar to that of a Kroupa (2001) MF, the mean MF slope increases by \u223c0.5 dex at tage/trh \u223c3. We also extended our analysis to bivariate correlations. The \u03c72 of a bi-linear \ufb01t of all the possible pairs of parameters has been calculated and compared. The smallest \u03c72 are all those found by assuming log trh as the independent variable. To estimate how signi\ufb01cant the improvement with respect to an univariate \ufb01t is, we applied the same Monte Carlo approach described above: we compared the \u03c72 of the c \u20dd2017 RAS, MNRAS 000, 1\u201314 10 Sollima et al. Figure 10. Univariate correlations between the global MF slope \u03b1 and various parameters. The statistical signi\ufb01cance (P) of each correlation is indicated. bivariate \ufb01t (assuming log trh as the \ufb01rst independent variable) with those obtained by randomly swapping the values of the adopted second independent variable. We found a marginally signi\ufb01cant (P=97.7%) improvement with respect to the univariate \ufb01t only by assuming as second independent variable fremn. Unfortunately, trh, fremn, \u03c1h and \u03b1 are all output parameters of the best \ufb01t multimass model adopted in this work. It is therefore possible that covariances between the uncertainties in these parameters conspire to spuriously create the quoted correlations. To test this hypothesis, we run a Markov-Chain Monte Carlo analysis on our target GCs. This algorithm samples the parameter space in the neighbourhood of the best \ufb01t parameters, providing a distribution of accepted trials which re\ufb02ect the actual probability distribution. The distribution of accepted trial values in the log trh \u2212\u03b1, fremn \u2212\u03b1 and log \u03c1h \u2212\u03b1 planes for the cluster NGC 288 are shown in Fig. 12, as an example. The covariance between \u03b1 and log trh is apparent with a tendency of solutions with longer trh to have shallower MFs, while no signi\ufb01cant slope with log \u03c1h or fremn is noticeable. A similar behaviour has been noticed in the other clusters with no signi\ufb01cant dependence of the bias orientation and strength on the position in these planes. Note that the direction of such a bias in the log trh \u2212\u03b1 plane is similar to that of the observed correlation. However, the shift in \u03b1 along the bias direction needed to erase any signi\ufb01cant correlation with log trh would be as large as \u2206\u03b1 \u223c0.8 at the extreme of this plot i.e. \u223c3 times larger than typical uncertainties. To further check that the observed correlation is not driven by the covariance spuriously introduced by the adopted \ufb01tting procedure, we correlated the derived MF slopes with the log trh values derived independently by McLaughlin & van der Marel (2005) \ufb01tting single mass King (1966) models. Also in this case, we found a con\ufb01dence level >99.9% that the two variables are correlated. So, while it is conceivable that the observed log trh \u2212\u03b1 correlation is sharpened by the covariance between errors, it cannot be completely produced by this bias. Another source of bias could be linked to an overestimate of the level of completeness. This could indeed spuriously deplete the MF at its low-mass end, in particular for c \u20dd2017 RAS, MNRAS 000, 1\u201314 The mass function of 35 Galactic GCs 11 Figure 11. MF slope \u03b1 as a function of the ratio between cluster age and present-day half-mass relaxation time for the 29 GCs of our sample. dense GCs characterized by short relaxation times. While we cannot completely exclude this occurrence, it is unlikely that a signi\ufb01cant bias in the estimated completeness is present above the magnitude limit corresponding to stellar masses m > 0.2 M\u2299, in the portion of the CMD used to estimate the MF slope. To check the possible e\ufb00ect of uncertainties in the completeness correction we repeated the analysis by using the MF slope \u03b1 calculated assuming a high m > 0.3 M\u2299 cut and excluding all those clusters with completeness levels <50% within their core radii at masses < 0.25 M\u2299(see Leigh et al. 2012). Although only 15 GCs survive to this severe criterion, the correlation between \u03b1 and log trh remains signi\ufb01cant at 99.9%, while the signi\ufb01cance levels of the other correlations drop below 75%. On the basis of the above test, we conclude that the log trh \u2212\u03b1 correlation we observe among the GCs of our sample is robust and real. 7 DISCUSSION Through a comparison of the deepest available HST photometric data with multimass King-Michie models we derived the MFs of 35 Galactic GCs just above the hydrogen burning limit as well as structural parameters, masses, M/L ratios and fraction of remnants for a subset of 29 GCs with available radial velocity information. The MFs of GCs are generally well described by powerlaws, in particular when clusters with relatively shallow MF slopes (\u03b1 > \u22121) are analysed. Noticeable deviations from power-laws are evident in clusters whose MFs are steeper than \u03b1 = \u22121. In particular, in these cases a bend in the MF is appreciable at masses m \u223c0.4 M\u2299with a significant depletion of low-mass stars. This evidence has been previously reported by De Marchi & Paresce (1997) and De Marchi, Paresce & Portegies-Zwart (2010) who also de\ufb01ned a relation linking the position of the bend with the dissolution timescale. These GCs have half-mass relaxation times of trh > 6 Gyr, and it is possible that their MFs have not been signi\ufb01cantly altered by dynamical evolution e\ufb00ects. We will discuss these deviations in greater detail in a second paper (Baumgardt & Sollima 2017) where we compare the MF slopes derived in this work with the results of N-body simulations. In this interpretation, the convex shape of their MFs might resemble the original shape of the IMF, in agreement with the prediction of Kroupa (2001) and Chabrier (2003). By correlating the derived MF slopes with di\ufb00erent structural and orbital cluster parameters we found significant and tight correlations with the half-mass relaxation time. Although covariance between uncertainties can spuriously enhance the strength of the log trh \u2212\u03b1 correlation, we believe that it is real since i) its extent exceeds the range over which the above mentioned bias would produce a sizeable e\ufb00ect, and ii) it is signi\ufb01cant using independent estimates of trh. This correlation is expected as a result of the natural evolution of collisional stellar systems. Indeed, twobody relaxation is the main mechanism leading to the segregation of low-mass stars to the outer cluster parts, where they can be easily lost by tidal stripping (Vesperini & Heggie 1997; Baumgardt & Makino 2003; Leigh et al. 2012). So, the shorter the timescale of internal dynamical evolution the more e\ufb03cient is the depletion of the MF. However, the location of N-body simulations in the log trh \u2212\u03b1 plane is highly sensitive to the original slope of the IMF, with clusters starting with a steeper IMF reaching also steeper present-day MFs after a given number of elapsed relaxation times than clusters starting with \ufb02atter IMFs (Webb & Vesperini 2016). Thus, a signi\ufb01cant spread in this relation would be apparent if cluster-to-cluster variations of the IMF were present at the epoch of their formation. On the other hand, all surveys of N-body simulations performed so far, showed that two-body relaxation is expected to produce a slow variation of the MF slope. In particular, simulations starting with a Kroupa (2001) IMF take \u223c13 half-mass relaxation times to \ufb02atten their MF up to a slope of \u03b1 = \u22121 and reach a \ufb02at \u03b1 = 0 slope only close to dissolution (Baumgardt & Makino 2003; Webb & Vesperini 2014; Lamers et al. 2013). In such a picture, it is hard to explain the large range in \u03b1 covered by the GCs of our sample, in particular in the less evolved tage/trh < 5 regime, without any primordial spread in their IMFs. In this last case, however, a correlation between the IMF slope and the present-day half-mass relaxation time would be necessary to reproduce the observed log trh \u2212\u03b1 correlation. The universality of the IMF of Milky Way GCs has important implications for the thermodynamics of the gas clouds from which GCs formed at high-redshift. Theoretical arguments indeed suggest a dependence of the IMF on the metal content and the initial density of the cluster because of their e\ufb00ect on the Jeans mass and on the e\ufb03ciency of radiative feedback (Silk 1977; Adams & Fatuzzo 1996; Larson 1998; Klessen, Spaans & Jappsen 2007) although the actual impact of these processes is uncertain. Whether Milky Way GCs were born with a Universal IMF or not, provides insight on the e\ufb03ciency of these mechanisms in the environmental conditions of GCs at their birth. It is interesting to consider the evidence found in stellar systems populating regions of the MV \u2212reff plane contiguous to GCs. In this regard, while c \u20dd2017 RAS, MNRAS 000, 1\u201314 12 Sollima et al. Figure 12. Bottom panels: distribution of the accepted trials of the Markov-Chain Monte Carlo in the log trh \u2212\u03b1 (left), fremn \u2212\u03b1 (middle) and log \u03c1h \u2212\u03b1 (right) planes. Top panels: distribution of the 29 analysed clusters in the log trh \u2212\u03b1 (left), fremn \u2212\u03b1 (middle) and log \u03c1h \u2212\u03b1 (right) planes. The orientation of the biases are indicated by arrows. Grillmair et al. (1998) and Wyse et al. (2002) derived MFs for Draco and Ursa Minor dwarf spheroidals which are consistent with a Salpeter (1955) IMF, Geha et al. (2013) found evidence of MF variations correlated with the mean metallicity in a sample of ultra-faint dwarf galaxies. Since these systems are dynamically unevolved, these variations can be only interpreted as primordial. This study has been however questioned by El-Badry, Weisz & Quataert (2017) who found that signi\ufb01cant MF di\ufb00erences cannot be detected unless the photometric data used is signi\ufb01cantly deeper than that currently available. On the other hand, Weisz et al. (2013) analysed a large sample of young clusters and associations whose MFs are available in the literature. In spite of the large cluster-to-cluster di\ufb00erences, a careful revision of the associated errors indicates that the hypothesis that they are consistent with a single IMF slope cannot be ruled out. Hence, due to the above con\ufb02icting results, it is not clear if a common mechanism of star formation was at work for GCs and less massive and dense stellar systems. Interestingly, Baumgardt & Makino (2003), Lamers et al (2013) and Webb & Leigh (2015) found a unique relation linking the present-day MF slope and the fraction of mass lost by their simulated GCs. Such a relation, which is valid only if a universal IMF is assumed, appears to be almost insensitive to the strength of the tidal \ufb01eld, the type of cluster orbit, and to the initial mass and size of the cluster. The MFs derived here have slopes which imply a huge amount of mass lost (> 70%) by the majority of GCs in our sample. By inverting eq. 14 of Baumgardt & Makino (2003) and adopting the present-day masses listed in Table 1, we estimated the amount of mass lost by each cluster during its evolution. Assuming that our sample covers \u223c20% of the GC system of the Milky Way, a global mass of \u223c2\u00d7108 M\u2299, mainly in lowmass stars, could have been released in the Galactic halo by GCs. In spite of the large uncertainties in the Galactic halo mass (Morrison 1993; Bell et al. 2008; Deason, Belokurov & Evans 2011), this could constitute a signi\ufb01cant contribution to the total mass budget of the halo. This is in agreement with the prediction by Martell & Grebel (2010) based on the fraction of halo stars showing the chemical signature of GCs c \u20dd2017 RAS, MNRAS 000, 1\u201314 The mass function of 35 Galactic GCs 13 stars. In this picture, one would expect a signi\ufb01cant excess of low-mass stars in the MF of halo stars. Such a prediction could be probably veri\ufb01ed by the incoming data provided by the GAIA survey. Another signi\ufb01cant correlation has been found between the present-day MF slopes and the fraction of dark mass. The natural interpretation of this correlation is that dark remnants (mainly constituted by white dwarfs) have masses larger than the average cluster stars and are being more e\ufb03ciently retained. Moreover, the fraction of white dwarfs steadily increase with time as less massive (and more abundant) stars approach this late stage of their evolution. Studies based on N-body simulations have shown that, because of the two above mentioned processes, the fraction of mass contained in remnants increases as two-body relaxation proceeds (Baumgardt & Makino 2003; Contenta, Varri & Heggie 2015). Such a correlation becomes less signi\ufb01cant when dense GCs, subject to low completeness at low masses are excluded. Signi\ufb01cant correlations with the half-mass and (marginally) with the central density (obviously related to trh) have also been found, in agreement with previous \ufb01nding by Paust et al. (2010). All the correlations with orbital parameters and position in the Galaxy suggested by previous studies based on the analysis of small samples of GCs (Capaccioli et al. 1993; Djorgovski et al. 1993; Piotto & Zoccali 1999), have been found to be less signi\ufb01cant although they cannot be completely ruled out. No signi\ufb01cant correlation has been found with the cluster concentration, as previously suggested by De Marchi et al. (2007). Note that, while the uncertainties on the individual MF slopes do not allow to exclude the presence of such a correlation, for most GCs studied by De Marchi et al. (2007) the slope of the global MF has been assumed to be that measured in an external region close to the half-mass radius. However, in high-concentration clusters the analysed \ufb01elds are often located well beyond the half-mass radii estimated here, a region where the MF is expected to be steeper because of mass segregation e\ufb00ects. In particular, there are three high concentration GCs out of 6 in their sample where the MF is calculated between 3 and 7 half-mass radii. This could create a spurious correlation between MF slope and concentration. It is worth stressing that our results are based on an analysis conducted in the central region of GCs where mass segregation e\ufb00ects are particularly strong. As a consequence, the derived global MFs are sensitive to the recipe of mass segregation of the adopted multimass models. In Sollima et al. (2015) we showed that such an assumption can potentially lead to biases in the estimated MF slopes as large as \u2206\u03b1 \u223c0.2, i.e. comparable with the estimated random uncertainties (see Sect. 5). Although the magnitude of such a bias cannot alter the conclusions of this paper, the present analysis would greatly bene\ufb01t from constraints on the MF measured in the outer regions of these clusters (see e.g. Sollima et al. 2017). ACKNOWLEDGMENTS We warmly thank Michele Bellazzini, Enrico Vesperini and Luca Ciotti for useful discussions. We also thank the anonymous referee for his/her helpful comments and suggestions.",
                    "introduction": "One of the long-standing issues of stellar astrophysics is the understanding of the mechanisms determining the mass dis- tribution of stars. This topic represents one of the central questions in the theory of star formation and has strong rel- evance for many areas of astrophysics. The original distri- bution of stellar masses, commonly referred to as the Initial Mass Function (IMF), is indeed a key ingredient in models of stellar population synthesis, chemical evolution of clusters and galaxies, dynamical evolution of stellar systems and, in general, in any topic involving the role of baryons. In this regard, the universality of the IMF, its shape and the parameters driving its hypothetical variation are ques- tions still far from being completely understood from both \u22c6E-mail: antonio.sollima@oabo.inaf.it a theoretical and an observational point of view. Indeed, many complex processes a\ufb00ect the e\ufb03ciency of fragmenta- tion of a molecular cloud (dependence of the Jeans mass from thermodynamical parameters, competitive accretion, metal line-driven cooling, etc.; Silk 1977; Fleck 1982; Bon- nell et al. 1997; Nakamura & Umemura 2001). A practical di\ufb03culty in observationally constraining the IMF resides in its temporal evolution, which strongly depends on the char- acteristics of the considered stellar population and on its environment. An ideal class of astrophysical objects where to perform an analysis of the IMF should be young, dy- namically unevolved stellar populations containing a large number of coeval and chemically homogeneous stars cover- ing a wide range of masses. None of the known star forming complexes satisfy all the above requirements so, from the pionering study by Salpeter (1955), many studies concen- trated on the determination of the IMF shape in the Galac- c \u20dd2017 RAS 2 Sollima et al. tic \ufb01eld, in OB associations (Miller & Scalo 1979; Kroupa 2001; Chabrier 2003) and, more recently, in dwarf galax- ies (Geha et al. 2013). Despite the huge observational e\ufb00ort made during the last 60 years, there is still no clear evidence for systematic variations of the IMF and con\ufb02icting results have been reported in the past (see Bastian, Covey & Meyer 2010 for a recent review). Globular clusters (GCs) are in principle among the best places to investigate the distribution of stellar masses at the low-mass end of the MF (0.1 < M/M\u2299< 1). They are composed out of hundred of thousands to millions of stars, located at the same distance and formed in a short time in- terval from a chemically relatively homogeneous cloud cov- ering a wide range of masses. Moreover, there is a signi\ufb01cant number of GCs at distances <20 kpc for which it is possi- ble to perform a statistically meaningful sampling of their stellar population down to the hydrogen-burning limit with a good level of completeness. On the other hand, the re- laxation times of globular clusters are often smaller than their ages so that the large number of interactions among their stars produces a mass-dependent distribution of ki- netic properties (energies and angular momenta). This re- \ufb02ects into the time evolution of the MF since low-mass stars progressively gain energy, being more prone to evaporation. As mass-loss proceeds independently, the MF tends to \ufb02at- ten on timescales depending on both the internal structure of the cluster and the strength of the external tidal \ufb01eld (Baumgardt & Makino 2003 ; Lamers, Baumgardt & Gieles 2013). Moreover, the tendency toward energy equipartition leads to a radial segregation of di\ufb00erent mass groups with the most massive stars moving on less energetic orbits pref- erentially con\ufb01ned to the innermost cluster regions, while low-mass stars di\ufb00use into an extended halo. For all these reasons, the present-day MF measured in a particular re- gion of a GC does not re\ufb02ect either its IMF nor its global MF. The derivation of the present-day global MF is however still possible by correcting the locally estimated MF by the mass-segregation e\ufb00ects predicted by some suitable dynam- ical model (see e.g. McClure et al. 1986; Paust et al. 2010). Such corrections depend on the cluster concentration, MF and distance from the cluster centre but they appear to be generally small close to the half-mass radius (Baumgardt & Makino 2003). So, an alternative approach is to estimate the MF in this region of the cluster and assume it as a good rep- resentation of the global MF (e.g. Piotto & Zoccali 1999). On the theoretical side, many surveys of N-body simulations have been performed to investigate the evolution of the MF in GC-like objects (Vesperini & Heggie 1997; Baumgardt & Makino 2003; Lamers, Baumgardt & Gieles 2013; Webb & Vesperini 2014, 2016). In particular, Leigh et al. (2012) used a set of N-body runs assuming di\ufb00erent masses, concentra- tions, orbital eccentricities and tidal environments to repro- duce the MFs of a sample of 27 Galactic GCs and showed that the natural evolution of a universal IMF could actually produce the observed cluster-to-cluster di\ufb00erences. Observationally, since the early 1980\u2019s many studies fo- cussed on the determination of the MF in individual GCs (without correcting for incompleteness, e.g. Da Costa 1982; Richer et al. 1990; Santiago, Elson & Gilmore 1996; Chabrier & Mera 1997; Paresce & De Marchi 2000; Pulone et al. 2003; Paust, Wilson & van Belle 2014). The \ufb01rst comprehensive studies of the MFs in a number of GCs large enough to ex- plore possible correlations with various cluster parameters have been those by Capaccioli, Piotto & Stiavelli (1993) and Djorgovski, Piotto & Capaccioli (1993) who collected the MFs measured by di\ufb00erent authors for a sample of 17 Galac- tic GCs and reported a dependence of their slopes (measured using stars with masses m > 0.5M\u2299) with the cluster po- sition in the Galaxy. Piotto & Zoccali (1999) analysed in a homogeneous way deep Hubble Space Telescope (HST) im- ages taken near the half-mass radii of seven globular clusters reaching a limiting mass of m \u223c0.3M\u2299. They found that the MF slopes correlate with the orbital destruction rates of the clusters in the Galaxy and anticorrelate with their half-mass relaxation times although their small sample hampered any \ufb01rm conclusion on the signi\ufb01cance of these correlations. De Marchi, Paresce & Pulone (2007) used a sample of HST and Very Large Telescope data for a sample of 20 GCs and found a well de\ufb01nd correlation between the slope of their MFs and their King model concentration parameter c. Finally, Paust et al. (2010) derived the central and global present-day MFs of 17 GCs as part of the ACS Survey of Galactic Globular Clusters treasury project (Sarajedini et al. 2007) by com- paring ACS/HST photometric data with multimass dynam- ical models. They found a signi\ufb01cant correlation between the MF slope and the central density (or equivalently the central surface brightness), while detecting only marginal statisti- cal signi\ufb01cance of the previously reported correlations with other parameters. In this paper we use the ACS treasury project database to extend the census of GC MFs to a sample of 35 clusters, more than doubling the sample already analysed by Paust et al. (2010). By means of a comparison with multimass analyt- ical models we derive the global MFs of the analysed clus- ters and investigate possible correlations with their struc- tural and dynamical parameters. In Sec. 2 we present the database used in this work. The adopted dynamical models are described in Sec. 3. Sec. 4 is devoted to the description of the algorithm adopted to determine global MFs and other structural parameters. The obtained MFs and the analysis of their shapes are presented in Sec. 5. In Sec. 6 we search for correlations with various cluster parameters. We \ufb01nally discuss our results in Sec. 7."
                }
            ],
            "Carlos Eduardo Barbosa": [
                {
                    "url": "http://arxiv.org/abs/1603.02202v1",
                    "title": "The Hydra I cluster core. I. Stellar populations in the cD galaxy NGC 3311",
                    "abstract": "(Abridged for arXiv) The history of the mass assembly of brightest cluster\ngalaxies may be studied by the mapping the stellar populations at large radial\ndistances from the galaxy centre. We provide extended and robust measurements\nof the stellar population parameters in NGC 3311, the cD galaxy at the centre\nof the Hydra I cluster and out to three effective radii. Using seven\nabsorption-features defined in the Lick/IDS system and single stellar\npopulations models, we obtained luminosity-weighted ages, metallicities and\nalpha element abundances. The trends in the Lick indices and the distribution\nof the stellar population parameters indicate that the stars of NGC 3311 may be\ndivided into two radial regimes, one within and the another beyond one\neffective radius, $R_e = 8.4$ kpc, similar to the distinction between inner\ngalaxy and external halo derived from the NGC 3311 velocity dispersion profile.\nThe inner galaxy ($R\\leq R_e$) is old (age $\\sim 14$ Gyr), have negative\nmetallicity gradients and positive alpha element gradients. The external halo\nis also very old, but the metal and element abundances of the external halo\nhave both a large scatter, indicating that stars from a variety of satellites\nwith different masses have been accreted. The region in the extended halo\nassociated with the off-centred envelope at 0$^o$ < P.A.< 90$^o$ (Arnaboldi et\nal. 2012) has higher metallicity with respect to the symmetric external halo.\nThe different stellar populations in the inner galaxy and extended halo reflect\nthe dominance of in situ stars in the former and the accreted origin for the\nlarge majority of the stars in the latter. These results provide supporting\nevidence to the recent theoretical models of formation of massive ellipticals\nas a two-phase process.",
                    "authors": "Carlos Eduardo Barbosa, Magda Arnaboldi, Lodovico Coccato, Michael Hilker, Cl\u00e1udia Mendes de Oliveira, Tom Richtler",
                    "published": "2016-03-07",
                    "updated": "2016-03-07",
                    "primary_cat": "astro-ph.GA",
                    "cats": [
                        "astro-ph.GA"
                    ],
                    "main_content": "In this study we explore a new spectroscopic data set for the Hydra I cluster. The data was observed at the Very Large Telescope (VLT) at Paranal, Chile, using the UT1 8.2m telescope with the FOcal Reducer/low dispersion Spectrograph 2 (FORS2, Appenzeller et al. 1998) in the multi-object spectroscopic mode with the Mask Exchange Unit (MXU), obtained under ESO programme ID 088.B-0448B (PI: Richtler). NGC 3311 spans a large area of the sky, and thus its observation out to large galactocentric distances requires a field-of-view beyond the area of most integral field units available to date. In order to survey an area of 3\u00d73 arcmin2 around NGC 3311, which translates into projected distances of \u223c30 kpc, we sampled regions of the stellar halo devoid of contamination of point sources with small slits, with typical size of 1\"\u00d75\", using 6 masks which sample the stellar halo in shells: cen1, cen2, inn1 inn2, out1 and out2. We used the grism 1400V with the standard collimator to obtain a dispersion of 0.25\u00c5 pixel\u22121, which gives a spectral resolution of R = 2100 at 5200\u00c5. The exposure times for the ceni and inni masks covering the central region are 2\u00d71400s, while it is 6 \u00d7 1400s for the outi masks. This observing strategy resulted in 135 slitlets dedicated to the observation of NGC 3311 and NGC 3309. The numbers of extracted spectra is smaller though, because we set a minimum signal-to-noise (S/N) of 10 in our observations, in order to constrain the stellar population parameters. A total of 117 spectra are used in our analysis. They are indicated by the red slits in Fig. 1. Article number, page 2 of 19 C. E. Barbosa et al.: The Hydra I cluster core I. Stellar populations in the cD galaxy NGC 3311 Fig. 1. Distribution of the signal-to-noise (S/N) of the scienti\ufb01c spectra in our sample. The position of the slits is shown as red bars, and the colours of the polygon, calculated by Voronoi Tessellation, indicate the S/N ratio according to the scale in the colour bar in the bottom left corner. Slits with white background were excluded from the analysis due to their low quality (S/N< 10). Black lines show the V-band contours in the range from 20 to 23.5 mag arcsec\u22122 in intervals of 0.5 mag arcsec\u22122, from Arnaboldi et al. (2012). The geometry of the polygons is shown herefater in all the other maps in this study. The reduction processes for extracting the scienti\ufb01c spectra, including bias subtraction, \ufb02at \ufb01elding correction, and wavelength calibration, were performed using custom IRAF scripts. We have used the long-slit spectrum of a spectrophotometric standard star, HD 102070, to test the e\ufb00ect of the \ufb02ux calibration on the Lick indices, which are used for the analysis of the stellar populations. This test has shown that the median change in the equivalent width of the indices is of 0.5% and, therefore, there is no need of \ufb02ux calibrate our spectra. The spectrum for sky subtraction of each slit was obtained simultaneously to the observations at slits in the periphery of the CCD, using the same x-axis position of the data, which ensured that science and sky spectra share the same wavelength range and exposure time for the subtraction. The wavelength range for spectra varies slightly as a function of the x-axis in the CCD, but in most cases the interval 4800 \u2272\u03bb (\u00c5)\u22725800 is available. For consistency, we calculated the signal-to-noise ratio per angstrom (S/N) of each spectrum in the range 5200 \u2264\u03bb (\u00c5) \u22645500, and the distribution of the S/N is presented by the polygons in Fig. 1. In this case, and in all the maps shown in this work, we present the distribution of parameters using these polygons calculated using Voronoi tessellation and the V-band contours from observations in Arnaboldi et al. (2012) in order to improve the visualization. 3. Line strength indices 3.1. Equivalent widths of Lick indices The stellar population properties are studied by the analysis of spectral absorption features using line-strength indices in the Lick/IDS system (Worthey 1994; Trager et al. 1998), which consists in calculating the equivalent widths (EW) of absorption features in a given central band amidst two pseudo-continuum sidebands. This process was carried out as follows. We obtained the line-of-sight velocity distribution (LOSVD) for each spectrum using the pPXF code (Cappellari & Emsellem 2004) considering four Gauss-Hermite LOSVD moments and additive polynomials of order 12 in order to compensate for the variations in the continuum. The adopted stellar templates come from the Single Stellar Population (SSP) models of the MILES library (S\u00e1nchez-Bl\u00e1zquez et al. 2006), with ages from 1 to 15 Gyr, and metallicities in the range \u22120.7 \u2264[Z/H]\u22640.2. They are computed for a Salpeter Initial Mass Function with slope of 1.3. The template spectra from the MILES library have a resolution of FWHM=2.5\u00c5, which is slightly larger than that our observations, FWHM=2.1\u00c5. We then convolved our spectra with a Gaussian \ufb01lter to match the resolution of the MILES stellar library. In most cases, the best \ufb01t was obtained by a linear combination of a small number of SSPs, but in a few cases a secondary nebular component was accounted for in the templates, which included emission lines for H\u03b2 (4861\u00c5), NI (5200\u00c5) and OIII (4957\u00c5 and 5007\u00c5 at \ufb01xed ratio of 1:3), that is subtracted o\ufb00 the observed spectrum, if present. For the measurement of the Lick indices, we convolve our spectra to match the resolution of the Lick/IDS system, using Gaussian \ufb01lters of varied resolution according to Worthey & Ottaviani (1997), before measuring the EWs using a custom Python code. To correct for the intrinsic broadening of the absorption features, we used the ratio of the equivalent widths in the best \ufb01t from pPXF before and after the LOSVD convolution as in Coccato et al. (2010a), using the relation I = I\u2032 0 I\u2032 LOSVD \u00b7 Imeas (1) where I\u2032 LOSVD and I\u2032 0 are the indices measured in the best \ufb01t spectra from pPXF with and without the LOSVD convolution, and Imeas and I are the measured and the corrected indices for the extracted spectra. Finally, we also corrected the indices for the instrumental o\ufb00sets by the observation of the standard star HD 102070, for which Lick indices were determined by Schiavon (2007). Although not all indices are determined for HD 102070 in the spectral region of our data set, the relative small value of the correction in most cases and the good agreement with previous measurements for NGC 3311 from Loubser & S\u00e1nchez-Bl\u00e1zquez (2012) assure us that any systematics are relatively small. Uncertainties for the Lick indices were estimated by Monte Carlo simulations with perturbations in the velocity dispersion and the addition of a bootstrapped noise, based on the residuals of the pPXF models. In Fig. 2, we show typical examples of the extracted spectrum in our data set, including the best \ufb01t and residuals calculated with pPXF and the position of the Lick indices bands. In columns 5 to 11 of Table 1 we show the values for the corrected Lick indices of our extracted spectra. 3.2. Effect of systematic errors due to sky subtraction Elliptical galaxies usually present large variances in their stellar population properties at large radii, such as observed in high S/N integral \ufb01eld observations from the SAURON survey (Kuntschner et al. 2006, 2010), and our results show similar trends. One question is whether varying S/N from the inner regions to large radii may be the primary source of scatter in the derived stellar population parameters, as function of radius. In Article number, page 3 of 19 A&A proofs: manuscript no. main Fig. 2. Examples of the LOSVD \ufb01tting process with pPXF in our dataset. The sky subtracted spectra (black) are superposed by the best \ufb01t templates (red) obtained by a combination of SSP spectra from the MILES library (S\u00e1nchez-Bl\u00e1zquez et al. 2006), emission lines and an additive polynomial of order 12, convolved with the line-of-sight velocity distribution with four moments. The best \ufb01t emission lines (blue) are subtracted from the spectra to avoid contamination on top of the absorption features. Residuals from the \ufb01ts are shown in the bottom (green dots). The Lick indices are measured at the location of the vertical shades by the measurement of the equivalent width in central bands (dark grey) compared to the level of the two pseudo continuum side bands (light gray). order to verify whether this result is related to di\ufb00erent S/N, we performed the following test. Since the main source of uncertainty is the sky subtraction, we performed several measurements of the Lick indices with di\ufb00erent values of under/over sky subtraction at the level of \u00b11% of the total sky in each spectrum. This percentage was obtained by a visual inspection of our spectra after the inclusion of this systematic error, which showed that errors of this magnitude would leave easily recognizable features resembling the sky spectra in the 2D spectra of low signal-tonoise spectra (S/N\u223c15). The result of this test is presented in Fig. A.1, where the difference of the EW of the indices, \u03b4ILick, is plotted as a function of radius. The deviations are calculated using a running standard deviation, indicated by the grey shaded area. For a typical spectrum with S/N\u223c20, the variations of the measured EWs for the Lick indices are \u03b4H\u03b2 =0.21 \u00c5(12%), \u03b4Fe5015 =0.43 \u00c5(25%), \u03b4Mg b =0.35 \u00c5(11%), \u03b4Fe5270 =0.22 \u00c5(18%), \u03b4Fe5335 =0.30 \u00c5(8%), \u03b4Fe5406 =0.20 \u00c5(10%) and \u03b4Fe5709 =0.06 \u00c5(6%). The same test is also performed for the stellar population parameters, using the methods described in Section 4, resulting in changes of \u03b4log Age (years)=0.05 dex, \u03b4[Z/H]=0.48 dex, \u03b4[\u03b1/Fe]=0.14 dex and \u03b4[Fe/H]=0.45 dex (see Fig. A.2). In the following analysis, we include the results of this test in Figs. 4 and 7, when we compare the dispersion due to systematic e\ufb00ects caused by the sky subtraction with the scatter of the measured Lick indices and stellar population parameters. 3.3. Spatial distribution and gradients of the Lick indices The maps of the values for six measured Lick indices are presented in Fig. 3, including H\u03b2, Fe5015, Mg b, Fe5270, Fe5335 and Fe5406. The index Fe5709 is not displayed in the \ufb01gure because it is measured only in a fraction of our spectra, due to issues with the red continuum for some observational masks, but it is also used for the modelling of stellar populations whenever possible. These maps indicate that each index has a particular pattern, and the central region of NGC 3311 stands out by having a relatively weaker H\u03b2 absorption and stronger metal line indices than the outskirts. The large scale behavior of the Lick indices can be observed in Fig. 4, where the Lick indices are displayed as a function of the projected galactic log-radial distance from the centre of NGC 3311, in units of e\ufb00ective radius. The results from our measurements are shown as circles of di\ufb00erent colours according to the signal-to-noise of the spectra. We also include a comparison with the long-slit data from the literature including Loubser et al. (2009), Coccato et al. (2011), and Loubser & S\u00e1nchez-Bl\u00e1zquez (2012). Our indices are not only in good agreement with the literature, but also complement the data from Loubser & S\u00e1nchezBl\u00e1zquez (2012) by extending the radial coverage. One important characteristic of Fig. 4 is the large scatter in the external halo, as we already commented in Section 3.2. This scatter is larger than that caused by the systematic e\ufb00ects of over/under subtraction of the sky by \u00b11%, shown in the \ufb01gure by the grey shaded areas. Hence one also expects a large true scatter in the abundance and age distributions at large radii. Further evidence for the intrinsic nature of the scatter at R \u223cRe and outwards is the signi\ufb01cant variance of the stellar population parameters derived for the highest S/N spectra in the data set, shown by the dark blue circles. Another important feature of Fig. 4 is the presence of a break in the radial gradients, from the inner to the outer pro\ufb01les. This break occurs at about one e\ufb00ective radius (Re = 8.4 kpc), which is close to the expected transition between the in situ and accreted components according to models (e.g. Cooper et al. 2015). Therefore, to quantify the mean trends of the Lick indices we divided them into two radial regions, the inner galaxy (R \u2264Re) and the extended halo (R > Re). In each of these regions, we measured the radial gradients using the equation ILick(X) = ILick(0) + \u2206ILick \u00b7 X, (2) where X = log(R/Re) is the logarithm of the projected galactocentric distance R, normalized by the e\ufb00ective radius Re, ILick(X) are the corrected Lick indices as a function of X, and \u2206ILick is the Article number, page 4 of 19 C. E. Barbosa et al.: The Hydra I cluster core I. Stellar populations in the cD galaxy NGC 3311 Fig. 3. Spatial distribution of the equivalent width of six Lick indices: H\u03b2, Fe5015, Mg b, Fe5270, Fe5335 and Fe5406. Black lines indicate the contours of the V-band image from Arnaboldi et al. (2012) between 20 to 23.5 mag arcsec\u22122 in steps of 0.5 mag arcsec\u22122. These maps illustrate the presence of an homogeneous inner region, and a large scatter at large radii, for all indices. Table 2. Linear regression coe\ufb03cients for the Lick indices as function of radius Inner galaxy (1) Extended halo (2) ILick(0) \u2206ILick ILick(0) \u2206ILick Index (\u00c5) (\u00c5/ dex) (\u00c5) (\u00c5/ dex) H\u03b2 1.1\u00b10.1 -0.1\u00b10.2 1.5\u00b10.1 0.2\u00b10.5 Fe5015 5.6\u00b10.3 1.9\u00b10.5 4.1\u00b10.4 -2.8\u00b11.3 Mg b 4.7\u00b10.1 -0.7\u00b10.2 4.4\u00b10.2 -1.8\u00b10.8 Fe5270 2.7\u00b10.2 -0.7\u00b10.4 2.4\u00b10.2 1.5\u00b10.9 Fe5335 2.7\u00b10.1 -0.4\u00b10.2 2.7\u00b10.2 -0.1\u00b10.9 Fe5406 2.0\u00b10.2 -0.4\u00b10.3 1.8\u00b10.2 0.5\u00b10.8 Fe5709 0.7\u00b10.1 -0.1\u00b10.1 0.6\u00b10.1 1.1\u00b10.6 Notes. (1) Linear regression coe\ufb03cients for the Lick indices as function of radius in the inner galaxy (R \u2264Re), derived according to equation (2), where ILick(0) indicates the value of the indices at one e\ufb00ective radius and \u2206ILick indicates the gradients. (2) Same as (1) for the external halo (R > Re) region. calculated gradient. The gradient is determined from a \u03c72 minimization weighted by the uncertainties of the data points. We do not remove any outliers, but we implement a geometric selection by excluding the spectra that are i) very close to NGC 3309 and ii) on top of HCC 007. The coe\ufb03cients of the linear regressions are presented in Table 2 and the best \ufb01t is shown by the black dashed lines in Fig. 4. The main result of this section is summarized in Fig. 4. The distribution of the measured values for the Lick indices in the inner galaxy are di\ufb00erent from the distribution of the values of the same indices in the external halo. The break occurs at R = Re for all indices. This implies that independent of the stellar population models that may translate the equivalent widths of the absorption features into other physically relevant quantities, there is going to be a break in the stellar population properties with di\ufb00erent values for the inner galaxy and the external halo. 4. Stellar populations We adopted the model from Thomas et al. (2011) to derive luminosity-weighted stellar population parameters \u2013 age, total metallicity ([Z/H]) and alpha element abundance ([\u03b1/Fe]) \u2013, which are computed using a Salpeter initial stellar mass function. Also, we estimated the iron abundance using the relation (Thomas et al. 2003) [Z/H] = [Fe/H] + A[\u03b1/Fe] (3) considering the factor A = 0.94 (Trager et al. 2000). All those parameters will help to understand the mass assembly history of stars in NGC 3311. The inferred ages may constrain the time since the last burst of star formation, the metallicities are a proxy for the mass of the parent halo where such stars were formed and Article number, page 5 of 19 A&A proofs: manuscript no. main Fig. 4. Lick indices as a function of the distance from the centre of NGC 3311. The EWs measured for our spectra are shown by full circles, with di\ufb00erent colors according to their S/N, as indicated in the top panel. Long-slit data from the literature is also displayed, including Coccato et al. (2011) as orange triangles, Loubser & S\u00e1nchez-Bl\u00e1zquez (2012) as red squares and Loubser et al. (2009) as red arrows. The two black dashed lines indicate the gradients obtained by linear regression in the two regions corresponding to the inner galaxy and the external halo. The grey shaded areas around the dashed lines represent the variance in the equivalent width generated by a systematic error in the sky subtraction by \u00b11%. The di\ufb00erent gradients indicate di\ufb00erent mechanisms for the assembly of the stellar halos. the alpha element abundances set constraints on the star formation time-scales (Thomas et al. 2005). Before we describe in detail the methods to compute the stellar population parameters, we list here distinct features of this modelling approach. We assume that the single stellar population (SSP) approximation is valid locally for each of our spectra, while we may be observing composite stellar populations (CSP). Each of the SSP parameters is sensitive to a di\ufb00erent stellar population, which may or may not be the one dominating the stellar mass. In our discussion, we are going to use the interpretation of the stellar population parameters according to Serra & Trager (2007), which relate SSP-equivalent parameters to CSPs as follows. Ages are biased towards the age of the youngest stellar populations, even in cases where they have only a small fraction of the mass, and therefore spectra with very low ages are not considered to be young, but instead old populations with a contribution of young stars. In case of the element abundances, these re\ufb02ect the distribution of the most massive components in the composite stellar populations and, therefore, approximately re\ufb02ect the mass-weighted properties. 4.1. Determination of SSP properties using Markov Chains We used Monte Carlo Markov Chains (MCMC, Markov 1913) to obtain SSP parameters, \u03b8=(logAge, [Fe/H], [\u03b1/Fe]) from the information contained in the set of Lick indices, D, available for each spectrum. A complete discussion of the MCMC method can be obtained elsewhere (e.g., MacKay 2003; Wall & Jenkins 2012), and here we only summarize the main concepts. The idea is to infer the posterior probability distribution of the parameters given the data, p(\u03b8|D), using Bayes\u2019 theorem, p(\u03b8|D) \u221dp(\u03b8)p(D|\u03b8), (4) where p(\u03b8) is the prior distribution and p(D|\u03b8) is the likelihood distribution. We assume that the priors are uniform within the ranges of the models from Thomas et al. (2011) extrapolated in metallicity, 0.1 \u2264Age(Gyr)\u226415, \u22122.25 \u2264[Z/H] \u22640.90 and \u22120.3 \u2264[\u03b1/Fe] \u22640.5, and that the likelihood distributions are Gaussian functions with standard deviations equal to the uncertainties of the measurements of the Lick indices. The calculations of the samples were performed with the PyMC package (Patil et al. 2010) using the Metropolis-Hastings algorithm with SSP models linearly interpolated for sub grid resolution. Fig. 5 illustrates the posterior distribution in two cases. The panels in the lower left show projections of the parameter space which indicate that parameters are not independent from each other. In particular, a small age-metallicity degeneracy is present (Worthey 1994). However, the relevant statistics are obtained by the marginalization of the parameters, indicated by the histograms, which already take these e\ufb00ects into account. For symmetric posterior distributions, such as the metallicities in both examples of Fig. 5, we \ufb01t a simple Gaussian in order to obtain the mode and the standard deviation. However, in several cases the distributions are skewed towards the limits of the models, such as the ages in Fig. 5, which required a \ufb01t of a Generalized Extreme Value (GEV) function. In these cases, we have used the mode as relevant statistic, and the uncertainties are calculated by determining two iso-probability values encompassing the maximum probabilities for which the posteriori distribution integrals add up to 68% of the area under the curve, similarly to the 1\u03c3 deviations of a Gaussian distribution. The results of this analysis are presented in columns 12 to 14 of Table 1. In low S/N regimes, the posterior distributions become \ufb02at due to the larger uncertainties in the Lick indices. To Article number, page 6 of 19 C. E. Barbosa et al.: The Hydra I cluster core I. Stellar populations in the cD galaxy NGC 3311 Fig. 5. Examples of the posterior distributions for two spectra using the MCMC method. The panels in the main diagonal show histograms of the marginalized distributions, which are used for the determination of the representative values and their uncertainties. The thick red lines show the best \ufb01t to the posterior samples, either a Gaussian or a Generalized Extreme Value function. Projections of the posterior distributions in the lower left panels show the correlations among parameters. The histograms in the upper right corner of each panel indicate the maximum probabilities and the 1\u03c3 deviations of the stellar population parameters in each case. avoid such unconstrained parameters in the analysis, we have set a maximum limit of 0.2, 0.7, 0.2 and 0.8 dex in the uncertainties of log (Age), [\u03b1/Fe], [Z/H] and [Fe/H] respectively. 4.2. Spatial distribution and gradients of SSP parameters In Fig. 6, we present the spatial distribution of the four stellar population parameters, i.e. log(Age), [Z/H], [\u03b1/Fe] and [Fe/H]. As observed in the distribution of Lick indices, the large scale distribution of the stellar populations is scattered, predominantly in the outer regions, while the inner galaxy displays a more regular behaviour. The central region shows rather old ages and super solar abundances. The external halo is much more diverse, presenting some large scale structures uncorrelated to the isophotes. However, considering the low spatial resolution of our observations, the relative small S/N in several of these spectra, and the expected spread in stellar populations, we consider that most of the apparent structures may be explained by random \ufb02uctuations. To describe the large-scale distribution, we again recur to the analysis of the radial trends and their gradients. In Fig. 7, we plot the stellar population parameter values determined from this work, in circles with di\ufb00erent grades of blue according to their S/N, as function of both the radial distance from the centre of NGC 3311 and also as a function of the V-band surface brightness at the location of the slits (left and central panels, respectively). We also show the stellar population parameters derived from the observations of Loubser & S\u00e1nchez-Bl\u00e1zquez (2012) and Thomas et al. (2011), as red squares and orange triangles respectively, calculated from their published values of the Lick indices, using our MCMC approach for consistency. We also show the central stellar population parameters from Loubser et al. (2009) using a red arrow indicating the published value in their paper. There is a considerable scatter in the external halo properties, similarly to that of the Lick indices plotted in Fig. 4. Once more, we compare this scatter with the systematic e\ufb00ect of an incorrect sky subtraction by \u00b11%, as displayed by the grey shaded areas. The comparison shows that the observed scatter is larger than that caused by a systematic e\ufb00ect in the sky subtraction of \u00b11%. In order to reproduce a scatter similar to the one measured in the external halo, an error of \u223c6% is necessary, which is way larger than any of the residuals in our extracted spectra. Therefore, we have evidence that the scatter at large radii is an intrinsic property of the external stellar halo. Similarly to the method deployed for the Lick indices, we quantify the radial trends in the stellar population properties using gradients which are computed separately for the inner galaxy and the external halo. The separation between these two regions is set at the projected distance of 1Re from the centre, which is approximately represented by the isophotal surface brightness level of \u00b5v \u224822.2 mag arcsec\u22122. We used equation (2) to parametrize the gradients; this time we did use two parameters for the abscissa, X = {log(R/Re), \u00b5v}. For this calculation of the gradients, we excluded the slits around NGC 3309 and the three slits covering the dwarf galaxy HCC 007 at the south of NGC 3311 to avoid contamination. One important remark is that the stellar population gradients as function of the radius from the centre of NGC 3311 is our primary diagnostic to characterize the global variations in stellar population parameters, and as such, is going to be discussed in detail in the following. We expect the gradients as function of the local surface brightness values to be a\ufb00ected by the presence of substructures, as it is the case for the external halo of NGC 3311 (see Arnaboldi et al. 2012), and hence have a larger scatter than radial gradients. 5. Correspondence among stellar populations, surface brightness components and kinematical structures in the inner galaxy and external halo of NGC 3311 The presence of a break in the measured Lick indices and the clearly distinct distribution of the stellar population parameters for the inner galaxy (R < Re) and the external halo point towards di\ufb00erent formation channels for the stars in these two regions. We derive consistent values for the ages, the total metallicity and gradients in [\u03b1/Fe] and [Fe/H] with very small scatter for the inner galaxy. The distribution of values derived for the external halo have a very large scatter in comparison. The \ufb01ndings for the inner galaxy are consistent with the expectations from Article number, page 7 of 19 A&A proofs: manuscript no. main Fig. 6. Maps of the modeled luminosity-weighted stellar population properties: ages (top left), total metallicity (top right), alpha-element abundance (bottom left) and iron abundance (bottom right). Black lines display the V-band surface brightness contours from Arnaboldi et al. (2012) in the range from 20 to 23.5 in steps of 0.5 mag arcsec\u22122. Colours indicate the SSP equivalent parameters according to the colour-bars in the bottom left section of each panel. The inner galaxy (R <\u223c10 kpc) is characterized by homogenous old age, high metallicity and super solar [\u03b1/Fe]; the outer halo shows a more complex behavior; see extended discussion in Section 6. the in situ formation, that maintains gradients from the time of initial rapid star formation. Di\ufb00erently, the larger scatter of the values in the external halo suggests that these stars come from the debris of gravitationally disrupted galaxies, as suggested by classical model (Dressler 1979) for the formation of cD halos. Thus the breaks at 1Re are interpreted as transition from the in situ to the accreted stellar populations, and are observed in other giant ellipticals from the MASSIVE survey (Greene et al. 2013, 2015). In NGC 3311, such a break in the stellar properties of the inner galaxy and the external halo correlates with variations of the velocity dispersion pro\ufb01le. Within one Re, stars move under the in\ufb02uence of the galaxy mass, reaching a \u03c30 \u2248160 km s\u22121 at the centre. At one Re and slightly larger radii, the line-of-sight (LOS) velocity dispersion has a positive gradient reaching \u03c3(R) \u2248400 km s\u22121 at 30 kpc (Ventimiglia et al. 2010; Richtler et al. 2011, Paper II). Such an increase in \u03c3(R) with radius indicates that the stars are progressively driven by the massive external halo associated with the Hydra I cluster, as mapped by the hot X-ray emission (Hayakawa et al. 2004). We now discuss the properties of the external halo of NGC 3311, de\ufb01ned as the region R > Re. This halo is not homogeneous, and the presence of additional components can be physically motivated. Using deep V-band imaging, Arnaboldi Article number, page 8 of 19 C. E. Barbosa et al.: The Hydra I cluster core I. Stellar populations in the cD galaxy NGC 3311 Fig. 7. Gradients of the stellar population parameters. Left: Ages, [Z/H], [\u03b1/Fe] and [Fe/H] as function of the log-distance to the centre of NGC 3311. Circles indicate data points from this work, coloured according to their signal-to-noise as dark blue (S/N> 30), light blue (15 \u2264S/N\u226430) and white (S/N< 15). Data from Loubser et al. (2009) and Coccato et al. (2011) are shown by the red arrow and orange triangles, respectively. New calculated values for the stellar population parameters based on data from Loubser & S\u00e1nchez-Bl\u00e1zquez (2012) are indicated by red squares. Dot-dashed and dashed lines indicate the regression for the inner and external halo, respectively, with the gradients displayed in the bottom left of each panel. The gray shades represent the systematic error of under/over subtraction of the sky by 1%. Centre: Same as for the left panels, but with gradients measured as a function of the V-band surface brightness. Right: Histograms of the distribution of the stellar population parameters, combining our data with those of Loubser & S\u00e1nchez-Bl\u00e1zquez (2012), with the inner galaxy and external halo shown in blue and grey bins respectively. The gradients in the inner galaxy are consistent with the predictions from a quasi-monolithic collapse model, while the shallow azimuthally-averaged gradients and the large scatter in the outer halo are consistent with the results of accreted stars from a variety of di\ufb00erent progenitors. et al. (2012) showed that the light of NGC 3311 is described primarily by a single S\u00e9rsic function with index n \u224810 at all radii. There is no break or no photometric signature of the twocomponent structure expected in a cD galaxy: the cluster dominated halo is not obvious in the photometry. This S\u00e9rsic n = 10 component centred on NGC 3311 \ufb01ts most of the light at all directions and is responsible for the featureless appearance observed in the panel A of Fig. 8. However, once the symmetric main component is subtracted o\ufb00, Arnaboldi et al. (2012) detected an additional feature in the galaxy light, the o\ufb00-centred envelope, that is located at a projected distance of 18 kpc from the centre of NGC 3311, towards the North-East direction (panel B of Fig. 8). At the location of the o\ufb00-centred envelope, there is an excess emission in X-rays (Hayakawa et al. 2004, 2006, see panel C) and a group of dwarf galaxies are found around this position, with high relative LOS velocities of \u223c1000 km s\u22121 (Misgeld et al. 2008) with respect of the systemic velocity of the Hydra I cluster. At the optical wavelengths, the o\ufb00-centred envelope is fainter than the symmetric main halo, contributing up to a fraction of \u224830% of the light (Coccato et al. 2011; Arnaboldi et al. 2012). The o\ufb00-centred envelope is also associated with kinematical signatures. Ventimiglia et al. (2011) showed that the line-ofsight velocity distribution (LOSVD) of planetary nebulae in the cluster core around NGC 3311 halo is multi-peaked, with three distinct components: a broad asymmetric component with velocities of \u223c3100 km s\u22121, a blue-shifted north-south elongated component at \u223c1800 km s\u22121 and a red-shifted component at \u223c5000 km s\u22121, at the location of the o\ufb00-centred envelope. Furthermore Arnaboldi et al. (2012) showed that asymmetric features in the velocity dispersion and the LOS velocity pro\ufb01les correlate with the spatial location of the o\ufb00-centred envelope. That Article number, page 9 of 19 A&A proofs: manuscript no. main Table 3. Linear regression coe\ufb03cients for the \ufb01tting of the stellar population parameters Inner galaxy (1) External halo (2) Property I(0) \u2206I I(0) \u2206I (dex) (dex / dex) (dex) (dex / dex) log Age (yr) 10.16 \u00b1 0.01 \u22120.00 \u00b1 0.01 10.14 \u00b1 0.01 \u22120.02 \u00b1 0.02 [Z/H] 0.07 \u00b1 0.11 \u22120.23 \u00b1 0.18 0.00 \u00b1 0.15 \u22120.46 \u00b1 0.39 [\u03b1/Fe] 0.41 \u00b1 0.03 0.18 \u00b1 0.06 0.38 \u00b1 0.08 \u22120.20 \u00b1 0.22 [Fe/H] \u22120.15 \u00b1 0.08 \u22120.16 \u00b1 0.08 \u22120.36 \u00b1 0.16 0.14 \u00b1 0.43 Notes. (1) Linear regression coe\ufb03cients for the \ufb01tting of the stellar population parameters in the inner galaxy (R \u2264Re) according to equation (2), parametrized by the logarithm of the radius to the centre of NGC 3311. I(0) indicates the value of the stellar population properties at one e\ufb00ective radius, while \u2206I indicates the gradient. (2) Same as (1) for the outer halo (R > Re) region. Table 4. Linear regression coe\ufb03cients as presented in Table 3, parametrized by the V-band surface brightness. Inner galaxy (\u00b5V \u226422.2 mag arcsec\u22122) External halo (\u00b5V > 22.2 mag arcsec\u22122) Property I(22.2) \u2206I I(22.2) \u2206I (dex) (dex / (mag arcsec\u22122)) (dex) (dex (mag arcsec\u22122)) log Age (yr) 10.19 \u00b1 0.05 \u22120.00 \u00b1 0.01 10.36 \u00b1 0.11 \u22120.01 \u00b1 0.01 [Z/H] 2.06 \u00b1 1.50 \u22120.09 \u00b1 0.07 0.33 \u00b1 1.20 \u22120.02 \u00b1 0.05 [\u03b1/Fe] \u22121.36 \u00b1 0.47 0.08 \u00b1 0.02 1.58 \u00b1 0.62 \u22120.06 \u00b1 0.03 [Fe/H] 2.16 \u00b1 1.25 \u22120.11 \u00b1 0.06 \u22121.01 \u00b1 1.27 0.03 \u00b1 0.05 Fig. 8. Evidence for a large-scale component in the external halo of NGC 3311. (A-B) V-band image and residual from the S\u00e9rsic n = 10 model from Arnaboldi et al. (2012) illustration the presence of an o\ufb00-centred envelope. (C) XMM-Newton X-rays image from Hayakawa et al. (2006) indicating an excess emission at the same position of the o\ufb00-centred envelope. Red circles indicate the position of dwarf galaxies from the catalog of Misgeld et al. (2008). is, at the location of the envelope, the LOS velocities (LOSVs) are redshifted with respect to the centre of NGC 3311 and the velocity dispersion is larger than at the symmetric location in the external halo, opposite the galaxy centre. Such features can be explained by the superposition along the LOS of two distinct structural components, the S\u00e9rsic n=10 halo and the o\ufb00-centred envelope, with di\ufb00erent LOSVs by \u226550 kms\u22121. Therefore, the external halo properties may be associated with two structural components: the \u201csymmetric\u201d S\u00e9rsic n = 10 halo, which is found at all azimuthal angles, and the o\ufb00-centred envelope in the North East quadrant. The exact boundaries of these components are not well de\ufb01ned, hence we adopt a simple scheme to seek for their signatures in the distribution of the parameters for the stellar populations. The properties of the stellar population in the symmetric external halo are derived for R > Re and 90\u25e6\u2264PA \u2264360\u25e6, while the population of the o\ufb00-centred halo is studied in the quadrant at 0\u25e6< PA < 90\u25e6. As the symmetric halo contributes 70% or even larger fractions to the light at the location of the o\ufb00-centred envelope, we would expect to only detect small variations in the distributions of the stellar population parameters at the location of the o\ufb00-centred envelope with respect to the symmetric halo distribution. 6. Properties of the stellar populations of the stellar light in NGC 3311 6.1. Stellar populations in the inner galaxy The stellar population properties of the inner galaxy (R \u2272Re) have well constrained values as indicated by the blue histograms on the right side of Fig. 7. The radial linear gradients of the stellar parameters are minor. There are three deviating data points: one at the position of the dust lane in the central kpc of NGC 3311 (Arnaboldi et al. 2012), and two in other regions Article number, page 10 of 19 C. E. Barbosa et al.: The Hydra I cluster core I. Stellar populations in the cD galaxy NGC 3311 further out, see Loubser et al. (2009) and Loubser & S\u00e1nchezBl\u00e1zquez (2012), The stars of the inner galaxy are old, compatible with the oldest modelled stellar populations (15 Gyr), with no gradient in age. The total metallicity of the stars is super solar, with a mild gradient of \u22120.23\u00b10.18 dex dex\u22121, while the alpha element abundance is high at the centre, [\u03b1/Fe]\u22480.2 dex, with a positive gradient of 0.18 \u00b1 0.06 dex dex\u22121. The resulting iron abundance is close to solar with a gradient of \u22120.16 \u00b1 0.08 dex dex\u22121. The very old age of NGC 3311 is expected for BCGs. OlivaAltamirano et al. (2015) observed that one-third of their BCG sample has similarly old stellar populations (age > 12 Gyr), while Loubser et al. (2009) found that about 50% of the BCGs have central old stellar populations. The \ufb02at age gradient and the abundance gradients are consistent with the values observed in BCGs by Oliva-Altamirano et al. (2015). 6.2. Stellar populations in the external halo The properties of the outer stellar halo of NGC 3311 are considerably di\ufb00erent from those inferred for the inner galaxy, as shown in Fig. 7, left and central panels at R \u2273Re and \u00b5v \u227322.2 mag arcsec\u22122. We detect a shallow age gradient of \u2206log Age = \u22120.02 \u00b1 0.02 dex dex\u22121 in the external halo, which is compatible with the \ufb02at gradient in the inner galaxy. The total metallicity gradient is steeper than that of the inner galaxy, with \u2206[Z/H] = \u22120.46 \u00b1 0.39 dex dex\u22121, and an inversion of the radial trends is observed in the alpha element abundance, with \u2206[\u03b1/Fe] = \u22120.20\u00b10.22 dex dex\u22121, and in the abundance of iron, with \u2206[Fe/H] = 0.14 \u00b1 0.43 dex dex\u22121. In addition to the average radial trends, the clear feature of the outer stellar halo of NGC 3311 is the considerable larger scatter of the stellar population parameters. The histograms on the right side of Fig. 7, show the distribution of stellar population properties for the inner galaxy (blue) and outer stellar halo (gray). The large scatter is present for the SSP parameters of high S/N (\u226540) spectra and at a radius of R \u223c0.6Re = 5.3 kpc, as indicated by the dark blue circles in the radial plots for [Z/H], [\u03b1/Fe] and [Fe/H] in Fig. 7. Moreover, the width of the distribution of the stellar population parameters is larger than what is expected from a systematic error in the sky subtraction of \u00b11%, as indicated by the grey shaded areas shown around the mean gradients. In the histograms on the right side of Fig. 7, the positions of the mean peak of the distributions and their widths are di\ufb00erent in the inner galaxy and external halo. A common characteristic of these distributions is that their widths for the external halo are twice as large as those for the inner galaxy. In the case of the [Z/H] and [\u03b1/Fe] distributions, there are multiple peaks for the external halo. Therefore, contrary to the inner galaxy, which can be explained by a rapid process of collapse and merger of gas-rich lumps, the outer stellar halo was most likely built up by accretion of stars from a variety of progenitors, with di\ufb00erent masses and star formation histories. We now investigate whether there are di\ufb00erences in the stellar population parameters between the o\ufb00-centred envelope and the rest of the external halo of NGC 3311. Fig. 9 shows the distribution of the stellar population parameters for the o\ufb00-centred envelope (red) and the rest of the external halo (grey). To determine the number of peaks that are statistically signi\ufb01cant in each case, we have used Gaussian Mixture Models (GMM) to estimate the number of populations which minimize the Bayesian Information Criteria (BIC), whose results are summarized in Table 5. The [\u03b1/Fe] distributions for the o\ufb00-centred envelope and Fig. 9. Distribution of stellar population parameters of the o\ufb00-centred envelope (red) and the symmetric halo (gray). The histograms are normalized, and the number of spectra (N) used in each case is shown in the legend of each panel. Dashed lines indicate the components of the GMM analysis, while the arrows indicate the position of the peak of each component. The o\ufb00-centred envelope is responsible for a signi\ufb01cant shift of the metallicity where it is located, while ages and alphaelement abundance distributions are similar to those inferred for the symmetric halo. symmetric halo are those for which two components are statistically favoured with respect to the single peak distribution. The distributions for the ages and metallicities can be relatively well described by single Gaussian functions instead. The GMM models are shown in Fig. 9 by dashed lines, with arrows indicating the position of the peak for each component. We used the Kolmogorov-Smirnov (KS) test to statistically compare the distributions of the stellar population parameters for the o\ufb00-centred envelope and the symmetric halo. The result of the KS tests indicates that the age and the alpha element abundances of these two components may have been drawn from the same parent distribution, with probabilities of 78 and 32% respectively. In both components, stars are predominantly old, with ages of \u223c14 Gyr, compatible with the oldest stellar populations in the models of Thomas et al. (2011). This old age distribution extends the results from Coccato et al. (2011) to the entire halo, and is also supported by the lack of features in the UV emission from GALEX observations (Gil de Paz et al. 2007). The age is the only external halo property for which the gradient is representative of the vast majority of the observed data points. The distribution of alpha element abundance in the symmetric halo and in the o\ufb00-centred envelope show similar multimodal distributions, modelled as a mixture of two Gaussian components. The main contribution to the alpha element abundance are stars with [\u03b1/Fe]\u22480.4 dex and spread of 0.1 dex, observed in 64% of the cases, while the secondary population has an abundance of [\u03b1/Fe]\u2248\u22120.1 dex and spread of 0.15 dex. The explanation for almost identical alpha element abundance at the o\ufb00centred envelope and in the symmetric halo is that this property is robust against a contamination of a minor component to the Article number, page 11 of 19 A&A proofs: manuscript no. main Table 5. Properties of the Gaussian Mixture Models with lowest Bayesian Information Criteria (BIC) for the o\ufb00-centred envelope and the symmetric halo. Property Halo N Mean Sigma Weight (1) (2) (3) (4) (5) (6) log Age Envelope 18 10.13 0.05 1.0 (Gyr) Sym. Halo 48 10.13 0.04 1.0 [Z/H] Envelope 20 0.10 0.33 1.0 Sym. Halo 52 -0.24 0.64 1.0 [\u03b1/Fe] Envelope 19 0.37 0.08 0.74 -0.14 0.13 0.26 Sym. Halo 48 0.39 0.09 0.57 -0.04 0.16 0.43 [Fe/H] Envelope 20 -0.12 0.41 1.0 Sym. Halo 49 -0.38 0.68 1.0 Notes. (1) Stellar population parameters. (2) External halo component (R > Re), de\ufb01ned as envelope for the NE quadrant of our observation and symmetric halo otherwise. (3) Number of data points used in the statistics. (4-5) Mean and standard deviation of the Gaussian Mixture Model component. (6) Weight of the component in the Gaussian Mixture Model. total integrated light, as indicated by the simulations of Coccato et al. (2011). Comparing the SSP parameters of a superposition of a typical, alpha-enhanced symmetric halo spectrum ([Z/H]= \u22120.34 dex, [\u03b1/Fe]=0.50 dex) with the properties of the dwarf galaxy HCC 026 ([Z/H]= \u22120.85 dex, [\u03b1/Fe]=0.03 dex), they have noticed that a fraction of 35% in the light is necessary to decrease the element abundance by only 0.05 dex. There may be speci\ufb01c regions in the o\ufb00-centred envelope where this fraction may be slightly larger, especially at those regions with the largest velocity dispersion observed in Paper II but, considering the total light, the fraction of light at the sub structure should not exceed 30%, con\ufb01rming the \ufb01ndings of Coccato et al. (2011) and in agreement with the estimates of Arnaboldi et al. (2012). Di\ufb00erently from the age and [\u03b1/Fe] distributions, the total metallicity and the iron abundance distributions do di\ufb00er between the o\ufb00-centred envelope and the symmetric halo. The probability that these distributions are drawn from the same parent distributions are low, i.e. \u223c1% and \u223c3%, respectively. The total metallicity distribution of the o\ufb00-centred envelope is most discrepant. The di\ufb00erence is clearly shown in Fig. 9: the metallicity distribution of the stellar populations at the location of the o\ufb00-set envelope is a single peaked distribution centred at [Z/H]= 0.1 dex and width of 0.33 dex, while the metallicity of the symmetric halo is a much broader distribution, with mean value [Z/H]= \u22120.24 dex and width of 0.64 dex. The stars in the quadrant where the o\ufb00-centred envelope is located have higher metallicities than most of the stars at the same radii, except for the stars sampled by spectra extracted in proximity of the giant companion NGC 3309. A similar result holds for the iron abundance, with the symmetric halo having [Fe/H]= \u22120.38 dex and dispersion of 0.68 dex, while the mean abundances of the o\ufb00-centred envelope is [Fe/H]= \u22120.12 with a dispersion of 0.41 dex. Since the light at the location of the o\ufb00-centred envelope is given by the superposition of this component and the symmetric halo, the intrinsic metallicity of the stars in the envelope may be signi\ufb01cantly higher than solar. Our derived stellar population parameters for the external halo of NGC 3311 are compatible with the previous results from Coccato et al. (2011), and are similar to the stellar populations of other cD galaxy halos, such as NGC 4889 in the Coma cluster (Coccato et al. 2010b) and NGC 6166 in the Abell 2199 cluster (Bender et al. 2015). These physical properties are also similar to those inferred for the stellar populations in other BCGs (Spolaor et al. 2008) and massive early-type galaxies (Spolaor et al. 2010; Greene et al. 2012, 2013, 2015). 7. Implications for the assembly history of NGC 3311 Recent cosmological models for the formation of large earlytype galaxies predict that the majority of stars in the external halos originated from satellite galaxies in the so-called two-phase scenario (e.g. De Lucia & Blaizot 2007; Naab et al. 2009; Oser et al. 2010; Cooper et al. 2013). In the next sections, we are going to compare our results with recent modelling of BCGs in order to relate the inferred distributions of the stellar population parameters with the physical mechanisms involved in the formation of extended halos of BCGs in clusters. 7.1. The inner galaxy As presented in the previous sections, the distribution and the distinct radial gradients of the age, [Z/H], [Fe/H] and [\u03b1/Fe] of the stellar populations in the inner galaxy are consistent with stars born in situ. According to models of Cooper et al. (2013), the large fraction of in situ stars in the central regions of BCGs is expected to occur up to a stellar mass threshold of M200 \u22721013M\u2299, as for more massive galaxies the accreted stars become increasingly dominant even in their innermost regions (Cooper et al. 2015). NGC 3311 is very close to this boundary, with M200 \u22480.63M500 = 6.3\u00b71013M\u2299(Pi\ufb00aretti et al. 2011), and our determination of the stellar population parameters show the presence of in situ and accreted stars in two radial regions, hence in agreement with the predictions of Cooper et al. (2013). We can also compare our results with those for other massive early-type galaxies. The total metallicity gradient of the inner galaxy in NGC 3311, \u2206[Z/H]= \u22120.23\u00b10.18 dex dex\u22121, is comparable to the gradients of other BCG galaxies (Oliva-Altamirano et al. 2015) and non-BCGs (Kuntschner et al. 2010). Positive [\u03b1/Fe] gradients are also common among early-type galaxies (Kuntschner et al. 2010) and BCGs (Brough et al. 2007) and, therefore, the mechanisms that set the gradients in BCGs must be similar to those that form ordinary early-type galaxies. In a simple, quasi-monolithic scenario, such gradients can be explained in an outside-in scenario (e.g., Pipino et al. 2006, 2008, 2010). In this context, early-type galaxies are formed by the merging of gas-rich lumps which produces an intense star formation, but with a di\ufb00erential rate at di\ufb00erent radii. Star formation in the outer regions around 1Re is characterized by short time-scales and strong stellar winds that deplete the iron e\ufb03ciently, whereas star formation is the core is prolonged and metals, in particular iron, are kept due to the strong gravitational potential. This produces positive alpha element gradients and negative total metallicity gradients. The abundance gradients of the inner galaxy of NGC 3311 are compatible with the results of such models considering a few episodes of dry mergers (Pipino et al. 2010). Article number, page 12 of 19 C. E. Barbosa et al.: The Hydra I cluster core I. Stellar populations in the cD galaxy NGC 3311 7.2. The extended symmetric halo With reference to the main peak of the alpha element abundance distribution, see Fig. 9, the extended halo can be described as a mix of old stars, with metallicities of [Z/H]\u2248\u22120.25 and [\u03b1/Fe]\u2248 0.4, at \ufb01rst order. As discussed earlier, the high value for the \u03b1 abundance does not imply that all stars were formed in galaxies with high [\u03b1/Fe], as this quantity does not change a lot by the contamination of less alpha enhanced stars. Still the majority of the stars in the external halo may have indeed high [\u03b1/Fe]. In the nearby universe, high [\u03b1/Fe] stars are those: 1. Stars produced in disky galaxies with truncated star formation. Greene et al. (2012, 2013) have shown that the metallicity and the alpha element abundance at the outskirts of massive galaxies are similar to those found in the Milk-Way thick disk, which is predicted to have been formed in short timescales (Chiappini et al. 1997). These disks could have been destroyed in interactions and mergers very early, as galaxy encounters at high redshift were much more common than at the present day universe. 2. Stars from galaxies in compact groups. de la Rosa et al. (2007) have found that galaxies with \u03c30 \u2272160 km s\u22121 in Hickson Compact Groups have larger [Mg/Fe] and lower [Z/H] compared to \ufb01eld galaxies of similar masses, and proposed that such galaxies may have their otherwise extended star formation quenched by mergers. 3. Stars in the outskirts of massive early-type galaxies with declining metallicity gradients and \ufb02at-to-positive alpha element gradients (Coccato et al. 2011). Negative metallicity gradients extending to the outer radii are found in most earlytype galaxies (e.g. Baes et al. 2007; La Barbera et al. 2012). Flat and positive [\u03b1/Fe] gradients are commonly found in early-type galaxies at small radii (Kuntschner et al. 2010), and there is evidence that at least metallicity gradients extend to larger radii (La Barbera et al. 2012; Pastorello et al. 2014). In other nearby clusters, such as Virgo and Fornax, declining metallicity gradients and \ufb02at alpha element abundances are found in almost all cases (Spolaor et al. 2010), but there is no such information for the giant ellipticals in the Hydra I cluster. If those have similar gradients, the central stellar populations of the Hydra I ellipticals should exhibit high [Z/H] and [\u03b1/Fe], similar to those in the extended halo of NGC 3311 (Coccato et al. 2011). All of the above galaxies could have provided stars that are now found to contribute most of the light of the symmetric external halo. They do not exclude each other necessarily, as they could have been di\ufb00erent parts of the same process in a hierarchical scenario. More importantly, however, is that the high [\u03b1/Fe] indicates star formation happening on short time-scales of \u22480.1 Gyr, according to the approximation of Thomas et al. (2005). We can also estimate the most likely masses of the progenitors of the stars in the external halo from the metallicity distribution in Fig. 9. Translating these metallicities into stellar masses according to the relations from Gallazzi et al. (2005), the typical galaxy contributing to the formation of the extended symmetric halo are Milky Way-like galaxies, including mostly galaxies in the range \u223c1010M\u2299to \u223c1012M\u2299. The extrapolation of the inner galaxy gradient in [\u03b1/Fe] matches the position of the dominant alpha element abundance in the external halo, indicating that these stars may have similar origins. Cosmological hydrodynamical simulations from Murante et al. (2007) indeed indicate that most of the di\ufb00use halo is composed of stars liberated from the most massive galaxies in episodes of major mergers related to the formation of the cD galaxy, where tidal shocking and stripping of massive galaxies are able to unbound up to 30% of their stellar mass. In agreement with several predictions from the models of Murante et al. (2007), semi-analytical models of Contini et al. (2014), including disruption of galaxies and tidal interactions, are able to reproduce both the typical masses of the progenitors in our observations as well as the typical total metallicities. Therefore, our observations are in agreement with models in which the assembly of the BCG is directly connected with the formation of the di\ufb00use halo. The [\u03b1/Fe] distribution of the symmetric halo indicates the presence of a secondary population, with solar and sub-solar \u03b1abundances. These lower alpha element abundances suggest a much more extended star formation, \u223c15 Gyr, according to the approximation of Thomas et al. (2005). In this case, there is already one galaxy in the Hydra I cluster which has similar properties, the dwarf galaxy HCC 026. This dwarf galaxy has solar alpha-abundance, [\u03b1/Fe]= \u22120.03\u00b10.05 dex, and low metallicity, [Z/H]=\u22120.85 \u00b1 0.03 (Coccato et al. 2011). HCC 026 is part of a group of dwarf galaxies at the same location of the o\ufb00-centred envelope (Misgeld et al. 2008) and it has strong tidal tails that indicate that this galaxy is being disrupted by the tidal \ufb01eld close to the cluster centre (Arnaboldi et al. 2012). Hence HCC 026 is the typical object that contributes to the late accretion events that build up the halo today. Such solar and sub-solar \u03b1 abundance populations are inferred from a substantial fraction of the extracted spectra, in about 40% of the total sample in the external halo. Hence accretion of stars from disrupted dwarfs or irregular galaxies is an important channel for the late build-up of the external halo. Very recent observations of the planetary nebulae in the halo of M87 and the intracluster light in the Virgo core showed that the contribution from Magellanic clouds-like irregular galaxies is responsible for a sizeable fraction of the halo light being added in the last Gyr to the M87 halo and ICL (Longobardi et al. 2015a,b). Models from Murante et al. (2007) indicate that low-mass galaxies (M\u2217< 1010M\u2299) may contribute to the formation of the diffuse halo, but numerical issues related to the particle resolution of low-mass galaxies did not allow them to set proper constraints on this secondary population. Our current results for NGC 3311 and the recent \ufb01ndings for M87 indicate that it is of importance to study the details of the late mass accretion, which is responsible for a sizeable fraction of the chemical composition and kinematics of the halos of massive nearby galaxies. 7.3. The metallicity distribution of the off-centred envelope The stellar populations located at the o\ufb00-centred envelope show an enhancement of metals in comparison with the rest of the symmetric halo, while the alpha element abundance and age distributions are similar. The strongly peaked metallicity distribution centred around [Z/H]\u22480.1 indicates that the stars associated with the substructure were formed in massive galaxies. According to Murante et al. (2007), massive ellipticals can lose up to 30% of their stars during their merging events with the cD and these stars would then contribute to the build up of the external halo. One can then ask how this external high metallicity halo component acquired an o\ufb00set and became o\ufb00-centred with respect to the high surface brightness, highly concentrated inner galaxy. O\ufb00-centred outer components in BGCs are rather frequent: for a sample of 24 clusters, Gonzalez et al. (2005) showed that a Article number, page 13 of 19 A&A proofs: manuscript no. main two-component \ufb01t to the light pro\ufb01les of BCGs provides an improved match to the data and that the two photometric components are misaligned in 60% of the sample. In the Gonzalez et al. (2005) sample, the cluster Abell 1651 has a cD galaxy where the two components have di\ufb00erent centres, with the outer component being o\ufb00-centred by 15 kpc linear distance in projection, i.e. very similar to what is observed for NGC 3311. As observed in cosmological simulations (e.g. Murante et al. 2007), the highly radial orbits of the dark halos of massive ellipticals and their tidal interaction with the cD dark halo may cause a de\ufb02ection of the central part of the cD from its dark halo, while the outer envelopes maintain their orbital directions, thus creating an o\ufb00set between core and halo in the cD galaxy. Candidate dark halos responsible for a tidal interaction with NGC 3311 are the dark halo associated with the group of infalling dwarfs or the dark halo associated with NGC 3309. These tidal interactions would then be similar to what is observed in the Coma cluster core (Gerhard et al. 2007). Such mechanisms may also explain the gas stripping of NGC 3311 as observed in the X-rays Hayakawa et al. (2004, 2006), as the mass of the gas is compatible with the mass of NGC 3311. 8. Summary and conclusions We performed a spatially extended survey of the stellar populations in NGC 3311, the brightest galaxy of the Hydra I cluster. By the analysis of the absorption line equivalent widths using a Bayesian framework with Monte Carlo Markov Chains, we probed luminosity-weighted parameters \u2013 age, [Z/H], [\u03b1/Fe] and [Fe/H] \u2013 out to \u223c3Re. This enabled the characterisation of the stellar content of three physically motivated components of this system: the inner galaxy, the symmetric external halo and the o\ufb00-centred envelope. The inner stellar halo (R < Re) presents stellar populations typical of massive early-type galaxies, including old ages, high metallicities and high alpha element abundances. Similar to other BCGs, the inner galaxy has a well-de\ufb01ned negative metallicity and positive alpha element abundance gradient which can be explained by a quasi-monolithic scenario involving a few dry mergers. These gradients and the smaller velocity dispersion of the inner galaxy are clear indications that the stars in this region were formed in situ in the early phases of galaxy formation. The stellar component of the outer symmetric stellar halo is characterized by a large spread of the stellar parameter values rather than by clearly de\ufb01ned radial gradients. This region is characterized also by high velocity dispersions which are indicative that these stars are driven by the cluster\u2019s potential and are generated by accumulation of tidal debris. While the mean value of the metallicity distribution in this region indicates subsolar abundances, the [\u03b1/Fe] distribution of the symmetric halo is bimodal, with high (\u223c0.4) and low (\u223c0) components. The majority of stars in the symmetric halo are generated in galaxies with a rapid star formation and short time-scales, in agreement with models for the formation of cD envelopes (e.g. Murante et al. 2004, 2007; Contini et al. 2014). However, a substantial fraction of stars, about 40%, has a low [\u03b1/Fe] value, which indicates that stars from less massive galaxies are also added to the cD halo. Their association with dwarf galaxies currently being disrupted at the position of the o\ufb00-set envelope indicate that the growth of the cD halo is an on-going process, which is fed by late mass accretion. Finally, the stellar populations at the position of the o\ufb00centred envelope, a substructure also observed in photometry, X-rays and kinematics, indicates that the dark matter halo of an infalling group may have interacted with the BCG halo, causing the stripping of gas and stars. We conclude that massive satellite galaxies in the vicinity of NGC 3311 merged with the central cD in early times and formed its symmetric outer halo, while at present time the build up process of the extended halo is still on-going, as indicated by the presence of an infalling group of dwarfs that are adding their stars to the halo now. Tidal interactions between the dark halos of the infalling group, of NGC 3309 and NGC 3311 may be responsible for the stripping of stars and gas in the halo of NGC 3311. Although very challenging from the observational point of view, the halos of cD galaxies provide important constraints on the formation and morphological transformation of galaxies in nearby clusters. Acknowledgements. We would like to thank Dr. Ilani Loubser for kindly sharing data for the inner regions of NGC 3311. We would like to thank the referee for his/her constructive comments. This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. CEB and CMdO are grateful to the S\u00e3o Paulo Research Foundation (FAPESP) funding (Procs. 2011/21325-0, 2012/226763 and 2014/07684-5). TR acknowledges \ufb01nancial support from FONDECYT project Nr. 1100620, and from the BASAL Centro de Astrof\u00edsica y Tecnologias A\ufb01nes (CATA) PFB-06/2007. TR also thanks ESO/Garching for a visitorship.",
                    "introduction": "Brightest Cluster Galaxies (BCGs) are the giant early-type galaxies found at the core of galaxy clusters. BCGs often display extended, di\ufb00use stellar halos, known as cD envelopes, which are believed to be composed of stars stripped from satellite galaxies interacting with the cluster\u2019s halo by tidal interactions and dynamical friction (Gallagher & Ostriker 1972; Dressler 1979). Due to the long relaxation times at large radii, stellar ha- los are not well-mixed and, therefore, preserve chemodynamical signatures of the past accretion events which have survived to \u22c6Based on observations made with ESO Telescopes at the La Silla Paranal Observatory under programme ID 088.B-0448(B) PI Richtler. \u22c6\u22c6Corresponding author: carlos.barbosa@usp.br present day and can be used to access the history of the galaxy mass assembly. The initial processes of galaxy formation through monolithic collapse do set abundance gradients, which are modi\ufb01ed by the subsequent history of accretion over time. Initial strong metal- licity gradients arise naturally in galaxies formed by the collapse of gas clouds in the monolithic scenario (Larson 1974) or by the merging of numerous gas rich sub-galaxies (Kobayashi 2004). The subsequent evolution via major mergers is able to dilute metallicity gradients by the mixing of stars in the central re- gions of galaxies (White 1980; Kobayashi 2004), while minor mergers may form gradients at larger radii by the deposit of stars with di\ufb00erent abundances (Villumsen 1983; Hirschmann et al. 2015). Observations in the last decade, such as the population of compact massive objects at high redshift (van Dokkum et al. Article number, page 1 of 19 arXiv:1603.02202v1  [astro-ph.GA]  7 Mar 2016 A&A proofs: manuscript no. main 2008; van der Wel et al. 2014) and the evolution of sizes and concentrations with redshift (Naab et al. 2009), suggest that mas- sive ellipticals are formed by di\ufb00erent processes over time in the two-phase scenario (De Lucia & Blaizot 2007; Oser et al. 2010). Galaxies are formed at high redshift (z \u22733) during star for- mation events triggered by rapid dissipative processes, such as cold accretion of gas through \ufb01laments (Kere\u0161 et al. 2005; Dekel et al. 2009) or gas-rich major mergers (Robertson et al. 2006), followed by an extended accretion of stars of smaller galaxies, usually at large galactic radii. In the two-phase scenario, stars inhabiting a halo can be di- vided into two categories according to the sub-halo in which they have been formed: in situ and accreted. The in situ stars were formed in the most massive sub-halo of a galaxy during the \ufb01rst phase of galaxy formation, which resulted in stars with relatively high metallicity, due to their deep gravitational potential that can retain the metals ejected by supernovae (Tremonti et al. 2004), and high alpha element abundance due to the rapid time-scales of star formation (see, e.g., Thomas et al. 2005). The accreted stars were formed in galaxies with a variety of masses and, con- sequently, have di\ufb00erent abundances and ages. Spatially, in situ stars are centrally concentrated and usually dominate the light in the central \u223c5 \u221210 kpc of elliptical galaxies, contributing sig- ni\ufb01cantly to the stellar halo out to \u223c30 kpc, while the accreted stars are less centrally concentrated and dominate the light in the outer regions (Oser et al. 2010; Cooper et al. 2013). From a dynamical point of view, in situ stars have su\ufb00ered violent re- laxation processes in the early phases of the galaxy formation, while the accreted stars may be still unrelaxed, especially at the largest radii, and thus may exhibit an inhomogeneous spatial dis- tribution which survived to the present day (Cooper et al. 2015). The observational test for this model of galaxy formation relies on the measurement of stellar population parameters in early-type galaxies out to large radii, but the low surface bright- ness in these regions makes spectroscopic measurements di\ufb03- cult. Nevertheless, current state-of-the art investigations seem in agreement with the predictions from the two-phase scenario. In the case of NGC 4889 in the Coma cluster, Coccato et al. (2010b) showed that there are di\ufb00erent populations in the core and halo consistent with the idea of accreted stars dominating the light at radii R > 18 kpc. Similarly, di\ufb00erences between the inner and outer stellar populations have been found for other cD galax- ies such as NGC 3311 (Coccato et al. 2011), M49 (Mihos et al. 2013), M87 (Virgo cluster, Montes et al. 2014) and NGC 6166 (Abell 2199, Bender et al. 2015), and even in several non BCGs (Pastorello et al. 2014). However, these studies provide limited information about the distribution of the metal abundances and ages, because they were performed either by photometry, which has good spatial information but does not provide detailed abun- dances and ages, or by long-slit spectroscopy, which is limited to the slit position, but provides abundance and age information in detail. Ideally we would like to be able to collect the metal abun- dance and age information over the entire spatial extension of the galaxy light, for an extensive mapping of its physical properties. In this work we study the galaxy NGC 3311, the cD of the Hydra I cluster, in order to provide the \ufb01rst bi-dimensional and large scale view of the stellar population of this system, which together with the detailed kinematic study (paper II) can shed further insights in a number of speci\ufb01c formation scenarios that have been recently proposed for this system. NGC 3311 has a radial velocity of \u223c3800 km s\u22121 and a positive velocity disper- sion pro\ufb01le (Ventimiglia et al. 2010), indicating that its extended halo is driven by the cluster potential at R > 8 kpc and may be composed of the debris shredded from satellite galaxies falling into the cluster\u2019s centre (Coccato et al. 2011). Furthermore, such rising velocity dispersion pro\ufb01le seems to be asymmetric at large radii, as observed at di\ufb00erent position angles (Ventimiglia et al. 2010; Richtler et al. 2011). A scenario of on-going interactions and extended built-up of the stellar mass is also supported by the presence of multiple components in the line-of-sight velocity distribution of the planetary nebulae in NGC 3311 (Ventimiglia et al. 2011), of substructures and tails in the halo light distri- bution (Arnaboldi et al. 2012) and by the distribution of dwarf galaxies around NGC 3311 (Misgeld et al. 2008). In the accompanying paper on the kinematics of NGC 3311 (Paper II, Hilker et al. in prep.), we focus on the kinematic prop- erties, discuss the implications for the mass pro\ufb01le of NGC 3311 and explore possible formation histories of the massive star clus- ters observed by Misgeld et al. (2011). In the current paper, we present the spatial map of the stellar population parameters, ages and abundances, out to large radii. The article is organized as follow. In Section 2 we describe our data set and the methods of data reduction. In Section 3 we describe the measurements for the absorption features using Lick indices, and in Section 4 we convert this information into physical parameters of the stel- lar populations. In Section 5, we discuss the correspondence of the stellar populations with kinematic and morphological struc- tures, which are discussed in detail in Section 6. In Section 7 we discuss our main \ufb01ndings in line with recent observational and theoretical works and provide an updated view of the NGC 3311 halo formation based on recent works. Finally, we proceed to an overview and conclusion of this work in Section 8. We assume a distance to the core of the Hydra cluster of 50.7 Mpc, calculated by the Hubble \ufb02ow considering a radial velocity of 3777 km s\u22121 (Struble & Rood 1999) and H0 = 70.5 km s\u22121 Mpc\u22121 (Ko- matsu et al. 2009). The adopted e\ufb00ective radius for NGC 3311 is Re = 8.4 kpc, which is the mean value of the isophotal analysis in the V-band from Arnaboldi et al. (2012)."
                }
            ],
            "Renyue Cen": [
                {
                    "url": "http://arxiv.org/abs/2012.02230v1",
                    "title": "Physics of Non-Universal Larson's Relation",
                    "abstract": "From a new perspective, we re-examine self-gravity and turbulence jointly, in\nhopes of understanding the physical basis for one of the most important\nempirical relations governing clouds in the interstellar medium (ISM), the\nLarson's Relation relating velocity dispersion ($\\sigma_R$) to cloud size\n($R$). We report on two key new findings. First, the correct form of the\nLarson's Relation is $\\sigma_R=\\alpha_v^{1/5}\\sigma_{pc}(R/1pc)^{3/5}$, where\n$\\alpha_v$ is the virial parameter of clouds and $\\sigma_{pc}$ is the strength\nof the turbulence, if the turbulence has the Kolmogorov spectrum. Second, the\namplitude of the Larson's Relation, $\\sigma_{pc}$, is not universal, differing\nby a factor of about two between clouds on the Galactic disk and those at the\nGalactic center, evidenced by observational data.",
                    "authors": "Renyue Cen",
                    "published": "2020-12-03",
                    "updated": "2020-12-03",
                    "primary_cat": "astro-ph.GA",
                    "cats": [
                        "astro-ph.GA"
                    ],
                    "main_content": "(1998), encapsulates the transition from turbulence dominated energy regime to a subsonic regime, 1 Princeton University Observatory, Princeton, NJ 08544; cen@astro.princeton.edu arXiv:2012.02230v1  [astro-ph.GA]  3 Dec 2020 2 where the sum of the thermal, magnetic and possibly other forms of energy dominates over turbulent energy. The turbulence is then often thought of cascading down between these two scales. In contrast to this simple cascading (down) of eddies in the gravity-free case, a new conceptual notion that we put forth here is that the dynamic interactions between turbulence and gravity occurring on all scales result in the formation of clouds, within which self-gravitational force becomes important (not necessarily dominant in general), on all scales. While the formation of clouds is originally driven by supersonic turbulence, gravity acts to both solidify them and in some cases detach them from the turbulence, hence provides a feedback loop to the turbulence itself, where the clouds may be visualized as the boundary conditions (on all scales) for the turbulence. As such, we shall call such an additionally constrained turbulence a \u201ccloud bound turbulence chain\" (CBTC), as opposed to a gravity-free turbulence. The singular coherence scale (\u223c0.1pc) above represents the smallest cloud of our CBTC. Based on this conception, we attempt to rederive the (revised) Larson\u2019s Relation, and compare to observations. 2. LARSON\u2019S RELATION: CONFLUENCE OF SUPERSONIC TURBULENCE AND SELF-GRAVITY In the ISM, self-gravity has the tendency to organize and fortify suitable regions into their own entities, playing a countervailing role against supersonic turbulence that would otherwise produce only transient structures. For a powerlaw radial density pro\ufb01le of slope \u2212\u03b2, the self-gravitating potential energy is W = \u22123\u2212\u03b2 5\u22122\u03b2 GM2 R R , where R and M are the radius and mass of the cloud. As we will show later, the density pro\ufb01le of gas clouds in the supersonic regime is expected to have \u03b2 = 4/5, thus we will use W = \u221211 17 GM2 R for all subsequent calculations. For a self-gravitating sphere of the same density pro\ufb01le, the mean velocity dispersion within radius R is related to the 1-d velocity dispersion at separation R by \u00af \u03c32 R = 11 14\u03c32 R. However, it proves more convenient to use \u00af \u03c3R instead of \u03c3R, since the former is a more used observable. Hence, we shall use \u00af \u03c3R for all subsequent expressions; for brevity, we use \u03c3R to represent \u00af \u03c3R hereafter. To reduce cumbersomeness in expressions, we neglect all other forms of energy but only to keep the gravitational energy W and gas kinetic energy K; it is straight-forward to include those neglected, by modifying the expression for virial parameter. We thus de\ufb01ne the virial parameter \u03b1v as \u03b1v = \u22122K W . The self-gravitating tendency may then be formulated as a 3-d region in the four-dimensional parameter space of (R, \u03c3R, \u03c1R, \u03b1v): \u03c32 R = \u03b1v 11 51 GM R = \u03b1v 44\u03c0 153 G\u03c1RR2 = \u03b1v 11\u03c0 51 G\u03a3RR. (1) where G is gravitational constant, and \u03c1R and \u03a3R are the mean volume and surface density within radius R. If \u03b1v and \u03c3R are independent, which we will show is the case, the region would look like a thick plane. Eq (1) is essentially the proposed modi\ufb01cation to Larson\u2019s Relation by Heyer et al. (2009). More comparisons will be made in \u00a73. Kolmogorov (1941) power spectrum is derived for homogeneous and isotropic three-dimensional subsonic turbulence in incompressible \ufb02ows, valid in the energy conserving inertial range. In contrast, the kinetic energy in the supersonic compressible turbulence in ISM is dissipative on all scales due to shocks and radiative processes in the ISM. It thus, at \ufb01rst instant, might suggest that the Kolmogorov turbulence may provide an inadequate description of the compressible turbulence of the ISM. Fleck (1983) suggests that the relation between a scaled velocity vR and scale R of compressible turbulence be expressed as vR \u2261\u03c11/3 R \u03c3R = AR1/3, (2) 3 which constitutes a plane in the parameter space of (R, \u03c3R, \u03c1R), generally different from that of selfgravity (Eq 1), where A is a constant. The expression essentially asserts that a constant volumetric energy density transfer rate in compressible \ufb02ow is transmitted down the turbulence cascading scale. Eq (2) reduces to the original Kolmogorov form for incompressible \ufb02ow that is a line in the two-dimensional parameter space of (R, uR). A formal proof of the existence of an inertial range for highly compressible turbulence is given by Aluie (2011, 2013), validating the density-weighted velocity formulation. Importantly, numerical simulations show that the spectrum of vR indeed follows remarkably well the Kolmogorov spectrum for the isothermal ISM (e.g., Kritsuk et al. 2007, 2013). We thus continue to use the nomenclature of Kolmogorov compressible turbulence, despite its oxymoronic sounding, given the spectral slope we adopt and its empirical validity to describe the turbulence of the isothermal ISM. The general physical arguments and quantitative conclusions reached are little altered with relatively small variations of the slope of the turbulence power spectrum. As a related note, in the subsonic compressible turbulence, with gravity also playing an important role, such as in dark cores in molecular clouds, the physical premise for the argument of energy transmission through the inertia scale range ceases to apply with respect to the total velocity. This may be understood in that the turbulence chain driven at some large scales no longer is the primary driver of velocity in the subsonic regime. Rather, the velocity \ufb01eld is driven jointly by turbulence, thermal (and possible other forms of) pressure, and gravity (Myers 1983). Combining Eq (1) and Eq (2) gives \u03c3R = \u03b11/5 v ( 44 153A3G)1/5R3/5. (3) Because A is unknown but a constant, we simply introduce another parameter, \u03c3pc, which denotes the 1-d mean turbulence velocity dispersion within a region of radius 1 parsec, to express the strength of the turbulence. Now Eq (3) is simpli\ufb01ed to \u03c3R = \u03b11/5 v \u03c3pc( R 1pc)3/5. (4) Looking at Eq (4), it may seem puzzling as to why the virial parameter \u03b1v appears in this expression that is supposedly an expression of the strength of the turbulence chain. But it is expected. The appearance of \u03b1v (and the disappearance of gas density \u03c1) in this expression re\ufb02ects the feedback of the boundary condition at the clouds that terminates the turbulence chain at the small scale end, in lieu of gas density. To see that we may express the cloud density in terms of \u03c3pc: npc = \u03b1\u22123/5 v 153 44\u03c0 \u03c32 pc Gmp(1pc)2 = 1.04 \u00d7 104cm\u22123\u03b1\u22123/5 v ( \u03c3pc 1 km/s)2, (5) where npc is the mean density within a cloud of radius 1pc with a virial parameter \u03b1v. Eq (4) is the (revised) Larson\u2019s \ufb01rst relation, relating the velocity dispersion to the size of the cloud. Let us now proceed to compare this relation to observational data. Figure (1) shows the observational data along with best powerlaw \ufb01ts. We \ufb01t the data to a powerlaw of the form \u03c3R = \u03b11/5 v \u03c3pc( R 1pc)\u03b2, (6) 4 -1.5 -1 -0.5 0 0.5 1 1.5 2 log R (pc) -1.5 -1 -0.5 0 0.5 1 log  pc (km/s) Galactic disk clouds obs data  best fit:  pc=0.46km/s, =0.57  2  lower slope: =0.56  2  upper slope: =0.59 Figure 1. Top panel shows the velocity as a function of its size for the observed molecular clouds on the Galactic disk (open red circles), from Dame et al. (1986), Solomon et al. (1987),Heyer et al. (2001), Heyer & Brunt (2004), Ridge et al. (2006), Narayanan et al. (2008) and Ripple et al. (2013). Bottom panel shows the velocity as a function of its size, for the observed molecular clouds at the Galactic center from the CHIMPS2 survey (Eden et al. 2020) (open red circles) and the SEDIGISM (Duarte-Cabral et al. 2020) (solid black squares). In each panel, we show as red solid line as the best powerlaw \ufb01t using linear regression, along with the 2\u03c3 upper and lower slopes shown as dotted and dashed lines, respectively, obtained with bootstrapping. leaving both the amplitude \u03c3pc and the exponent \u03b2 as two free parameters. Moreover, we perform bootstrap resampling to obtain upper and lower 2\u03c3 limits of the \ufb01tting parameters by \ufb01tting both parameters. 5 We \ufb01nd the best parameters and the \u00b12\u03c3 limits for the disk clouds to be best \ufb01t : \u03c3pc = 0.46 \u00b1 0.03 km/s and \u03b2 = 0.57 \u00b1 0.02 +2\u03c3 : \u03c3pc = 0.48 and \u03b2 = 0.59 \u22122\u03c3 : \u03c3pc = 0.45 and \u03b2 = 0.56, (7) shown as the solid, dotted and dash lines, respectively, in the top panel of Figure (1). Repeating the calculation for the clouds at the Galactic center yields the best parameters and the \u00b12\u03c3 limits best \ufb01t : \u03c3pc = 1.03 \u00b1 0.01 km/s and \u03b2 = 0.63 \u00b1 0.01 +2\u03c3 : \u03c3pc = 1.02 and \u03b2 = 0.65 \u22122\u03c3 : \u03c3pc = 1.05 and \u03b2 = 0.61, (8) shown as the solid, dotted and dash lines, respectively, in the bottom panel of Figure (1). We note that the errorbars of the best using the linear regression method is not necessarily consistent with and often larger than the 2\u03c3 range obtained using bootstrap, due to the latter\u2019s larger sample size with bootstrapping. The discrepancy is more noticeable for the disk clouds due to the smaller observational data sample size, as compared to that of the Galactic center clouds. Nevertheless, even in the absence of this shift for the best slope, the traditional exponent of the Larson\u2019s Relation of 1/2 is inconsistent with the disk data at 100% level if bootstrap is used and at 3.5\u03c3 if the direct regression is used, whereas a slope of 0.6 is about 1.5\u03c3 away. If considering the clouds at the Galactic center, the contrast is still larger. So far, we have not considered possible (perhaps different) systematics for the observations of the Galactic disk clouds as compared to the Galactic center clouds. The fact that the best \ufb01tting slope of the disk clouds of 0.57 and that of the Galactic center clouds of 0.63 equidistantly \ufb02ank our proposed slope of 0.60 is intriguing. It may be caused by some additional physics that are not considered in our simpli\ufb01ed treatment but operates to varying degrees of importance in the cases. It may also be caused by data inhomogeneities in the plotted plane, which may already be visible. We shall take the simpler interpretation that both slopes are intrinsically equal to 0.60 and the apparent values are due to some observational systematics, although we are not in a position to justify this assertion. This new Larson\u2019s Relation with the exponent 3/5 is in excellent agreement with observational data. Heyer & Brunt (2004) measure the value of the scaling exponent of 0.59 \u00b1 0.07 in the spatial range of 1 \u221250pc [corresponding to the original range of Larson (1981) and Solomon et al. (1987)], while \ufb01tting the entire spatial range of 0.03 \u221250pc probed they get 0.62 \u00b1 0.09. It is clear now that it is not just the gravity alone that gives rise to the Larson\u2019s Relation, rather it is a combination of gravity and turbulence physics that naturally yields it. Larson 1981 invoked virial equilibrium to explain his relation. What is new here is that the intersection of gravity and turbulence provides a signi\ufb01cantly better \ufb01t for data. Forcing the slope of 0.6 to both data sets, the best \ufb01t \u03c3pc is found to be \u03c3pc = 0.44 \u00b1 0.02 km/s for Galactic disk clouds \u03c3pc = 1.08 \u00b1 0.01 km/s for Galactic center clouds (9) From data in our Galaxy alone, one can thus already conclude that CBTCs vary in different environments within a galaxy. A two-sample KS test between the \u03c3pc distribution of the Galactic disk clouds 6 and that of the Galactic center clouds gives a p-value p = 5 \u00d7 10\u221220, indicating they are statistically different. It follows then that CBTCs and hence Larson\u2019s Relation may vary across galaxies and in different environments within galaxies. This prediction is supported by recent observations of molecular clouds in other galaxies (e.g., Donovan Meyer et al. 2013; Hughes et al. 2013; Colombo et al. 2014; Krieger et al. 2020). Historically, from Eq (1) we see that, if one insists expressing the Larson\u2019s \ufb01rst relation with the exponent close to 0.5, the original Larson\u2019s \ufb01rst relation would be gas cloud surface density dependent, a point later re-iterated (Heyer et al. 2009). But if the range in \u03a3R is suf\ufb01ciently narrow, one would obtain the original scale of a slope of 1/2, which may be the reason for that result obtained by Larson (1981). Thus, the original Larson\u2019s \ufb01rst relation has a limited scope and is applicable only when the range of surface density is narrow enough. In contrast, the revised Larson\u2019s Relation, Eq (4), is expected to be valid universally, except that the strength parameter, \u03c3pc, is expected to vary across different environments and across galaxies. To illustrate this point better, let us express \u03c3pc in terms of direct observables, involving gas surface density. Combining Eq (1) and Eq (4) gives \u03c3pc = \u03b13/10 v ( \u03a3R 341 M\u2299pc\u22122)1/2( R 1pc)\u22121/10 km/s. (10) The large difference between the Larson\u2019s Relation for the disk clouds and the Galactic center clouds strongly indicates an important role played by turbulence and that the CBTCs in the disk and at the Galactic centers are different, since gravity is the same. While one may use Eq (4) or Eq (10) or other variants to drive \u03c3pc empirically with three observables, such a derivation does not address the physical origin of the magnitude of \u03c3pc. A simple top-down illustrative method to derive \u03c3pc is given in \u00a74. We should note that our adoption of the Kolmogorov turbulence spectrum is largely motivated by available simulations. The obtained consistency with observations suggests it may be valid. The agreement with the observed fractal dimension in \u00a73 is consistent with Kolmogorov spectrum as well. Nonetheless, in general, the turbulence spectrum may not adhere strictly to that of Kolmogorov type. A more general form of Eq (4) may be written as \u03c3R \u221d\u03b11/5 v R(3\u03c6+2)/5. (11) For the Kolmogorov turbulence, we have \u03c6 = 1/3, which yields an exponent of 0.6. For Burgers (1948) turbulence, we have \u03c6 = 1/2, corresponding to an exponent 0.7, while the turbulence in a strong magnetic \ufb01eld may have a Iroshnikov-Kraichnan (Iroshnikov 1964; Kraichnan 1965) type with \u03c6 = 1/4, which would yield an exponent of 0.55. If one were to ascribe the difference in the exponent for the Galactic disk and Galactic center clouds to physical differences in the respective turbulence, one possible exit is that the turbulence on the Galactic disk is closer to that of Iroshnikov-Kraichnan type than the turbulence at the Galactic center. This requires further work to clarify that is beyond the scope of this paper. Nonetheless, none of different types of turbulence is expected to yield the conventional exponent for the Larson\u2019s Relation of 0.5. Another point maybe worth noting is that there are clouds with \u03b1v < 1, i.e., over-virialized clouds. Obviously, these clouds seem unlikely to be evolutionary descendants of clouds that had \u03b1 = 1 and subsequently endured some gravitational collapse. If that were the case, it would imply a turbulence dissipation time signi\ufb01cantly less than the free-fall time of the system, inconsistent with simulations (e.g., Stone et al. 1998). Therefore, we suspect that these low \u03b1v systems are a direct product of 7 turbulence, clouds that have relatively low velocity dispersion for their gravitational strength and are probably transient, due to the randomness of the turbulence. To further clarify the nature of these special clouds, we show in Figure (2) the cloud mass as a function of its virial parameter. To our surprise, clouds with \u03b1v < 1 span the entire mass range. This may be consistent with the randomness of the turbulence suggested above. We note, however, that some of the most massive clouds (\u2265106 M\u2299), i.e., giant molecular clouds, may be a collection of uncommunicative, smaller clouds in an apparent contiguous region, where the measured velocity dispersions re\ufb02ect those of their smaller constituents, while the overall gravitational energy increases with congregation; we note that the velocity dispersion in this case may be signi\ufb01cantly anisotropic. Finally, the ubiquitous existence of gravitationally unbound clouds is simply due to insuf\ufb01cient gravitational force relative to the turbulence velocity \ufb01eld in these clouds. A point made here is that gravitationally unbound clouds are not necessarily those that become gravitationally bound \ufb01rst and later become unbound due to internal stellar feedback or cloud-cloud collisions (e.g., Dobbs et al. 2011). In Figure (2) it is seen that the clouds at the Galactic center (black squares) show a noticeable gap in mass, from \u223c3 M\u2299to \u223c30 M\u2299. It is not clear to us what might have caused this. There is a separate ridge (horizontally oriented) of clouds near the bottom of the plot for the Galactic center clouds with masses around one solar mass. These low mass clouds appear to be mostly unbound. While it is not de\ufb01nitive, these clouds may be the counterpart of sub-solar mass clouds on the Galactic disk called \u201cdroplets\" with odd \u201cvirial\" properties (Chen et al. 2019a,b), although we are not sure why their typical mass is about 1 M\u2299instead of \u223c0.4 M\u2299found for the droplets. These small systems have large virial parameters but remain bound by external (thermal and turbulent) pressure. The connection between these systems and the CBTC that we envision here may no longer be direct, and considerations of some additional physics may be required to place these systems also within the general framework outlined here. We defer this to a later work. Another word to further clarify the physical meaning of Eq (4) may be in order, which, let us recall, is a result derived based on the joint action of the statistical order imposed by turbulence of strength \u00af \u03c3pc (with a small dispersion) and the natural selection effect by self-gravity, with (the inverse of) \u03b1v describing the strength of the latter acting against the former. If \u03b1v is much greater than unity, gravitational force would be too feeble to hold the cloud together long enough to dissipate the excess energy to allow for further consistent gravitational contraction in the presence of internal and external disruptive force of turbulence. Thus, the observed clouds with \u03b1v greatly exceeding unity that are products of supersonic turbulence are likely transient in nature. Nonetheless, they may be useful for some physical analysis. They may be considered good candidates for analyses where a statistical equilibrium is a useful assumption. At the other end, when \u03b1v is close to unity, gravitational collapse of a cloud may ensue, detaching it from the parent CBTC. However, as noted in Figure (2), one should exercise caution to treat clouds with an apparent \u03b1v less than unity that may not be genuinely coherent gravitational entities, ready to run away and collapse. We shall not delve into this further but note that these apparently over-virialized clouds may not possess the usual gravitationally induced density strati\ufb01cation and may lack a coherent structure (such as a well de\ufb01ned center). 8 Figure 2. shows cloud mass as a function of \u03b1v for the Galactic disk clouds (open red circle) and Galactic center clouds (open black squares). The two vertical lines indicate clouds with \u03b1v = 1 and 2, respectively, for reference. 3. FRACTAL DIMENSION OF THE ISM Using Eq (1) and Eq (4), we may express the cloud density-size relation: nR = \u03b1\u22123/5 v 153 44\u03c0 \u03c32 pc Gmp(1pc)2( R 1pc)\u22124/5 = 1.0 \u00d7 104\u03b1\u22123/5 v ( \u03c3pc 1 km/s)2( R 1pc)\u22124/5 cm\u22123, (12) where nR is the mean hydrogen number density within radius R and mp is proton mass. Then, the size-cloud mass relation follows: MR = 2.6 \u00d7 102\u03b1\u22123/5 v ( \u03c3pc 1 km/s)2( R 1pc)11/5 M\u2299. (13) Since \u03b1v and R are uncorrelated, for clouds generated by a same CBTC (a \u03c3pc with dispersion), we see that MR \u221dR11/5. This mass-size relation with a slope of 2.2 is in excellent agreement with observed value of 2.2 \u00b1 0.1 (Heyer et al. 2001), and 2.36 \u00b1 0.04 (Roman-Duval et al. 2010). There are many different techniques used to measure cloud mass and size. We stress that the size-mass relation depends on how clouds are de\ufb01ned or selected. For the same reason that the original Larson\u2019s size-velocity dispersion relation has an exponent of 1/2, the original Larson\u2019s sizemass relation has an exponent of 2. Both are due to a small surface density range of the clouds (e.g., Beaumont et al. 2012). The exponent in Eq (13) expresses the size-mass relation for clouds at a \ufb01xed virial parameter. 9 In the context of a fractal, self-similar structure, which may approximate the ISM reasonably well, Eq (13) indicates that the fractal dimension of the ISM is D = 2.2 (Mandelbrot 1983) with the implied size function of the form n(L)dL \u221dL\u2212D\u22121dL \u221dL\u221216/5dL. (14) The slope 16/5 in Eq (14) is in excellent agreement with the observed value of 3.2\u00b10.1 for CO detected molecular clouds in the Milky Way spanning the range of \u223c1 \u2212100pc (Heyer et al. 2001). The fractal dimension of the ISM of D = 2.2 corresponds to density power spectrum of Pk \u221dkD\u22123 \u221d k\u22120.8. It is helpful to have an intuitive visualization of this outcome. In the process of energy transmitting downward along the spatial/mass scale via supersonic motion, shocks and radiative cooling, density structure (density \ufb02uctuation spectrum) is generated. In three dimensional space, an ideal, long and uniform \ufb01lament will have a density power spectrum Pk \u221dk\u22121 on scales below the length of the \ufb01lament. Similarly, a uniform sheet corresponds to Pk \u221dk\u22122, whereas a point corresponding to a density power spectrum of Pk = k0. In absence of self-gravity, compressive supersonic turbulence with suf\ufb01cient cooling has the tendency to form \ufb01laments where two planar shocks intersect. In realistic situations with self-gravity, \ufb01laments have varying lengths and the actual density power spectrum is expected to deviate somewhat from this, depending on the nature of driving and energy distribution of the driving, and the power spectrum is in general Pk \u221dk\u2212\u03b2 with \u03b2 < 1. Nevertheless, as long as the energy in the turbulence is dominated on the large scales, \u03b2 is not likely to be much less than unity. Thus, we see that the Kolmogorov compressive turbulence generated, gravitationally signi\ufb01cant structures, in the presence of rapid radiative cooling, have a density structure that is dominated by \ufb01lamentary structures with a small mixture of knots. 4. ESTIMATE \u03c3PC FOR VISCOUSLY DRIVEN TURBULENCE In the normal situation where star formation occurs on a disk, it is reasonable to assume that the radius of the largest turbulence \u201ccloud\", which will be the driving scale of the CBTC, is equal to the scale height of the disk for isotropic turbulence. This driving scale, Rd, can be expressed as Rd = CRg\u03c32 d(Rg) v2 c(Rg) , (15) where \u03c3d(Rg) is the velocity dispersion on the driving scale Rd at a galacto-centric radius Rg, which is also the vertical dispersion, vc(Rg) is the circular velocity at radius Rg, and C is a constant of order unity to absorb uncertainty. We shall assume that the energy source is the rotational energy at the location, where the turbulence may be driven by some viscous processes on the disk. With such an assertion, one can relate \u03c3d to Rd by \u03c3d = 2BRd\u2126(Rg), (16) where \u2126(Rg) is the angular velocity at the radius Rg for a Mestel disk that we will adopt as a reasonable approximation, and B is another constant of order unity to absorb uncertainty. For a gas cloud (assumed to be uniform) of radius Rd, we can express the virial parameter by \u03b1d = 3\u03c32 d(Rg) 3 5 GMd Rd = 15\u03c32 d 4\u03c0G\u03c1dR2 d , (17) where \u03c1d is the gas density at the driving scale. With Eq (15,16,17) we can compute \u03c3pc using Eq (4); \u03c3pc = 0.44 km/s( D 2.3)\u22121/5( \u03a3d 5 M\u2299pc\u22122)1/5( vc 220 km/s)3/5( Rg 8kpc)\u22122/5, (18) 10 where we have de\ufb01ned another constant D \u2261B/C. Eq (18) is expressed such that if the \ufb01ducial values are taken, we obtain \u03c3pc = 0.44 km/s for disk clouds center near the solar radius, as derived earlier (see Eq 9). Aside from the unknown combination of D, all other \ufb01ducial values are well observed, including the gas surface density of 5 M\u2299pc\u22122 (e.g., Sofue 2017). Interestingly, if we use the same D = 2.9 value along with the relevant values for other parameters for the Galactic center, \u03a3d = 30 M\u2299pc\u22122 (Sofue 2017), Rg = 500pc (within which the Galactic center clouds are observed), vc = 250 km/s (Sofue 2017), we obtain \u03c3pc = 2.1 km/s, larger than the value of 1.08 km/s \u00b1 0.01dex, derived for the clouds at the Galactice center (see Eq 9). Although the expectation that \u03c3pc at the Galactic center is larger than that on the Galactic disk is in agreement with the derived values, the numerical discrepancy may be due to a number of causes. It may be in part due to different observational systematics for disk clouds and center clouds. It may be in part due to that the treatment of the central region of the Galaxy as a disk breaks down or that the effective viscosity in the two regions are different. It is notable that our simple calculations do not require participation of some other physical processes that might be relevant, including magnetic \ufb01eld, stellar feedback. While this is not a vigorous proof of the veracity of our assumptions, the found agreement between the predicted \u03c3pc and the directly calculated value for the Galactic center clouds is a validation of our basic assumptions and the resulting outcomes, that is, turbulence and gravity play a dominant role in shaping the interstellar medium and the formation of clouds down to at least the sonic scale. 5. CONCLUSIONS An analysis of a joint action of compressive turbulence and self-gravity is performed. Physically, it may be considered that the turbulence is bookended by the gravitationally signi\ufb01cant clouds at the small scales, as opposed to the driving scale on large scale. We denote such a turbulence chain as \u201ccloud bound turbulence chain\" (CBTC). The (new) Larson\u2019s Relation, \u03c3R = \u03b11/5 v \u03c3pc(R/1pc)3/5, relating the velocity dispersion \u03c3R to the size R of a cloud, is derived, where \u03b1v is the virial parameter of the cloud and \u03c3pc, the velocity dispersion of the turbulence at 1 pc, encodes the strength of the CBTC. Although implicit in the assumption is that the turbulence is supersonic, the new Larson\u2019s Relation is shown to hold at least down to the transonic scale of 0.05pc. The conventional exponent of 1/2 for the Larson\u2019s Relation is shown to be excluded. The most signi\ufb01cant \ufb01nding is not necessarily the derivation of this relation naturally and the exponent 3/5 being in good agreement with observations. It is prudent to remind ourselves that this exponent depends on the assumed Kolmogorov spectral index for the turbulence according and error treatments of cloud measurements can certainly be improved that may change its value to some extent. Rather, it is the fact, which is made plain by the analysis as well as empirical evidence, that, while the exponent of the Larson\u2019s Relation may be universal or close to universal, the amplititude, \u03c3pc, is not and may differ greatly. The latter is environment dependent, re\ufb02ecting the dependence of \u03c3pc of a CBTC on environment. The recognition of and evidence for the non-universality of the Larson\u2019s Relation is of foundamental physical importance. The implications may be profound for star formation process, which is thought to be dependent on the Mach number of turbulence, which in turn is linearly proportional to \u03c3pc. Our analysis also yields a by-product with respect to some properties of the fractal nature of the ISM. We show that the fractal dimension of the ISM is 11/5, cloud (linear) size function of n(R)dR \u221d R16/5dR, both in nearly exact agreement with observations. 11 I would like to thank the referee Dr. Alyssa Goodman for a constructive report that helped signi\ufb01cantly improve the paper. I thank Dr. Mark Heyer for kindly providing the observational data in suitable formats, Dr. Eric Koch for kindly sharing the CHIMPS2 survey data, along with Drs. Erik Rosolowsky, David Eden and Nico Krieger, Dr. Frederic Schuller for kindly sharing the SEDIGISM survey data, Dr. Nico Krieger for his kind help with obtaining data, and many colleagues for useful discussions. This work is supported in part by grant NASA NNX11AI23G.",
                    "introduction": "1."
                },
                {
                    "url": "http://arxiv.org/abs/2001.11083v1",
                    "title": "Physics of Prodigious Lyman Continuum Leakers",
                    "abstract": "An analysis of the dynamics of a star formation event is performed. It is\nshown that galaxies able to drive leftover gas to sufficient altitudes in a few\nmillion years are characterized by two basic properties: small sizes (<1kpc)\nand high star formation rate surface densities (Sigma_SFR > 10 Msun/yr/kpc2).\nFor the parameter space of relevance, the outflow is primarily driven by\nsupernovae with radiation pressure being significant but subdominant. Our\nanalysis provides the unifying physical origin for a diverse set of observed\nLyC leakers, including the green-peas galaxies, [SII]-weak galaxies,\nLyman-alpha emitters, with these two characteristics as the common denominator.\nAmong verifiable physical properties of LyC leakers, we predict that (1) the\nnewly formed stellar masses are are typically in the range of 1e8-1e10 Msun,\nexcept perhaps ULIRGs, (2) the outflow velocities are typically in the range\ntypically of 100-600km/s, but may exceed 1e3 km/s in ULIRGs, with a strong\npositive correlation between the stellar masses formed and the outflow\nvelocities, (3) the overall escape fraction of galaxies is expected to increase\nwith increasing redshift, given the cosmological trend that galaxies become\ndenser and more compact with increasing redshift. In addition, two interesting\nby-product predictions are also borne out. First, ULIRGs appear to be in a\nparameter region where they should be prodigious LyC leakers, unless there is a\nlarge ram-pressure. Second, Lyman break galaxies (LBGs) are not supposed to be\nprodigious LyC leakers in our model, given their claimed effective radii\nexceeding 1kpc.",
                    "authors": "Renyue Cen",
                    "published": "2020-01-29",
                    "updated": "2020-01-29",
                    "primary_cat": "astro-ph.GA",
                    "cats": [
                        "astro-ph.GA"
                    ],
                    "main_content": "We explore if gas density-bound structures in star forming galaxies may be produced. The following treatment is undoubtedly simplified but capture the essence of the physics, and is primarily a means to identify likely physical parameter space that is relevant for making galaxies with high LyC escape fractions. A gas cloud of initial mass Mgas,0 with a half light radius rh and a star formation rate SFR gives rise to an outward radial force on the gas cloud itself due to supernova explosion generated radial momentum equal to FSN = SFR \u00d7 pSN \u00d7 M \u22121 SN, (1) where pSN = 3 \u00d7 105 M\u2299km/s is the terminal momentum generated per supernova (e.g., Kimm & Cen 2014), MSN is the amount of stellar mass formed to produce one supernova, which is equal to \u2013 3 \u2013 about (50, 75, 100) M\u2299for (Chabrier, Kroupa, Salpeter) initial mass function (IMF), respectively. The exact value of pSN weakly depends on density and metallicity of the ambient gas. For simplicity without loss of validity given the concerned precision of our treatment, we use the above \ufb01ducial value. Another mechanical form of feedback from massive stars is fast stellar winds due to O stars. The total energy from stellar winds is about a factor of ten lower than the total energy from supernovae (e.g., Leitherer et al. 1999). Since stellar winds roughly track core collapse supernovae, we simply omit stellar winds bearing a loss of accuracy at 10% level. The second important outward force on the gas is the radiation pressure on dust grains, equal to Frad = SFR \u00d7 \u03b1 \u00d7 c [1 \u2212exp (\u2212\u03a3gas\u03baUV )] (1 + \u03a3gas\u03baFIR), (2) where \u03b1 = 3.6 \u00d7 10\u22124 is an adopted nuclear synthesis energy conversion e\ufb03ciency from rest mass to radiation, c speed of light, \u03baUV = 1800cm2 g\u22121 and \u03baFIR = 20cm2 g\u22121 the opacity at UV (e.g., Draine 2003) and dust processed radiation far infrared (FIR) radiation (e.g., Lenz et al. 2017), respectively, \u03a3gas the surface density of the gas. The exact value of \u03baUV matters little in the regime of interest but variations of the value of \u03baFIR does matter to some extent. To place the two forces in relative terms, we note that at \u03a3gas = 1.3 \u00d7 104 M\u2299pc\u22122, the radiation pressure due to IR photons equals the ram pressure due to supernova blastwaves, with the former and latter dominating at the higher and lower surface densities, respectively. There are two relevant inward forces. The mean gravitational force, when averaged over an isothermal sphere, which is assumed, is Fg = ln(rmax/rmin)GMgas,0Mgas(t) 4r2 h , (3) where rmin to rmax are minimum and maximum radii of the gas cloud being expelled. For our calculations below we adopt rmin = 100pc and rmax = rh; the results depend weakly on the particular choices of these two radii. We note that Mgas(t) is the remaining mass of the gas cloud when it starts to be lifted at time tL by the combined force of supernova driven momentum \ufb02ux and radiation momentum \ufb02ux against inward forces, with Mgas,0 \u2212Mgas(tL) having formed into stars. Another inward force is that due to ram pressure, which we parameterize in terms of gas infall rate in units of star formation rate: Frp = \u02d9 Minfvinf = \u03b7 \u00d7 SFR \u00d7 \u0012GMgas,0 rh \u00131/2 , (4) where \u03b7 is the ratio of mass infall rate to SFR. The relevant physical regime in hand is how to drive the gas by the combined force of supernovae and radiation against the combined force of gravitational force and ram-pressure. A key physical requirement, we propose, is that the feedback process needs to promptly lift the entire remaining gas cloud to a su\ufb03cient height such that it piles itself into a (thin) shell that subsequently fragments while continuing moving out, in order to make a copious LyC leaker. It seems appropriate to de\ufb01ne \u201ca su\ufb03cient height\u201d as a height on the order of rh, which we simplify to be just rh. The above \u2013 4 \u2013 de\ufb01nition may be expressed as (FSN + Frad \u2212Fg \u2212Frp)(th \u2212tL) = Mgas(tL)vh and 2rh = (th \u2212tL)vh, (5) where vh is the shell velocity when reaching rh at time th, and Mgas(tL) is the gas cloud mass at tL when it begins its ascent. 0 1 2 3 log t (Myr) -5 -4 -3 -2 log NccSN (yr-1) per SFR=1Msun/yr from t=0 Fig. 1.\u2014 shows the supernova rate for a star formation event at a star formation rate of 1 M\u2299/yr starting at time t = 0 as a function of time. This plot is produced using Eq (A.2) of Zapartas et al. (2017) of the core-collapse supernova rate including both single stars and binary mergers. We note that at t \u2265200Myr the saturation rate corresponds to one supernova per 78 M\u2299of stars formed, approximately in agreement with what a Kroupa IMF gives. We may relate the initial gas mass Mgas,0 to SFR that is observable by using an empirically found relation: SFR = c\u2217Mgas,0/tdyn, (6) where G is the gravitational constant, tdyn = q 3\u03c0 32G\u03c1t is the dynamical time of the system with \u03c1t being the total density, the sum of gas and stars within rh, star formation e\ufb03ciency per dynamical time is found to be c\u2217= 0.01 (Krumholz et al. 2012). Note that the SFR above is the SFR up to the time tL, when it is shut down upon the uplift of the gas cloud. \u2013 5 \u2013 We compute the rate of supernova explosion more precisely. This is needed because as soon as the combined outward force of supernova feedback and radiation pressure is stronger than inward forces at time tL, we need to stop star formation then. It is possible in some cases that the star formation has not lasted long enough to reach the saturation supernova rate. We use a recent, comprehensive analysis of Zapartas et al. (2017) that takes into account both single and binary stellar populations, including supernovae due to binary mergers. We convolve the \ufb01tting formula (A.2) in Zapartas et al. (2017) that is composed of three separate temporal segments, 3 \u221225Myr and 25 \u221248Myr due to massive single stars and 448 \u2212200Myr due to binary merger produced corecollapse supernovae, with a constant star formation rate SFR (Eq 6) starting at time t = 0. Figure (1) shows the resulting instantaneous supernova rate as a function of time for a star formation event at a constant SFR = 1 M\u2299/yr. Then, MSN(t) = 1 M\u2299/NccSN (where NccSN is the y-axis shown in Figure 1) as a function of time since the start of the starburst, in lieu of a constant value of MSN that is the saturation value at t \u2265200Mpr, in Eq (1), where appropriate. We note that at t \u2265200Myr the saturation rate corresponds to one supernova per 78 M\u2299of stars formed, approximately corresponding to a Kroupa IMF. Figure (2) shows the results by integrating Eq (5). The solid red contours labelled in units of Myr shows the time, th \u2212tL, which it takes to drive the gas to an altitude of rh. Earlier we have mentioned the need of \u201cpromptly\u201d driving the gas away, which we now elaborate. For any starburst event, massive O stars formed that dominate the LyC radiation die in about 5Myr. Therefore, the time elapsed since the end of the starburst of the observed prodigious LyC leakers should not be longer than that time scale, i.e., th \u2212tL \u22645Myr. Comparing the th \u2212tL = 5Myr contour with the black solid triangles indicates that all the observed LyC leakers lie in the parameter region with th \u2212tL \u22645Myr, except J0921 with rh = 0.78kpc, SFR = 7.68 M\u2299yr\u22121 and M\u2217= 6.3 \u00d7 1010 M\u2299 and J0926 with rh = 0.69kpc, SFR = 3.47 M\u2299yr\u22121 and M\u2217= 1.3 \u00d7 109 M\u2299(Alexandro\ufb00et al. 2015). In the entire region of possible prodigious LyC leakers we point out that the outward force is dominated by supernova driven momentum, although in a thin top-left wedge region the radiation pressure alone is also able to counter the gravity. It is very clear that all LyC leakers live in a parameter space generally denoted as Lyman alpha emitters, as indicated by the large, cyan-shaded region (e.g., Gawiser et al. 2007; Bond et al. 2009). However, it is also clear that not all LAEs are LyC leakers, as noted by the magenta dots that are observed to be LyC non-leakers. We interpret this as that the gas being lifted by the supernova driven momentum is fragmentary such that obscuration or transparency of the LyC sources are sightline dependent even when the gas cloud as a whole is expelled to a high altitude. We note that, if one includes binary evolution e\ufb00ects, such as merger produced blue stragglers or stripped hot helium stars, additional O stars like stars will emerge with some delay of order 10Myr. Each of these two delayed components may mount to about 10% of LyC photons produced by initial starburst (Eldridge et al. 2017). This may be a signi\ufb01cant addition of LyC sources. Nevertheless, given the closely spaced red contours in Figure (2), we see that none of our conclusions will be signi\ufb01cantly altered, if we use th \u2212tL = 10Myr instead of th \u2212tL = 5Myr. In the right-side, large gulf region occupying about one half of the plot area, gravity dominates over the combined outward force of supernova explosion driven momentum \ufb02ux and radiation pressure. In this region, no complete lift-up of gas to rh is possible regardless of the duration of \u2013 6 \u2013 Fig. 2.\u2014 shows the time that it takes to evacuate the gas to an altitude of rh, th\u2212tL, as the solid red contours labelled in units of Myr, with labels \u201c1\u201d, \u201c3\u201d, \u201c5\u201d, \u201c10\u201d, \u201c30\u201d and \u201c100\u201d. Shown as dotted black contours are the log of the stellar mass in units of M\u2299formed from this episode, with labels \u201c8\u201d, \u201c9\u201d, \u201c10\u201d and \u201c11\u201d. The dashed blue contours depict the radial velocity of gas being lifted in units of km/s, with labels \u201c10\u201d, \u201c30\u201d, \u201c100\u201d, \u201c300\u201d and \u201c600\u201d. The shaded light blue, light green, light red and dark blue regions indicate approximately regions normally referred to Lyman alpha emitters (LAEs), Lyman break galaxies (LBGs) at high redshift, ultra luminous infrared galaxies (ULIRGs), and z \u223c1 star-forming but non-LyC leaking dwarf galaxies, respectively. The LAE region is obtained by using a radius range of 0.1 \u22121.4kpc and a range of SFR of 1 \u2212100 M\u2299yr\u22121 (e.g., Gawiser et al. 2007; Bond et al. 2009). The LBG region is obtained by using a radius range of 1.2 \u22122.5kpc and a range of SFR of 5 \u2212100 M\u2299yr\u22121 (Giavalisco 2002). The ULIRG region is approximately delineated by a radius range of 0.1\u22121.5kpc and a range of SFR of 120\u22121200 M\u2299yr\u22121 (e.g., Spence et al. 2018). The location of the Milky Way galaxy is indicated by a black star near the lower-right corner. The sample of star-forming but non-LyC leaking dwarf galaxies at z \u223c1 with SFR < 10 M\u2299yr\u22121 (Rutkowski et al. 2016) is the blue shaded region labelled as \u201cz \u223c1 SFR < 10 M\u2299/yr\u201d. Finally, the observed galaxies with large LyC escape fractions are shown as black downward-pointing triangles from various sources (e.g., Alexandro\ufb00et al. 2015; Izotov et al. 2016a,b, 2018a,b; Wang et al. 2019), where some galaxies known as LAEs but with little LyC escape are shown as solid magenta dots (Alexandro\ufb00et al. 2015). In all cases for M\u2217, rh and SFR of observed LyC leakers and non-leakers we use updated values from Wang et al. (2019). the star formation episode. This region contain the blue shaded region labelled as \u201cz \u223c1 SFR \u2013 7 \u2013 < 10 M\u2299/yr\u201d, which is a sample of star-forming dwarf galaxies at z \u223c1 with SFR < 10 M\u2299yr\u22121 that do not show signi\ufb01cant LyC leakage (Rutkowski et al. 2016). The fact that this region lies in the region of the parameter space that is part of the LAE region and indeed is expected not to have large LyC escape is quite remarkable, because the author was not aware of this data set until was brought attention to it by the referee. Also in the large gulf region are the LBGs, as indicated by the green-shaded region (Giavalisco 2002), suggesting that LBGs are not likely to be copious LyC leakers. However, recent observations (Steidel et al. 2018) indicate a mean fesc = 0.09 \u00b1 0.01 for a subsample of LBGs. This directly contradicts our conclusions. One possible way of reconciliation is that the observed e\ufb00ective radii of LBGs in UV may be over-estimates of the e\ufb00ective radii of the star-forming regions; if the actual radii of star-forming regions are in the range of 300\u2212500pc, LBGs would be located in the region of LyC leakers. Alternatively, star-forming regions of LBGs may be composed of much more compact sub-regions. While not direct proof, it is intriguing to note that Overzier et al. (2009) \ufb01nd that the three brightest of their sample of thirty galaxies low-redshift analogs of LBGs at z = 0.10.3 that they examine in detail indeed have very compact sizes, with e\ufb00ective radii no larger than 70 \u2212160 pc. Thus, it would be signi\ufb01cant to carry out high resolution FIR observations, such as by ALMA, of LBGs to verify if the total star-forming regions are in fact more compact. As another example, the star near the bottom-right is the location of the Milky Way, which is also inside the LyC non-leaker region. So our Galaxy is unlikely to be a very good LyC leaker for an extragalactic observer. On the other hand, a class of very luminous galaxies ULIRGs occupies a region that may straddle the LyC leaker and non-leaker region. ULIRGs are in a special region of the parameter space. It is known that ULIRGs are copious FIR emitters, not known to be LyC leakers. We suggest that ULIRGs may belong to a class of its own, where ram-pressure due to gas infall may have helped con\ufb01ne the gas to (1) make them LyC non-leakers and (2) allow for star formation to proceed over a much longer period than indicated by the red contours, despite the strong outward momentum \ufb02ux driven by ongoing star formation. One way to test this scenario is to search for redshifted 21 cm absorption lines in ULIRGs, if suitable background radio quasars/galaxies or intrinsic central radio quasars/galaxies or possible other bright radio sources. Nevertheless, we would like to point out that ULIRGs should vary as well. Imagine a merger or other signi\ufb01cant event drives an episode of cold gas in\ufb02ow. The episode spans a period and the starburst triggered goes from the initial phase of buildup when the star formation rate is extremely subdominant to the in\ufb02ow gas rate. An estimate of possible gas in\ufb02ow rates is in order to illustrate the physical plausibility of this scenario. Let us assume that a merger of two galaxies each of halo mass of 1012 M\u2299and gas mass 1.6 \u00d7 1011 M\u2299triggers a ULIRG event and that 10% of the total gas mass falling onto the central region of size 1kpc at a velocity of 300 km/s. Then we obtain a gas infall rate of \u02d9 Min = 1.0\u00d7104 M\u2299yr\u22121, which would correspond yield \u03b7 = (100, 10) for SFR equal to (100, 1000) M\u2299yr\u22121, respectively. In Figure (3) we see that, once the infall rate drops below about 30 times the SFR, gas in ULIRGs would be lifted up by supernovae. This leads to a maximum SFR in ULIRGs that is estimated as follows using this speci\ufb01c merger example. During the buildup phase of the ULIRG, since the gas infall rate exceeds greatly the SFR, one can equate the gas mass to the total dynamical mass. Thus, we have SFR = c\u2217Mgas[r/(GMgas/r)1/2]\u22121. Equating \u03b7SFR (with \u03b7 = 30) to \u02d9 Min, we \ufb01nd the amount of gas accumulated at the maximum gas mass is \u2013 8 \u2013 Mgas,max = 6.3 \u00d7 1010 M\u2299, corresponding to a maximum SFR SFRmax = 330 M\u2299yr\u22121 in this case. Thus, our analysis indicates that the physical reason for an apparent maximum SFR in ULIRGs and SMGs may be due to a competition between the maximum ram-pressure con\ufb01nement of gas and internal supernovae blastwave and radiation pressure. This contrasts with and calls into question the conventional view of radiation-pressure alone induced limit on maximum SFR (e.g., Thompson et al. 2005). We deferred a more detailed analysis on this subject to a separate paper. At a later point in time it may be transitioned su\ufb03ciently rapidly, at least for a subset of ULIRGs, to a phase that is ubiquitous in out\ufb02ows. Some ULIRGs at this later phase may become signi\ufb01cant LyC leakers, if and when the gas in\ufb02ow rate drops below about 10 times SFR, as shown in Figure (3) by varying the ram-pressure (the \u03b7 parameter, see Eq 4). This new prediction is in fact consistent with some observational evidence that shows signi\ufb01cant Ly\u03b1 and possibly LyC escape fractions in the advanced stages of ULIRGs (e.g., Martin et al. 2015). These ULIRGs also seem to show blueshifted out\ufb02ow. It ought to be noted that their measured fesc is relative to the observed FUV luminosity (i.e., the unobscured region) but not relative to the total SFR, which is di\ufb03cult to measure. Thus, the escape of LyC in these late stage ULIRGs is a relative statement compared to ULIRGs that are ram-pressure con\ufb01ned and are not LyC leakers in the sense that, although in the former the stellar feedback processes may be able to lift gas up, likely still substantial in\ufb02ow gas may be able to continue to provide a large amount of obscuring material, albeit less than at earlier phase with a stronger ram-pressure con\ufb01nement and heavier obscuration. Let us now turn to the black dotted contours showing the log of the stellar mass in units of M\u2299formed from this episode presumably triggered by a gas accretion event. Two points are worth noting here. First, in the region where LyC leakers are observed, the expected stellar mass formed in a single star formation episode is in the range of 108 \u22121010 M\u2299. The observed green-peas galaxies (e.g., Schaerer et al. 2016; Izotov et al. 2016a,b, 2018a,b, 2019) have stellar masses indeed falling in this range. This suggests that a large fraction or all of the stars in green-peas galaxies may be formed in this most recent star formation episode. However, some of the [SII]-weak selected galaxies have stellar masses signi\ufb01cantly exceeding 1010 M\u2299(Wang et al. 2019). We suggest that in those cases a large fraction of the stars are formed in previous star formation episodes and spatially more extended than the most recent episode. In both cases green-peas galaxies and [SII]-weak galaxies given the central concentration of this most recent star formation episode, it is likely triggered by a low-angular momentum gas in\ufb02ow event. It would be rewarding to searches for signs of such a triggering event, such as nearby companions or post merger features. Second, there are discontinuities of the contour lines going from the gravity-dominated lower-right region to the outward force dominated upper-left region. This is because, while the gas forms to stars unimpeded in the former, a portion of the gas is blown away in the latter. Finally, let us turn our attention to the velocity of the gas moving out, as indicated by the blue dashed contours. We see that the outward velocity is in the range of 100 \u2212600 km/s. This is a prediction that can be veri\ufb01ed by observations when a reasonably large set of data becomes available. Worth noting is that LyC leakers do not necessarily possess outsized out\ufb02ow velocities. At the present time, the sample of LyC leakers is still relative small but the approximate range of wind speeds in the range of 150\u2212420 km/s if one uses directly the separation of Ly\u03b1 peaks as a proxy \u2013 9 \u2013 Fig. 3.\u2014 Top panel is similar to Figure (2) with one change: \u03b7 = 10 is used here instead of \u03b7 = 0 (see Eq 4) in Figure (2). Bottom panel is similar to the top panel with \u03b7 = 30. \u2013 10 \u2013 Fig. 4.\u2014 shows the median velocity as a function of stellar mass formed in the episode, along with lower and upper quartiles shown as the errorbars, for two cases with \u03b7 = 0 and \u03b7 = 30. (Izotov et al. 2016b,a). We note that given the scattering e\ufb00ects of Ly\u03b1 photons the separation of Ly\u03b1 peaks generally may only represent an upper limit on the velocity dispersion, which in turn may be on the same order of the out\ufb02ow velocity. For a general comparison to young star-forming galaxies without considering LyC escape, Bradshaw et al. (2013) \ufb01nd out\ufb02ow velocities typically in the range of 0 \u2212650 km/s for young star-forming galaxies with stellar mass of \u223c109.5 M\u2299, which is consistent with predicted velocity range. Finally, Chisholm et al. (2017) \ufb01nd that LyC leakers (with fesc \u22655%) spans an out\ufb02ow velocity range of 50\u2212500 km/s (probed by Si II), consistent with our model. Henry et al. (2015) show out\ufb02ow velocities probed by a variety of ions from Si II to Si IV of a range of 50 \u2212550 km/s for green pea galaxies, consistent with our model once again. Because the velocity contours are more parallel than perpendicular to the stellar mass contours, a related prediction is that the out\ufb02ow velocity is expected to be positively correlated with the newly formed stellar mass. Figure (4) shows the median velocity as a function of stellar mass formed in the episode, along with lower and upper quartiles shown as the errorbars, for two cases with \u03b7 = 0 and \u03b7 = 30. We see clearly a positive correlation between the out\ufb02ow velocity of LyC leakers and the amount of stars formed in the episode, with median velocity going from \u223c100 km/s at 108 M\u2299 to 600 \u2212700 km/s at 1010 M\u2299. For the very high end of the stellar mass of 1011 M\u2299formed in the episode, the out\ufb02ow velocities are expected to exceed 103 km/s. With more data this unique prediction should be testable. \u2013 11 \u2013 3. Comparisons to Some Previous Works We thank the author for the very detailed comparison with the work I suggested. Since the reader might be unfamiliar with the details of the work which spans observations, simulations, and semi-analytical techniques, I suggest an introductory sentence for each paragraph. Heckman (2001) are among the \ufb01rst to attempt to infer the physical conditions of LyC escape in starburst galaxies combining observational evidence with basic physical considerations in the context of a superbubble driven by supernova explosions. They propose that strong starbursts clear channels through the neutral ISM to facilitate LyC escape. They ultimately reach the conclusion that the empirical evidence does not demonstrate that galactic winds inevitably produce large values of LyC escape fraction in local starbursts. In other words, galactic out\ufb02ows appear to be a necessary but not su\ufb03cient condition that creates an ISM porous to ionizing radiation. This idea is advanced here in a quantitative fashion. We show that only very compact, high surface density starbursting regions are capable of evacuating embedding gas su\ufb03ciently promptly to allow for an environment where a signi\ufb01cant amount of LyC escape becomes possible. We argue that this may apply to both a compact starburst at the center of a galaxy or a high density patch of a spatially extended starburst, because the dynamics are the same in both cases. Nevertheless, we agree with Heckman (2001) that even in this case the condition created by compact strong starbursts may be a necessary one, due to variations of obscurations along lines of sight, because in most cases gas is only lifted to a limited altitude forming a gas shell that is presumably prone to fragmentation. In a semi-analytic treatment of escape fraction as a function of star formation surface density, applied to the Eagle simulation, Sharma et al. (2016) adopt a threshold star formation surface density \u03a3SFR = 0.1 M\u2299yr\u22121 kpc\u22122 on a scale of \u223c1kpc, motivated by an apparent threshold for driving galactic winds. Our analysis shows that on 1kpc scale, such a star formation surface density falls short by a factor of 1000 for making conditions to allow for a high LyC escape fraction (see Figure 2). However, when one moves to a smaller size of 0.5kpc, this threshold star formation surface density lands in the region where gas may be driven away but on a time scale much longer than 5Myr. In fact, at \u03a3SFR = 0.1 M\u2299yr\u22121 kpc\u22122 there is no parameter space for a high LyC escape fraction regardless of size. For a star formation surface density \u03a3SFR = 1 M\u2299yr\u22121 kpc\u22122, a region of size \u223c0.1kpc can now possess necessary conditions for a high LyC escape fraction. Thus, the overall LyC escape fraction in Eagle simulation they analyze may have been over-estimated. On the other hand, limited numerical resolution may have caused an underestimation of the star formation surface density in the simulated galaxies there. Thus, the overall net e\ufb00ect is unclear, if all galaxies were resolved and a correct threshold star formation surface density applied. What is likely is that their assessment of the relative contributions of large and small galaxies may have been signi\ufb01cantly biased for large ones due to the lenient condition. Based on an empirical model introduced in (Tacchella et al. 2018) that stipulates the SFR to be dependent on halo accretion rate with a redshift-independent star formation e\ufb03ciency calibrated by N-body simulations, Naidu et al. (2019) analyze how observations of electron scattering optical depth and IGM ionization states may be used to constrain cosmological reionization. Their main assumption is that the LyC escape fraction is constant for all galaxies. Their main conclusion is that bright galaxies (MUV < \u221216) are primarily responsible for producing most of the ionizing photons, \u2013 12 \u2013 in order to produce a rapid reionization process consistent with observations. Our analysis indicates that the assumption of a constant LyC escape fraction for all galaxies may be far from being correct. However, if the bright galaxies are dominated by strong compact central starbursts with high star formation surface densities, an assumed constant LyC escape fraction for all galaxies may lead to a conclusion, as they do, that faint galaxies make minor contribution to reionization; this conclusion itself ultimately may not be incorrect, though. It is also worth noting that the galaxy luminosity in their model is substantially shallower than observations below MUV > \u221218. This discrepancy may have, in part, contributed to the more diminished role of faint galaxies in their modeling. These coupled e\ufb00ects suggest an improved, more detailed analysis may be desirable, to better learn the intricate physics. The dynamics for a central starburst analyzed here in principle is applicable to a compact starbursting subregion within a more extended starbursting disk. The complication in the latter case is that neighboring regions on the disk would unavoidably elevate some gas to varying altitudes, resulting in an environment for the compact starbursting region in question that is subject to more obscuring gas, in lines of sight deviated from the polar direction. Nevertheless, we do expect that the LyC escape is, on average, an increasing function of the star formation surface density within an extended starburst, unless ram-pressure becomes a dominant con\ufb01ning process, as likely in the case of most ULIRGs with respect to the star formation rate surface density. 4. Discussion and Conclusions A simple analysis of the dynamics of star forming clouds is performed. The dynamical players include supernova driven outward momentum \ufb02ux, radiation pressure, gravitational force and ram pressure due to infalling gas. The single most signi\ufb01cant \ufb01nding, evident in Figure (2), is that galaxies able to promptly drive leftover gas away are characterized by two basic properties: small sizes (\u22641kpc) and high star formation rate surface densities (\u03a3SFR \u226510 M\u2299yr\u22121 kpc\u22122). These characteristics are dictated by the twin requirements for removing obscurating material promptly: expelling the gas to a high altitude of the size of the system itself within a few million years since the end of the starburst (which coincides with the onset of the lifto\ufb00of the leftover gas from star formation). As a matter of fact, the only physical commonality among the distinct classes of observed galaxies known to be LyC leakers green-peas galaxies, [SII]-weak galaxies, some LAEs are their high star formation rate surface densities and compact sizes. Our analysis now provides a unifying physical origin for LyC leakers. On the other hand, some other observed properties that di\ufb00er among di\ufb00erent classes are merely symptoms and consequences as a result of gas expulsion, such as those related to density-bound structures and their manifestations due to much reduced gas density around star formation regions in the form of line emission and absorption by a relatively modest amount of gas along the line of sight (OIII emission, weak [SII] line, strong Ly\u03b1 emission, etc). The compactness of the starburst region likely requires some triggering event to drive the gas to the central region of a new galaxy or an old galaxy rejuvenated. Hence, looking for signs of signi\ufb01cant gravitational interactions, such as nearby companions or post merger features will shed useful light. \u2013 13 \u2013 In light of this clari\ufb01cation of the physical origin of prodigious LyC leakers, a more robust way to search and identify LyC leakers may be to focus on their basic physical properties of compactness and high SFR surface density, in addition to likely symptoms as a result of gas expulsion. While such an approach will unite the various disparate kinds of observed LyC leakers physically, it will also help broaden the range of methods that may be employed to search for LyC leakers, which may be important for an adequate account of the overall abundance of LyC leakers. For this undertaking, it is useful to highlight three other veri\ufb01able predictions for LyC leakers from this analysis: (1) the newly formed stellar masses are in the range of 108 \u22121010 M\u2299, (2) the out\ufb02ow velocities are in the range typically of 100\u2212600 km/s, (3) there a positive correlation between the stellar masses formed and the out\ufb02ow velocities. Furthermore, two interesting by-product predictions are also borne out. First, ULIRGs appear to be in a parameter region where they should be prodigious LyC leakers, unless there is a large ram-pressure due to infalling gas with a rate exceeding about 30 times the star formation rate. Then, unavoidably, towards the tail end of a ULIRG event when the ram-pressure relents, advanced ULIRGs may turn signi\ufb01cant LyC leakers. Second, Lyman break galaxies with size exceeding 1kpc are shown not to be prodigious LyC leakers. Thus, if LBGs have signi\ufb01cant LyC leakage, as latest observations appear to suggest, it may be that the e\ufb00ective radii of their star forming regions have been over-estimated by a factor of 2 \u22124. Finally, an important physical trend is noted. In a hierarchical structure formation model, galaxies at high redshift are, as a whole, more compact and have higher star formation rate surface densities, simply due to the fact of the universal expansion. In addition, more ubiquitous interactions among galaxies help drive low angular momentum to the central regions of galaxies to facilitate formation of compact systems, on top of already relatively smaller physical sizes of galaxies at high redshift. Therefore, given what is learned in this analysis, it may be predicted that the LyC escape fraction of galaxies is expected to increase with increasing redshift at a given star formation rate, a given stellar mass, a given luminosity or a given physical size of galaxies. We can also predict that the overall escape fraction for galaxy population as a whole is expected to increase with increasing redshift. This trend helps understand why galaxies at EoR may have much higher escape fractions than their lower redshift counterparts (e.g., Wise & Cen 2009; Kimm & Cen 2014) and help provide the physical basis for stellar reionization. We note in passing that simulations that are not able to at least fully resolve star formation regions of size of 100pc or so may yield results signi\ufb01cantly removed from reality, exacerbating plaguing issues, such as overcooling, over-metal enrichment, under-prediction of LyC photon, etc. I would like to thank Tim Heckman and Masami Ouchi for discussion, Bengjie Wang and Tim Heckman for sharing observational data prior to publication, and the warm hospitality of IPMU where this work was initiated. The research is supported in part by NASA grant 80NSSC18K1101. \u2013 14 \u2013",
                    "introduction": "Understanding how Lyman continuum photons (LyC) escape from galaxies is necessary for understanding the epoch of reionization (EoR), one of the last major frontiers of astrophysics. High resolution cosmological hydrodynamic galaxy formation simulations have widely evidenced that supernova feedback driven blastwaves are the primary facilitator to evacuate or create major pores in the interstellar medium to enable the escape of LyC (e.g., Wise & Cen 2009; Kimm & Cen 2014; Cen & Kimm 2015; Ma et al. 2016; Kimm et al. 2019). Since LyC escape is not directly measurable 1Princeton University Observatory, Princeton, NJ 08544; cen@astro.princeton.edu arXiv:2001.11083v1  [astro-ph.GA]  29 Jan 2020 \u2013 2 \u2013 at EoR due to its limited mean free path, it is imperative to ascertain this unknown by establishing observable proxies for the escape fraction, fesc, when both proxies and fesc are measurable at lower redshift, based upon a satisfactory physical understanding. Observationally, in the low-z (z < 0.4) universe the majority of galaxies with large fesc values turn out to belong to the compact, so-called green-peas galaxies from the SDSS sample, character- ized by their low stellar masses, low metallicities, very strong nebular emission-lines (H\u03b2 equivalent widths > 200\u02da A) and very high \ufb02ux ratios of [OIII]5007/[OII]3727 > 5 (e.g., Schaerer et al. 2016; Izotov et al. 2016a,b, 2018a,b, 2019). Interestingly, the green-peas galaxies have star-formation rate surface densities of 10 \u2212100 M\u2299yr\u22121kpc\u22122, which are much higher than typical star-forming galax- ies in the local universe but may be similar to those at EoR. Another class of low redshift galaxies that have high LyC escape fraction is identi\ufb01ed by their high Ly\u03b1 emission (e.g., Verhamme et al. 2015, 2017), which typically have star-formation rate surface densities of \u223c10 M\u2299yr\u22121kpc\u22122. At z \u223c3 LyC escape is detected in dozens of individual galaxies (e.g., Mostardi et al. 2015; Vanzella et al. 2016; Shapley et al. 2016; Steidel et al. 2018), some of which also show intense [OIII] emission that are consistent with low-z observations and characteristic of galaxies at EoR (e.g., Fletcher et al. 2019). Furthermore, recently, another set of galaxies with relatively weak [SII] nebular emission lines are also observed to show high LyC escape (Wang et al. 2019). The low-redshift green-peas galaxies, z \u223c3 high LyC leakers and the [SII]-weak LyC leaking galaxies are di\ufb00erent in various respects, such as stellar mass, metallicity, dust content and ISM properties. But all appear to share two common characteristics: all four have very high star-formation rate surface densities and relatively compact sizes. This Letter aims to understand if supernova feedback may be the common physical process that underwrites the commonality shared by these di\ufb00erent classes of galaxies observed. We will show that this is indeed the case. This \ufb01nding thus provides a physical basis to help identify galaxies with high LyC leakage at the epoch of reionization by indirect but robust markers that can be established at more accessible redshift and for why dwarf galaxies at EoR are much more capable of enabling high LyC escape fraction than typical low redshift counterparts."
                },
                {
                    "url": "http://arxiv.org/abs/1912.04372v1",
                    "title": "On Post-Starburst Galaxies Dominating Tidal Disruption Events",
                    "abstract": "A starburst induced by a galaxy merger may create a relatively thin central\nstellar disk at radius $\\le 100$pc. We calculate the rate of tidal disruption\nevents (TDEs) by the inspiraling secondary supermassive black (SMBH) through\nthe disk. With a small enough stellar velocity dispersion ($\\sigma/v_c \\le\n0.1$) in the disk, it is shown that $10^5-10^6$ TDEs of solar-type main\nsequence stars per post-starburst galaxy (PSB) can be produced to explain their\ndominance in producing observed TDEs. Although the time it takes to bring the\nsecondary SMBH to the disk apparently varies in the range of $\\sim 0.1-1$Gyr\nsince the starburst, depending on its landing location and subsequently due to\ndynamical friction with stars exterior to the central stellar disk in question,\nthe vast majority of TDEs by the secondary SMBH in any individual PSB occurs\nwithin a space of time shorter than $\\sim 30$Myr. Five unique testable\npredictions of this model are suggested.",
                    "authors": "Renyue Cen",
                    "published": "2019-12-09",
                    "updated": "2019-12-09",
                    "primary_cat": "astro-ph.HE",
                    "cats": [
                        "astro-ph.HE",
                        "astro-ph.GA"
                    ],
                    "main_content": "The physical setting of the problem in hand is as follows. Two gas-rich galaxies each with a SMBH at their respective centers merge. A starburst occurs in the process, peaking at the time of the coalescence of the two galaxies, followed by a rapid decline in star formation rate (e.g., Hopkins et al. 2006). The merger of the two SMBHs may be delayed in time, relative to the starburst peak, as simulations have shown. The typical time delay is in the range of 0.1 \u22121Gyr, not including an additional possible barrier at about parsec scale. For the TDE rates derived in the present model, the parsec barrier has no effect. We adopt a flat rotation curve throughout. High resolution cosmological zoom-in simulations covering galactic and central regions with a resolution as high as 0.1pc (Hopkins & Quataert 2010, 2011) support this assumption. For the present purpose there is little to be gained by attempting to treat the situation with additional nuance than this. While the stars dominate the gravity in this radial range, exterior to rout we assume the dark matter conspires to guarantee a continuous flat rotation curve for simplicity and and we do not treat the region interior to rin. We assume that the stellar subsystem is composed of a geometrically flat stellar disk with a mass fraction \u03b7 and a spherical component with a mass fraction 1 \u2212\u03b7. In the radial range of [rin, rout], the stellar volume mass density in the disk can be expressed as \u03c1\u2217(r) = \u03b7v2 c 4\u03c0Gr \u03b7v2 c 4\u03c0Gr2(vc \u03c3 vc \u03c3 ), (1) where vc and \u03c3 are the rotation velocity of and velocity dispersion (assumed to be isotropic) in the disk, respectively, at the cylindrical radius, r. The Mestel stellar disk\u2019s mass surface density is \u03a3\u2217(r) = \u03b7v2 c 2\u03c0G \u03b7v2 c 2\u03c0Gr. (2) Let us for simplicity assume a single population of solar mass stars to yield the stellar number density in the disk n\u2217(r) = \u03b7v3 c 4\u03c0Gr2\u03c3 \u03b7v c 4\u03c0Gr2\u03c3 M\u2299 . (3) Given this physical backdrop, the process that we are interested in is the inspiral of the secondary SMBH through the flat stellar disk. We denote the inspiraling SMBH as \u201cthe secondary\u201d of mass M2, as opposed to the central SMBH denoted of mass M1. To present a concrete set of quantitative results we shall choose a fiducial case of two merging galaxies each with a SMBH of mass M1 = M2 = 107 M\u2299and vc = 159 km/s to denominate relevant terms, following the relation between galaxy stellar mass and SMBH mass. The merged galaxy is assumed to slide along the Tremaine et al. (2002) relation so to have a rotation velocity of vc = 21/4 \u00d7 159 km/s = 189 km/s, which is assumed to have achieved after the merger of the galaxies but prior to inspiral of the secondary through the central stellar disk. The total stellar mass interior to r (including both the disk and bulge): M(< r) = 107( r 1.2p r 1.2pc)( vc 189 km vc 189 km/s)2 M\u2299. (4) \u2013 3 \u2013 On the grounds that dynamical friction induced inspiral stalls at the radius where the interior stellar mass on the disk is equal to the mass of the inspiraling SMBH, we de\ufb01ne the inner radius rin as rin = 1.2( M2 107 M\u2299 )( vc 189 km/s)\u22122 pc. (5) When the secondary, if with zero orbital eccentricity, moves at the circular velocity vc at any given radius, the stars at the same radius moves at a lower azimuthal velocity v\u03c6. The asymmetric drift, v\u03c6 \u2212vc, the relative velocity of stars to a notional circular velocity at the radius, is governed physically by the Jeans third equation (Binney & Tremaine 1987) and observed in our solar neighborhood (e.g., Golubov et al. 2013; Sharma et al. 2014). For an isotropic velocity dispersion of stars in the disk with a local dispersion \u03c3 \u2261\u03c3R = \u03c3\u03c6 = \u03c3z \u226avc, which we shall assume, and for a \ufb02at rotation curve, we have v2 \u2261vc \u2212v\u03c6 = \u03c32 vc = 0.1\u03c3(10\u03c3 vc ), (6) For a relatively thin disk with \u03c3 \u22640.1vc that are of relevance here, v2 \u226a\u03c3. Note that v\u03c6 < vc, i.e., stars collectively move more slowly than the circular velocity at that location. The physical meaning of the asymmetric drift is easily understood in terms of the presence of an equivalent negative radial pressure gradient in the stars due to local velocity dispersion, as the Jeans equation displays. This lag, direction-wise, may be understood in another intuitive way. Stars with nonzero velocity dispersion, i.e., not strictly on circular orbits, have non-zero eccentricities. In any non-Keplerian orbit, which is the case here for a \ufb02at rotation curve, the epicyclic frequency is larger than the azimuthal frequency, causing perigalacticon to precess backwards relative to zero eccentricity orbits. Because of \ufb01nite v2, the secondary experiences a dynamical friction force. This is important because it means that the secondary in a circular orbit in a disk in the absence of any bulge component can still experience a dynamical friction and move inward. In a two-dimensional con\ufb01guration the primary dynamical e\ufb00ect is due to close encounters between the secondary and stars (Rybicki 1972), as opposed to the usual three-dimensional con\ufb01guration where distant encounters dominate (Chandrasekhar 1943). If the in\ufb02uence radius of the secondary, de\ufb01ned as r2 \u2261GM2/\u03c32, is greater than the half-thickness of the stellar disk, h, then the situation is considered to be two-dimensional. We have r2 h = 1.2(10\u03c3 vc )\u22123( M2 107 M\u2299 )( vc 189 km/s)\u22122( r 1kpc)\u22121. (7) Thus, for the \ufb01ducial case considered of M2 = 107 and vc = 189 km/s, in the regime of interest here with \u03c3/vc \u22640.1, the two-dimensional condition is satis\ufb01ed for radius r \u22641kpc. The two-dimensional dynamical friction force is (Quinn & Goodman 1986, Eq III.3) Fd f = \u22122\u03c0G\u03a3\u2217M2 (\u221a 2\u03c0 4 v \u03c3 exp (\u2212v2 4\u03c32) \u00d7 \u0014 I0( v2 4\u03c32) + I1( v2 4\u03c32) \u0015) , (8) \u2013 4 \u2013 where v is the velocity of the secondary relative to the stars, I0 and I1 are modi\ufb01ed Bessel functions of the \ufb01rst kind (Abramowitz & Stegun 1972). In the limit v \u226a\u03c3, Fd f = \u2212 r \u03c03 2 G\u03a3\u2217M2v \u03c3 . (9) In this limit, for our case, a rotating disk, we may follow the procedure of Chandrasekhar (1943) by elementarily integrating the spatial range on the disk from \u2212h to +h over which the shear velocity is subdominant to the velocity dispersion (along with the integrations over the distribution over the angle between velocity vectors and the Maxwellian velocity distribution) to derive the frictional force: F \u2032 d f = \u22123 \u221a 2\u03c0h\u03a3\u2217\u03c3v = \u22123 \u221a 2\u03c0G\u03a3\u2217M2v \u03c3 . (10) It is seen that Eq (10) and Eq (9) di\ufb00er only by a factor of unity (\u03c0/6), re\ufb02ecting again close encounters being largely responsible for dynamical frictional force in the two-dimensional case. For simplicity, without introducing a large error, and given the ambiguity in choosing the radial extent of integration used to derive Eq (10), we just use Eq (9) for all subsequent calculations. The dynamical friction time for the two-dimensional component is then t2d \u2261(d ln r dt )\u22121 = M2vc Fd f v v2 = rv \u03b7vcv2 (\u221a 2\u03c0 4 v \u03c3 exp (\u2212v2 4\u03c32) \u00d7 \u0014 I0( v2 4\u03c32) + I1( v2 4\u03c32) \u0015)\u22121 , (11) where the v2/v factor is the tangential fraction of the dynamical friction force, and v is the total velocity of the secondary relative to local stars, v = q v2 2 + v2 r with vr = r td f (12) being the radial drift velocity of the secondary and v2 the asymmetric drift velocity (Eq 6). In addition, the dynamical friction time due to the three-dimensional component is t3d = 2v3r2[erf(X) \u22122X exp (\u2212X2)/\u221a\u03c0]\u22121 3v2 c ln \u039bGM2(1 \u2212\u03b7) (13) (Binney & Tremaine 1987), where X = v/ \u221a 2\u03c3 and we adopt a Coulomb logarithm ln \u039b equal to three. Then, the overall dynamical friction time is td f = (t\u22121 2d + t\u22121 3d )\u22121, (14) which will be used throughout our subsequent calculations. Figure 1 shows the dynamical friction time (tdf, Eq 14) for two cases: \u03b7 = 0.5 with \u03c3/vc = 0.1 (solid thin black curve) and \u03b7 = 0.9 with \u03c3/vc = 0.1 (solid thick black curve), both with vc = 189 km/s and M2 = 107 M\u2299, along with the breakdowns due to the two-dimensional and three-dimensional components. We see that for \u03b7 < 0.9 and \u03c3/vc = 0.1 the overall dynamical friction induced inspiral is due to the three-dimensional component at r \u226410pc; in fact, for any applicable cases (see \ufb01gures below), in the inner region \u2013 5 \u2013 0 1 2 3 4 log r (pc) -1 0 1 2 3 4 log tdf (Myr)  t2d  =0.5, /vc=0.1  t3d  =0.5  tdf  =0.5, /vc=0.1  t2d  =0.9, /vc=0.1  t3d  =0.9  tdf  =0.9, /vc=0.1 Fig. 1.\u2014 shows the dynamical friction time (tdf, Eq 14) for two cases: \u03b7 = 0.5 with \u03c3/vc = 0.1 (solid thin black curve) and \u03b7 = 0.9 with \u03c3/vc = 0.1 (solid thick black curve), both with vc = 189 km/s and M2 = 107 M\u2299. Also shown as the dotted blue and dashed red curves are their respective two-dimensional (t2d, Eq 11) and three-dimensional dynamic friction time (t3d, Eq 13). In the two-dimensional case, the \ufb02at regime at the small radius end is due to the dynamical friction time that is constrained by the limited radial range due to the rotational velocity shear (tdf,2d, Eq 11), whereas the ascending portion at the large radius end is determined by td f,2d (Eq 11). of r = 1 \u221210pc the three-dimensional dynamical friction dominates and sets the time scale of the inspiral in that radial range. It is important to note, however, that the TDE rate is mainly due to the interaction of the inspiraling secondary and stars in the disk, as we show below, thanks to its high volume density of stars. Let us now examine the TDE rate by the secondary during its inspiral. Because the stars are essentially collisionless, they can accrete onto the secondary only at a rate about equal to the cross section of the secondary times the mass \ufb02ux, v\u03c1\u2217(Eddington 1926), as opposed to a higher, Bondi rate for collisional matter. The e\ufb00ective cross section of the secondary may be identi\ufb01ed with the tidal capture cross section, which is larger than but on the same order as the tidal disruption cross section, although what happens to the stars once captured is complex. We estimate the TDE rate based on stars that directly plunge into the radius twice the tidal radius. We now derive a general expression of TDE events for both non-zero relative bulk velocity of the secondary to stars and non-zero velocity dispersion of stars with the latter being assumed to already have a relaxed Maxwellian distribution. If the secondary moves through a static \u2013 6 \u2013 sea of stars of density n\u2217at a velocity v, the rate of stars entering the loss cone would be R(v|\u03c3 = 0) = \u03c0r2 t n\u2217v(1 + 2GM2 v2rt ), (15) where rt is the tidal radius of the loss cone surface: rt = r\u2217(M2 m\u2217 )1/3 = 1.5 \u00d7 1013( M2 107 M\u2299 )1/3( r\u2217 R\u2299 )( m\u2217 M\u2299 )\u22121/3 cm = 1.09rsch(M2)( M2 108 M\u2299 )\u22122/3( r\u2217 R\u2299 )( m\u2217 M\u2299 )\u22121/3, (16) with m\u2217and r\u2217being the stellar mass and radius, respectively, and rsch(M2) the Schwarzschild radius of the secondary. For the secondary moving through stars with a Maxwellian velocity distribution of dispersion \u03c3 at a mean relative velocity v, one may convolve R(v|\u03c3 = 0) in Eq (15) with the velocity distribution to obtain the overall rate. Choosing the direction of v in plus x-direction, we have R(v, \u03c3) = Z +\u221e \u2212\u221e Z +\u221e 0 \u03c0r2 t n\u2217 q (v \u2212vx)2 + v2 t \u001a 1 + 2GM2 [(v \u2212vx)2 + v2 t ]rt \u001b \u00d7 1 \u221a 2\u03c0\u03c33 exp \u0002 \u2212(v2 x + v2 t )/2\u03c32\u0003 vtdvxdvt, (17) where v2 t = v2 y + v2 z, and the outer and inner integrals are for vx and vt, respectively. With a bit manipulation one \ufb01nds R(v, \u03c3) = \u03c0r2 t n\u2217\u03c3 (r 2 \u03c0 exp (\u2212v2/2\u03c32) + v \u03c3 erf ( v \u221a 2\u03c3) + 2\u03c3 v \u0014 exp (\u2212v2/2\u03c32) \u22121 + erf ( v \u221a 2\u03c3) \u0015) + \u03c0n\u2217j2 lc v \u0014 erf ( v \u221a 2\u03c3) + 1 \u2212exp (\u2212v2/2\u03c32) \u0015 , (18) where the \ufb01rst and second terms correspond to their counterparts in Eq (15) with the latter due to gravitational focusing, and jlc is the angular momentum at loss cone surface about the secondary on a circular orbit: jlc = q GM 4/3 2 m\u22121/3 \u2217 r\u2217= 1.4 \u00d7 1023( M2 107 M\u2299 )2/3( m\u2217 M\u2299 )\u22121/6( r\u2217 R\u2299 )1/2cm2/s. (19) For extreme events like TDEs the orbital velocity at tidal radius rt is much larger than typical velocity of stars at in\ufb01nity relative to the secondary, so the second term in Eq (18) dominates. Thus, for the sake of conciseness we shall neglect the \ufb01rst term with negligible loss of accuracy in our case. The radial distribution of TDEs may be expressed as dNtde d ln r = R(v, \u03c3)td f = \u03b7v3 cj2 lctd f 4Gm\u2217\u03c3vr2 \u0014 erf ( v \u221a 2\u03c3) + 1 \u2212exp (\u2212v2/2\u03c32) \u0015 . (20) \u2013 7 \u2013 A key notable point in terms of the time scale is that the vast majority of TDEs in a PSB in our model likely occur within a time scale that is signi\ufb01cantly less than the age since starburst of PSBs of 0.1 \u22121Gyr. Thus, if our model were to explain the observed TDEs in PSBs, which show an apparent delay, relative to the starburst event itself, of up to \u223c1 Gyr, this indicates that it is the time that it takes to bring the secondary into the central stellar disk region and to be co-planar that determines the observed temporal distribution relative to the starburst, before the secondary interacts with the central stellar disk that subsequently dominates the TDE events. Such an expectation is quite plausible in the context of galaxy mergers, as evidenced by galaxy merger simulations. A systematic simulation survey of black hole mergers in the context of galaxy mergers is not available, due to the computational cost, daunting physical complexity and a large parameter space. Nonetheless, valuable information from existing simulations may be extracted. Our survey of literature is by no means exhaustive but hoped to be representative. In the merger simulations of Hopkins et al. (2006) it is seen in their Figure 13 that the \ufb01nal starburst occurs at 1.5Gyr since the beginning of the merger for a black hole pair of mass 3 \u00d7 107 M\u2299each. We can not \ufb01nd information about the black hole separation at this time. But from their visualization plots it seems that by this time the galaxies are largely merged, with separations likely less than a few kpc at most. In Johansson et al. (2009, Figure 14) one sees that by the time the starburst ends at simulation time t \u223c1.8Gyr, the separation of the binary BHs is \u223c1kpc. Using the three-dimensional dynamical friction time formula (Chandrasekhar 1943), we \ufb01nd tDF = 1.7Gyr and 0.43Gyr for a 1 \u00d7 107 M\u2299 black hole at 1kpc and 0.5kpc, respectively, in a spherical system with a circular velocity of 189 km/s. In the 1:4 merger simulations Callegari et al. (2009) \ufb01nd that once the separation of the galaxy pair (and BH pair) reaches 10kpc, it takes about 0.5Gyr to reach \u223c0.1kpc. This suggests that so long as the starburst does not end before the BH reaches 10kpc separation, the BH merger would occur in the time frame of 0.1 \u22121Gyr. In the most comprehensive study so far Tamburello et al. (2017) \ufb01nd that the black hole pair reaches a separation of \u223c100pc in the range of 0.11 \u22120.79Gyr from a sample of about two dozen merger simulations (see Table 2 in their paper), although there is a small fraction of cases where mergers never occur. Observationally, French et al. (2017) infer a post-starburst age in the range 0.06\u22121Gyr from eight TDE cases; when 1\u03c3 error bars are included, the range of post-starburst ages extends to 0.05 \u22121.2Gyr. This range of PSB age of \u22641Gyr seems accommodatable by the galaxy merger dynamics to bring the secondary close to the central region from extant simulations. As it is clear now that it is the total number of TDEs per galaxy that is predicted for a given physical con\ufb01guration of the system, including \u03c3/vc, \u03b7, vc and M2. If, for some reason, the secondary black hole reaches the central disk in a shorter span of time since the starburst for some subset of starburst galaxies, then their apparent rate will be inversely proportional to time interval between the starburst to the arrival at the central disk. Perhaps the apparently higher rate of TDEs in ULIRGs (Tadhunter et al. 2017) is due to this reason. One important requirement concerns bringing the secondary to be co-planar with the central stellar disk. Mergers of two galaxies possess some axisymmetry dictated by the orbital angular momentum of the merger and formation of a disky component due to gas dissipational processes. Thus, it is likely that the orientation of the orbit of the secondary may be largely co-planar initially. Tamburello et al. (2017) show that a \ufb02at disk is formed in the central region due to gas in\ufb02ow, \u2013 8 \u2013 although the exact scale height is likely limited by their \ufb01nite resolution. Without rigorous proof one has to contend with the possibility that the secondary is not exactly co-planar with the central stellar disk, when it is still at some large radius. Even in this case, the orbital plane of the secondary will be re-aligned with the central stellar disk during the inward migration via dynamical friction. Binney (1977) shows that in an oblate system with anisotropic velocity distribution, the dynamical friction drag tends to align the inspiraling object with the disk plane, so long as not on a polar orbit initially. The timescale on which this occurs is precisely the timescale for the action of dynamical friction. The basic analytic framework of Binney (1977) is shown to provide a much better agreement with simulations for inclination dependent dynamical friction time scale than the classic formulation of Chandrasekhar (1943) for \ufb02attened systems. More importantly, the decay rate of the orbital inclination that is not observed using the classic approach is quantitatively reproduced in simulations (Pe\u02dc narrubia et al. 2004) when anisotropic dynamical friction formulae (Binney 1977) are used. In the simulations (Pe\u02dc narrubia et al. 2002, 2004) a relatively modest amount of anisotropy (q = 0.6) is employed for the dark matter halo to show the e\ufb03cacy of the inclination decay of satellite orbits in a \ufb02attened host system. In the inner regions of interest here, baryons dominate dynamically and starburst is presumably triggered by a strong gas in\ufb02ow due to galaxy merger, and turbulent dissipation and gas cooling are likely strong to yield \ufb02attened systems. This is of course fully in accord and self-consistent with the presumed existence of a thin \ufb02at central stellar disk that is the foundation of our working hypothesis. The inclination decay of the secondary, if initially exists, can be due to dynamical friction with the stars on a larger spatial scale with an overall anisotropic velocity distribution, i.e., larger than the central stellar disk of size of \u223c100pc, that operate on a time scale likely in the range of 0.1 \u22121Gyr. Note for example the dynamical friction time is we \ufb01nd tDF = 1Gyr and 0.1Gyr for a 1 \u00d7 107 M\u2299black hole at 0.77kpc and 0.24kpc, respectively, in a spherical system with a circular velocity of 189 km/s. Thus, the co-planar condition for the orbital plane of the secondary and the central stellar disk is physically plausible, when it reaches the outer edge of the central disk. Even if the central disk and the orbit of the secondary is misaligned when the latter reaches the outer edge of the former, dynamical friction from that point onward will subsequently align it with the disk on the dynamical friction time scale, i.e., order of an e-folding in radius. Since most of the TDEs occur in the innermost region, one or two e-folding in radius can be spent to re-align the secondary with the central stellar disk with little e\ufb00ect on the overall TDE rate (and repeating time scale). Another issue worth clarifying is the orbital eccentricity of the inspiraling black hole, since we have implicitly assumed zero eccentricity in the derivation of Eq (8,9,10). However, this assumption serves only as a su\ufb03cient but not necessary condition for dynamical friction to operate. That it, even in a zero eccentricity orbit, the secondary still experiences dynamical friction force due to the non-zero asymmetric drift velocity v2 = \u03c32/vc. Any signi\ufb01cant eccentricity would render the relative velocity of the inspiraling black hole to the embedding stars possibly signi\ufb01cantly above \u223c\u03c32/vc, which would increase an additional dynamic friction force in the radial direction, leaving the tangential dynamic friction force unchanged. Nonetheless, one notes that if the secondary were in a radial orbit, then the \u201ccruise\u201d radial velocity due to the balance between gravity and the dynamical friction force due to the three-dimensional component (that dominates at small radii) can be shown to be equal to vc. In this case, we \ufb01nd that the total number of TDEs per PSB is \u2013 9 \u2013 in the range of \u2264103 for the \ufb01ducial case of M2 = 107 and vc = 189 km/s. Such a case would be much lower and hence inconsistent with the observationally inferred TDE rate of 105 \u2212106 per PSB (French et al. 2016). Therefore, one needs to make sure that increasing radialization of the orbit of the secondary is avoided, if the initial eccentricity is not identically zero. We now check two approximately bracketing cases to settle the issue. First, let us continue to consider the case of an isothermal sphere density pro\ufb01le. The apsides in a gravitational potential \u03c6(r) with speci\ufb01c energy E and speci\ufb01c angular momentum J are the two roots of the following equation (Eq 3-13 in Binney & Tremaine 1987): De\ufb01ning the orbital eccentricity e as ra/rp = (1 + e)/(1 \u2212e) with ra = r0(1 + e) [and rp = r0(1 \u2212e)], where rp and ra are the perigalacticon and apogalacticon distance, respectively, it can then be shown that, to the lowest order in e, the speci\ufb01c total energy and speci\ufb01c angular momentum are E = (1 2 + 7e2 6 )v2 c and J = r 1 \u22125e2 3 vcr0, (21) where we have de\ufb01ned the normalization of the logarithmic gravitational potential energy for an isothernal density pro\ufb01le such that \u03c6(r) = v2 c ln r r0 without loss of generality. Note that additional, higher order terms in e would be needed when e \u2192 p 3/5 as Eq (21) shows and it is also possible that orbits become unstable when e becomes too large. We consider here that e is not too large initially. From Eq (21) it is seen that E is a function of and decreases with decreasing eccentricity e. This indicates that in the presence of any energy dissipation, the orbit tends to zero eccentricity. It is also seen that the rate of decrease of eccentricity is de/dE \u221d1/e hence the time scale of circularization takes place on the similar time scale as the energy dissipation time scale (i.e, the dynamical friction time scale) when e \u226b0 but accelerates when e \u21920. Thus, the circularization time scale is about equal to dynamical friction time scale, if the orbit starts with a signi\ufb01cant eccentricity but may take a much shorter time scale for an initially nearly circular orbit. We stress that this outcome of circularization is derived based on a logarithmic potential corresponding to a \ufb02at rotation curve. While it is a good assumption, as simulations have shown, it is still prudent to stress that circularization is not necessarily the only outcome in general, as we show now. Consider next the following simpli\ufb01ed problem: the black hole moving in an eccentric orbit about a dominant point mass is subject to a frictional force that is a function of both the distance to the center and velocity. We assume that the gravitational e\ufb00ect due to the frictional matter is negligible. A further simplication is made for the convenience of calculation: the dynamical e\ufb00ect due to the frictional force is small enough so that a Keplerian (closed) orbit remains a good approximation for each full orbit. We adopt the units such that the speci\ufb01c total energy of the orbiting black hole is E = \u22121 2, and the speci\ufb01c angular momentum is J = \u221a 1 \u2212e2. With the familiar expressions for the distance to the focus r, the tangential velocity v\u03c6 and the magnitude of the total velocity v: r = (1 \u2212e2) (1 + e cos \u03b8), v\u03b8 \u2261rd\u03b8 dt = (1 + e cos \u03b8) (1 \u2212e2)1/2 , v = r 2 r \u22121, (22) where \u03b8 is the true anomaly, being zero at perigalacticon. Since e2 = 1 + 2EJ2, utilizing various expressions above, we have \u2206e = (1 \u2212e2)1/2e\u22121 \u0002 (1 \u2212e2)1/2\u2206E \u2212\u2206J \u0003 \u2261(1 \u2212e2)1/2e\u22121I, (23) \u2013 10 \u2013 where we shall de\ufb01ne \u2206e, \u2206E and \u2206J as the change of eccentricity, speci\ufb01c total energy and speci\ufb01c angular momentum, respectively, per full radial orbit. We now examine the term I de\ufb01ned by the last de\ufb01nition equality in Eq (23). To be tractable, let the acceleration due to frictional force have the following powerlaw velocity and radial dependencies: \u20d7 a = \u2212Ar\u03b1v\u03b2\u20d7 v, (24) where A is a positive constant, \u03b2 a constant, \u03b1 a constant slope, and \u20d7 v and v the velocity vector and its magnitude, noting that the radial dependence is inherited from the density\u2019s radial pro\ufb01le, \u03c1(r) \u221dr\u03b1. While \u03b1 may be non-positive in most physical contexts, our derivation does not impose any constraint. Gathering, we express I \u2261(1 \u2212e2)1/2\u2206E \u2212\u2206J = \u22122(1 \u2212e2)1/2A Z P/2 0 r\u03b1v\u03b2(\u20d7 v \u00b7 \u20d7 v)dt + 2A Z P/2 0 r\u03b1v\u03b2|\u20d7 r \u00d7 \u20d7 v|dt = 2A Z \u0398 0 r\u03b1\u2212\u03b2/2+1(2 \u2212r)\u03b2/2(r \u22121)d\u03b8, (25) where P is the period of a full radial orbit with the integration going from perigalacticon to apogalacticon, and \u0398 the azimuthal advance per half radial period, equal to \u03c0 in this case of closed orbits. To proceed, we change the integration element from d\u03b8 to the length element along the ellipse dl = rd\u03b8. Now the last equality in Eq (25) becomes I = 2A Z C/2 0 r\u03b1\u2212\u03b2/2(2 \u2212r)\u03b2/2(r \u22121)dl, (26) where C/2 is the half circumference of the orbit with the integration going from perigalacticon to apogalacticon. With the integration variable now changed to l that is invariant of the vantage point, one is free to move the center from one focus to the other by switching the radius from r to 2 \u2212r to obtain an identity I = \u22122A Z C/2 0 r\u03b2/2(2 \u2212r)\u03b1\u2212\u03b2/2(r \u22121)dl. (27) Taking the arithmetic average of Eq (26) and Eq (27), one obtains I = Z C/2 0 A(r \u22121)[r\u03b1\u2212\u03b2/2(2 \u2212r)\u03b2/2 \u2212r\u03b2/2(2 \u2212r)\u03b1\u2212\u03b2/2]dl. (28) One sees that for \u03b1 = \u03b2, I in Eq (28) is identically zero, meaning \u2206e = 0 in Eq (23) for any initial e. This thus indicates that the orbital eccentricity of a slowly inspiraling black hole under a frictional force of the form \u2212A(rv)\u03b1\u20d7 v (where A is a positive constant) is non-changing. For \u03b1 > \u03b2, \u2206e will be greater than zero, meaning that the orbit will be increasingly radialized during the inspiral, whereas for \u03b1 < \u03b2 the orbit will be increasingly circularized. Physically, this can be understood as a result of relatively higher loss of angular momentum per unit loss of energy hence gain of eccentricity at the perigalacticon as compared to a lower gain of angular momentum per unit gain of energy hence gain \u2013 11 \u2013 of eccentricity at the apogalacticon, for \u03b1 > \u03b2, thus leading to a net radialization over a complete orbit. For \u03b1 < \u03b2, the opposite holds. Let us consider two relevant applications of this result. First, in the standard three-dimensional dynamical friction case (Chandrasekhar 1943), \u03b2 = \u22123. Thus, unless the density slope is steeper than \u22123, the eccentricity is to increase under such frictional force, thus leading to radialization of the orbit spiraling inward. Second, in the standard two-dimensional dynamical friction case (Eq 8), we \u03b2 = \u22121 for v/\u03c3 \u226b1 and \u03b2 = 0 for v/\u03c3 \u226a1. Therefore, in this case, for any density pro\ufb01le that increases with decreasing radius, the orbit tends to circularize with time. In a more detailed calculation using dynamical friction formula that includes e\ufb00ects due to stars moving faster than the inspiraling black hole, Dosopoulou & Antonini (2017) conclude that for \u03b1 < \u223c\u22122, the orbit of the inspiraling black hole tends to radialization, overlapping with the radialization range of \u03b1 \u2264\u22123 found here. Overall, considerations of two bracketing examples suggest that, on the one hand, orbital circularization is likely achieved if the density pro\ufb01le is close isothermal regardless whether the medium for dynamical friction is also gravitationally dominant. On the other hand, at the other end of the spectrum where the central mass gravitationally dominates, the dynamical friction may lead to radialization if the velocity distribution of the medium is largely three-dimensional, whereas it leads to circularization if the velocity distribution of the medium is largely two-dimensional. Since in an oblate velocity distribution, dynamical friction leads to inspiraling black hole becoming co-planar, circularization should also ensue in this case so long as enough dynamical friction takes place after becoming co-planar. Thus, in the physical con\ufb01guration of an overall oblate stellar distribution along with a thin stellar disk in the central region that we propose here, the only likely situation where circularization does not occur is when the secondary black hole directly lands at a radius to which the interior stellar mass is not signi\ufb01cantly greater than the mass of the inspiraling black hole. Such a situation is not expected to happen in practice. Anyway, since we have already assumed that the inner rin (Eq 5) is where the interior stellar mass of the disk is equal to the mass of the inspiraling black hole, such a situation is moot. 3. Predictions 3.1. TDE Repeaters To illustrate, in the limit v \u226b\u03c3, which is the case when the secondary has migrated into the inner region of the disk, the second term of Eq (18) gives R(v, \u03c3) = \u03b7v3 cj2 lc 2Gm\u2217\u03c3vr2 = 0.034\u03b7( vc 189 km/s)( vc 10\u03c3)(vc v )( jlc 1.2 \u00d7 1023cm2/s)2( r 1pc)\u22122 yr\u22121, (29) which is indicative that TDEs may re-occur in the same PSBs within an accessible time scale. To gain a more quantitative assessment, we have performed a simple analysis with the following steps. (1) We use (the inverse of) Eq (18) to obtain the mean expectation value of time interval between two successive TDEs, \u00af \u2206t, when one just occurred at a radius r. (2) With the expectation value \u00af \u2206t we use the normalized Poisson distribution to obtain the probability distribution function as a function of time interval (\u2206t) between the TDE that just occurred at r and the next one, P(r, \u2206t). \u2013 12 \u2013 (3) We convolve P(r, \u2206t) with Eq (20) to obtain the overall mean probability distribution function as a function of time interval, P(\u2206t). Generally, P(\u2206t) is a function of three variables, \u03b7, \u03c3/vc and M2 (if M1 can be related to M2 or expressed by vc). The total number of TDEs per PSB, Ntde (Eq 20), is a function of \u03b7, \u03c3/vc and M2 as well. Therefore, if observations can provide constraints on Ntde, only two degrees of freedom are left. 0.001 0.001 0.001 0.001 0.001 0.1 0.1 0.1 0.1 0.1 1 1 1 1 1 3 3 3 3 10 10 10 25 25 0.1 0.1 0.1 0.1 0.1 1 1 1 1 1 3 3 3 3 3 10 10 10 10 25 25 25 50 50 4 4 4 4 4 4.5 4.5 4.5 4.5 4.5 5 5 5 5 5 6 6 6 6 6 0.5 0.6 0.7 0.8 0.9 1 0 0.05 0.1 0.15 0.2 /vc repeat probability in 1 yr repeat probability in 5 yr total TDE per galaxy, M2=107 cs=10km/s Fig. 2.\u2014 shows contours of probability P(\u2206t) in percent for repeating TDEs within a time interval of \u2206t = 1yr (blue dotted contours) and \u2206t = 5yr (red dot-dashed contours), respectively, on the two-dimensional parameter plane of (\u03b7, \u03c3/vc), where \u03c3 is the velocity dispersion of stars in the disk and \u03b7 is the fraction of stellar mass on the disk. The black contours are log Ntde per PSB. Also shown as horizontal magenta dot-dashed line is an indicative case where the vertical velocity dispersion is equal to sound speed of atomic cooling gas gas of temperature 104K, out of which stars in the disk may have formed. The \ufb01ducial values used are M2 = 107 M\u2299and rin = 1.2pc. Note that in computing the cross section of TDEs, we remove the area inside the event horizon of the secondary assuming a Schwarzschild black hole for all calculations. In Figure 2 we place contours of P(\u2206t) for \u2206t = 1yr (blue dotted contours) and \u2206t = 5yr (red dot-dashed contours), respectively, on the two-dimensional parameter plane of (\u03b7, \u03c3/vc). The two black contours are the current observational constraint of Ntde = 105 \u2212106 per PSB, corresponding to 10\u22124 \u221210\u22123yr\u22121 per PSB with a time span of 1Gyr (French et al. 2016) [also see Law-Smith et al. (2017); Graur et al. (2018)]. Also shown as horizontal magenta dot-dashed line is an indicative case where the vertical velocity dispersion is equal to sound speed of atomic cooling gas gas of \u2013 13 \u2013 temperature 104K, out of which stars in the disk may have formed. Several points are noted. First, as expected, the total number of TDEs per PSB tends to increase towards the lower-right corner of high \u03b7 and low \u03c3/vc, due primarily to the increase of the number density of stars in the disk. Second, if disk thickness is not less than 10 km/s, due to either fragmentation of gas disk at atomic cooling temperature and/or possible additional heating subsequent to formation of the stellar disk including heating by the secondary itself during its inspiral, then, an observational constraint of Ntde > 105 per PSB would require \u03b7 \u22650.87 (where the purple line intersects that black contour curve), i.e., the disk component is dominant in the inner region. Third, an observational constraint of Ntde > 105 per PSB also indicates that the thickness of the disk cannot exceed \u03c3/vc \u223c0.1, a limiting case when \u03b7 = 1. Finally, for Ntde = 105 per PSB, we see that there are regions where a repeater could occur with 2 \u221210% probability within a year per PSB in this particular case. Within \ufb01ve years, there is parameter space where 12 \u221228% probability is seen in this particular case. While rin may be low-bounded by Eq (5), it is possible that star formation may be truncated or \ufb02attned at a larger radius. Thus, we check how results depend on this. In the top-left panel of Figure 3 show a case that is the same as that shown in Figure 2 except one di\ufb00erence: rin = 3.6pc instead of 1.2pc. It is seen that the available parameter space for producing Ntde = 105 \u2212106 per PSB is compressed towards lower \u03c3/vc and higher \u03b7. But there is parameter space still available for explaining the observed abundance of TDEs even in this case. A large change is in TDE repeat frequencies: it is seen that there is no parameter space where a TDE may repeat at a probability greater than 0.1% within one year. There is a limited region in the parameter space where 0.1% probability exists for a TDE to repeat within 5 yr. It is possible to argue both ways as to which physical con\ufb01guration of the two cases shown is more \ufb01ne-tuned. Absence of some introduced scale, it seems more natural to suppose that the stellar disk could extend to some small radii of no particular choice, with rin imposed only because of the dynamical reason for the secondary to inspiral, as in Eq (5). Thus, we suggest that rin = 1.2pc in this case is a less \ufb01ne-tuned outcome. Recall that the maximum black hole mass for disrupting a main sequence star is about 108 M\u2299 for a Schwarzschild black hole (see Eq 5). The top-right panel of Figure 3 displays the case for M2 = 5 \u00d7 107 M\u2299with an appropriate rin according to Eq (5). A comparison between it and Figure 2 indicates that a more massive black hole tends to only slightly enhance both the overall rate of TDEs per galaxy and the probability of repeaters on relevant times scales. However, the range of \u03b7 for achieving the same Ntde = 105 is enlarged, when constraining \u03c3 \u223c10 km/s, to \u03b7 \u22650.5. But the overall rate and repeater probability contours do not change dramatically. The reason for this week dependence on M2 is due to a larger, removed cross section inside the event horizon that almost compensates the increased tidal radius for a larger black hole, among other factors. Next, we consider a case of merger of two lower mass galaxies, with M1 = M2 = 4 \u00d7 106 M\u2299, and rin determined according to Eq (5). The bottom-left panel of Figure 3 shows the result, for which we note three points. First, the model can no longer accommodate the observed > 105 TDEs per PSB, except in a very small parameter space at \u03b7 > 0.98 and \u03c3/vc \u223c0.07 \u22120.08. Second, in the available parameter space, the repeating rate is, however, comparable to the \ufb01ducial case shown in Figure 2. Combining results for the models, we conclude that, while the overall abundance of \u2013 14 \u2013 0.001 0.001 0.001 0.001 0.1 0.1 0.1 0.1 1 1 1 1 3 3 3 10 10 25 0.1 0.1 0.1 0.1 1 1 1 1 3 3 3 3 10 10 10 25 25 50 4 4 4 4 4 4.5 4.5 4.5 4.5 5 5 5 5 6 6 6 6 0.5 0.6 0.7 0.8 0.9 1 0 0.05 0.1 0.15 /vc repeat probability in 1 yr repeat probability in 5 yr total TDE per galaxy, M2=107, 3  rin cs=10km/s 0.001 0.001 0.1 0.1 0.1 0.1 0.1 1 1 1 1 1 3 3 3 3 3 10 10 10 25 25 0.1 0.1 0.1 1 1 1 1 1 3 3 3 3 3 10 10 10 10 10 25 25 25 50 50 4 4 4 4.5 4.5 4.5 4.5 4.5 5 5 5 5 5 6 6 6 6 6 0.5 0.6 0.7 0.8 0.9 1 0 0.05 0.1 0.15 0.2 /vc repeat probability in 1 yr repeat probability in 5 yr total TDE per galaxy, M2=5  107 cs=10km/s 0.001 0.001 0.001 0.001 0.1 0.1 0.1 0.1 0.1 1 1 1 1 3 3 3 10 10 25 0.1 0.1 0.1 0.1 0.1 1 1 1 1 1 3 3 3 3 3 10 10 10 25 25 50 4 4 4 4 4 4.5 4.5 4.5 4.5 4.5 5 5 5 5 5 6 6 6 6 6 0.5 0.6 0.7 0.8 0.9 1 0 0.05 0.1 0.15 0.2 /vc repeat probability in 1 yr repeat probability in 5 yr total TDE per galaxy, M2=4  106 cs=10km/s 0.001 0.001 0.001 0.001 0.1 0.1 0.1 0.1 1 1 1 1 1 3 3 3 3 3 10 10 10 10 10 25 25 25 25 0.1 0.1 0.1 0.1 1 1 1 1 1 3 3 3 3 3 10 10 10 10 10 25 25 25 25 25 50 50 50 50 50 4 4 4 4.5 4.5 4.5 4.5 4.5 5 5 5 5 5 6 6 6 6 0.5 0.6 0.7 0.8 0.9 1 0 0.05 0.1 0.15 0.2 /vc repeat probability in 1 yr repeat probability in 5 yr total TDE per galaxy,  (r/100pc)-0.1 cs=10km/s Fig. 3.\u2014 Top-left: the physical parameters of this model are identical to those used for Figure 2 except one di\ufb00erence: rin = 3.6pc instead of 1.2pc. Top-right: the physical parameters of this model are identical to those used for Figure 2 except one di\ufb00erence: M2 = 5\u00d7107 M\u2299with an appropriate rin according to Eq (5). Bottom left: the physical parameters of this model are identical to those used for Figure 2 except one di\ufb00erence: M2 = 4 \u00d7 106 M\u2299with an appropriate rin according to Eq (5). Bottom right: the physical parameters of this model are identical to those used for Figure 2 except one di\ufb00erence: the mass fraction in the disk is allowed to increase slowly inward, equal to lesser of \u03b7(r/100pc)\u22120.1 and unity. TDEs increases with the black hole mass, the repeating rate per PSB depend weakly on the SMBH mass for a given Ntde, as long as the inner radius of the central stellar disk is not cuto\ufb00. Finally, the bottom-right panel of Figure 3 shows the result for a case where we let the mass fraction of the disk component to increase inward from 100pc to rin as \u03b7(r/100)\u22120.1, capped of course at unity. We see that the available parameter space is signi\ufb01cantly enlarged compared to the \ufb01ducial case, with the shape of contours seen to \ufb02atten out horizontally, while the repeater probability at a given Ntde remains roughly in the same range. \u2013 15 \u2013 To summarize, in our model the overall rate of TDEs per PSB, averaged over time, is set by the long dynamical friction process for the secondary to inspiral following galaxy merger. A unique characteristics of our model is that once having reached and aligned with the central stellar disk, the overall migration time interval over which the bulk of the TDEs occur is much shorter than the typical lifetime of PSBs of \u223c1Gyr. Consequently, one important prediction of this model is that TDEs may repeat on a reasonable time scale. While a precise repeating rate is di\ufb03cult to nail down, because we are not certain about the parameter space of (\u03b7, \u03c3/vc) that nature picks, we see that within (1,5) years the repeating probability falls in the range of (0.1 \u221210%, 3 \u221230%) if Ntde = 105, under the condition that M2 = 4 \u00d7 106 \u22125 \u00d7 107 M\u2299and no inner cutto\ufb00of stellar disk (i.e., rin is determined by Eq 5). Thus, assuming Ntde = 105 and with a sample of 1000 TDEs, it appears that at least one repeat may be detected within one year; alternatively, with a sample of 30 TDEs, at least one repeat may be detected within \ufb01ve years. If the current observationally inferred Ntde range of 105 \u2212106 indeed holds up, the above estimated range of repeating probability would be an underestimate. If observations do \ufb01nd such repeaters, they would provide strong support for this model. With enough statistics and time baseline, it may then be possible to tease out useful information on the physical con\ufb01guration of the central disk in terms of parameter space of (\u03b7, \u03c3/vc, M2). A statistical comparison between the number of PSBs with TDEs and those without may additionally shed luminous light on the temporal distribution of TDEs in PSBs and the distribution of the time for the secondary to land on the central stellar disk, which may be ultimately linked to galaxy formation process. As a reference, in a model with a delay time distribution (DTD) of t\u22120.5 (Stone et al. 2018), generously extending to 1Myr at low end and normalized to Ntde = 106 TDEs over 1Gyr in a PSB, the probability of repeaters within \ufb01ve years is practically zero (2.1 \u00d7 10\u221232). It is appropriate to prudently ask the following question: is the condition that required to accommodate the observed TDE rates in PSBs physically plausible? In particular, is \u03c3/vc \u223c0.1 viable? Let us examine what this means with respect to the column density, volumetric density and temperature of the gas disk forming the disk stars. Adopting vc = 189 km/s for a Mestel disk, we \ufb01nd that surface density \u03a3(r) = 276(r/1pc)\u22121g cm\u22122 and a volumetric density nH = 2.7 \u00d7 108(v/10\u03c3)(r/1pc)\u22122 cm\u22123. The mid-plane pressure due to gravitational mass above is p = \u03c0G\u03a32(r)/2 = 8.0 \u00d7 10\u22124(r/1pc)\u22122dyn cm\u22122. This means that, if the downward gravity is balanced by thermal pressure, the gas temperature would have to be 2.2 \u00d7 104(10\u03c3/vc) K, where a molecular weight of unity is used for simplicity. We see that \u03c3/vc = 0.1 and 0.05 would imply a gas temperature of 2.2 \u00d7 104 K and 1.1 \u00d7 104 K, respectively. This is in the exact regime where gas has been cooled rapidly by atomic cooling processes after infall shock but has yet to be cooled further down by molecular cooling (and low temperature metal cooling) processes. At a density of 5.4 \u00d7 108 cm\u22123 and T = 1.1 \u00d7 104K for \u03c3/vc = 0.05 at r = 1pc, the Jeans mass is 7.3 \u00d7 102 M\u2299. It indicates that the gas disk at r \u223c1pc would fragment at T \u223c104K, which may subsequently form stars directly from atomic cooling gas or may go through the molecular phase \ufb01rst and then form stars. In either case, it appears quite plausible that a disk of height to radius ratio of 0.05 \u22120.1 for vc = 189 km/s at r \u223c1pc and larger radii (note the weaker increase of Jeans mass than the mass on the Mestel disk with increasing radius at a given gas temperature). It is in fact quite remarkable that this completely independent assessment of the likely \u03c3/vc from a physical point of view of gas cooling and fragmentation is almost exactly what is required for producing the observed abundance \u2013 16 \u2013 of TDEs in PSBs. 3.2. TDEs Spatially O\ufb00set from Center and Complexities of Debris Dynamics 0 1 2 3 log r (pc) 2 3 4 5 log Ntde(>r) for solid curves -2 -1 0 1  black dot in Figure 2  red square in Figure 2 -2 -1 0 1 log   t(<r) (yr) for dashed curves Fig. 4.\u2014 shows as solid curves the cumulative (from large to small radius) radial distributions of TDEs for two cases, corresponding to the case with (\u03b7, \u03c3/vc) = (0.9, 0.059) shown as a solid black dot in Figure 2 and the case with (\u03b7, \u03c3/vc) = (0.98, 0.088) shown as a solid red square in Figure 2. Also shown as corresponding dashed curves are the mean interval between successive TDEs cumulative up to that point from the small radius end, as indicated by the right y-axis. TDEs in our model do not occur about the central black hole. Figure 4 shows the cumulative (from large to small radius) radial distributions of TDEs for two combinations of (\u03b7, \u03c3/vc) indicated as the black dot and red square in Figure 2. We see that depending on the physical con\ufb01guration (\u03b7, \u03c3, vc, rin and M2) of the system the distribution varies. Despite the uncertainties, in the two cases it is seen that 90% of TDEs occur with a spatial o\ufb00set of 15\u221250pc from the central black hole. Trying to detect this spatial o\ufb00set will be a challenging but rewarding undertaking. If con\ufb01rmed, it would provide unambiguous evidence for TDEs occurring around the secondary that is inspiraling and would have profound implications for dynamics of SMBH inspiral and galaxy formation as a whole. It will also have important implications for future gravitational wave observations aimed at detecting mergers of SMBHs, e.g., by LISA. As an example, an angular separation of 0\u201d.1 would correspond \u2013 17 \u2013 to an o\ufb00set of 12pc at a distance of 25Mpc. Such an o\ufb00set would have been resolved even with current capabilities. Leloudas et al. (2016) measure a spatial o\ufb00set of 131\u00b1192pc, corresponding to an angular o\ufb00set of 36 mas \u00b1 53 mas for ASASSN-15lh at z = 0.2326; in this case, due to the large distance the o\ufb00set is ambiguous. Combining detections of TDEs from large upcoming surveys, including the Zwicky Transient Facility (ZTF), eROSITA, the Large Synoptic Survey Telescope (LSST), with the next-generation large ground-based telescopes with AO capabilities may routinely enable this for nearby sources, which will certainly provide a strong test of the model once a su\ufb03cient sample is produced and statistical characterization possible. For a typical main sequence star TDE, the inbound debris at the deepest orbits has an energy of about (\u2212vorbv\u2217), where vorb is orbital velocity at the tidal radius and v\u2217stellar escape velocity, roughly corresponding to an orbital period of order one year. Debris with an energy that is ten times lower will have an orbital period of about 30yr, and so on. Let us take debris on a one-year orbit to illustrate. For a secondary of mass 107 M\u2299, it corresponds to an eccentric orbit with a semi-major axis of \u223c10\u22123pc. If the period of the secondary is on an orbit of radius 1pc about the center of the galaxy, then its period is 3.3 \u00d7 104yr and the rate of spatial displacement of the secondary would be \u223c10\u22124pc/yr. The tidal radius of main sequence stars about the secondary is 5 \u00d7 10\u22126pc (Eq 16). Thus, when the debris is at the apobothron about the secondary, the e\ufb00ect of accelerated motion of the secondary is at a level of 10\u22124pc/10\u22123pc \u223c10% per orbit of the debris, where the debris may be be able to make orbital adjustments to follow the gravitational center of the secondary in a fashion akin to a three-dimension precession. However, when the debris is at the peribothron (i.e., around the tidal radius), it will not be able to make orbital adjustments promptly enough to form a smooth orbit due to the accelerated motion of the secondary. While detailed simulations will be required to obtain more quantitatively precise results for a wide variety of orbital con\ufb01gurations of the secondary, it is not di\ufb03cult to see that light curves and also the spectral properties of TDEs could be much more varied than the case of a static black hole. The static SMBH at the center of the galaxy may also produce TDEs. In this case, the relativistic precession is often invoked to cause debris to interact and circularize. For reference, we merely restate that the GR precession period Ppr of a debris with an orbital period Pde with eccentricity e at the tidal radius is Ppr = Pde(1 \u2212e2) 3 ( c vt )2 = 3.4Pde(1 \u2212e2)( M2 107 M\u2299 )\u22122/3( r\u2217 R\u2299 )( m\u2217 M\u2299 )\u2212/3, (30) where vt is the orbital velocity at tidal radius as the peribothron. It is seen that for debris on orbits of periods on the order of one year, relativistic precession will circularize debris on the order of the period. In this simpler case, the structure would remain two-dimensional throughout. Therefore, light curves are expected to be smooth. 3.3. Narrow and Extended Narrow Line Regions in Post-Starburst Galaxies Are there some possible e\ufb00ects of the UV radiation from the TDEs on gas on galactic scales? Let us examine three time scales. First, the light travel time to 1 \u221210kpc from the central region \u2013 18 \u2013 where TDEs take place is about ttr = 3\u00d7103\u22123\u00d7104yr. Second, for a gas cloud of hydrogen volume density nH and temperature of 104K, the recombination time is trec = 1.2 \u00d7 103(nH/100cm\u22123)\u22121yr. Third, the time interval between successive TDE events, \u2206ttde. In Figure 4 we show as dashed lines \u2206ttde cumulatively as a function of radius inside-out. We see \u2206ttde \u223c1 \u221230yr over the bulk of the \u223c105 TDE events in each case. If both conditions, \u2206ttde \u2264ttr and \u2206ttde \u2264trec, are satis\ufb01ed, which is true as long as nH is not greater than 104cm\u22123 or so, then, the gas cloud would \u201csee\u201d a steady UV light bulb at the center over a period of 1Myr or so, and is kept fully ionized despite the actual \u201c\ufb02ickering\u201d of light, over this period of a \ufb02urry of TDEs. While the electron densities in some inner narrow line regions may exceed 104 cm\u22123, the observationally inferred electron densities on scales of kpc or larger are found to be in the range from a few 102 cm\u22123 to mid 103 cm\u22123 (e.g., Nesvadba et al. 2006; Greene et al. 2011; Arav et al. 2013). One notes that for a given PSB of an age 0.1\u22121Gyr, this intense period of TDEs makes up only small fraction, 0.1 \u221210%, of the their overall age. Thus, it is likely that a blind survey of PSBs will only see a small fraction of them capable of enabling narrow or extended narrow line regions. For PSBs with observed TDEs it may be expected that most of them may possess narrow or extended narrow line regions, to the extent that suitable gas clouds on these scales exists. In other words, the fraction of PSBs with narrow or extended narrow line regions for those experiencing TDEs is now primarily a function of the abundance of gas clouds on these scales, not the availability of radiation sources to ionize them. Since PSBs have experienced a signi\ufb01cant merger event in the last 0.1 \u22121Gyrs, it may be that such gas clouds are ubiquitous due to the merger and/or subsequent starburst driven out\ufb02ows and/or interactions between out\ufb02ows and accreting gas on galactic scales. We suggest that an observational campaign to search for narrow or extended narrow line regions in PSBs, especially those with detected TDEs, may be very useful to provide an additional, indirect test of the model. Possibly related, the observed enhancement of LINERs in PSB galaxies (e.g., Yan et al. 2006; Yang et al. 2006) may be powered by TDEs in both radiation and, in part, the emitting gas that is the unbound debris. 4. Conclusions Under a simple tractable example of an isothermal stellar distribution with a Mestel disk component of mass fraction \u03b7 with a small velocity dispersion (\u03c3/vc \u22640.1) and a three-dimensional spherical component of mass fraction 1\u2212\u03b7, we calculate the dynamics of the inspiral of the secondary SMBH through the disk midplane, with the aim to quantify the tidal disruption event rates by the inspiraling SMBH. We envision that such a central stellar disk of size \u2264100pc may be produced following a galaxy merger and it a part of the starburst that subsequently fades to turn into a post-starburst galaxy some 0.1 \u22121Gyr later. Insofaras the secondary is made co-planar with the disk, the results depend little on either the outer or the inner radius of the disk, as long as the disk is not cuto\ufb00prematurely in the interior. Coplanarity may be inevitable for a system even with a moderate amount of oblateness and an anisotropic velocity distribution, where the dynamical friction drag tends to align the inspiraling object with the disk plane on the dynamical friction time scale. At radii larger than 30 \u2212100pc (depending on the relative mass fractions of the disk and the \u2013 19 \u2013 bulge components) the inspiraling SMBH moves relative to the stars in the disk, at a low velocity often referred to the asymmetric drift in our Galaxy, and experiences an e\ufb03cient two-dimensional dynamical frictional force. At smaller radii, dynamical friction of the secondary with the bulge stars may be expected to be more e\ufb03cient in the viable parameter space in our model. In either regime, the TDEs are produced by stars in the disk. The two main parameters are the ratio of velocity dispersion to the circular velocity \u03c3/vc and the fraction mass of the disk component \u03b7 in the region. With \u03c3/vc \u223c0.03 \u22120.15 and \u03b7 > 0.7, it is shown that 105 \u2212106 TDEs of solar mass main sequence stars per post-starburst galaxy may be produced by the secondary of mass 106 \u2212108 M\u2299. The vast majority of TDEs by the secondary in a post-starbust galaxy occurs within a space of time of \u223c30Myr or shorter. Thus, the apparent age distribution of post-starburst galaxies of \u223c0.1 \u22121Gyr is not the duration over which TDEs occur in any individual post-starburst galaxy, rather it re\ufb02ects the rich variety of galaxy mergers and the range in time that it takes to bring the secondary to the central disk. To further test this model, we provide \ufb01ve unique predictions. \u2022 A unique prediction of this model is that TDEs may repeat on a time scale amenable to astronomers. While a precise repeating rate is di\ufb03cult to nail down, our model shows that, normalizing to a rate of 105 TDEs per post-starburst galaxy, with a sample of 1000 TDEs, at least one repeater may be detected within one year. Alternatively, on a time scale of \ufb01ve years with a sample of 30 TDEs, at least one repeater may be expected to occur. This will be imminently testable. \u2022 The second unique prediction is that the TDEs are expected to display a spatial o\ufb00set from the galactic center of \u223c1\u2212300pc for \u226599% of the TDEs. Combining upcoming detections of TDEs from ZTF, eROSITA and LSST with the next-generation large ground-based telescopes with AO capabilities should be able to detect this within a distance of 50 \u2212500Mpc for o\ufb00sets of 1 \u221210pc, which will provide an unambiguous test of the model, once a su\ufb03cient sample is produced and statistical characterization made. If detected, it will also shed useful light on future gravitational wave observations aimed at detecting mergers of SMBHs, e.g., by LISA. \u2022 Third, the accelerated motion of the secondary during the return \ufb02ight of the debris may cause their orbits to be three-dimensional to form a three-dimensional structure at some radius outside the tidal radius. This may complicate the prediction and possibly leads to a rich variety of light curves of TDEs. Detailed calculation on this front is deferred. \u2022 Fourth, the high cadence of TDEs may serve as a quasi-continuous UV source for galactic scale gas, since both the light travel and gas recombination times are longer that the mean cadence. Thus, it may be expected that post-starburst galaxies, especially those with detected TDEs, may possess narrow or extended narrow line regions, to the extent that the galaxy merger and/or the starburst driven out\ufb02ows have created suitable clouds there for the radiation to illuminate. A systematic survey can verify this. \u2022 Finally, since it is the inspiraling secondary disrupting the stars, the central SMBH is no longer required to be less massive than 108 M\u2299for a galaxy to produce TDEs. We note that the mass of the central SMBH for the TDE event ASASSN-15lh (Leloudas et al. 2016) is inferred to be (3 \u22126) \u00d7 108 M\u2299, based on the stellar mass or luminosity of the host galaxy, which would solidly \u2013 20 \u2013 place it in the impotent SMBH camp for producing TDEs of main sequence stars. The authors suggest a Kerr black hole to marginally get by. In our model, this is not a problem, since the mass of the secondary black hole could be lower than that of the central one. Incidentally, this TDE has a measured spatial o\ufb00set of 131pc from the galactic center, albeit with an undesirable 1\u03c3 errorbar of 192pc presently. I would like to thank an anonymous referee for critical and constructive reports and for checking every single term of the equations that greatly helped improve the paper. I would like to thank Ben Shappe, Decker French, Jane Dai, Iair Acavi and Tsvi Piran for helpful discussion, and Nick Stone for a wonderful talk that spawned this inquiry. I would like to thank Yukawa Insitute of Theoretical Physics for providing opportunity at short notice in the Yukawa seminar to give a talk on this work pre-publication. The research is supported in part by NASA grant 80NSSC18K1101.",
                    "introduction": "When a star happens to plunge inside the tidal radius of a supermassive black hole, it will be torn apart, producing a tidal disruption event (TDE) that provides a useful tool to probe gas and stellar dynamics around SMBH, and galaxy formation process potentially. For a solar mass main sequence star, the tidal radius is greater than the Schwarzschild radius for a SMBH less massive than 108 M\u2299. For sub-giant or giant stars, still more massive SMBHs are also able to produce TDEs, although their observable time scales become impractically long. Post-starburst galaxies, sometimes called E+A or K+A\u2019s, are characterized by spectra that are consistent with a starburst 0.1 \u22121Gyr ago followed by dormancy. They constitute a fraction of 0.2 \u22122%, depending on the observational de\ufb01nition, of all galaxies of comparable stellar masses at low redshift (e.g., Pattarakijwanich et al. 2016). Yet, current observations indicate that an overwhelming fraction of tidal disruption events (TDEs), presumably normal main sequence stars tidally torn apart by SMBHs at the center of galaxies, appear to occur in PSBs. For example, all six TDEs observed by ASASSN survey appear to occur in galaxies with spectral characteristics of PSBs (French et al. 2016; Law-Smith et al. 2017; Graur et al. 2018). This suggests that stars in PSBs have a factor about 100 more likely to provide TDEs. For a recent survey of models, see an excellent review by Stone et al. (2018). In this Letter a solution to this puzzle is sought and found. We show that an inspiraling SMBH plowing through the stellar disk that is part of the starburst can produce a su\ufb03cient number of TDEs to explain the observations. We also suggest several tests for the model. 1Princeton University Observatory, Princeton, NJ 08544; cen@astro.princeton.edu arXiv:1912.04372v1  [astro-ph.HE]  9 Dec 2019 \u2013 2 \u2013"
                },
                {
                    "url": "http://arxiv.org/abs/1609.03583v1",
                    "title": "UV Absorption Line Ratios in Circumgalactic Medium at Low Redshift in Realistic Cosmological Hydrodynamic Simulations",
                    "abstract": "Utilizing high-resolution cosmological hydrodynamic simulations we\ninvestigate various ultra-violet absorption lines in the circumgalactic medium\nof star forming galaxies at low redshift, in hopes of checking and alleviating\nthe claimed observational conundrum of the ratio of NV to OVI absorbers, among\nothers. We find a satisfactory agreement between simulations and extant\nobservational data with respect to the ratios of the following four line pairs\nexamined, NV/OVI, SiIV/OVI, NIII/OVI and NII/OVI. For the pairs involving\nnitrogen lines, we examine two cases of nitrogen abundance, one with constant\nN/O ratio and the other with varying N/O ratio, with the latter motivated by\ntheoretical considerations of two different synthetic sources of nitrogen that\nis empirically verified independently. Along a separate vector, for all line\npairs, we examine two cases of radiation field, one with the Haardt-Madau\nbackground radiation field and the other with an additional local radiation\nfield sourced by hot gas in the host galaxy. In all cases, two-sample\nKolmogorov-Smirnov tests indicate excellent agreements. We find that the\napparent agreements between simulations and observations will be strongly\ntested, if the bulk of current upper limits of various line ratios are turned\ninto actual detections. We show that an increase in observational sensitivity\nby 0.2 dex will already start to significantly constrain the models.",
                    "authors": "Renyue Cen, Mohammadtaher Safarzadeh",
                    "published": "2016-09-12",
                    "updated": "2016-09-12",
                    "primary_cat": "astro-ph.GA",
                    "cats": [
                        "astro-ph.GA"
                    ],
                    "main_content": "2.1. Hydrocode and Simulation Parameters We perform cosmological simulations with the AMR Eulerian hydro code, Enzo (Bryan et al. 2014). We use the following cosmological parameters that are consistent with the WMAP7-normalized (Komatsu et al. 2011) LCDM model: \u2126M = 0.28, \u2126b = 0.046, \u2126\u039b = 0.72, \u03c38 = 0.82, H0 = 100hkms\u22121Mpc\u22121 = 70kms\u22121Mpc\u22121 and n = 0.96. These parameters are also consistent with the latest Planck results (Planck Collaboration et al. 2014), if one adopts the Hubble constant that is the average between Planck value and those derived based on SNe Ia and HST key program (Riess et al. 2011; Freedman et al. 2012). We use the power spectrum transfer functions for cold dark matter particles and baryons using fitting formulae from Eisenstein & Hu (1999). We use the Enzo inits program to generate initial conditions. First we ran a low resolution simulation with a periodic box of 120h\u22121Mpc on a side. We identified two regions separately, one centered on a cluster of mass of \u223c2 \u00d7 1014 M\u2299and the other centered on a void region at z = 0. We then re-simulate each of the two regions separately with high resolution, but embedded in the outer 120h\u22121Mpc box to properly take into account large-scale tidal field and appropriate boundary conditions at the surface of the refined region. We name the simulation centered on the cluster \u201cC\" run and the one centered on the void \u201cV\" run. The refined region for \u201cC\" run has a size of 21 \u00d7 24 \u00d7 20h\u22123Mpc3 and that for \u201cV\" run is 31 \u00d7 31 \u00d7 35h\u22123Mpc3. At their respective volumes, they represent 1.8\u03c3 and \u22121.0\u03c3 fluctuations. The root grid has a size of 1283 with 1283 dark matter particles. The initial static grids in the two refined boxes correspond to a 10243 grid on the outer box. The initial number of dark matter particles in the two refined boxes correspond to 10243 particles on the outer box. This translates to initial condition in the refined region having a mean interparticleseparation of 117h\u22121 kpc comoving and dark matter particle mass of 1.07 \u00d7 108h\u22121 M\u2299. The refined region is surrounded by two layers (each of \u223c1h\u22121Mpc) of buffer zones with particle masses successively larger by a factor of 8 for each layer, which then connects with the outer root grid that has a dark matter particle mass 83 times that in the refined region. The initial density fluctuations are included up to the Nyquist frequency in the refined region. The surrounding volume outside the refined region is also followed hydrodynamically, which is important in order to properly capture matter and energy exchanges at the boundaries of the refined region. Because we still can not run a very large volume simulation with adequate resolution and physics, we choose these two runs of moderate volumes to represent two opposite environments that possibly bracket the universal average. We choose a varying mesh refinement criterion scheme such that the resolution is always \u2013 4 \u2013 better than 460/h proper parsecs within the re\ufb01ned region, corresponding to a maximum mesh re\ufb01nement level of 9 above z = 3, of 10 at z = 1 \u22123 and 11 at z = 0 \u22121. The simulations include a metagalactic UV background (Haardt & Madau 2012), and a model for shielding of UV radiation (Cen et al. 2005). The simulations also include metallicity-dependent radiative cooling and heating (Cen et al. 1995). The Enzo version used includes metallicity-dependent radiative cooling extended down to 10K, molecular formation on dust grains, photoelectric heating and other features that are different from or not in the public version of Enzo code. We clarify that our group has included metal cooling and metal heating (due to photoionization of metals) in all our studies since Cen et al. (1995) for the avoidance of doubt (e.g., Wiersma et al. 2009; Tepper-Garc\u00eda et al. 2011). Star particles are created in cells that satisfy a set of criteria for star formation proposed by Cen & Ostriker (1992). Each star particle is tagged with its initial mass, creation time, and metallicity; star particles typically have masses of \u223c105\u22126 M\u2299. Supernova feedback from star formation is modeled following Cen et al. (2005). Feedback energy and ejected metal-enriched mass are distributed into 27 local gas cells centered at the star particle in question, weighted by the speci\ufb01c volume of each cell (i.e., weighting is equal to the inverse of density), which is to mimic the physical process of supernova blastwave propagation that tends to channel energy, momentum and mass into the least dense regions (with the least resistance and cooling). We allow the whole feedback processes to be hydrodynamically coupled to surroundings and subject to relevant physical processes, such as cooling and heating, as in nature. The extremely inhomogeneous metal enrichment process demands that both metals and energy (and momentum) are correctly modeled so that they are transported into right directions in a physically sound (albeit still approximate at the current resolution) way, at least in a statistical sense. In our simulations metals are followed hydrodynamically by solving the metal density continuity equation with sources (from star formation feedback) and sinks (due to subsequent star formation). Thus, metal mixing and diffusion through advection, turbulence and other hydrodynamic processes are properly treated in our simulations. The primary advantages of this supernova energy based feedback mechanism are threefold. First, nature does drive winds in this way and energy input is realistic. Second, it has only one free parameter eSN, namely, the fraction of the rest mass energy of stars formed that is deposited as thermal energy on the cell scale at the location of supernovae. Third, the processes are treated physically, obeying their respective conservation laws (where they apply), allowing transport of metals, mass, energy and momentum to be treated self-consistently and taking into account relevant heating/cooling processes at all times. We use eSN = 1 \u00d7 10\u22125 in these simulations. The total amount of explosion kinetic energy from Type II supernovae with a Chabrier IMF translates to eSN = 6.6 \u00d7 10\u22126. Observations of local starburst galaxies indicate that nearly all of the star formation produced kinetic energy (due to Type II supernovae) is used to power galactic superwinds (e.g., Heckman 2001). Given the uncertainties on the evolution of IMF with redshift (i.e., possibly more top heavy at higher redshift) and the fact that newly discovered prompt Type I supernovae contribute a comparable amount of energy compared to Type II supernovae, it seems that our adopted value for eSN is consistent with observations \u2013 5 \u2013 and physically realistic. The validity of this thermal energy-based feedback approach comes empirically. In Cen (2012b) the metal distribution in and around galaxies over a wide range of redshift (z = 0 \u22125) is shown to be in excellent agreement with respect to the properties of observed damped Ly\u03b1 systems (Rafelski et al. 2012), whereas in Cen (2012a) we further show that the properties of OVI absorption lines at low redshift, including their abundance, Doppler-column density distribution, temperature range, metallicity and coincidence between OVII and OVI lines, are all in good agreement with observations (Danforth & Shull 2008; Tripp et al. 2008; Yao et al. 2009). This is non-trivial by any means, because they require that the transport of metals and energy from galaxies to star formation sites to megaparsec scale be correctly modeled as a function of distance over the entire cosmic timeline, at least in a statistical sense. 2.2. Analysis Method We identify galaxies at each redshift in the simulations using the HOP algorithm (Eisenstein & Hut 1998) operating on the stellar particles, which is tested to be robust and insensitive to speci\ufb01c choices of concerned parameters within reasonable ranges. Satellites within a galaxy down to mass of \u223c109 M\u2299are clearly identi\ufb01ed separately in most cases. The luminosity of each stellar particle in each of the Sloan Digital Sky Survey (SDSS) \ufb01ve bands is computed using the GISSEL stellar synthesis code (Bruzual & Charlot 2003), by supplying the formation time, metallicity and stellar mass. Collecting luminosity and other quantities of member stellar particles, gas cells and dark matter particles yields the following physical parameters for each galaxy: position, velocity, total mass, stellar mass, gas mass, mean formation time, mean stellar metallicity, mean gas metallicity, SFR, luminosities in \ufb01ve SDSS bands (and various colors) and others. We show, among others, that the simulated luminosity functions of galaxies at z = 0 are reasonably matched to observations (Cen & Chisari 2011). In the analysis presented here we choose randomly ten galaxies from our simulation that have properties that are similar to observed galaxies in the COS-HALO program (Werk et al. 2013, 2014) with respect to the star formation rate (SFR) and stellar mass. Some relevant properties of the ten simulated galaxies are tabulated in Table 1. A central galaxy is de\ufb01ned to be one that is not within the virial radius of a larger (halo-mass-wise) galaxy. To assist performing post-simulation analysis of the galaxies, we construct lookup tables of the abundances of various ions of elements nitrogen, oxygen and silicon as a function of logarithm of temperature (log T) and logarithm of ionization parameter (log U), for solar metallicity, using the photoionization code CLOUDY (v13.03; Ferland et al. 2013). For each selected simulated galaxy, we construct a cube with size of 320 kpc centered on the galaxy with resolution of 625 pc. We make the simplifying but reasonable assumption that the relevant absorbers are optically thin. Our calculations are performed for two cases of ionizing radiation \ufb01eld that the CGM in each galaxy is assumed to be exposed to. In the \ufb01rst \u2013 6 \u2013 Stellar M [1010 M\u2299] Halo M [1011 M\u2299] SFR [ M\u2299/yr] <T>[104K] <Z>(gas)[ Z\u2299] central galaxy 1.37 1.37 1.0 27.95 0.23 yes 1.56 1.17 1.5 13.77 0.31 yes 2.25 10.4 1.6 36.76 0.20 no 3.00 4.36 1.7 16.89 0.27 no 2.91 2.05 1.0 10.10 0.23 yes 3.03 2.45 1.6 14.74 0.30 yes 3.63 3.89 2.2 93.48 0.27 yes 3.24 4.92 1.8 25.05 0.16 yes 3.68 6.22 2.6 15.44 0.18 yes 3.97 3.19 1.6 20.79 0.13 yes Table 1: Properties of 10 simulated galaxies used in this study. case, we only use the HM background UV radiation \ufb01eld at z = 0. In the second case, we compute the ionizing UV radiation due to local, shocked heated gas within each concerned galaxy and use the sum of that and the HM background. The local UV ionizing radiation is computed as follows. We compute the emissivity (e\u03bd) [ergs\u22121cm3Hz\u22121sr\u22121] for each cell given its temperature and metallicity at the relevant energies, E = 47.3eV for SiIV, E = 97.88 eV for NV, E = 47.4 eV for NIII, E = 29.6 eV for NII and E = 138.1 eV for OVI ion. This is done by integrating the diffuse spectrum from CLOUDY between 97.88 eV, 1.2 \u00d7 97.88 eV for NV, as an example (similarly for other ions). The diffuse emission includes all gas processes, the free-free emission, radiative free-bound recombination, two-photon emission, and electron scattering, among others, for all elements in the calculation. For each cell the total luminosity density is computed as n2 \u00d7 \u2206V \u00d7 L\u03bd where n is the density and \u2206V its volume. The sum of local ionizing UV radiation luminosity density at a relevant wavelength is L\u03bb. To approximately account for the spatial distribution of local UV radiation sources without the expense of detailed radiative transfer, we compute the half luminosity radius (Re) of a galaxy, within which half of the local radiation luminosity in that galaxy originates. Then, we assign the local \ufb02ux to each cell with distance r from the center of the galaxy, approximately, as F\u03bb,r = L\u03bb 4\u03c0r2[1 + 2e\u2212r/(2Re)]. (1) The new ionization radiation \u201cbackground\" at each cell with the inclusion of the local emission is computed as Fnew = FHM,\u03bb+Fr,\u03bb, where FHM,\u03bb is the \ufb02ux of the HM background radiation at the relevant wavelength \u03bb. Since the local radiation is mostly dominated by dense hot gaseous regions that tend to be spatially centrally concentrated, our neglect of its possible attenuation likely makes the second case of radiation \ufb01eld (HM+local) an upper limit. Thus, the two choices of radiation \ufb01eld likely bracket all possible cases. Each cell has a size of 625 pc within a cube of 320 kpc centered on each selected sim\u2013 7 \u2013 ulated galaxy, we convert the density nH and the radiation F at the cell to the ionization parameter U = F/cnH at the radiation energy in question, where c is speed of light. Using U and temperature of the cell, we \ufb01nd the abundances of various ions for each cell using the pre-computed CLOUDY lookup tables, which is then multiplied by the metallicity of the cell in solar units. We use the updated solar abundances of these elements from Asplund et al. (2009), in the notation of log \u03f5x = log(Nx/NH) + 12 listed in Table 2. Table 2 lists the UV lines analyzed in this paper, where each doublet is listed using two rows. The information for each line is listed, including wavelength (column 2), oscillator strength (column 3), lower and upper energy levels of the transition (columns 4,5) and abundance of the element (column 6). In column 7, we list the lower column density threshold in constructing covering fractions of the lines (see Figure 4). Each of the lower column density thresholds is chosen to be the minimum of the upper limits for each respective ion. For computing the frequency of the line ratios, essentially some line to the OVI line in all cases, we choose the cut for the OVI column density at log NOVI > 14, which approximately corresponds to the lowest column density of detected OVI absorbers. Note that all of the lines studied here are resonant lines. Ion wavelength[\u00c5] oscillator strength lower level upper level log \u03f5 log Ncut NV 1238.8 1.56e-1 2S1/2 2P1/2 7.83 13.42 NV 1242.8 7.8e-2 2S1/2 2P3/2 7.83 13.42 NIII 989.7 1.23e-1 2P1/2 2D3/2 7.83 13.50 NII 1083.9 1.11e-1 3P0 3D1 7.83 13.46 OVI 1031.9 1.33e-1 2S1/2 2P3/2 8.69 13.27 OVI 1037.6 6.6e-2 2S1/2 2P1/2 8.69 13.27 SiIV 1393.7 5.13e-1 2S1/2 2P3/2 7.51 12.38 SiIV 1402.7 2.55e-1 2S1/2 2P1/2 7.51 12.38 Table 2: Properties of UV lines analyzed in this study. Unlike oxygen and silicon, nitrogen stems from both primary and secondary producers and consequently nitrogen abundance is theoretically expected to be a function of overall metallicity, for which oxygen abundance is a good proxy. This theoretical expectation is con\ufb01rmed by observations. We use the \ufb01tting formula of Moll\u00e1 et al. (2006), which is normalized at solar value, to express the N/O ratio as a function of O/H ratio: log(N/O) = \u22121149.31 + 1115.23x \u2212438.87x2 + 90.05x3 \u221210.20x4 + 0.61x5 \u22120.015x6, (2) where x = 12 + log(O/H). In subsequent analysis, where nitrogen is concerned, we perform the analysis twice, one assuming N/O to be independent of O/H and another using Eq (2). To give the magnitude of the effect, we note that at (0.03, 0.1, 0.3) Z\u2299for oxygen abundance, N/O value is (0.27, 0.28, 0.4) in solar units. \u2013 8 \u2013 3. Results Total gas Temp Metallicity SiIV NV OVI 19 20 21 22 4 5 6 \u22122 \u22121 0 10 11 12 13 14 15 16 9 10 11 12 13 14 15 10 11 12 13 14 15 16 Fig. 1.\u2014 shows projection plots along one of the axes of the 320 kpc cube for one of the galaxies listed in Table 1. From top-left in clockwise direction are logarithm of total hydrogen column density (top-left), logarithm of the density-weighted gas temperature (top-middle), logarithm of the density-weighted gas metallicity in solar units (top-right), logarithm of OVI column density (bottom-right), logarithm of NV column density (bottom-middle) and logarithm of SiIV column density (bottom-left). Before presenting quantitative results, we show visually some basic quantities for a few galaxies in Figures1, 2, 3. Some features are easily visible just from these three random examples. First, large variations from galaxy to galaxy are evident, for each of the displayed variables. Physically, this stems from density and thermodynamic structures of each galaxy being subject to its unique exterior and interior forces, including halo mass, gas in\ufb02ow and associated dynamic and thermodynamic effects, feedback from star formation and related dynamic and thermodynamic effects, As an illustrative example, in Figure1, we see the temperature at the lower-left triangle mostly in the range of 105.5 \u2212106K, compared to the temperature at the upper-right triangle mostly in the range of 104.5 \u2212105K. We do not investigate here further into the dynamic causes of such temperature patterns with possible physical processes including merger shocks and stellar feedback (i.e., supernova) shocks. Second, the temperature distribution of the CGM is far from uniform. Indeed, the CGM is of multi-phase in nature, typically spanning the range of 104 \u2212106K within the \u223c150 kpc radial range for the galax\u2013 9 \u2013 Total gas Temp Metallicity SiIV NV OVI 18 19 20 21 22 4 5 6 \u22123 \u22122 \u22121 0 10 11 12 13 14 15 16 8 9 10 11 12 13 14 9 10 11 12 13 14 15 Fig. 2.\u2014 shows the same as in Figure 1 but for another galaxy. Total gas Temp Metallicity SiIV NV OVI 18 19 20 21 22 4 5 6 \u22122 \u22121 0 9 10 11 12 13 14 15 9 10 11 12 13 14 15 10 11 12 13 14 15 16 Fig. 3.\u2014 shows the same as in Figure 1 for yet another galaxy. \u2013 10 \u2013 ies examined. This property is of critical importance to the line ratios that we obtain in the simulations. Third, the metallicity distribution in the CGM is highly inhomogeneous, typically spanning 10\u22122 \u2212100 Z\u2299. Fourth, although the number of galaxies looked at is small, we \ufb01nd that star-forming galaxies, as those selected in this investigation, tend to be involved in signi\ufb01cant mergers. This in turn suggests that signi\ufb01cant mergers may be a necessary ingredient in driving signi\ufb01cant star formation activities in galaxies at low redshift. We now turn to quantitative results. The top-left panel of Figure 4 shows the column density distributions of the \ufb01ve lines. Due to our projection method, the number of weaker lines are underestimated due to blending. The turndown of the number of the OVI lines below column density 1013cm\u22122 is probably due to that. This is unlikely to signi\ufb01cantly affect our results below, since our coincidence analysis is focused on OVI absorbers with column density higher than 1014cm\u22122. The covering fractions shown in Figure 4 may be somewhat overestimated, since the column density cutoff for OVI is 1013.27cm\u22122; a comparison between the cutoff column densities listed in Table 2 and the behavior of the column density histograms shown in the top-left panel of Figure 4 for the other four lines (SiIV, NV, NIII and NII) suggests that the covering fractions for these four lines are unlikely affected signi\ufb01cantly due to blending. The remaining three panels of Figure 4 show covering fraction of OVI and SiIV (top-right panel), NV, NIII, NII lines with constant N/O ratio (bottom-left panel) and with N/O as a function of O/H (Eq 2, bottom-right panel). Several interesting properties may be noted. First, there is a signi\ufb01cant drop of covering fraction, by a factor of 2 \u221210, from the central regions (a few kpc) to \u223c150 kpc. This is likely due primarily to a combination of the general trend of decreasing gas density and decreasing metallicity of the CGM with increasing galacto-centric radius. In spite of this covering fraction decrease with radius, most of the absorbers are located at large impact parameters, since the area increases with radius at a higher rate, for example, by a factor of 64 from 20 kpc to 160 kpc. Second, the OVI covering fraction (top panel) is large and largest among the examined lines, ranging from 80 \u221290% at \u226410 kpc to \u223c50% at \u2264150 kpc, given the chosen column density thresholds listed in Table 2. This is in good agreement with observations (e.g., Chen & Mulchaey 2009; Prochaska et al. 2011). Third, it is particularly noteworthy that there is essentially no difference between HM and HM+local cases for the OVI covering fraction. This indicates that photoionization plays a negligible role in the abundance of OVI. In other words, OVI is produced by collisional processes, powered by feedback and gravitational shocks, which will be veri\ufb01ed subsequently [see Cen (2013) for a detailed discussion on the varying contributions of stellar feedback versus gravitational shocks in different types of galaxies]. Fourth, a stronger radiation \ufb01eld tend to increase the abundance of NII and NIII but the opposite is true for NV. But the difference between HM and HM+local cases for both NII and NIII are fairly minor, indicating that collisional processes are the primary powering source for producing NII and NIII. This is not the case for SiIV and NV, where the differences between HM and HM+local cases are substantial and the differences are larger toward small impact parameters. This suggests that a higher HM+local radiation is able to produce NV for high density gas in the inner regions of star-forming galaxies, while \u2013 11 \u2013 11 12 13 14 15 16 logN[cm\u22122] 0.0 0.1 0.2 0.3 0.4 0.5 0.6 PDF HM OVI SiIV NV NIII NII 0 20 40 60 80 100 120 140 160 ImpactParameter[kpc] 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 CoveringFraction OVI[HM] OVI[HM+Local] SiIV[HM] SiIV[HM+Local] 0 20 40 60 80 100 120 140 160 ImpactParameter[kpc] 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 CoveringFraction constant[N/O] NV[HM] NV[HM+Local] NIII[HM] NIII[HM+Local] NII[HM] NII[HM+Local] 0 20 40 60 80 100 120 140 160 ImpactParameter[kpc] 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 CoveringFraction varying[N/O] NV[HM] NV[HM+Local] NIII[HM] NIII[HM+Local] NII[HM] NII[HM+Local] Fig. 4.\u2014 Top-left panel: shows the column density distributions for all \ufb01ve lines in the case with HM, and for the three nitrogen lines with varying N/O (Eq 2). Top-right panel: shows the covering fraction as a function of the galacto-centric impact parameter for OVI absorbers with column density above 1013.27cm\u22122 with HM (solid blue curve) and with HM+local (dotdashed blue curve), for SiIV absorbers with column density above 1012.38cm\u22122 with HM (solid green curve) and with HM+local (dot-dashed green curve). Bottom-left panel: shows the same as in the top panel but for the three nitrogen absorption lines with column density above 1013.43cm\u22122 for NV (blue curves), 1013.50cm\u22122 for NIII (red curves) and 1013.46cm\u22122 for NII (green curves), under the assumption that N/O ratio is independent of metallicity. The solid curves correspond to the case with only HM radiation background, whereas the dot-dashed curves are for the case with HM+local radiation. Bottom-right panel: shows the same as for the bottom-left panel, except that we use Eq (2) for nitrogen abundance as a function of oxygen abundance. the outer regions are mainly dominated by collisional processes, consistent with a trend of increasing temperature with increasing galacto-centric radius found in Cen (2013). Finally, comparing the bottom-left and bottom-right panels, we see signi\ufb01cant differences between constant N/O case (left) and varying N/O case (Eq 2, right). A closer look reveals that the \u2013 12 \u2013 \u22122.5 \u22122.0 \u22121.5 \u22121.0 \u22120.5 0.0 logN(NV)/N(OVI) 0.0 0.5 1.0 1.5 2.0 PDF [HM, constantN/O] [HM+local, constantN/O] \u22122.5 \u22122.0 \u22121.5 \u22121.0 \u22120.5 0.0 logN(NV)/N(OVI) 0.0 0.5 1.0 1.5 2.0 PDF [HM, varyingN/O] [HM+local, varyingN/O] \u22122.5 \u22122.0 \u22121.5 \u22121.0 \u22120.5 0.0 0.5 1.0 logN(NIII)/N(OVI) 0.0 0.2 0.4 0.6 0.8 1.0 PDF [HM, constantN/O] [HM+local, constantN/O] \u22122.5 \u22122.0 \u22121.5 \u22121.0 \u22120.5 0.0 0.5 1.0 logN(NIII)/N(OVI) 0.0 0.2 0.4 0.6 0.8 1.0 PDF [HM, varyingN/O] [HM+local, varyingN/O] \u22122.5 \u22122.0 \u22121.5 \u22121.0 \u22120.5 0.0 0.5 1.0 logN(NII)/N(OVI) 0.0 0.2 0.4 0.6 0.8 1.0 PDF [HM, constantN/O] [HM+local, constantN/O] \u22122.5 \u22122.0 \u22121.5 \u22121.0 \u22120.5 0.0 logN(NII)/N(OVI) 0.0 0.2 0.4 0.6 0.8 1.0 PDF [HM, varyingN/O] [HM+local, varyingN/O] Fig. 5.\u2014 Top row: shows the probability distribution function (PDF) of the ratio of N(NV)/N(OVI) for all OVI absorbers with N(OVI) > 1014cm\u22122 with constant N/O ratio (left) and varying N/O as a function of O/H (Eq 2). Middle row: the same for NIII/OVI. Bottom row: the same for NII/OVI. (Blue, red) histograms are for (HM, HM+local) radiation \ufb01eld. The observational data are shown for three separate types: black dots are those with both lines detected, left green arrows are those where the numerator line is an upper limit and the denominator line a detection, and brown left arrows are those where the numerator line is an upper limit and the denominator line a lower limit. The y coordinates of the points are arbitrary. \u2013 13 \u2013 difference increases with increasing impact parameter, re\ufb02ecting the trend of decreasing gas metallicity (O/H) with increasing impact parameter. Also revealed is that the decreases in covering fraction from constant N/O to varying N/O case for different lines differ signi\ufb01cantly, re\ufb02ecting the complex multi-phase medium with inhomogeneous, temperature-and-densitydependent metallicity distribution; while the decrease for NIII is relatively small (a factor of less than two for all impact parameters), the decreases for NII and NV are quite large, a factor of larger than two at < 150 kpc. As we will quantify using KS tests subsequently, the signi\ufb01cant reduction in nitrogen abundance with the varying N/O case results in noticeably better KS test p-values with respect to NII/OVI, NIII/OVI, NV/OVII column density ratios. We now make direct comparisons to observations with respect to the ratio of column densities for four absorption line pairs. Figure 5 shows the probability distribution functions of N(NV)/N(OVI) (top row), N(NIII)/N(OVI) (middle row) and N(NII)/N(OVI) (bottom row), with each row further separated for constant N/O (left) and varying N/O cases (right). Due to the fact that the vast majority of NII, NIII and NV absorbers have metallicities in the range of [O/H] = \u22121 to \u22120.5 (see Figure 7 below), the horizontal shifts of the peaks of the PDFs for the ratios of all three nitrogen lines to OVI are substantial, of order 0.5 dex. The shifts have noticeable effects on the KS tests between simulations and observations below given in Table 3. An examination by eye between the simulation results and observational data comes with the visual impression that all cases agree reasonably well with observations, which will be veri\ufb01ed quantitatively. Figure 6 shows the probability distribution functions of N(SiIV)/N(OVI) column density ratios. Once again, visual examination suggests agreement with simulations and observations. Line ratio HM HM+Local NV/OVI[constant N/O] 0.33 0.37 NII/OVI[constant N/O] 0.93 0.99 NIII/OVI[constant N/O] 0.28 0.49 NV/OVI[varying N/O] 0.99 0.99 NII/OVI[varying N/O] 0.99 0.99 NIII/OVI[varying N/O] 0.91 0.96 SiIV/OVI 0.9 0.98 Table 3: Two-sample KS test p-values for column density ratio distributions of four absorption line pairs, including cases with constant and varying N/O ratios and HM versus HM+local radiation \ufb01eld To gain a more quantitative statistical test between simulations and observations, we perform two-sample KS tests between simulated and observed column density ratios for four pairs of lines, NV/OVI, NII/NV, NIII/OVI and SiIV/OVI. Since most of the observational data are upper and lower limits, instead of actual detections, our analysis is performed as follows. For the case where the numerator line is an upper limit and the denominator line is a detection, we allow the ratio to be drawn from the simulation distribution with value upper-bounded by \u2013 14 \u2013 \u22122.5 \u22122.0 \u22121.5 \u22121.0 \u22120.5 0.0 logN(SiIV)/N(OVI) 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 PDF [HM] [HM+local] Fig. 6.\u2014 shows the PDF of the ratio of N(SiIV)/N(OVI) for all OVI absorbers with N(OVI) > 1014cm\u22122. The points are observational data divided into three separate types: the black dots are those with both lines in the ratio detected, the left green arrows are those where SiIV line is an upper limit and OVI line is a detection, and the brown left arrows are those where SiIV line is an upper limit and OVI line is a lower limit. The blue histograms are for HM radiation \ufb01eld, whereas the red histograms are for HM+local radiation \ufb01eld. The y coordinates of the points are arbitrary. the upper limit. The same is done for the case where the numerator line is an upper limit and the denominator line is a lower limit. Then, in conjunction with detections, where both lines are detected, we perform a two-sample KS test for each of the four line pairs, NV/OVI, NII/NV, NIII/OVI and SiIV/OVI, between simulations and observations. Needless to say, our presently adopted procedure to treat the upper and lower limits cases favors agreement with observations and simulations. Nevertheless, the procedure is consistent with the current data. The results are tabulated in Table 3. Clearly, no major disagreements can be claimed as to reject the simulation results in all four cases, (constant N/O, varying N/O) times (HM, HM+local). However, there are hints, at face value, that the constant N/O cases are less preferred than the varying N/O cases. Nonetheless, it is premature to make any \ufb01rm statistical conclusion on that at this juncture. Thus, the only robust conclusion we can reach at this time is that our simulation predictions are fully consistent with extant observational data with respect to the four line ratios, NV/OVI, NII/NV, NIII/OVI and SiIV/OVI. What would exponentially increase the statistical power of testing the models is to turn these current upper limits into real detections. We have performed the following exercise to demonstrate this point. Let us assume that all current upper limits of the column density ratios become detections and the detection values are lower than current upper limits uniformly by a factor of \u2206dex. We \ufb01nd that, if \u2206= (0.18, 0.16), the KS p-values for the NV/OVI line ratio become (0.05, 0.05) for the (HM, HM+local) cases with constant N/O; with \u2206= (0.21, 0.20), the KS p-values for the NV/OVI line ratio become (0.01, 0.01) for the (HM, HM+local) cases with \u2013 15 \u2013 constant N/O. For the varying N/O cases, the situation is non-monotonic in the following sense: the KS p-values for the NV/OVI line ratio are (0, 0) for the (HM, HM+local) with \u2206= (0, 0), increasing to a maximum of (0.5, 0.8) with \u2206= (0.70, 0.63), then downturning to (0.01, 0.01) with \u2206= (0.83, 0.78). Obviously, a uniform shift is an oversimpli\ufb01cation. Nevertheless, this shows clearly an urgent need to increase observational sensitivity in order to place signi\ufb01cantly stronger constraints on models than currently possible. When all line pairs are deployed, the statistical power will be still, likely much, greater. 11 12 13 14 15 16 logNOVI[cm\u22122] \u22123.5 \u22123.0 \u22122.5 \u22122.0 \u22121.5 \u22121.0 \u22120.5 0.0 0.5 logZ[Z\u2299] [HM] 11 12 13 14 15 16 logNNV[cm\u22122] \u22123.0 \u22122.5 \u22122.0 \u22121.5 \u22121.0 \u22120.5 0.0 0.5 logZ[Z\u2299] [HM] 11 12 13 14 15 16 logNSiIV[cm\u22122] \u22122.0 \u22121.5 \u22121.0 \u22120.5 0.0 0.5 logZ[Z\u2299] [HM] 11 12 13 14 15 16 logNNIII[cm\u22122] \u22122.5 \u22122.0 \u22121.5 \u22121.0 \u22120.5 0.0 0.5 logZ[Z\u2299] [HM] Fig. 7.\u2014 shows the number density of absorption lines in the column density-metallicity plane for OVI (top-left panel), NV (top-right panel), NIII (bottom-right panel) and SiIV (bottomleft panel). The contour levels are evenly spaced in log-scale spanning the range of 0.5 and half of maximum density in each panel. Only the HM case with varying N/H case is shown for all lines, because the difference between HM and HM+local cases is found to be relatively small. Finally, we turn to a closer examination of the physical conditions that give rise to the various absorption lines in our simulations shown above. In Figure 7 we show the number density of lines in the column density-metallicity plane for OVI (top-left panel), NV (top-right panel), NIII \u2013 16 \u2013 11 12 13 14 15 16 logNOVI[cm\u22122] 4.5 5.0 5.5 6.0 6.5 logT[K] [HM] 11 12 13 14 15 16 logNNV[cm\u22122] 4.0 4.5 5.0 5.5 6.0 logT[K] [HM] 11 12 13 14 15 16 logNSiIV[cm\u22122] 4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.6 logT[K] [HM] 11 12 13 14 15 16 logNNIII[cm\u22122] 4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4 logT[K] [HM] Fig. 8.\u2014 shows the number density of absorption lines in the column density-temperature plane for OVI (top-left panel), NV (top-right panel), NIII (bottom-right panel) and SiIV (bottomleft panel). The contour levels are evenly spaced in log-scale spanning the range of 0.5 and half of maximum density in each panel. Only the HM case with varying N/H case is shown for all lines, because the difference between HM and HM+local cases is found to be relatively small. (bottom-right panel) and SiIV (bottom-left panel). Overall, while there is a signi\ufb01cant span in metallicity, with as low as [Z/H] = \u22123.5 at the low column density end for OVI, the vast majority of absorbers have metallicities falling into the range [O/H] = \u22122 to \u22120.5 for OVI, [O/H] = \u22122 to \u22120.5 for NV, [O/H] = \u22122 to \u22120.5 for NV and [O/H] = \u22121 to \u22120.5 for SiIV. At the high column density end, we see [O/H] \u223c\u22120.5 to 0 for OVI, [O/H] \u223c\u22120.5 to 0.5 for NV, [O/H] \u223c0 to 0.5 for NIII and [O/H] \u223c0 to 0.5 for SiIV. These trends and signi\ufb01cant disparities between different lines are a results of complex multi-phase CGM with a very inhomogeneous metallicity distribution. Simplistic collisional excitation/ionization models are unlikely to be able to capture all of the key elements of the physical processes involved and may lead to conclusions that are not necessarily conformal to direct analyses of the simulations. \u2013 17 \u2013 Figure 8 shows the number density of lines in the column density-temperature plane for OVI (top-left panel), NV (top-right panel), NIII (bottom-right panel) and SiIV (bottom-left panel). To set the context of collisionally dominated ionization processes, we note that, under the assumption of collisional ionization equilibrium, as in CLOUDY, the peak temperature for the element in question with Half-Width-Half-Maximum is approximately (3.0\u00b10.5)\u00d7105K for OVI, (2.0\u00b10.5)\u00d7105K for NV, 7.5+5.0 \u22123.0\u00d7104K for NIII and 7.3+1.8 \u22122.2\u00d7104K for SiIV (e.g., Gnat & Sternberg 2007). A one-to-one comparison between each of these four peak temperature (and its width) and the contour levels indicates that for OVI and NV lines the collisional ionization dominates the process for creating OVI at NOVI \u22651014cm\u22122 and NVI at NNV \u22651013cm\u22122, respectively, manifested in the horizontal extension of the contours pointing to the right at the temperature (with an appropriate width) in question. The same can be said about the SiIV line at the high column end NSiIV \u22651015cm\u22122; however, at lower NSiIV values (\u22641015cm\u22122), the contours are no longer aligned horizontally, indicative of enhanced contribution of photoionization due to lower ionization potential of SiIII (33.49eV) versus say OV (77.41eV). Similar statements about NIII lines to those for SiIV can be made due to similar reasons. Overall, the similarity between OVI and NV lines suggests that collisional ionization processes are dominant and results with respect to these two lines are relatively immune to uncertainties in the radiation \ufb01eld used. However, the apparent insensitivity of results on the radiation \ufb01eld with detailed calculation we have performed, in the way of comparing HM and HM+local results, indicates that the net effect due to an increase of radiation \ufb01eld is relatively small due to the large ranges of density and metallicity of gas involved, although the actual situation appears to be more intertwined because of nonlinear relationships between density, metallicity, ionization parameter and column density. As an example, as shown earlier in Figure 4, a stronger radiation \ufb01eld tend to increase the abundance of NIII, although the difference between HM and HM+local cases for is apparently minor, seeming to suggest con\ufb02ictingly that collisional processes are the primary powering source for producing NIII. A more thorough theoretical study and a more detailed comparison to observations will be desirable, when a larger observational sample with more sensitive column density detection limits becomes available. As we have demonstrated, a fraction of a dex increase in sensitivity may warrant a revisit to a detailed comparison. 4. Conclusions In light of a recent conclusion that the observed line ratios of UV absorbers in the CGM may pose a signi\ufb01cant challenge for theoretical models (Werk et al. 2016), we study \ufb01ve UV absorption lines, OVI \u03bb\u03bb1032, 1038, SiIV \u03bb\u03bb1394, 1402, NV \u03bb\u03bb1239, 1243, NIII \u03bb990, NII \u03bb1084, in the CGM of simulated galaxies, utilizing ab initio ultra-high resolution (LAOZI) hydrodynamical simulations. Our simulated galaxies are chosen to have stellar masses and star formation rates similar to their observed counterpart. We examine uncertainties related to the radiation background by computing separately for two cases of radiation \ufb01eld, one with the HM radiation background and the other with both \u2013 18 \u2013 HM and local radiation due to hot gas in the host galaxy. Separately and orthogonally, we examine two separate cases of nitrogen to oxygen ratio, in one case with constant N/O and in the other with varying N/O that is theoretically consistent with two different synthetic sources of nitrogen and observationally con\ufb01rmed by independent observations. Werk et al. (2016) \ufb01nd constant density photoionization models to be excluded by the data. They \ufb01nd collisional (both in and out of equilibrium) ionization to be only broadly consistent with the data. They suggest either collisionally-ionized gas cooling behind a fast shock or a highly structured gas photo-ionized by a local high energy source as plausible models to account of the observed OVI column density range and line ratios. In contrast, we do not \ufb01nd signi\ufb01cant dif\ufb01culty in accounting for the same observational data in our cosmological simulations that capture the complex multi-phase structure of the CGM, as re\ufb02ected by the acceptable KS test p-values for column density ratios of four pairs of lines NV/OVI, SiIV/OVI, NIII/OVI and NII/OVI examined. Inter-comparisons between results from different models employing different radiation \ufb01elds in our simulations and comparisons between properties of the absorbers and expectations of collisional ionization indicate that collisional ionization play a major role in producing all the lines studied in realistic CGM produced in cosmological simulations. Photoionization process plays a signi\ufb01cant role as well, to a varying degree, depending on the ion in question, although it seems clear that for NV and OVI lines photoionization effect is relatively minor. The success of our largely collisional ionization model in all cases is, however, in a significant part, due to very accommodative observational line ratio data points that are dominated, in number, by upper limits rather than actual detections. We \ufb01nd the apparent satisfactory agreement between simulations and extant observational data can be strongly tested and different cases (different radiation \ufb01elds and different N/O ratio assumptions) differentiated, if most of the current upper limits in the observational data become detections. To demonstrate the power, we show, as an example, that if the upper limits of NV/OVI become detections with values that are lower by a mere \u223c0.20 dex than their respective current upper limits, the KS p-value for the NV/OVI line ratio becomes \u223c0.01 for the constant N/O case and \u223c0 for the varying N/O case. If, on the other hand, the actual detection values turn out to be lower than current upper limits by 0.6 \u22120.7 dex, then the varying N/O case obtains a satisfactory p-value of (0.5, 0.8), whereas the constant N/O case is endowed with a p-value equal to zero. Thus, it is highly desirable to increase the observational sensitivity and/or enlarge observational data sample size, in order to have a de\ufb01nitive test. We are grateful to Jessica Werk for sharing observational data with us prior to publication and stimulating discussion. We thank J. Xavier Prochaska for useful discussion. We have used the very useful and versatile analysis software yt version 2.6 (Turk et al. 2011) for some of our analysis. Computing resources were in part provided by the NASA HighEnd Computing (HEC) Program through the NASA Advanced Supercomputing (NAS) Division at Ames \u2013 19 \u2013 Research Center. The research is supported in part by NASA grant NNX11AI23G.",
                    "introduction": "The nature of halo gas (a.k.a. circumgalactic medium; CGM hereafter), on galactocentric distances of 10 \u2212500 kpc, is a problem of signi\ufb01cant ongoing interest in galaxy formation. Halo gas links galaxies from the intergalactic medium and is the conduit for exchange of mat- ter energy density, momentum, angular momentum and metals between star formation and active galactic nucleus induced out\ufb02ow and gravitational in\ufb02ow of gas. Thus, understanding halo gas is imperative before a satisfactory theory of galaxy formation and evolution may be constructed. There has been recent rapid advances on the observational front to address this 1Princeton University Observatory, Princeton, NJ 08544; cen@astro.princeton.edu 2School of Earth and Space Exploration, Arizona State University, Tempe, AZ 85287-1404, USA; Johns Hop- kins University, Department of Physics and Astronomy, Baltimore, MD 21218, USA arXiv:1609.03583v1  [astro-ph.GA]  12 Sep 2016 \u2013 2 \u2013 important issue, made possible primarily by HST observations (e.g., Chen & Mulchaey 2009; Prochaska et al. 2011; Tumlinson et al. 2011; Tripp et al. 2011; Thom et al. 2012; Werk et al. 2013, 2014; Peeples et al. 2014; Werk et al. 2016). In Cen (2013) we investigate the overall gas composition with respect to the density, temperature and metallicity and \ufb01nd that, on aver- age, for > 0.1L\u2217(red, blue) galaxies cold (T < 105K) gas is the primary component in the inner regions, with its mass comprising 50% of all gas within r = (30, 150) kpc. At r > (30, 200) kpc for (red, blue) galaxies, the hot (T > 107K) component becomes the majority component. The warm (T = 105\u22127K) component is, on average, a perpetual minority in both red and blue galaxies, with its contribution peaking at \u223c30% at r = 100\u2212300 kpc in blue galaxies and never exceeding 5% in red galaxies. These \ufb01ndings are in agreement with recent observations in many aspects, in particular with respect to the amount of warm gas in star forming galaxies and the amount of cold gas in early type galaxies at low redshift, both of which are physically intriguing and at \ufb01rst instant less than intuitive. In light of a new observational development with respect to the NV to OVI absorption line ratio and in particular the apparent need of seemingly complicated, perhaps contrived, models to explain the data, we here perform a detailed analysis of our high resolution cosmological hydrodynamic simulations to assess whether ab initio cosmological simulations are capable of accounting for this particular observation, in the larger context of the success of the model able to match the overall composition of halo gas, among others. It is particularly relevant to note that the good agreement between our simulations and observations with respect OVI \u03bb\u03bb1032, 1038 absorption lines, presented earlier in Cen (2012a), suggests that the statistical descrip- tion of the properties of the warm component in the simulations - mass, spatial distribution, density, temperature, metallicity, and their environmental dependences - has now been \ufb01rmly validated and provides a critical anchor point for our model. Consequently, this additional, independent analysis with respect to NV/OVI ratio and other ratios becomes very powerful to further strengthen or falsify our model or our simulations. Our \ufb01ndings here are both encouraging and intriguing. If one uses a \ufb01xed, solar N/O ratio regardless of the O/H ratio, our model is acceptable, with all 4 KS (Kolmogorov-Smirnov) test p-values greater than 0.28 for either Haardt-Madau (Haardt & Madau 2012, HM hereafter) or HM+local radiation \ufb01eld, where the local radiation \ufb01eld is due to hot gas in the host galaxy. If one allows for a dependence of the N/O ratio on the O/H ratio, both measured by indepen- dent observations and motivated by theoretical considerations of two different sources of N, then our model is able to account for the observations highly successfully, with all KS test p-values exceeding 0.9. We additionally examine the following absorption line column density ratios where comparisons to observations may be made in a reasonable statistical fashion, SiIV/OVI, NII/OVI and NIII/OVI, and \ufb01nd that the ratios from our simulations are fully consistent with observations. We also investigate the model where UV radiation from local shock heated gas in concerned galaxies are added to the HM background, which is found to also agree with observations with comparable p-values for all line ratios examined. However, these good agreements come about because observational data points are dominated by upper and lower \u2013 3 \u2013 limits instead of actual detections. We discuss how some moderate improvment in observa- tional sensitivity may provide much stronger tests of models."
                },
                {
                    "url": "http://arxiv.org/abs/1606.05930v2",
                    "title": "Constraint on Matter Power Spectrum on $10^6-10^9M_\\odot$ Scales from ${\\large\u03c4_e}$",
                    "abstract": "An analysis of the physics-rich endgame of reionization at $z=5.7$ is\nperformed, utilizing jointly the observations of the Ly$\\alpha$ forest, the\nmean free path of ionizing photons, the luminosity function of galaxies and new\nphysical insight. We find that an upper limit on ${\\rm \\tau_e}$ provides a\nconstraint on the minimum mean free path (of ionizing photons) that is\nprimarily due to dwarf galaxies, which in turn yields a new and yet the\nstrongest constraint on the matter power spectrum on $10^6-10^9M_\\odot$ scales.\nWith the latest Planck measurements of ${\\rm \\tau_e = 0.055 \\pm 0.009}$, we can\nplace an upper limit of $(8.9\\times 10^6, 3.8\\times 10^7, 4.2\\times\n10^8)M_\\odot$ on the lower cutoff mass of the halo mass function, or equivalent\na lower limit on warm dark matter particle mass ${\\rm m_x \\ge (15.1, 9.8,\n4.6)keV}$ or on sterile neutrino mass ${\\rm m_s \\ge (161, 90, 33)keV}$, at $(1,\n1.4, 2.2)\\sigma$ confidence level, respectively.",
                    "authors": "Renyue Cen",
                    "published": "2016-06-20",
                    "updated": "2016-09-14",
                    "primary_cat": "astro-ph.CO",
                    "cats": [
                        "astro-ph.CO"
                    ],
                    "main_content": "2.1. Global Balance of Emission and Recombination The hydrogen recombination rate per unit comoving volume at redshift z is \u02d9 Nrec = CHII\u03b1B(T)[1 + Yp/4(1 \u2212Yp)]n2 H,0(1 + z)3 (1) and the corresponding helium I recombination rate is \u02d9 NHeI,rec = CHII\u03b1B(HeI, T)[1 + Yp/4(1 \u2212Yp)][Yp/4(1 \u2212Yp)]n2 H,0(1 + z)3, (2) \u2212 \u2212 where nH,0 = 2.0 \u00d7 10\u22127(\u2126B/0.048)cm\u22123 is the mean hydrogen number density at z = 0, Yp = 0.24 the primordial helium mass fraction, CHII is the clumping factor of the recombining medium. The case B recombination coefficient \u03b1B(T) = (2.59, 2.52) \u00d7 10\u221213 cm3s\u22121 at T = (104, 2 \u00d7 104)K (Osterbrock 1989). The case B He I recombination coefficient is \u03b1B(HeI, T) = (2.73, 1.55) \u00d7 10\u221213 cm3 s\u22121 at T = (104, 2 \u00d7 104)K (Osterbrock 1989). To prevent the already ionized IGM from recombining, the amount of ionizing photons entering the IGM has to be, at least, equal to the total recombination rate, resulting in the well known minimum requirement of ionizing photon production rate (e.g., Madau et al. 1999) \u02d9 Nion,global\u2265\u02d9 Nrec + \u02d9 NHeI,rec = 3.4 \u00d7 1050(CHII/3.2)(\u2126b/0.048)2((1 + z)/6.7)3cMpc\u22123s\u22121 for T = 104K = 3.2 \u00d7 1050(C/3.2)(\u2126/0.048)2((1 + z)/6.7)3cMpc\u22123s\u22121 for T = 2 \u00d7 1 \u00d7 = 3.2 \u00d7 1050(CHII/3.2)(\u2126b/0.048)2((1 + z)/6.7)3cMpc\u22123s\u22121 for T = 2 \u00d7 104K, (3) assuming that helium II is not ionized. We shall call this constraint expressed in Eq 3 \u201cglobal constraint\". For clarity we will adopt the convention to use cMpc and pMpc to denote comoving and proper Mpc, respectively. Early hydrodynamical simulations suggest CHII \u223c10 \u221240 at z < 8 (e.g., Gnedin & Ostriker 1997). More recent simulations that separate out dense interstellar medium (ISM) from the IGM indicate a lower CHII \u223c1 \u22126 at z \u223c6 (e.g., Sokasian et al. 2003; Iliev et al. 2006; Pawlik et al. 2009; Shull et al. 2012; Finlator et al. 2012). Pawlik et al. (2009) give CHII = 3.2 for z \u226410 = 1 + exp (\u22120.28z + = 3.2 for z \u226410 = 1 + exp (\u22120.28z + 3.59) for z > 10, (4) which we will use in the calculations below. As we demonstrate later, the value CHII = 3.2 at z = 5.7 is concordant between considerations of global and local ionization balances. 2.2. Local Balance of Ionization and Recombination A second, independent determination of ionizing photon production rate can be obtained from the Ly\u03b1 optical depth around cosmic mean density, \u03c4Ly\u03b1, i.e., the Gunn & Peterson (1965) \u2013 4 \u2013 optical depth, at z = 5.7, where observational measurements are available. Because of the large cross section of neutral hydrogen for Ly\u03b1 scattering, \u03c4Ly\u03b1 is the most sensitive probe of neutral medium in the low neutral-fraction regime. From the SDSS observations of high redshift quasar absorption spectra \u03c4Ly\u03b1 is directly measured (Fan et al. 2002; Fan et al. 2006). When analyzed in conjunction with density distributions of the IGM from hydrodynamic simulations, one can infer both the volume weighted neutral fraction and the ionization rate \u0393, expressed in units of 10\u221212s\u22121, \u0393\u221212. Because the mean density regions that determine the volumeweighted neutral fraction are well resolved in simulations (i.e., the simulation resolution is much \ufb01ner than the Jeans scale of the photoionized IGM), the uncertainty on the determined volume-weighted neutral fraction is small and does not depend sensitively on cosmological parameters, either. The analysis performed by Cen & McDonald (2002) uses a smaller sample of SDSS quasars coupled with simulations of Cen et al. (1994). The analysis performed by Fan et al. (2006) utilizes a larger quasars sample and the density distribution function of MiraldaEscud\u00e9 et al. (2000). Both studies derive, independently, \u0393\u221212 \u223c0.20. For the subsequent calculations, we will use \u0393\u221212 = 0.20+0.11 \u22120.06 (5) at z = 5.7 from Fan et al. (2006). Under the assumption that the spatial scales of \ufb02uctuations (or clustering scales) for both sources and sinks are substantially smaller than the mean free path \u03bbmfp of LyC photons, then the (approximately uniform) ionizing \ufb02ux at any spatial point is Fion = Z \u221e 0 \u02d9 Nion,IGM 4\u03c0r2 exp (\u2212r/\u03bbmfp)4\u03c0r2dr = \u02d9 Nion,IGM\u03bbmfp, (6) where \u02d9 Nion,IGM is the mean emissivity of ionizing photons entering the IGM. We note that the 2-point correlation length of galaxies at z = 5.7 is 4 \u22125cMpc (e.g., Ouchi et al. 2010), much smaller than \u03bbmfp \u223c30\u221260cMpc, which we will discuss later. Therefore, the above assumption is a good one, so long as stellar sources are the main driver of cosmological reionization. We expect that radiation \ufb02ux \ufb02uctuations would be on the order of the ratio of the two lengths scales above, i.e., \u223c10%. As we will show later that, in the context of the \u039bCDM model, \u03bbmfp depends on \u0393 approximately as \u03bbmfp \u221d\u0393\u22120.28. Thus, we expect that the uniform radiation assumption is accurate statistically for computing the mean \u03bbmfp at 1\u22123% level, with negligible systematic biases. The hydrogen ionization rate \u0393 = Fion\u00af \u03c3ion = \u02d9 Nion,IGM\u03bbmfp\u00af \u03c3ion, (7) where \u00af \u03c3ion is the spectrum-weighted mean photoionization cross section, \u00af \u03c3ion \u2261 R \u221e 13.6eV f\u03bd h\u03bd\u03c3H(\u03bd)d\u03bd R \u221e 13.6eV f\u03bd h\u03bdd\u03bd , (8) where \u03c3H(\u03bd) is the photon energy-dependent hydrogen ionization cross section, f\u03bd is the ionizing photon spectrum. We will use f\u03bd for Pop II stars of metallicity Z = 0.05 Z\u2299from Tumlinson \u2013 5 \u2013 et al. (2001), which may be approximated as f\u03bd\u221d\u03bd0 for \u03bd = 13.6 \u221224.6eV \u221d\u03bd\u22121 for \u03bd = 24.6 \u221246eV \u221d\u03bd\u2212\u221e for \u03bd > 46eV, which results in the \ufb01ducial value that we will use in our calculations at z = 5.7, \u00af \u03c3ion = 3.16 \u00d7 10\u221218 cm2. (9) Combining Eq (5, 7, 9) gives the constraint on comoving emissivity at z = 5.7 from GunnPeterson optical depth, named \"local constraint\", \u02d9 Nion,local = 2.7 \u00d7 1050(\u0393\u221212 0.2 )( \u00af \u03c3ion 3.16 \u00d7 10\u221218cm2)\u22121( \u03bbmfp 7.6pMpc)\u22121cMpc\u22123s\u22121. (10) In Eq 10 it is seen that there is a signi\ufb01cant, linearly inverse dependence of \u02d9 Nion,local on \u03bbmfp, which we now discuss in length observationally here and theoretically in the next subsection. Traditionally, \u03bbmfp is determined by counting the incidence frequency of Lyman limit systems (LLSs) (e.g., Storrie-Lombardi et al. 1994; Stengler-Larrea et al. 1995; Songaila & Cowie 2010; Ribaudo et al. 2011; O\u2019Meara et al. 2013) and generally found to be in the range of \u03bbmfp = 5 \u221210 pMpc at z = 5.7, when extrapolated from lower redshift trends. This method to determine \u03bbmfp contains some ambiguity as to the dependence of the incidence frequency on exact choice of column density threshold of LLSs, and uncertainties related to absorption system identi\ufb01cations (such as line blending) and collective absorption due to clustering of absorbers. A more direct approach to determining \u03bbmfp is to measure the optical depth at Lyman limit directly, as pioneered by Prochaska et al. (2009). A recent application of that technique to a large sample of (163) high redshift quasars is cast into \ufb01tting formula \u03bbmfp = 37[(1 + z)/5]\u22125.4\u00b10.4pMpc that covers up to redshift z = 5.5 (Worseck et al. 2014). Extrapolating this formula to z = 5.7 results in a median value of 7.6 pMc, \u03bbmfp = 7.6+1.0 \u22120.8 pMpc, (11) with the 1 and 2\u03c3 range of 6.8 \u22128.6 pMpc and 6.0 \u22129.6 pMpc, respectively. It is seen that the directly measured \u03bbmfp are in broad agreement with those based on counting LLSs, which is reassuring. Nevertheless, it is prudent to bear in mind a signi\ufb01cant caveat that \u03bbmfp at z = 5.7 is not directly observed but requires extrapolation from lower redshift data. 2.3. Concordance of Independent Observations at z = 5.7 We now combine three independent sets of observational constraints on \u02d9 Nion, \u0393 and \u03bbmfp on the \u0393 \u2212\u03bbmfp plane, shown in Figure 1: (1) the observed \u03bbmfp from Worseck et al. (2014) \u2013 6 \u2013 -13.5 -13 -12.5 -12 log ! (s-1) 5 6 7 8 9 10 11 12 6mfp (pMpc) Worseck + 14 : '2<(6mfp) Fan + 06 : '1<(!) _ Nion;global CHII = 3:2 _ Nion;global CHII = 4:5 _ Nion;global CHII = 9:6 LCDM w= Mcut = 1:6 # 108MLCDM w= Mcut = 5:8 # 107MLCDM w= Mcut = 2:7 # 107MLCDM w= Mcut = 8:6 # 106MFig. 1.\u2014 shows four independent sets of constraints on the \u0393 \u2212\u03bbmfp plane: (1) the observed \u03bbmfp from Worseck et al. (2014) based on LyC optical depth observed at z < 5.5 extrapolate to z = 5.7 (see Eq 11) shown as the red solid curve (mean), thick red dashed curves (1\u03c3) and thin red dashed curves (2\u03c3); (2) the observationally inferred 1\u03c3 range of \u0393 based on measurement of Ly\u03b1 absorption optical depth at z = 5.7 from Fan et al. (2006) shown as the two vertical green dashed lines (see Eq 5); (3) lower bound based on a global balance between emissivity and recombination with Eq 3 assuming clumping factor CHII = (3.2, 4.5, 9.6) and gas temperature T = 104 K, shown as dotted black (thick, median thick, thin) curves; (4) the selfconsistently calculated relation between \u0393 and \u03bbmfp in the standard \u039bCDM model with a lower halo mass cutoff of (1.6 \u00d7 108, 5.8 \u00d7 107, 2.7 \u00d7 107, 8.6 \u00d7 106) M\u2299, respectively, corresponding to a virial temperature cutoff of Tv,cuto\ufb00= (104, 5 \u00d7 103, 3 \u00d7 103, 1.4 \u00d7 103)K. based on Lyman continuum radiation optical depth at z = 5.7 (see Eq 11) are shown as the red solid curve (mean), thick red dashed curves (1\u03c3) and thin red dashed curves (2\u03c3); (2) the observationally inferred 1\u03c3 range of \u0393 based on measurement of Ly\u03b1 absorption optical depth at z = 5.7 from Fan et al. (2006) are shown as the two vertical green dashed lines (see Eq 5); (3) lower bound based on a global balance between emissivity and recombination with Eq 3 assuming clumping factor CHII = (3.2, 4.5, 9.6) and gas temperature T = 104 K, shown as dotted black (thick, median thick, thin) curves. To be conservative, we will use the 2\u03c3 range of \u03bbmfp from Worseck et al. (2014) for our \u2013 7 \u2013 discussion, because of the possible additional, systematic uncertainty of using an extrapolated value from the observed highest redshift of z = 5.5 to z = 5.7. Thus, the allowed parameter space is enclosed by the two thin dashed red horizontal lines and the two vertical dashed green lines. This space is then further constrained by the requirement that only to the right of each of the dotted black curves is attainable, depending on the assumed clumpying factor CHII. The placement of this additional requirement on the plane suggests that CHII > 5 at z = 5.7 may not be feasible but the values in Eq 4 that is obtained from recent radiation hydrodynamic simulations and adopted here are fully consistent with this constraint. It is by no means guaranteed a priori that there is any parameter space left when all these three independent observational constraints are considered, due to uncertainties in individual observations. Hence, the fact that there is suggests a concordance among the independent observations. 2.4. Global Stellar Emissivity of Ionizing Photons at z = 5.7 Figure 1 in \u00a72.4 summarizes the current state of constraints on the required emissivity of ionizing photons in the IGM at z = 5.7, in order to (1) keep the IGM ionized globally, (2) keep the IGM ionized locally as demanded by the optical depths probed by the hydrogen Lyman series absorption lines. The multi-faceted agreement is indeed quite remarkable, providing a validation of the different observations at z = 5.7 (in some cases extrapolation is needed) in the post-overlap epoch. We now address \u201csources\" of ionizing photons, in a fully self-consistent fashion, in the standard cold dark matter model. We follow the approach taken by Trac et al. (2015), to which the reader is referred for a more detailed description. Brie\ufb02y, the method uses direct observations of galaxy luminosity functions at high redshift in the Hubble UDF to calibrate the star formation parameters in the model based on halo mass accretion rate functions in the \u039bCDM model. Figure 2 shows a comparison of rest-frame FUV luminosity functions between the model based on the most recent cosmological parameters and observations at various redshifts. The observed LFs are most reliable at z \u22646 and become less so towards higher redshifts, and perhaps less than trustworthy beyond z = 8 due to lack of spectroscopic con\ufb01rmation at present. For a given small region/area, such as the UDF , cosmic variance becomes more problematic towards higher redshift. Additionally, it is possible that the observed LFs at high redshifts, in the midst of reionization, may be masked by possible reionization effects; this issue is signi\ufb01cantly more acute for Ly\u03b1 emitting galaxies (e.g., Mesinger et al. 2004; Haiman & Cen 2005; Dijkstra et al. 2007). These problems can be circumvented, if we normalize the model at z = 6 and use the \u201cglobal\" LFs from the model at high redshifts where direct observations lack or are unreliable. We take this approach. From Figure 2 we see that the model LFs match observations well at z = 6, 7. The agreement is still good at z = 8, albeit with \u201cnoisier\" observational data. There is very little to \u2013 8 \u2013 -24 -22 -20 -18 -16 -14 -12 -10 MUV -7 -6 -5 -4 -3 -2 -1 0 log dn/dMUV (cMpc-3) z=6, H0 = 70, \u2126M = 0.30 z=7, n=0.96, \u03c38 = 0.82 z=8 z=10 z=15 z=6, Bouwens+15 z=7, Bouwens+15 z=8, Bouwens+15 z=10, Bouwens+15 Fig. 2.\u2014 shows the galaxy luminosity functions predicted by the \u039bCDM model at z = 6 (red solid curve), 7 (blue dashed curve), 8 (magenta dotted curve), 10 (cyan dot-dashed curve) and 15 (black dotted curve), which are compared to the observations at the four corresponding redshifts, shown as various symbols with corresponding colors. The observational data are from Bouwens et al. (2015). glean from the comparison at z = 10, simply because the observational data lack both quantity and quality. Integrating the Schechter \ufb01ts of the Bouwens et al. (2015) LF at z = 6 yields the intrinsic ionizing photon production rate from galaxies of \u02d9 Nion,int = 1051.52cMpc\u22123 s\u22121 for MUV,limit = \u221212 = 1051.57cMpc\u22123 s\u22121 for MUV,limit = \u221210 = 1051.61cMpc\u22123 s\u22121 for MUV,limit = \u22128. (12) In obtaining \u02d9 Nion,int, we have used a relation between ionizing photo production rate per unit FUV spectral density from (Robertson et al. 2013), \u03beion \u2261 \u02d9 Nion/cMpc\u22123 s\u22121 LUV/erg s\u22121 Hz\u22121 cMpc\u22123 = 1025.2, (13) which is based on the observed FUV spectral index \u03b2 \u223c\u22122 for high redshift galaxies. Note \u03b2 is in de\ufb01ned in spectrum f\u03bbd\u03bb \u221d\u03bb\u03b2d\u03bb, or f\u03bdd\u03bd \u221d\u03bd\u22122\u2212\u03b2d\u03bd, in the FUV spectral range. The accuracy of the normalization of our model is such that the model LF at z = 6 gives the same integrated light density as the observed one to the third digit. \u2013 9 \u2013 Integrating the LF based on the \u039bCDM model yield \u02d9 Nion,int(z = 5.7) = 1051.6cMpc\u22123 s\u22121, weakly dependent on MUV lower limit. Dividing \u02d9 Nion,IGM in Eq 1 by \u02d9 Nion,int(z = 5.7) gives the mean luminosity-weighted escape fraction of Lyman continuum fesc,z=5.7 \u2261 \u02d9 Nion,IGM \u02d9 Nion,int = 10   \u02d9 Nion,IGM 1050.6cMpc\u22123 s\u22121 ! \u0012 \u03beion 1025.2 \u0013\u22121 %. (14) We will show in \u00a74 how \u02d9 Nion,IGM plays a key role in determining a lower bound on \u03c4e and how that in turn allow for a strong constraint on \u03bbmfp hence Mcut. 3. Reionization Histories Constrained by the State of IGM at z = 5.7 Any reionization history must satisfy the state of the IGM at z = 5.7 and the fact that the IGM is opaque to Ly\u03b1 photon at just above that redshift. In this sense, the history of cosmological reionization becomes a boundary value problem, where we solve the evolution of HII volume fraction QHII with the following equation: dQHII(z) dt = \u02d9 Nion,IGM(z) nH,0 \u2212QHII(z) trec(z) , (15) where nH,0 is the comoving mean number hydrogen density, and trec(z) = [CHII(z) \u03b1B(T) (1 + Yp/4[1 \u2212Yp]) nH,0 (1 + z)3]\u22121 is the mean recombination time of ionized hydrogen in HII regions. Any solution to Eq 15 satis\ufb01es the following two boundary conditions: fesc \u02d9 Nion,int\u00af \u03c3ion\u03bbmfp|z=5.7 = \u02d9 Nion,IGM\u00af \u03c3ion\u03bbmfp|z=5.7 = 0.20+0.11 \u22120.06 \u00d7 10\u221212s\u22121 (16) and QHII|z=5.7 = 1.0. (17) In Eq 15 at z > 5.7, since \u02d9 Nion,int(z) is \ufb01xed by the \u039bCDM model (see Figure 2), we are left with only one degree of freedom, namely, the evolution of fesc with redshift. We model the redshift evolution of fesc using a simple powerlaw form: fesc(z) = fesc,z=5.7 \u00121 + z 6.7 \u0013\u03c7 . (18) Note that fesc(z) in Eq 3, like fesc,z=5.7 in Eq 14, is averaged over all the galaxies at a given redshift; in other words, fesc(z) is the ratio of the total number of ionizing photons entering the IGM to the total number of ionizing photons produced. There is one additional physical process that is largely unconstrained by the state of the IGM at z = 5.7 but is important for the overall reionization history and integral electron scattering optical depth. That is, a change of IMF at some high redshift from regular Pop II stars to a perhaps more top-heavy and/or metal-free IMF , which may lead to a quantitative transition in ionizing photon production ef\ufb01ciency per unit \u2013 10 \u2013 stellar mass, \u03f5ion. Thanks to our lack of knowledge with regard to this process, we choose to model \u03f5ion generally, albeit in a simple way, as \u03f5ion = \u03f5ion,PopII + (\u03f5ion,PopIII \u2212\u03f5ion,PopII)H(\u2126\u2217[z] \u2212\u2126PopIII,crit), (19) where \u03f5ion,PopIII and \u03f5ion,PopII are ionizing photon production ef\ufb01ciency per unit stellar mass for Pop III and Pop II IMF , respectively. We adopt \u03f5ion,PopII = 3500 photons/baryon and \u03f5ion,PopIII = 70000 photons/baryon (e.g., Bromm et al. 2001), resulting in ratio of \u03f5ion,PopII/\u03f5ion,PopIII = 20, which enters our calculations. The transition between Pop III and Pop II is modeled by a smoothed Heavyside step function H(\u2126\u2217[z] \u2212\u2126PopIII,crit) = (1 + exp [\u22122(\u2126\u2217(z)/\u2126PopIII,crit \u22121)/\u03c3PopIII])\u22121, (20) where \u2126\u2217(z) is the amount of stars formed by redshift z computed in the \u039bCDM model in units of critical density, \u2126PopIII,crit, controls the transition from Pop III to Pop II when the amount of stars formed by some redshift in units of critical density has reached this value, and \u03c3PopIII controls the width of this transition in units of \u2126PopIII,crit; when \u03c3PopIII = 0, one recovers the unsmoothed Heavyside step function. So far, we have three parameters to model the evolution of ionizing photon beyond z = 5.7, \u03c7, \u2126PopIII,crit and \u03c3PopIII. As we will show later, the dependence of results on \u03c3PopIII is suf\ufb01ciently weak that \u03c3PopIII can effectively be considered \ufb01xed, as long as its value is not too large. Therefore, we effectively have two free parameters in our model, \u03c7 and \u2126PopIII,crit. Given that we have one equation, Eq 15, the general expectation is that there will be a family of solutions that will be able to meet the two boundary conditions, Eq 16, 17. Conversely, though, solving Eq 15 to obtain QHII(z = 5.7) = 1 does not necessarily result in an IGM at z = 5.7 that is consistent with the constraint imposed by the observations of Ly\u03b1 optical depth, i.e., Eq 3, a point already noted by others (e.g., Robertson et al. 2013). For each solution of QHII(z), we compute the total electron scattering optical depth from z = 0 to recombination redshift zrec by \u03c4e = Z zrec 0 fe(1 \u2212fs \u2212fn)QHII\u03c3TnH,0[c/H(z)](1 + z)\u22121dz, (21) where fe accounts for redshift evolution of helium contribution, we use fe = (0.76 + 0.24/0.76/4) for z > 2.8 and fe = (0.76 + 0.24/0.76/2) for z \u22642.8, approximating He II reionization as a step function at z = 2.8, which is consistent with the observed He II absorption optical depth data of (Worseck et al. 2011), interpreted in the context of He II reionization simulations of (McQuinn et al. 2009). And fs and fn account for stellar density and neutral hydrogen density, respectively, which do not contribute to electron density. Wilkins et al. (2008) give \u2126\u2217(z = 0) = 2.5 \u00d7 10\u22123, while (Grazian et al. 2015) yield \u2126\u2217(z = 6) = 3.7 \u00d7 10\u22125. We interpolate between these two points to \ufb01nd an approximate stellar evolution \ufb01t as \u2126\u2217(z) = 2.5 \u00d7 10\u22123(1 + z)\u22122.1, translating to fs = 0.052(1 + z)\u22122.1. Post-reionization most of the neutral hydrogen resides in DLAs and the observational data on the evolution of DLAs are available, albeit with signi\ufb01cant errorbars. We approximate the data presented in Noterdaeme et al. (2009) by piece-wise powerlaws as follows: \u2126HI = 0.4 \u00d7 10\u22123 at z = 0, which evolves linearly to \u2126HI = 0.9 \u00d7 10\u22123 at z = 0.5, \u2013 11 \u2013 0.047 0.047 0.047 0.047 0.047 0.047 0.047 0.047 0.047 0.047 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.064 0.064 0.064 0.064 0.064 0.064 0.064 0.064 0.073 0.073 0.073 0.073 0.073 0.073 0.073 0.073 0.082 0.082 0.082 0.082 0.082 50.55 50.55 50.55 50.55 50.55 50.55 50.55 50.55 50.55 50.66 50.66 50.66 50.66 50.66 50.66 50.66 50.66 50.71 50.71 50.71 50.71 50.71 50.71 50.71 50.71 50.765 50.765 50.765 50.765 50.765 50.765 50.765 50.851 50.851 50.851 50.851 50.851 50.851 50.916 50.916 50.916 50.916 50.916 50.916 -6 -5 -4 -3 -2 -1 0 1 2 3 4 \u03c7 -10 -9 -8 -7 -6 -5 -4.5 log \u2126PopIII,crit Fig. 3.\u2014 shows the contours of \u03c4e (red) and \u02d9 Nion,IGM(z = 5.7) (black) in the \u03c7 \u2212 \u2126PopIII,crit plane for \u03c3PopIII = 0.25. The red contours are labelled with \u03c4e values, whereas the black contours are labelled with log \u02d9 Nion,IGM(z = 5.7) values. The four blue solid dots indicate four possible solutions of QHII(z) that yield total electron optical depths of \u03c4e = (0.055, 0.064, 0.073, 0.082), respectively, from left to right. The three green solid dots indicate another set of three possible solutions of QHII(z) that yield total electron optical depths of \u03c4e = (0.082, 0.073, 0.064), respectively, from top to bottom. The black solid dot is a solution with \u03c4e = 0.055. These speci\ufb01c solutions are discussed in the text. which remains at \u2126HI = 0.9\u00d710\u22123 at z = 0.5\u22123, after which it linearly rises \u2126HI = 1.2\u00d710\u22123 at z = 3.5, followed by a constant \u2126HI = 1.2 \u00d7 10\u22123 at z = 3.5 \u22125.7. Figure 3 shows the case with \u03c3PopIII = 0.25, to be examined in greater details. We have examined cases with \u03c3PopIII = 0.5, 0.25, 0.05, 0.01 and \ufb01nd that the results, as displayed in Figure 3 in terms of the contours, depend weakly on \u03c3PopIII. We note that the conclusions obtained are generic and more importantly, the solution family obtained that is still viable is very insensitive to the choice of \u03c3PopIII. It proves useful for our discussion to rewrite one of the boundary value constraints, namely, Eq 16, as \u02d9 Nion,IGM(z = 5.7) = (1.8 \u22124.1) \u00d7 1050 \u0014\u03bbmfp(z = 5.7) 7.6pMpc \u0015\u22121 cMpc\u22123 s\u22121, (22) \u2013 12 \u2013 where the range inside the \ufb01rst pair of parentheses on the right hand side corresponds to 1\u03c3 lower and upper limits of Eq 5. In this parameter space of \u03c7 \u2212\u2126PopIII,crit shown in Figure 3 we have solutions to Eq 15 that satisfy Eq 17, i.e., the universal reionization completes exactly at z = 5.7 with varying \u02d9 Nion,IGM(z = 5.7) shown as the black contours. Superimposed as the red contours are values of \u03c4e for each solution. 0 2 4 6 8 10 12 14 16 18 20 z 10-3 10-2 10-1 100 Q(z)  & \u03c4e(>z) Q(z) and \u03c4e solutions:  four blue dots in Fig 5 red: \u03c4e; blue: Q  \u03c4e(tot)=0.055 \u03c4e(tot)=0.064 \u03c4e(tot)=0.073 \u03c4e(tot)=0.082 Fig. 4.\u2014 shows each of the four solutions of QHII(z) (blue curves) indicated by the four blue solid dots in Figure 3, along with the respective cumulative \u03c4e (red curves). It is now clear that the value of \u02d9 Nion,IGM(z = 5.7) plays a key role in determining the viability of each solution of QHII(z). Under the two boundary conditions, Eq 16 and 17, two families of solutions are possible, each of which is simultaneously consistent with the latest values of \u03c4e from Planck Collaboration et al. (2016) observations. Indicated by the four blue dots in Figure 3 are four solutions in the (we call) \u201cPop III-supported\" family with \u03c4e = (0.055, 0.064, 0.073, 0.082) corresponding to the (central, +1\u03c3, +2\u03c3, +3\u03c3) values from Planck Collaboration et al. (2016). Figure 4 shows each of the four solutions of QHII(z) (blue curves) indicated by the four blue solid dots in Figure 3, along with the respective cumulative \u03c4e (red curves). The common characteristics of these solutions in this solution family are that (1) \u03c7 < 0, indicating that the escape fraction decreases with increasing redshift, (2) the Pop III stars make a signi\ufb01cant and late contribution to the overall ionizing photon budget. The combination of negative \u03c7 and late, signi\ufb01cant Pop III contribution permits a slight dip in ionized fraction at a redshift slightly higher \u2013 13 \u2013 than z = 5.7, to satisfy 17. This set of solutions, however, may be inconsistent with some other independent observations. Here we provide some notable examples. 15 15 15 15 30 30 30 30 40 40 40 40 50 50 50 50 70 70 70 70 100 100 100 100 150 150 150 150 50.56 50.56 50.56 50.56 50.56 50.71 50.71 50.71 50.71 50.71 50.765 50.765 50.765 50.765 50.765 0.046 0.046 0.055 0.055 0.055 0.055 0.055 0.055 0.064 0.064 0.064 0.064 0.064 0.064 0.073 0.073 0.073 0.073 0.073 0.082 0.082 0.082 0.082 -6 -5 -4 -3 -2 -1 0 1 2 3 \u03c7 -6 -5 -4.5 log \u2126PopIII,crit nion/nH \u03c4e \u02d9 Nion,IGM@z = 5.7 Fig. 5.\u2014 shows contours of the ratio of the number of ionizing photon produced per hydrogen atom (red), along with contours of \u03c4e (blue) and of log \u02d9 Nion,IGM(z = 5.7) (black). Figure 5 shows contours of the ratio of the number ionizing photon produced per hydrogen atom (red). Fang & Cen (2004) perform a detailed analysis of metal enrichment history and show that Pop III to Pop II transition occurs when 3 \u221220 ionizing photons per hydrogen atom, depending on the model for the IMF , have been produced by Pop III stars, based on considerations of primary atomic cooling agents, CII and OI, at low temperature, corresponding to [C/H]crit = \u22123.5 and [O/H]crit = \u22123.1 (Bromm & Loeb 2003). For the four solutions, indicated by the four blue dots in Figure 5, we see much higher, 80 \u2212110 ionizing photons per hydrogen atom have been produced at the model transition \u2126PopIII,crit, in order to attain the solutions. Note that in the scenario of dust cooling induced fragmentation (Schneider & Omukai 2010), the critical transition metallicity is 1 \u22123 orders of magnitude lower that is still more stringent. These considerations indicate that these QHII(z) solutions are self-inconsistent, in the sense that the required Pop III contribution in order for the solutions to be possible is unattainable. A second example concerns the neutral fraction of the IGM during the epoch of reionization at z > 6. In a recent careful analysis of possible signatures of damping wing absorption pro\ufb01les of the Ly\u03b1 emission line of quasar J1120+0641 at z = 7.1, under the assumption that DLAs, being suf\ufb01ciently rare, are not responsible for the absorption of the Ly\u03b1 emission \u2013 14 \u2013 redward of the line, Greig et al. (2016) conclude that the mean neutral fraction of the IGM is 0.40+0.41 \u22120.32 (2\u03c3). All of the four solutions shown in Figure 4 have the mean neutral fraction signi\ufb01cantly less than a few percent, thus are ruled out at > 2.5\u03c3 level. 0 2 4 6 8 10 12 14 16 18 20 z 10-3 10-2 10-1 100 Q(z)  & \u03c4e(>z) Q(z) and \u03c4e solutions:  three green and one black dots in Fig 4 red: \u03c4e; blue: Q  \u03c4e(tot)=0.082 \u03c4e(tot)=0.073 \u03c4e(tot)=0.064 \u03c4e(tot)=0.055 1-xHI(z=7): Greig etal 2016 Fig. 6.\u2014 shows each of the four solutions of QHII(z) (blue curves) indicated by the three green (for \u03c4e = (0.064, 0.0740.082)) and one black (for \u03c4e = 0.055) solid dots in Figure 3, along with the respective cumulative \u03c4e(> z) (red curves). Indicated by the magenta solid dot is an observational measurement of neutral fraction of the IGM at z = 7.1 by Greig et al. (2016) based on the damping wing signature imprinted on the red side of the Ly\u03b1 emission line of quasar J1120+0641. Let us now turn to the other solution family with reduced Pop III contribution that is additionally con\ufb01ned to much higher redshift. Figure 6 shows each of the three solutions of QHII(z) (blue curves) indicated by the three green and one solid dots in Figure 3, along with the respective cumulative \u03c4e (red curves). Several trends shared by solutions in this solution family may be noted. First, QHII(z) increases exponentially as a function of redshift in the range of z = 5.7 to z = 9 \u221214, depending on the value of total \u03c4e; a lower total \u03c4e corresponds to a higher redshift, but lower value of QHII(z) base, from which the exponential growth starts. All four solutions are consistent with the observationally inferred mean neutral fraction of the IGM at z = 7.1, shown as a magenta dot with 1\u03c3 range (Greig et al. 2016). Second, there is a distinct, separate peak QHII(z) at z = 14\u221218, for \u03c4e = 0.082 \u22120.064 (in that order) with height of (0.4 \u22120.07) (in the same order). This high redshift peak of QHII(z) is due to contributions from Pop III stars. The exact height and duration of this peak may depend on the assumptions concerning the transition from Pop III to Pop II temporally and spatially, that will require \u2013 15 \u2013 detailed modeling beyond the scope of this work. We note, however, that the results do not change signi\ufb01cantly when values of \u03c3III = 0.01 \u22121 are used (0.25 is used for the case shown in Figure 6), suggesting that the existence, the QHII(z) value of the peak and the peak redshift are fairly robust. We also note that all these solutions lie below \u2126PopIII,crit = 10\u22126.4, which, when compared with Figure 5, indicates a consistency in terms of Pop III stars forming in the metallicity regime that is physically plausible, if low temperature atomic cooling, not dust cooling, dictates fragmentation of star-forming gas clouds. Finally, it is seen that these solutions have \u03c7 \u22650, indicating that the escape fraction increases with increasing redshift, perhaps not an unexpected result based on physical considerations that galaxies at high redshifts are less massive, their star-formation episodes more bursty and consequently their interstellar medium more porous to allow for more ionizing photons to escape. Simulation results are consistent with this trend (e.g., Kimm & Cen 2014). In summary, this solution family are self-consistent. If, however, \u03c4e = 0.055 holds up, there is no solution of QHII(z) with log \u02d9 Nion,IGM(z = 5.7) = 50.71. In order to get a solution with \u03c4e = 0.055, one requires log \u02d9 Nion,IGM(z = 5.7) = 50.765, which, with the conservative choice of +1\u03c3 value \u0393\u221212 = 0.31 (see Eq 5), in turn requires \u03bbmfp(z = 5.7) = 5.3pMpc, which would be at about 2.9\u03c3 lower bound of the observationally inferred value. In combination with the +1\u03c3 value of \u039312 used, such an event would be a 3.0\u03c3 occurrence, suggesting tension, which we examine in the next section. 4. \u03bbmfp(z = 5.7): A Strong Test of Matter Power Spectrum on Small Scales We were left in a state of signi\ufb01cant tension between accommodating \u03c4e = 0.055 and \u03bbmfp(z = 5.7) based on the extrapolated observational data at z < 5.5 in \u00a73. The tension may be alleviated, if one chooses not to strongly advocate the central value of \u03c4e = 0.055 (Planck Collaboration et al. 2016) but instead emphasize the harmonious concordance between \u03bbmfp(z = 5.7), \u0393(z = 5.7) and \u03c4e \u22650.64. We take this discrepancy in a somewhat different way and suggest that the extrapolation of the lower redshift measurement of \u03bbmfp should be taken with caution, despite the smooth trend seen in the observed redshift range (z = 2.3\u22125.5). We take a step further yet to perform a theoretical analysis to better understand the physical origin of \u03bbmfp(z = 5.7) in the context of the standard cosmological model. It is useful to separate out the overall \u03bbmfp into two components in the post-overlap epoch at z = 5.7, one due to the \u201ctranslucent\", general volume-\ufb01lling low density IGM that collectively attenuates ionizing photons and the other due to \"opaque\" disks (like LLSs) that block entirely all incident ionizing photons. We shall denote them \u03bbmfp,IGM and \u03bbmfp,halo, respectively. The total \u03bbmfp is \u03bbmfp = (\u03bb\u22121 mfp,halo + \u03bb\u22121 mfp,IGM)\u22121. (23) \u2013 16 \u2013 The \u03bbmfp,IGM can be approximated by the volume-weighted neutral fraction of the IGM as \u03bbmfp,IGM = (\u00af \u03c3ionfHI,volnH,0(1 + z)3)\u22121 = 19.5(1 + z 6.7 )\u22123( \u00af \u03c3ion 3.16 \u00d7 10\u221218cm2)\u22121( fHI,vol 0.9 \u00d7 10\u22124)\u22121 pMpc, (24) where fHI,vol = 0.9 \u00d7 10\u22124 is the volume-weighted neutral fraction of the IGM, inferred by the directly observed Ly\u03b1 (and higher order Lyman transitions) optical depth at z = 5.7 (Fan et al. 2006). As we have argued earlier, while the mass-weighted neutral fraction determined from such a method may be signi\ufb01cantly model-dependent, the volume-weighted neutral fraction is not expected to be, because it is free from clumping factor dependence and most of the optical depth contributions stem from low-density regions of optical depth of order unity whose Jeans scales are typically resolved in most simulations used. \u03bbmfp,halo stems from self-shielding dense gas in halos. A computation of \u03bbmfp,halo may not seem a well posed problem at \ufb01rst sight, because it would appear to depend on both the abundance of halos and their cross sections (the sizes of radiation blocking disks). It is not immediately obvious how one may precisely speci\ufb01y their cross sections, even if their abundance is known. We show that this ambiguity can be removed, when considerations are given to the physical conditions of halo gas as a function of halo-centric radius and a \u201ccorrect\" de\ufb01nition of \u03bbmfp,halo is adopted, which we now describe. After the HII regions have overlapped in the aftermath of reionization, neutral gas in halos essentially becomes a set of disconnected isolated islands that are increasingly self-shielded and optically thick to ionizing photons toward to the centers of halos. Under the assumption of spherical symmetry, for a given halo, we can compute the column density as a function of halo-centric radius r outside-in as NHI(r) = Z \u221e r xHI(r\u2032)\u03b4(r\u2032)nH,0(1 + z)3dr\u2032, (25) where \u03b4(r) \u2261n(r)/\u00af n is overdensity, for which we use the universal halo density pro\ufb01le (NFW, Navarro et al. 1997) with gas following mass over the relevant radial range (e.g., Komatsu & Seljak 2001). In the core region of a halo the gas density is constrained such that the gas entropy does not fall below the entropy of the gas at the mean density and cosmic microwave background temperature. In practice, the upper limit of the integral in Eq 25 is chosen when \u03b4 = 1 (i.e., the mean density) but its precise value makes no material difference to the calculated NHI(r) in the range of relevance. The local neutral fraction xHI(r) at radius r can be computed using the local balance between recombination and photoionization through a spherical radiative transfer: \u0393 exp [\u2212NHI(r)\u00af \u03c3ion]xHI(r) = [1 \u2212xHI(r)]2[1 + Yp/4(1 \u2212Yp)]\u03b1B(T)\u03b4(r)nH,0(1 + z)3, (26) where \u0393 is the \u201cbackground\" ionization rate prior to signi\ufb01cant attenuation when approaching the halo. We solve Eq (25,26) numerically to obtain NHI(r) and xHI(r), for a given \u0393. \u2013 17 \u2013 -1 -0.5 0 0.5 log r/rv 14 15 16 17 18 19 20 21 22 log NHI (cm-2)  rv=1 pkpc  rv=10 pkpc -2 -1 -0.5 0 0.5 log r/rv 0 0.5 1 1.5 ALL(<r)/\u03c0 rv 2  rv=1 pkpc  rv=10 pkpc -1 0 1 log rv (pkpc) 0 0.5 1 1.5 2 ALL(rv)/\u03c0 rv 2 6 7 8 9 10 11 12 13 log Mh (Msun) -7 -6 -5 -4 -3 -2 -1 0 1 2 3 dALL/dlog M (pkpc2 cMpc-3)  dALL,tot/dlog Mh  ALL,tot(>Mh)  halo MF Fig. 7.\u2014 Top-left panel: shows the integrated column density (from outside inward down to the halo-centric radius r) as a function of r (in units of virial radius rv), for two cases with virial radius rv equal to 1 pkpc (black solid curve) and 10 pkpc (red dashed curve) at z = 5.7 [with corresponding virial (temperature, mass) of (1.5 \u00d7 103K, 9.7 \u00d7 106 M\u2299) and (1.5 \u00d7 105K, 9.7 \u00d7 109 M\u2299), respectively], using \ufb01ducial values for various parameters: \u0393\u221212 = 0.2, \u00af \u03c3ion = 3.16 \u00d7 10\u221218 cm2. For the NFW pro\ufb01le we use a concentration parameter C = 5 in both cases. Top-right panel: shows the cumulative cross section for ionizing photons of a halo ALL(< rp) in units of the virial area (\u03c0r2 v) as a function of halo-centric radius in units of the virial radius rv for the two halos shown in the top-left panel of Figure 7. Bottom-left panel: shown the effective total cross section for Lyman continuum photons in units of halo virial area as a function of halo virial radius at z = 5.7. Bottom-right panel: shows the differential function dALL,tot/d log Mh \u2261n(Mh)M ln 10ALL(Mh) as a function of Mh (solid blue curve), its cumulative function ALL,tot(> Mh) (dotted blue curve), along with the halo mass function n(Mh)M ln 10 as a function of Mh (dashed red curve). In the top-left panel of Figure 7 we show the integrated column density (from outside inward down to the radius r) as a function of halo-centric radius r (in units of virial radius rv) for two cases with virial radius rv equal to 1 pkpc (black solid curve) and 10 pkpc (red dashed \u2013 18 \u2013 curve), respectively. We see that at about r/rv \u223c3 the column density is well below 1017cm\u22122, con\ufb01rming that the exact integration starting radius is not important for column densities in the relevant range for signi\ufb01cant attenuation of LyC photons. In both cases we also see that there is a rapid upturn of the column density starting around \u223c1018cm\u22122, indicating the radial location of the beginning of self-shield and transition from a highly ionized to an increasingly neutral medium. The rapid ascent suddely \ufb02attens out at \u223c1020cm\u22122, sigalling the arrival of a largely neutral medium, coincidental with column density similar to that of the damped Lyman alpha systems (DLAs). It is instructive to note that the transition from ionized to an increasingly neutral medium is halo virial radius (or halo mass) dependent, with a larger halo transitioning at a larger radius in units of its virial radius. This indicates that the density of the ionizing front propagating into halos is halo mass dependent, suggesting that the common practice of using a constant density as a proxy for the density of ionization front (e.g., Miralda-Escud\u00e9 et al. 2000) could potentially be slightly extended, although a more detailed analysis should be performed to assess this. To devise an appropriate method to compute the effective cross section ALL for LyC photons for a given halo, it is useful to gain a more clear understanding of the physical meaning of \u03bbmfp,halo. For a line of sight cross area of size \u2206A, if it is completely opaque to ionizing photons, then the effective area for intercepting LyC photons would be just equal to \u2206A. For a cross area of size \u2206A that is not completely opaque to LyC photons, one may de\ufb01ne the effective area for intercepting ionizing photons \u2206ALL, which is \u2206ALL = \u2206A[1 \u2212exp (\u2212NHI\u00af \u03c3ion)], (27) where NHI is the column density integrated along that line of sight (not the radially integrated column density shown in the top-left panel of Figure 7), which is computed using NHI(r) and xHI(r) that we have numerically obtained solving Eq (25,26). Upon integrating the projected area of a halo, we obtain the cumulative cross section for ionizing photons of a halo as a function of projected radius rp ALL(< rp) = Z rp 0 2\u03c0r\u2032 p[1 \u2212exp (\u2212NHI(r\u2032 p)\u00af \u03c3ion)]dr\u2032 p. (28) The top-right panel of Figure 7 shows ALL(< rp) in units of the virial area (\u03c0r2 v) as a function of halo-centric radius in units of the virial radius rv for the two halos shown in the top-left panel of Figure 7. To re-iterate a point made earlier, the total effective cross section is larger for larger halos in units of the virial area, shown quantitatively in the bottom-left panel of Figure 7. In the calculations performed involving the NFW pro\ufb01le, one needs to specify the concentration parameter c, which has been computed by a number of groups (e.g., Bullock et al. 2001; Wechsler et al. 2002; Angel et al. 2016; Ricotti et al. 2007). We adopt the results of Dolag et al. (2004): c = 9.6(Mh/1014 M\u2299)\u22120.10(1 + z)\u22121; the results obtained do not sensitively depend on slightly different formulae of c in the literature. \u2013 19 \u2013 We compute \u03bbmfp,halo by \u03bb\u22121 mfp,halo = Z \u221e Mcut n(Mh)Mh ln 10 ALL(Mh)d log Mh, (29) where ALL(Mh) is the total cross section of LyC photons for a halo of mass Mh; n(Mh) is the halo mass function at the redshift in question. The bottom-right panel of Figure 7 shows cross section function, n(Mh)Mh ln 10 ALL(Mh) (solid blue curve), its cumulative function ALL,tot(> Mh) (dotted blue curve), along with mass function, n(Mh)M ln 10(dashed red curve), as a function of Mh. We see that the cross section function is signi\ufb01cantly \ufb02atter than the halo mass function, due to the fact that the cross section in units of virial area is higher with increasing halo mass, i.e., ALL(Mh)/M2/3 h correlates positively with Mh, shown in the bottom-left panel of Figure 7. Nonetheless, ALL scales still sub-linearly with Mh, causing n(Mh)M ln 10ALL(Mh) to increase with decreasing halo mass Mh. The \u0393 \u2212\u03bbmfp relation in the standard \u039bCDM model for four cases of Mcut = (1.6 \u00d7 108, 5.8 \u00d7 107, 2.7 \u00d7 107, 8.6 \u00d7 106) M\u2299, corresponding to a halo virial temperature cutoff of Tv,cuto\ufb00= (104, 5 \u00d7 103, 3 \u00d7 103, 1.4 \u00d7 103)K, are shown also in Figure 1 as the blue curves. First of all our results af\ufb01rm a general self-consistency between radiation \ufb01eld and ionization structures around halos in the \u039bCDM model, since the theoretically predicted relation (the blue curves) can go through this already tightly constrained parameter space. This is a strong and unique support for the \u039bCDM model with respect to its matter density power spectrum (both amplitude and shape) on small scales corresponding to halo masses approximately in the range of 107 \u22121010 M\u2299. It is noted that this constraint on matter power spectrum is based entirely on the consideration of the halos as \u201csinks\" of ionizing photons. We point out the fact that \u03bbmfp,halo depends sensitively on the lower mass cutoff Mcut in the integral in Eq 29, as shown in the bottom-right panel of Figure 7. We show that this dependence provides a new, sensitive probe of the small-scale power in the cosmological model, when confronted with measurements of \u03c4e. It is useful to note that in computing \u03bbmfp,halo we have neglected possible constribution due to collisional ionization in halos with virial temperature signi\ufb01cantly above 104K. Thus, our computed \u03bbmfp,halo is somewhat overestimated and our subsequent conclusion drawn on small-scale power conservative. Figure 8 shows \u03bbmfp as a function of the lower mass cutoff Mcut in the integral in Eq 29 (blue solid curve). Shown as symbols are four cases along the curve, with (log Mcut/ M\u2299, \u03bbmfp/pMpc, log \u02d9 Nion,IGM/cMpc\u22123s\u22121, \u03c4e) equal to (5.10, 3.7, 50.916, 0.047) (green star), (6.95, 5.3, 50.765, 0.055) (red dots), (7.58, 6.8, 50.660, 0.064) (magenta square) and (8.67, 10.5, 50.550, 0.073) (black diamond). Each set of four numbers has the following relational meaning: for a given measurement of \u03c4e, the minimum required ionizing photon emissivity entering the IGM is log \u02d9 Nion,IGM in order for that \u03c4e to be a possible solution, which in turn corresponds to a mean free path of \u03bbmfp, which can be achieved if the lower mass cutoff of the halo mass function is Mcut. We see that the dependence of \u03bbmfp on Mcut is signi\ufb01cant, which provides a new constraint on the small-scale power in the cosmological model at a level that has hitherto been out of reach. \u2013 20 \u2013 5 6 7 8 9 log Mcut (Msun) 3 4 5 6 7 8 9 10 11 12 \u03bbmfp (pMpc) (log Mcut, \u03bbmfp, log \u02d9 Nion,IGM, \u03c4e) \u03bbmfp \u2212Mcut relation (5.10, 3.7, 50.916, 0.047) (6.95, 5.3, 50.765, 0.055) (7.58, 6.8, 50.660, 0.064) (8.67, 10.5, 50.550,0.073) Fig. 8.\u2014 shows \u03bbmfp as a function of the lower mass cutoff Mcut in the integral in Eq 29 (blue solid curve). Also shown as symbols are four cases along the curve, with (log Mcut/ M\u2299, \u03bbmfp/pMpc, log \u02d9 Nion,IGM/cMpc\u22123s\u22121, \u03c4e) equal to (5.10, 3.7, 50.916, 0.047) (green star), (6.95, 5.3, 50.765, 0.055) (red dot), (7.58, 6.8, 50.660, 0.064) (magenta square) and (8.67, 10.5, 50.550, 0.073) (black diamond). The thin blue dashed line is obtained when no entropy \ufb02oor due to that of mean cosmic gas is imposed. The thin, black dot-dashed and red dotted curves are obtained assuming there is no contribution from halos with virial temperature greater than 3 \u00d7 105K and 3 \u00d7 104K, respectively The dependence of \u03bbmfp on Mcut shown in Figure 8 can be translated into a constraint on dark matter particles. Here, we take warm dark matter as an example. In the warm dark matter model the smoothing scale, de\ufb01ned as the comoving half-wavelength of the mode for which the linear perturbation amplitude is suppressed by 2, is Rs = 0.48(\u2126M/0.25)0.11(h/0.7)\u22121.22(mx/keV)\u22121.11h\u22121Mpc (30) for a warm dark matter particle mass of mx (e.g., Viel et al. 2005), which we adopt as a proxy for a sharp cutoff (or free-streaming scale of particles). The equivalent free-streaming halo mass is then Ms = 5.8 \u00d7 1010(\u2126M/0.3)1.33(h/0.7)\u22124.66(mx/keV)\u22123.33 M\u2299. (31) Given the dependence chain of log Mcut on \u03bbmfp on \u02d9 Nion,IGM on \u03c4e, we obtain the lower bound on the mass mx of thermally produced warm dark matter particles as a function of \u03c4e shown as \u2013 21 \u2013 0.045 0.05 0.055 0.06 0.065 0.07 0.075 \u03c4e 5 10 30 50 100 300 500 1000 mx & ms (keV) mx=mass of thermal WDM particles ms=mass of sterile neutrinos Fig. 9.\u2014 shows the lower bound on the mass mx of thermally produced warm dark matter particles as a function of \u03c4e (blue solid curve). Similarly, the red dashed curve shows the lower bound on the mass ms of sterile neutrinos as a function of \u03c4e. the blue solid curve in Figure 9. The lower bound on the mass mx of thermally produced warm dark matter particles can be translated similarly to a lower bound constraint on the mass ms of sterile neutrinos produced via active-sterile neutrino oscillations obeying approximately a generalized Fermi-Dirac distribution. In this case, the effect of sterile neutrino is approximately the same as for thermally produced warm dark matter by using the following expression to relate the two masses (Colombi et al. 1996; Viel et al. 2005): ms = 4.46keV( mx 1keV)4/3( 0.12 \u2126Mh2)1/3. (32) The result is shown as the red dashed curve in Figure 9. The current best constraint on mx based on Ly\u03b1 forest is mx \u22653.3keV(2\u03c3) (Viel et al. 2013), improving upon earlier studies that generally constrain mx \u22650.5 \u22121keV (e.g., Narayanan et al. 2000; Barkana et al. 2001; Viel et al. 2005; Abazajian 2006). Combining with the 1\u03c3 upper limit used for \u0393 in our calculations, we \ufb01nd mx \u2265(15.1, 9.8, 4.6)keV at (1, 1.4, 2.2\u03c3) C.L., (33) based on \u03c4e = 0.055 \u00b1 0.009 and +1\u03c3 on \u0393. The corresponding constraint on sterile neutrino mass is ms \u2265(161, 90, 33)keV at (1, 1.4, 2.2\u03c3) C.L., (34) \u2013 22 \u2013 which basically rules out, for example, 7keV sterile neutrino dark matter model (Bezrukov & Gorbunov 2014; Park et al. 2014; Abazajian 2014). The lower bound placed on warm dark matter particle mass (or in general, on the small-scale power) hinges on the assumption that dark matter halos make up the bulk of the Lyman limit systems at z = 5.7. Are there possible caveats with respect to this assumption? Let us examine this. Under a physically plausible scenario of stellar reionization, there are possibly two additional kinds of (signi\ufb01cantly) neutral systems to serve as Lyman limit systems to contribute to the absorption of LyC photons. The \ufb01rst kind is neutral regions that envelope the expanding HII regions. Let us suppose that each HII region that is expanding has a radius of R and the neutral region surrounding it has a thickness of \u2206R. Analysis of the Ly\u03b1 forest at z = 5.7 indicates a volume-weighted neutral fraction of the IGM fHI,V \u223c0.9 \u00d7 10\u22124 at z = 5.7 (Fan et al. 2006). This provides a constraint on the possible size of \u2206R: \u2206R \u2264fHI,VR 3 . (35) The ionization front propagation speed at z = 5.7 is vIF = F \u00af nH = \u0393 \u00af \u03c3\u00af n = 1.7 \u00d7 104(\u0393\u221212 0.31 )( \u00af \u03c3 3.16 \u00d7 10\u221218cm2)\u22121 km s\u22121, (36) where \u00af nH is mean hydrogen number density at z = 5.7. Thus, the time it takes to sweep through the radial shell of thickness \u2206R would be \u2206t = \u2206R vIF \u2264fHI,VR 3vIF = 9.4 \u00d7 103( R 5.3pMpc)( fHI,V 0.9 \u00d7 10\u22124)(\u0393\u221212 0.31 )\u22121( \u00af \u03c3 3.16 \u00d7 10\u221218) yrs. (37) Thus, for any reasonable values of the parameters involved, \u2206t is much shorter than the Hubble time at z = 5.7 (which is about 1 Gyr). This suggests that such a con\ufb01guration is highly unlikely. Note that our assumption that these shells surround spherical HII regions is not necessary but only for the ease of illustration. If these spherical shells are replaced by pancaky bridges or \ufb01lamentary bridges between (or connecting) HII regions, the results and conclusions based on the above analysis remain largely the same, as long as the size of these pancakes or \ufb01laments are on the same order of \u223c10pMpc; in terms of our conclusion reached, even for a size of 1000pMpc, our conclusion remains unchanged. The second kind of possible neutral regions may be comprised of patches of neutral islands in the voids that are last reionized. We approximate them as opaque spheres with a radius of rvoid and a mean separation between them of dvoid, which can be related to the observed fHI,V: 4\u03c0 3 r3 voidd\u22123 void \u2264fHI,V. (38) The mean free path to LyC photons due to these islands would be \u03bbmfp,void = d3 void \u03c0r2 void \u2265(4 3)2/3\u03c0\u22121/3dvoidf\u22122/3 HI,V = 412dvoid( fHI,V 0.9 \u00d7 10\u22124)\u22122/3. (39) \u2013 23 \u2013 The typical separations of voids, i.e., dvoid, has to be on the order of the clustering scale of galaxies, which is about 4 \u22125cMpc (e.g., Ouchi et al. 2010), or larger. This suggests that \u03bbmfp,void \u2265245 pMpc at z = 5.7, implying that possible, to-be-last-reionized neutral islands in voids do not contribute much to the mean free path of LyC photons at z = 5.7. We thus conclude that halos likely contribute predominantly to the mean free path of LyC photons at z = 5.7 (likely at all lower redshifts as well, for that matter). Finally, we note that for simplicity we have adopted the assumption of sphericity of gas distribution in and around halos in question. Any deviation from sphericity would result in a reduction in cross section hence a more stringent demand for more small scale power. In addition, we note that baryonic fraction may be lower than the mean universal fraction. Furthermore, some gas in large halos with virial temperature higher than \u223c104K may be heated up to remove itself from the HI category. To give a sense of the magnitude of this effect we show in Figure 8 two additional cases where we assume that halos with virial temperature greater than 3 \u00d7 105K (thin, black dot-dashed curve) and 3 \u00d7 104K (thin red dotted curve), respectively, do not contribute to \u03bbmfp. We see a signi\ufb01cant effect; numerically, to attain \u03bbmfp = (5.3, 6.8, 10.5)pMpc in order to yield \u03c4e = (0.047, 0.055, 0.064, 0.073), respectively, the required log Mcut changes from (8.67, 7.58, 6.95) for no upper cutoff to (8.54, 7.51, 6.89) for upper cutoff of virial temperature of 3 \u00d7 105K, to (7.92, 7.07, 6.51) for upper cutoff of virial temperature of 3 \u00d7 104K. Moreover, internal ionizing radiation may reduce the HI fraction. Therefore, our assumptions and derived limits on small-scale power and on dark matter particle mass are all on the conservative side. 5. Discussion 5.1. Rapid Reionization Towards z = 5.7 The intrinsic emissivities of LyC photons at z = 5.7 and z = 6 are almost identical. We can use this fact to outline the nature of percolation of HII regions near the end of the reionization. We \ufb01rst note that we \ufb01nd that the theoretically derived relation of \u0393 \u2212\u03bbmfp at z = 6 is nearly identical to that at z = 5.7 at the visual resolution of eye when overplotted in Figure 1. It means, if the universe were in the post-overlap regime already at z = 6, its volume-weighted neutral fraction ought to be similar to that at z = 5.7. In other words, \u03bbmfp due to halos (mostly) based on \u039bCDM model and emissivity at z = 6 can easily accommodate a transparent universe similar to the one observed at z = 5.7. The observations indicate otherwise: fHI,V \u223c0.9 \u00d7 10\u22124 at z = 5.7 versus fHI,V > 2 \u00d7 10\u22124 at z = 6 (Fan et al. 2006). Thus, the universe is not fully ionized at z = 6 in the way of imposing a smaller \u03bbmfp hence a lower \u0393 for a given \u02d9 Nion,IGM. The likely, perhaps only, consistent solution would be that HII regions have not overlapped at z = 6 so that neutral patches in the IGM (not in the halos) render \u03bbmfp much lower than the notional \u03bbmfp,IGM and \u03bbmfp,halo in the post-overlap epoch. The inferred value of \u0393\u221212 < 0.02 at z = 6 (based on Ly\u03b3 absorption) (Cen & McDonald 2002; Fan et al. 2006) suggests that \u03bbmfp at z = 6 is an order of magnitude lower than that at z = 5.7. \u2013 24 \u2013 This is clear and fairly direct evidence that the percolation of HII regions is not yet complete at z = 6, indicating that the universe is in a rapid transitory phase from z = 6 to z = 5.7 clearing up some of the last neutral patches that dominate the mean free path, in a monotonic and irriversible process. Topologically, this indicates that HII regions transition from a set of isolated islands at z = 6 to a connected network of swiss-cheese-like HII region at z = 5.7. This expected rapid reionization process is consistent with and required by the necessary small values of \u03bbmfp \u22646.8pMpc at z = 5.7 to achieve \u03c4e \u22640.064, which in turn requires contribution from minihalos (those with virial temperature less than 104K or virial mass less than 1.6 \u00d7 108 M\u2299at z = 5.7). Gas in minihalo, when exposed to ionizing photons, responds dynamically by slowly evaporating through the action of thermal pressure of photoheated gas. Iliev et al. (2005) show that it takes about 100 \u2212200Myr to photoevaporate a minihalo of mass 107 M\u2299at z = 9. This process is expected to take longer for more massive minihalos. In our case, a minihalo of mass 107 M\u2299is relevant for \u03c4e = 0.055 (see the red dot in Figure 8); for \u03c4e = 0.064 minihalos of mass 1.6 \u00d7 108 M\u2299would be relevant (see the magenta square in Figure 8). Thus, it is probably true that, for the range of interest, the time scale taken for photoevaporation of relevant minihalos is 100 \u2212200Myr or longer. We note that the universal age difference from z = 6 to z = 5.7 is 63Myr, from z = 7 to z = 5.7 is 231Myr. We see in Figure 6 that the neutral fraction at z = 7 is about 40%, meaning about 40% of minihalos have not yet been exposed to ionizing radiation at z = 7. Thus, it is probable that a signi\ufb01cant fraction, perhaps a large majority, of minihalos have not lost gas in their inner regions (that actually contribute to the mean free path of LyC photons) by z = 5.7, permitting the possibility that they contribute signi\ufb01cantly to the mean free path of LyC photons, if necessary. 5.2. On fesc of Galaxies at Epoch of Reionization Using Eq 14, the four points (represented by the four symbols) in Figure 8 give fesc = (20.7, 14.6, 11.5, 8.9)%, in order to arrive at the reionization solutions constrained by the state of the IGM at z = 5.7 with \u03c4e = (0.047, 0.055, 0.064, 0.073), respectively. This required fesc based on the observed state of the IGM at z = 5.7 is consistent with computed fesc,comp = 10 \u221214% based on state-of-the-art high resolution cosmological radiation hydrodynamic simulations of dwarf galaxies at the epoch of reionization of Kimm & Cen (2014). We point out that the upper value (14%) includes contributions from runaway OB stars. It is noteworthy that fesc,comp is effectively a measure of the porosity of the interstellar medium, where LyC photons escape through transparent holes into the IGM. Therefore, a correct treatment/implementation of supernova feedback is essential, as is in Kimm & Cen (2014) but not in any other simulations that the author is aware of. Including Wolf-Rayet stars for Pop II stellar population, which empirically are much more abundant in local metallicity environment that is expected for galaxies at the epoch of reionization, may further increase the ratio of LyC photons to FUV photons, i.e., \u03beion, thus lessen the requirement for a high fesc. Thus, it seems that \u2013 25 \u2013 the stellar emissivity observed is adequate for maintaining the state of the IGM in terms of global and local ionization balance. It should be noted that these changes have no effect on solutions of reionization history that we have obtained, which depends directly on \u02d9 Nion,IGM. 5.3. Dichotomy in the Evolution of Lyman Alpha Emitters z > 6 In Figure 3 we see that solutions without Pop III contributions require \u03c7 = (0.7, 2.2, 3.6) for \u03c4e = (0.055, 0.064, 0.073), respectively. In general, the solutions even with Pop III contributions requires \u03c7 > 0 as long as \u03c4e \u22650.052. We note that the overall fesc tends to correlate with the porosity of the ISM, while individual fesc is strongly dependent on the line of sight of the observer (e.g., Cen & Kimm 2015). A positive \u03c7 > 0 is physically consistent with the expectation that smaller galaxies, having shallower gravitational potential wells, may be more susceptible to feedback processes from supernovae and have more porous ISM. Simulation results are consistent with this expected trend (e.g., Kimm & Cen 2014). Is there observational evidence that the escape of Ly\u03b1 and of LyC photons are both correlated with ISM posority? Jones et al. (2013) \ufb01nd an interesting trend of lower covering fractions of low-ionization gas for galaxies with strong Ly\u03b1 emission, providing evidence for a reduction in the average HI covering fraction (hence an increase in the escape fraction of ionizing radiation) is correlated with increase in Ly\u03b1 emission. Shapley et al. (2003) \ufb01nd that the blueshifts of interstellar absorption lines in LAEs and LBGs are similar at \u223c\u2212200 km s\u22121, suggesting that the velocity of out\ufb02ows in LAEs and LBGs are comparable. But their study also reveals a trend that Ly\u03b1 EW increases with decreasing \u2206vem\u2212abs in the EW range of \u221215 to +50\u00c5. Furthermore, they con\ufb01rm that \u2206vLy\u03b1 of LAEs is systematically smaller than the values of LBGs, with \u2206vLy\u03b1 of about 200 km s\u22121 for LAEs compared to about 400 km s\u22121 for LBGs. Moreover, they clarify that \u2206vLy\u03b1 decreases with increasing EW of Ly\u03b1. Recently, Shibuya et al. (2014) \ufb01nd an anti-correlation between Ly\u03b1 EW and the covering fraction estimated from the depth of absorption lines, which is an indicator of average neutral hydrogen column density. Their results support the idea that neutral column density is a key quantity determining Ly\u03b1 emissivity, consistent with the notion that the escape of LyC and Ly\u03b1 is correlated with each other and due to lower column density holes in the ISM. The combination of these facts leads one to conclude that the Ly\u03b1 velocity offset is positively correlated with NHI and negatively correlated with EW, exactly predicted from results based on Ly\u03b1 radiative transfer calculations (e.g., Zheng et al. 2010). None of these properties concerning Ly\u03b1 emission can be attributed to differences in the out\ufb02ow velocity, which do not appear to exist between LAEs and LBGs. Taken together, intrinsically, one would have expected then that the escape of Ly\u03b1 photons should be made easier with increasing redshift; i.e., both the ratio of Lyman alpha emitters to overall galaxy population at a chosen Ly\u03b1 EW or the overall Ly\u03b1 luminosity to FUV luminosity ratio as a whole are expected to increase with redshift beyond z = 5.7. Such an expectation is not borne out with observations. At some EW cuts, observations \u2013 26 \u2013 have consistently found that the fraction of LAEs out of LBGs decreases by a signi\ufb01cant factor from redshift z = 6 to z = 8 (e.g., Treu et al. 2013; Vanzella et al. 2014; Faisst et al. 2014; Schenker et al. 2014; Tilvi et al. 2014; Furusawa et al. 2016). This observational evidence strongly suggests that the intergalactic medium may have increasingly diminished the observability of the Ly\u03b1 from z \u223c6 to z \u223c8, consistent with the rapid reionization picture depicted in Figure 6). Physically, this is due to the fact that signi\ufb01cantly neutral IGM limits the size of Stromgren sphere around galaxies (Cen & Haiman 2000). Caruana et al. (2014) conclude that the neutral fraction of the IGM at z \u223c7 to be \u223c0.5, which would be consistent with our computed model shown in Figure 6). On the other hand, even if the IGM is indeed masking the appearance of the Ly\u03b1 emission for most, relatively low luminosity galaxies at the epoch of reionization, for rare, very luminous galaxies (which each are also likely clustered with other galaxies) with large Stromgren spheres, their Ly\u03b1 emission lines may be unaffected or possibly enhanced (given \u03c7 > 0), under suitable conditions. A corroborative or con\ufb01rmative piece of evidence for this may be that, if a strong Ly\u03b1 line is detected, the emission region could, but not necessarily required to, be compact spatially and in velocity space due to lack of scattering. There are observational indications that this may in fact be the case. Sobral et al. (2015) observe a luminous Ly\u03b1 source (CR7) with luminosity of 1043.93\u00b10.05 erg/s at z = 6.6 (the most luminous Ly\u03b1 emitter ever found at z > 6) but with a narrow FWHM of 266\u00b115 km s\u22121. Hu et al. (2016) detect a luminous Ly\u03b1 emitting galaxy, COLA1, with luminosity of 1043.9 erg/s at z = 6.593. COLA1 shows a multi-component Ly\u03b1 pro\ufb01le with a blue wing, suggesting a large and highly Stromgren sphere perhaps well extending into the infall region. Matthee et al. (2015) have argued that there is little evolution in the luminosity function of the most luminous LAEs at these redshifts, suggesting that these objects lie in large HII regions and protect themselves from changes in IGM neutral fraction, consistent with the expectation, at least in principle. More pinpointed analysis will be desirable in this respect, combining reionization simulations with detailed radiative transfer of Ly\u03b1 photons. In summary, we expect that there is a dichotomy in the evolution of Ly\u03b1 emitting galaxies. For relatively low Ly\u03b1 luminosity galaxies, their emission lines will be progressively diminished with increasing redshift due to the increasingly neutral IGM beyond z \u223c6. On the other hand, for the most luminous Ly\u03b1 emitters, under suitable conditions, their Stromgren spheres are large enough to allow their Ly\u03b1 line to escape unscathed by the neutral IGM. Both are consistent with present tentative observational evidence. 6. Conclusions We utilize the joint observations of the Ly\u03b1 forest, the mean free path of ionizing photons \u03bbmfp, the luminosity function of galaxies and the total electron scattering optical depth \u03c4e, and theoretical insight on a relation between matter power spectrum and \u03bbmfp, to perform a detailed \u2013 27 \u2013 analysis of the solutions of cosmic reionization history that satisfy the observed boundary conditions of the IGM at z = 5.7. We summarize results and conclusions. (1) A theoretical relation between the mean free path and ionization rate at z = 5.7, requiring only the matter power spectrum, is derived. More scale power on 106 \u2212109 M\u2299 scales leads to lower mean free path. (2) A negative relation is found between the minimum effective ionizing photon emissivity for the IGM at z = 5.7 and the electron scattering optical depth \u03c4e. A higher emissivity is coupled with a less steep increase of ionizing photon escape fraction with increasing redshift, resulting in a later reionization episode hence a lower \u03c4e. (3) The minimum required mean escape fraction of ionizing photons from galaxies at z = 5.7 is found to be fesc = (20.7, 14.6, 11.5, 8.9) \u0000 \u03beion 1025.2 \u0001\u22121 % for \u03c4e = (0.047, 0.055, 0.064, 0.073), respectively, where \u03beion is the ratio of ionizing photo production rate (in cMpc\u22123 s\u22121) to FUV spectral density (in erg s\u22121 Hz\u22121 cMpc\u22123). The escape fraction is predicted to increase with increasing redshift, with the rate of increase required higher for higher \u03c4e. (4) While there is a family of possible solution, the 50% ionization fraction redshift lies in a relatively narrow range of z = 6.5 \u22127.5 for \u03c4e = 0.050 \u22120.082. The late reionization suggests that relatively low luminosity Ly\u03b1 emitters beyond z = 6, incapable of carving out a suf\ufb01ciently large Stromgren sphere, will be increasingly diminished, although the most luminous Ly\u03b1 emitters may possess a large enough Stromgren sphere to allow unimpeded transmission of their Ly\u03b1 lines, possibly characterized by compact spatial or velocity extent. (5) Topologically, reasonable arguments lead to the picture that the universe transitions from a set of isolated HII bubbles of typical individual sizes probably no greater than 1pMpc at z = 6 to a set of isolated neutral islands centered on halos that are embedded in one connected of HII region at z = 5.7. (6) A positive relation is found between \u03c4e and the maximum mean free path of ionizing photons at z = 5.7. The outcome comes about because the product of the free path and emissivity of ionizing photons at z = 5.7 is constrained by the observed Gunn-Peterson optical depth. The maximum mean free path at z = 5.7 is (3.7, 5.3, 6.8, 10.5)pMpc in order to yield \u03c4e = (0.047, 0.055, 0.064, 0.073), respectively. We do not \ufb01nd it possible to \ufb01nd a reionization solution with \u03c4e < 0.047 that satis\ufb01es all observed conditions. (7) The electron scattering optical depth \u03c4e thus provides a constraint on the mean free path, which in turn yields a new and powerful constraint on the matter power spectrum on 106\u2212 109 M\u2299scales at z = 5.7. With the latest Planck measurements of \u03c4e = 0.055 \u00b1 0.009, we can place an upper limit of (8.9 \u00d7 106, 3.8 \u00d7 107, 4.2 \u00d7 108) M\u2299on the cutoff mass of the halo mass function, or equivalent a lower limit on warm dark matter particle mass mx \u2265(15.1, 9.8, 4.6)keV or on sterile neutrino mass ms \u2265(161, 90, 33)keV in the warm dark matter model, at (1, 1.4, 2.2)\u03c3 con\ufb01dence level. (8) It is clear that a solution to the missing satellite problem (Klypin et al. 1999; Moore \u2013 28 \u2013 et al. 1999) is unattainable via the route of warm dark matter particle origin, because of the strong constraint on the upper bound on dwarf halo mass of \u22644.2 \u00d7 108 M\u2299at 2.2\u03c3 found. I thank Xiaohui Fan, Jordi Miralda-Escude, Graca Rocha and Hy Trac for helpful discussion. I also thank an anonymous referee for useful and constructive comments. This work is supported in part by grants NNX12AF91G and AST15-15389.",
                    "introduction": "The Gunn & Peterson (1965) optical depth of Ly\u03b1 photons provides the strongest and most sensitive constraint on the neutral hydrogen fraction of the intergalactic medium (IGM). The integrated electron scattering optical depth of the universe provides a complementary constraint on the ionized fraction of the IGM, but is insensitive to the neutral hydrogen fraction as long as the IGM is mostly ionized. Recent measurements of the electron scattering optical depths of the IGM by the cosmic microwave background radiation experiments (e.g., Hinshaw et al. 2013; Planck Collaboration et al. 2015) suggest that it may be signi\ufb01cantly below redshift z = 12 before the universe becomes half reionized. The observations of the high redshift (z > 6) quasar absorption spectra from the Sloan Digital Sky Survey (SDSS) and others (e.g., Fan et al. 2006) and arguments based on the slowly and continuously evolving IGM opacity (e.g., Becker et al. 2007) suggest that only at z = 5.7 the universe is suf\ufb01ciently ionized to allow for detectable transmission of Ly\u03b1 photons hence de\ufb01nitive measurements of (low enough) Ly\u03b1 (and higher order Lyman series) optical depth. It is generally accepted that stars are primarily responsible for producing most of the ion- izing photons for cosmological reionization. While it seems relatively secure to further suggest that the reionization process has begun at z \u226510 based on analysis of expected emergence of \ufb01rst galaxies in the standard cold dark matter model (e.g., Trac et al. 2015), the combination of these independent observational indications now paints a reionization picture that is rapidly arXiv:1606.05930v2  [astro-ph.CO]  14 Sep 2016 \u2013 2 \u2013 evolving at z = 6\u221210. Two important implications are that the so-called \ufb01rst galaxies that form out of primordial gas may be closer to us than thought before and that Popolation III (Pop III) stars formed with metal-free gas may extend to more accessible redshifts. In this contribution we perform a detailed analysis of the endgame of the cosmological reionization at z = 5.7. We examine joint constraints on the IGM from considerations of both global and local ionization balances observationally and, for the \ufb01rst time, self-consistently in the context of the standard cold dark matter model. We \ufb01nd reasonable concordance between Ly\u03b1 optical depth, Lyman continuum (LyC) mean free path (mfp) \u03bbmfp and global recombination rate of hydrogen observationally and theoretically. We solve the global reionization equation, given the emissivity evolution in the context of the standard cold dark matter model normalized to the boundary conditions of required emissivity at z = 5.7 and reionization completing at z = 5.7. We provide a detailed analysis of the attainable solutions of reionization histories to shed light on the overall topological evolution of the HII regions, the evolution of the Ly\u03b1 emitters, the neutral fraction of the IGM, and a new and powerful constraint on the matter power spectrum on small scales hence dark matter particle properties. Our focus here is on placing a yet the strongest constraint on the scale-scale power in the cosmological model and, speci\ufb01cally, the strongest lower bound on the mass of warm dak matter particles. The physical insight on this particular point is new and may be described brie\ufb02y as follows. The state of the IGM at z = 5.7 is well \ufb01xed by the Gunn & Peterson (1965) optical depth of Ly\u03b1 photons, which in turn provides a tight constraint on the photoionization rate \u0393 at z = 5.7 in the post-reionization epoch. Since \u0393 at z = 5.7 is equal to \u02d9 Nion,IGM\u03bbmfp\u00af \u03c3ion, where \u02d9 Nion,IGM is the global mean of effective ionization photon emissivity at z = 5.7, \u03bbmfp is the mean free path of ionizing photons at z = 5.7 and \u00af \u03c3ion is the spectrum-weighted mean photoionization cross section, a constant. Thus, a tight constraint on \u0393 at z = 5.7 is equivalent to an equally tight constraint on the product \u02d9 Nion,IGM\u03bbmfp at z = 5.7. Note that \u02d9 Nion,IGM already takes into account the escape fraction of ionizing photon from ionization sources (e.g., galax- ies and others). The degeneracy between \u02d9 Nion,IGM and \u03bbmfp can be broken, if one considers, jointly, a separate constraint placed by an upper limit on the integrated electron scattering optical depth of the universe \u03c4e from the latest cosmic microwave background radiation exper- iments (e.g., Planck Collaboration et al. 2016). This is where our new physical insight comes in. We point out that, when the product \u02d9 Nion,IGM\u03bbmfp is \ufb01xed, a higher \u03bbmfp would require a lower \u02d9 Nion,IGM, which in turn would cause the reionization process to shift to lower redshift hence give rise to a lower \u03c4e. In other words, there is a negative correlation between \u03bbmfp and \u03c4e. Since more small-scale power results in a lower \u03bbmfp, there is then a negative correlation between the amount of small-scale power and \u03c4e - more small-scale power leads to lower \u03c4e. As a result, an upper bound on \u03c4e placed by the latest CMB observations would translate to a lower bound on the amount of small-scale power hence a lower bound on the particle mass in the context of the warm dark matter model. This is the scienti\ufb01c focus of this paper. \u2013 3 \u2013"
                },
                {
                    "url": "http://arxiv.org/abs/1604.06473v1",
                    "title": "Testing Models of Quasar Hosts With Strong Gravitational Lensing by Quasar Hosts",
                    "abstract": "We perform a statistical analysis of strong gravitational lensing by quasar\nhosts of background galaxies, in the two competing models of dark matter halos\nof quasars, HOD and CS models. Utilizing the BolshoiP Simulation we demonstrate\nthat strong gravitational lensing provides a potentially very powerful test of\nmodels of quasar hosting halos. For quasars at $z=0.5$, the lensing probability\nby quasars of background galaxies in the HOD model is higher than that of the\nCS model by two orders of magnitude or more for lensing image separations in\nthe range of $\\theta\\sim 1.2-12~$arcsec. To observationally test this, we show\nthat, as an example, at the depth of the CANDELS wide field survey and with a\nquasar sample of $1000$ at $z=0.5$, the two models can be differentiated at\n$3-4\\sigma$ confidence level.",
                    "authors": "Renyue Cen, Mohammadtaher Safarzadeh",
                    "published": "2016-04-21",
                    "updated": "2016-04-21",
                    "primary_cat": "astro-ph.GA",
                    "cats": [
                        "astro-ph.GA"
                    ],
                    "main_content": "arXiv:1604.06473v1  [astro-ph.GA]  21 Apr 2016 2 distinguish between these two competing models, namely strong gravitational lensing by quasar hosting galaxies of background galaxies, which may \ufb01nally put to rest the issue of the halo masses of quasar hosts. 2. SIMULATIONS AND ANALYSIS METHOD We utilize the Bolshoi Simulation (Klypin et al. 2011) to perform the analysis. A set of properties of this simulation that meet our requirements includes a large box of 250h\u22121Mpc, a relatively good mass resolution with dark matter particles of mass 1.3 \u00d7 108h\u22121 M\u2299, and a spatial resolution of 1 h\u22121 kpc comoving. The mass and spatial resolutions are adequate for capturing halos of masses greater than 2 \u00d7 1010 M\u2299, which are resolved by at least about 100 particles and 40 spatial resolution elements for the virial diameter. Since the mass range of interest here is \u22651011 M\u2299, all halos concerned are well resolved. Dark matter halos are found through a friends-of-friends (FOF) algorithm. The adopted \u039bCDM cosmology parameters are \u2126m = 0.27, \u2126b = 0.045, \u2126\u039b = 0.75, \u03c38 = 0.82 and n = 0.95, where the Hubble constant is H0 = 100h km s\u22121 Mpc\u22121 with h = 0.70. We select quasars host halos from z = 0.5 data output of the Bolshoi Simulation, using the detailed prescriptions for both CS and HOD models, described in Cen & Safarzadeh (2015a). For the purpose of computing lensing statistics, we project all particles in the z = 0.5 simulation box along the x-axis onto a plane with spatial resolution of 4 proper kpc. At the location of each quasar halo, we compute the radial pro\ufb01le of the projected dark matter density centered on the halo. In addition to the dark matter, we also model the baryons\u2019 contribution to the projected surface density. Following the parametrization of Behroozi et al. (2013), we assign a baryon fraction to the dark matter halos as a function of the halo mass. The baryon mass is distributed and projected assuming a Singular Isothermal Sphere (SIS) model. The SIS radius for the baryons is de\ufb01ned to be rSIS = 2 \u00d7 re\ufb00where the effective radius is computed following van der Wel et al. (2014) \ufb01ts for elliptical galaxies in that redshift range: re\ufb00= 100.78( M 5 \u00d7 1010 M\u2299 )0.22 (1) The projected surface density, without and with baryonic correction, subtracted by the mean surface density of the box (\u223c3 \u00d7 107M\u2299/kpc2), is compared to critical surface density. We compute the surface density of the halos in radial bins and the radius within which the mean surface density is equal to \u03a3crit is de\ufb01ned as the Einstein radius rE for that halo, with the corresponding angle subtended being \u03b8E = rE/DL, where DL is the angular diameter distance to the quasar host (i.e., the lens). The critical density for strong lensing is \u03a3crit = c2 4\u03c0G DS DLDLS , (2) at redshift zl; in this paper, we consider zL = 0.5 for illustration. Here DS is the angular diameter distance to the source and DLS is the angular diameter distance between the lens and the source. We note that for sources at zs > 2 the critical density for strong lensing by a lens at zl = 0.5 is approximately constant \u223c109M\u2299/kpc2, which rises slowly to \u223c2 \u00d7 109M\u2299/kpc2, at zs = 1, followed by a steep rise to zs = 0.5. We compute the surface densities of 10,000 quasar host halos for both CS and HOD models and obtain the probability distribution function (PDF) of the lensed image angular separation statistics for each model. In order to make quantitative calculations for lensing statistics of background galaxies, we assess the lensing cross section in the source plane as follows. We assume an SIS model for the lens in which all the sources in the background whose un-de\ufb02ected photons pass within the lens\u2019s rE are lensed to give two images, with the cross section in the source plane giving two images being \u03c3 = \u03c0r2 E (Turner et al. 1984). De\ufb01ning the impact parameter as (f \u2261\u03b8Q/\u03b8E), lensing of background galaxies with f < 1 gives two images. The ampli\ufb01cation as a function of impact parameter is r = 1+f 1\u2212f . Averaging the ampli\ufb01cation over the cross section gives a factor of four total ampli\ufb01cation due to lensing inside the critical radius. In our case, we demand that both images are observed in order for us to be sure of a strong lensing event. With that requirement, we \ufb01nd that, in a magnitude limited survey, for sources within a given redshift interval, the effective source plane galaxy number density turns out to be unchanged. In other words, although we can probe to fainter limits because of the total ampli\ufb01cation power, the number of pairs of images both detectable is unchanged, with the effective source plane across section remaining at \u03c3 = \u03c0r2 E. Then, we obtain the number of multiply imaged galaxies as function of image separation \u2206\u03b8 = 2\u03b8E for a given \u03a3gal for each model. We compare the distributions of \u2206\u03b8 between the HOD and CS models We compute \u03c72 to statistically evaluate the size of quasar samples and the number density of background galaxies required in order to differentiate between the HOD and CS models, using Poisson statistics. 3 The difference between the models for each radial bin is computed as follow: \u03c32 i = (NCS,i \u2212NHOD,i)2 NCS,i + NHOD,i (3) for i denotes the radial bin and NCS,i = \u03a3gal \u00d7 2\u03c0ridr \u00d7 NQSO \u00d7 PCS,i, where PCS,i is the probability of the CS model in ith radial bin at ri. The same is adopted for HOD model. The total difference taking into account all the radial bins is computed as follow and shown in Figure 3 below. \u03c32 tot = X \u03c32 i (4) 3. RESULTS 0 2 4 6 8 10 12 \u03b8(arcsec) 10\u22125 10\u22124 10\u22123 10\u22122 10\u22121 100 Probability(>\u03b8) HOD: DM+Baryon CS: DM+Baryon HOD: DM CS: DM Figure 1. shows the cumulative probability distribution functions of image separations \u03b8 in the HOD (blue curves) and CS (red curves) models, without (dashed curves) and with (solid curves) baryons, respectively. The result is based on 13,000 quasar host halo candidates in each model at z=0.5, viewed along each of the three orthogonal directions, resulting in a total of 39,000 effective candidates. The errorbars are based on Poisson statistics. Figure 1 shows the cumulative probability distribution function of image separations in the HOD (blue curves) and CS (red curves) models, without (dashed curves) and with (solid curves) baryons, respectively. We see that the large difference in masses of quasar host halos between HOD and CS models is most vividly displayed: the lensing probability in the HOD model is higher than that of the CS model by two orders of magnitude or more over the range \u03b8 \u223c1 \u22125 arcsec. Above \u223c6 arcsec image separation there is no case in the CS model, whereas the lensing probability in the HOD model is still at \u223c10\u22124 \u221210\u22123 at \u223c10 \u221212 arcsec. We note that 1 arcsec corresponds to 6.2kpc at z = 0.5. The pixel size of the mass projection map at z = 0.5 corresponds to 0.65 arcsec in angular size. Thus, we do not include bins at \u03b8 < 1.2 arcsec in our considerations of differentiations between the two models. The large differences between the HOD and CS models shown in Figure 1, can be understood by looking at Figure 2, which shows a comparison between the normalized probability distribution functions of masses of all quasar host halos (solid curves) and of those capable of producing strong lensing with image separation \u03b8 > 1.2 arcsec (dashed curves). We see that the vast majority of quasar host halos producing strong lensing with image separations \u03b8 > 1.2 arcsec have masses greater than 1012.5 M\u2299, peaking at 1013 \u22121013.5 M\u2299. Even though the overall number of quasar hosts are the same in the two models, their abundances for halos of masses around the peak (1013 \u22121013.5 M\u2299) differ by about two orders of magnitude, which evidently can account for most of the differences between the two lensing probabilities seen in Figure 1. There may be other conceivable 4 11.0 11.5 12.0 12.5 13.0 13.5 14.0 14.5 15.0 logMh[M\u2299] 10\u22123 10\u22122 10\u22121 100 101 102 PDF CS HOD CS, \u03b8 > 1.2arcsec HOD, \u03b8 > 1.2arcsec Figure 2. shows the normalized probability distribution functions of quasar host halo masses in the HOD (blue solid curve) and CS (red solid curve) models, respectively, based on 13,000 halos used for Figure 1. The corresponding dashed curves are the normalized probability distribution functions of masses of selected quasar host halos capable of producing strong lensing with image separation \u03b8 > 1.2 arcsec. It is useful to note that the quasars at z \u223c0.5 that the models model have bolometric luminosity threshold of 1045.1erg/s (Cen & Safarzadeh 2015a). differences, such as the density slopes in the central regions, possibly due for example to difference residing environments of halos of the same masses, between the two quasar host halos in the two models. But as a whole, these other possible differences, if any, do not appear to make a large difference to the overall lensing probability. Given the results shown in Figure 1, we now estimate the observational samples, a combination of the number of target lenses (i.e., quasar hosts), NQSO, and the surface density of background galaxies, \u03a3gal (in arcsec\u22122), that are required to differentiate between the CS and HOD models. To be speci\ufb01c, we assume that the quasar hosts are at redshift z = 0.5. Figure 3 shows the con\ufb01dence levels of statistical differentiation between the two models, based on Eq (3,4). We note that the results only depend on the product NQSO\u03a3gal but we show four separate cases of NQSO for ease of assessment. For example, for a quasar sample of 100, a surface density of background galaxies of \u03a3gal = 0.1 arcsec\u22122 will allow for a 2.5\u03c3 test between the two models. For a quasar sample of 1000, \u03a3gal = 0.023 arcsec\u22122 produces a 4\u03c3 test. To illustrate the observational feasibility of testing the models, Figure 4 shows the cumulative surface number density of galaxies observed in the Hubble F160W \ufb01lter down to 50% completeness level in HUDF (Beckwith et al. 2006) (blue curve) and CANDELS deep (green curve) and shallow (red curve) tier observations (Grogin et al. 2011; Koekemoer et al. 2011). Numerically, we see that \u03a3gal(> z = 1 \u22122) \u223c0.01 \u22120.02 arcsec\u22122 for the CANDELS wide \ufb01eld survey; a survey of this depth with 1000 quasar at z = 0.5 would be able to differentiate between the two models at \u223c3 \u22124\u03c3 con\ufb01dence level. At the depth of HUDF \u03a3gal(> z = 1 \u22122) \u223c0.05 \u22120.08 arcsec\u22122, which could yield \u22652\u03c3 con\ufb01dence level with only about 200 quasars at z = 0.5. 5 10\u22126 10\u22125 10\u22124 10\u22123 10\u22122 10\u22121 100 \u03a3gal(arcsec\u22122) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 \u03c3 NQSO = 1e+02 NQSO = 1e+03 NQSO = 1e+04 NQSO = 1e+05 Figure 3. shows the con\ufb01dence levels of statistical differentiation between the two models as a function of the surface density of background galaxies, \u03a3gal (in arcsec\u22122), based on Eq (3,4). Four cases of NQSO are shown. We assume that the quasar hosts are at redshift z = 0.5. NQSO is the number of target lenses (i.e., quasar hosts). Poisson statistics are used for the errorbars. 0 1 2 3 4 5 6 7 z 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 \u03a3gal(arcsec\u22122) HUDF CANDELS Deep CANDELS Wide Figure 4. Shows the cumulative surface number density of galaxies observed in the Hubble F160W \ufb01lter down to 50% completeness level in HUDF (Beckwith et al. 2006) and CANDELS deep and shallow tier observations (Grogin et al. 2011; Koekemoer et al. 2011). The completeness level at 50% corresponds to mAB(F160W) = 25.9, 26.6, 28.1 for the CANDELS wide, deep and HUDF, respectively. Data is from the compilation of Guo et al. (2013). 4. CONCLUSIONS We perform a statistical analysis of strong gravitational lensing by quasar hosts of background galaxies, utilizing BolshoiP Simulation. We demonstrate that strong gravitational lensing provides a potentially very powerful test of models of quasar hosting halos. Our focus is at z = 0.5, where the difference in the halo masses of quasar 6 hosts between competing models is large and where the placement of lenses is near optimal for lensing of high redshift galaxies. Our initial expectation that the large difference in masses of quasar host halos between HOD (Zheng et al. 2005, 2007; Shen et al. 2013) and CS (Cen & Safarzadeh 2015a) model a threshold mass of (1 \u22123) \u00d7 1011 M\u2299 in the CS model verus a median halo mass of 6 \u00d7 1012 M\u2299in the HOD model at z \u223c0.5 should be strongly discernible in strong lensing statistics is clearly borne out. We \ufb01nd that the lensing probability in the HOD model is higher than that of the CS model by two orders of magnitude or more for lensing image separations in the range of \u03b8 \u223c1 \u22125 arcsec. Above \u223c6 arcsec image separation there is no case in the CS model, whereas the lensing probability in the HOD model is still at \u223c10\u22124 \u221210\u22123 at image separation of \u223c10 \u221212 arcsec. Translating this large theoretical difference between HOD and CS models into observables, we show that, as an example, at the depth of the CANDELS wide \ufb01eld survey and with a quasar sample of 1000 at z = 0.5, the two models can be differentiated at \u223c3 \u22124\u03c3 con\ufb01dence level. The overall statistical power depends on the product NQSO\u03a3gal, where NQSO is the quasar sample size and \u03a3gal is the surface density of detectable background galaxies. In a pioneering observational study, Courbin et al. (2012) report three cases of QSO lenses at z \u223c0.2\u22120.3 with velocity dispersion of the QSO hosts in the range of 210\u2212285 km s\u22121. It is likely that, with a concerted effort, strong gravitational lensing by quasars may provide the most de\ufb01nitive and direct test of host halo models for quasars. We are grateful to Anatoly Klypin for providing us with the projected mass maps of Bolshoi-Planck simulation in a most prompt fashion. We thank Tommaso Treu for useful discussion. This work is supported in part by grants NNX12AF91G and AST15-15389.",
                    "introduction": "1."
                },
                {
                    "url": "http://arxiv.org/abs/1604.01986v1",
                    "title": "Upper Limit on Star Formation and Metal Enrichment in Minihalos",
                    "abstract": "An analysis of negative radiative feedback from resident stars in minihalos\nis performed. It is found that the most effective mechanism to suppress star\nformation is provided by infrared photons from resident stars via\nphoto-detachment of ${\\rm H^-}$. It is shown that a stringent upper bound on\n(total stellar mass, metallicity) of ($\\sim 1000{\\rm M_\\odot}$, $-3.3\\pm 0.2$)\nin any newly minted atomic cooling halo can be placed, with the actual values\npossibly significantly lower. This has both important physical ramifications on\nformation of stars and supermassive black seeds in atomic cooling halos at high\nredshift, pertaining to processes of low temperature metal cooling, dust\nformation and fragmentation, and direct consequences on the faint end galaxy\nluminosity function at high redshift and cosmological reionization. The\nluminosity function of galaxies at the epoch of reionization may be\nsubstantially affected due to the combined effect of a diminished role of\nminihalos and an enhanced contribution from Pop III stars in atomic cooling\nhalos. Upcoming results on reionization optical depth from Planck\nHigh-Frequency Instrument data may provide a significant constraint on and a\nunique probe of this star formation physical process in minihalos. As a\nnumerical example, in the absence of significant contributions from minihalos\nwith virial masses below $1.5\\times 10^{8}{\\rm M_\\odot}$ the reionization\noptical depth is expected to be no greater than $0.065$, whereas allowing for\nminihalos of masses as low as ($10^7{\\rm M_\\odot}$, $10^{6.5}{\\rm M_\\odot}$) to\nform stars unconstrained by this self-regulation physical process, the\nreionization optical depth is expected to exceed $(0.075,0.085)$, respectively.",
                    "authors": "Renyue Cen",
                    "published": "2016-04-07",
                    "updated": "2016-04-07",
                    "primary_cat": "astro-ph.GA",
                    "cats": [
                        "astro-ph.GA"
                    ],
                    "main_content": "Minihalos are defined as small dark matter halos with virial temperature below that for efficient atomic cooling (i.e., Tv \u2264104K). Minihalos form early in the standard cold dark matter model and are only relevant for high redshift. Star formation may start in minihalos with Tv as low as \u223c1000K or so. The relation between halo virial mass (Mv) and virial temperature (Tv) is \ufffd \ufffd3  \ufffd \ufffd3  \ufffd \ufffd\u22121  \ufffd \ufffd\u22123 Mv = 108h\u22121 M\u2299 \ufffd Tv 1.98 \u00d7 1 d \u2126 are d 1.98 \u00d7 104K \u2126 are densit \ufffd3 2 ty p 3 2 \ufffd0.6 \u00b5P  parame \u00b5P \ufffd3 2 ete 3 2 \ufffd\u2126m \u2126z m er and \u2126z m \u2206c 18\u03c02 \ufffd\u22121 2 molog 1 2 \ufffd1 + z 10 gical con 10 \ufffd\u22123 2 nstan 2 , (1) \ufffd  \u00d7 \ufffd  \ufffd \ufffd  \ufffd \ufffd  \ufffd \ufffd where z is redshift, \u2126m and \u2126\u039b are density parameter and cosmological constant at redshift zero, respectively; \u2126z m \u2261[1 + (\u2126\u039b/\u2126m)(1 + z)\u22123]\u22121 is the density parameter at redshift z; \u2206c = 18\u03c02 + 82d \u221239d2 and d = \u2126z m \u22121 (see Barkana & Loeb 2001 for more details). The corresponding physical virial radius is rv = 0.784h\u22121kpc \ufffd Tv 1.98 \u00d7 1 1.98 \u00d7 104K \ufffd1 2 1 2 \ufffd0.6 \u00b5P \u00b5P \ufffd1 2 1 2 \ufffd\u2126m \u2126z m \u2126z m \u2206c 18\u03c02 \ufffd\u22121 2 1 2 \ufffd1 + z 10 10 \ufffd\u22121 2 2 . (2) In minihalos at high redshift, molecular hydrogen H2 is the primary gas cooling agent, before a significant amount of metals is present. In the absence of a significant amount of dust grains, the dominant H2 formation channel is via a two-step gas phase process (e.g., Draine 2003), first with radiative association: H + e\u2212\u2192H\u2212+ h\u03bd, (3) followed by associative detachment: H\u2212+ H \u2192H2 + e\u2212. (4) Given this formation channel, if one is interested in suppressing H2 formation, there are two main ways to achieve that goal. One is by destruction of formed H2 molecules through the photo-dissociation process by photons in the LW band of h\u03bd = 11.2 \u221213.6eV: H2 + h\u03bd \u2192H + H. (5) The other is by reducing the density of H\u2212, to which the rate of H2 formation is proportional, by infrared (IR) photons of energy h\u03bd \u22650.755eV via the photo-detachment process: H\u2212+ h\u03bd \u2192H + e\u2212. (6) \u2013 3 \u2013 For simplicity, we assume that the initial mass function (IMF) of Population III (Pop III) stars has a powerlaw distribution of the same Salpeter slope: n(M\u2217)dM\u2217= CM\u22122.35dM\u2217, (7) with an upper mass cutoff 100 M\u2299and a lower mass cutoff Mlow that we will vary to understand its in\ufb02uence on the results; C is a constant normalizing the stellar abundance per unit of star formation rate. We stress that our results are rather insensitive to either Mlow or the slope of the IMF . Then, one can compute the intrinsic spectral luminosity (in units of erg sec\u22121 Hz\u22121 sr\u22121) per stellar mass at any photon energy \u03bd as L\u03bd = Z th 0 Z 100 M\u2299 Llow \u03b8(tms \u2212th + tf) \u02d9 M\u2217(tf)J\u03bd(M\u2217)n(M\u2217)dM\u2217dtf, (8) where J\u03bd(M\u2217) is the mean spectral luminosity of a star of mass M\u2217at photon energy h\u03bd in the main sequence; \u03b8(x) is the Heaviside theta function; tms(M\u2217) is the star\u2019s main sequence lifetime; tf and th are the formation time of the star in question and the time under consideration when the luminosity is computed; \u02d9 M\u2217(tf) is star formation rate at time tf. The left panel of Figure 1 shows the individual intrinsic Pop-III stellar black-body spectrum per unit stellar mass times the main sequence lifetime for a range of masses for individual Pop III stars (indicated in the legend in units of solar mass), based on data from Marigo et al. (2001). It is easy to see that low mass stars are more ef\ufb01cient producers of IR photons (indicated by the vertical dashed magenta line); for 1 M\u2299to 20 M\u2299, a decrease of approximately 100 for IR intensity per unit stellar mass is observed. For the LW band photons (indicated by the two vertical dashed black lines), the opposite holds: a decrease of approximately four orders of magnitude is seen from 20 M\u2299to 1 M\u2299. In the right panel of Figure 1 we show comparisons the IR (LW) intensities of a single star of mass indicated by the x-axis in magenta (black) solid curves for redshifts z = 25 (z = 7), to be compared to the the threshold intensities for completion suppression of H2 formation by the respective processes shown as the horizontal dashed lines with the corresponding colors. See below for how the the threshold intensities are computed. Wolcott-Green & Haiman (2012) show that complete suppression of H2 formation in minihalos at high redshift is possible by either LW photo-dissociation or IR photo-detachment process. Based on a detailed modeling, they derive a critical radiation intensity for complete suppression of H2 formation of JLW,crit = 1.5 \u00d7 10\u221221ergs\u22121cm\u22122Hz\u22121sr\u22121 (9) at the LW band via photo-dissociation process alone, and a critical radiation intensity of JIR,crit = 6.1 \u00d7 10\u221220ergs\u22121cm\u22122Hz\u22121sr\u22121 (10) at the IR band (h\u03bd = 2eV) via photodetachment process alone, under the assumption of the existence of the respective backgrounds, not internal radiation. \u2013 4 \u2013 log h\u03bd(eV) 0 1 2 log J \u00d7 tms/M\u2217(erg/Hz/sr/M\u2299) 30 31 32 33 34 35 36 100 70 50 30 20 10 6 3 2 1.5 1 logM\u2217(M\u2299) 0 1 2 log J(erg/cm2/s/Hz/sr) -22 -21 -20 -19 -18 -17 z=25 z=7 z=25 z=7 Single star IR intensity IR suppression threshold Single star LW intensity LW suppression threshold Fig. 1.\u2014 Left panel: shows the intrinsic black-body spectra of individual Pop-III stars per unit stellar mass, multiplied by the main sequence lifetime, for a set of stellar masses (in units of solar mass) indicated in the legend. Also shown as the vertical magenta dashed line is the photon energy of 2eV for the photo-detachment process. The LW band is indicated by the two black vertical dashed lines. Right panel: shows the radiation intensity at 2eV (magenta solid curves) and 11.2eV (black solid curves) for a single star of mass shown on the x-axis. The star is assumed to be located at the center and the intensity is measured at the core radius of the minihalo (see text for de\ufb01nition of core radius). Two cases are shown, one for a minihalo at z = 25 with virial temperature of 103 K (upper solid curves) and the other at z = 7 with virial temperature of 104 K (lower solid curves). For both IR and LW photons, no absorption is assumed for this illustration. The horizontal dashed lines with the same corresponding colors are the threshold intensity for complete suppression of H2 formation by the respective processes. We consider the requirement of suppression of either H2 or H\u2212formation in the central core region of minihalos, which is likely most stringent compared to less dense gas at larger radii. Following Shapiro et al. (1999) we adopt the core radius and density to be rc = rv/29.4, \u2013 5 \u2013 which is then rc = 26.7h\u22121pc \u0012 Tv 1.98 \u00d7 104K \u0013 1 2 \u00120.6 \u00b5P \u0013 1 2 \u0012\u2126m \u2126z m \u2206c 18\u03c02 \u0013\u22121 2 \u00121 + z 10 \u0013\u22121 2 . (11) and hydrogen number density in the core is nc = 514nv (nv is the gas number density at the virial radius): nc = 4.5cm\u22123 \u00121 + z 10 \u00133 . (12) Since we use the numerical results from Wolcott-Green & Haiman (2012) on photo-detachment, it will be instructive to gain a physical understanding of its origin. The photodetachment cross section is \u03c3\u2212= 2.1 \u00d7 10\u221216(\u03f5 \u22120.755)3/2 \u03f53.11 cm2 (13) where \u03f5 is the photon energy in units of eV. The radiative association rate coef\ufb01cient is k\u2212= 1.3\u00d710\u22129cm3 s\u22121. Thus, with JIR,crit = 6.1 \u00d7 10\u221220erg/s/cm2/Hz/sr at 2eV and minihalo core density of nc = 31cm\u22123 at z = 18 (see Equation 1) (z = 18 is used in Wolcott-Green & Haiman (2012)) and assuming that the spectrum shape of \u221d\u03bd0 in the range 0.755 \u221213.6eV, one \ufb01nds that the ratio of photo-detachment rate to radiative association rate is 0.46; the ratio becomes 1.5 if one assumes the spectrum shape of \u221d\u03bd+1. Note that in the Raleigh-Jeans limit the spectral shape goes as \u221d\u03bd+2 (see Figure 1). We now see that when the photo-detachment rate and radiative association rate are approximately equal in the minihalo core, H2 formation is effectively completely suppressed, as one would have expected. This thus provides an order of magnitude understanding of the Wolcott-Green & Haiman (2012) results. Given the expected little dust content in very metal poor gas in minihalos, the optical depth for IR photons at 2eV is negligible. As a numerical example, the core hydrogen column density would be Nc \u2261rcnc = 1.5 \u00d7 1020cm\u22122 for a minihalo of Tv = 104 K at z = 8. Using the gas to dust column ratio (Draine 2003) with the assumption that dust content is linearly proportional to metallicity yields AV = 0.08(Z/ Z\u2299) mag in this case. It is easy to see that we may safely neglect optical depth effect for IR photons in question. For LW photons, H2 self-shielding effect may be important. We include, conservatively, for maximum H2 self-shielding of LW radiation by placing all sources at the center of the minihalo with the self-shielding reduction of LW photons using the accurate \ufb01tting formula from Draine & Bertoldi (1996) for a halo at z = 7 with Tv = 104 K, corresponding Doppler parameter b = 13 km s\u22121, H2 fraction of fH2 = 10\u22123 and H2 column density equal to fH2rcnc. This case is contrasted with the hypothetical case where self-shielding is neglected. The left panel of Figure 2 shows the critical cumulative stellar mass required to completely suppress further star formation, as a function of the lower mass cutoff of the IMF Mlow, following a minihalo of Tv = 103K at z = 25 through its becoming an atomic cooling halo at z = 7. In making this plot, we have adopted a Monte Carlo approach to randomly sample the IMF , assuming each starburst lasts about 4Myr, a time scale to approximate the effect of \u2013 6 \u2013 log Mlow (Msun) 0 0.5 1 1.5 upper limit on log total stellar mass 2 3 4 5 6 7 Detachment Dissociation w/o self-shield Dissociation w/ self-shield log Mlow (Msun) 0 0.5 1 1.5 upper limit on metallicity [Fe/H] -3.5 -3 Detachment:atomic halo@z=7 Fig. 2.\u2014 Left panel: shows the critical cumulative stellar mass for complete suppression of H2 formation, as a function of the lower mass cutoff of the IMF Mlow, via either the photodissociation process by LW photons with (blue open squares) and without H2 self-shielding of LW photons (blue solid squares) or the photo-detachment process by infrared photons (red solid dots). In this example, we assume that a minihalo of virial temperature Tv = 103K is formed at z = 25 when star formation commences, and the critical stellar mass (i.e., upper limit on total stellar mass) is evaluated at z = 7 when the minihalo has grown to a virial temperature of Tv = 104K. Right panel: shows the upper bound on the mean gas metallicity, corresponding to the critical stellar mass shown in the left panel, evaluated at z = 7 when the minihalo has grown to a virial temperature of Tv = 104K. In both panels, the errorbars indicate the dispersions obtained by Monte Carlo realizations of different star formation histories, described in the text. supernova blowout. While simulations have shown that the separation of episodic starbursts is about 20 \u2212100Myr (e.g., Kimm & Cen 2014) for atomic cooling halos, we expect that the separations for minihalos would be larger, thanks to the more violent blowouts of gas by supernovae out of shallower potential wells and less ef\ufb01cient cooling in minihalos for gas return. To stay on the conservative side, we use temporal separations between star formation episodes of 20Myr. In general, a larger separation gives a lower total stellar mass, because the radiative \u2013 7 \u2013 suppression effects are almost entirely dominated by stars formed within the ongoing starburst (not by stars from previous starbursts) and often the radiation from a single star is enough to provide the necessary suppression (see the right panel of Figure 1). On details regarding the Monte Carlo realizations, within each starburst, we randomly draw stars from the IMF with a lower mass cutoff of Mlow, until the radiation intensity in IR or UV, separately, at the core radius exceeds the required threshold. We keep track of stars formed in starbursts at higher redshift and take into account their radiative contributions given their main sequence lifetimes. Since we can not \u201cdraw\" a fractional star, in cases where a single star would already exceed the required threshold, stellar mass is higher than if fractional stars can be drawn. Based on the Monte Carlo random sampling procedure to draw stellar distribution from the IMF , the obtained dispersion are shown as vertical bars on symbols in both panels of Figure 2. It is evident that, taking into account H2 self-shielding of LW photons, for the entire range of Mlow considered, the destructive effect due to photo-detachment is larger by two-three orders of magnitude than that due to photo-dissociation taking into account attenuation for LW photons. Thus, we will use the photo-detachment effect to place an upper bound on stellar mass that can form before further H2 formation hence star formation is completely suppressed. The amount of stars formed within minihalos is small, at \u223c103 M\u2299, prior to the minihalo becoming an atomic halo. This self-regulation of star formation in minihalos likely have a signi\ufb01cant impact on the possible contribution of minihalos to reionization. A full characterization of this effect would need detailed simulations with this important process included. Wise et al. (2014) \ufb01nd stellar mass of 103.5 \u2212104.0 M\u2299in minihalos of mass 106.5 \u2212107.5 M\u2299, which is approximately a factor of at least 3 \u221210 higher than allowed, even compared to the largest possible minihalos (before their becoming atomic cooling halos) considered here, as shown in the left panel of Figure 2. We note that the amount stars formed are a result of accumulation of the number of star formation episodes. We have \"maximized\" the stellar mass by using a conservative episodic interval and considering the maximum minihalos at a low redshift z = 7. Obviously, for smaller minihalos at higher redshift with longer \u201cquiet\" periods the amount of stellar mass formed will be smaller. This suggests that the contribution of stars formed in minihalos to reionization may be substantially reduced. We estimate that the contribution of minihalos to cosmological reionization photon budget is likely limited to a few percent. Next, we consider the metal enrichment due to stars formed in minihalos. To compute that, we use the relation between the nickel (which decays to iron) mass produced by a supernova of mechanical explosion energy E: log Mni M\u2299 = 1.49 log E 1050 erg \u22122.9 (14) (Pejcha & Prieto 2015) and the relation between explosion energy E and the main sequence stellar mass M: E 1051 erg = ( M 10.8 M\u2299 )2 (15) \u2013 8 \u2013 (Poznanski 2013). We assume all stars with main sequence mass above 8 M\u2299explode as supernavae, except the two intervals 17 \u221223 M\u2299and \u226540 M\u2299, which produce black holes based on the so-called compact parameter \u03be as a physical variable (e.g., O\u2019Connor & Ott 2011; Pejcha & Thompson 2015). The right panel of Figure 2 shows the expected average metallicity when an atomic cooling halo is reached at z = 7. corresponding to the critical stellar mass shown as solid red dots in the left panel of Figure 2. We see that, on average, the expected maximum metallicity due to stars formed in minihalos falls into the range of \u22123.3\u00b10.2 in solar units, for Mlow = 1 \u221230 M\u2299. We use iron mass fraction of 1.77 \u00d7 10\u22123 as solar abundance (Asplund et al. 2009). We have conservatively assumed that enrichment process takes places in a closed-box fashion, with respect to metals produced. Furthermore, we have simplistically assumed that none of the metals produced is not incorporated back into subsequent stars. In reality, retainment of metals produced by stars in minihalos is probably far from complete, given their shallow potential wells, i.e., it is not a closed box. Furthermore, some of the earlier produced metals inevitably get reformed into stars. These conservative approaches used, along with our conservative adoption of 20Myr starburst separation, indicate that that the actual metallicity due to stars in minihalos may be signi\ufb01cantly below the maximum allowed values indicated in the right panel of Figure 2. In other words, we expect that the metallicity \ufb02oor put in by stars formed in previous minihalos, when an atomic cooling halo is formed, is likely signi\ufb01cantly below \u22123.3\u00b10.2 in solar units. There is one possible caveat in the arguments leading to the results. Despite the resultant low metallicity due to self-suppression of star formation by negative IR radiation feedback, the metallicity is not zero. Thus, it is prudent to check if the metallicity is suf\ufb01ciently low to justify the neglect of low-temperature metal cooling. We \ufb01nd that, using [Z/H] = \u22123 and molecular hydrogen fraction of fH2 = 10\u22123, the ratio of the cooling rate of metal lines (primarily due to OI, CII, SiII aand FeII) to that of molecular hydrogen is found to be (4.1\u00d710\u22122, 1.6\u00d710\u22123, 2.6\u00d710\u22124) at temperature T = (103, 103.5, 104) K (Maio et al. 2007), respectively. Empirically, experimental simulations have found that, in lieu of molecular hydrogen cooling, low-temperature metal cooling with a metallicity of [Z/H] \u223c\u22121.5 produces cooling effect comparable to that molecular hydrogen fraction with fH2 = 10\u22123 (Kimm 2016, private communications), which is consistent with above estimates based on cooling rates. Thus, the low-temperature metal cooling is probably no more than (\u223c2%, 0.1%, 0.01%) of the molecular hydrogen cooling in the case of absent negative feedback examined here, if [Z/H] \u2264\u22123.3, in minihalos with virial temperatures Tv = (103, 103.5, 104) K, respectively. Therefore, the low-temperature metal cooling is unlikely to be able to make up the \u201clost\" H2 cooling, due to negative feedback from local radiation, to alter the suppression of star formation. \u2013 9 \u2013 3. Discussion and Conclusions This study investigates the radiative feedback from resident stars in minihalos. We \ufb01nd that photo-detachment of H\u2212by infrared photons of energy h\u03bd \u22650.755eV emitted by resident stars in minihalos is the most effective mechanism to suppress and hence self-regulate star formation within. The negative feedback effect due to Lyman-Werner photons would have been more effective, if the gas is transparent; however, H2 self-shielding substantially reduces its effect to become subdominant to that of photo-detachment process. We \ufb01nd that the amount of stars formed in minihalos is capped at about 103 M\u2299, regardless of the lower mass cutoff of the initial mass function. As a result, it is shown that a stringent upper bound of metallicity of \u22123.3 \u00b1 0.2 relative to the solar value due to stars formed in minihalos can be placed; the actual amount of stars and metallicity achieved by stars in minihalos may be signi\ufb01cantly lower, because the various assumptions adopted, when needed, have been chosen to err, generously, on the conservative side to ensure that our results with respect to star formation in minihalos represent an upper bound. The self-regulation of star formation in minihalos likely has a signi\ufb01cant impact on the possible contribution of minihalos to reionization. In Kimm & Cen (2014, Figure 14) it is shown that, in the absence of signi\ufb01cant contributions from minihalos with virial masses below 1.5 \u00d7 108 M\u2299, as an example, corresponding to minihalo threshold at z = 9 (see Equation 2), the reionization optical depth is expected to be no greater than 0.065. On the other hand, allowing for minihalos of masses as low as (107 M\u2299, 106.5 M\u2299) to form stars unconstrained by this self-regulation physical process, the reionization optical depth would exceed (0.075, 0.085), respectively, in general agreement with earlier results under similar assumptions with respect to dramatically increased contributions especially with very massive Pop III stars (e.g., Cen 2003a,b; Wyithe & Cen 2007). While these values are all consistent with the most recent Planck results (Planck Collaboration et al. 2015, \u03c4e = 0.066\u00b10.016) at < 1.2\u03c3 level, upcoming results from Planck High-Frequency Instrument (HFI) data may provide a signi\ufb01cant constraint on the star formation physics in minihalos. The \ufb01ndings will also have profound rami\ufb01cations on star formation and formation of supermassive black seeds in atomic cooling halos at high redshift, due to processes related to metal cooling, dust formation and fragmentation. As an example, low-temperature metal cooling may be suppressed (e.g., Bromm & Loeb 2003) to increase the probability of extending the formation of Pop III stars. Although simulations will be needed, this does suggest that, with a much lower mean metallicity, in conjunction with inhomogeneous metal enrichment processes, pockets of Pop III stars in atomic cooling halos may be more widespread than thought. The combination of a reduction of star formation in minihalo and a possible increase in stellar luminosity in atomic cooling halos (due to Pop III stars) will alter both the slope and cutoff of the luminosity function of galaxies at the faint end at the epoch of reionization (Kimm & Cen 2014; Trac et al. 2015). There may be two possible signatures in the luminosity function at the epoch of reionization. First, a possible steepening at the faint end right before a dramatic \ufb02at\u2013 10 \u2013 tening or downturn at the transition between the atomic cooling halo to minihalo mass may be expected; the steepening is due to the increased proportion of metal-free stars in lower mass atomic cooling halos. Second, due to generally increased variations in Pop III star fractions, in conjunction with stochastic starbursts, the shape of the luminosity function at the high end is likely to resemble powerlaws than exponential. On a separate, but potentially related subject, we note that metallicities of stars in both types of globular clusters, in the bimodal metallicity distribution (e.g., Forbes et al. 1997; Harris et al. 2006), are signi\ufb01cantly higher than \u22123. This indicates that, in scenarios where globular clusters are formed in dwarf, atomic cooling galaxies (Kimm et al. 2016), most of the metals ought to originate from previous generation of stars formed in either other and/or progenitor atomic cooling halos prior to forming globular clusters at the centers of these dwarf galaxies. Given the much reduced star formation hence metallicity in minihalos, it would seem conceivable that Pop III stars formed in atomic cooling halos may make a signi\ufb01cant contribution to the pre-enrichment (of, say, Fe) of the gas forming the \ufb01rst-generation stars in globular clusters. I thank Zoltan Haiman, Kohei Inayoshi, Taysum Kimm, John Wise and Jemma WolcottGreen for useful discussion and communications, Paola Marigo for stellar track data, Alexander Heger, Berhnard Mueller and Ondrej Pejcha for educational discussion on supernova related issues, and Umberto Maio for sharing low temperature cooling data \ufb01les. This work is supported in part by grants NNX12AF91G and AST15-15389.",
                    "introduction": "Star formation in minihalos is a fundamental issue, because it is responsible for enriching the primordial gas with \ufb01rst metals that shape the subsequent formation of stars and possibly supermassive black hole seeds in atomic cooling halos. Since the pioneering works (e.g., Abel et al. 2002; Bromm et al. 2002; Nakamura & Umemura 2002), most studies have focused on formation of individual stars (e.g., Hirano et al. 2014). So far studies of the effects of external Lyman-Werner band (LW) (h\u03bd = 11.2 \u221213.6eV) radiation background (e.g., Machacek et al. 2001; Wise & Abel 2007; O\u2019Shea & Norman 2008), external IR radiation background (e.g., Chuzhoy et al. 2007; Hirano et al. 2015) on gas chemistry and thermodynamics hence star formation in minihalos have produced signi\ufb01cant physical insight. We assess the effects of these two - LW photo-dissociation and IR photo-detachment - H2 formation suppressing pro- cesses due to resident stellar population within minihalos, instead of the respective collective arXiv:1604.01986v1  [astro-ph.GA]  7 Apr 2016 \u2013 2 \u2013 backgrounds widely considered. We show that photo-detachment process of H2 by infrared photons of energy h\u03bd \u22650.755eV produced by resident stars places a strong upper bound on stellar mass and metals that may be formed in minihalos. This upper limit needs to be taken into account in the general considerations of galaxy formation at high redshift."
                },
                {
                    "url": "http://arxiv.org/abs/1507.07934v1",
                    "title": "Testing Dark Matter Halo Models of Quasars With Thermal Sunyaev-Zeldovich Effect",
                    "abstract": "A statistical analysis of stacked Compton$-y$ maps of quasar hosts with a\nmedian redshift of $1.5$ using Millennium Simulation is performed to address\ntwo issues, one on the feedback energy from quasars and the other on testing\ndark matter halo models for quasar hosts. On the first, we find that, at the\nresolution of FWHM=$10$ arcmin obtained by Planck data, the observed thermal\nSunyaev-Zeldovich (tSZ) effect can be entirely accounted for and explained by\nthe thermal energy of halos sourced by gravitational collapse of halos, without\na need to invoke additional, large energy sources, such as quasar or stellar\nfeedback. Allowing for uncertainties of dust temperature in the calibration of\nobserved Comton$-y$ maps, the maximum additional feedback energy is $\\sim 25\\%$\nof that previously suggested. Second, we show that, with FWHM=$1$ arcmin beam,\ntSZ measurements will provide a potentially powerful test of quasar-hosting\ndark matter halo models, limited only by possible observational systematic\nuncertainties, not by statistical ones, even in the presence of possible quasar\nfeedback.",
                    "authors": "Renyue Cen, Mohammadtaher Safarzadeh",
                    "published": "2015-07-28",
                    "updated": "2015-07-28",
                    "primary_cat": "astro-ph.GA",
                    "cats": [
                        "astro-ph.GA"
                    ],
                    "main_content": "We utilize the Millennium Simulation (Springel et al. 2005) to perform the analysis. A set of properties of this simulation that meet our requirements includes a large box of 500h\u22121Mpc, a relatively good mass resolution with dark matter particles of mass 8.6 \u00d7 108h\u22121 M\u2299, and a spatial resolution of 5 h\u22121 kpc comoving. The mass and spatial resolutions are adequate for capturing halos of masses greater than 1011 M\u2299, which are resolved by at least about 100 particles and 40 spatial resolution elements for the virial diameter. Dark matter haloes are found through a friends-of-friends (FOF) algorithm. Satellite halos orbiting within each virialized halo are identified applying a SUBFIND algorithm (Springel et al. 2001). The adopted \u039bCDM cosmology parameters are \u2126m = 0.25, \u2126b = 0.045, \u2126\u039b = 0.75, \u03c38 = 0.9 and n = 1, where the Hubble constant is H0 = 100h km s\u22121 Mpc\u22121 with h = 0.73. We do not expect that our results strongly depend on the choice of cosmological parameters within reasonable ranges, such as those from Komatsu et al. (2011). The steps taken to construct the tSZ maps are as follow. For each model (either CS or HOD) quasar model, we sample the quasar host dark matter halos at each redshift, z = 0.5, 1.4 and 3.2. For each quasar host, we select all halos within a projected radius of 80 arcmin centered at the quasar in a cylinder with the depth equal to the length of the simulation box in a given direction. The thermal energy of a halo of mass Mh is calculated using Eth = 3\u2126b 2\u2126m 3\u2126b 2\u2126m Mh\u03c32 (1) where Mh is the halo mass and \u03c3 the 1-d velocity dispersion computed as \ufffd \ufffd\ufffd \ufffd \u03c3 = 0.01 \u00d7 \ufffdMh M\u2299 h halo is then dist M\u2299  dist \ufffd1/3\ufffd\u2126M(z = 0) \u2126M(z) ributed uniformly \u2126M(z) \ufffd1/6 (1 + z)1/2[km/s]. (2) y in projected area inside its virial radius \ufffd \u2299 \ufffd\ufffd \ufffd The energy of each halo is then distributed uniformly in projected area inside its virial radius rv. To construct SZ maps, we project the energy of each halo using a cloud-in-cell technique in 2-d. We obtain the Compton-y parameter corresponding to total projected thermal energy Eth/A at each pixel with:  2\u03c3E y = 0.88 \u00d7 0.588 \u00d7 2\u03c3TEth 3mec2A 2\u03c3TEth 3mec2A (3) \u2013 3 \u2013 where A is the area of the pixel, \u03c3T the Thomson scattering cross section, me the electron mass, c the speed of light, and 0.88 and 0.58 accounts for electron density to mass density, and molecular weight, respectively. We limit the dark matter halos that contribute to the y calculation to the mass range [3 \u00d7 1012, 5.5 \u00d7 1014] M\u2299at z = 0.5 and [3 \u00d7 1012, 6.5 \u00d7 1014] M\u2299 at both z = 1.4 and 3.2. The upper mass limits is used in order to enable comparisons to observations, accounting for the fact that in the Planck observation generated y maps the clusters more massive than these indicated upper limits are masked out (Planck Collaboration et al. 2014). The lower mass limits re\ufb02ect the fact that less massive halos would be cold stream dominated instead of virial shock heated gas dominated; changing the lower mass limit from 3 \u00d7 1012 M\u2299to 1 \u00d7 1012 M\u2299only slightly increases the computed y parameter. To enable comparison with the observed Compton-y maps stacked over a range of redshift z \u223c0.1 \u22123.0 with median redshift of zmed \u223c1.5 (Ruan et al. 2015), we appropriately assign weightings of (36%, 51%, 13%) for z = (0.5, 1.4, 3.2) maps, respectively, and sum up the contributions from the three redshifts. These weightings are adopted to mimic the redshift distribution of stacked quasars used in the observational anaylysis. To compute the variance of the y-parameter we make nine maps each averaged over 1/9th of total individual Comptony maps of the quasar hosts at each redshift for either of the HOD or CS models. Then we have 9 \u00d7 9 \u00d7 9 = 729 possible \ufb01nal maps constructed with the weightings de\ufb01ned above. The dispersion and the mean is then computed considering these 729 \ufb01nal maps. In addition, we construct isolated quasar host only y maps, with only the quasar host halo\u2019s energy contributing to the \ufb01nal tSZ map. In other words, in those isolated quasar y maps, we exclude effects from projected, clustered neighboring halos. 3. Validating Quasar Models with Planck Thermal Sunyaev-Zeldovich Effect Maps We \ufb01rst validate the quasar models by comparing them to Planck observations. Figure 1 shows Compton-y maps for \ufb01ve randomly selected quasar maps at z = 1.4 (including the projection effects) in the \ufb01ve panels other than the top-left panel and the averaged over 10,000 such individual maps is shown in the top-left panel. Each individual map is centered on the quasar halo from the CS model. Halos that contribute to the signal are in the mass range we describe above and in some cases the quasar halo itself does not contribute to the signal if its mass fall outside the mass range. The left panel of Figure 2 shows the Compton-y radial pro\ufb01le obtained by sampling for CS (blue shaded region) and HOD (purple shaded region) model, respectively. Overplotted is the result obtained by stacking the Planck tSZ maps for quasars in the redshift range (0.1, 3.0) with median redshift of 1.5 (green shaded region, Ruan et al. 2015). To compare with Planck tSZ maps, we smooth our synthetic maps with a beam of FWHM=10 arcmin. We see that, at the resolution of Planck of FWHM=10 arcmin, both CS and HOD model are consistent with the observed level of tSZ being contributed entirely by shocked heated, virialized gas \u2013 4 \u2013 \u221230 \u221220 \u221210 0 10 20 30 arcmin \u221230 \u221220 \u221210 0 10 20 30 arcmin mean tSZ Compton\u2013y map 2.9e-07 3.0e-07 3.1e-07 3.2e-07 3.3e-07 3.4e-07 3.5e-07 3.6e-07 \u221230 \u221220 \u221210 0 10 20 30 arcmin \u221230 \u221220 \u221210 0 10 20 30 arcmin 0.0e+00 1.5e-07 3.0e-07 4.5e-07 6.0e-07 7.5e-07 9.0e-07 1.0e-06 1.2e-06 1.3e-06 \u221230 \u221220 \u221210 0 10 20 30 arcmin \u221230 \u221220 \u221210 0 10 20 30 arcmin 0.0e+00 1.5e-07 3.0e-07 4.5e-07 6.0e-07 7.5e-07 9.0e-07 1.0e-06 1.2e-06 1.3e-06 \u221230 \u221220 \u221210 0 10 20 30 arcmin \u221230 \u221220 \u221210 0 10 20 30 arcmin 0.0e+00 1.5e-07 3.0e-07 4.5e-07 6.0e-07 7.5e-07 9.0e-07 1.0e-06 1.2e-06 1.3e-06 \u221230 \u221220 \u221210 0 10 20 30 arcmin \u221230 \u221220 \u221210 0 10 20 30 arcmin 0.0e+00 1.5e-07 3.0e-07 4.5e-07 6.0e-07 7.5e-07 9.0e-07 1.0e-06 1.2e-06 1.3e-06 \u221230 \u221220 \u221210 0 10 20 30 arcmin \u221230 \u221220 \u221210 0 10 20 30 arcmin 0.0e+00 1.5e-07 3.0e-07 4.5e-07 6.0e-07 7.5e-07 9.0e-07 1.0e-06 1.2e-06 1.3e-06 Fig. 1.\u2014 Top-left panel show the average Compton-y map of 10,000 individual maps centered on the quasar host sampled from CS model at z = 1.4. The other \ufb01ve panels show \ufb01ve randomly selected individual maps for \ufb01ve quasar halos. The pixel size is 0.034 arcmin. within massive halos. Given our generous mass limit of contributing halos and neglect of gravitationally shock heated gas outside the virial radius, it is likely that the estimates for CS and HOD models shown in the left panel of Figure 2 are somewhat under-estimated. Thus, in disagreement with Ruan et al. (2015) with respect to feedback energy from other nongravitational sources, we see little evidence for a need of a large contribution to the tSZ from non-gravitational energy sources, including quasars or stars. \u2013 5 \u2013 To better understand this discrepancy, we show in right panel of Figure 2 the Compton-y pro\ufb01le in HOD model, when only the quasar-hosting halo contributes to the thermal energy in the map, neglecting the contribution from clustered neighboring halos. We see that the isolated quasar map yields a tSZ signal peaked around y \u223c1.4 \u00d7 10\u22128 (black curve with shaded area) versus y \u223c3.0 \u00d7 10\u22127 as seen in the left panel where all neighboring halos are included. It is hence very clear that the overall Compton-y parameter re\ufb02ects the collective thermal energy contribution of halos clustered around the quasar hosting halos in both CS and HOD models. The collective effect exceeds that of the quasar host halo by more than an order of magnitude. We attribute the suggested need of additional quasar feedback energy in order to account for the observed tSZ effect proposed by Ruan et al. (2015) to the fact that projection effects due to clustered halos are not taken into account in their analysis. In right panel of Figure 2 we also show the mean tSZ signals for quasars at three different redshifts separately. Since in this case no projected structures are included, the results are commensurate with the quasar halo masses in the models that increase with increasing redshift. In the (HOD, CS) model (Cen & Safarzadeh 2015), the lower mass threshold of quasar hosts is [2 \u00d7 1013, (2 \u22125) \u00d7 1012] M\u2299at z = 3.2, [5.8\u00d71012, (2\u22125)\u00d71011] M\u2299at z = 1.4 and [5.7\u00d71012, (1\u22123)\u00d71011] M\u2299at z = 0.5. It is also worth noting that, in the absence of projection effects, the quasar tSZ signal in the CS model is about a factor of 5 (at z = 3.2) to 25 (at z = 0.5) lower than in the HOD model, due to differences in the quasar host halo masses in the two models. It should be made clear that the projection effects are present at all redshifts. In the middle panel of Figure 2 we show the average Compton-y pro\ufb01le per quasar for the CS (solid curves) and HOD (dashed curves) model separately at z = 0.5 (blue), z = 1.4 (green) and z = 3.2 (red), including projection effects. Two trends are seen and fully understandable. First, overall, the tSZ signal per quasar, with projected structures, increases with decreasing redsh\ufb01t, in the range from z = 0.5 to z = 3.2. This is expected due to continued growth of cosmic structure with time. We note that, if we had not removed the most massive clusters in our tSZ maps (to account for the masking-out of massive clusters in Planck maps (Planck Collaboration et al. 2014), the increase with decreasing redshift would be stronger. Second, the ratio of tSZ signal with projection effects to that without projection effects increases strongly with decreasing redshift, due to the combined effect of decreasing quasar host halo mass and increasing clustering around massive halos with decreasing redshift. In the left panel of Figure 2 the observed y-map values are not dust-corrected. The correction amplitude for dust effect with the procedure used by Ruan et al. (2015), by applying the channel weights from the Hill & Spergel (2014) y-map construction to dust-like (modi\ufb01ed blackbody) spectra, depends sensitively on dust temperature assumed. Greco & Hill (2015, private communications) show that for a dust temperature of 34 K used in Ruan et al. (2015), the y-map response is indeed negative over the entire redshift range of the quasar sample, resulting in an increase in total thermal energy in the y-map by about 37%; for lower dust temperatures, the y-map response becomes less negative and could go positive below some temperature for all redshifts; for dust temperature of 20 K, the y-map response is very slightly \u2013 6 \u2013 0 5 10 15 20 25 30 QSO\u2013centric distance (arcmin) 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 mean tSZ Compton\u2013y \u00d7 107 smoothed w/ Planck FWHM = 10 arcmin CS QSO Halo Model HOD QSO Halo Model Ruan et al 2015 0 2 4 6 8 10 12 14 QSO\u2013centric distance (arcmin) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 mean tSZ Compton\u2013y \u00d7 107 CS , z = 0.5 CS , z = 1.4 CS , z = 3.2 HOD , z = 0.5 HOD , z = 1.4 HOD , z = 3.2 0 2 4 6 8 10 12 14 QSO\u2013centric distance (arcmin) 0 1 2 3 4 5 6 mean tSZ Compton\u2013y without projected structure CS, z = 0.5 (y \u00d7 109) CS, z = 1.4 (y \u00d7 109) CS, z = 3.2 (y \u00d7 109) HOD, z = 0.5 (y \u00d7 108) HOD, z = 1.4 (y \u00d7 108) HOD, z = 3.2 (y \u00d7 108) HOD, (y \u00d7 108) Fig. 2.\u2014 Left panel shows the mean Compton-y pro\ufb01le of quasars, including projection effects, for the CS (blue shaded region) and HOD (purple shaded region) model, respectively, for a synthetic sample of quasars with redshift distribution [z = (0.1, 3.0) with median redshift of 1.5] mimicing that of the observed sample used in Ruan et al. (2015). The radial pro\ufb01le of the observed quasars (Ruan et al. 2015) is overplotted as the green shaded region without dust correction. We have normalized the observed radial pro\ufb01le with that of the models at 30 arcmin radius, which corresponds to the \u201cbackground\". Middle panel shows the mean Compton-y pro\ufb01le of a quasar, including projection effects, at three separate redshifts, z = 0.5 (blue curves), z = 1.4 (green curves) and z = 3.2 (red curves), for the CS (solid curves) and HOD (dashed curves) model separately. Right panel is similar to the middle panel, except that only the quasar-hosting halo contributes to the thermal energy in the map, without considering the contribution from other halos due to projection effects. Also shown in black is the mean Compton-y pro\ufb01le in HOD model, without projection effects, with appropriate weightings in accordance with that of the observed sample used in Ruan et al. (2015). negative at z < 1.4 but signi\ufb01cantly positive at z > 1.4, with the net y-map response for the quasar sample slightly positive. With regard to dust temperature, observational evidence is varied but data suggesting lower temperatures are widespread. For example, Schlegel et al. (1998) indicate dust temperature of 17 \u221221 K in our own Galaxy; Kashiwagi & Suto (2015) suggest a dust temperature of 18 K for dust around galaxies from far-infrared image stacking analysis; Greco et al. (2014) suggest an overall dust temperature of 20 K in modeling the cosmic infrared background. Thus, the contribution of dust emission itself to y-map depends signi\ufb01cantly on the dust temperature and the exact temperature of dust is uncertain at best and the actual y-map response is thus uncertain. Even if we take the dust-corrected y-map from Ruan et al. (2015), given our results that the dust-uncorrected y values can be explained soley by gravitational energy of halos hosting QSOs and neighboring ones, the QSO contribution is at most about 1/4 of what is inferred in Ruan et al. (2015). \u2013 7 \u2013 4. Testing Competing Quasar Models with Arc-Minute Resolution Thermal Sunyaev-Zeldovich Effect Maps Having validated both the CS and HOD models by the Planck tSZ data on 10 arcmin scales in the previous section, here we propose a test to differentiate between them. Figure 3 shows the stacked tSZ map of quasars with a median redshift of 1.5 smoothed with FWHM=1 arcmin in the CS (left panel) and HOD (right panel) model. The difference between the two model is visually striking: the HOD model, being hosted by much more massive halos than the CS model, displays a much more peaked tSZ pro\ufb01le at the arcmin scales. The reason is that one arcmin corresponds to 516 kpc at z = 1.5, indicating that individual quasar hosting halos of mass \u22651013 M\u2299in the HOD model are no longer signi\ufb01cantly smoothed out by a 1 arcmin beam. The quasar hosting halos in the CS model, on the other hand, have much lower masses than those in the HOD model and hence have much lower tSZ effect at the arcmin scale. At the arcmin scale, projection effects are much reduced compared to the 10 arcmin scale. \u22124 \u22122 0 2 4 arcmin \u22124 \u22122 0 2 4 arcmin CS model mean tSZ Compton\u2013y map 3.2e-07 4.0e-07 4.8e-07 5.6e-07 6.4e-07 7.2e-07 8.0e-07 8.8e-07 9.6e-07 \u22124 \u22122 0 2 4 arcmin \u22124 \u22122 0 2 4 arcmin HOD model mean tSZ Compton\u2013y map 3.2e-07 4.0e-07 4.8e-07 5.6e-07 6.4e-07 7.2e-07 8.0e-07 8.8e-07 9.6e-07 Fig. 3.\u2014 Left panel shows the stacked tSZ map of quasars with a median redshift of 1.5 smoothed with FWHM=1 arcmin in the CS model. Right panel shows the same for HOD model. Figure 4 quanti\ufb01es what is seen in Figure 3 for the two quasar models. We see that, with FWHM=1 arcmin, the central value of y parameter differs by a factor of about two in the two models: (1.0 \u00b1 0.05) \u00d7 10\u22126 in the HOD model versus (0.55 \u00b1 0.03) \u00d7 10\u22126 in the CS model. This is a large difference and can be easily tested. Before quantifying how the two models may be differentiated, it is useful to understand the distribution of contributions from individual y maps to the averaged y map. Figure 5 shows the probability distribution function (PDF) of y parameter of the central region of radius 1 arcmin of 10,000 individual quasar hosting halos (including projection effects) smoothed with FWHM=1 arcmin (red histogram) and smoothed with FWHM=10 arcmin (blue histogram). It is evident \u2013 8 \u2013 0 2 4 6 8 10 QSO\u2013centric distance (arcmin) 0.2 0.4 0.6 0.8 1.0 1.2 mean tSZ Compton\u2013y \u00d7 106 smoothed w/ FWHM = 1 arcmin CS QSO Halo Model HOD QSO Halo Model Fig. 4.\u2014 shows the predicted radial Compton-y pro\ufb01le of CS and HOD model smoothed with 1 arcmin FWHM. \u22129.5 \u22129.0 \u22128.5 \u22128.0 \u22127.5 \u22127.0 \u22126.5 \u22126.0 \u22125.5 \u22125.0 log Compton\u2013y parameter 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Normalized distribution FWHM = 10 arcmin FWHM = 1 arcmin Fig. 5.\u2014 shows the probability distribution function (PDF) of y parameter of the central region of radius 1 arcmin of 10,000 individual quasar hosting halos (including projection effects) smoothed with FWHM=1 arcmin (red histogram) and smoothed with FWHM=10 arcmin (blue histogram) in the CS model. The vertical lines color indicate the median and inter-quartile of the contribution to the mean y value of similar color histograms. that the distribution of log y in both cases is close to gaussian hence the distribution of y is approximately lognormal. This indicates that the overall contribution to the stacked maps is \u2013 9 \u2013 skewed to the high end of the y distribution. We \ufb01nd that 7.8%, 12.1% and 22.5% of high y quasar halos contribute to 25%, 50% and 75% of the overall y value in the case with FWHM= 1 arcmin, 6.3%, 9.6% and 18.4% in the case with FWHM= 10 arcmin. Given the non-gaussian nature, we use bootstrap to estimate errors on the mean y value. We \ufb01nd that the fractional error on the mean, computed by bootstrap sampling from our 10,000 samples, is 3.7% and 3.2% for FWHM=10 arcmin and 1 arcmin cases, respectively. Thus, with a sample of 26, 000 quasars as in Ruan et al. (2015), the fractional error on the mean would be 2% for FWHM=1 arcmin case. Since the fractional difference between the HOD (ycentral = (1.0 \u00b1 0.05) \u00d7 10\u22126) and the CS (ycentral = (0.55 \u00b1 0.03) \u00d7 10\u22126 is 60%, this means that the HOD and CS model can be distinguished at \u223c30\u03c3 level, if statistical uncertainties are the only uncertainties. It is thus likely that the signi\ufb01cance level of differentiating the two models using arcmin scale tSZ effect around quasars will be limited by systematic uncertainties. As stated in \u00a73, there is a possibility that a signi\ufb01cant fraction (\u223c25%) of the observed thermal energy based on y-maps may be due to non-gravitational heating, such as quasar feedback suggested by Ruan et al. (2015). Under the reasonable assumption that the energy from quasar feedback accumulates over time, say via episodic high-energy radio jets, the quasar feedback energy would be proportional to the galaxy stellar mass or approximately the halo mass, given the observed correlation between supermassive black hole mass and the bulge stellar mass or velocity dispersion (e.g., Magorrian et al. 1998; Richstone et al. 1998; Gebhardt et al. 2000; Ferrarese & Merritt 2000; Tremaine et al. 2002). If we further assume that the radial pro\ufb01le of the deposited energy from quasar feedback is the same as that of thermal energy sourced by gravitational energy, it follows then that the central y-value of the (HOD,CS) model would be boosted from [(1.0 \u00b1 0.05) \u00d7 10\u22126, (0.55 \u00b1 0.03) \u00d7 10\u22126] shown in Figure 4 to [(1.4 \u00b1 0.07) \u00d7 10\u22126, (0.77 \u00b1 0.04) \u00d7 10\u22126]. With the inclusion of this systematic uncertainty on quasar feedback energy, the expected central y-value ranges would become [(1.0 \u22121.4) \u00d7 10\u22126, (0.55 \u22120.77) \u00d7 10\u22126], respectively, for the (HOD,CS) model, which remain strongly testable with arcmin resolution tSZ observations. 5. Conclusions We perform a statistical analysis of stacked y maps of quasar hosts using Millennium Simulation. Two signi\ufb01cant \ufb01ndings may be summarized. First, at the available resolution of FWHM=10 arcmin obtained by Planck data, the observed tSZ effect can be entirely accounted for and explained by thermal energy of halos sourced by gravitational collapse. No additional energy source is required at this conjunction. It must be noted that at FWHM=10 arcmin projection effects are important with contribution to y parameter by clustered halos with the \u223c10 arcmin scale dominating over the host halos themselves by an order of magnitude. Considering uncertainties of dust temperature in the calibration of observed y-maps, the maximum quasar feedback energy is about 25% of that suggested (Ruan et al. 2015). \u2013 10 \u2013 Second, we show that, at FWHM=1 arcmin beam, the central value of y parameter is (1.0 \u00b1 0.05) \u00d7 10\u22126 and (0.55 \u00b1 0.03) \u00d7 10\u22126 in the HOD and CS model, respectively, because of the signi\ufb01cant differences in the masses of quasar hosting halos in the two models. At z \u223c 0.5 \u22122, the host halos in the CS model have masses of \u223c1011 \u22121012 M\u2299, compared to (0.5 \u2212 2) \u00d7 1013 M\u2299in the HOD model. With an observational sample of 26, 000 quasars, one will be able to distinguish between the HOD and CS models at a very high con\ufb01dence level statistically , indicating that that the signi\ufb01cance level will only be limited by systematic uncertainties. With possible quasar feedback, the expected central y-value uncertainty ranges would be enlarge to become [(1.0\u22121.4)\u00d710\u22126, (0.55\u22120.77)\u00d710\u22126], respectively, for the (HOD,CS) model, which remain strongly testable with arcmin resolution tSZ observations. Upcoming observations, such as Advanced ACT (Calabrese et al. 2014), may be able to provide a de\ufb01nitive test. We are grateful to Dr. Ruan for sending us the data and useful discussion. We also would like to thank Dr. Colin Hill for useful discussion. This work is supported in part by grant NASA NNX11AI23G. The Millennium simulation data bases used in this paper and the web application providing online access to them were constructed as part of the activities of the German Astrophysical Virtual Observatory.",
                    "introduction": "The nature of the dark matter halos hosting quasars remain debatable. There are primar- ily two competing models. One is the traditional, popular HOD (halo occupation distribution) model, which is based on assigning a probability function to quasars to reside in a halo of a given mass in order to match the observed quasar clustering strength (Zheng et al. 2005, 2007; Shen et al. 2013). The other model is a physically motivated model recently put forth (Cen & Safarzadeh 2015, \u2019CS model\u2019 hereafter). While the CS model, like the HOD based model, matches the observed clustering of quasars, the masses of the dark matter halos in the CS model are very different from those of the HOD based model. For example, at z \u223c0.5 \u22122, the host halos in the CS model have masses of \u223c1011 \u22121012 M\u2299, compared to (0.5 \u22122) \u00d7 1013 M\u2299in the HOD model. This then offers a critical differentiator between the CS and HOD models, namely, the cold gas content in quasars host galaxies. Speci\ufb01cally, because of the large halos mass required in the HOD 1Princeton University Observatory, Princeton, NJ 08544; cen@astro.princeton.edu 2Johns Hopkins University, Department of Physics and Astronomy, Baltimore, MD 21218, USA arXiv:1507.07934v1  [astro-ph.GA]  28 Jul 2015 \u2013 2 \u2013 model, quasars hosts have much lower content of cold gas than in the CS model. Cen & Safarzadeh (2015) have shown that the CS model is in excellent with the observed cover- ing fraction of 60% \u221270% for Lyman limit systems within the virial radius of z \u223c2 quasars (Prochaska et al. 2013). On the other hand, the HOD model is inconsistent with observations of the high covering fraction of Lyman limit systems in quasar host galaxies. Given the funda- mental importance of the nature of dark matter halos hosting quasars, in this Letter we present another potentially powerful test to distinguish between these two competing models. We show that upcoming measurements of thermal Sunyaev-Zeldovich effect at arc-minute resolution (or better) should be able to differentiate between them with high con\ufb01dence."
                },
                {
                    "url": "http://arxiv.org/abs/1504.07248v1",
                    "title": "Coevolution Between Supermassive Black Holes and Bulges Is Not Via Internal Feedback Regulation But By Rationed Gas Supply Due To Angular Momentum Distribution",
                    "abstract": "We reason that, without physical fine-tuning, neither the supermassive black\nholes (SMBHs) nor the stellar bulges can self-regulate or inter-regulate by\ndriving away already fallen cold gas to produce the observed correlation\nbetween them. We suggest an alternative scenario where the observed mass ratios\nof the SMBHs to bulges reflect the angular momentum distribution of infallen\ngas such that the mass reaching the stable accretion disc is a small fraction\nof that reaching the bulge region, averaged over the cosmological time scales.\nWe test this scenario using high resolution, large-scale cosmological\nhydrodynamic simulations (without AGN feedback), assuming the angular momentum\ndistribution of gas landing in the bulge region to yield a Mestel disc that is\nsupported by independent simulations resolving the Bondi radii of SMBHs. A mass\nratio of $0.1-0.3\\%$ between the very low angular momentum gas that free-falls\nto the sub-parsec region to accrete to the SMBH and the overall star formation\nrate is found. This ratio is found to increase with increasing redshift to\nwithin a factor of $\\sim 2$, suggesting that the SMBH to bulge ratio is nearly\nredshift independent, with a modest increase with redshift, a testable\nprediction. Furthermore, the duty cycle of active galactic nuclei (AGN) with\nhigh Eddington ratios is expected to increase significantly with redshift.\nFinally, while SMBHs and bulges are found to coevolve on $\\sim 30-150$Myr time\nscales or longer, there is indication that, on shorer time scales, the SMBH\naccretion rate and star formation may be less correlated.",
                    "authors": "Renyue Cen",
                    "published": "2015-04-27",
                    "updated": "2015-04-27",
                    "primary_cat": "astro-ph.GA",
                    "cats": [
                        "astro-ph.GA"
                    ],
                    "main_content": "With the ACS Virgo Cluster Survey of early-type galaxies spanning four decades in mass, C\u00f4t\u00e9 et al. (2006) and Ferrarese et al. (2006) find a transition at MB,0 = \u221220.5, where the brighter galaxies lack resolved stellar nuclei and SMBHs dominate the CMO mass, while fainter ones have resolved stellar nuclei that dominate the CMO mass. Furthermore, the logarithm of the mean nucleus-to-galaxy luminosity ratio in fainter, nucleated galaxies, \u22122.49 \u00b1 \u22120.09 (\u03c3 = 0.59 \u00b1 \u22120.10) is indistinguishable from that of the SMBH-to-bulge mass ratio, \u22122.61 \u00b1 \u22120.07 (\u03c3 = 0.45 \u00b1 \u22120.09). A similar result is found by Wehner & Harris (2006) using a different data set. Turner et al. (2012) find an identical relation using early-type galaxies in the ACS Fornax Cluster Survey. We express the universal scaling relation between CMOs and bulges as MCMO = MBH + MNSC = \u03b1 MBG, (1) whereby with the transition between NSC and SMBH occurs at MB \u223c\u221220.5 or stellar mass MBG0 = (3\u22124)\u00d71010 M\u2299, and \u03b1 = 2.5\u00d710\u22123 (C\u00f4t\u00e9 et al. 2006; Ferrarese et al. 2006; Wehner & Harris 2006; Turner et al. 2012). One may express regulation of the growth of bulges as eBH MBH + eNSC MNSC + eBG MBG = f\u03c3\u03b2 MBG, (2) where eBH, eNSC and eBG are the feedback strength coefficients per unit mass of the respective components exerted on the stellar bulge and the ejected gas mass is equal to fMBG; \u03c3 is the velocity dispersion of the stellar bulge; \u03b2 is a parameter that absorbs uncertainties regarding the dynamics of concerned feedback processes, with \u03b2 = 2 for energy-conserving feedback (eBH, eNSC and eBG have units of energy per unit mass) and \u03b2 = 1 for momentum-conserving \u2013 3 \u2013 feedback (eBH, eNSC and eBG have units of momentum per unit mass). Note that a signi\ufb01cant feedback regulation means f \u226b1. Insights can be gained by asking the following question: Can the feedback from SMBH and NSCs conspire to regulate the growth of the stellar bulge, i.e., eBH MBH + eNSC MNSC = f\u03c3\u03b2 MBG? (3) The single powerlaw relation between MCMO and MBG across four decades in bulge mass can be understood, only if the negative feedback per unit stellar mass of the NSC and of the SMBH are approximately the same, eBH \u2248eNSC, barring the unknown physical reason for the right hand side of Eq (3) the required amount of notional feedback to regulate the bulge growth to change character abruptly at MBG = MBG0. Although having eBH \u2248eNSC may be possible, it would render a negative answer to the question above (Eq 3), as follows. In the momentum driven regime, since the feedback from the nuclear cluster is subject to higher densities and shorter cooling timescales hence diminished strength in comparison to that in the stellar bulge, i.e., eBG > eNSC. In the energy driven feedback scenario, eBG = eNSC. Since MNSC \u226aMBG, the supernova feedback from stars in the bulge would vastly exceed that from the NSC. This thus invalidates the statement that the NSC and SMBH provide the necessary feedback to regulate the growth of the bulge. The only scenario left for the SMBH to regulate the bulge growth is to force eNSC = 0 and assume the feedback per unit SMBH mass, while constant at MBG > MBG0, to become negligible at about MBG = MBG0. In both the momentum (\u03b2 = 1, Ostriker et al. 2010) and energy feedback scenario (\u03b2 = 2, Faucher-Gigu\u00e8re & Quataert 2012), the amount of momentum or energy per unit SMBH mass, eBH, is ultimately proportional to the driving energy (\u221dMBHc2, where c is speed of light). Thus, there exists no known process to suddenly make eBH drop to zero at some speci\ufb01c MBH, while being constant otherwise. If negative feedback is needed to internally regulate the bulge, the only alternative left is stellar feedback from bulge stars themselves, i.e., eBG = f\u03c3\u03b2. (4) Under the assumption that the feedback strength from stars per unit mass (eBG) is constant, one obtains f \u221d\u03c3\u2212\u03b2, which has the same dependence on \u03c3 as the predicted mass loading factors for both momentum (\u03b2 = 1) or energy (\u03b2 = 2) driven winds (e.g., Murray et al. 2005). Therefore, bulge self-regulation, if required, would be physically supportable and selfconsistent. If bulge is self-regulated, then, under the assumption that eNSC = eBG, NSC may also be self-regulated. The correlation between MMCO and MBG would then require that the mass loading factor for the SMBH is the same as for the NSC, i.e., eBH = eNSC, which is a \ufb01ne-tuned outcome. In the absence of inter-regulation between CMOs and bulges, the proportions of the amount of gas feeding the nuclear and bulge regions must be proportional to the observed MCMO/ MBG ratio. \u2013 4 \u2013 3. An Alternative Scenario: Rationed Cold Gas Supply to Nuclear and Bulge Regions Over Cosmological Time Scales Our arguments in the previous section indicate that the observed MCMOMBG correlation requires the same proportionality in the initial amounts of gas feeding the respective regions, averaged over the cosmological time scales. We test this scenario using direct cosmological simulations. 3.1. Simulation Characteristics See Cen (2014) for a more detailed description of the ab initio LAOZI simulations. Brie\ufb02y, we use the WMAP7-normalized (Komatsu et al. 2011) \u039bCDM model: \u2126M = 0.28, \u2126b = 0.046, \u2126\u039b = 0.72, \u03c38 = 0.82, H0 = 100h km s\u22121Mpc\u22121 = 70 km s\u22121Mpc\u22121 and n = 0.96. A zoom-in box of size 21 \u00d7 24 \u00d7 20h\u22123Mpc3 comoving is embedded in a 120 h\u22121Mpc periodic box. The maximum resolution is better than 111h\u22121pc (physical) at all times. Star formation follows the prescription of Cen & Ostriker (1992). Supernova feedback from star formation is modeled following Cen et al. (2005) with feedback energy being distributed into 27 local gas cells weighted by the speci\ufb01c volume of each cell, to mimic the process of supernova blastwave propagation to channel more energy into the less dense regions. We exclude AGN feedback in order to ascertain the lack of need for it. 3.2. Construction of Gas Feeding Histories of Simulated Galaxies Galaxies are identi\ufb01ed using the HOP algorithm (Eisenstein & Hut 1998) grouping stellar particles. Galaxy catalogs are constructed from z = 0.62 to z = 1.40 with an increment of \u2206z = 0.02 and from z = 1.40 to z = 6 with \u2206z = 0.05, having a temporal resolution of 30\u2212150Myr. For each galaxy at z = 0.62 a genealogical line is constructed up to z = 6, where the parent of each galaxy is identi\ufb01ed with the one at the next higher redshift with the most overlap in stellar mass. At each redshift, we compute the amount (Mc) and mean speci\ufb01c angular momentum (Jc) of gas in the central 1kpc region. To proceed, an ansatz is made: the gas mass with angular momentum lower than Jn is Mc(\u03b2Jn/(1 + \u03b2)Jc)\u03b2. We use \u03b2 = 1, which corresponds to a Mestel (1963) disc of surface density \u03a3(r) \u221dr\u22121. \u03b2 = 1 is motivated by simulations of Hopkins & Quataert (2010, 2011) with resolution as high as 0.1pc. Figure 12 of Hopkins & Quataert (2010) shows that the evolved density runs of the gas discs, on average, follow the \u03a3(r) \u221dr\u22121 pro\ufb01le from 0.1pc to 1kpc. In all of the six individual cases with signi\ufb01cant gas in\ufb02ow, shown in Figures (2, 3) of Hopkins & Quataert (2011), the \u03a3(r) \u221dr\u22121 pro\ufb01le provides an excellent \ufb01t. We compute the 1-d stellar velocity dispersion \u03c3 within the effective radius for each galaxy in the simulation at any redshift and assume an SMBH of \u2013 5 \u2013 mass equal to MBH = 108 M\u2299(\u03c3/200 km/s)4 (Tremaine et al. 2002). The Bondi radius is rB = 2G MBH/3\u03c32 = 7.2pc(\u03c3/200 km/s)2, (5) and the speci\ufb01c angular momentum at rB is JB = \u221a 2rB\u03c3. (6) The gas landing within r0 is assumed to accrete to the SMBH, where at r > r0 the disc has Toomre Q parameter below unity and is hence consumed by star formation. Expressing various parameters by their \ufb01ducial values, we have r0 = 0.42(\u03b1/0.1)2/5(lE/0.1)\u22122/5( MBH/108 M\u2299)3/25(Ma/0.1)14/25(\u03ba/\u03bae)4/25 pc (7) (Eq 42, Goodman 2003), where \u03b1 is radiative ef\ufb01ciency, lE luminosity in Eddington units, Ma Mach number of the viscous disc at r0, and \u03ba and \u03bae opacity and electron-scattering opacity, respectively. Hence the feeding rate to the accretion disc that eventually accretes to the SMBH is \u02d9 Mfeed = Mc((r0/rB)1/2JB/Jc)t\u22121 dyn, (8) where the angular momentum at r0 is J0 = (r0/rB)1/2JB for a Keplerian disc and tdyn = 1kpc/ \u221a 3\u03c3 is the free-fall time at 1kpc. For our analysis, we use r0 = 0.42( MBH/108 M\u2299)3/25 pc, (9) bearing in mind that uncertainties are at least on the order of unity. To see how uncertainty in \u03b2 affects results, we note, a 25% deviation in \u03b2 from unity causes \u02d9 Mfeed in Eq (8) to change by a factor of 2.7, which can be compensated by adjusting each of the parameters in Eq (7) except MBH by a factor of 2.5 appropriately. 3.3. Results We de\ufb01ne a ratio R \u2261500 \u02d9 Mfeed/SFR (SFR is the star formation rate) such that, if R is about unity, the observed SMBH to bulge mass ratio of \u223c0.2% (e.g., Marconi & Hunt 2003; H\u00e4ring & Rix 2004) would be borne out. Transformation from stellar disc(s) to a bulge is not addressed here. It is noted, however, that stellar discs formed from multiple gas in\ufb02ows of inclined angles over the lifetime of a galaxy may be conducive to bulge formation. Note that SFR is computed directly during the simulation, whereas the SMBH accretion rate is computed in post-processing by evaluating Eq (8). Figure 1 shows histories of \u02d9 Mfeed (blue) and R (red) for four random example galaxies. The most noticeable feature is that, without any intentional tuning, R hovers close to unity with \ufb02uctuations of order unity. Figure 2 shows R as a function of redshift. We see that R increases with increasing redshift from \u223c0.7 at z = 0.6 \u22121 to \u223c1.5 at z = 3 \u22124 for galaxies with 1010.5\u221211 M\u2299(green), \u2013 6 \u2013 0.5 1 2 3 4 5 -4 -3 -2 -1 0 1 log M*=11.96 0.5 1 2 3 4 5 -4 -3 -2 -1 0 1 log M*=11.46 z 0.5 1 2 3 4 5 log \u02d9 Mfeed(M\u2299/yr)(blue) & log 500 \u02d9 Mfeed/SFR (red) -4 -3 -2 -1 0 1 log M*=11.18 z 0.5 1 2 3 4 5 -4 -3 -2 -1 0 1 log M*=10.8 Fig. 1.\u2014 shows histories of the feeding rate \u02d9 Mfeed (blue) and R \u2261500 \u02d9 Mfeed/SFR (red) for four random galaxies. The logarithm of the stellar mass for each galaxy at z = 0.62 is indicated at the top of each panel. with similar trends for other mass ranges. We highlight three implications. First, the observed SMBH to bulge ratio is readily achievable in a cosmological setting, with a slight tendency for more massive galaxies to have higher R. This is due to the rationing of gas supply to the central regions of galaxies: a small amount of gas of the lowest angular momentum feeds the SMBH accretion disc, while the rest builds up the stellar bulge, with the demarcation line determined by the accretion disc stability condition. Note that our analysis is solely based on the angular momentum distribution of gas that has already landed in the central 1kpc region. The frequency of gas in\ufb02ow events into the central regions and the mass distribution of events are computed directly in our simulations. Second, R increases with increasing redshift, to within a factor of \u223c2. The trend with redshift is expected in a cosmological context, because both the frequency and strength of galaxy interactions increase with increasing redshift, yielding overall in\ufb02ow gas of lower angular momentum hence a larger R at high redshift. Third, the smoothness of R on cosmological time scales (\u2265100Myr) suggests that the dispersion of R is modest, around order unity, at all redshifts, consistent with the dispersion of the observed \u2013 7 \u2013 redshift 1 2 3 500 \u02d9 MBH/SFR 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 log M*=10.5-11 log M*=10-10.5 log M*= 9.5-10 Fig. 2.\u2014 shows the median of R as a function of redshift, separately for three stellar mass ranges 109.5\u221210 M\u2299(red), 1010\u221210.5 M\u2299(blue) and 1010.5\u221211 M\u2299(green). The stellar mass is measured at the redshift in question. The vertical errorbars indicate the interquartile range, whereas the horizontal errorbars represent the redshift range of the bin. The red and blue points are horizontally slightly right-shifted for clarity of display. There are (659, 2214) galaxies with stellar mass in the range 1010.5\u221211 M\u2299for z = (3 \u22124, 0.62 \u22121), respectively. correlation locally (note that the comparison is made between computed \u02d9 Mfeed/SFR and observed MBH/ MBG). Future observations at high redshift may be able to test these predictions. Although R is relatively smooth over cosmological time scales, the gas in\ufb02ow rate varies up to an order of magnitude (Figure 1). The \ufb02uctuations in the in\ufb02ow rate are caused by a variety of physical processes, including interactions between galaxies in close proximity, minor mergers and occasional major mergers. We have not studied in suf\ufb01cient detail to ascertain whether secular processes play any major role. Is SMBH accretion rate directly dictated by the feeding rate from galactic scales? Figure 3 shows the probability distribution of feeding rate in units of Eddington rate as a function of Eddington ratio. The Eddington ratio is based on the assumed MBH from the observed MBH \u2212\u03c3 relation. At z \u223c0.6 where comparisons with observations may be made, the com\u2013 8 \u2013 log \u03f5E -3 -2 -1 0 log dP/dlog \u03f5E -4 -3 -2 -1 0 M\u2217= 1010.5\u221211M\u2299 z=0.6-1 z=1-2 z=2-3 z=3-4 obs at z~0.6: Aird+12 Fig. 3.\u2014 shows the probability distribution of feeding rate in units of Eddington rate per logarithmic Eddington ratio interval, as a function of Eddington ratio, in four redshift ranges, z = 0.62 \u22121 (solid red), z = 1 \u22122 (dotted blue), z = 2 \u22123 (dashed green), and z = 3 \u22124 (dot-dashed black) for galaxies in the stellar mass range of 1010.5\u221211 M\u2299(other stellar mass ranges have similar properties). Also show as solid dots is the observed powerlaw distribution with a slope of \u223c\u22120.6 at z \u223c0.6 from Aird et al. (2012). The slope of the solid red curve is \u22123.3 measured for the log eE range from \u22122.3 to \u22121.6 indicated by the red dashed line. puted distribution is steeper, computed slope \u22123.3 versus \u22120.60 observed. This indicates that accretion onto the SMBHs is \u201c\ufb01ltered\" through physical processes operating on the accretion disc. This suggests that temporal correlation between AGN and star formation activities in individual galaxies below 30 \u2212150Myr is expected to be weak, in excellent agreement with observations (e.g., Hickox et al. 2014). A comparison between the distribution of the feeding rate to the accretion disc (red curve) and that of the observed Eddington ratio (black dots) suggests that at z \u223c0.6 accretion discs around SMBHs spend most of the time accumulating gas, at feeding rate below 1% Eddington ratio and that the apparent powerlaw distribution of Eddington ratio may be a result of superposition of AGN internal light pro\ufb01les that are universal in shape (i.e., slope of \u223c\u22120.6). We see that the computed feeding rate distribution shifts to \u2013 9 \u2013 the right \u223c0.5 dex per unit redshift, indicating that the duty cycle of luminous AGNs increases with redshift. 4. Conclusions We have shown that, baring implausible physical \ufb01ne-tuning, neither the central massive objects SMBHs or NSCs nor the stellar bulges can be regulated by blowing away the majority of gas that has already landed, to explain the observed CMO-bulge relation. This leaves us with only one viable option. That is, the ratio of feeding rate to the nuclear region to that to the bulge is proportioned cosmologically. We test this scenario using high resolution, large-scale cosmological hydrodynamic simulations without AGN feedback. Our analysis \ufb01nds a proportionality, \u223c0.1 \u22120.3%, between the feeding rate of very low angular momentum gas that can free-fall to the sub-parsec region to accrete to the SMBH and the star formation rate in the galaxy. There is indication that this ratio increases with increasing redshift to within a factor of \u223c2, suggesting that the SMBH to bulge ratio is nearly redshift independent, with a modest increase with redshift. We predict that the duty cycle of luminous AGNs increases with redshift. While SMBHs and bulges are found to coevolve on \u226530 \u2212150Myr time scales, there is indication that, on smaller time scales, the SMBH accretion and star formation may be less or not correlated, which is likely due to variations of AGN activities on smaller time scales dictated by physics of accretion disc. While our analysis disfavor internal regulation in terms of blowing gas away with the required proportionality, \u201crandom\" internal regulation by blowing some gas away without the said proportionality is not ruled out and in fact may be common, manifested as galactic superwinds or AGN winds. Nor do we disfavor feedback processes that control the overall amount of cold gas supply, termed \"global feedback\". Global feedback re\ufb02ects the collective effects of stellar evolution (supernovae, winds, etc) and SMBH accretion (winds, radio jets, etc) as well as gravitational shock heating due to structure formation and photoionization heating, among others. They impact the thermodynamical state of the interstellar, circumgalactic and intergalactic medium. We emphasize that, even if global feedback controls the overall cold gas supply and its temporal distribution on cosmological time scales, it is not responsible for the proportional growth of SMBHs and galaxies. An implication is that the distinction between forming a NSC or SMBH may hinge on the existence of a massive enough initial black hole seed. Thus, the demarcation bulge mass of MBG0 = (3\u22124)\u00d71010 M\u2299is suggestive that only the progenitors of the massive enough galaxies have formed massive black hole seeds at some high redshift, with less massive galaxies seeded by NSCs or neither. Subsequently, those with initial massive black hole seeds are able to accrete the infallen gas and grow to SMBHs over time, whereas those without massive black hole seeds turn the infallen gas in the nuclear regions into stars to grow the NSCs. Let us suppose that CMOs of initial mass MCMO,init created at some high redshift in dwarf galaxies have \u2013 10 \u2013 migrated to the centers of larger galaxies to serve as central seeds. The rationed gas supply would then yield \ufb01nal MCMO/ MBG = (\u03b1 MBG+MCMO,init)/( MBG+MCMO,init). Thus, for those galaxies lacking signi\ufb01cant, subsequent growth of the CMO, i.e., \u03b1 MBG is not much greater than MCMO,init, the CMO-bulge mass scaling relation will be sublinear, which may explain the observed shallower scaling relation between NSCs and bulges at the low end of bulge mass (e.g., Erwin & Gadotti 2012; Leigh et al. 2012; Scott & Graham 2013; den Brok et al. 2014). Galaxies with a massive initial black hole seed may form a NSC as well, consistent with observations (e.g., Seth et al. 2008; Gonz\u00e1lez Delgado et al. 2008), although the stellar component in the vicinity of an SMBH may be altered by subsequent, additional processes, such inspiral of another SMBH (e.g., Milosavljevi\u00b4 c et al. 2002). This study is related to Escala (2006, 2007), who studied gas accretion processes surrounding the SMBH; we explicitly avoid detailed accretion physics by focusing on the amount of mass that enters the \u201cfeeding\" zone to the SMBH. This work reaches conclusions similar to that of Angl\u00e9s-Alc\u00e1zar et al. (2015) with respect to the MBH \u2212MBG ratio, with a contrasting difference on the role of feedback. While Angl\u00e9s-Alc\u00e1zar et al. (2015) requires that only a small fraction of the gas at subparsec scales is actually accreted by the SMBH, with the rest lost to winds and out\ufb02ows, we suggest that the gas disc beyond the Toomre unstable radius is instead consumed by star formation, without requiring blowing away most of the gas by the SMBH. I am indebted to an anonymous referee for the most detailed, cogent, critical yet civilized reports, which have immensely helped improve the presentation and clarify numerous issues. I thank Dr. Guangtun Zhu for very helpful discussion. This work is supported in part by grant NASA NNX11AI23G.",
                    "introduction": "There is mounting evidence that massive bulges in the nearby universe harbor central SMBHs of mass 106 \u2212109 M\u2299. The correlation between SMBH mass ( MBH) and the bulge (BG) mass ( MBG) or velocity dispersion (\u03c3) (e.g., Magorrian et al. 1998; Richstone et al. 1998; Gebhardt et al. 2000; Ferrarese & Merritt 2000; Tremaine et al. 2002) suggests coevolution. Although alternative models for producing this observed relation are available (e.g., Ostriker 2000; Adams et al. 2001; Colgate et al. 2003; Cen 2007), the correlation is often construed as 1Princeton University Observatory, Princeton, NJ 08544; cen@astro.princeton.edu arXiv:1504.07248v1  [astro-ph.GA]  27 Apr 2015 \u2013 2 \u2013 evidence for AGN feedback to regulate the growth of SMBHs and bulges. The idea that AGN feedback may alleviate problems in galaxy formation models (e.g., Kauffmann & Haehnelt 2000; Croton et al. 2006; Somerville et al. 2008) further enhances its appeal. The three- dimensional hydrodynamic simulations successfully reproduced the observed MBH/ MBG ratio (e.g., Di Matteo et al. 2005; Hopkins et al. 2006), providing the physical basis for this scenario. This Letter has two goals. First, we make a qualitative examination of the implications of the observed relation between bulges and the central massive objects (CMOs), wherein the two follow a linear relation over four decades in mass. It is shown that neither the SMBHs nor the nuclear star clusters (NSCs) nor the stellar bulges could have played a dominant role in regulating the growth of any of the three components in the way of blowing away a signi\ufb01cant fraction of gas already landed in the respective regions so as to produce the CMO-bulge relation. Second, an alternative model is put forth wherein the correlation between SMBH mass and bulge mass is dictated by the angular momentum distribution of the infalling gas. We successfully test this new scenario using ab initio Large-scale Adaptive-mesh-re\ufb01nement Omniscient Zoom-In (LAOZI) cosmological hydrodynamic simulations."
                },
                {
                    "url": "http://arxiv.org/abs/1502.04026v1",
                    "title": "Quantifying Distributions of Lyman Continuum Escape Fraction",
                    "abstract": "Simulations have indicated that most of the escaped Lyman continuum photons\nescape through a minority of solid angles with near complete transparency, with\nthe remaining majority of the solid angles largely opaque, resulting in a very\nbroad and skewed probability distribution function (PDF) of the escape fraction\nwhen viewed at different angles. Thus, the escape fraction of Lyman continuum\nphotons of a galaxy observed along a line of sight merely represents the\nproperties of the interstellar medium along that line of sight, which may be an\nill-representation of true escape fraction of the galaxy averaged over its full\nsky. Here we study how Lyman continuum photons escape from galaxies at $z=4-6$,\nutilizing high-resolution large-scale cosmological radiation-hydrodynamic\nsimulations. We compute the PDF of the mean escape fraction ($\\left<f_{\\rm\nesc,1D}\\right>$) averaged over mock observational samples, as a function of the\nsample size, compared to the true mean (had you an infinite sample size). We\nfind that, when the sample size is small, the apparent mean skews to the low\nend. For example, for a true mean of 6.7%, an observational sample of (2,10,50)\ngalaxies at $z=4$ would have have 2.5% probability of obtaining the sample mean\nlower than $\\left<f_{\\rm esc,1D}\\right>=$(0.007%, 1.8%, 4.1%) and 2.5%\nprobability of obtaining the sample mean being greater than (43%, 18%, 11%).\nOur simulations suggest that at least $\\sim$ 100 galaxies should be stacked in\norder to constrain the true escape fraction within 20% uncertainty.",
                    "authors": "Renyue Cen, Taysun Kimm",
                    "published": "2015-02-13",
                    "updated": "2015-02-13",
                    "primary_cat": "astro-ph.GA",
                    "cats": [
                        "astro-ph.GA"
                    ],
                    "main_content": "To investigate how LyC photons escape from their host halos, we make use of the cosmological radiation hydrodynamic simulation performed using the Eulerian adaptive mesh refinement code, ramses (Teyssier 2002; Rosdahl et al. 2013, ver. 3.07). The reader is referred to Kimm & Cen (2014, , the FRU run) for details, where a detailed prescription for a new, greatly improved treatment of stellar feedback in the form of supernova explosion is given. Specifically, the new feedback model follows the dynamics of the explosion blast waves that capture the solution for all phases (from early free expansion to late snowplow), independent of simulation resolution and allow for anisotropic propagation. The initial condition for the simulation is generated using the MUSIC software (Hahn & Abel 2011), with the WMAP7 parameters (Komatsu et al. 2011): (\u2126m, \u2126\u039b, \u2126b, h, \u03c38, ns = 0.272, 0.728, 0.045, 0.702, 0.82, 0.96). We adopt a large volume of (25Mpc/h)3 (comoving) to include the effect of large-scale tidal fields on the galaxy assembly. The entire box is covered with 2563 the effect of large-scale tidal fields on the galaxy assembly. The entire box is covered with 256 root grids, and high-resolution dark matter particles of mass Mdm = 1.6 \u00d7 105 M\u2299are employed in the zoomed-in region of 3.8 \u00d7 4.8 \u00d7 9.6 Mpc3. We allow for 12 more levels of grid refinement based on the density and mass enclosed within a cell in the zoomed-in region to have a maximum spatial resolution of 4.2 pc (physical). Star formation is modeled by creating normal and runaway particles in a dense cell (nH \u2265100 cm\u22123) with the convergent flow condition (Kimm & Cen 2014, the FRU run). The minimum mass of a normal (runaway) star particle is 34.2 M\u2299(14.6 M\u2299). We use the mean frequency of Type II supernova explosions of 0.02 M\u2299 \u22121, assuming the Chabrier initial mass function. Dark matter halos are identified using the HaloMaker (Tweed et al. 2009). Eight consecutive snapshots are analyzed at each redshift (3.96 \u2264z \u22644.00, 4.92 \u2264z \u22645.12, and 5.91 \u2264z \u22646.00) to increase the sample size in our calculations. At each snapshot there are \u2248 142, 137, and 104 halos in the halo mass range of 109 \u2264Mvir < 1010 M\u2299, and 15, 10, and 7 halos with mass Mvir \u22651010 M\u2299. The most massive galaxy at z = 4 (5, 6) has stellar mass of 1.6\u00d7109 M\u2299 (6.0 \u00d7 108, 2.5 \u00d7 107 M\u2299), and host halo mass 8.8 \u00d7 1010 M\u2299(5.2 \u00d7 1010, 4.1 \u00d7 1011 M\u2299) The escape fraction is computed as follows. We cast 768 rays per star particle and follow their \u2013 3 \u2013 propagation through the galaxy. Each ray carries the spectral energy distribution (SED), including its LyC emission, determined using Sturburst99 (Leitherer et al. 1999), given the age, metallicity, and mass of the star particle. The LyC photons are attenuated by neutral hydrogen (Osterbrock & Ferland 2006) and SMC-type dust (Draine et al. 2007) in the process of propagation. For a conservative estimate, we assume the dust-to-metal ratio of 0.4. We also simply assume that dust is destroyed in hot gas (T > 106 K). We note that attenuation due to dust is only signi\ufb01cant in the most massive galaxy (Mstar = 1.1 \u00d7 109 M\u2299, \u03c4d = 0.58) in our sample. The second most massive galaxy (Mstar = 3.6 \u00d7 108 M\u2299) shows \u03c4d = 0.29, meaning that it reduces the number of photons by only < 30%. Given that the dust-to-metal ratio is even smaller than 0.4 in low-metallicity systems (Lisenfeld & Ferrara 1998; Engelbracht et al. 2008; Galametz et al. 2011; Fisher et al. 2013), it is likely that the attenuation by dust is even less signi\ufb01cant in our simulated galaxies. We de\ufb01ne the true escape fraction of the galaxy as the ratio of the sum of all outward \ufb02uxes at the virial sphere to the sum of the initially emitted \ufb02uxes of all stellar particles in the galaxy; we shall call this fesc,3D. In addition, an observer at in\ufb01nity at a random point in the sky of the galaxy collects all LyC \ufb02uxes and de\ufb01nes the escape fraction along that particular line of sight; this is called fesc,1D. 3. Probability Distribution Functions of LyC Photon Escape Fraction It is useful to give a qualitative visual illustration of how LyC photons may escape from galaxies at z = 4. Figure 1 shows three examples of an all-sky map the sky an observer sitting at the center of the galaxy would see of the neutral hydrogen column density. We note that 8 dex of dynamical range is plotted and recall that at the Lyman limit a neutral hydrogen column density of \u223c1017cm\u22122 would provide an optical depth of \u223c1. As a result, LyC photons can only escape through highly ionized or evacuated \u201choles\u201d indicated by dark blue colors on the maps and the transition from near transparency to very opaque is fast. This indicates that the escaping LyC photons are dominated by those that escape through completely unobscured channels and the amount of escaped LyC photons for a given galaxy depends strongly on the direction. Moreover, it is evident that, in addition to large variations from position to position on the sky for a given galaxy, there are large variations of the overall column density structures from galaxy to galaxy. For example, the galaxy in the top-left panel shows no transparent sky patches at all, which is typical for galaxies during times of intense starburst as shown in Kimm & Cen (Figure 4 2014). On the other hand, the galaxy in the bottom panel has large swaths of connected transparent patches that cover nearly one half of the sky, typical for galaxies at periods following the blowout of gas subsequent to intense starburst (Figure 4 Kimm & Cen 2014). This qualitative behavior is also found earlier in independent simulations by Wise & Cen (2009). Let us now turn to more quantitative results. Figure 2 shows the probability distribution of the apparent escape fraction for massive halos (top) and less massive halos (bottom) at z = 4 (left column) and z = 6 (right column). Black histograms show the distribution of the true (3D) escape fraction of each sample (i.e., from the viewpoint of the overall intergalactic medium), while red histograms show the PDF of the apparent escape fraction (i.e., from the point of view of observers placed at a far distance). Note that the distribution of the true escape fraction is noisier than that of \u2013 4 \u2013 16.0   24.0 log NHI   16.0   24.0 log NHI   16.0   24.0 log NHI   Fig. 1.\u2014 shows three examples of all-sky maps the sky an observer sitting at the center of the galaxy would see of the neutral hydrogen for most massive (Mvir = 7.8 \u00d7 1010 M\u2299, top left panel), second massive (6.1 \u00d7 1010 M\u2299, top right panel), and a smaller halo (1.8 \u00d7 109 M\u2299, bottom). The observer is placed at the center of the halo. Note that the actual escape fraction presented later is computed by ray-tracing LyC photons of all stellar particles spatially distributed through the clumpy interstellar medium until escaping through the virial sphere. The true escape fraction of LyC photons of these halos are 5.4%, 12%, and 5.0%, respectively. the apparent escape fraction due to the smaller sample size for the former, because for (3D) escape fraction each galaxy is counted once but for the apparent escape fraction each galaxy is sampled many times. In terms of the mean escape fraction, there is a trend that, at a given redshift, the galaxies embedded in more massive halos tend to have a lower mean escape fraction. There is also a weak trend that the escape fraction increases with redshift. For example, the true (3D) median escape fractions are (7.0%, 9.5%) for the halos of masses (\u22651010, 109 \u22121010) M\u2299, respectively, at z = 4; the true (3D) median escape fractions are (8.8%, 29%) for the halos of masses (\u22651010, 109 \u22121010) M\u2299, respectively, at z = 6. Upon a close examination we suggest that the redshift dependence can be attributed, in part, to the following \ufb01ndings. At a given halo mass, the speci\ufb01c star formation rate decreases with decreasing redshifts at 4 \u2264z \u22646. As star formation becomes less episodic at lower redshifts, it takes longer to blow out the star-forming clouds via SNe. Consequently, a larger fraction of LyC photons is absorbed by their birth clouds. We also \ufb01nd that the speci\ufb01c star formation rate does not change notably at z > 6 while the mean density \u2013 5 \u2013 -6 -5 -4 -3 -2 -1 0 -2 -1 0 1 log PDF <fesc,3D>med=0.070 <fesc,1D>med=0.039 z~4 Mvir*1010Msun (N=123) -6 -5 -4 -3 -2 -1 0 log fesc,1D -2 -1 0 1 log PDF <fesc,3D>med=0.095 <fesc,1D>med=0.059 109<Mvir<1010Msun (N=1110) -6 -5 -4 -3 -2 -1 0 -2 -1 0 1 log PDF <fesc,3D>med=0.088 <fesc,1D>med=0.068 z~6 Mvir*1010Msun (N=23) -6 -5 -4 -3 -2 -1 0 log fesc,1D -2 -1 0 1 log PDF <fesc,3D>med=0.286 <fesc,1D>med=0.204 109<Mvir<1010Msun (N=467) Fig. 2.\u2014 shows the probability distribution of the apparent escape fraction for massive halos (top panel) and less massive halos (bottom panel) for z = 4 (left column) and z = 6 (right column). Black histograms show the distribution of the true escape fraction of each sample, while red histograms show the PDF of the apparent escape fraction. The median of the distribution is shown as arrows. of the halo increases with redshifts, explaining an opposite trend found in Kimm & Cen (2014) at 7 \u2264z \u226411. The predicted median escape fraction for halos with 109 \u2264Mhalo \u22641011 M\u2299at 4 \u2264z \u22646 is generally smaller than the previous studies (10 \u221230% Razoumov & Sommer-Larsen 2010; Yajima et al. 2014), although the trend at z < 6 is broadly consistent with Razoumov & Sommer-Larsen (2010). Nevertheless, it is prudent to bear in mind that the sometimes con\ufb02icting results and trends among studies with respect to redshift may be in part due to still limited galaxy sample sizes. Figure 3 is similar to Figure 2, except the galaxy sample is subdivided according to their star formation rates (SFRs). We note that this division according to SFRs introduces subtle degeneracies. For example, a lower SFR does not necessarily correspond to a less massive galaxy; instead, a lower SFR may correspond to the phase of a galaxy between two star formation bursts. The significantly higher escape fraction for the lowest SFR bin (bottom panels) is, to the most part, due to a post-starburst phase when the interstellar medium has been cleared out by the preceding burst and SFR has abated, as noted in Kimm & Cen (2014). Thus, if we do not consider the lowest SFR bin, it seems that the mean escape fraction does not strongly depend on SFR at z = 4\u22126. The escape fraction from the most actively star-forming galaxy sample with 0.3 < SFR < 10 M\u2299/yr be compared with that of Lyman alpha emitters or faint LBGs. Our simulations suggest that the median fesc,1D of the sample is 5.1%, which is consistent with fesc,1D = 5 \u221215% inferred from narrow band \ufb01lter imaging observations of 91 LAEs (Mostardi et al. 2013). We note that, given the wide distribution of the simulated apparent escape fraction (0.1% \u2272fesc,1D \u227223% or 0.001% \u2272fesc,1D \u227247% for the \u2013 6 \u2013 1 and 1.5 \u03c3 range, respectively), our results are also compatible with the individual detection of LyC \ufb02uxes from 7 LBGs (Iwata et al. 2009, 5.5 \u2272fesc,1D \u227255% for the intrinsic UV to LyC \ufb02ux ratio of 3.). -6 -5 -4 -3 -2 -1 0 -2 -1 0 1 log PDF <fesc,3D>med=0.065 <fesc,1D>med=0.051 0.3)SFR<10 (N=99) z~4 -6 -5 -4 -3 -2 -1 0 -2 -1 0 1 log PDF <fesc,3D>med=0.042 <fesc,1D>med=0.030 0.01)SFR<0.3 (N=296) -6 -5 -4 -3 -2 -1 0 -2 -1 0 1 log PDF <fesc,3D>med=0.146 <fesc,1D>med=0.068 SFR<0.01 (N=784) log fesc,1D -6 -5 -4 -3 -2 -1 0 -2 -1 0 1 log PDF <fesc,3D>med=0.088 <fesc,1D>med=0.059 0.3)SFR<10 (N=17) z~6 -6 -5 -4 -3 -2 -1 0 -2 -1 0 1 log PDF <fesc,3D>med=0.089 <fesc,1D>med=0.059 0.01)SFR<0.3 (N=91) -6 -5 -4 -3 -2 -1 0 -2 -1 0 1 log PDF <fesc,3D>med=0.364 <fesc,1D>med=0.269 SFR<0.01 (N=359) log fesc,1D Fig. 3.\u2014 is similar to Figure 2, except the galaxy sample is subdivided according to their star formation rates, SFR=0.3 to 10 M\u2299/yr (top panel), 0.01 to 0.3 M\u2299/yr (middle panel), and < 0.01 M\u2299/yr (bottom panel). Evidently, the distribution of the apparent LyC escape fraction is very broad and skewed toward the lower end. The reason for this behavior is understandable. In the case of the galaxies with low fesc,3d values, the LyC photons escape normally through transparent holes with small solid angles. Since not all of these holes are seen to an observer, the distribution of fesc,1d for individual galaxies tends to get skewed toward the lower end of the distribution. As a result, the medians of the two distributions, shown as arrows in Figure 2, are about a factor of \u223c2 smaller than the mean. More importantly, it suggests that an observational sample of limited size may underestimate the true mean escape fraction. The top two panels of Figure 4 show the probability distribution function of the apparent mean for a given observational sample size Nstack for the high mass (top) and low mass (bottom) sample, respectively. We compute the apparent mean of a sample of galaxies using LyC photon (or SFR)-weighted mean escape fraction, which is exactly equivalent to stacking the galaxies. The bottom two panels of Figure 4 are similar to top two panels in Figure 4, for the subsamples with di\ufb00erent star formation rates. What we see in these \ufb01gures is that the probability distribution is rather broad. It is thus clear that it is not a robust exercise to try to infer the mean escape fraction based on a small sample (\u226410) of galaxies, whether individually measured or through stacking. Table 1 provides a quantitative assessment of the uncertainties, which shows the 1 and 2\u03c3 \u2013 7 \u2013 probability intervals of fractional lower and upper deviations from the true mean escape fraction. Some relatively mild trends are seen that are consistent with earlier observations of the \ufb01gures. Speci\ufb01cally, the convergence to the true mean escape fraction in terms of sample sizes is faster towards high redshift, towards higher halo mass, and towards higher star formation rates. Let us take a few numerical examples. We see that with a sample of 50 galaxies of halo mass in the range of (1010 \u22121011) M\u2299at z = 4 the 2\u03c3 fractional range of the escape fraction is 58% to 159%, which improves to a range of 68% to 140% when a sample of 100 galaxies is used. Note that the observations of Mostardi et al. (2013) have 49 Lyman break galaxies and 91 Lyman alpha emitters at z \u223c2.85. At z = 6 for the (1010 \u22121011) M\u2299halo mass range, we see that with a sample of 20 galaxies, the 2\u03c3 fractional range of the escape fraction is 59% to 161%, comparable to that of a sample of 50 galaxies at z = 4, as a result of bene\ufb01ting from the faster convergence at higher redshift. On the other hand, at z = 5 for the (0.3 \u221210) M\u2299yr\u22121 star formation rate range, the 2\u03c3 fractional range of the escape fraction is 56% to 163% with a sample of 20 galaxies, which is improved to 71% to 137% with a sample of 50 galaxies. Finally, we note that the actual observed Lyman continuum escape fraction has additionally su\ufb00ered from possible absorbers in the intergalactic medium, primarily Lyman limit systems. Since the background galaxy and the foreground absorbers are physically unrelated, we may consider the e\ufb00ects from the internal factors in galaxies and those from the intergalactic medium completely independent. Thus, in this case, assuming no knowledge of the foreground absorbers, the overall distribution would be the convolution of the two, resulting a still broader overall distribution than derived above considering internal factors alone. In reality, however, one may be able to remove, to a large degree, the Lyman continuum opacity due to intergalactic absorbers by making use of a tight correlation between Ly\u03b1 and LyC absorption (Inoue & Kamaya 2008). \u2013 8 \u2013 -4 -3 -2 -1 0 0.0 0.2 0.4 0.6 0.8 1.0 Nstack=1 Nstack=2 Nstack=5 Nstack=10 Nstack=20 Nstack=50 Nstack=100 Nstack=1000 <fesc,3D>=0.067 1010)Mvir<1011MO  \u2022 -4 -3 -2 -1 0 log <fesc> 0.0 0.2 0.4 0.6 0.8 1.0 <fesc,3D>=0.11 109)Mvir<1010MO  \u2022 cumulatative PDF z~4 -4 -3 -2 -1 0 0.0 0.2 0.4 0.6 0.8 1.0 Nstack=1 Nstack=2 Nstack=5 Nstack=10 Nstack=20 Nstack=50 Nstack=100 Nstack=1000 <fesc,3D>=0.069 1010)Mvir<1011MO  \u2022 -4 -3 -2 -1 0 log <fesc> 0.0 0.2 0.4 0.6 0.8 1.0 <fesc,3D>=0.075 109)Mvir<1010MO  \u2022 cumulatative PDF z~6 -4 -3 -2 -1 0 0.0 0.2 0.4 0.6 0.8 1.0 Nstack=1 Nstack=2 Nstack=5 Nstack=10 Nstack=20 Nstack=50 Nstack=100 Nstack=1000 <fesc,3D>=0.078 0.3)SFR<10 -4 -3 -2 -1 0 0.0 0.2 0.4 0.6 0.8 1.0 <fesc,3D>=0.090 0.01)SFR<0.3 -4 -3 -2 -1 0 0.0 0.2 0.4 0.6 0.8 1.0 <fesc,3D>=0.099 SFR<0.01 cumulatative PDF log <fesc> z~4 -4 -3 -2 -1 0 0.0 0.2 0.4 0.6 0.8 1.0 Nstack=1 Nstack=2 Nstack=5 Nstack=10 Nstack=20 Nstack=50 Nstack=100 Nstack=1000 <fesc,3D>=0.063 0.3)SFR<10 -4 -3 -2 -1 0 0.0 0.2 0.4 0.6 0.8 1.0 <fesc,3D>=0.085 0.01)SFR<0.3 -4 -3 -2 -1 0 0.0 0.2 0.4 0.6 0.8 1.0 <fesc,3D>=0.030 SFR<0.01 cumulatative PDF log <fesc> z~6 Fig. 4.\u2014 Top two panels show the probability distribution function of the apparent mean for a given observational sample size Nstack for the high mass (top) and low mass (bottom) sample, respectively. The mean is computed by weighting the number of photons produced in each galaxies to mimic the stacking of the SED in observations. The true mean of the distribution is denoted in each panel. Bottom two panels are the same as the top two panels, but for the subsamples with di\ufb00erent star formation rates, as indicated in the legend. \u2013 9 \u2013 4. Conclusions We have simulated a signi\ufb01cant sample of galaxies that are resolved at 4 parsec scales, important for capturing the structure of the interstellar medium (e.g., Joung & Mac Low 2006). We have also implemented a much improved supernova feedback method that captures all phases of the SedovTaylor explosion solution and has been shown to yield the correct \ufb01nal momentum driven by the explosion regardless of the numerical resolution (Kimm & Cen 2014). An adequate treatment of both these two requirements is imperative, before one can start properly addressing the issue of LyC escape, because most of the escape LyC photons escape through \u201choles\u201d in the interstellar medium, instead of them uniformly leaking out in a \u201ctranslucent\u201d medium. In Kimm & Cen (2014) we address the escape fraction for galaxies at the epoch of reionization, to provide the physical basis for stellar reionization. Here we quantify the distribution of escape fraction for galaxies as a whole, at a range of redshift from z = 4 to z = 6. In general, it is found that the LyC escape fraction depends strongly on the view angle of the observer and the overall distribution of the escape fraction sampled over many sightlines is very broad. The distribution narrows with increasing halo mass or SFR or redshift. This broad distribution introduces large sampling uncertainties, when the galaxy sample size is limited. For example, a sample of 50 galaxies of halo mass in the range of (1010 \u22121011) M\u2299at z = 4 produces the 2\u03c3 fractional range of the escape fraction of 58%-159%. At z = 5 a sample of 20 galaxies with star formation rate in the range of (0.3 \u221210) M\u2299yr\u22121 gives the 2\u03c3 fractional range of the escape fraction is 56%-163%. Our analysis suggests that at least on order of tens of galaxies is needed, before one is con\ufb01dent at the 2\u03c3 level that the mean escape fraction measured does not deviate from the truth by 30-50% at z = 4 \u22126 for galaxies hosted by halos of mass in the range 1010 \u22121011 M\u2299. We thank Rogier Windhorst for useful discussion. Computing resources were in part provided by the NASA HighEnd Computing (HEC) Program through the NASA Advanced Supercomputing (NAS) Division at Ames Research Center. The research is supported in part by NSF grant AST1108700 and NASA grant NNX12AF91G.",
                    "introduction": "A fraction of the Lyman continuum (LyC) photons generated by young massive stars is believed to escape from the host galaxies to enter the intergalactic space. This is a fundamental quantity to determine the epoch and pace of cosmological reionization, provided that the universe is reionized by stars (e.g., Gnedin 2000; Cen 2003). After the completion of cosmological reionization, it plays another important role in determining the ultra-violet (UV) radiation background (on both sides of the Lyman limit) in conjunction with another major source of UV photons - quasars - that progressively gains importance at lower redshift (e.g., Faucher-Gigu` ere et al. 2008; Fontanot et al. 2014). Observations of star-forming galaxies at high redshifts (z \u223c3) suggest a wide range of the escape fraction of ionizing photons. While only a small fraction of LyC photons (\u2272a few percent) escapes from their host galaxies in the majority of the Lyman break galaxy samples, a non-negligible 1Princeton University Observatory, Princeton, NJ 08544; cen@astro.princeton.edu 2Princeton University Observatory, Princeton, NJ 08544; kimm@astro.princeton.edu arXiv:1502.04026v1  [astro-ph.GA]  13 Feb 2015 \u2013 2 \u2013 number of them (\u223c10%) shows high levels of LyC \ufb02ux corresponding to \u27e8fesc,1D\u27e9\u223c10% (Shapley et al. 2006; Iwata et al. 2009; Nestor et al. 2011, 2013; Mostardi et al. 2013). Cooke et al. (2014) claim that the mean escape fraction may be even higher (\u27e8fesc, 1D\u27e9\u223c16%) if the observational sample is not biased toward the galaxies with a strong Lyman limit break. It is not well understood quantitatively, however, what the probability distribution function (PDF) of the LyC escape fraction is and how a limited observational sample size with individually measured escape fractions can be properly interpreted, because of both possible large variations of the escape fraction from sightline to sightline for a given galaxy and possible large variations from galaxy to galaxy. The purpose of this Letter is to quantify how LyC photons escape, in order to provide a useful framework for interpreting and understanding the true photon escape fraction given limited observational sample sizes."
                },
                {
                    "url": "http://arxiv.org/abs/1412.4075v1",
                    "title": "A New Model for Dark Matter Halos Hosting Quasars",
                    "abstract": "A new model for quasar-hosting dark matter halos, meeting two physical\nconditions, is put forth. First, significant interactions are taken into\nconsideration to trigger quasar activities. Second, satellites in very massive\nhalos at low redshift are removed from consideration, due to their deficiency\nof cold gas. We analyze the {\\em Millennium Simulation} to find halos that meet\nthese two conditions and simultaneously match two-point auto-correlation\nfunctions of quasars and cross-correlation functions between quasars and\ngalaxies at $z=0.5-3.2$. %The found halos have some distinct properties worth\nnoting. The masses of found quasar hosts decrease with decreasing redshift,\nwith the mass thresholds being $[(2-5)\\times 10^{12}, (2-5)\\times 10^{11},\n(1-3)\\times 10^{11}]\\msun$ for median luminosities of $\\sim[10^{46}, 10^{46},\n10^{45}]$erg/s at $z=(3.2, 1.4, 0.53)$, respectively, an order of magnitude\nlower than those inferred based on halo occupation distribution modeling. In\nthis model quasar hosts are primarily massive central halos at $z\\ge 2-3$ but\nincreasingly dominated by lower mass satellite halos experiencing major\ninteractions towards lower redshift. But below $z=1$ satellite halos in groups\nmore massive than $\\sim 2\\times 10^{13}\\msun$ do not host quasars. Whether for\ncentral or satellite halos, imposing the condition of significant interactions\nsubstantially boosts the clustering strength compared to the total population\nwith the same mass cut. The inferred lifetimes of quasars at $z=0.5-3.2$ of\n$3-30$Myr are in agreement with observations. Quasars at $z\\sim 2$ would be\nhosted by halos of mass $\\sim 5\\times 10^{11}\\msun$ in this model, compared to\n$\\sim 3\\times 10^{12}\\msun$ previously thought, which would help reconcile with\nthe observed, otherwise puzzling high covering fractions for Lyman limit\nsystems around quasars.",
                    "authors": "Renyue Cen, Mohammadtaher Safarzadeh",
                    "published": "2014-12-12",
                    "updated": "2014-12-12",
                    "primary_cat": "astro-ph.CO",
                    "cats": [
                        "astro-ph.CO",
                        "astro-ph.GA"
                    ],
                    "main_content": "We utilize the Millennium Simulation (Springel et al. 2005) to perform the analysis, whose properties meet our requirements, including a large box of 500h\u22121Mpc, a mass resolution with dark matter particles of mass 8.6 \u00d7 108h\u22121 M\u2299, and a spatial resolution of 5 h\u22121 kpc comoving. Halos are found using a friends-of-friends (FOF) algorithm. Satellite halos are separated out using the SUBFIND algorithm (Springel et al. 2001). The adopted \u039bCDM cosmology parameters are \u2126m = 0.25, \u2126b = 0.045, \u2126\u039b = 0.75, \u03c38 = 0.9 and n = 1, and H0 = 100h km s\u22121 Mpc\u22121 with h = 0.73. Given the periodic box we compute the 2-point auto-correlation function (ACF) \u03be(rp, \u03c0) of a halo sample by  DD \u03be(rp, \u03c0) = DD RR DD RR \u22121, (1)  plane and along the line of sight, respectively, where rp and \u03c0 is the pair separation in the sky plane and along the line of sight, respectively, DD and RR are the normalized numbers of quasar-qausar and random-random pairs in each bin (rp \u22121 2\u2206rp \u2192rp + 1 2\u2206rp, \u03c0 \u22121 2\u2206\u03c0 \u2192\u03c0 + 1 2\u2206\u03c0). The cross-correlation function (CCF) is similarly computed: 1 2\u2206rp \u2192rp + 1 2 uted: 1 2\u2206rp, \u03c0 \u22121 2 1 2\u2206\u03c0 \u2192\u03c0 + 1 2 (rp \u22121 2\u2206rp \u2192rp + 1 2\u2206rp, \u03c0 \u22121 2\u2206\u03c0 \u2192\u03c0 + 1 2\u2206\u03c0). The cross-correlation function (CCF) is similarly computed:  DD \u03be(rp, \u03c0) = D1D2 RR D1D2 R1R2 \u22121, (2) where D1 and D2 correspond to galaxies and quasars. R1 and R2 correspond to randomly distributed galaxies and quasars that are computed analytically. The projected 2-point correlation function wp(rp) is: (Davis & Peebles 1983) wp(rp) = 2 \ufffd\u221e 0 \u221e 0 d\u03c0 \u03bes(rp, \u03c0) . (3) In practice, the integration is up to \u03c0max. We use \u03c0max = (100, 80, 70)h\u22121Mpc comoving at z = (3.2, 1.4, 0.5), respectively, as in observations. 3. A New Model for QSO-Hosting Dark Matter Halos at z = 0.5 \u22123.2 Our physical modeling is motivated by insights on cosmic gas evolution from cosmological hydrodynamic simulations and observations. Simulations show four significant trends. First, cosmological structures collapse to form sheet, filaments and halos, and shock heat the gas to progressively higher temperatures with decreasing redshift (e.g., Cen & Ostriker 1999). Second, overdense regions where larger halos are preferentially located begin to be heated earlier and have higher temperatures than lower density regions at any given time, causing specific star formation rates of larger galaxies \u2013 3 \u2013 10-2 10-1 100 101 102 rp [h\u22121 Mpc] 10-1 100 101 102 103 104 105 wp (rp )[h\u22121 Mpc] z=3.2 ACF mh,0 =2e12,DR0 =1 ACF mh,0 =2e12,DR0 =3 ACF mh,0 =5e12,DR0 =3 ACF Mth =1e13 obs: Shen+07 QSO ACF Fig. 1.\u2014 shows the ACF of quasar hosts at z = 3.2 for two cases of mh,0 = (2\u00d71012, 5\u00d71012) M\u2299with DR0 = 3 shown as (open red squares, solid yellow hexagons), respectively. For mh,0 = 2 \u00d7 1012 M\u2299 one additional case is shown for DR0 = 1 (solid green diamonds). For comparison, a plain threshold mass case with Mth = 1013 M\u2299is shown as open blue circles. Poisson errorbars are only plotted for blue circles. Black triangles is the observed ACF (Shen et al. 2007a), using 4426 spectroscopically identi\ufb01ed quasars at 2.9 < z < 5.4 (median \u00af z = 3.2), from the SDSS DR5 (Schneider et al. 2005; Adelman-McCarthy et al. 2006). to fall below the general dimming trend at higher redshift than less massive galaxies and galaxies with high sSFR to gradually shift to lower density environments at lower redshift. This physical process of di\ufb00erential gravitational heating with respect to redshift is able to explain the apparent cosmic downsizing phenomenon (e.g., Cowie et al. 1996), the cosmic star formation history (e.g., Hopkins & Beacom 2006), and galaxy color migration (Cen 2011, 2014). Third, quasars appear to occur in congested environments, as evidenced by high bias inferred based on their strong clustering, with the apparent merger fraction of bright QSOs (L > 1046erg/s) approaching unity (e.g., Hickox et al. 2014). Finally, a quasar host galaxy presumably channels a signi\ufb01cant amount of gas into its central black hole, which we interpret as the galaxy being rich in cold gas. This requirement would exclude satellite halos of high mass halos at lower redshift when the latter become hot gas dominated (e.g., Feldmann et al. 2011; Cen 2014). These physical considerations provide the basis for the construction of the new model detailed below in steps. First, for z > 1. (1) All central and satellites halos with virial mass > mh,0 constitute the baseline sample, denoted as SA. (2) Each halo in SA is then selected with the following probability, PDF(DR), computed as follows. For a halo X of mass mh, we make a neighbor list of all neighbor halos with mass \u2265mh/2. For each neighbor halo on the neighbor list, we compute DRn = dn/rv,n, where dn is the distance from X to, and rv is the virial radius of, the neighbor in question. We then \ufb01nd the minimum of all DRn\u2019s, \u2013 4 \u2013 10-2 10-1 100 101 102 rp [h\u22121 Mpc] 10-1 100 101 102 103 104 wp (rp )[h\u22121 Mpc] z=1.4 ACF Mth =6e12 ACF mh,0 =2e11,DR0 =1 ACF mh,0 =2e11,DR0 =0.5 ACF mh,0 =5e11,DR0 =0.5 obs: Richardson+12 QSO ACF Fig. 2.\u2014 shows ACF of quasar hosts at z = 1.4 for three cases: (mh,0, DR0) = (2 \u00d7 1011 M\u2299, 0.5) (open blue squares), (5 \u00d7 1011 M\u2299, 0.5) (open red diamonds) and (2 \u00d7 1011 M\u2299, 1.0) (solid green hexagons). For comparison, a plain threshold mass case with Mth = 6 \u00d7 1012 M\u2299is shown as solid yellow circles. Poisson errorbars are only plotted for red diamonds. Black triangles are the observed ACF quasars (Richardson et al. 2012), using a sample of 47,699 quasars with a median redshift of \u00af z = 1.4, drawn from the DR7 spectroscopic quasar catalog (Schneider et al. 2010; Shen et al. 2011) for large scales and 386 quasars for small scales (< 1 Mpc/h) from (Hennawi et al. 2006). calling it DR for halo X. PDF(DR) is de\ufb01ned as PDF(DR) = 1 for DR < DR0; PDF(DR) = (DR0/DR)3 for DR \u2265DR0. (4) Our choice of the speci\ufb01c PDF is somewhat arbitrary but serves to re\ufb02ect our assertion that the probability of dark matter halos hosting quasars decreases if the degree of interactions decreases, when DR > DR0. The results remain little changed, for example, had we used a steeper powerlaw of 4 instead of 3. At z < 1, when the mean SFR in the universe starts a steep drop (Hopkins & Beacom 2006), we impose an additional criterion (3) to account for the gravitational heating. (3) Those halos that are within the virial radius of massive halos > Mh,0 are removed, for z < 1. In essence, we model the quasar hosts at z > 1 with two parameters, mh,0 and DR0 and at z < 1 with three parameters, mh,0, DR0 and Mh,0. We present results in the order of decreasing redshift. Figure 1 shows ACF of quasar hosts at z = 3.2 for three cases: (mh,0, DR0) = (2 \u00d7 1012 M\u2299, 3), (5 \u00d7 1012 M\u2299, 3) and (2 \u00d7 1012 M\u2299, 1). Based on halo occupation distribution (HOD) modeling, Richardson et al. (2012) infer median mass of quasar host halos at z \u223c3.2 of Mcen = 14.1+5.8 \u22126.9 \u00d7 1012 h\u22121 M\u2299, consistent with the threshold mass case with Mth = 1013 M\u2299. All model ACFs fall below the observed data at rp \u226530Mpc/h, due to simulation box size. The ACF amplitude is seen to increase with increasing mh,0. The ACF with a smaller value of DR0 steepens at a smaller rp and rises further toward lower rp. This \u2013 5 \u2013 behavior is understandable, since a lower DR0 overweighs pairs at smaller separations. The extant observations do not allow useful constraints on DR0 at z = 3.2. We see from visual examination that mh,0 = (2\u22125)\u00d71012 M\u2299provides an excellent \ufb01t to the observed ACF for rp = 2 \u221230h\u22121Mpc. Figure 2 shows ACF of quasar hosts at z = 1.4 for three cases: (mh,0, DR0) = (2 \u00d7 1011 M\u2299, 0.5), (5 \u00d7 1011 M\u2299, 0.5) and (2 \u00d7 1011 M\u2299, 1.0). The threshold mass case with Mth = 6 \u00d7 1012 M\u2299provides a good match to the observational data for rp = 1 \u221230h\u22121Mpc, consistent with HOD modeling by Richardson et al. (2012), who constrain the median mass of the central host halos to be Mcen = 4.1+0.3 \u22120.4 \u00d7 1012 h\u22121 M\u2299. We see that mh,0 = (2 \u22125) \u00d7 1011 M\u2299provides excellent \ufb01ts to the observed ACF for rp = 1 \u221240h\u22121Mpc. The observed ACF extends down to about 20h\u22121kpc, which allows us to constrain DR0. We see that, varying DR0 from 1.0 to 0.5, the amplitude of the ACF at rp \u22641h\u22121Mpc increases, with DR0 = 0.5 providing a good match. The physical implication is that quasar activities at z = 1.4 seem to be triggered when a halo of mass \u2265(2 \u22125) \u00d7 1011 M\u2299interact signi\ufb01cantly with another halo of comparable mass, in contrast to the z = 3.2 quasars that are primarily hosted by central galaxies with no major companions. 10-1 100 101 rp [h\u22121 Mpc] 100 101 102 103 wp (rp )[h\u22121 Mpc] z=0.51 CCF Mth =3.5e12 ACF Mth =1e13/h obs: Shen+13 CMASS ACF obs: Shen+13 QSO-CMASS CCF 10-1 100 101 rp [h\u22121 Mpc] 100 101 102 103 wp (rp )[h\u22121 Mpc] z=0.51 CCF mh,e =2e11,Mh,0 =2e13,DR0 =0.5 CCF mh,0 =2e11,Mh,0 =2e13,DR0 =1 CCF mh,0 =5e10,Mh,0 =2e13,DR0 =1 CCF mh,0 =2e11,Mh,0 =1e13,DR0 =1 obs: Shen+13 QSO-CMASS CCF Fig. 3.\u2014 Left panel shows the ACF of halos of masses above Mth = 1 \u00d7 1013h\u22121 M\u2299(open yellow squares), \u201cmock CMASS galaxies\u201d, and the CCF between halos of mass above 3.5 \u00d7 1012 M\u2299 and CMASS galaxies (open red pentagons). Black solid dots and triangles are the observed quasar-CMASS galaxy CCF and CMASS galaxy ACF (shown in both left and right panels), respectively, at z \u223c0.53 from Shen et al. (2013). The CMASS sample of 349,608 galaxies at z \u223c0.53 (White et al. 2011; Anderson et al. 2012) is from the Baryon Oscillation Spectroscopic Survey (Schlegel et al. 2009; Dawson et al. 2013). The sample of 8198 quasars at 0.3 < z < 0.9 (\u27e8z\u27e9\u223c0.53) is from the DR7 (Abazajian et al. 2009) spectroscopic quasar sample from SDSS I/II (Schneider et al. 2010). Right panel shows the model quasar-CMASS galaxy CCF at z = 0.51 for four cases with (mh,0, Mh,0, DR0) = (2 \u00d7 1011 M\u2299, 2 \u00d7 1013 M\u2299, 0.5) (solid red diamonds), (2 \u00d7 1011 M\u2299, 2 \u00d7 1013 M\u2299, 1.0) (solid green hexagons), (5 \u00d7 1010 M\u2299, 2 \u00d7 1013 M\u2299, 1.0) (open blue squares) and (2 \u00d7 1011 M\u2299, 1 \u00d7 1013 M\u2299, 1.0) (open yellow stars). Finally, Figure 3 shows results at z = 0.51. The left panel shows the ACF of halos of \u2013 6 \u2013 masses above the threshold 1013h\u22121 M\u2299mock CMASS galaxies which provides a good match to the observed ACF of CMASS galaxies. Consistent with previous analysis, we see that the CCF between halos of mass above the threshold 3.5 \u00d7 1012 M\u2299and mock CMASS galaxies match the observed counterpart. The right panel of Figure 3 shows the mock quasar-CMASS galaxy CCF at z = 0.51 for four cases with di\ufb00erent combinations of (mh,0, Mh,0, DR0). The case with (mh,0, Mh,0, DR0) = [(1 \u22123) \u00d7 1011 M\u2299, 2 \u00d7 1013 M\u2299, 0.5] provides an adequate match to the observation, while (mh,0, Mh,0, DR0) = (5 \u00d7 1010 M\u2299, 2 \u00d7 1013 M\u2299, 1.0) appears to underestimate the CCF. The case with (2 \u00d7 1011 M\u2299, 1 \u00d7 1013 M\u2299, 1.0) signi\ufb01cantly underestimates the observed ACF at rp < 0.5h\u22121Mpc. This indicates that halos of masses greater than mh,0 = (1 \u22123) \u00d7 1011 M\u2299 residing in environment of groups of masses (1 \u22122) \u00d7 1013 M\u2299are primarily responsible for the strong clustering at rp < 0.5h\u22121Mpc. It is interesting to note that the exclusion halo mass of Mh,0 = 2.0 \u00d7 1013 M\u2299, to account for environment heating e\ufb00ects, is physically self-consistent with the fact that the red CMASS galaxies are red due to the same environment e\ufb00ects hence have about the same halo mass (Mth = 1013h\u22121 M\u2299). 4. Predictions and Tests of our Model 10.0 10.5 11.0 11.5 12.0 12.5 13.0 13.5 14.0 14.5 log[Mh /(M \u2299)] 0 1 2 3 4 5 dp/dlogM our model range, z=3.2 Richardson+12, z=3.2 our model range, z=1.4 Richardson+12, z=1.4 our model range, z=0.53 Shen+13, z=0.53 Fig. 4.\u2014 shows the QSO-hosting halo mass distributions at z = 3.2 (solid red curves), z = 1.4 (solid blue curves) and z = 0.53 (solid green curves). We show two bracketing (approximately \u00b11\u03c3 for the computed correlation functions) models at each redshift. The corresponding distributions based on HOD modeling are shown in dashed curves. The short vertical bars with matching colors and line types indicate the median halo masses of their respective distributions. We have demonstrated that our physically based model can account for the observed clustering of quasars at z = 3.2, 1.4, 0.53. Figure 4 contrasts the sharp di\ufb00erences between our model and the conventional HOD based modeling; the halo masses in our model are an order of magnitude lower than those inferred from HOD modeling. Our model gives quasar-hosting halo mass threshold of \u2013 7 \u2013 [(2 \u22125) \u00d7 1012, (2 \u22125) \u00d7 1011, (1 \u22123) \u00d7 1011)] M\u2299at z = (3.2, 1.4, 0.53), respectively. compared to median mass of (14.1+5.8 \u22126.9\u00d71012, 4.1+0.3 \u22120.4\u00d71012, 4.0\u00d71012)h\u22121 M\u2299based on HOD modeling (Richardson et al. 2012; Shen et al. 2013). Although we have not made \ufb01tting for quasars at redshift higher than z = 3.2, we anticipate that the quasars at higher redshifts that have comparable luminosities as those at z = 3.2 will primarily be hosted by central galaxies of mass \u223c(2 \u22125) \u00d7 1012 M\u2299. We note that the median luminosity of the observed quasars decreases from \u223c1046erg/s at z \u22651.4 to \u223c1045erg/s at z = 0.53, which re\ufb02ects the known downsizing scenario and is in accord with the decreasing halo mass with decreasing redshift inferred in our model. Our results and detailed comparions with HOD based modeling are also tabulated in Table 1, along with inferred quasar duty cycles and lifetimes. Can we di\ufb00erentiate between these two models? Trainor & Steidel (2012) cross correlate 1558 galaxies with spectroscopic redshifts with 15 of the most luminous (\u22651014 L\u2299, M1450 \u223c\u221230) quasars at z \u223c2.7. Even for these hyperluminous quasars (HLQSOs), they infer host halo mass of log(Mh/ M\u2299) = 12.3 \u00b1 0.5, which is in very good agreement with our model (Mh \u223c(2\u22125)\u00d71012 M\u2299) but much smaller than inferred from HOD modeling. They also \ufb01nd that, on average, the HLQSOs lie within signi\ufb01cant galaxy over-densities, characterized by a velocity dispersion \u03c3v \u223c200 km/s and a transverse angular scale of \u223c25\u201d (\u223c200 physical kpc), which they argue correspond to small groups with log(Mh/ M\u2299) \u223c13. The rare HLQSOs are apparently not hosted by rare dark matter halos. This is fully consistent with our suggestion that dark matter halo mass is not the sole determining factor of quasar luminosities and that interactions may be instrumental to triggering quasar activities. Another, independent method to infer halo masses of quasar hosts is to measure their cold gas content. Prochaska et al. (2013) detect about 60% \u221270% covering fraction of Lyman limit systems within the virial radius of z \u223c2 quasars, using the binary quasar sample (Hennawi et al. 2006). This has created signi\ufb01cant tension: hydrodynamic simulations of the cold dark matter model yield less than 20% covering fraction for halos of mass \u223c3\u00d71012 M\u2299(Faucher-Giguere et al. 2014); halos of still higher mass have still lower covering fractions. On the other hand, the simulations show a \u223c60% covering fraction if the mass of quasar-hosting halos is \u223c3 \u00d7 1011 M\u2299. This indicates that the lower halo masses for quasar hosts in our model can explain the high content of neutral gas in z \u223c2 quasars. The mean quasar lifetime may be estimated by equating it to tH \u00d7 fq, where tH is the Hubble time at the redshift in question and fq the duty cycle of quasar hosting halos. Existing observational constraints provide useful range for tq for quasars at z \u223c3. Lifetimes based on halo abundances from clustering analyses of quasars have been given by many authors (e.g., Martini & Weinberg 2001; Porciani et al. 2004; Shen et al. 2007b); in our case, this is a degenerate derivation. Thus, it is useful to have a survey of quasar lifetimes based on other, independent methods. Jakobsen et al. (2003) derive tq > 10Myr, Worseck et al. (2007) give tq > 25Myr, Gon\u00b8 calves et al. (2008) yield tq = 16 \u221233Myr, and McQuinn & Worseck (2014) yield tq => 10Myr for quasars at z \u22482 \u22123, all based on the method of quasar proximity e\ufb00ect. Bolton et al. (2012) obtain tq > 3Myr using line-of-sight thermal proximity e\ufb00ect. Trainor & Steidel (2013), using a novel method of Ly\u03b1 emitters (LAEs) exhibiting \ufb02uorescent emission via the reprocessing of ionizing radiation from \u2013 8 \u2013 nearby hyperluminous QSOs, \ufb01nd 1 \u2264tq \u226420Myr at z = 2.5 \u22122.9. We see that all these estimates are consistent with our model. As a comparison, the inferred tHOD q \u223c400Myr at z = 3.2 from HOD modeling. Finally, self-consistently reproducing the quasar luminosity functions (e.g., Wyithe & Loeb 2002, 2003; Shen 2009; Conroy & White 2013) will provide another test, which we defer to a separate study. Table 1: Comparing Our Model With HOD Modeling w.r.t. Halo Mass and Quasar Lifetime (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) zmed Lbol nobs nsim mh,0 fq tq MHOD h fHOD q tHOD q log(erg s ) \u00d710\u22127 \u00d710\u22124 \u00d71012 \u00d710\u22123 [Myr] \u00d71012 \u00d710\u22123 [Myr] 3.2 46.3 2.5 0.2 \u22120.9 2 \u22125 3 \u221213 5-26 20 215 425 1.4 46.1 30 9 \u221244 0.2 \u22120.5 0.6 \u22123 3-15 5.8 1.8 7.5 0.53 45.1 50 29 \u221285 0.1 \u22120.3 0.6 \u22122 5-15 5.7 1.3 10 Column (1) zmed is the median redshift of the sample that is analyzed. Column (2) Lbol is the median bolometric luminosity of the observed quasar sample obtained using conversions in (Richards et al. 2006; Runnoe et al. 2012). Column (3) nobs is the number density of the observed quasar sample (Shen & Kelly 2012) in [Mpc3h\u22123], multiplied by a factor of 2.5 to account for the fact that about 60% of quasars belong to the so-called type II quasars based on low redshift observations (Zakamska et al. 2003), which are missed in the quoted observational sample. We note that the percentage of obscured quasars appear to increase with redshift (e.g., Ballantyne et al. 2006; Treister & Urry 2006). Thus, the values of tq may be underestimated. Column (4) mh,0 is the lower mass threshold dark matter halos hosting quasars in [M\u2299]. Column (5) nsim is the number density of the dark matter halos hosting quasars with mass \u2265mh,0 in [Mpc\u22123h3]. Column (6) fq \u2261nobs/nsim is the duty cycle of the quasars in our model. Column (7) tq is the mean quasar lifetime in our model de\ufb01ned as tH \u00d7 fq, where tH is the Hubble time at the redshift in question. Column (8) MHOD h,med is the derived host halo mass of the observed population of quasars derived from HOD modeling (Richardson et al. 2012; Shen et al. 2013) in [M\u2299]. Column (9) fHOD q is the duty cycle of the observed population of quasars based on HOD modeling, using the type II quasars-corrected abundance in Column (3). Column (10) tHOD q is the life time of the quasars based on fHOD q in Column (9). 5. Conclusions We put forth new model for dark matter halos that host quasars. Our model is substantially di\ufb00erent from previous models based on simple lower mass threshold or HOD based lower mass threshold. Instead, we impose two conditions that are physically based. First condition is that signi\ufb01cant interactions with other halos are a necessary ingredient to trigger quasar activities. \u2013 9 \u2013 Second, satellite halos within the virial radius of large halos above certain mass at low redshift are removed from consideration, since they are hot gas dominated. We investigate this model utilizing halo catalogs from the Millennium Simulation. By requiring simultaneously that halos meet these two conditions and match two-point auto-correlation functions of quasars and cross-correlation functions between quasars and galaxies, we are able to identify quasar hosting halos. The resulting host halos are distinctly di\ufb00erent from other models. Quasar hosts are less massive, by an order of magnitude, than inferred based on either simple halo mass threshold or HOD models. The lower halo mass threshold of quasar hosts are predicted to be [(2\u22125)\u00d71012, (2\u22125)\u00d71011, (1\u22123)\u00d71011] M\u2299 at z = (3.2, 1.4, 0.53), respectively, compared to median mass of (14.1+5.8 \u22126.9 \u00d71012, 4.1+0.3 \u22120.4 \u00d71012, 4.0\u00d7 1012)h\u22121 M\u2299based on HOD modeling. It is noted that, for either central or satellite halos, imposing the condition of signi\ufb01cant interactions substantially boosts the clustering strength compared to the total population with the same mass cut, which is the reason why our lower mass halos can equally well match observed clustering of quasars. At z \u22652 the quasar hosts are primarily central galaxies and major interactions at close separations do not appear to be necessary, whereas at z < 2 the quasar hosts mostly are satellite galaxies which experience major interactions to trigger the quasar activities. Below z = 1 satellite galaxies in groups of mass \u22652 \u00d7 1013 M\u2299do not host quasars due to lack of cold gas. The mean quasar lifetime is, nearly invariably, expected to be in the range of 3 \u221230Myr for the redshift range examined z = 0.5 \u22123.2, which is in good agreement with observations. A unique and discriminatory property is that, unlike other previous models, the quasar hosting galaxies in this model are expected to be cold gas rich and have much higher covering fractions for Lyman limit systems, better in line with observed 60 \u221270% covering fraction within the virial radius of z \u223c2 quasars. We are grateful to Dr. Zheng Zheng for allowing us to his program to ACF and CCF, to Dr. Jonathan Richardson and Dr. Yue Shen for sending us the observed ACF and CCF at z = 1.4 and z = 3.2, and at z = 0.53, respectively. We also would like to thank Dr. Zheng for useful discussion. This work is supported in part by grant NASA NNX11AI23G. The Millennium simulation data bases used in this paper and the web application providing online access to them were constructed as part of the activities of the German Astrophysical Virtual Observatory.",
                    "introduction": "Masses of dark matter halos hosting quasars are not directly measured. They are inferred by indirect methods, such as via their clustering properties (i.e., auto-correlation function, ACF, or cross-correlation function, CCF). Using ACF or CCF can yield solutions on the (lower) threshold halo masses. The solution on halo mass based on such a method is not unique, to be illustrated by a simple example. Let us suppose a sample composed of halos of large mass M and an equal number of small halos of mass m, coming in tight pairs of M and m with a separation much small than the scale for the correlation function of interest. For such a sample, the ACF of halos of mass M is essentially identical to that of m or cross correlation between M and m. Although dark matter halos in the standard hierarchical cold dark matter model are less simple, the feature that small 1Princeton University Observatory, Princeton, NJ 08544; cen@astro.princeton.edu 2Johns Hopkins University, Department of Physics and Astronomy, Baltimore, MD 21218, USA arXiv:1412.4075v1  [astro-ph.CO]  12 Dec 2014 \u2013 2 \u2013 mass halos tend to cluster around massive halos is generic. This example suggests that alternative solutions of dark matter halos hosting quasars exist. It would then be of interest to \ufb01nd models that are based on our understanding of the thermal dynamic evolution of gas in halos and other physical considerations, which is the purpose of this Letter."
                },
                {
                    "url": "http://arxiv.org/abs/1409.6755v1",
                    "title": "Diverse Properties of Interstellar Medium Embedding Gamma-Ray Bursts at the Epoch of Reionization",
                    "abstract": "Analysis is performed on ultra-high resolution large-scale cosmological\nradiation-hydrodynamic simulations to, for the first time, quantify the\nphysical environment of long-duration gamma-ray bursts (GRBs) at the epoch of\nreionization. We find that, on parsec scales, 13% of GRBs remain in high\ndensity ($\\ge 10^4$cm$^{-3}$) low-temperature star-forming regions, whereas 87%\nof GRBs occur in low-density ($\\sim 10^{-2.5}$cm$^{-3}$) high temperature\nregions heated by supernovae. More importantly, the spectral properties of GRB\nafterglows, such as the neutral hydrogen column density, total hydrogen column\ndensity, dust column density, gas temperature and metallicity of intervening\nabsorbers, vary strongly from sightline to sightline. Although our model\nexplains extant limited observationally inferred values with respect to\ncircumburst density, metallicity, column density and dust properties, a\nsubstantially larger sample of high-z GRB afterglows would be required to\nfacilitate a statistically solid test of the model. Our findings indicate that\nany attempt to infer the physical properties (such as metallicity) of the\ninterstellar medium of the host galaxy based on a very small number of (usually\none) sightlines would be precarious. Utilizing high-z GRBs to probe\ninterstellar medium and intergalactic medium should be undertaken properly\ntaking into consideration the physical diversities of the interstellar medium.",
                    "authors": "Renyue Cen, Taysun Kimm",
                    "published": "2014-09-23",
                    "updated": "2014-09-23",
                    "primary_cat": "astro-ph.HE",
                    "cats": [
                        "astro-ph.HE"
                    ],
                    "main_content": "The simulations are performed using the Eulerian adaptive mesh refinement code, ramses (Teyssier 2002, ver. 3.07), with concurrent multi-group radiative transfer (RT) calculation (Rosdahl et al. 2013). The reader is referred to Kimm & Cen (2014) for details. Notably, a new treatment of supernova feedback is implemented, which is shown to capture the Sedov solution for all phases (from early free expansion to late snowplow). The initial condition for the cosmological simulations is generated using the MUSIC software (Hahn & Abel 2011), with the WMAP7 parameters (Komatsu et al. 2011): (\u2126m, \u2126\u039b, \u2126b, h, \u03c38, ns = 0.272, 0.728, 0.045, 0.702, 0.82, 0.96). The total simulated volume of (25Mpc/h)3 (comoving) is covered with 2563 root grids, and 3 more levels are added to a rectangular region of 3.8 \u00d7 4.8 \u00d7 9.6 Mpc to achieve a high dark matter mass resolution of mdm = 1.6 \u00d7 105 M\u2299. In the zoomed-in region, cells are further refined (12 more levels) based on the density and mass enclosed within a cell. The corresponding maximum spatial resolution of the simulation is 4.2 pc (physical). The simulation is found to be consistent with a variety of observations, including the luminosity function at z \u223c7. Normal and runaway star particles are created in convergent flows with a local hydrogen number density nth \u2265100 cm\u22123 (FRU run, Kimm & Cen 2014), based on the Schmidt law (Schmidt 1959). Note that the threshold is motivated by the density of a Larson-Penston profile (Larson 1969; Penston 1969) at 0.5\u2206xmin, \u03c1LP \u22488.86c2 s/\u03c0 G \u2206x2 min, where cs is the sound speed at the typical temperature of the ISM (\u223c30K) and \u2206xmin is the finest cell resolution. Additionally, we ensure that the gas is Jeans unstable, and that the cooling time is shorter than the dynamical time (e.g. Cen & Ostriker 1992). We assume that 2% of the star-forming gas is converted into stars per its free-fall time (tff) (Krumholz & Tan 2007). The mass of each star particle is determined as m\u22c6= \u03b1 Np\u03c1th \u2206x3 min, where \u03c1th is the threshold density, and \u03b1 is a parameter that controls the minimum mass of a star particle (m\u22c6,min). Np is an integer multiple of m\u22c6,min to be formed in a cell, which is drawn from a Poisson random distribution, P(Np) = (\u03bbNp/Np!) exp (\u2212\u03bb) with the Poissonian mean \u03bb \u2261\u03f5 \ufffd \u03c1\u2206x3 \ufffd\ufffd \u2206tsim \ufffd , where \u2206t is the simulation time step. The resulting cell, which is drawn from a Po Poissonian mean \u03bb \u2261\u03f5\u22c6 \ufffd \u03c1\u2206x3 m\u22c6,min minimum mass of a normal (ru m\u22c6,min isson ra \ufffd\ufffd \u2206tsim tff naway) tf cell, which is drawn from a Poisson random distribution, P(Np) = (\u03bbNp/Np!) exp (\u2212\u03bb) with the Poissonian mean \u03bb \u2261\u03f5\u22c6 \ufffd \u03c1\u2206x3 m\u22c6,min \ufffd\ufffd \u2206tsim tff \ufffd , where \u2206tsim is the simulation time step. The resulting minimum mass of a normal (runaway) star particle is 34.2 M\u2299(14.6 M\u2299). We adopt the Chabrier initial mass function to compute the mean frequency of Type II supernova explosions per solar mass (0.02M \u22121 \u2299). Dark matter halos are identified using the Amiga halo finder (Knollmann & Knebe 2009). This yields 731 halos of mass 108 \u2264Mvir < 3 \u00d7 1010 M\u2299at z = 7. We adopt the assumption that long-duration GRB rate is proportional to type II supernova rate; short-duration GRBs are not addressed here since they appear not to be associated with massive stars and are hosted by elliptical galaxies (Berger 2013). For our analysis we use all snapshots between z = 7.5 and z = 7. 3. Results We present results from our simulations and make comparisons to available observations. As will be clear later, we generally find broad agreement between our model and observations, although larger observational samples of GRB afterglows would be needed to fully test the model. \u2013 3 \u2013 3.1. Properties of Embedding Interstellar Medium on Parsec Scales We \ufb01rst describe the physical conditions of the ISM that embeds GRBs on pc scales. The left (right) panel of Figure 1 shows the distribution of GRB rate in the density-temperature (densitymetallicity) parameter space. We see two separate concentrations of GRBs in the n \u2212T plane, with (nH, T) equal to (10\u22122.5cm\u22123, 107.5K) and (104.0cm\u22123, 103.8K), respectively. It must be made clear that the density and temperature are de\ufb01ned on the local gas cell of scale of a few pc that a GRB sits. The appearance of GRB afterglow spectra depends, in most case, more strongly on the properties of gas along the line of sight rather than the gas immediately embedding them, as will be shown later. It is seen that most of the GRBs reside in the low density, high temperature peak, contributing to 87% of GRBs. It is easy to identify two corresponding concentrations in the Z \u2212n plane in the right panel: the low density, high temperature peak corresponds the high metallicity peak in the range [\u22121.5, 0.5] in solar units, while the high density, low temperature peak corresponds the low metallicity peak in the range [\u22122, \u22121]. We note that super solar metallicities in hot winds driven by type II supernova explosions in starburst galaxies in conditions similar to those of our simulated galaxies are locally observed. For example, Konami et al. (2011) observe metallicity of hot X-ray gas of 2 \u22123 times the solar value in M82. Martin et al. (2002) \ufb01nd that the best \ufb01t model for the hot X-ray gas metallicity in dwarf starburst galaxy NGC 1569 is solar, although a metallicity as high as 5 times solar still gives \u03c72 value only about 0.1% larger than the best \ufb01t model; on the contrary, the model with 0.25 times solar has much worse \u03c72 value. The extant observations of GRB afterglow spectra do not have the capability to detect the metallicity of the X-ray absorbing medium of relatively low column density. Metallicities of lower temperature gas phases are observed and are predicted to be substantially sub solar, as will be shown in Figure 3 later. The (nH, T) = (104.0cm\u22123, 103.8K) peak coincides with the cores of dense gas clouds in the simulation, where star formation is centered. The temperature of 103.8K is mostly produced by atomic hydrogen cooling and the lower temperature extension due to metal cooling included in the simulation. As a numerical example, for a gas parcel of density 104cm\u22123, temperature of 104K and metallicity of 1% of solar value, the cooling time is about 400 yrs, which is much shorter than relevant dynamic time scales. It is thus clear that the cold density phase seen our simulation is easily understandable. However, due to lack of treatment for molecular hydrogen cooling, gas is unable to cool signi\ufb01cantly below \u223c104K. Had we included molecular hydrogen cooling and low temperature metal cooling, we expect the gas to cool approximately isobarically to about 20K. Thus, we prefer not to infer any observable properties of GRBs that would depend strongly on the nature of this cold gas phase, such as molecular clouds. It is more appropriate to treat (nH, T) = (104.0cm\u22123, 103.8K) as bounds: (nH, T) = (> 104.0cm\u22123, < 103.8K). This is also why we present our results for the highdensity low-temperature regions as bounds in the abstract and conclusions sections as well as places where clari\ufb01cation is helpful. The noticeable sub-dominance of GRBs residing in very high density (n \u223c104cm\u22123), star-forming regions suggests that a large number of stars are displaced from their birth clouds. This may be achieved by a substantial relative motions between stars and their birth clouds due to hydrodynamic interactions of the later or dynamical e\ufb00ects of stars. As a numerical illustration for the former possibility, a relative motion of 10 km/s between the birth cloud and the \u2013 4 \u2013 -6 -4 -2 0 2 4 6 log nH [cm-3] 0 2 4 6 8 10 log T [K] log NHI>19 log NHI<19 50% 90% 99% -6 -4 -2 0 2 4 6 log nH [cm-3] -3 -2 -1 0 1 log Z [ZO  \u2022 ] log NHI>19 log NHI<19 50% 90% 99% Fig. 1.\u2014 Left panel: shows the distribution of GRB rate in the density-temperature (n \u2212T) parameter space. Note that the density and temperature are de\ufb01ned on the local gas cell of scale of a few pc that a GRB sits in and it will be made clear later that the appearance of GRB afterglows is in most cases more dependent on the properties of gas along the line of sight. We have further divided the GRBs into two groups with respect to intervening neutral hydrogen column density: NHI > 1019cm\u22122 (red) and NHI < 1019cm\u22122 (blue), details of which will be given in subsequent \ufb01gures. The contour levels speci\ufb01ed indicate the fraction of GRBs enclosed. Right panel: shows the distribution of GRB rate in the density-metallicity (n \u2212Z) parameter space. star would yield a displacement of 100pc in a lifetime of 10Myr. We note that the runaway OB stars in our simulation have typical velocities relative to the birth clouds of 20 \u221240 km/s. Thus the runaway OB stars have contributed signi\ufb01cantly to the displacing GRBs from their birth clouds. The GRBs being in hot low density environment is also a result of supernova heating by earlier supernovae exploding in the birth clouds. We estimate that these two e\ufb00ects are responsible about equally for placing most of the GRBs in low-density high temperature regions. While it is not possible to locate GRBs within the host galaxies at high redshift at this time, observations of low redshift GRBs may still be instructive. Le Floc\u2019h et al. (2012) show that GRB 980425 occurring in a nearby (z = 0.0085) SBc-type dwarf galaxy appears to be displaced from the nearest H II region by 0.9kpc, which is in fact signi\ufb01cantly larger than the displacement distances for the vast majority of our simulated GRBs in high redshift galaxies. Interestingly, the optical afterglow luminosity has a bimodal distribution at 12 hours after trigger (Nardini et al. 2008). The bimodal distribution of volumetric density seen in the left panel of Figure 1 alone should produce a bimodal distribution of the afterglows with respect to break frequencies, luminosities, and break times, etc (e.g., Sari et al. 1998). We cannot make detailed comparisons, because the circumburst density of the high nH GRB subset is underestimated due to our limited resolution and because it remains uncertain if the appearance of GRB afterglows \u2013 5 \u2013 would also depend strongly on intervening material (dust obscuration, etc). It is suggestive that the complex situations seen in simulations may account for the observed bimodality of afterglows without having to invoke intrinsic bimodality of GRBs. 3.2. Strong Variations of Intervening Gas and Dust along Di\ufb00erent Sightlines One of the most important points that this paper hopes to highlight and convey is that the appearances of the afterglows of GRBs are not solely determined by the circumburst medium in their immediate vicinity (e.g., the physical conditions shown in Figure 1 are on pc scales centered on GRBs). They also strongly depend on the line of sight beyond the immediate circumburst medium through the ISM in the host galaxy, which we now quantify. Let us \ufb01rst give the meaning for our chosen value of the intervening neutral hydrogen column density NHI = 1019cm\u22122, which is used in Figure 1 to separate GRBs into separate groups. Figure 2 shows the distribution of neutral hydrogen column density integrated along the line of sight for all GRBs, separately for halos in \ufb01ve mass ranges. A bimodal distribution of NHI is seen, peaked at NHI \u223c1021\u221222cm\u22122 and NHI \u223c1016\u221217cm\u22122, respectively, well separated by NHI \u223c1019cm\u22122. It is clear that the bimodality exists for all halo masses surveyed. The low NHI peak is rather broad, extending all the way to NHI = 1011cm\u22122, suggesting some locations of GRBs well into the di\ufb00used hot ISM. There is a noticeable dip in the neutral hydrogen column density distribution at \u223c1014cm\u22122 for the most massive galaxies of \u22651010 M\u2299. We attribute this to more signi\ufb01cant shock heating in the most massive halos. Returning to Figure 1, it is now easy to see that the GRBs in the low NHI (\u22641019cm\u22122) peak in Figure 2 is composed of only one set of GRBs situated in low density environment around (10\u22122.5cm\u22123, 107.5K), seen as the red contours in Figure 1. The high NHI (\u22651019cm\u22122) peak in Figure 2, on the other hand, consists of a combination of two separate populations with distinctly di\ufb00erent circumburst medium, which correspond to two separate loci of the blue contours at (10\u22122.5cm\u22123, 107.5K) and (104.0cm\u22123, 103.8K) in Figure 1. The apparently two di\ufb00erent groups of GRBs situated around (nH, T) = (10\u22122.5cm\u22123, 107.5K) one with low NHI\u22641019cm\u22122 (red) and the other with low NHI\u22651019cm\u22122 (blue) are due entirely to the line of sight through the ISM of the host galaxy. Overall, we \ufb01nd that 38% of GRBs have NHI\u22641017cm\u22122 (i.e., optically thin to Lyman continuum), whereas 44% have NHI\u22651020.3cm\u22122 (i.e, containing a damped Lyman-alpha system). It is clear that various properties of the afterglows of GRBs, even sitting in the same very local environment on pc scales, may appear di\ufb00erent due to di\ufb00erent intervening interstellar gas and dust along the line of sight through the host galaxy. In summary so far, there are three separate populations of GRB afterglows are expected, if our model is correct. One might classify them in the following simple way: (1) HnHN=(high volumetric density n \u223c104cm\u22123, high neutral column density NHI\u22651019cm\u22122), (2) LnHN=(low volumetric density n \u223c10\u22122.5cm\u22123, high neutral column density NHI\u22651019cm\u22122), (3) LnLN=(low volumetric density n \u223c10\u22122.5cm\u22123, high neutral column density NHI\u22641019cm\u22122). Again, types (2) and (3) are a result of di\ufb00erent viewing angles, where type (2) is due to viewing angles through largely hot ionized gas and type (3) viewing angles going through cold and dense gas in addition. \u2013 6 \u2013 12 15 18 21 24 log NHI [cm-2] -2.5 -2.0 -1.5 -1.0 -0.5 log PDF log Mh=[ 8.0, 8.5) log Mh=[ 8.5, 9.0) log Mh=[ 9.0, 9.5) log Mh=[ 9.5,10.0) log Mh=[10.0,11.5) Fig. 2.\u2014 shows the probability distribution functions (PDF) of neutral hydrogen column density for all GRBs, separated according to the halo masses indicated in the legend. Laskar et al. (2014) analyze multi-wavelength observations of the afterglow of GRB 120521C (z \u223c6) and re-analyze two previous GRBs at z > 6 (GRB 050904 and 090423), and conclude that the circumburst medium has a volumetric density of nH \u22640.05cm\u22123 that is constant. The GRBs in the LnHN or LnLN group provide the right match to the observations. While the statistic is still small, it is expected that about 87% of GRBs should arise in in either the LnHN or LnLN group. Observations of GRB 050904 at z = 6.3 reveal that it contains a damped Lyman alpha systems (DLAs) system in the host galaxy of column density NHI = 1021.6cm\u22122 and metallicity of Z = \u22122.6 to \u22121 (Totani et al. 2006; Kawai et al. 2006). Based on X-ray observations, Campana et al. (2007) conclude that Z \u22650.03 Z\u2299for GRB 050904. The evidence thus suggests that GRB 050904 likely resides in a dense environment, although it cannot be completely sure because the metallicity range of the low-density peak (right panel of Figure 1) overlaps with the observed range. It is useful at this juncture to distinguish between the metallicity of the local environment of a GRB and that of absorbers in the GRB afterglow spectrum. Let us now turn to the expected metallicity of UV/optical absorbers in the GRB after\ufb02ow spectra. Figure 3 shows the PDFs of total hydrogen-column-density-weighted metallicity of gas along the line of sight, excluding gas hotter than 106K, for the three sub-populations of GRBs. We see that for all three GRB groups the metallicity of the absorbers in the GRB spectra peaks in the range \u22123 to \u22121. Thus, it is now clear that our model can easily account for the observed properties of GRB 050904. The additional evidence that, based on the analysis of the equivalent width ratio of the \ufb01ne structure transition lines Si II* \u03bb1264.7\u02da A and Si II \u03bb1260.4\u02da A, infers the electron density \u2013 7 \u2013 -3 -2 -1 0 1 log <Zgas / Zsun> -3 -2 -1 0 log PDF log NHI * 19 (nH * 10 cm-3) log NHI * 19 (nH < 10 cm-3) log NHI < 19 (nH < 10 cm-3) Fig. 3.\u2014 shows the PDFs of total hydrogen column density weighted metallicity of gas along the line of sight, excluding gas hotter than 106K, for the three sub-populations of GRBs: GRBs in (nH, T) = (10\u22122.5cm\u22123, 107.5K) with NHI \u22641019cm\u22122 (red dashed, LnLN group), (nH, T) = (10\u22122.5cm\u22123, 107.5K) with NHI \u22651019cm\u22122 (green dotted, LnHN group), and (nH, T) = (104.0cm\u22123, 103.75K) with NHI \u22651019cm\u22122 (blue solid, HnHN group). of log ne = 2.3 \u00b1 0.7. Furthermore, the magnitude of the optical afterglow at 3.4 days after the burst favors a high density circumburst medium. In combination, it appears that GRB 050904 is likely in a dense environment being to the HnHN group. This appears to be at some minor odds with our model, since we only expect that 13% of GRBs to arise in the HnHN group. It would be highly desirable to obtain a larger sample of high-z GRBs to provide a statistically \ufb01rmer test. Analyses of observations of GRB 130606A at z = 5.9 indicate that it likely contains a sub-DLA system of NHI \u223c1019.8cm\u22122 in the host galaxy (Totani et al. 2013; Castro-Tirado et al. 2013). The inferred low metallicity of \u22121.8 to \u22120.8 in solar units (Castro-Tirado et al. 2013) and \u22121.3 to \u22120.5 (Chornock et al. 2013), in conjunction with the NHI, suggests that GRB 130606A may reside in a low density environment with a foreground sub-DLA system in the host galaxy. This proposal is consistent with the evidence of detection of highly ionized species (e.g., N V and Si IV) (Castro-Tirado et al. 2013). It seems likely that GRB 130606A belongs to the LnHN group. It is easy to see that in our model the metallicity distribution of UV/optical absorbers in GRB afterglow spectra is wide, which itself is due to the very inhomegeneous metallicity distributions in the ISM of the host galaxies. Thus, it would be a rather chancy practice trying to infer the metallicity of the host galaxy solely based on a small number of (typically one) GRB afterglow absorption spectra. \u2013 8 \u2013 The reader has already seen clearly that the distributions of all concerned physical quantities, including metallicity, density, total and neutral hydrogen column density, are wide. We will add yet one more quantity and show the cumulative distributions of the ratio of neutral hydrogen to total hydrogen column density for the three groups in the right panel of Figure 4. We see that for GRBs in the LnLN group the neutral hydrogen to total hydrogen column ratio is signi\ufb01cantly less than unity. Even for the HnHN and LnHN groups, (10%,14%) of GRBs have the ratio less than 0.1. In other words, it is generally a pretty bad assumption that the apparent absorbers in the GRB afterglow spectra are mainly neutral. This indicates that the so-called \u201cmissing gas problem\u201d (e.g., Schady et al. 2011) may be accommodated in this model. 16 18 20 22 24 26 log NH [cm-2] -3 -2 -1 0 log PDF log NHI * 19 (nH * 10 cm-3) log NHI * 19 (nH < 10 cm-3) log NHI < 19 (nH < 10 cm-3) -10 -8 -6 -4 -2 0 log NHI / NH -3 -2 -1 0 1 log cumulative fraction log NHI * 19 (nH * 10 cm-3) log NHI * 19 (nH < 10 cm-3) log NHI < 19 (nH < 10 cm-3) Fig. 4.\u2014 Left panel: shows the PDFs of total hydrogen column density for the three subpopulations of GRBs: GRBs in (nH, T) = (10\u22122.5cm\u22123, 107.5K) with NHI \u22641019cm\u22122 (red dashed, LnLN group), (nH, T) = (10\u22122.5cm\u22123, 107.5K) with NHI \u22651019cm\u22122 (green dotted, HnLN group), and (nH, T) = (104.0cm\u22123, 103.75K) with NHI \u22651019cm\u22122 (blue solid, HnHN group). Right panel: shows the cumulative PDFs of the ratio of NHI/NH. The left panel of Figure 4 shows the PDFs of the total hydrogen column density for the three sub-populations of GRBs, which is most relevant for probing GRB X-ray afterglows and hence a useful test of our model. One expectation from our model is that the vast majority of GRBs sitting in low density circumburst medium (LnHN + LnLN) do not have Compton thick obscuring gas. This prediction is veri\ufb01able with a combination of afterglow light curves and X-ray observations. On the other hand, one expects from our model that a signi\ufb01cant fraction of the GRBs sitting in high density circumburst medium (HnHN) have an extended high NH tail and dominate the GRBs with NH \u22651023cm\u22122. Quantitatively, we \ufb01nd that (45%, 3%) of GRBs have NH \u2265(1023, 1024)cm\u22122; it is noted that these two numbers are likely lower bounds due to possible numerical resolution e\ufb00ects. As already noted earlier, it is seen from the right panel that the GRBs in the LnLN group are intervened by highly ionized gas peaking at an average neutral fraction of \u223c10\u22124, with no cases having a neutral fraction exceeding 10\u22121. In contrast, for GRBs in both the HnLN and HnHN \u2013 9 \u2013 groups, more than 50% of them have an average neutral fraction greater than \u223c10\u22121. -6 -4 -2 0 2 log (NH /1021cm-2)(Z/ZO  \u2022 ) -3 -2 -1 0 log PDF log NHI * 19 (nH * 10 cm-3) log NHI * 19 (nH < 10 cm-3) log NHI < 19 (nH < 10 cm-3) T < 106 K 3 4 5 6 log <T> [K] -2 -1 0 1 log PDF log NHI * 19 (nH * 10 cm-3) log NHI * 19 (nH < 10 cm-3) log NHI < 19 (nH < 10 cm-3) Fig. 5.\u2014 Left panel: shows the PDFs of metallicity weighted total hydrogen column density, (NH/1021cm\u22122)(Z/ Z\u2299, excluding gas with temperature greater than 106K, for the three sub-populations of GRBs: GRBs in (nH, T) = (10\u22122.5cm\u22123, 107.5K) with NHI \u22641019cm\u22122 (red dashed), (nH, T) = (10\u22122.5cm\u22123, 107.5K) with NHI \u22651019cm\u22122 (green dotted), and (nH, T) = (104.0cm\u22123, 103.75K) with NHI \u22651019cm\u22122 (blue solid). The exclusion of \u2265106K gas is to intended for the situation that dust is e\ufb03ciently destroyed in hot gas. According to Draine (2003), AV \u2248(NH/1021cm\u22122)(Z/ Z\u2299. Right panel: shows the PDFs of gas temperature weighted by NHZ, excluding gas with temperature greater than 106K. We now turn to the issue of dust obscuration. The left panel of Figure 5 shows the PDFs of visual extinction AV . It is noted that the simulation does not follow dust formation explicitly. Thus, we have adopted the well known empirical relation between metal column density and visual extinction: AV = (NH/1021cm\u22122)(Z/ Z\u2299) (Draine 2003). While the applicability of the relation derived from local observations is uncertain, detailed analysis of galaxy colors at EoR suggest that the simulated galaxies based on this relations give rise to self-consistent results when comparing to observations (Kimm & Cen 2013; Cen & Kimm 2014). Moreover, direct observations of dust suggest that this relation holds well in other galaxies locally, and galaxies and damped Lyman alpha systems at moderate to high redshift (e.g., Draine et al. 2007; De Cia et al. 2013; Draine et al. 2014; Fisher et al. 2014). Nevertheless, it is possible that the normalization factor in front of the relation is probably uncertain to order of unity. It is evident that a signi\ufb01cant fraction of GRBs in the high HnHL group (blue solid curve) are heavily dust obscured, with (53%,16%) of GRBs in the HnHL group have AV \u2265(1, 10). At the other extreme, we see that the GRBs in the LnLN group (red dashed curve) have negligible dust columns with no case of AV \u22650.3; nevertheless, it is worth pointing out that, even for this set of GRBs 12% has an AV \u22650.03 due largely to dust in high temperature gas. The GRBs in the LnHN group (green dotted curve) situates inbetween the above \u2013 10 \u2013 two groups, with a small but non-negligible fraction (7%) at AV > 1. Observationally, the issue of dust in high-z GRB hosts is less than settled. Zafar et al. (2010), based on a re-analysis of the multiepoch data of the afterglow of GRB 050904 at z = 6.3, conclude that there is no evidence of dust. Given that the neutral column density of the in situ DLA for GRB 050904 is NHI = 1021.6cm\u22122 and low metallicity Z = \u22122.6 to \u22121 (Totani et al. 2006; Kawai et al. 2006), an AV \u223c0.01 is possible, if one adopts the lower metallicity value that is statistically allowed in our model (see the right panel of Figure 1). Thus, both the low extinction and a standard ratio of dust to metals are still consistent with the observations. Our model indicates that 9% of GRBs have AV \u22651. Thus, with a z \u22656 GRB sample of size 11, one expects to see one GRBs with nH \u223c104cm\u22123 that is signi\ufb01cantly obscured by dust with AV > 1. This may be testable with SWIFT data relatively soon. The right panel of Figure 5 shows the PDFs of average gas temperature weighted by NHZ, excluding gas with temperature greater than 106K (the exclusion is a crude way to say that dust in gas hotter than 106K is destroyed). The purpose of this plot is to provide an indication the diversity of intervening gas with dust. One notes that the lines of sight of HnHL GRBs contain dust in cold medium (T \u2264104K), whereas those of high LnHN GRBs are dominated by dust residing in gas T \u223c104\u22125K, and the LnLN GRBs are intervened by dust in hotter gas of T \u2265105K. Under the assumption that the hotter gas is presumably produced by shocks, which are more destructive to larger dust grains, one might suggest that dust becomes increasingly grayer from HnHL to LnHN to LnLN. One expectation is that some lines of sight, especially those for the HnLN and HnHN groups the total dust arise from multiple, di\ufb00erent temperature regions. This may provide a physical explanation for the observational indications of multiple dust components (e.g., Zafar et al. 2012). As a side note on the SFR of GRB hosts. Basa et al. (2012) place the star formation rate (SFR) of GRB 080913 at z = 6.7 to be less than 0.9 M\u2299/yr. Berger et al. (2007) obtain an upper bound on the star formation rate of GRB 050904 at z = 6.3 less than 5.7 M\u2299/yr. From the simulations we \ufb01nd that (42%, 57%, 66%) of GRBs occur in galaxies with SFR less than (0.3, 1.0, 3.0) M\u2299/yr. Thus, while simulations and observations are in good agreement, larger data sets are needed to place the comparisons on a solid statistical ground. Finally, we must stress that the analysis performed here has focused on the ISM embedding the GRBs at EoR. The exact details of the state of the IGM at EoR are uncertain both observationally and theoretically. The theoretical di\ufb03culty is in part computational, because we do not have the capability to simulate a large enough volume to capture of the reionization of the IGM selfconsistently, while still having enough resolution for the ISM. The goal of this work is to present the signatures of the ISM theoretically, which is lacking. It may be argued that the properties of ISM in galaxies are somewhat detached from the properties of the IGM on large scales; in other words, the observed spectra of GRB afterglows at EoR may be considered to be imprinted by both ISM and IGM as a linear superposition. Consequently, a proper understanding of the ISM will not only aid in the interpretation of the ISM of galaxies at EoR but also is highly needed for proper interpretation of the properties (neutral fraction, topology, etc) of the IGM at EoR. \u2013 11 \u2013 4. Conclusions We perform an analysis to quantify the physical condition of the ISM embedding GRBs as well as intervening gas in the host galaxies at high redshift z \u22656. Our analysis is based on a zoomed-in cosmological radiation hydrodynamics simulation of 3.8 \u00d7 4.8 \u00d7 9.6 Mpc3 box (comoving) with 731 halos of mass 108 \u2264Mvir < 3 \u00d7 1010 M\u2299at z = 7 at high spatial (\u223c4 pc, physical) and stellar mass resolution of 49 M\u2299. The following are new \ufb01ndings. On parsec scales, GRBs are concentrated in two regions in density-temperature-metallicity space, with (nH, T, Z) being (10\u22122.5cm\u22123, 107.5K, \u22121.5 to 0.5) and (> 104.0cm\u22123, < 103.8K, \u22122.5 to\u2212 1), consisting of 87% and 13% of GRBs, respectively. The appearance of GRB afterglows, however, also strongly depends on the line of sight thanks to varying physical properties of intervening gas and dust in the host galaxy, which in turn splits the low density peak into two subsets. As a result, three separate apparent groups of GRB afterglows composing of (13%,37%,50%) are expected to arise with the following physical properties: (1) a cold neutral circumburst gas of hydrogen density of nH \u223c104cm\u22123, neutral hydrogen column density 90% range of NHI \u223c1021.0 \u22121023.3cm\u22122, total hydrogen column density 90% range of NH \u223c1021.6\u22121023.8cm\u22122, with (53%,16%) having AV greater than (1,10), (2) a hot circumburst gas of hydrogen density of nH \u223c10\u22122.5cm\u22123, neutral hydrogen column density 90% range of NHI \u223c1019.5 \u22121022.3cm\u22122, total hydrogen column density 90% range of NH \u223c1020.6 \u22121022.5cm\u22122, with (7%,1%) having AV greater than (1,10), (3) a hot circumburst gas of hydrogen density of nH \u223c10\u22122.5cm\u22123, neutral hydrogen column density 90% range of NHI \u223c 1010.5 \u22121018.0cm\u22122, total hydrogen column density 90% range of NH \u223c1018.7 \u22121021.1cm\u22122, with (0.2%,0%) having AV greater than (1,10). Common among all three groups of GRBs is that the metallicity of proximity optical/UV absorbers in the afterglow spectra is expected to be in the range of Z = \u22123 to \u22121. The strikingly diverse physical properties metallicity, neutral hydrogen column density, total column density, gas temperature, dust column of intervening absorbers of GRB afterglows as well as the bimodal physical properties of local (parsec-scale) environment indicates that a solid statistical comparison between the model predictions and observations needs to await a large observational sample of GRBs at the EoR. It is obvious that the available small sample of GRB afterglows complicates the task of interpretating the ISM of a small number of GRB host galaxies and the additional task of inferring the state of the IGM at EoR. Nevertheless, utilizing high-z GRBs to probe interstellar medium and intergalactic medium must be undertaken properly taking into consideration the physical diversities of the interstellar medium. The analysis presented will provide a physical framework to be confronted by future observations statistically. Fruchter et al. (2006) \ufb01nd that GRBs are more concentrated in the very brightest regions of their host galaxies than are the core-collapse supernovae. Our analysis so far has assumed that the two populations are just proportional to one another. One may turn the argument around and use the observed distributions of GRBs that depend on both embedding environment and intervening material to test the connection between GRBs and star formation. Needless to say, larger samples will be able to shed light on this extremely important issue, which will have strong bearings on relating GRB rates to cosmological reionization. \u2013 12 \u2013 Acknowledgements We would like to thank Omer Bromberg for discussion. Computing resources were in part provided by the NASA HighEnd Computing (HEC) Program through the NASA Advanced Supercomputing (NAS) Division at Ames Research Center. The research is supported in part by NSF grant AST-1108700 and NASA grant NNX12AF91G.",
                    "introduction": "Very high redshift (z \u22656) gamma-ray bursts (GRBs) (e.g., Greiner et al. 2009; Tanvir et al. 2009; Cucchiara et al. 2011) provide an excellent probe of both the interstellar (ISM) and inter- galactic medium (IGM) at the epoch of reionization (EoR) using absorption spectrum techniques thanks to their simple power-law afterglow spectra and high luminosity (Lamb & Reichart 2000), complimentary to quasar absorption spectrum observations (Fan et al. 2006). Here we present a \ufb01rst, detailed analysis of the physical properties of ISM surrounding GRBs, utilizing state-of-the-art radiation-hydrodynamic simulations, with the hope that they may aid in proper interpretations of observations of GRB afterglows at EoR with respect to both ISM and IGM. 1Princeton University Observatory, Princeton, NJ 08544; cen@astro.princeton.edu 2Princeton University Observatory, Princeton, NJ 08544; kimm@astro.princeton.edu arXiv:1409.6755v1  [astro-ph.HE]  23 Sep 2014 \u2013 2 \u2013"
                },
                {
                    "url": "http://arxiv.org/abs/1406.1467v1",
                    "title": "Gaussian Random Field: Physical Origin of Sersic Profiles",
                    "abstract": "While the Sersic profile family provide adequate fits for the surface\nbrightness profiles of observed galaxies, the physical origin is unknown. We\nshow that, if the cosmological density field are seeded by random gaussian\nfluctuations, as in the standard cold dark matter model, galaxies with steep\ncentral profiles have simultaneously extended envelopes of shallow profiles in\nthe outskirts, whereas galaxies with shallow central profiles are accompanied\nby steep density profiles in the outskirts. These properties are in accord with\nthose of the Sersic profile family. Moreover, galaxies with steep central\nprofiles form their central regions in smaller denser subunits that possibly\nmerge subsequently, which naturally leads to formation of bulges. In contrast,\ngalaxies with shallow central profiles form their central regions in a coherent\nfashion without significant substructure, a necessary condition for disk galaxy\nformation. Thus, the scenario is self-consistent with respect to the\ncorrelation between observed galaxy morphology and Sersic index. We predict\nfurther that clusters of galaxies should display a similar trend, which should\nbe verifiable observationally.",
                    "authors": "Renyue Cen",
                    "published": "2014-06-05",
                    "updated": "2014-06-05",
                    "primary_cat": "astro-ph.GA",
                    "cats": [
                        "astro-ph.GA"
                    ],
                    "main_content": "The standard cosmological constant dominated cold dark matter cosmological model has a number of distinct features. One of the most important is that the initial density fluctuations are gaussian and random. As a result, the statistical properties are fully determined by a vector quantity, namely, the linear power spectrum of the density fluctuations, Pk, which is well determined by observations from the microwave experiments and others (e.g., Komatsu et al. 2011). Observational evidence is that allowed deviations from gaussianity are at the level of 10\u22123 and less in the linear regime (Planck Collaboration et al. 2013). In a gaussian random field, different waves are superimposed on one another in a random fashion, with the ensemble of waves at a given length following gaussian distribution and the square of the mean equal to the amplitude of the power spectrum at that wavelength. Here, a simple illustration is shown to contain rich physics and can already account for the basic trend of the Sersic profiles, which, more importantly, are additionally in accord with properties of galaxies other than the profiles. Figure 1 shows an example of the formation of a massive galaxy that contains small-scale fluctuations with large amplitude (left panel) and an example of the formation of a massive galaxy that contains small-scale fluctuations with small amplitude (right panel). In both panels peaks that are above the horizontal red dot-dashed line would have collapsed by z = 1. Our choice of redshift z = 1 has no material consequence and we expect the generic trends should not depend on that choice. In the left panel we see that, between the two points where the blue dashed curve intersect the horizontal red dot-dashed line, there are three separate density peaks with peak amplitude of 6\u22127. Thus, a significant portion of the three peaks would have collapsed by redshift z = 4 \u22126 to form three separate galaxies. Note that structures formed at higher redshifts tend to be denser than structures formed at lower redshifts. Therefore, these earlier structures would settle to form the dense central region. Although it is probable that the galaxies formed at the three separate peaks subsequently merge to form a dense elliptical galaxy, our conclusion of forming a dense central region \u2013 3 \u2013 \u22123 \u22122 \u22121 0 1 2 3 \u22128 \u22127 \u22126 \u22125 \u22124 \u22123 \u22122 \u22121 0 1 2 3 4 5 6 7 8 9 10 elliptical formation steep central profile with extended envelope spatial scale density fluctuation amplitude      long wave fluctuations  total fluctuations  collapse amplitude \u22123 \u22122 \u22121 0 1 2 3 \u22128 \u22127 \u22126 \u22125 \u22124 \u22123 \u22122 \u22121 0 1 2 3 4 5 6 7 8 9 10 spatial scale     spiral formation shallow central profile with steep outer profile  long wave fluctuations  total fluctuations  collapse amplitude Fig. 1.\u2014 Left panel: shows an example of the formation of a massive galaxy at z = 1 that is overall determined by the large waves indicated by the blue dashed curve. On top of the large linear wave, there is small-scale linear wave of length 1/8 of the large one with a \ufb02uctuation amplitude 1.5 times larger than the large wave. Both long and short waves are chosen to be sinusoidal for the illustration. The sum of the long and short waves is shown as the black solid curve. The horizontal red dot-dashed line of amplitude value 1.68 indicates the amplitude of the \ufb02uctuation that has collapsed by z = 1. Right panel: same as the left panel except the small-scale wave has a \ufb02uctuation amplitude 10 times smaller than the large wave. Note that the examples are shown in 1-d but meant to be in 3-d. in this case does not necessarily require all of them to merge. Moreover, there are two somewhat smaller peaks at x values of \u223c\u22121.5 and \u223c+1.5 of amplitude \u223c4.5, which would have collapsed by redshift z = 2 \u22124. In addition, there two still smaller peaks at x values of \u223c\u22122.5 and \u223c+2.5 of amplitude \u223c2.5, which would have collapsed by redshift z = 1 \u22122. It is reasonable to expect that the four outer small galaxies would accrete onto the central galaxy to form the outer envelope by z = 0. Thus, this con\ufb01guration would form a central dense structure with a steep pro\ufb01le due to the early formation of the central subunits and their subsequent descent to the center (and possible merging), and an extended envelope due to later infall of small galaxies that form in outer regions at some earlier times, resulting in a pro\ufb01le resembling a Sersic pro\ufb01le with n \u226b1. This overall picture seems to resemble two-phase formation scenario for elliptical galaxies from detailed cosmological hydrodynamic simulations (Oser et al. 2010; Lackner et al. 2011). \u2013 4 \u2013 In the right panel we see that, between the two points where the blue dashed curve intersect the horizontal red dot-dashed line, there is no signi\ufb01cant substructure. Therefore, the collapse of the central region will be rather coherent without signi\ufb01cant central condensation (i.e., without a stellar bulge). Furthermore, there is no signi\ufb01cant density peak outside the central region that has collapsed; as a result, there is little stellar envelope due to late infall of small galaxies. Thus, this con\ufb01guration would form a galaxy with a shallow central density slope and a very steep outer slope. We suggest that this con\ufb01guration would form a bulge-less spiral galaxy with a pro\ufb01le similar to a Sersic pro\ufb01le with n = 1. A corollary is that the con\ufb01guration depicted in the right panel would occur in a \u201cquiet\u201d environment, which may be quantitatively described as having a small pair-wise velocity dispersion (Davis & Peebles 1983) or a high Mach number (Suto et al. 1992). Our local environment appears to belong to this category. Perhaps this explains why there is preponderence of giant bulge-less galaxies in our neighborhood (Kormendy et al. 2010). This does not necessarily suggest that the observed large fraction (\u223c50%) of large bulge-less galaxies in our local universe is representative for the universe as a whole. Our own expectation is that the fraction of large bulge-less galaxies, averaged over the entire universe, will be substantially lower than that seen in the very local neighborhood. Future surveys with resolutions as good as those for local galaxies now can check this. It is easy to imagine a variety of con\ufb01gurations that may fall in-between these two (nearly) bookend examples. Since the gaussian density \ufb02uctuation is \u201ccompensated\u201d in the sense that the large density peak tends to be sandwiched by a pair of troughs, the expected trend is this: a larger degree of central substructure is accompanied by a larger degree of substructure in the outskirts, whereas a lesser degree of central substructure is accompanied by a lesser degree of substructure in the outskirts. Since the total density \ufb02uctuations are linear combinations of each independent waves, one can generalize the con\ufb01gurations from two waves to an arbitrary number of waves but the trend seen in Figure 1 remains. In short, the generic trend obtained essentially hinges on two important features of the gaussian random \ufb01eld: each density wave is compensated and independent. 3. Discussion and Conclusions Based on a simple analysis we show that gaussian random \ufb01eld provides the physical origin for the observed Sersic pro\ufb01les. The two unique properties of the gaussian random \ufb01eld waves are compensated and independent dictate that a more central concentrated stellar structure of a galaxy is simultaneously accompanied by an extended stellar envelope, and vice versa. Additionally, those with steep inner slopes are expected to contain signi\ufb01cant subunits that form early and coalescence later, which are consistent with the paradigm of merger driven formation of elliptical galaxies, whether being dry (van Albada 1982) or wet (Hopkins et al. 2006). On the other hand, those with shallow inner slopes are expected to contain little substructure, which would bode well for the formation of disk galaxies. Thus, the picture is self-consistent. This analysis is illustrative and qualitative. It will be useful later to formulate a model that is quantitative and statistical in the context of the gaussian \ufb01eld statistics (e.g., Bardeen et al. 1986; Bond et al. 1991). The task in hand is, however, still more complex than a full statistical analysis \u2013 5 \u2013 of the gaussian random \ufb01eld, because baryonic physics is expected to play an important role. Cosmological reionization (a.k.a, photoheating of the intergalactic medium), gravitational shock heating due to large-scale structure formation and feedback from stellar evolution and supermassive black hole growth may quantitatively change the stellar makeup in both the \u201ccentral region\u201d and \u201couter region\u201d shown in Figure 1, perhaps to varying degrees. Nevertheless, we see no physical reason that any of these baryonic processes will alter qualitatively the systematic trend that is illustrated in the previous section. Since the examples shown in Figure 1 are generic in terms of spatial scales, we expect that our argument is applicable on other scales. If the above analysis on galaxies is extended to clusters of galaxies, the following new predictions are made. Clusters of galaxies are expected to display a similar trend or a family of density pro\ufb01les from concentrated ones resembling those of elliptical galaxies with large Sersic index n to less concentrated ones resembling those of disk galaxies with small Sersic index n. For this purpose, the characterization of density pro\ufb01les of clusters of galaxies should be performed with respect to the stellar component. Procedurally, one \ufb01rst identi\ufb01es the virial radius of the cluster and then \ufb01nds the best Sersic \ufb01t within the virial radius. Two critical issues are that cluster members are properly identi\ufb01ed and projection e\ufb00ects minimized, and that intra-cluster light is accounted for. As an example, clusters with cD galaxies should display the shallowest slope and the most extended distribution of galaxies in the outer regions, resulting in a very high n value if \ufb01t with Sersic pro\ufb01le for the stellar density. This prediction is veri\ufb01able. Although a tight correlation between the presence of cooling \ufb02ows in X-ray clusters and the presence of cD galaxies at the center is observed, it becomes natural to expect such an outcome from our analysis, because the presence of cD galaxies means early formation of at least the \u201cseed\u201d of the central region that is denser in gas and dark matter as well as in stars. I thank an anonymous referee for an especially positive report and very useful suggestions that have improved the paper. This work is supported in part by NASA grant NNX11AI23G.",
                    "introduction": "The process of galaxy formation has likely imprinted useful information in the stellar structures. A great amount of e\ufb00ort has been invested in characterizing detailed stellar structures of galaxies of all types, dating back to Plummer (1911) for globular clusters and Reynolds (1913) for the Andromeda, and if one is so inclined, to Kant (1755) who might be the \ufb01rst contemplating the shape of the Milky Way and island universes. In modern times, among the best known examples, the de Vaucouleurs (1948) law - surface brightness I(R) \u221de\u2212kR1/4 (where R is radius and k a normalization constant) - describes giant elliptical galaxies well, whereas the King (1962) law appears to provide better \ufb01ts for fainter elliptical galaxies; disk galaxies are in most cases described by the exponential disk model (Hodge 1971): I(R) \u221de\u2212kR. The major advantage of Sersic (1968) pro\ufb01le family - I(R) \u221de\u2212kR1/n - is that they provide an encompassing set of pro\ufb01les with n from less than 1 to as large as 10, including the exponential disk (n = 1) and de Vaucouleurs (n = 4) model. Even at the age of sophisticated hydrodynamic simulations, the physical origin of the Sersic pro\ufb01le family that have well described all galaxies remains enigmatic. This author is of the opinion that the nature of galaxy formation process in the context of modern cosmological structure forma- tion model is perhaps too complex to warrant any possibility of analytic \ufb01ts to be accurate beyond the zero-th order. While e\ufb00orts to characterize deviations from or additions to the standard \ufb01ts are 1Princeton University Observatory, Princeton, NJ 08544; cen@astro.princeton.edu arXiv:1406.1467v1  [astro-ph.GA]  5 Jun 2014 \u2013 2 \u2013 not only necessary but also very important to account for rich galaxy data (e.g., Lauer et al. 1995), it would also seem bene\ufb01cial to construe the basic trend displayed by the wide applicability of the Sersic pro\ufb01le family to enhance our physical understanding of the galaxy formation process. In this Letter we provide a basic physical understanding of the Sersic pro\ufb01le family in the context of the standard cosmological model with gaussian random density \ufb01eld. Our simple analysis provides, for the \ufb01rst time, a self-consistent physical origin for the Sersic pro\ufb01le family. This also opens up the possibilities to explore the physical links to other properties of galaxies, since, for example, it comes natural and apparently inevitable that the steep pro\ufb01led galaxies have a much higher fraction of substructures that form early and interactions/mergers among them would lead to formation of elliptical galaxies, enabling a self-consistent picture. This study is the \ufb01fth paper in the series \u201cOn the Origin of the Hubble Sequence\u201d."
                },
                {
                    "url": "http://arxiv.org/abs/1405.0516v1",
                    "title": "Evolution of Cold Streams and Emergence of the Hubble Sequence",
                    "abstract": "A new physical framework for the emergence of the Hubble sequence is\noutlined, based on novel analyses performed to quantify the evolution of cold\nstreams of a large sample of galaxies from a state-of-the-art ultra-high\nresolution, large-scale adaptive mesh-refinement hydrodynamic simulation in a\nfully cosmological setting. It is found that the following three key physical\nvariables of galactic cold inflows crossing the virial sphere substantially\ndecrease with decreasing redshift: the number of streams N_{90} that make up\n90% of concurrent inflow mass flux, average inflow rate per stream dot M_{90}\nand mean (mass flux weighted) gas density in the streams n_{gas}. Another key\nvariable, the stream dimensionless angular momentum parameter lambda, instead\nis found to increase with decreasing redshift. Assimilating these trends and\nothers leads naturally to a physically coherent scenario for the emergence of\nthe Hubble sequence, including the following expectations: (1) the predominance\nof a mixture of disproportionately small irregular and complex disk galaxies at\nz>2 when most galaxies have multiple concurrent streams, (2) the beginning of\nthe appearance of flocculent spirals at z~1-2 when the number of concurrent\nstreams are about 2-3, (3) the grand-design spiral galaxies appear at z<1 when\ngalaxies with only one major cold stream significantly emerge. These expected\ngeneral trends are in good accord with observations. Early type galaxies are\nthose that have entered a perennial state of zero cold gas stream, with their\nabundance increasing with decreasing redshift.",
                    "authors": "Renyue Cen",
                    "published": "2014-05-02",
                    "updated": "2014-05-02",
                    "primary_cat": "astro-ph.GA",
                    "cats": [
                        "astro-ph.GA"
                    ],
                    "main_content": "The reader is referred to Cen (2014b) for detailed descriptions of our simulations. Briefly, a zoom-in region of comoving size of 21 \u00d7 24 \u00d7 20h\u22123Mpc3 is embedded in a 120h\u22121Mpc periodic box and resolved at 114h\u22121pc physical. Cosmological parameters are from WMAP7 (Komatsu et al. 2011): \u2126M = 0.28, \u2126b = 0.046, \u2126\u039b = 0.72, \u03c38 = 0.82, H0 = 100h km s\u22121Mpc\u22121 = 70 km s\u22121Mpc\u22121 2011): \u2126M = 0.28, \u2126b = 0.046, \u2126\u039b = 0.72, \u03c38 = 0.82, H0 = 100h km sMpc\u2212 = 70 km sMpc\u2212 and n = 0.96. The zoom-in region is centered on a cluster of mass of \u223c3 \u00d7 1014 M\u2299at z = 0 hence represents a 1.8\u03c3 fluctuation for the volume. As a result, the development of structure formation is somewhat more advanced compared to that of the cosmic mean, and we take that into account when drawing conclusions with respect to the universe as a whole. Equations governing motions of dark matter, gas and stars, and thermodynamic state of gas are followed, using the adaptive mesh \u2013 3 \u2013 re\ufb01nement cosmological hydrodynamic code Enzo (Bryan et al. 2014). The simulations include a metagalactic UV background (Haardt & Madau 2012) with self-shielding (Cen et al. 2005), a metallicity-dependent radiative cooling (Cen et al. 1995). Star particles are created in cells that satisfy a set of criteria (Cen & Ostriker 1992), essentially equivalent to the Kennicutt (1998) law. Each star particle is tagged with its initial mass, creation time, and metallicity; star particles typically have masses of \u223c106 M\u2299. Supernova feedback from star formation is modeled following Cen et al. (2005). At any epoch stellar particles are grouped using HOP (Eisenstein & Hut 1998) to create galaxy catalogs. For each galaxy we have its exact star formation history, given its member stellar particles formation times. None of the galaxies used in the analysis contains more than 1% in mass, within the virial radius, of dark matter particles other than the \ufb01nest particles. Galaxy catalogs are constructed from z = 0.62 to z = 1.40 at a redshift increment of \u2206z = 0.02 and from z = 1.40 to z = 6 at a redshift increment of \u2206z = 0.05. Thus, when we say, for example, galaxies of stellar masses 1010\u221211 M\u2299in the redshift range z = 2 \u22123, it means that we include galaxies with stellar masses from 1010 to 1011 M\u2299from 21 snapshots (z = 2, 2.05, ..., 2.95, 3). For the four redshift ranges analyzed, z = (0.62 \u22121, 1 \u22122, 2 \u22123, 3 \u22124), there are (5754, 9395, 4522, 1507) galaxies of stellar mass in the range 1010\u221211 M\u2299, and (628, 964, 232, 28) galaxies of stellar mass in the range 1011\u221212 M\u2299. Proper identi\ufb01cation of gas streams has not been demonstrated so far. Visual inspection may be able to pick out prominent ones, although it lacks the ability to separate out multi streams and becomes impractical for large samples. Real-space search for \ufb01lamentary structures for large-scale structure have enjoyed some successes (e.g., Bond et al. 2010) but the following two issues make them less usable for gas streams. First, non-radial streams could easily bend during travel, maybe resembling things that may look like spirals; even radial streams will bend due to \ufb02uid drag. Second, gas along a stream is generally broken up (due to thermal and gravitational instabilities as well as other interactions) to look more like a pearl necklace than a creek. We have explored using some constants of motion to devise an automated scheme and \ufb01nally focused on the angular momentum vector. We \ufb01nd that the following two variables the amplitude of the total speci\ufb01c angular momentum (J) and the cosine of the angle [cos(\u03b8)] between the total speci\ufb01c angular momentum and a \ufb01xed vector (say, z direction) de\ufb01ne a parameter space for identifying and separating out co-eval, distinct streams. Operationally, for a galaxy we accumulate in\ufb02ow gas \ufb02ux in the radial range (1 \u22121.3)rv (rv=virial radius) in the J \u2212cos(\u03b8) plane with 50 \u00d7 50 grid points, spanning uniformly the J range [0, 20] \u00d7 104 km/s kpc and cos(\u03b8) range [\u22121, 1]. In\ufb02ow gas is de\ufb01ned to be gas with the radial component of its velocity pointing to the center. Only gas with T \u2264105K is included. The mass \ufb02ux of each \ufb02uid cell i in the radial range (1 \u22121.3)rv is computed as 4\u03c0\u03c1ivi\u2206x2 i /\u03a3 \u2206x2 i r2 i , where \u03c1i is gas density, vi the radial velocity, \u2206xi the cell size, ri radial distance from the center, and the sum is performed over all cells in the radial range. The 4\u03c0 and the sum term serve to make sure that \ufb02uxes are properly normalized, when all the gas cells in the radial shell are collected, regardless of the thickness of the radial shell. Once mass \ufb02uxes are accumulated in the 2-d parameter plane, smoothing is applied to smooth out \ufb02uctuations among adjacent entries in the 2-d phase plane. The choice of the smoothing window size does not alter results in material way, as long as over smoothing is avoided; a 3-point boxcar smoothing is used. With the smoothed \ufb02ux map, we \u2013 4 \u2013 J (104 km/s kpc) cos(e)     1 2 3 0 1 2 3 4 5 6 7 8 9 \u22121 \u22120.5 0 0.5 1 log cold gas inflow flux (Msun/yr) \u22124 \u22123 \u22122 \u22121 0 1 2 Fig. 1.\u2014 Top panel: shows a 3-d visualization of a galaxy of stellar mass 4.7 \u00d7 1011 M\u2299at z = 3. The box has a width of 2.6 times the virial radius. The (yellow,purple) isodensity surfaces have values (\u223c10\u22122, \u223c10\u22121)cm\u22123. Bottom panel: shows the gas in\ufb02ow \ufb02ux in the radial range (1 \u22121.3)rv, in the two-dimensional J-cos(\u03b8) phase space. The total gas in\ufb02ow rate of the galaxy is 388 M\u2299yr\u22121 (and star formation rate of 254 M\u2299yr\u22121) and nine signi\ufb01cant streams are identi\ufb01ed. The top three streams make up 90% of the total in\ufb02ow rate and are labelled with numbers (1, 2, 3), with their respective in\ufb02ow rates being (211, 79, 61) M\u2299yr\u22121. \u2013 5 \u2013 employ a procedure analogous to the DENMAX scheme used to identify dark matter halos (Gelb & Bertschinger 1994). Each entry is propagated along the steepest uphill gradient until it reaches a local maximum of \ufb02ux and is said to belong to that local maximum. All entries in the 2-d phase plane belonging to a same maximum are collected together to de\ufb01ne one distinct stream, with a number of attributes, including mean location in the parameter plane, total \ufb02ux, \ufb02ux-weighted gas density, temperature. We rank order the streams according to their \ufb02uxes, and de\ufb01ne N90 to be the top number of streams that make up 90% of total concurrent cold gas in\ufb02ow rate. If the 90% falls between two streams, we linearly interpolate to \ufb01nd N90, which hence could be non-integer. When there is no signi\ufb01cant stream, N90 = 0. Figure 1 demonstrates how well this phase-space identi\ufb01cation scheme works. For this galaxy at z = 3 the identi\ufb01cation scheme \ufb01nds nine signi\ufb01cant streams with the top three streams making up 90% of the cold in\ufb02ux. Even through it is not easy to discern visually all streams, it appears that nine is consistent with the 3-d rendering in the top panel. The fact that the scheme picks out nine streams in this complex setting is a convincing demonstration of its e\ufb03cacy. It is evident that there are indeed three major streams around the virial sphere, seen as three prominent yellow tubes with purple spines. Part of the motivation of this paper is to demonstrate this method of cold stream identi\ufb01cation in a complex cosmological setting that may be used by other authors. 3. Results Figure 2 shows the PDF of the number of streams (N90). Three most important trends are immediately visible. First, larger galaxies tend to have more streams at z > 2, although for the two mass ranges considered the di\ufb00erences become insigni\ufb01cant at z \u22642. Second, N90 steadily and signi\ufb01cantly decreases with decreasing redshift. The median N90 is (2.3, 4.0) for (1010 \u22121011, 1011 \u2212 1012) M\u2299galaxies at z = 3 \u22124, which becomes (2.0, 3.5) at z = 2 \u22123, (1.6, 1.9) at z = 1 \u22122 and (1.0, 1.6) at z = 0.62 \u22121. Third, the rate of decrease of N90 with decreasing redshift appears to be faster for the higher mass galaxies. Figure 3 shows the PDF of cold in\ufb02ow rate per stream, \u02d9 M90, de\ufb01ned to be 90% of the total cold accretion rate divided by N90. There is a signi\ufb01cant decline with decreasing redshift, with the median \u02d9 M90 being (33, 52) M\u2299/yr for (1010 \u22121011, 1011 \u22121012) M\u2299galaxies at z = 3 \u22124, declining to (21, 50) M\u2299/yr at z = 2 \u22123, (13, 20) M\u2299/yr at z = 1 \u22122 and (5, 8) M\u2299/yr at z = 0.62 \u22121. The rapid decrease of both \u02d9 M90 and N90 (seen in Figure 2) with decreasing redshift makes it clear that the total cold gas in\ufb02ow rate has experienced a very dramatic decline with decreasing redshift a factor of \u223c10 from z = 3 \u22124 to z = 0.62 \u22121 at a given galaxy mass. This is consistent with the decline of the global evolution of star formation rate density seen in our simulations (Cen 2011) and observations (Hopkins & Beacom 2006). Analysis by Conselice et al. (2013) suggests that 66 \u00b1 20 of star formation be due to cold accretion, which would be further increased considering inevitable signi\ufb01cant out\ufb02ows, fully consistent with our predictions, although it is noted that they can not di\ufb00erentiate between accretion of cold streams or gas cooling from the hot halo. Simulations indicate, not shown here, the cold gas in\ufb02ow rate is on the order of and on average exceeds the star formation rate. \u2013 6 \u2013 0 1 2 3 4 5 6 7 8 0 0.1 0.2 0.3 0.4 0.5 PDF     z=3\u22124  1010\u221211  1011\u221212 0 1 2 3 4 5 6 7 8 0 0.1 0.2 0.3 0.4 0.5     z=2\u22123  1010\u221211  1011\u221212 0 1 2 3 4 5 6 7 8 0 0.1 0.2 0.3 0.4 0.5 N90 PDF     z=1\u22122  1010\u221211  1011\u221212 0 1 2 3 4 5 6 7 8 0 0.1 0.2 0.3 0.4 0.5 N90     z=0.62\u22121  1010\u221211  1011\u221212 Fig. 2.\u2014 shows the probability distribution functions (PDFs) of N90 in four separate redshift ranges, z = 3 \u22124 (top-left panel), z = 2 \u22123 (top-right panel), z = 1 \u22122 (bottom-left panel) and z = 0.62 \u22121 (bottom-right panel). In each panel, two di\ufb00erent stellar mass ranges are shown, 1010 \u22121011 M\u2299(blue histograms) and 1011 \u22121012 M\u2299(red histograms). The vertical dashed lines indicate the median of the PDF of the same color. Figure 4 shows the PDF of dimensionless spin parameter \u03bb (\u2261j/\u221a2GMvrv) for individual streams in the top N90, where j is the mass \ufb02ux-weighted mean speci\ufb01c angular momentum of a stream, and Mv and rv are the virial mass and radius of the galaxy. One feature is observed to stand out: lower mass galaxies (blue histograms) tend to have streams with higher \u03bb than more mass galaxies (red histograms). Whether this trend has some bearing on the dominance of elliptical galaxies at the high mass end among galaxies should be clari\ufb01ed with further studies. For the high stellar galaxies of 1011 \u22121012 M\u2299(red histograms) \u03bb evolves little over the entire redshift range, whereas the less massive subset (1010 \u22121011 M\u2299, blue histograms) displays a steady increase of \u03bb from z = 4 to z = 0.62. It is intriguing that the fraction of \u03bb exceeding 1 is substantial at z \u22642, which is likely instrumental to the emergence of large-scale spiral structures below z = 2. Figure 5 shows the PDF of mean density of in\ufb02ow cold gas. Three trends are noted. First, the stream density depends strongly on redshift, with the median being \u223c10\u22122cm\u22123 at z = 2 \u22124, \u223c10\u22123 \u221210\u22122.5cm\u22123 at z = 1 \u22122 and 10\u22123.5 \u221210\u22123cm\u22123 at z = 0.62 \u22121. Second, while the more massive galaxies, on average, tend to have somewhat higher stream gas density than less massive galaxies at lower redshift (z = 0.6 \u22121), the di\ufb00erence gradually diminishes towards higher redshift. This particular trend, while slightly puzzling, can be reconciled if there is a natural selection e\ufb00ect where strong streams can survive in the midst of gravitational heating environment. Third, at z = 0.62 \u22121 there is a dramatic increase of galaxies with very low density streams, which likely re\ufb02ects the increased importance of hot accretion at low redshift. \u2013 7 \u2013 0 25 50 75 100 125 150 0 0.1 0.2 PDF     z=3\u22124  1010\u221211  1011\u221212 0 25 50 75 100 125 150 0 0.1 0.2     z=2\u22123  1010\u221211  1011\u221212 0 25 50 75 100 125 150 0 0.1 0.2 0.3 0.4 0.5 0.6 \u02d9 M90 (M\u2299/yr) PDF     z=1\u22122  1010\u221211  1011\u221212 0 25 50 75 100 125 150 0 0.1 0.2 0.3 0.4 0.5 0.6 \u02d9 M90 (M\u2299/yr)     z=0.62\u22121  1010\u221211  1011\u221212 Fig. 3.\u2014 shows the PDF of cold in\ufb02ow rate per stream, \u02d9 M90, de\ufb01ned to be 90% of the total cold accretion rate divided by N90, for four separate redshift ranges, z = 3\u22124 (top-left panel), z = 2\u22123 (top-right panel), z = 1\u22122 (bottom-left panel) and z = 0.62\u22121 (bottom-right panel). In each panel, two di\ufb00erent stellar mass ranges are shown, 1010 \u22121011 M\u2299(blue histograms) and 1011 \u22121012 M\u2299 (red histograms). The vertical dashed lines indicate the median of the PDF of the same color. 4. A New Physical Scenario for the Emergence of the Hubble Sequence The quantitative, new characterizations and trends presented in \u00a73 on cold gas streams their number, mass \ufb02ux, density and angular momentum provide the physical basis to construct a working framework. Rather than detailed quantitative descriptions, which are beyond the scope of this Letter and will be carried out separately, we provide a set of three key physical elements as a useful guide to investigating, in the context of the standard cold dark matter model, the general morphological trends of galaxies with redshift the emergence of the Hubble sequence. A consequential but necessary ansatz is that the formation of prominent spiral structures as well as star formation in galaxies have cosmological origins and are primarily fed by cold streams. \u2022 Origin of Small, Clumpy Galaxies at z > 2 While galaxy mergers and interactions may play varying roles, ultimately, the morphological traits of galaxy formation are expected to be largely governed by the nature of gas supply and dynamics, with feedback perhaps playing a role of regulation of the quantity of star formation. Given that most galaxies at z > 2 have N90 \u22652 cold gas streams of high gas density (ngas) that is more conducive to fragmentations (e.g., Dekel et al. 2009b), the expectation is that feeding of and interactions between multiple concurrent streams at high redshift would result in a population of galaxies with fragmented, clumpy and frequently multiple (gaseous and stellar) disks. This is in line with the observed increasing dominance of a mixture of disk-like, irregular and clumpy galaxies towards high redshift (e.g., F\u00a8 orster Schreiber et al. 2009; \u2013 8 \u2013 0 1 2 3 4 0 0.1 0.2 PDF     z=3\u22124  1010\u221211  1011\u221212 0 1 2 3 4 0 0.1 0.2     z=2\u22123  1010\u221211  1011\u221212 0 1 2 3 4 0 0.1 0.2 h PDF     z=1\u22122  1010\u221211  1011\u221212 0 1 2 3 4 0 0.1 0.2 h     z=0.62\u22121  1010\u221211  1011\u221212 Fig. 4.\u2014 shows the PDF of \u03bb (\u2261j/\u221a2GMvrv) for individual streams in the top N90, for four separate redshift ranges, z = 3 \u22124 (top-left panel), z = 2 \u22123 (top-right panel), z = 1 \u22122 (bottomleft panel) and z = 0.62 \u22121 (bottom-right panel). In each panel, two di\ufb00erent stellar mass ranges are shown, 1010 \u22121011 M\u2299(blue histograms) and 1011 \u22121012 M\u2299(red histograms). The vertical dashed lines indicate the median of the PDF of the same color. Chevance et al. 2012; Murata et al. 2014). Interactions of streams are e\ufb00ective at producing low angular momentum gas, with the expectation that galaxies at high redshift are disproportionately small in size compared to their low redshift counterparts, a trend that is observed (e.g., Trujillo et al. 2006) and seen in simulations (e.g., Joung et al. 2009). \u2022 Emergence of Spiral Structures at z \u22642 Galaxies have multiple concurrent cold streams (N90) of high accretion rates ( \u02d9 M90), lower angular momenta (\u03bb) and high gas densities (ngas) at z > 2, each of which is detrimental to the formation of grand spiral structures. It appears that nature has arranged against grand design spiral formation at high redshift with plenty of insurance. While one can not come up with a set of su\ufb03cient conditions for the emergence of grand design spirals, it seems physically reasonable to assume that not having more than one concurrent major cold streams is requisite for the emergence of grand design spirals. Our analysis indicates that this condition is expected to occur at z \u22641, suggesting that major spiral galaxies begin to emerge at z \u22641. The signi\ufb01cantly larger \u03bb for galaxies in the stellar mass range 1010\u221211 M\u2299than 1011\u221212 M\u2299(see Figure 4) is interesting, implying that the largest galaxies in the universe at any redshift possess less favorable conditions to form large spirals. Between z = 1 \u22122, about one half of the galaxies have one or two concurrent streams, which we suggest give rise to \ufb02occulent spirals stemming from a collection of disjoint but relatively frequent in\ufb02ow streams. These expectations are in agreement with extant observational indications (e.g., Elmegreen & Elmegreen 2014). \u2013 9 \u2013 \u22126 \u22125 \u22124 \u22123 \u22122 \u22121 0 0 0.1 PDF     z=3\u22124  1010\u221211  1011\u221212 \u22126 \u22125 \u22124 \u22123 \u22122 \u22121 0 0 0.1     z=2\u22123  1010\u221211  1011\u221212 \u22126 \u22125 \u22124 \u22123 \u22122 \u22121 0 0 0.1 0.2 0.3 log ngas (cm\u22123) PDF     z=1\u22122  1010\u221211  1011\u221212 \u22126 \u22125 \u22124 \u22123 \u22122 \u22121 0 0 0.1 0.2 0.3 log ngas (cm\u22123)     z=0.62\u22121  1010\u221211  1011\u221212 Fig. 5.\u2014 shows the PDF of mean density of in\ufb02ow cold gas in four separate redshift ranges, z = 3\u22124 (top-left panel), z = 2\u22123 (top-right panel), z = 1\u22122 (bottom-left panel) and z = 0.62\u22121 (bottomright panel). In each panel, two di\ufb00erent stellar mass ranges are shown, 1010 \u22121011 M\u2299(blue histograms) and 1011 \u22121012 M\u2299(red histograms). The mean density is averaged over all streams for each individual galaxy, weighted by in\ufb02ow mass \ufb02uxes of individual streams. The vertical dashed lines indicate the median of the PDF of the same color. \u2022 Conditions for Early Type Galaxy Formation The physical conditions for the emergence of early type galaxies are naturally diametrically opposed to those of irregular galaxies. For early type galaxies there is no cold gas stream with no recurrence. This condition is physically more natural than the proposed transition to hot accretion based on halo mass threshold (Kere\u02c7 s et al. 2005; Dekel & Birnboim 2006; Nelson et al. 2013), which would be inconsistent with signi\ufb01cant star formation in massive galaxies at high redshift (Dekel et al. 2009a). High density environment is shown to be a good proxy for the emergence of early type galaxies (Cen 2014b). Because of the association of massive halos with high overdensities of large-scale structure, more massive early type galaxies are expected to have emerged earlier, consistent with observations (e.g., Mortlock et al. 2013). For the same reason, early type galaxies are expected to be somewhat older in clusters than in \ufb01eld, in agreement with observations (e.g., Thomas et al. 2005). One also expects that, while early type galaxies occur at all redshifts, their abundance is expected to increase with decreasing redshift as more regions become dynamically hot, in agreement with observations (e.g., Renzini 2006). However, below z \u223c1 the rate of increase of the abundance of giant ellipticals is expected to drop o\ufb00, as the nonlinear Mnl starts to signi\ufb01cantly exceed the mass scales of giant ellipticals, in agreement with observations (e.g., Borch et al. 2006). \u2013 10 \u2013 The analysis program yt (Turk et al. 2011) is used to perform some of the analysis. Computing resources were in part provided by the NASA HighEnd Computing (HEC) Program through the NASA Advanced Supercomputing (NAS) Division at Ames Research Center. This work is supported in part by grant NASA NNX11AI23G.",
                    "introduction": "Despite the commendable successes, a systematic physical theory for the origin of the Hubble (1926) sequence - the holy grail of galaxy formation - remains elusive. While the greatly increased richness in observational data has prompted revisions in the classi\ufb01cation (van den Bergh 1976; Sandage & Binggeli 1984; Cappellari et al. 2011; Kormendy & Bender 2012) that have provided more coherence along each sequence and counterpart identi\ufb01cations across di\ufb00erent sequences (e.g., S0 versus S sequences), it has not, for the most part, signi\ufb01cantly improved the clarity of our physical understanding of the Hubble sequence. It seems that this perpetual state of perplexity does not stem from lack of freedom to parameterize input physics, such as in the semi-analytic and other 1Princeton University Observatory, Princeton, NJ 08544; cen@astro.princeton.edu arXiv:1405.0516v1  [astro-ph.GA]  2 May 2014 \u2013 2 \u2013 phenomenological approaches. Rather, there are key physical ingredients that are not understood to even be parameterized. One such physical ingredient is the environment, which is a hard problem to address computationally, due to the twin requirements of capturing large-scale environment and small-scale structure, and di\ufb03cult to parameterize due to diversity. Our recent analysis has shown that the quenching and color migration for the vast majority of galaxies may be primarily due to environment e\ufb00ects (Cen 2014b), which has recently received signi\ufb01cant observational support (e.g., Lin et al. 2014; Carollo et al. 2014; Muzzin et al. 2014). There are enough both direct evidence and theoretical insights gained in galaxy interactions (e.g., Mihos & Hernquist 1996) or analytic analyses (e.g., Fall & Efstathiou 1980; Mo et al. 1998) to conclude that angular momentum is another key physical ingredient in galaxy formation theory. The possibility that the angular momentum dynamics of gas accretion is complex in a cosmological setting and di\ufb00erent from that of dark matter (Bullock et al. 2001) is under-appreciated. Recent studies begin to show that angular momentum dynamics of gas and stars in the inner regions are only loosely, at best, related to that of dark matter halos (e.g., Hahn et al. 2010; Cen 2014a). One could suggest that the diversity of galaxies and its evolution - the Hubble sequence and its emergence - may be substantially governed by the complexity and trends of dynamics of cold (T < 105K) gas streams with respect to their number, mass \ufb02ux, density and angular momentum, since they provide the main fuel for galaxy formation. Such suggestion is, so far, without formal proof. This study provides analyses on cold streams, utilizing a large sample of ultra-highly resolved galaxies from an ab initio Large-scale Adaptive-mesh-re\ufb01nement Omniscient Zoom-In cosmological hydrodynamic simulation (LAOZI) of the standard cold dark matter model. It is shown that the cold gas accretion \ufb02ows display physical trends that can provide a self-consistent account for the origin of the emergence of the Hubble sequence. This study is built on insights from recent innovative work (Kere\u02c7 s et al. 2005; Dekel & Birnboim 2006; Nelson et al. 2013) that suggests, to varying degrees, a two-mode gas accretion onto galaxies, in contrast to the classic description of gas cooling following virialization heating (Rees & Ostriker 1977; Silk 1977; Binney 1977; White & Rees 1978). There are currently signi\ufb01cant quantitative di\ufb00erences concerning the cold streams from di\ufb00erent simulation groups (see references above), which may be, in part, due to di\ufb00erent tracking methods. The method for identifying cold gas streams described in \u00a72 may be used to enable a uniform comparison."
                },
                {
                    "url": "http://arxiv.org/abs/1403.5274v1",
                    "title": "Frequent Spin Reorientation of Galaxies due to Local Interactions",
                    "abstract": "We study the evolution of angular momenta of ($M_*=10^{10}-10^{12}\\msun$)\ngalaxies utilizing large-scale ultra-high resolution cosmological hydrodynamic\nsimulations and find that spin of the stellar component changes direction\nfrequently, caused by major mergers, minor mergers, significant gas inflows and\ntorques by nearby systems. The rate and nature of change of spin direction can\nnot be accounted for by large-scale tidal torques, because the latter fall\nshort in rates by orders of magnitude and because the apparent random swings of\nthe spin direction are inconsistent with alignment by linear density field. The\nimplications for galaxy formation as well as intrinsic alignment of galaxies\nare profound. Assuming the large-scale tidal field is the sole alignment agent,\na new picture emerging is that intrinsic alignment of galaxies would be a\nbalance between slow large-scale coherent torquing and fast spin reorientation\nby local interactions. What is still open is whether other processes, such as\nfeeding galaxies with gas and stars along filaments or sheets, introduce\ncoherence for spin directions of galaxies along the respective structures.",
                    "authors": "Renyue Cen",
                    "published": "2014-03-20",
                    "updated": "2014-03-20",
                    "primary_cat": "astro-ph.CO",
                    "cats": [
                        "astro-ph.CO",
                        "astro-ph.GA"
                    ],
                    "main_content": "The reader is referred to Cen (2014) for detailed descriptions of our simulations and validations. Briefly, we perform cosmological simulations with the adaptive mesh refinement hydrocode, Enzo (The Enzo Collaboration et al. 2013). The periodic box has a size of 120h\u22121Mpc, within which a zoom-in box of a comoving size of 21 \u00d7 24 \u00d7 20h\u22123Mpc3 is emdedded. The resolution is better than 114h\u22121pc (physical). The cosmological parameters are the same as the WMAP7-normalized (Komatsu et al. 2010) \u039bCDM model. We identify galaxies using the HOP algorithm (Eisenstein & Hut 1998) operating on the stellar particles. A sample of \u2265300 galaxies with stellar masses greater than 1010 M\u2299are used. For each galaxy at z = 0.62 a genealogical line is constructed from z = 0.62 to z = 6 by connecting galaxy catalogs at a series of redshifts. Galaxy catalogs are constructed from z = 0.62 to z = 1.40 at a redshift increment of \u2206z = 0.02 (corresponding to \u2206t = 81Myr at z = 1) and from z = 1.40 to z = 6 at a redshift increment of \u2206z = 0.05 (corresponding to \u2206t = 80Myr at z = 2). The parent of each galaxy is identified with the one at the next higher redshift catalog that has the most overlap in stellar mass. We compute the specific angular momentum vector \u20d7 ji for stars of each galaxy within a radius r at each output snapshot i. The time derivative of \u20d7 ji is computed as |d\u20d7 ji/dt| \u2261|\u20d7 ji+1 \u2212\u20d7 ji|/(ti+1 \u2212ti). (1) One notes that due to the finite number of outputs for our simulation data, d\u20d7 j\u2217/dt is somewhat underestimated in cases of rapid changes of angular momentum on time scales shorter than our snapshot intervals. A similar definition for gas is also used. We denote t1 as the time required to change the spin vector by 1 degree of arc at each snapshot for each galaxy, defined as t1 \u2261 \u03c0 180(ti+1 \u2212ti)acos\u22121(\u02c6 ji+1 \u00b7 \u02c6 ji), (2) \u03c0 180(ti+1 \u2212ti)acos\u22121(\u02c6 ji+1 \u00b7 \u02c6 ji), (2) where \u02c6 ji is the unit vector of \u20d7 ji. For the first time, we address the evolution of the spin of galaxies statistically in a cosmological setting. All length units below will be physical. 3. Results Figure 1 shows the dot product of the unit vector of the specific angular momentum of the central 3kpc radius stellar region and an arbitrary fixed unit vector as a function of \u2013 3 \u2013 0.5 1 2 3 4 5 \u22121 \u22120.5 0 0.5 1 \u02c6 j\u2217\u00b7 \u02c6 n     log M*=11.65 log M* 0.5 1 2 3 4 5 \u22121 \u22120.5 0 0.5 1 log M*=11.16 0.5 1 2 3 4 5 \u22121 \u22120.5 0 0.5 1 \u02c6 j\u2217\u00b7 \u02c6 n log M*=10.99 0.5 1 2 3 4 5 \u22121 \u22120.5 0 0.5 1 log M*=10.88 0.5 1 2 3 4 5 \u22121 \u22120.5 0 0.5 1 \u02c6 j\u2217\u00b7 \u02c6 n z log M*=10.5 0.5 1 2 3 4 5 \u22121 \u22120.5 0 0.5 1 z log M*=10.25 Fig. 1.\u2014 shows in blue the dot product of the unit vector of the speci\ufb01c angular momentum of the central 3kpc stellar region and an arbitrary \ufb01xed (in time) unit vector as a function of redshift. Each panel shows a random galaxy with its \ufb01nal stellar mass at z = 0.62 as indicated at the top of the panel. Also shown in each panel as a red dashed line is the logarithm of the stellar mass with an arbitrary vertical o\ufb00set. redshift in blue. It is visible that a signi\ufb01cant increase in stellar mass within a short period of time (i.e., mergers) is often accompanied by dramatic changes in angular momentum vectors. We note that the angular momentum vector of a galaxy over its history displays a substantial amount of change even in \u201cquiet\u201d times without major mergers. Ensuing analysis provides some physical insight into this. The top panel of Figure 2 shows the PDF of the time derivative of speci\ufb01c angular momentum of the central 3kpc radius stellar regions for galaxies of stellar mass in the range 1011 \u22121012 M\u2299. The middle panel shows the same as in the top panel, except it is for the central 7kpc radius stellar regions. We see that the overall rate of change of angular momenta is signi\ufb01cantly higher at z = 1 \u22123 compared to that at z = 0.6 \u22121. The distribution of |d\u20d7 j\u2217/dt| has an extended tail at the high-end, due to major mergers; due to our \ufb01nite time sampling these rates are capped by the frequency of our snapshots. \u2013 4 \u2013 1 2 3 4 0 0.1 0.2 log|d\u20d7 j\u2217(3kpc )/dt| (kpc km/s/Gyr) PDF     z=0.62\u22121 z=1\u22122 z=2\u22123 1 2 3 4 0 0.1 0.2 log|d\u20d7 jg as(3kpc )/dt| (kpc km/s/Gyr) PDF Ms = 1011 \u22121012M\u2299 1 2 3 4 0 0.1 0.2 log|d\u20d7 j\u2217(7kpc )/dt| (kpc km/s/Gyr) PDF Fig. 2.\u2014 Top panel: the probability distribution function (PDF) of the amplitude of the time derivative of speci\ufb01c angular momentum of the central 3kpc radius stellar regions (see Eq 1) for galaxies of total stellar mass in the range 1011 \u22121012 M\u2299in three di\ufb00erent redshift ranges, z = 0.62 \u22121 (black histograms), z = 1 \u22122 (red histograms), z = 2 \u22123 (green histograms), respectively. As an intuitive example, if a Milky Way-like galaxy of size 10kpc and rotation velocity of 200km/s changes its spin direction by 90 degress in one current Hubble time, it would correspond to a value log |dj/dt| equal to 2.3 in the x-axis. Middle panel: same as the top panel but for the central 7kpc radius stellar region. Bottom panel: same as the top panel but for gas in the central 3kpc radius region. Consistent with the expected decline of major merger rate below z \u223c1, the high |d\u20d7 j\u2217/dt| tail of the distribution at z = 0.6\u22121 is signi\ufb01cantly less pronounced. No major di\ufb00erence is seen between 3kpc and 7kpc cases, suggesting that angular momentum changes within the two radii are approximately in tandem and our analysis is robust using 3kpc. The choice of 3\u22127 proper kpc is appropriate by noting that a (spiral, elliptical) galaxy of stellar mass 1012 M\u2299 is observed to have a size of (10.8, 15.1)kpc (Shen et al. 2003) for low redshift galaxies. The size roughly scales with the root of the stellar mass and decreases with increasing redshift (e.g., Trujillo et al. 2006). \u2013 5 \u2013 \u22123 \u22122 \u22121 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 log CPDF     mass and redshift dependence  1011\u221212, z=0.62\u22121  1011\u221212, z=1\u22122  1011\u221212, z=2\u22123  1010\u221211, z=0.62\u22121  1010\u221211, z=1\u22122  1010\u221211, z=2\u22123 \u22123 \u22122 \u22121 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 log CPDF     all Ms=1010\u221211Msun environment dependence  b=1\u221210,z=0.62\u22121  b=102\u2212103,z=0.62\u22121  b=1\u221210,z=1\u22122  b=102\u2212103,z=1\u22122 \u22123 \u22122 \u22121 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 log t1 (Gyr) log CPDF     all Ms=1010\u221211Msun galaxy type dependence  blue,z=0.62\u22121  blue,z=1\u22122  blue,z=2\u22123  red,z=0.62\u22121  red,z=1\u22122  red,z=2\u22123 Fig. 3.\u2014 Top panel: shows the cumulative PDF (CPDF) of the time taken to change the direction of spin of the central 3kpc radius stellar region by 1 degree of arc, t1 (Eq 2) for galaxies of total stellar mass in the range 1010 \u22121011 M\u2299(blue curves) and 1011 \u22121012 M\u2299 (red curves) in three di\ufb00erent redshift ranges, z = 0.62 \u22121 (solid curves), z = 1 \u22122 (dotted curves), z = 2 \u22123 (dashed curves), respectively. Middle panel: shows the of t1 for galaxies of total stellar mass in the range 1010 \u22121011 M\u2299in low-density (\u03b40.5 = 1 \u221210); solid curves) and high-density environment (\u03b40.5 = 102 \u2212103); dotted curves), in two redshift rangess, z = 0.62 \u22121 (black curves) and z = 1 \u22122 (magenta curves), respectively. The environment overdensity \u03b40.5 is de\ufb01ned to be the overdensity of total matter in a sphere of radius 0.5h\u22121Mpc comoving. Bottom panel: shows the CPDF of t1 for blue (g \u2212r < 0.6; blue curves) and red (g \u2212r > 0.6, red curves) galaxies of total stellar mass in the range 1010 \u22121011 M\u2299in three di\ufb00erent redshift ranges, z = 0.62 \u22121 (solid curves), z = 1 \u22122 (dotted curves), z = 2 \u22123 (dashed curves), respectively. \u2013 6 \u2013 The bottom panel of Figure 2 shows the PDF for gas in the central 3kpc radius region. We see that the speci\ufb01c angular momenta of the gas within central 3kpc change at rates 5 \u221210 times higher than that of stars (top panel of Figure 2). There is no doubt that gas in\ufb02ows contribute signi\ufb01cantly to the change of the stellar angular momentum in two ways. First, signi\ufb01cant gas in\ufb02ows at inclined angles to the stellar mid-plane may torque the stars (and vice versa). Second, new gas that reaches there will form new stars that have di\ufb00erent angular momentum vector and cause the overall angular momentum to change in both direction and magnitude. At high redshift the orientation of the gas in\ufb02ows on large scales are not well correlated with that of the stars or gas that is already there. Since the amount of gas tend to be smaller than that of stars, it is easier to alter the angular momentum of the gas than that of the stars. In the absence of major mergers, we expect minor stellar mergers could also alter the angular momentum vector. Figure 3 shows the CPDF of the time to change the direction of spin of the central 3kpc radius stellar region by 1 degree of arc, for dependence on mass and redshift (top panel), environment (middle panel) and galaxy type (bottom panel). Consistent with Figure 2 we see that the frequency of spin direction change increases with redshift; the median t1 decreases by 60\u221280% from z = 0.62\u22121 to z = 2\u22123 with the higher mass group corresponding to the high end of the range of change. The median t1 decreases by 10\u221220% from Ms = 1011\u221212 M\u2299 to Ms = 1010\u221211 M\u2299with the dependence on mass somewhat stronger at low redshift than at high redshift. That less massive galaxies tend to experience more rapid changes of speci\ufb01c angular momenta is anecdotally apparent in Figure 3. We also \ufb01nd large mis-alignment between inner stellar (and gas) regions with outer halos (not presented here), in broad agreement with the conclusions of Hahn et al. (2010). A dependence on environment is seen in the middle panel, with the median t1 decreasing by a factor of 1.9 \u22122.7 from \u03b40.5 = 1 \u221210 to \u03b40.5 = 102 \u2212103; the environment dependence weakens at higher redshift. This \ufb01nding that the spin direction of galaxies changes more frequently in dense environment can be attributed to enhanced local interactions there. In the bottom panel the dependence on galaxy type gives mixed trends. For blue (g \u2212r < 0.60) galaxies the median t1 decreases steadily from z = 2 \u22123 to z = 0.62 \u22121 by a factor of \u223c2.3, whereas for red (g \u2212r > 0.60) galaxies the median t1 hardly changes from z = 2\u22123 to z = 0.62\u22121. The median t1 for red galaxies is comparable to that of blue galaxies at z = 2\u22123; at lower redshift the median t1 for red galaxies becomes progressively lower compared to that of blue galaxies, mainly due to the latter increasing with decreasing redshift. In Cen (2014) we show that the vast majority of red galaxies do not gain signi\ufb01cant stellar mass in the red sequence. Thus we conclude that the rapid change of spin direction for red galaxies are due to torques by nearby galaxies, whereas blue galaxies are subject to all three local interactions gas accretion, stellar accretion and torques. It is instructive to put the frequency of spin direction change into some perspective. For \u2013 7 \u2013 a point mass of M at a distance d, the torque of M on the galaxy with a quadrupole moment Q and angular momentum \u20d7 J is \u03c4 = | d \u20d7 J dt | = 3 4 GMQ d3 sin(2\u03b8) (e.g., Peebles 1969), where \u03b8 is the angle between the separation vector and the symmetry axis of the galaxy. Expressing \u03c4 in terms of overdensity \u03b4 of the region centered on mass M, \u03c4 = \u03c0G\u03c10(1+z)3\u03b4Q sin(2\u03b8), where z is redshift, \u03c10 the mean mass density at z = 0. Approximating spirals as \ufb02at axisymmetric uniform disks with a = b = \u221ec (giving the quadrupole moment of Q = 2ma2/5) and full rotation support. This allows to express the torquing time tq, de\ufb01ned to be the time taken to change the spin direction by 1 degree of arc, tq = \u03c0 180 |\u20d7 j\u2217|m \u03c4(z, m, T), (3) giving tq = 2.5Gyr for \u03b4 = 200, z = 1 and sin(2\u03b8) = 1 for spiral galaxies. Comparing to the median t1 \u223c10\u22123 \u221210\u22122Gyr seen in Figure 3, it is evident that the rapid spin reorientation of galaxies can not possibly be due to tidal torques by large-scale structure. It is noted that the intrinsic alignment sourced by primordial large-scale gravitational \ufb01eld is inconsistent with the frequent directional change shown in Figure 1. Under the (unproven) assumption that the large-scale tidal \ufb01eld is the sole alignment agent, any alignment between galaxies on large-scales would result from a balance between the fast reorientation rate due to local processes and slow coherent torques by large-scale structure, which is expressed as the ratio t1 to tq, denoted as t1/(t1+tq). If the quadrupole of the galaxy is, in this case, produced by loal interactions, independent of the large-scale tidal \ufb01eld, the alignment in this simpli\ufb01ed model would be linear [instead of quadratic, see Hirata & Seljak (2004)] to the large-scale gravitational tidal \ufb01eld. We obtain \ufb01nally the expression for the mean value of t1/(t1 + tq) weighted by the distribution of t1 [P(t1), shown in Figure 3], denoted as \u03b7(z, m, T): \u03b7(z, m, T) \u2261 Z \u0012 t1 t1 + tq(z, m, T) \u0013 Pz,m,T(t1)dt1, (4) at redshift z for galaxies of mass m and type T (spiral or elliptical). We approximate elliptical galaxies as oblate axisymmetric spheroids with a = b = 2c and vrot/\u03c3 = 0.2, resulting in the quadrupole moment of Q = 3ma2/10. The sizes of galaxies are adopted from observations by Shen et al. (2003). The bias factor is from Tegmark et al. (2004) adjusted to \u03c38 = 0.8. The stellar mass to light ratio as a function of absolute magnitude is taken from from Kau\ufb00mann et al. (2003). We incorporate these into \u03c4 to get \u03c4(z, m, T) = \u03c0G\u03c10(1 + z)3D+(z)b(m)Q(m, T)[\u03b4 sin(2\u03b8)] (5) as well as into j in Equations (3) for di\ufb00erent galaxy types, where D+(z) is the linear density growth factor normalized to be unity at z = 0, b(m) is the bias factor of galaxies of mass m, \u2013 8 \u2013 10 11 12 \u22125 \u22124 \u22123 \u22122 logM\u2217(M\u2299) \u03b7(z, m, T )     ellipticals z=0.62\u22120.78 spirals z=0.62\u22120.78 ellipticals z=0.8\u22121.2 spirals z=0.8\u22121.2 ellipticals z=1.5\u22122.5 spirals z=1.5\u22122.5 Fig. 4.\u2014 shows \u03b7 (see Equation 4 for de\ufb01nition) as a function of galaxy mass and type at three di\ufb00erent redshift ranges. Spiral and elliptical galaxies are shown are shown in blue and red, respectively, for z = 0.62 \u22120.78 (solid dots), z = 0.8 \u22121.2 (open squares) and z = 1.5 \u22122.5 (stars). The model results are obtained using [\u03b4 sin(2\u03b8)] = 1 (see Equation 5). The errorbars in the x-axis indicate the mass bin sizes. The results using Equation (4), in conjunction with Equations (3, 5), are shown in Figure 4. As in the linear alignment model (e.g., Catelan et al. 2001), the di\ufb03culty is to de\ufb01ne a demarcating scale between local and linear large-scale structures. We tentatively have left the scalings to be relative, absorbed into [\u03b4 sin(2\u03b8)]. If compelled to give an estimate relevant to weak lensing, one might choose [\u03b4 sin(2\u03b8)] to be in the range 1\u221210. In this case, we get a tangential sheer \u03b3T that is 1\u221210 times \u03b7 in Figure 4, resulting in \u03b3T of \u2212(0.2\u22122)% for the most massive elliptical galaxies (i.e., luminous red galaxies, LRGs, red dots in Figure 4), which, coincidentally, falls in the range of observed GI (galaxy-gravitational tidal \ufb01eld) signal for LRGs (e.g., Mandelbaum et al. 2006; Hirata et al. 2007; Joachimi et al. 2011). The negative sign comes about, because the galaxies, under the torque of a central mass, have a tendency to align their disks in the radial direction that is dynamically stable. Three separate trends with respect to z, m and T are seen: the alignment (1) decreases with increasing redshift, (2) decreases with decreasing stellar mass, and (3) is larger for \u2013 9 \u2013 elliptical galaxies than for spiral galaxies. The \ufb01rst two trends are accounted for by trends of t1 seen in Figure 3. The last trend requires some discussion. The bottom panel of Figure 3 shows that ellipticals have shorter t1 than spirals, due to a large part to their residing in overdense environments and in addition to their having a lower overall speci\ufb01c angular momentum amplitude. However, also because the speci\ufb01c angular momentum of ellipticals is a factor of 5 lower than that of spiral galaxies, elliptical galaxies are easier to slew. It is argubly a relatively more straight-forward comparison to observations of (radial) alignments of satellite galaxies with respect to the central galaxies of groups and clusters. But this is in fact complicated by (at least) four issues. First, the observed detection and non-detection of radial alignment of galaxies around groups and clusters of galaxies concern radial ranges that are already mostly in the nonlinear regime (i.e., overdensity \u03b4 \u226b1). Second, most of the observed galaxy samples analyzed contain of order 100-10000 galaxies, hence statistical uncertainties are in the range of 1 \u221210%. Third, observed samples likely contain a large number of projected galaxies with physical separations that are much larger than their lateral distance from the cluster/group center; the degree of projection e\ufb00ects is strongly dependent on the orientation of the line of sight (e.g., viewing a cluster along a \ufb01lament) and signi\ufb01cantly complicates interpretation of results. Fourth, on some very small scales, binary interactions between a satellite and the central galaxy may play the dominant role. A combination of these factors may explain the current confused state with con\ufb02icting observational results (e.g., Bernstein & Norberg 2002; Pereira & Kuhn 2005; Agustsson & Brainerd 2006; Torlina et al. 2007; Faltenbacher et al. 2007; Hao et al. 2011). Nonetheless, we expect that the radial alignment, if exists, is expected to decrease with increasing redshift, perhaps already hinted by some observations (e.g., Hung & Ebeling 2012), and with decreasing cluster mass at a \ufb01xed radius. The simple model presented has two notable caveats. First, it assumes that the only alignment mechanism is gravitational torque by some large-scale structure. So far we have presented only the relative scalings among di\ufb00erent galaxies under this assumption, but not the absolute magnitude. We cannot justify this rather critical assumption with con\ufb01dence at this time. Second, one notes that a signi\ufb01cant portion of the galaxy spin direction reorientation is likely due to gas feeding and substructure merging. Thus, it is not unreasonable to expect that the gas feeding and substructure merging have some preferred directions, such as along the \ufb01laments and sheets. In this case, while galaxy spin direction changes frequenctly as shown here, it may do so with some degree of coherence over some scales (such as the scale of \ufb01laments), either temporaneously or through long-term memory of large-scale structure (e.g., Libeskind et al. 2012). If this were true, it then suggests that intrinsic alignments may be a result of balance between high-frequency random re-orientation at short time scales and some sort of large-scale \u201cmean\u201d feeding pattern on long time scales. There is some empirical evidence for galaxies to be aligned with large-scale structures in a sense that is consistent with this \u201cfeeding\u201d picture (e.g., Zhang et al. 2013; Li et al. 2013). It should be a priority \u2013 10 \u2013 to understand this issue systematically. 4. Conclusions Utilizing ab initio Large-scale Adaptive-mesh-re\ufb01nement Omniscient Zoom-In cosmological hydrodynamic simulations (LAOZI Simulation) of the standard cold dark matter model, we study the evolution of angular momenta of massive (M\u2217= 1010 \u22121012 M\u2299) galaxies. The simulation has an ultra-high resolution of \u2264114pc/h and contains more than 300 galaxies with stellar mass greater than 1010 M\u2299. We \ufb01nd that spin of the stellar component changes direction frequently, caused by major mergers, minor mergers, signi\ufb01cant gas in\ufb02ows and torques by nearby systems, with a median time in the range 1 \u221210Myr for directional change of spin vector by 1 degree of arc. The spin of the gas component changes at a factor of 5\u221210 higher rates than the stellar component. Because the processes that are responsible are mostly in the nonlinear regime. we do not expect that the \ufb01ndings signi\ufb01cantly depend on precise cosmological parameters, The rate of change of spin direction can not be accounted for by large-scale tidal torques, because the latter fall short in rates by 2 \u22123 orders of magnitude. In addition, the nature of change of spin direction apparent random swings is inconsistent with alignment by linear density \ufb01eld. A new paradigm emerging with respect to intrinsic alignment of galaxies is that it is determined, primarily, by a balance between slow large-scale coherent torquing (if it were the sole alignment process) and fast spin reorientation by local interactions. This suggests that a signi\ufb01cant revision to the large-scale tidal torque based alignment theory is perhaps in order. A simple analysis presented here indicates that intrinsic alignment of galaxies is dependent on redshift, luminosity, environment and galaxy type. Speci\ufb01cally, it is found that the alignment (1) decreases with increasing redshift, (2) decreases with decreasing stellar mass, and (3) is larger for elliptical galaxies than for spiral galaxies. While no detailed comparisons are made, the found trends appear to be broadly consistent with and thus provide the physical basis for the observed trends. What remains open is whether other processes, such as feeding galaxies with gas and stars along \ufb01laments or sheets, introduce some coherence of their own kind for spin direction of galaxies along the respective structures. This will require a separate study in greater detail. I would like to thank Claire Lackner for providing the SQL based merger tree construction software, and (Turk et al. 2011) for providing the very useful analysis and visualization program yt. Computing resources were in part provided by the NASA High-End Computing \u2013 11 \u2013 (HEC) Program through the NASA Advanced Supercomputing (NAS) Division at Ames Research Center. This work is supported in part by grant NASA NNX11AI23G. The simulation data are available from the author upon request.",
                    "introduction": "The angular momentum or spin of galaxies is a physical quantity that is far from being fully understood but is of fundamental importance to galaxy formation and cosmological applications. While N-body simulations have shed useful light on spin properties of dark matter halos (e.g., Vitvitska et al. 2002), it is expected that, given the vastly di\ufb00erent scales between the stellar component and dark matter halo component and di\ufb00erent physical pro- cesses governing stellar, gas and dark matter components, the angular momentum dynamics of galaxies may be quite di\ufb00erent and not necessarily inferable from N-body simulations with any reasonable accuracy. We herewith perform a detailed analysis of the dynamics of spin of galaxies in a full cosmological context, utilizing ab initio LAOZI cosmological hydrody- namic simulations of the standard cold dark matter model (Cen 2014) with an unprecedented 1Princeton University Observatory, Princeton, NJ 08544; cen@astro.princeton.edu arXiv:1403.5274v1  [astro-ph.CO]  20 Mar 2014 \u2013 2 \u2013 galaxy sample size and ultra-high numerical resolution. This paper is the second in the series \u201cOn the Origin of the Hubble Sequence\u201d."
                },
                {
                    "url": "http://arxiv.org/abs/1403.5265v1",
                    "title": "Temporal Self-Organization in Galaxy Formation",
                    "abstract": "We report on the discovery of a relation between the number of star formation\n(SF) peaks per unit time, $\\nu_{\\rm peak}$, and the size of the temporal\nsmoothing window function, $\\Delta t$, used to define the peaks: $\\nu_{\\rm\npeak}\\propto\\Delta t^{1-\\phi}$ ($\\phi\\sim 1.618$). This relation holds over the\nrange of $\\Delta t=10$ to $1000$Myr that can be reliably computed, using a\nlarge sample of galaxies obtained from a state-of-the-art cosmological\nhydrodynamic simulation. This means that the temporal distribution of SF peaks\nin galaxies as a population is fractal with a Hausdorff fractal dimension equal\nto $\\phi-1$. This finding reveals, for the first time, that the superficially\nchaotic process of galaxy formation is underlined by a temporal\nself-organization up to at least one gigayear. It is tempting to suggest that,\ngiven the known existence of spatial fractals (such as the power-law two-point\nfunction of galaxies), there is a joint spatio-temporal self-organization in\ngalaxy formation. From an observational perspective, it will be urgent to\ndevise diagnostics to probe SF histories of galaxies with good temporal\nresolution to facilitate a test of this prediction. If confirmed, it would\nprovide unambiguous evidence for a new picture of galaxy formation that is\ninteraction driven, cooperative and coherent in and between time and space.\nUnravelling its origin may hold the key to understanding galaxy formation.",
                    "authors": "Renyue Cen",
                    "published": "2014-03-20",
                    "updated": "2014-03-20",
                    "primary_cat": "astro-ph.GA",
                    "cats": [
                        "astro-ph.GA"
                    ],
                    "main_content": "The reader is referred to Cen (2014) for detailed descriptions of our simulations and the list of its empirical validations therein. Briefly, a zoom-in region of comoving size of 21 \u00d7 24 \u00d7 20h\u22123Mpc3 is embedded in a 120h\u22121Mpc periodic box and resolved to better than 114h\u22121pc (physical). We use the following cosmological parameters that are consistent with the WMAP7-normalized (Komatsu et al. 2011) \u039bCDM model: \u2126M = 0.28, \u2126b = 0.046, \u2126\u039b = 0.72, \u03c38 = 0.82, H0 = 100h km s\u22121Mpc\u22121 = 70 km s\u22121Mpc\u22121 and n = 0.96. Equations governing motions of dark matter, gas and stars, and thermodynamic state of gas are followed forward in time from redshift 100 to 0.62, using the adaptive mesh refinement cosmological hydrodynamic code Enzo (The Enzo Collaboration et al. 2013), which includes all important microphysics and major feedback processes that are well measured. Stellar particles (equivalent to coeval stellar cluster of mass \u223c105 M\u2299) are created from gas clouds meeting certain physical conditions over time, based on the empirical Kennicutt-Schmidt law (Kennicutt 1998). Stellar particles at any time may be grouped together spatially using the HOP algorithm (Eisenstein & Hut 1998) to create galaxy catalogs, which are tested to be robust and insensitive to specific choices of concerned parameters within reasonable ranges. For each galaxy we have its exact star formation history, given its member stellar particles formation times. A total of (2090, 965, 296, 94, 32, 10) galaxies are found with stellar masses greater than (109.5, 1010, 1010.5, 1011, 1011.5, 1012) M\u2299at z = 0.62. \u2013 3 \u2013 For each galaxy we create an uniform time grid of star formation rate at a time resolution of 3Myr from redshift 20 to 0.62, which we call the \u201cunsmoothed\u201d SF history, denoted as S(t). We then smooth S(t) using a square window of full width equal to ts to create a locally-averaged version, denoted as \u00af S(t), which is de\ufb01ned to be \u00af S(t) \u2261 1 ts R t+ts/2 t\u2212ts/2 S(t\u2032)dt\u2032. Another variable is then de\ufb01ned from \u00af S(t): \u03b4(t) \u2261S(t) \u2212\u00af S(t). We smooth \u03b4(t) with a gaussian window of radius tg to yield \u00af \u03b4(t). We obtain \ufb01nally Ss(t) \u2261\u00af S(t)+ \u00af \u03b4(t). We identify SF peaks in Ss(t) as follows. Each SF peak is de\ufb01ned as a contiguous region between two consecutive local minima in Ss(t), say, at time t1 and t2. We sum up S(t) in the same temporal region [t1, t2] to get the total stellar mass for the peak. For each galaxy, we catalog and rank order a complete list of peaks each containing the following information: the total stellar mass, the point in time of maximum SFR and the rank. The number of top SF peaks that make up 50% and 90% of total amount of stellar mass of a galaxy at z = 0.62 is denoted, n50 and n90, respectively. We note that the main purpose of smoothing \u03b4(t) with the gaussian window is to make the automated peak identi\ufb01cation method umambiguous. Thus, it is ts that serves as a time \u201cruler\u201d. We use tg = ts/2 and \ufb01nd the slope of the scaling relation found does not depend on ts/tg within the concerned accuracies. 0 1 2 3 4 5 6 7 8 0 1 2 3 log M*=11.12 log SFR (Msun/yr)     original smoothed 0 1 2 3 4 5 6 7 8 0 1 2 3 log M*=10.73 0 1 2 3 4 5 6 7 8 0 1 2 log M*=10.52 0 1 2 3 4 5 6 7 8 0 1 2 log M*=10.31 t (Gyr)  log SFR (Msun/yr) 3 4 5 0 1 2 log M*=10.31 t (Gyr)  4 4.1 4.2 4.3 4.4 4.5 0 1 2 log M*=10.31 t (Gyr)  Fig. 1.\u2014 shows the star formation histories for four galaxies (the top row plus the bottomleft panel) selected semi-randomly covering mass range of interest at z = 0.62. The time starts at the big bang as zero. The red curves are for unsmoothed SF histories S(t). The blue curves are for the corresponding smoothed SF histories Ss(t), with ts = 200 Myr. In each panel, the galaxy stellar mass at z = 0.62 is indicated at the top. The bottom-middle and -right panels are zoom-in views of the same galaxy shown in the bottom-left panel. \u2013 4 \u2013 3. Results We start by showing the star formation histories for four galaxies in Figure 1. We see that our adaptive smoothing scheme appropriately retains major SF peaks but smooths out high-frequency peaks on scales smaller than the ruler size ts, exactly serving the purpose. We also see that there are temporal structures from \u223c1Myr to \u223c1Gyr. Although it is di\ufb03cult to quantify visually the nature of the temporal structures, there is a hint that a signi\ufb01cant SF peak is often sandwiched by periods of diminished SF activities or less signi\ufb01cant SF peaks. It is evident that the histories of individual galaxies vary substantially with respect to both the trend on long time scales and \ufb02uctuations on short time scales. Anectodal evidence that is consistent with the global evolution of SFR density (Hopkins & Beacom 2006) is that, for the galaxy population as a whole, the majority of galaxies are on a downward trend of SFR with increasing time (decreasing redshift) from t \u223c2 \u22123Gyr (corresponding to z = 2 to 3). It is seen that SF in galaxies is usually not monolithic. A typical galaxy is found to have a polylithic temporal structure of star formation, consisting of a series of quasi-monoliths occurring in time in an apparently chaotic fashion. Not only is there no evidence that a typical galaxy forms most of its stars in a single burst, but also the SF history over any scale does not display a form that may be represented by any simple analytic functions (such as an exponential). A qualitatively similar appearance of oscillatory star formation rates are seen 1 2 3 4 5 6 7 8 910 15 20 25 30 35 40 0 0.1 0.2 n50 (red)  & n90 (blue) PDF      n50  n90  median of n50  median of n90 Fig. 2.\u2014 shows the probability distribution function (PDF) of the number of top SF peaks contributing to 50% (n50) and 90% (n90), respectively, of total stellar mass at z = 0.62 for all galaxies more massive than 1010 M\u2299. The vertical red and and blue dashed lines indicate the median of the respective historgrams. The peaks are identi\ufb01ed with ts = 200Myr. \u2013 5 \u2013 in Hopkins et al. (2013), although detailed quantitative comparisons are not available at this time. One take-away message is this: galaxy formation is a chaotic process and conclusions about the galaxy population as a whole based on an unrepresentative sample of galaxies should be taken cautiously. Another is that the often adopted simple temporal pro\ufb01les for star formation (such as exponential decay or delta function) in interpreting observational results should be reconsidered. We now turn to quantitative results. Figure 2 shows the PDFs of n50 and n90 with ts = 200Myr. We see that the number of peaking containing 50% of stellar mass (n50) falls in the range of \u223c1 \u221210 peaks, whereas the number of peaks containing 90% of stellar mass (n90) displays a much broader range of \u223c5\u221240. We note that, had we restricted the galaxy stellar mass range to 1010\u221211 or 1011\u221212 M\u2299, the results do not change signi\ufb01cantly. It is clear that there are large variations from galaxy to galaxy with respect to individual SF histories, as was already hinted in in Figure 1. Behind this chaos, however, collectively, an order is found, as will be shown in Figure 4. 1 2 3 0 1 2 log n50  & n90     log M*=11.12  90%  q90=\u22120.585  50%  q50=\u22120.49 1 2 3 0 1 2     log M*=10.73  q90=\u22120.515  q50=\u22120.39 1 2 3 0 1 2 log ts (Myr) log n50  & n90     log M*=10.52  q90=\u22120.63  q50=\u22120.55 1 2 3 0 1 2 log ts (Myr)     log M*=10.31  q90=\u22120.535  q50=\u22120.55 Fig. 3.\u2014 shows n50 (red dots) and n90 (blue squares) as a function of temporal smoothing window ts for the four galaxies shown in Figure 1. Linear \ufb01ts to the log ts log n50 and log ts log n90 are shown as dashed lines with the respective colors. Figure 3 shows n50 (red dots) and n90 (blue squares) as a function of temporal smoothing window ts for the four galaxies shown in Figure 1. We see that powerlaw \ufb01ts n50 \u221dt\u03c650 s and n90 \u221dt\u03c690 s provide reasonable approximations. Collecting all galaxies with stellar masses greater than 1010 M\u2299at z = 0.62 the results are shown in Figure 4. The top panel of Figure 4 shows the PDF of \u03c650 (red histogram) and \u03c690 (blue historgram). We see that there \u2013 6 \u2013 are substantial variations among galaxies, which is expected. The most signi\ufb01cant point is that a typical galaxy has \u03c650 and \u03c690 around \u22120.6. In other words, the galaxy population, collectively taken as a whole, displays signi\ufb01cant orderliness. This point is re-enforced in the bottom panel of Figure 4, which is similar to Figure 3. But here, instead of showing powerlaw \ufb01ts for individual galaxies, we compute the median of n50 (red dots) and n90 (blue squares) for all galaxies \ufb01rst as a function of ts and then show the \ufb01ts to the medians. It is intriguing that a slope about \u22120.618 (= 1 \u2212\u03c6) provides a quite good \ufb01t, where \u03c6 = 1.618 is often called the golden ratio. \u22121 \u22120.9 \u22120.8 \u22120.7 \u22120.6 \u22120.5 \u22120.4 \u22120.3 \u22120.2 \u22120.1 0 0 0.05 0.1 q50 (red)  & q90 (blue) PDF      q50  q90  median(q50)=\u22120.612  median(q90)=\u22120.574 1 2 3 0 1 2 log ts (Myr) log median n50 & n90      median n50  median n90  n50=1.38(ts/1Gyr)\u22120.618  n90=5.83(ts/1Gyr)\u22120.618 Fig. 4.\u2014 Top panel shows the PDF of \u03c650 (red histogram) and \u03c690 (blue historgram) in the \ufb01t n50 \u221dt\u03c650 s and n90 \u221dt\u03c690 s for all galaxies with stellar masses greater than 1010 M\u2299at z = 0.62. The vertical red and and blue dashed lines indicate the median of the red and blue historgrams, respectively. Bottom panel shows the median of n50 (red dots) and n90 (blue squares), respectively, for all galaxies with stellar masses greater than 1010 M\u2299at z = 0.62, as a function of temporal smoothing window ts. The vertical errorbars indicate the 25%-75% range. The red and and blue dashed lines indicate \ufb01ts with a slope \u22120.618. 4. Discussion and Conclusions This paper is the third in the series \u201cOn the Origin of the Hubble Sequence\u201d. Utilizing ab initio Large-scale Adaptive-mesh-re\ufb01nement Omniscient Zoom-In cosmological hydrodynamic simulations (LAOZI Simulations) of the standard cold dark matter model, we \u2013 7 \u2013 undertake a unique study of the statistical properties of star formation episodes in galaxies. We \ufb01nd a relation between the number of star formation (SF) peaks per unit time, \u03bdpeak, and the size of the temporal smoothing window function, \u2206t, used to de\ufb01ne the peaks: \u03bdpeak \u221d\u2206t1\u2212\u03c6 (\u03c6 \u223c1.618), valid over the range of \u2206t = 0.01 \u22121Gyr. It is expected that the \ufb01ndings do not signi\ufb01cantly depend on precise cosmological parameters, since the responsible processes are mostly in the nonlinear regime, although it remains to be seen if the relation extends to below 10Myr, where non-gravitational processes, including feedback processes, may introduce time scales of their own. The implication is profound: galaxy formation is temporally fractal and displays a self-organization up to at least one gigayear, with a Hausdor\ufb00(1919) dimension equal to \u03c6 \u22121. We attribute this temporal self-organization, tentatively, to interactions between galaxies that presumably trigger star formation peaks and are organized temporally in a way that is yet to be quantitatively understood. Qualitatively, the found results may be explained as follows. One could envision that galaxies are normally (at least at high redshift) embedded in a gas reservoir, which is the potential fuel of star formation. When there is a trigger, some of this gas is driven inward to fuel star formation. The triggers are likely due to signi\ufb01cant interactions between galaxies, such as major and minor mergers or close \ufb02y-bys of signi\ufb01cant galaxies, or some torquing events, or some hydrodynamic events. The triggers may be democratically distributed temporally in the sense that at a given time baseline a large trigger is not usually preceded or followed by another large trigger, but rather by small triggers. One might even argue that in some rare cases, even if a large trigger does follow a preceding large one, a signi\ufb01cant \u201cdrawdown\u201d of gas by the preceding SF peak may cause the second SF peak to be less powerful that it otherwise would. Such compensated behavior could give rise to the temporal structures seen. Were the triggers distributed randomly, then \u03c6 would be 2. Should the triggers be completely correlated (i.e., a delta function in time), then \u03c6 would be 1. Since the triggering of SF peaks by galaxy interactions implies spatial correlations of galaxies, and given that galaxies are known to exhibit spatial fractals, such as the powerlaw galaxy two-point correlation function (e.g., Peebles 1980), our results are strongly indicative that galaxy formation may be governed by a fundamental joint spatio-temporal self-organization. Understanding the origin of this self-organization may hold a key to understanding galaxy formation. Observational diagnostics to probe SF histories of galaxies with competitively good temporal resolution from a few Myr to Gyr, especially those that are applicable to a suf\ufb01cient sample of galaxies, are highly wanted, in order to test the predictions made here. In addition, with the development of this new line of inquiry, more accurate observational characterizations of galaxy clustering at high redshift at the peak of star formation will be useful. \u2013 8 \u2013 In spite of the apparent coincidence, it would be premature to emphatically relate \u03c6 to the golden ratio. Nonetheless, the ubiquitous manifestations of the golden ratio in nature suggest that further investigations with higher statistical accuracies may be warranted. Could the galaxy formation be golden after all? I would like to thank Claire Lackner for providing the SQL based merger tree construction software. The analysis program yt (Turk et al. 2011) is used to perform some of the analysis. Computing resources were in part provided by the NASA HighEnd Computing (HEC) Program through the NASA Advanced Supercomputing (NAS) Division at Ames Research Center. This work is supported in part by grant NASA NNX11AI23G.",
                    "introduction": "Galaxy formation involves a large set of physical processes - cosmological expansion, gravity, hydrodynamics, atomic physics and feedback from star formation, stellar evolution and black hole growth - and spans large dynamic ranges in time (at least 0.1Myr to 10Gyr) and space (at least 1pc to 100Mpc). Some of the most interesting results on galaxy formation are thus obtained using large-scale simulations, providing fundamental insights on a variety of di\ufb00erent aspects (e.g., Frenk et al. 1988; Cen et al. 1994; Gnedin 1998; Klypin et al. 1999; Moore et al. 1999; Cen & Ostriker 1999; Wechsler et al. 2002; Abel et al. 2002; Bromm et al. 2002; Springel et al. 2005; Kere\u02c7 s et al. 2005; Hopkins et al. 2006; Croton et al. 2006; Naab et al. 2006; Bournaud et al. 2007; Diemand et al. 2008; Dekel et al. 2009; Schaye et al. 2010). The spatial distributions of galaxies have been extensively studied observationally, primarily 1Princeton University Observatory, Princeton, NJ 08544; cen@astro.princeton.edu arXiv:1403.5265v1  [astro-ph.GA]  20 Mar 2014 \u2013 2 \u2013 at low redshift. Among the most striking is the nature\u2019s ability to maintain a powerlaw galaxy-galay two-point correlation function over a signi\ufb01cant range (\u223c0.1\u221210h\u22121Mpc) (e.g., Groth & Peebles 1977), although there is evidence of a slight in\ufb02ection at \u223c1 \u22122h\u22121Mpc in recent analysis (e.g., Zehavi et al. 2004). This spatial regularity is not inherited from the linear power spectrum but must be a result of cooperation between nonlinear evolution and galaxy formation. In self-gravitating systems, such as galaxies, the temporal and spatial structures may be related. This may be seen by two examples. First, for an isolated (non- dissipative) spherical system, the collapse time of each shell (assuming no shell crossings) is uniquely determined by the interior mass and speci\ufb01c energy of the shell that in turn is determined by the density structures. Second, during the growth of a typical galaxy, in addition to direct acquisition of stars via mergers and accretion (along with dark matter), signi\ufb01cant spatial interactions may induce signi\ufb01cant star formation activities hence leave temporal imprints in its star formation history. Taking these indications together suggests that one should bene\ufb01t by tackling the problem of galaxy formation combining the spatial and temporal information. Here, as a step in that direction, we perform a novel analysis, utilizing the ab initio LAOZI adaptive mesh re\ufb01nement cosmological hydrodynamic simulation, to understand the statistical properties of star formation episodes in galaxies."
                },
                {
                    "url": "http://arxiv.org/abs/1311.5916v2",
                    "title": "On the Origin of the Hubble Sequence: I. Insights on Galaxy Color Migration from Cosmological Simulations",
                    "abstract": "An analysis of more than 3000 galaxies resolved at better than 114 pc/h at\nz=0.62 in a LAOZI cosmological adaptive mesh refinement hydrodynamic simulation\nis performed and insights gained on star formation quenching and color\nmigration. The vast majority of red galaxies are found to be within three\nvirial radii of a larger galaxy, at the onset of quenching when the specific\nstar formation rate experiences the sharpest decline to fall below\n~10^{-2}-10^{-1}/Gyr (depending on the redshift). We shall thus call this\nmechanism \"environment quenching\", which encompasses satellite quenching. Two\nphysical processes are largely responsible: ram-pressure stripping first\ndisconnects the galaxy from the cold gas supply on large scales, followed by a\nlonger period of cold gas starvation taking place in high velocity dispersion\nenvironment, during the early part of which the existing dense cold gas in the\ncentral region (<10kpc) is consumed by in situ star formation. Quenching is\nfound to be more efficient, but not faster, on average, in denser environment.\nThroughout this quenching period and the ensuing one in the red sequence\ngalaxies follow nearly vertical tracks in the color-stellar-mass diagram. In\ncontrast, individual galaxies of all masses grow most of their stellar masses\nin the blue cloud, prior to the onset of quenching, and progressively more\nmassive blue galaxies with already relatively older mean stellar ages continue\nto enter the red sequence. Consequently, correlations among observables of red\ngalaxies - such as the age-mass relation - are largely inherited from their\nblue progenitors at the onset of quenching. While the color makeup of the\nentire galaxy population strongly depends on environment, which is a direct\nresult of environment quenching, physical properties of blue galaxies as a\nsub-population show little dependence on environment.",
                    "authors": "Renyue Cen",
                    "published": "2013-11-22",
                    "updated": "2014-01-15",
                    "primary_cat": "astro-ph.CO",
                    "cats": [
                        "astro-ph.CO"
                    ],
                    "main_content": "2.1. Hydrocode and Simulation Parameters We perform cosmological simulations with the AMR Eulerian hydro code, Enzo (Bryan & Norman 1999; Joung et al. 2009). First we run a low resolution simulation with a periodic box of 120 h\u22121Mpc (comoving) on a side. We identify a region centered on a cluster of mass of \u223c 3 \u00d7 1014 M\u2299at z = 0. We then resimulate with high resolution of the chosen region embedded in the outer 120h\u22121Mpc box to properly take into account the large-scale tidal field and appropriate boundary conditions at the surface of a refined region. The refined region has a comoving size of 21 \u00d7 24 \u00d7 20h\u22123Mpc3 and represents a +1.8\u03c3 matter density fluctuation on that volume. The dark matter particle mass in the refined region is 1.3 \u00d7 107h\u22121 M\u2299. The refined region is surrounded by three layers (each of \u223c1h\u22121Mpc) of buffer zones with particle masses successively larger by a factor of 8 for each layer, which then connects with the outer root grid that has a dark matter particle mass 84 times that in the refined region. We choose the mesh refinement criterion such that the resolution is always smaller than 111h\u22121pc (physical), corresponding to a maximum mesh refinement level of 13 at z = 0. An identical comparison run that has four times better resolution of 29pc/h was also run down to z = 3 and some relevant comparisons between the two simulations are made to understand effects of limited resolution on our results. The simulations include a metagalactic UV background (Haardt & Madau 1996), and a model for self-shielding of UV radiation (Cen et al. 2005). They include metallicity-dependent radiative cooling (Cen et al. 1995). Our simulations also solve relevant gas chemistry chains for molecular hydrogen formation (Abel et al. 1997), molecular formation on dust grains (Joung et al. 2009), and metal cooling extended down to 10 K (Dalgarno & McCray 1972). Star particles are created in cells that satisfy a set of criteria for SF proposed by Cen & Ostriker (1992). Each star particle is tagged with its initial mass, creation time, and metallicity; star particles typically have masses of \u223c106 M\u2299. Supernova feedback from SF is modeled following Cen et al. (2005). Feedback energy and ejected metal-enriched mass are distributed into 27 local gas cells centered at the star particle in question, weighted by the specific volume of each cell, which is to mimic the physical process of supernova blastwave propagation that tends to channel energy, momentum and mass into the least dense regions (with the least resistance and cooling). The primary advantages of this supernova energy based feedback mechanism are three-fold. First, nature does drive winds in this way and energy input is realistic. Second, it has only one free parameter eSN, namely, the fraction of the rest mass energy of stars formed that is deposited as thermal energy on the cell scale at the location of supernovae. Third, the processes are treated physically, obeying their respective conservation laws (where they apply), allowing transport of metals, mass, energy and momentum to be treated selfconsistently and taking into account relevant heating/cooling processes at all times. We allow the entire feedback processes to be hydrodynamically coupled to surroundings and subject to relevant physical processes, such as cooling and heating. The total amount of explosion kinetic energy from Type II supernovae with a Chabrier initial mass function (IMF) is 6.6 \u00d7 10\u22126M\u2217c2 (where c is the speed of light), for an amount M\u2217of star formed. Taking into account the contribution of prompt Type I supernovae, we use eSN = 1\u00d710\u22125 in our simulations. Observations of local starburst galaxies indicate that nearly all of the SF produced kinetic energy is used to power galactic superwinds (e.g., \u2013 6 \u2013 Heckman 2001). Supernova feedback is important primarily for regulating SF and for transporting energy and metals into the intergalactic medium. The extremely inhomogeneous metal enrichment process demands that both metals and energy (and momentum) are correctly modeled so that they are transported in a physically sound (albeit still approximate at the current resolution) way. We use the following cosmological parameters that are consistent with the WMAP7-normalized (Komatsu et al. 2010) \u039bCDM model: \u2126M = 0.28, \u2126b = 0.046, \u2126\u039b = 0.72, \u03c38 = 0.82, H0 = 100h km s\u22121Mpc\u22121 = 70 km s\u22121Mpc\u22121 and n = 0.96. These parameters are consistent with those from Planck \ufb01rst-year data (Planck Collaboration et al. 2013) if we average Planck derived H0 with SN Ia and HST based H0. We note that the size of the re\ufb01ned region, 21 \u00d7 24 \u00d7 20h\u22123Mpc3, is still relatively small and the region biased. This is, of course, designed on purpose. Because of that, however, we are not able to cover all possible environment, such as the center of a void. Also because of that, we have avoided addressing any measures that requires a precise characterization of the abundance of any large galaxy systems, such as the mass function or luminosity function of massive galaxies or groups. Despite that, measures that are characterized as a function of environment/system masses should still be valid. Our environment coverage is substantially larger than probed in, for example, Feldmann et al. (2011). In Tonnesen & Cen (2012) we show that the present simulation box (C box) (run to z = 0 with a lower resolution previously) spans a wide range in environment from rich clusters to the \ufb01eld, and there is a substantial overlap in the \ufb01eld environment with another simulation centered on a void (V box). It is the density peaks higher than we model here (i.e., more massive clusters of galaxies) that we fail to probe. As it should be clear later, this shortcoming should not a\ufb00ect any of our conclusions, which may be appropriately extrapolated. 2.2. Simulated Galaxy Catalogs We identify galaxies in our high resolution simulations using the HOP algorithm (Eisenstein & Hu 1999) operating on the stellar particles, which is tested to be robust and insensitive to speci\ufb01c choices of concerned parameters within reasonable ranges. Satellites within a galaxy down to mass of \u223c109 M\u2299are clearly identi\ufb01ed separately in most cases. The luminosity of each stellar particle in each of the Sloan Digital Sky Survey (SDSS) \ufb01ve bands is computed using the GISSEL stellar synthesis code (Bruzual & Charlot 2003), by supplying the formation time, metallicity and stellar mass. Collecting luminosity and other quantities of member stellar particles, gas cells and dark matter particles yields the following physical parameters for each galaxy: position, velocity, total mass, stellar mass, gas mass, mean formation time, mean stellar metallicity, mean gas metallicity, SFR, luminosities in \ufb01ve SDSS bands (and various colors) and others. At a spatial resolution of 159pc (physical) with thousands of well resolved galaxies at z \u223c0.6\u22126, the simulated galaxy catalogs present an excellent (by far, the best available) tool to study galaxy formation and evolution. \u2013 7 \u2013 2.3. Construction of Histories of Simulated Galaxies When we start the analysis for this paper, the simulation has reached z = 0.62. For each galaxy at z = 0.62 a genealogical line is constructed from z = 0.62 to z = 6 by connecting galaxy catalogs at a series of redshifts. Galaxy catalogs are constructed from z = 0.62 to z = 1.40 at a redshift increment of \u2206z = 0.02 and from z = 1.40 to z = 6 at a redshift increment of \u2206z = 0.05. The parent of each galaxy is identi\ufb01ed with the one at the next higher redshift catalog that has the most overlap in stellar mass. We call galaxies with g \u2212r < 0.55 \u201cblue\u201d, those with g \u2212r = 0.55 \u22120.65 \u201cgreen\u201d and those with g \u2212r > 0.65 \u201cred\u201d, in accord with the bimodal color distribution that we will show below and with that of observed galaxies (e.g., Blanton et al. 2003b), where g and r are magnitudes of SDSS g and r bands. In subsequent analysis, we will examine gasdynamic processes, e.g., cold gas loss or lack of cold gas accretion, under the working hypothesis that ram-pressure stripping and gas starvation are the primary detrimental processes to star formation. We should assume that other processes, such as hydrodynamical instabilities (e.g., RT, KH, tidal shocks, etc), may either be \u201clumped together\u201d with ram-pressure stripping or play some role to enhance cold gas destruction that is initiated by ram-pressure stripping. A word on tidal stripping may be instructive. It is noted that while tidal stripping would a\ufb00ect both stars and gas, ram-pressure operates only on the latter. As one will see later, in some cases the stellar masses of galaxies decrease with time, which are likely due to tidal e\ufb00ects. A simple argument suggests that ram-pressure e\ufb00ects are likely to be more far-reaching spatially and are more consistent with the environment e\ufb00ects becoming e\ufb00ective at 2-3 virial radii than tidal stripping that we will show later. Let us take a speci\ufb01c example to illustrate this. Let us assume that the primary and infalling galaxies have a velocity dispersion of \u03c31 and \u03c32, respectively, and that they both have isothermal sphere density pro\ufb01les for both dark matter and baryons. The virial radius is proportional to its velocity dispersion in each case. Under such a con\ufb01guration, we \ufb01nd that the tidal radius for the satellite galaxy at its virial radius is equal to the virial radius of the primary galaxy. On the other hand, the ram-pressure force on the gas in the satellite at its virial radius is already equal to the gravitational restoring by the satellite, when the satellite is (\u03c31/\u03c32) virial radii away from the primary galaxy. In reality, of course, the density pro\ufb01les for dark matter and baryons are di\ufb00erent and neither is isothermal, and the gas may display a varying degree of non-sphericity. But the relative importance of ram-pressure and tidal strippings is likely to remain the same for relatively di\ufb00use gas. The relative situation is unchanged, if one allows the gas to cool and condense. As an example, if the gas within the virial radius of the satellite and the primary galaxies in the above example is allowed to shrink spherically by a factor of 10 in radius (we will continue to assume that the velocity dispersion or rotation velocity remains \ufb02at and at the same amplitude), we \ufb01nd that the tidal stripping radius is now a factor of 10 smaller than before (equal to 0.1 times the virial radius of the primary galaxy), while the new ram-pressure stripping radius is \u03c31/\u03c32 times the new tidal stripping radius. As a third example, if the gas within the virial radius of the satellite galaxy in the above example is allowed to shrink spherically by a factor of 10 in radius but the gas in the primary galaxy does not shrink in size, it can be shown that in this case the tidal stripping radius is equal to 0.1 times the virial radius of the primary \u2013 8 \u2013 galaxy, while the new ram-pressure stripping radius is now 0.1 times (sigma1/sigma2) times the virial radius of the primary galaxy. As the last example, if the gas within the virial radius of the satellite galaxy in the above example is allowed to shrink by a factor of 10 in radius to become a disk but the gas in the primary galaxy does not shrink in size, it can be shown that in this case the tidal stripping radius is equal to 0.1 times the virial radius of the primary galaxy. The new ram-pressure stripping radius depends on the orientation of the motion vector and the normal of the disk: if the motion vector is normal to the disk, the tidal stripping radius is 0.1 times \u03c31/\u03c32 times the virial radius of the primary galaxy; if the motion vector is in the plane to the disk, the tidal stripping radius is zero. 3 4 5 6 7 8 \u22123 \u22122 \u22121 0 1 2 3 4 log variable quantities 11.5 3 4 5 6 7 8 \u22123 \u22122 \u22121 0 1 2 3 4     11.2 log ram pressure\u22122 log sSFR (Gyr\u22121) log halo mass\u221210 3 4 5 6 7 8 \u22123 \u22122 \u22121 0 1 2 3 4 t (Gyr) log variable quantities     11.2 log SFR (Msun/yr) log cold gas (<10kpc) \u2212 10 log cold gas (<100kpc) \u2212 10 3 4 5 6 7 8 \u22123 \u22122 \u22121 0 1 2 3 4 t (Gyr) 11.1 Fig. 1.\u2014 four panels show the histories of six variables for four randomly selected red galaxies with stellar mass of \u223c1011 M\u2299at z = 0.62: log SFR (in M\u2299/yr) (solid dots), log ram pressure (in Kelvin cm\u22123) 2 (stars), log cold gas within 10kpc (in M\u2299) -10 (open circles), log cold gas within 100kpc (in M\u2299) -10 (open squares), log sSFR (in Gyr\u22121) (down-pointing triangles) and log halo mass (in M\u2299) -10 (solid diamonds); The color of symbols at any given time corresponds the color of the galaxy at that time. The logarithm of the stellar mass at z = 0.62 is indicated in the upper-right corner in each panel. The vertical dashed line in each panel indicates the location of tq. We denote a point in time when the galaxy turns from blue to green as tg, a point in time when the galaxy turns from green to red as tr. Convention for time is that the Big Bang occurs at t = 0. We identify a point in time, searched over the range tg\u22122Gyr to tg+1Gyr, when the derivative of SFR with respect to time, dSFR/dt, is most negative, as tq (q stands for quenching); in practice, to reduce uncertainties due to temporal \ufb02uctuations in SFR, tq is set to equal to t(n+1) \u2013 9 \u2013 3 4 5 6 7 8 \u22123 \u22122 \u22121 0 1 2 3 4 log variable quantities 10.2 3 4 5 6 7 8 \u22123 \u22122 \u22121 0 1 2 3 4     10.1 log ram pressure\u22122 log sSFR (Gyr\u22121) log halo mass\u221210 3 4 5 6 7 8 \u22124 \u22123 \u22122 \u22121 0 1 2 3 t (Gyr) log variable quantities     10.1 log SFR (Msun/yr) log cold gas (<10kpc) \u2212 10 log cold gas (<100kpc) \u2212 10 3 4 5 6 7 8 \u22124 \u22123 \u22122 \u22121 0 1 2 3 t (Gyr) 10.2 Fig. 2.\u2014 four panels show the histories of six variables for four randomly selected red galaxies with stellar mass of \u223c1010 M\u2299at z = 0.62: log SFR (in M\u2299/yr) (solid dots), log ram pressure (in Kelvin cm\u22123) 2 (stars), log cold gas within 10kpc (in M\u2299) -10 (open circles), log cold gas within 100kpc (in M\u2299) -10 (open squares), log sSFR (in Gyr\u22121) (down-pointing triangles) and log halo mass (in M\u2299) -10 (solid diamonds); The color of symbols at any given time corresponds the color of the galaxy at that time. The logarithm of the stellar mass at z = 0.62 is indicated in the upper-right corner in each panel. The vertical dashed line in each panel indicates the location of tq. when the sliding-window di\ufb00erence (SFR(n + 3) \u2212SFR(n)/(t(n + 3) \u2212t(n)) is most negative, where t(1), t(2), ..., t(n), ... are the times of our data outputs, as noted earlier. Galaxies at tq are collectively called SFQs for star formation quenching galaxies. To demonstrate the reliability and accuracy of identi\ufb01cation of tq we show in Figure 1 the histories for a set of four randomly selected red galaxies at z = 0.62 of stellar mass \u223c1011 M\u2299. The vertical dashed line in each panel shows tq, which is the location of steepest drop of SFR (solid dots). In all four cases, our method identi\ufb01es the location accurately. Figure 2 is similar to Figure 1 but for galaxies of stellar mass \u223c1010 M\u2299, where we see our method identi\ufb01es tq with a similar accuracy. Similarly, we identify a point in time in the range tg\u22122Gyr to tg+1Gyr, when the derivative of the amount of cold gas, (M10, M30, M100) within radial ranges (0 \u221210, 0 \u221230, 0 \u2212100)kpc, with respect to time is most negative as (t30, t100, t300), respectively. We de\ufb01ne cold gas as gas with temperature less than 105K. The exponential decay time scale of SFR at tq is de\ufb01ned by \u03c4q \u2261 (d ln SFR/dt)\u22121. The exponential decay time scale of (M10, M30, M100) at (t30, t100, t300) are de\ufb01ned \u2013 10 \u2013 by [\u03c410 \u2261(d ln M10/dt)\u22121, \u03c430 \u2261(d ln M30/dt)\u22121, \u03c4100 \u2261(d ln M100/dt)\u22121]. The time interval between tq and tr is denoted as tqr, The time duration that the galaxy spends in the green valley before turning red is called tgreen. The time duration the galaxy has spent in the red sequence by z = 0.62 is denoted as tred. We make a needed simpli\ufb01cation by approximating the ram-pressure, denoted as p300, by p300 \u2261\u03c16(300)T(300), where \u03c16(300) and T(300), respectively, are the mean density of gas with temperature \u2265106K and T(300) the mean mass-weighted gas temperature within a proper radius of 300kpc centered on the galaxy in question. This tradeo\ufb00is made thanks chie\ufb02y to the di\ufb03culty of de\ufb01ning precisely the motion of a galaxy relative to its ambient gas environment, where the latter often has complex density and velocity structures, and the former has complex, generally nonspherical gas distribution geometry. In a gravitationally shock heated medium, this approximation should be reasonably good, because the ram-pressure is approximately equal to thermal pressure in post-shock regions. We de\ufb01ne a point in time searched over the time interval between tq\u22122Gyr and tq+1Gyrs, when the derivative of p300 with respect to time is maximum as tram, intended to serve as the point in time when ram-pressure has the steepest rise, As stated in the introduction, it is convenient to express gas cooling time that is proportional to gas entropy to the power 3/2, S3/2. Thus, we approximate gas starvation from large scales by the value of environmental entropy S300, de\ufb01ned to be the average gas entropy within a top-hat sphere of proper radius 300kpc. For convenience, frequently used symbols and their de\ufb01nitions are given in Table 1. 2.4. Tests and Validation of Simulation The galaxy formation simulation in a cosmological setting used here includes sophisticated physical treatment, ultra-high resolution and a very large galaxy sample to statistically address cosmological and astrophysical questions. While this simulation represents the current state-of-theart in these respects, feedback from SF is still far from being treated from \ufb01rst principles. Thus, it is necessary that we validate the feedback prescription empirically. In Cen (2012b) we presented an examination of the damped Lyman alpha systems (DLAs) and found that the simulations, for the \ufb01rst time, are able to match all observed properties of DLAs, including abundance, size, metallicity and kinematics. In particular, the metal distribution in and around galaxies over a wide range of redshift (z = 0 \u22125) is shown to be in excellent agreement with observations (Rafelski et al. 2012). The scales probed by DLAs range from stellar disks at low redshift to about one half of the virial radius at high redshift. In Cen (2012a) we further show that the properties of O VI absorption lines at low redshift, including their abundance, Doppler-column density distribution, temperature range, metallicity and coincidence between O VII and O VI lines, are all in good agreement with observations (Danforth & Shull 2008; Tripp et al. 2008; Yao et al. 2009). The agreement between simulations and observations with respect to O VI lines is recently shown to extend to the correlation between galaxies and O VI lines, the relative incidence ratio of O VI around red to blue galaxies, the amount of oxygen mass around red and blue galaxies as well \u2013 11 \u2013 Table 1. De\ufb01nitions of symbols and names symbol/name de\ufb01nition/meaning tg a point in time when galaxy has g \u2212r = 0.55 tr a point in time when galaxy has g \u2212r = 0.65 M10 amount of cold gas within a radius of 10kpc M30 amount of cold gas within a radius of 30kpc M100 amount of cold gas within a radius of 100kpc tq a point in time of quenching for SFR t10 a point time of quenching for M10 t30 a point time of quenching for M30 t100 a point time of quenching for M100 tram a point in time of largest \ufb01rst derivative of ram-pressure w.r.t time \u03c4q exponential decay time of SFR at tq \u03c410 exponential decay time of M10 at t10 \u03c430 exponential decay time of M30 at t30 \u03c4100 exponential decay time of M100 at t100 \u2206M\u2217 stellar mass change between tq and tr \u2206M10 M10 mass change between tq and tr \u2206M30 M30 mass change between tq and tr \u2206M100 M100 mass between tq and tr rSFR e e\ufb00ective radius of young stars formed within the past 100Myr T300 environmental temperature within physical radius of 300kpc S300 environmental entropy within physical radius of 300kpc p300 environmental pressure within physical radius of 300kpc \u03b42 environmental overdensity within comoving radius of 2h\u22121Mpc d/rc v distance to primary galaxy in units of virial radius of primary galaxy tqr time duration from tq to tr tgreen time spent in green valley tred time spent in red sequence Mc h halo mass of primary galaxy Ms \u2217/M c \u2217 stellar mass ratio of satellite to primary galaxy \u2013 12 \u2013 as cold gas around red galaxies (Cen 2013). In addition to agreements with observations with respect to circumgalactic and intergalactic medium, we \ufb01nd that our simulations are able to match the global SFR history (the Madau plot) and galaxy evolution (Cen 2011a), the luminosity function of galaxies at high (Cen 2011b) and low redshift (Cen 2011a), and the galaxy color distribution (Cen 2011a; Tonnesen & Cen 2012), within observational uncertainties. In Cen (2011a) we show that our simulations reproduce many trends in the global evolution of galaxies and various manifestations of the cosmic downsizing phenomenon. Speci\ufb01cally, our simulations show that, at any redshift, the speci\ufb01c star formation rate of galaxies, on average, correlates negatively with galaxy stellar mass, which seems to be the primary physical process for driving the cosmic downsizing phenomena observed. Smoothed particle hydrodynamic (SPH) simulations and semi-analytic methods, in comparison, appear to produce a positive correlation between the speci\ufb01c star formation rate of galaxies and galaxy stellar mass, which is opposite to what we \ufb01nd (e.g., Weinmann et al. 2012). These broad agreements between our simulations and observations indicate that, among others, our treatment of feedback processes from SF, i.e., the transport of metals and energy from galaxies, from SF sites to megaparsec scale (i.e., from interstellar to intergalactic medium) are realistically modeled as a function of distance and environment, at least in a statistical sense, and it is meaningful to employ our simulated galaxies, circumgalactic and intergalactic medium for understanding physical processes and for confrontations with other, independent observations. In order to determine what galaxies in our simulations to use in our subsequent analysis, we make an empirical numerical convergence test. Top-right panel in Figure 3 shows comparisons between galaxies of two simulations at z = 3 with di\ufb00erent resolutions for the luminosity functions in rest-frame g and r bands. The \ufb01ducial simulation has a resolution of 114pc/h and an identical comparison run has four times better resolution of 29pc/h. We are not able to make comparisons at redshift substantially lower than z = 3 at this time. In any case, we expect that the comparison at z = 3 is a more stringent test, because the resolution e\ufb00ect is likely more severe at higher redshift than at lower redshift in a hierarchical growth model where galaxies become increasingly larger with time. The comparisons are best done statistically, because not all individual galaxies can be identi\ufb01ed at a one-to-one basis due to resolution-dependent star formation and merging histories. Comparisons with respect to other measures, such as stellar mass function, SFR, etc, give comparable convergence. Based on results shown, we decide to place a lower stellar mass limit of 109.5 M\u2299, which is more than 75% complete for almost all relevant quantities, to the extent that we are able to make statistical comparisons between these two runs with respect to the global properties of galaxies (stellar mass, luminosity, SFR, sSFR, etc). In terms of checking the validity and applicability of the simulations, we also make comparisons for the galaxy cumulative mass function at z = 1 with observations in the top-left panel of Figure 3. We see that the simulated galaxies have a higher abundance than observed by a factor of 4 \u22125 in the low mass end and the di\ufb00erence increases towards higher mass end. This di\ufb00erence is expected, because the simulation volume is an overdense region that has a higher galaxy density overall and progressively higher densities for more rare, higher mass galaxies. This di\ufb00erence is also borne out in the comparisons between simulated and observed rest-frame g band galaxy luminosity \u2013 13 \u2013 9 10 11 \u22124 \u22123 \u22122 \u22121 log M* (Msun) log n(>M*) (h3Mpc\u22123)     CMF@z=1 van der Burg 2013 \u221226 \u221225 \u221224 \u221223 \u221222 \u221221 \u221220 \u22124 \u22123 \u22122 \u22121 Mg & Mr log n(<M) (h3Mpc\u22123)     g LF@z=3, 114pc/h g LF@z=3, 29pc/h r LF@z=3, 114pc/h r LF@z=3, 29pc/h \u221226 \u221225 \u221224 \u221223 \u221222 \u221221 \u221220 \u22124 \u22123 \u22122 \u22121 Mg & MB log n(<M) (h3Mpc\u22123)     g band LF@z=0.62 Ramos et al 2011 b band LF@z=1 Faber et al 2007 \u22121 \u22120.5 0 0.5 1 0 0.1 0.2 0.3 log re (kpc) PDF     114pc/h 29pc/h Fig. 3.\u2014 Top-left panel: galaxy stellar mass function (SMF) at z = 1 from the \ufb01ducial run with spatial resolution of 114pc/h (solid curve) and observations by van der Burg et al. (2013) at z = 1; the observational points have been shifted upward by 0.4dex. The vertical dotted line indicates the stellar mass cuto\ufb00of \u2265109.5 M\u2299that we apply to simulated galaxies. Top-right panel: galaxy luminosity function (LF) in SDSS g band (green) and r band (red) at z = 3 from the \ufb01ducial run (solid curves) and the higher resolution run (dashed curves) for galaxies with M\u2217\u2265109.5 M\u2299. Bottom-left panel: galaxy luminosity function (LF) in restframe g band (green) at z = 0.62 and B band (blue) at z = 1 for galaxies with M\u2217\u2265109.5 M\u2299, to compared from the corresponding observations of the same color dashed curves at z = 0.62(Ramos et al. 2011) and z = 1(Faber et al. 2007), respectively. The observational points have been shifted upward by 0.4dex. No dust e\ufb00ects have been included in the simulated luminosity functions. Bottom-right panel: the distribution of the recovered true stellar radii of all galaxies with M\u2217\u2265109.5 M\u2299at z = 3 from the \ufb01ducial (black) and the higher resolution run (red). The vertical lines indicate the e\ufb00ective resolutions of the two simulations, which are found to be 1.84 times the maximum re\ufb01ned resolution. function at z = 0.62 and B band luminosity function at z = 1 (lower-left panel of Figure 3). The di\ufb00erence between simulation and observations is also seen to increase with decreasing redshift, as expected. We note that at the high luminosity end dust e\ufb00ects may become very important, causing the apparent discrepancies between simulations and observations larger than they actually are. Overall, our simulation serves our purposes well for two reasons. First, it contains massive group/cluster systems as well as \ufb01eld regions that allow us to probe environment e\ufb00ects with enough leverage/range. Second, the faint end slope of the galaxy population matches observations well, albeit with a larger overall amplitude; as a result, relative, comparative statements that we \u2013 14 \u2013 will make across the stellar mass range 109.5 and 1011 M\u2299is approximately valid even though the absolute number of galaxies may be o\ufb00. As will become clear later, during quenching by ram-pressure stripping and gas starvation, star formation often continues in the central 10kpc regions of galaxies. Therefore, it is useful to have an estimate of the e\ufb00ective resolutions of simulations empirically as follows. Let us denote the actual resolution, given the maximum re\ufb01nement resolution of \u2206l, as \u2206x = C\u2206l, where C is a contant that is expected to be larger than but of order unity for a mesh code. We then assume that the computed e\ufb00ective stellar radius (enclosing 50% of stellar mass) of any galaxy is r2 c = r2 t + (\u2206x)2 = r2 t + (C\u2206l)2, (1) where rc is the actual e\ufb00ective radius from simulation and rt is the true e\ufb00ective radius if one had in\ufb01nite resolution. We have two equations of Eq 1 for the two simulations with di\ufb00erent resolutions (\u2206l = 114pc/h and \u2206l = 29pc/h) and two unknowns (constant C and vector rt). We solve for C by requiring the distributions of rt derived from the two simulations have the closest agreement; C = 1.84 is found. The bottom-right panel of Figure 3 shows the distributions of derived rt for all galaxies with stellar mass \u2265109.5 M\u2299from the two simulations with C = 1.84. The e\ufb00ective resolutions (C\u2206l) for the two runs, 312pc and 78pc, are indicated by the vertical dashed lines corresponding to the histograms with the same colors. As we will show later, the central gas within 10kpc is largely retained by the galaxy that is being subject to ram-pressure stripping. Clearly, our resolution is adequate to resolve gas distribution, where it is demanded to address ram-pressure stripping physics. On the other hand, consistent with other panels of Figure 3, we see that at the stellar mass cut of 109.5 M\u2299, while the majority of galaxies are e\ufb00ectively resolved with respect to their stellar distribution, a signi\ufb01cant fraction of galaxies in our selected sample with stellar mass close to 109.5 M\u2299is under-resolved in the central regions. We expect that, although our simulation may overestimate the ram-pressure stripping e\ufb00ects for the most inner regions for some of the smaller galaxies, the numerical e\ufb00ect on overall ram-pressure stripping process due to this limitation is likely small. This is because the amount of gas within our resolution limit (313pc) is small compared to the total mass of gas within (say) 10kpc, within which, we will show later, gas is little a\ufb00ected by ram-pressure stripping. In other words, an under-resolution should not materially impact the overall the amount of ram-pressure stripped gas, since the gas in the central region much larger than our resolution is not stripped anyway. 2.5. Bimodal Distribution of Galaxy Colors at z = 0.62 The main goal of this paper is to identify and understand the physical processes that produce the observed galaxy color bimodality. We \ufb01rst examine if our simulations actually reproduce the observed color bimodality. Figure 4 shows g \u2212r color distributions of simulated galaxies in three stellar mass ranges, 3 \u00d7 109 \u22121 \u00d7 1010 M\u2299(black), 1 \u00d7 1010 \u22123 \u00d7 1010 M\u2299(cyan) and > 3 \u00d7 1010 M\u2299 (magenta), at z = 0.62. The g-r color distributions show clear bimodalities for all three subsets of galaxies, with the red peak becoming more prominent for less luminous galaxies at z = 0.62, consistent with recent observations (e.g., Bell et al. 2004; Willmer et al. 2006; Bundy et al. 2006; \u2013 15 \u2013 Faber et al. 2007). We also caution that one should not overstate the success in this regard for two reasons. First, on the simulation side, since our simulation volume does not necessarily represent an \u201caverage\u201d volume of the universe, a direct comparison to observations would be di\ufb03cult. Second, observations at high redshift (i.e., z \u223c0.62) are perhaps less complete than at low redshift, and identi\ufb01cation of low mass (and especially low surface brightness) galaxies, in particular those that are satellite galaxies and red, may be challenged at present (e.g., Knobel et al. 2013). Our main purpose is to make a comparative study of galaxies of di\ufb00erent types in the simulation and to understand how blue galaxies turn red. It is intriguing to note that there is no lack of red dwarf galaxies. While a direct comparison to observations with respect to abundant red dwarf galaxies can not be made at z = 0.62, future observations may be able to check this. Since our simulation does not include AGN mechanical feedback, this suggests that the bimodal nature of galaxy colors does not necessarily require AGN feedback for galaxies in the mass ranges examined. This \ufb01nding is in agreement with Feldmann et al. (2011), who \ufb01nd that AGN feedback is not an essential ingredient for producing quiescent, red elliptical galaxies in galaxy groups. While SF feedback is included in our simulation, our subsequent analysis shows that environmental e\ufb00ects play the dominant role in driving galaxy color evolution and consequently color bimodality. Our results do not, however, exclude the possibility that AGN feedback may play an important role in regulating larger, central galaxies, such as cD galaxies at the centers of rich clusters of galaxies, for which we do not have a su\ufb03cient sample to make a statistical statement. Our earlier comparison between simulated luminosity functions of galaxies at z = 0 and SDSS observations indicates that some additional feedback, likely in the way of AGN, may be required to suppress star formation in the most massive galaxies (Cen 2011a). 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0 0.05 0.1 0.15 g\u2212r PDF(g\u2212r)     3\u00d7109\u22121\u00d71010Msun 1\u00d71010\u22123\u00d71010Msun >3\u00d71010Msun Fig. 4.\u2014 shows g \u2212r color distributions of simulated galaxies in three stellar mass ranges, 3\u00d7109 \u2212 1 \u00d7 1010 M\u2299(black), 1 \u00d7 1010 \u22123 \u00d7 1010 M\u2299(cyan) and > 3 \u00d7 1010 M\u2299(magenta), at z = 0.62. \u2013 16 \u2013 3. Results Most of our results shown are presented through a variety of comparisons of the dependencies of galaxies of di\ufb00erent types on a set of environmental variables, to learn how galaxies change color. We organize our analysis in an approximately chronological order. In \u00a73.1 we focus on processes around the \u201cquenching\u201d time, tq, followed by the ensuing period of gas starvation in hot environment in \u00a73.2. In \u00a73.3 we discuss stellar mass growth, evolution of stellar mass function of red galaxies and present galaxy color migration tracks. \u00a73.4 gives an example of consequences of the color migration picture galaxy age-mass relation. We present observable environmental dependence of galaxy makeup at z = 0.62 in \u00a73.5. 3.1. Ram-Pressure Stripping: Onset of Star Formation Quenching 0 1 2 3 1.5 2 2.5 3 log S300@tq (keV cm2) log oq (Myr) 0 1 2 3 4 1.5 2 2.5 3 log p300@tq (K cm\u22123) log oq (Myr) \u22121 0 1 2 1.5 2 2.5 3 log 1+b2@tq log oq (Myr) 1 2 3 4 5 1.5 2 2.5 3 d/rv c@tq log oq (Myr) red: satellites black: centrals     M* = 3\u00d7 109 M* = 1010 M* = 1011 Fig. 5.\u2014 shows \u03c4q, the exponential decay time of SFR, against four environmental variables at tq: ram-pressure p300 on 300kpc proper scale, environmental entropy S300 on 300kpc proper scale, distance to primary galaxy d/rc v in units of the primary galaxy\u2019s virial radius and environmental overdensity \u03b42 on 2h\u22121Mpc comoving scale. The magenta solid dots with dispersions are the means. Figure 5 shows the quenching time scale \u03c4q (star formation rate exponential decay time) against four environmental variables at the quenching time tq: ram-pressure p300, environmental entropy S300, distance to primary galaxy d/rc v and environmental overdensity \u03b42. It is useful to make clear some nomenclature here. We have used the distance to the primary galaxy, d/rc v, as an environment \u2013 17 \u2013 variable, which runs from zero to values signi\ufb01cant above unity. This is merely saying that any galaxy (except the most massive galaxy in the simulation) can \ufb01nd a larger galaxy at some distance, not necessarily at d/rc v \u22641. The de\ufb01nition of \u201csatellite galaxies\u201d is reserved only for those galaxies with d/rc v \u22641, shown clearly as red circles in the low-left panel of Figure 5. The black circles, labeled as \u201ccentrals\u201d are galaxies with d/rc v > 1, i.e., those that are not not \u201csatellite galaxies\u201d. The observation that galaxies are being quenched at all radii d/rc v > 1 as well as d/rc v < 1 indicates that the most likey physical mechanism for the onset of quenching is ram-pressure. Tidal stripping is not expected to be e\ufb00ective at removing gas (or stars) at d/rc v > 1 (see \u00a72.3 for a discussion). The fact that \u03c4q decreases with increasing p300 is self-consistent with ram-pressure being responsible for the onset of quenching. The outcome that \u03c4q only very weakly anti-correlates with p300 indicates that the onset of quenching is some \u201cthreshold\u201d event, which presumably occurs when the ram-pressure exceeds gravitational restoring force (i.e., the threshold), thus strongly re-enforcing the observation that ram-pressure is largely responsible for the onset of quenching. A \u201cthreshold\u201d type mechanism \ufb01ts nicely with the fact that the dispersion of \u03c4q at a given p300 is substantially larger than the correlation trend, because galaxies that cross the \u201cthreshold\u201d are expected to depend on very inhomogeneous internal properties among galaxies (see Figure 6 below). The weak anticorrelation between \u03c4q and \u03b42 stems from a broad positive correlation between p300 and \u03b42. The fact that there is no discernible correlation between \u03c4q and S300 indicates that the onset of quenching is not initiated by gas starvation. The most noticeable contrast to the weak trends noted above is the di\ufb00erence between satellite galaxies (at d/rc v < 1) and central galaxies (at d/rc v > 1), in that \u03c4q of the former is lower than that of the latter by a factor of \u223c2. This is naturally explained as follows. First, at d/rc v < 1 ram-pressure stripping and tidal stripping operate in tandem to accelerate the gas removal process, whereas at d/rc v > 1 ram-pressure stripping operates \u201calone\u201d to remove gas on somewhat longer time scales. Second, at d/rc v > 1 ram-pressure stripping is, on average, less strong than at d/rc v < 1. Possible internal variables that a\ufb00ect the e\ufb00ectiveness of ram-pressure stripping include the relative orientation of the normal of the gas disk and the motion vector, rotation velocity of the gas disk, whether gas disk spiral arms are trailing or not at time of ram-pressure stripping, gas surface density amplitude and pro\ufb01le, dark matter halo density pro\ufb01le. As an obvious example, galaxies that have their motion vector and disk normal aligned are likely to have maximum rampressure stripping e\ufb00ect, everything else being equal. In the other extreme when the two vectors are perpendicular to each other, the ram-pressure stripping e\ufb00ect may be minimized. Needless to say, given many factors involved, the onset of ram-pressure stripping e\ufb00ect will be multi-variant. We elaborate on the multi-variant nature of ram-pressure stripping with one example. The top-panel of Figure 6 shows \u03c4q as a function of the stellar surface density \u03a3e within the e\ufb00ective stellar radius re. We see a signi\ufb01cant positive correlation between \u03c4q and \u03a3e in the sense that it takes longer to rampressure-remove cold gas with higher central surface density (hence higher gravitational restoring force) galaxies. While this positive correlation between \u03c4q and \u03a3e is consistent with observational indications (e.g., Cheung et al. 2012), the underlying physical origin is in a sense subtle. Since rampressure stripping is a \u201cthreshold\u201d event, as noted earlier, when ram-pressure force just exceeds the internal gravitational restoring force, one would have expected that a high surface density would \u2013 18 \u2013 yield a shorter dynamic time hence a shorter \u03c4q. This is in fact an incorrect interpretation. Rather, the gas in the central regions where \u03a3e is measured is immune to ram-pressure stripping in the vast majority of cases (see Figure (8) below). Instead, a higher \u03a3e translates, on average, to a larger scale where gas is removed, which has a longer dynamic time hence a longer \u03c4q. 8 9 10 2.5 3 3.5 log Ye (Msun/kpc2) log tqr (Myr)     3\u00d7 109 1010 1011 8 9 10 1.5 2 2.5 3 log oq (Myr) red: satellites black: centrals Fig. 6.\u2014 Top panel: the exponential decay time scale of SFR, \u03c4q, as a function of the stellar surface density \u03a3e within the stellar e\ufb00ective radius re. Bottom panel: the time interval between onset of quenching and the time the galaxy turns red, tqr as a function of \u03a3e. The magenta dots are the averages at a given x-axis value. Taken together, we conclude that, while a high ram-pressure provides the conditions for rampressure stripping to take e\ufb00ect, the e\ufb00ectiveness or timescale for gas removal by ram-pressure stripping also depend on the internal structure of galaxies. It is very interesting to note that, unlike between tq and \u03a3e, tqr (the time interval between the onset of quenching tq and the time when the galaxy turns red) and \u03a3e shown in the bottom-panel of Figure 6, if anything, is weakly anticorrelated. We attribute this outcome to the phenomenon that galaxies with higher central surface \u2013 19 \u2013 density have a shorter time scale for consuming the existing cold gas hence, once the overall cold gas reservoir is removed. This explanation will be elaborated more later. \u22121 \u22120.8 \u22120.6 \u22120.4 \u22120.2 0 0.2 0.4 0.6 0.8 1 0 0.1 0.2 tq\u2212tram (Gyr) PDF     M*>3\u00d7 109 M*>3\u00d7 1010 Fig. 7.\u2014 the histograms of tq \u2212tram for red galaxies at z = 0.62, where tram is the point in time when the derivative of p300 with respect to time is maximum, and tq is the onset of quenching time for SFR. The vertical thick lines show the medians of the corresponding histograms of the same colors, and the vertical thin lines for each color are for 25% and 75% percentiles. We have made the case above that ram-pressure stripping is primarily responsible for the onset of quenching process based on evidence on the dependence of exponential decay time of SFR at the onset of quenching on environment variables. We now make a direct comparison between tq and tram. Figure (7) shows the histograms of tq \u2212tram. We see that the time di\ufb00erence between the two is centered around zero, indicating a casual connection between the onset of SFR quenching and the rapid rise of ram-pressure. The width of the distribution of a few hundred Myrs re\ufb02ects the fact that the exact strength of ram-pressure stripping required to dislodge the gas varies greatly, depending on many variables as discussed above. This is as yet the strongest supporting evidence for ram-pressure stripping being responsible for the onset of quenching, especially considering the conjunctional evidence that the onset of quenching could occur outside the virial radius of a larger neighboring galaxy where tidal stripping is expected to be less e\ufb00ective and yet ram-pressure is expected to become important. Evidence so far supports the notion that ram-pressure stripping is the initial driver for the decline of SFR in galaxies that are en route to the red sequence. The immediate question is then: What region in galaxies does ram-pressure stripping a\ufb00ect? To answer this question, we need to compare the amount of cold gas available at tq with the amount of star formation that ocurrs subsequently. We compute the following ratios: the ratios of the amount of stars formed during the time interval from tq to the time the galaxy turns red (tr) to the di\ufb00erence between the amount of \u2013 20 \u2013 \u22122 \u22121 0 1 0.1 0.2 0.3 0.4 M*>3x109 PDF \u22123 \u22122 \u22121 0 1 2 0 0.1 0.2 0.3 0.4 M*>3x1010 log\u22126 M*/6 MX PDF     X=10 X=30 X=100 Fig. 8.\u2014 shows the distribution of \u2212\u2206M\u2217/\u2206MX at three radial ranges, X = (10, 30, 100). \u2206M\u2217is the amount of stars formed during the time interval from the onset of quenching tq to the time the galaxy turns red tr, and \u2206MX is the di\ufb00erence of the amount of cold (T < 105K) gas within a radius X kpc between tr and tq. The vertical dashed lines show the medians of the corresponding histograms of the same colors. cold (T < 105K) gas at tq and tr, denoted as (\u2212\u2206M\u2217/\u2206M10, \u2212\u2206M\u2217/\u2206M30, \u2212\u2206M\u2217/\u2206M100) within three radii (10, 30, 100)kpc. The minus signs are intended to make the ratios positive, since stellar mass typically increase with time, whereas the cold gas mass for galaxies being quenched decreases. Note that \u2206M\u2217could be negative. We set a \ufb02oor value to the above ratios at 10\u22123. Figure (8) shows the distributions of \u2212\u2206M\u2217/\u2206MX, where X = (10, 30, 100). We see that for r \u226410kpc the peak of the distribution (red histograms) for all stellar masses is at \u2212\u2206M\u2217/\u2206M10 > 1, typically in the range of 2 \u221210, with the vast majority of cases at > 1. For a larger radius r \u226430kpc the distribution (green histograms) for all stellar masses is now peaked at \u2212\u2206M\u2217/\u2206M30 \u223c1 with about 50% at < 1, while for a still larger radius r \u2264100kpc the distribution (green histograms) it is now shifted to \u2212\u2206M\u2217/\u2206M100 \u22641 and more than 50% at less than (0.01, 0.4) for galaxies of stellar mass > (3 \u00d7 109, 3 \u00d7 1010) M\u2299, respectively. This is unambiguous evidence that ram-pressure stripping removes the majority of cold gas on scales \u226530kpc, while the cold gas within 10kpc is una\ufb00ected by ram-pressure stripping and consumed by subsequent in situ star formation. It is noted that the lack of e\ufb00ect on the cold gas at r < 10kpc by ram-pressure stripping seems universal, the gas removal by ram-pressure stripping at larger radii r > 30kpc varies substantially from galaxy to galaxy, which we argue is consistent with the large variations of \u03c4q seen in Figure 5. We thus conclude \u2013 21 \u2013 \u22121 \u22120.5 0 0.5 1 0 0.2 0.4 0.6 log re (SFR) (kpc) PDF     M*=3\u00d7 109 M*>3\u00d7 1010 \u22120.6 \u22120.4 \u22120.2 0 0.2 0 0.2 0.4 0.6 dre(SFR)/dlnSFR (kpc) PDF red     M*>3\u00d7 109 M*>3\u00d7 1010 Fig. 9.\u2014 Left panel shows the distribution of the e\ufb00ective radius of stars formed in the last 100Myrs, re(SFR), at tq for galaxies in two stellar mass ranges. The vertical dot-dashed line indicates the e\ufb00ective resolution of the simulation, taken from the bottom-right panel in Figure 3. Right panel shows the distribution of the ratio of the decline of re(SFR) with respect to the decline of SFR, d re(SFR)/d ln SFR at tq. In each panel, we di\ufb00erentiate between galaxies in three separate stellar mass ranges. The vertical lines show the medians of the corresponding histograms of the same colors. that there is continued nuclear SF in the quenching phase. Feldmann et al. (2011), based on a smaller sample of simulated galaxies that form a group of galaxies with a spatial resolution of 300pc (compared to 160pc here), \ufb01nd that in situ star formation is responsible for consuming a substantial fraction of the residual gas on small scales after gas accretion is stopped subsequent to the infall, consistent with our results. This outside-in ram-pressure stripping picture and continuous SF in the inner region that emerges from the above analysis has important implications and observable consequences, consistent with the latest observations (e.g., Gavazzi et al. 2013). We quantify how centrally concentrated the star formation is at the outset of SF quenching in Figure (9), in part to assess our ability to resolve SF during the quenching phase. The left panel shows the distribution of the e\ufb00ective radius of stars formed in the last 100Myrs prior to tq, denoted as rSFR e , for galaxies in two stellar mass ranges. The right panel shows the distribution of the ratio of the decline of rSFR e with respect to the decline of SFR, drSFR e /d ln SFR at tq. It is evident from Figure (9) that more massive galaxies tend to have larger rSFR e , as expected. It is also evident that the recent formation for the vast majority of galaxies occurs within a radius of a few kiloparsecs. It is noted that ongoing SF in a signi\ufb01cant fraction of galaxies with stellar masses \u22643 \u00d7 109 M\u2299is under-resolved, as indicated by the vertical dot-dashed line in the left panel. However, none of our subsequent conclusions would be much altered by this numerical e\ufb00ect, because (1) all of our conclusions appear to be universal across the stellar mass ranges and (2) the inner region of 10kpc is not much a\ufb00ected by ram-pressure stripping anyway (thus underresolving a small central fraction within 10kpc does not a\ufb00ect the overall ram-pressure stripping e\ufb00ects). What is interesting is that more than 50% of galaxies in both stellar mass ranges have negative values of drSFR e /d ln SFR at tq, indicating that, when the SFR decreases in the quenching \u2013 22 \u2013 phase, star formation proceeds at progressively larger radii in the central region. This result, while maybe somewhat counter-intuitive, is physically understandable. We attribute this inside-out star formation picture to the star formation rate surface density being a superlinear function of gas surface density in the Kennicutt-Schmidt (Schmidt 1959; Kennicutt 1998) law. The picture goes as follows: when gas supply from large scales (\u223c100kpc) is cut o\ufb00and under the assumption that gas in the central region does not re-distribute radially, the SFR diminishes faster with decreasing radius in the central region where SF occurs, causing the e\ufb00ective SF radius to increase with time and star formation rate to decline faster than cold gas content, while the overall SFR is declining. In summary, ram-pressure stripping is ine\ufb00ective in removing cold gas that is already present on scales of \u226410kpc but most e\ufb00ective in removing less dense gas on larger scales of \u226530kpc. The chief role played by ram-pressure stripping appears to disconnect galaxies from their cold reservoir on scales that are much larger the typical stellar radii. The time scale in question is then on the order of the dynamical time of galaxies at close to the virial radius. 3.2. Starving Galaxies to the Red Sequence and Environmental Sphere of In\ufb02uence The previous subsection details some of the e\ufb00ects on galaxies being quenched due to gas removal by ram-pressure stripping (in conjunction with other hydrodynamical processes) along with consumption by concurrent SF. Our attention is now turned to the subsequent evolution. Figure 10 plots tqr against four environmental variables at tq. From all panels we consistently see the expected trends: the time interval tqr from onset of quenching tq to turning red tr, on average, decreases with increasing environmental pressure, increasing environmental entropy, increasing environmental overdensity and decreasing distance to the primary galaxy. While there is a discernible di\ufb00erence in tqr between satellite galaxies and central galaxies, the di\ufb00erence is substantially smaller than that in the initial exponential decay time scale of SFR \u03c4q (see Figure 5). This observation makes it clear that the onset of quenching initiated by ram-pressure stripping does not determine the overall duration of quenching. Since all the environment variables used tend to broadly correlate with one another higher density regions tend to have higher temperatures, higher gas entropy and higher pressure it is not surprising that we see tqr are correlated with all of them in the expected sense. Earlier we have shown that tqr is weakly anti-correlated with the stellar surface density at re, \u03a3e (see bottom-panel of Figure 6). This suggests that the overall duration from onset of quenching to turning red is not a matter of a galaxy\u2019s ability to hold on to its existing cold gas but rather the extent of the external gas supply condition, i.e., environment. This hypothesis is signi\ufb01cantly a\ufb03rmed by noticing that the strongest anti-correlation is found between tqr and S300, among all environment variables examined. Thus, we conclude, given available evidence, that the eventual \u201cpush\u201d of galaxies into the red sequence is not as a spectacular event as the initial onset of quenching that is triggered by a cuto\ufb00of large-scale gas supply due to ram-pressure stripping, and is essentially the process of gas starvation, when the galaxy has entered a low cold gas density and/or high temperature and/or high velocity dispersion environment. We present distributions of tqr in Figure 11. The top-left panel shows the distribution of tqr for satellite galaxies (those with d/rc h \u22641), grouped into three primary halo mass ranges: \u2013 23 \u2013 0 1 2 2.5 3 3.5 log S300@tq (keV cm2) log tqr (Myr) 0 1 2 3 4 5 2.5 3 3.5 log p300@tq (K cm\u22123) log tqr (Myr)     M* = 3\u00d7 109 M* = 1010 M* = 1011 \u22121 0 1 2 2.5 3 3.5 log 1+b2@tq log tqr (Myr) red: satellites black: centrals 1 2 3 4 5 2.5 3 3.5 d/rv c@tq log tqr (Myr) Fig. 10.\u2014 shows tqr (time interval from the onset of quenching to the time the galaxy turns red) against four environmental variables at tq: ram-pressure p300 on 300kpc proper scale, environmental entropy S300 on 300kpc proper scale, distance to primary galaxy d/rc v in units of the primary galaxy\u2019s virial radius and environmental overdensity \u03b42 on 2h\u22121Mpc comoving scale. The red dash line in the upper-right panel is intended to indicate a visually noticeable trend. Red circles are satellite galaxies at tq, i.e., within the virial radius of a larger galaxy, and black circles are for non-satellite galaxies. The size of each circle indicates the stellar mass of a galaxy, as shown in the legend in the lower-left panel. M c h = 1011 \u22121012 M\u2299(black), M c h = 1012 \u22121013 M\u2299(green), M c h > 1013 M\u2299(red); the medians of the distributions are (1.2,1.3,1.2)Gyr, respectively. The top-right panel shows the distribution of tqr for satellite galaxies grouped into three ranges of the ratio of satellite to cental stellar mass: M s \u2217/M c \u2217= 0.1 \u22121 (black), M s \u2217/M c \u2217= 0.01 \u22120.1 (green), M s \u2217/M c \u2217= 0.001 \u22120.01 (red); the medians of the distributions of the three groups are nearly identical at \u223c1.3Gyr. The bottom-left panel shows the distribution of tqr for primary galaxies (those with d/rc h > 1), grouped into two halo mass ranges: M c h = 1010 \u22121011 M\u2299(black), and M c h = 1011 \u22121012 M\u2299(green). We see that the medians of the distributions are 1.2Gyr for both mass ranges. The bottom-right panel plots the distribution of all satellite galaxies and all central galaxies, along with a simple gaussian \ufb01t to the combined set. A look of the bottom-right panel of Figure 11 suggests that there is practically no di\ufb00erence between the two distributions. At \ufb01rst sight, this may seem incomprehensible. A closer examination reveals the underlying physics. \u2013 24 \u2013 \u22120.4 \u22120.2 0 0.2 0.4 0.6 0 0.1 0.2 0.3 0.4 log tqr (Gyr) PDF satellites     Mh c=1011\u221212 Mh c=1012\u221213 Mh c>1013 \u22120.4 \u22120.2 0 0.2 0.4 0.6 0 0.1 0.2 0.3 0.4 log tqr (Gyr) PDF satellites     M* s/M* c=0.1\u22121 M* s/M* c=10\u22122\u221210\u22121 M* s/M* c=10\u22123\u221210\u22122 \u22120.4 \u22120.2 0 0.2 0.4 0.6 0 0.1 0.2 0.3 0.4 log tqr (Gyr) PDF centrals     Mh c=1010\u221211 Mh c=1011\u221212 \u22120.4 \u22120.2 0 0.2 0.4 0.6 0 0.1 0.2 0.3 0.4 log tqr (Gyr) PDF     all satellites all centrals all galaxies Fig. 11.\u2014 Top-left panel: shows the distribution of tqr for satellite galaxies at z = 0.62, separated into three primary halo mass ranges: M c h = 1011 \u22121012 M\u2299(black), M c h = 1012 \u22121013 M\u2299(green), M c h > 1013 M\u2299(red). Top-right panel: shows the distribution of tqr for satellite galaxies at z = 0.62, separated into three ranges of satellite stellar mass to primary stellar mass ratio: M s \u2217/M c \u2217= 0.1 \u22121 (black), M s \u2217/M c \u2217= 0.01 \u22120.1 (green), M s \u2217/M c \u2217= 0.001 \u22120.01 (red). Bottom left panel: shows the distribution of tqr for primary galaxies at z = 0.62, separated into three primary halo mass ranges: M c h = 1010 \u22121011 M\u2299(black), M c h = 1011 \u22121012 M\u2299(green), M c h > 1012 M\u2299(red). The three vertical dashed lines of order (thin, thick, thin) are the (25%, 50%, 75%) percentiles for the histograms of the same color. Bottom right panel: shows the distribution of tqr for all satellite galaxies (blue), all primary galaxies (red) and all galaxies (black) at z = 0.62. An eye-balling lognormal \ufb01t is shown as the magenta line (see Eq 2). Figure 12 shows the distributions of d/rc v at tq for satellite (red) and central (black) red galaxies at z = 0.62. While it is not a surprise that the vast majority of the satellite galaxies at z = 0.62 have their onset of quenching taking place at d/rc v \u22643 at tq, it is evident that the same appears to be true for the central galaxies at z = 0.62. This observation supports the picture that both satellite and central red galaxies at z = 0.62 have been subject to similar environment e\ufb00ects that turn them red. It is noted again that this statement that red central galaxies have been subject to similar processes as the red satellite galaxies has been quantitatively con\ufb01rmed in Figure 11. \u2013 25 \u2013 0 1 2 3 4 5 0 0.05 0.1 0.15 d/rv c@tq PDF     M* > 3\u00d7 109 satellites at z=0.62 M* > 3\u00d7 109 centrals at z=0.62 Fig. 12.\u2014 shows the distribution of the relative distance d/rc v of progenitors at tq of red galaxies at z = 0.62 for two subsets of galaxies: the red histogram for those that are within the virial radius of a larger galaxy (i.e., satellite galaxies at z = 0.62) and the black histogram for those that are not within the virial radius of a larger galaxy at z = 0.62. The thick blue vertical dashed lines are 50% percentiles for all galaxies being quenched and the thin blue vertical dashed lines are 25% and 75% percentiles. The suggestion by Wetzel et al. (2013b) that some central galaxies are ejected satellite galaxies is consistent with our \ufb01ndings here. Our study thus clearly indicates that one should not confuse red central galaxies with their being quenched by processes other than environment. In fact, all available evidence suggests that it is environment quenching that plays the dominant role for the vast majority of galaxies that turn red, whether they become satellite galaxies at z = 0.62 or not. Feldmann et al. (2011), using a much smaller sample of simulated galaxies that form a group of galaxies, \ufb01nd that quenching of gas accretion starts at a few virial radii from the group center, in good agreement with our results. It is seen in Figure 12 that only about 20% of the onset of galaxy quenching occurs as satellites, i.e., within the virial radius of a larger galaxy, consistent with conclusion derived by others (e.g., van den Bosch et al. 2008). In the bottom-right panel of Figure 11 we provide an approximate \ufb01t to the distribution of tqr for all quenched galaxies normalized to galaxies at z = 0.62 as f(log tqr) = 1 2 log tmed \u221a 2\u03c0 exp \u0002 \u2212(log tqr/ log tmed \u22121)2/8 \u0003 , (2) where tqr and tmed are in Gyr and log tmed = 0.08 \u22121.5 \u00d7 log((1 + z)/1.62). The adopted log tmed = 0.08 \u22121.5 \u00d7 log(1 + z)/1.62 dependence on z is merely an estimate of the time scale, had it scaled \u2013 26 \u2013 with redshift proportional to the dynamical time of the universe. One is cautioned not to apply this literally. Nevertheless, it is likely that the median quenching time at lower redshift is longer than \u223c1.2Gyr at z = 0.62, perhaps in the range of 2 \u22123Gyr. Incidentally, this estimated quenching time, if extrapolated to z = 0, is consistent with theoretical interpretation of observational data in semi-analytic modeling or N-Body simulations (e.g., Taranu et al. 2012; Wetzel et al. 2013a). In semi-analytic modeling (e.g., Kimm et al. 2009), the quenching time is often taken to be a delta function. In other words, the satellite quenching process is assumed to be uniform, independent of the internal and external properties of the satellites. Our simulation results (see Eq 2) indicate that such a simplistic approach is not well motivated physically. We suggest that, if a spread in quenching time is introduced in the semi-analytic modeling, an improvement on the agreement between predictions based on semi-analytic modeling and observations may result in. In summary, we \ufb01nd that, within the environmental sphere of in\ufb02uence, galaxies are disconnected with their large-scale cold gas supply by ram-pressure stripping, and subsequently lack of gas cooling and/or accretion in high velocity environment ensures a prolonged period of gas starvation that ultimately turns galaxies red. This applies to satellite galaxies as well as the vast majority of \u201capparent\u201d central red galaxies. The dominance of environment quenching that is found in ab initio cosmological simulations here is in accord with observations (e.g., van den Bosch et al. 2008; Peng et al. 2012; Kovac et al. 2013). 3.3. Color Migration Tracks On its way to the red sequence, a galaxy has to pass through the green valley. Do all galaxies in the green valley migrate to the red sequence? We examine the entire population of green galaxies in the redshift range z = 1 \u22121.5. Tracing these green galaxies to z = 0.62, we \ufb01nd that for galaxies with stellar masses greater than (109.5, 1010, 1010.5) M\u2299, respectively, (40%, 40%, 48%) of galaxies in the green valley at z = 1 \u22121.5, do not become red galaxies by z = 0.62. While this is an important prediction of our simulations, we do not provide more information on how one might tell apart these two di\ufb00erent population of galaxies in the green valley, except to point out that attempts to identify galaxies in the green valley as progenitors of red galaxies may generate some confusion. We examine the distributions (not shown) of the time that red galaxies spent in the green valley, tgreen, en route to the red sequence. The trends with respect to Mh and M s \u2217/M c \u2217seen are similar to those seen in Figure 11. No signi\ufb01cant di\ufb00erentiation among halo masses of central galaxies is visible, once again supportive of environment quenching. Overall, one may summarize the results in three points. First, tgreen is almost universal, independent of being satellites or not, the mass, or the ratio of masses. Second, the range tgreen = 0.30 \u00b1 0.15Gyr appears to enclose most of the galaxies, although there is a signi\ufb01cant tail towards the high end for satellites in low mass central halos. Third, comparing tgreen \u223c0.3Gyr to the interval from onset of quenching to the time galaxy turning red of tqr = 1.2 \u22121.3Gyr, it indicates that, from the onset of quenching to turning red, typical galaxies spend about 25% of the time in the green valley. Let us now examine the migration tracks of galaxies that eventually enter the red sequence. \u2013 27 \u2013 9 10 11 12 \u22120.2 \u22120.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 log M* (Msun) g\u2212r     t(green)=200Myrs t(green)=500Myrs Fig. 13.\u2014 shows the evolutionary tracks of 30 semi-randomly selected galaxies on the stellar mass M\u2217-g-r color plane. The 30 galaxies are selected to be clustered around three masses, M\u2217= (109.5, 1010.1, 1011) M\u2299. Each track has a circle attached at the end of the green period to indicate the time spent in the green valley. We shall call this diagram \u201cskyrockets\u201d diagram of galaxy color migration. Figure 13 shows the color-stellar mass diagram for 30 semi-randomly selected red galaxies. It is striking that the color evolution in the green valley and red sequence is mostly vertical, i.e., not accompanied by signi\ufb01cant change in stellar mass. This means that the stellar mass growth of most galaxies must occur in the blue cloud. One can see easily that the blue tracks are mostly moving from lower left to upper right with time for g\u2212r \u22640.3, indicating that galaxies grow when in the blue cloud. In the blue cloud it is seen that there are occasional horizontal tracks, representing mergers that maintain overall color. These are mergers that do not result in red galaxies. The examples of these include the two most massive galaxies in the plot with \ufb01nal stellar masses of \u223c1011.6 M\u2299, where there is a major binary merger of (1011.25 + 1011.25) M\u2299at g \u2212r = 0.26. There are also cases where the tracks temporarily go from north-west to south-east, indicating signi\ufb01cant/major mergers that trigger starbursts that render the remnant galaxies bluer. This anecdotal evidence that galaxies do not signi\ufb01cantly grow mass in the red sequence will be con\ufb01rmed below quantitatively. Feldmann et al. (2011), using a small sample of simulated galaxies that form a group of galaxies, \ufb01nd that mergers and signi\ufb01cant mass growth in galaxies occur, prior to their entering groupd environment, consistent with the \ufb01ndings here. Thus, this \u201cskyrockets\u201d diagram of color-stellar mass evolution in Figure 13 turns out to be a fair representation of typical tracks of galaxies that become red galaxies. We address the stellar mass growth of red galaxies quantitatively in two di\ufb00erent ways. The left panel of Figure 14 shows the histogram of the ratio of stellar mass of red galaxies at z = 0.62 to their progenitor\u2019s stellar mass at the onset of quenching tq. We see that the overall stellar mass growth of red galaxies since the onset of quenching is relatively moderate, with the vast majority of \u2013 28 \u2013 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 M*/M* q PDF     >3\u00d7109 >3\u00d71010 9 10 11 \u22124 \u22123 \u22122 \u22121 10% increase log M* (Msun) log n(>M*) (h3Mpc\u22123)     CMF of red galaxies z=0.62 CMF of red galaxies z=0.86 Fig. 14.\u2014 Left panel: the histogram of the ratio of stellar mass of red galaxies at z = 0.62 to their progenitor\u2019s stellar mass at the onset of quenching tq, for two stellar mass ranges of the red galaxies at z = 0.62. Right panel: cumulative stellar mass functions of red galaxies at z = 0.62 (blue) and z = 1 (magenta). For the red galaxies at z = 0.62 we \ufb01nd that the median value of tq corresponds to redshift z \u223c0.86, thus the choice of z = 0.86. galaxies gaining less than 30% of their stellar mass during this period, consistent with observations (e.g., Peng et al. 2010, 2012). There is a non-negligible fraction of galaxies that experience a decline of stellar mass, due to tidal interactions and collisions. There is 5 \u221210% of red galaxies that gain more than \u226540% of their stellar mass during this period, possibly due to mergers and accretion of satellite galaxies. We do not address red galaxies more massive than 1012 M\u2299because of lack of a statistically signi\ufb01cant red sample. Since these larger galaxies tend to reside at the centers of groups and clusters, there is a larger probability that AGN feedback may play a signi\ufb01cant role in them. Empirical evidence suggests that radio jets get extinguished in the near vicinity of the central galaxies in groups/clusters (e.g., McNamara & Nulsen 2007), in sharp contrast to AGNs in isolated galaxies where jets, seen as large radio lobes, appear to deposit most of their energy on scales much larger than the star formation regions. Thus, AGN feedback in the central massive galaxies in clusters/groups may be energetically important to have a major e\ufb00ect on gas cooling and star formation in them (e.g., Omma & Binney 2004). Thus, our neglect of AGN feedback in the simulation cautions us to not draw any de\ufb01nitive conclusion with respect to this special class of galaxies at this time. The stellar mass growth of individual red galaxies shown in the left panel of Figure 14 contains very useful information. However, it does not address a related but separate question: How does the stellar mass function of red galaxies evolve with redshift? We address this question here. We compute the cumulative stellar mass function of red galaxies at z = 0.62 and z = 0.86, separately, and show them in the right panel of Figure 14. We see that for red galaxies with stellar masses greater than \u223c3 \u00d7 1010 M\u2299, when matched in abundance, the stellar masses grow a factor of \u223c1.6 from z = 0.86 to z = 0.62, much larger than 10% (for about 75% of galaxies) seen in the left panel of Figure 14. We refrain from making a direct comparison to observations in this case, because our \u2013 29 \u2013 limited simulation volume is highly biased with respect to the massive end of the mass function. We strict ourselves to a comparative analysis of galaxies in our simulation volume and ask the question of how red galaxies in our simulation volume grow with time. The most important point to note is that this apparent growth of stellar mass of red galaxies based on abundance matching could not be due to growth of individual red galaxies in the red sequence, since the actual stellar mass increase since the onset of quenching is moderate, \u226410% typically, seen in the left panel of Figure 14. Physically, this suggests that dry mergers do not play a major role in the \u201capparent\u201d stellar mass growth of red galaxies, consistent with observations (e.g., Pozzetti et al. 2007). Rather, galaxies grow their stellar mass when they are still in the blue cloud, illustrated in Figure 13. A physical picture of galaxy color migration emerges based on our results. The migration from the blue cloud to the red sequence proceeds in a staggered fashion: stellar masses of individual galaxies continuously grow, predominantly in the blue cloud, and blue galaxies over the entire mass range continuously migrate into the red sequence over time. Galaxies migrate from the blue cloud to the red sequence almost vertically in the usual color-magnitude diagram (see Figure 13). For simplicity we will call this type of color migration \u201cVertical Tracks\u201d, which correspond most closely to \u201cB tracks\u201d proposed by Faber et al. (2007), with the growth since the onset of quenching being moderate (\u226430%). 3.4. Galaxy Age-Mass and Age-Environment Relations The vertical tracks found have many implications on observables. The \ufb01rst question one asks is this: if galaxies follow the vertical tracks, is the galaxy age-mass relation consistent with observations? We address this question in this subsection. Figure 15 shows a scatter plot of red galaxies in the stellar mass M\u2217-mean galaxy formation time tf plane at z = 0.62 (top) and z = 1 (bottom), where tf is stellar formation time, not lookback time. The red galaxies are subdivided into two groups: centrals (black circles) and satellites (red circles). For the purpose of comparison to observations, we only show galaxies with high surface brightness of \u00b5B < 23 mag arcsec\u22122 (e.g., Impey & Bothun 1997). Several interesting results can be learned. First, no systematic di\ufb00erence between satellite and central galaxies is visible, supporting earlier \ufb01ndings that there is no appreciable di\ufb00erences between satellites and centrals with respect to duration from quenching to turning red tqr (Figure 11). Second, at any given redshift, the brightest red galaxies are relatively \u201cold\u201d (but not necessarily the oldest), of ages of several billion years (age = tH \u2212tf and tH = (7.85, 5.94)Gyr for z = (0.62, 1)), consistent with observations. Third, at stellar masses greater than 1010.2\u221210.7 M\u2299red galaxies have a nearly uniform mean age; the age spread at a given stellar mass of \u223c1Gyrs is consistent with observations (e.g., Demarco et al. 2010). Fourth, fainter red galaxies are younger than brighter red galaxies in the mass range 109.5\u221210.5 M\u2299; we see that the age di\ufb00erence between the two ends of the mass range is \u223c2.5Gyr and 1.3Gyr, respectively, at z = 0.62 and z = 1, suggesting a steepening with decreasing redshift of the age di\ufb00erence between galaxies of di\ufb00erent masses in the red sequence. Demarco et al. (2010) \ufb01nd an age di\ufb00erence between the faint and bright ends of red sequence galaxies of \u223c2Gyr at z = 0.84, in \u2013 30 \u2013 9 10 11 12 2 3 4 5 6 tf(high mass)=3.2 Gyr log tf (Gyr) red galaxies@z=0.62     centrals satellites mean <tf> symptotic 9 10 11 12 2 3 4 tf(high mass)=2.8 Gyr log M* (Msun) log tf (Gyr) red galaxies@z=1     centrals satellites mean <tf> symptotic Fig. 15.\u2014 shows a scatter plot of red galaxies in the stellar mass M\u2217-mean galaxy formation time tf plane at z = 0.62 (top) and z = 1 (bottom), where tf is stellar formation time, not lookback time. The red galaxies are subdivided into two groups: centrals (black circles) and satellites (red circles). For the purpose of comparison to observations, we only show galaxies with high surface brightness of < 23B mag arcsec\u22122 (e.g., Impey & Bothun 1997). The green horizontal dashed lines indicate the mean formation redshift of the most luminous red galaxies at the two redshifts. The magenta dots are the averages of tf at the stellar mass bins. excellent agreement with our results. The physical origin for the steepening with decreasing redshift of the age di\ufb00erence between galaxies of di\ufb00erent masses in the red sequence is traceable to the steepening of speci\ufb01c SFR with stellar mass with decreasing redshift that is, in a fundamental way, related to the cosmic downsizing phenomenon (Cen 2011a). It is interesting to note that, in Figure 15, scatters notwithstanding, there appears to be a critical stellar mass of \u223c1010.2\u221210.7 M\u2299, above which the age (or formation time) of red galaxies \ufb02attens out to a constant value. At least for the redshift range that we have examined, z = 0.62\u22121, this critical stellar mass appears to be redshift independent. At still higher redshift we do not have enough statistics to see if this critical mass remains the same. This critical mass is tantalizingly close to the division mass of \u223c1010.5 M\u2299discovered by Kau\ufb00mann et al. (2003) at low redshift, which appears to demarcate a number of interesting trends in galaxy properties. This physical origin of this mass is unclear and deferred to a future study. Given the \u201cvertical tracks\u201d, i.e., lack of signi\ufb01cant stellar mass growth subsequently to quench\u2013 31 \u2013 9 10 11 12 2 3 4 5 6 log tf (Gyr) red blue@z=0.80\u22120.94 9 10 11 12 2 3 4 5 6 non\u2212red blue@z=0.80\u22120.94 9 10 11 12 1.2 1.5 2 log M* (Msun) log tf (Gyr) blue@z=3, res=114pc/h 9 10 11 12 1.2 1.5 2 zf=4 log M* (Msun) blue@z=3, res=29pc/h Fig. 16.\u2014 shows the stellar mass M\u2217-mean galaxy formation time tf scatter plot for blue galaxies at z = 0.80\u22120.94 that become red galaxies (top left) and that do not become red galaxies (top right). Each small group of mostly linearly aligned circles is one galaxy that appears multiple times (maximum is 8). The blue dots indicate average values. The green horizontal dashed lines and the magenta dots are the same in the top panel of Figure (15), indicating the mean formation time of the most luminous red galaxies and the average formation time of red galaxies at z = 0.62. Bottom left panel: shows the stellar mass M\u2217-mean galaxy formation time tf scatter plot for blue galaxies at z = 3 with the \ufb01ducial resolution 114pc/h. Bottom right panel: shows the stellar mass M\u2217-mean galaxy formation time tf scatter plot for blue galaxies at z = 3 with the four times better resolution of 29pc/h. The blue dots indicate average values. ing, one may ask this: is the age-mass relation of red galaxies inherited from their blue progenitors? We will now address this question. To select progenitors of red galaxies at z = 0.62, we note that the majority of galaxies that turn red by z = 0.62 have tqr = 1\u22121.7Gyr. Thus, we choose galaxies in the redshift range z = 0.80\u22120.94 (8 snapshots with z = (0.80, 0.82, 0.84, 0.86, 0.88, 0.90, 0.92, 0.94)), where the Hubble time di\ufb00erences between z = 0.62 and z = 0.80 and z = 0.94 are (1.0, 1.7)Gyr, respectively, enclosing the vast majority of blue progenitors of red galaxies at z = 0.62 near the onset of quenching. We separate the blue galaxies into two groups: one group contains the blue progenitors of z = 0.62 red galaxies and the other group other blue galaxies that have not turned into red galaxies by z = 0.62. Figure 16 shows the stellar mass M\u2217-mean galaxy formation time tf scatter plot for blue galaxies at z = 0.80 \u22120.94 that are progenitors of red galaxies at z = 0.62 (top left) and those that do not become red galaxies (top right). Each small group of mostly linearly aligned circles is one galaxy that appears multiple times (maximum is 8). Within the scatters we see that the green dashed line, borrowed from Figure 15, provides a good match to the near constant \u2013 32 \u2013 age at the high mass end for the progenitors of red galaxies. The magenta dots, borrowed from Figure 15, match well the trend for the blue dots in the mass range 109.5\u221210.5 M\u2299. These results are fully consistent with our initial expectation based on the observation (of our simulation) of two physical processes: (1) that stellar mass growth is moderate during tqr hence evolution during tqr does not signi\ufb01cantly alter the mean star formation time of each galaxy, (2) less massive forming galaxies have higher sSFR than massive galaxies, causing a steepening of the age-mass relation at the low mass end. This explains the physical origin of the age-mass relation seen in Figure 15. It is prudent to make sure that these important general trends seen in the simulation are robust. In the bottom two panels of Figure 16 we make a comparison between blue galaxies of two simulations with di\ufb00erent resolutions, at z = 3. The bottom-left panel is from the \ufb01ducial simulation with a resolution of 114pc/h and the bottom-right panel is from an identical simulation with four times better resolution of 29pc/h. We see that both the age-mass trend at low mass end and the near constancy of stellar age at the high mass end are shared by the two simulations, suggesting that results from our \ufb01ducial simulation are su\ufb03ciently converged for the general trends presented at the level of concerned accuracies. A comparison between the top left and top right panels in Figure 16 makes it clear that the age-mass relation of the blue progenitors of red galaxies at quenching is, to a large degree, shared by blue galaxies that do not become red galaxies by z = 0.62. One subtle di\ufb00erence is that the most massive non-progenitor blue galaxies are slightly younger than the most massive progenitors of red galaxies, suggesting that the blue progenitors of red galaxies, on \u201ctheir way\u201d to become red galaxies, have started to \u201cforeshadow\u201d quenching e\ufb00ects mildly. 3.5. Environmental Dependencies of Various Galaxy Populations At a given redshift the cumulative environmental e\ufb00ects are imprinted on the relative distribution of galaxies of di\ufb00erent color types and possibly on the properties of galaxies within each type. We now present predictions of our simulations with respect to these aspects. Figure 17 shows distributions of three types of galaxies as a function of distance to the primary galaxy in units of the virial radius of the primary galaxy at z = 0.62. All galaxies with distance larger than 4 virial radii of the primary galaxy are added to the bin with d/rc v = 4 \u22125. We use the total galaxy population above the respective stellar mass threshold as a reference sample and distributions in the top (blue galaxies), middle (green galaxies) and bottom (red galaxies) panels are normalized relative to reference sample. Comparing the top (blue galaxies), middle (green galaxies) and bottom (red galaxies) panels, we see clear di\ufb00erences of environmental dependencies of the three types of galaxies. For blue galaxies, there is a de\ufb01cit at d/rc v \u22642, which is compensated by a comparable excess at d/rc v \u22653. The range d/rc v = 2 \u22123 seems to mark the region where an excess of green galaxies, about one half of which will become red galaxies during the next 1 \u22121.7Gyr. It is useful to recall that not all galaxies in the green valley will turn into red galaxies, which perhaps has contributed in part to some of the \u201cirregularities\u201d of the distribution of the green galaxies (middle panel). For red galaxies, we see a mirror image of blue galaxies: there is an excess at d/rc v \u22642 and a de\ufb01cit d/rc v \u22653. This trend is in agreement with observational indications (e.g., Woo et al. \u2013 33 \u2013 1 2 3 4 \u22120.5 0 0.5 1 PDFb/PDFt\u22121     blue galaxies >3\u00d7109 >1\u00d71010 >3\u00d71010 1 2 3 4 \u22120.5 0 0.5 PDFg/PDFt\u22121 green galaxies 0 1 2 3 4 5 \u22121 0 1 red galaxies d/rv c PDFr/PDFt\u22121 Fig. 17.\u2014 Top panel shows distribution of the distance to the nearest primary galaxy for blue galaxies at z = 0.62, PDFb/PDFt \u22121. The middle panel shows the normalized distribution of green galaxies, PDFg/PDFt \u22121. The bottom panel shows the normalized distribution of red galaxies, PDFr/PDFt \u22121. All galaxies with distance larger than 4 virial radii of the primary galaxy are added to the bin with d/rc v = 4 \u22125. 2013). The emerging picture found here that satellite quenching plays a dominant role in quenching galaxies is in accord with observations (e.g., van den Bosch et al. 2008; Peng et al. 2010, 2012). Figure 18 shows distributions of three types of galaxies as a function of environmental entropy S300. We see that the excess of red galaxies starts at S300 = 100 keV cm2 and rises toward higher entropy regions for red galaxies. The trend for blue galaxies is almost an inverted version of that for red galaxies. The trend for green galaxies lie in-between those for blue and red galaxies, as expected. In Cen (2011a) we put forth the notion that a critical entropy Sc = 100 keV cm2 (at z = 0.62 and weakly dependent on redshift), marks a transition to a regime of ine\ufb03cient gas cooling hence cold gas starvation, because above this entropy the gas cooling time exceeds the Hubble time. This is borne out with our more detailed analysis here. We also plot (not shown here) distributions of three types of galaxies as a function of the environmental pressure p300 and environmental overdensity \u03b42, respectively, and \ufb01nd that the trend is broadly similar to that see in Figure 18. Overall, our results are in accord with the observed density-morphology relation (e.g., Oemler 1974; Dressler 1980; Postman & Geller 1984; Cooper et al. 2006; Tanaka et al. 2007; Bundy et al. 2006; Quadri et al. 2012; Muzzin et al. 2012), and with the general observed trend of galaxy population becoming \u2013 34 \u2013 1 2 3 \u22120.5 0 1 PDFb/PDFt\u22121     blue galaxies >3\u00d7109 >1\u00d71010 >3\u00d71010 1 2 3 \u22120.5 0 1 PDFg/PDFt\u22121 green galaxies 1 2 3 \u22121 0 1 2 3 4 log S300 (keV cm2) PDFr/PDFt\u22121 red galaxies Fig. 18.\u2014 Top panel shows the normalized environmental entropy distribution of blue galaxies at z = 0.62, PDFb/PDFt \u22121. The middle panel shows the normalized di\ufb00erence distribution of green and blue galaxies, PDFg/PDFb \u22121. The bottom panel shows the normalized di\ufb00erence distribution of red and blue galaxies, PDFr/PDFb \u22121. bluer or mean/median speci\ufb01c star formation rate becoming higher towards underdense regions in the local universe (e.g., Lewis et al. 2002; Goto et al. 2003; G\u00b4 omez et al. 2003; Tanaka et al. 2004; Rojas et al. 2004). Having examined the dependencies of three types of galaxies on environmental variables, we now explore the dependencies on two additional variables: the mass of the halo of the primary galaxy and the secondary to primary galaxy stellar mass ratio. Figure 19 shows fractions of three populations of galaxies in terms of color (red, green, blue) as a function of secondary to primary galaxy stellar mass ratio. The (left, middle, right) columns are for primary galaxies of halo masses in three ranges (1011\u221212 M\u2299,1012\u221213 M\u2299,1013\u221214 M\u2299) respectively. The four rows from top to bottom are for secondaries within four di\ufb00erent radial shells centered on the primary galaxy (\u2264rc v, [1\u22122]rc v, [2\u22123]rc v, [3 \u22124]rc v). We adopt the following language to make comparative statements: the environment quenching is important if the fraction of blue galaxies is less than the fraction of red galaxies and vice versa. We see two separate trends in Figure 19. First, more massive environments are more able to quench star formation; for primary galaxies with halo masses in the range of 1013 \u22121014 M\u2299 the quenching appears to extend at least to [2 \u22123]rc v, whereas for primary galaxies with lower halo \u2013 35 \u2013 \u22122 \u22121 0 0.5 0.9 1 Mh c=1013\u221214 \u22122 \u22121 0 0.5 0.9 1 PDF (d=[2\u22123]rv c) \u22123 \u22122 \u22121 0 0.5 0.9 1 PDF (d=[2\u22123]rv c) log M* s/M* c \u22123 \u22122 \u22121 0 0.5 0.9 1 PDF (d=[2\u22123]rv c) log M* s/M* c \u22122 \u22121 0 0.5 0.9 1 Mh c=1012\u221213 PDF (d=[2\u22123]rv c) \u22122 \u22121 0 0.5 0.9 1 PDF (d=[2\u22123]rv c) \u22123 \u22122 \u22121 0 0.5 0.9 1 PDF (d=[2\u22123]rv c) log M* s/M* c \u22123 \u22122 \u22121 0 0.5 0.9 1 PDF (d=[2\u22123]rv c) log M* s/M* c \u22122 \u22121 0 0 0.5 0.9 Mh c=1011\u221212 PDF (d<rv c) \u22122 \u22121 0 0 0.5 0.9 PDF (d=[1\u22122]rv c) \u22123 \u22122 \u22121 0 0 0.5 0.9 log M* s/M* c PDF (d=[2\u22123]rv c)     red galaxies green galaxies blue galaxies \u22123 \u22122 \u22121 0 0 0.5 0.9 PDF (d=[3\u22124]rv c) log M* s/M* c Fig. 19.\u2014 shows fractions of three populations of galaxies in terms of color, (red, green, blue), as a function of satellite to primary galaxy stellar mass ratio. The (left, middle, right) columns are for primary halo mass of (1011\u221212 M\u2299,1012\u221213 M\u2299,1013\u221214 M\u2299). The four rows from top to bottom are for satellites within four di\ufb00erent radial shells centered on the primary galaxy (\u2264rc v, [1 \u22122]rc v, [2 \u22123]rc v, [3 \u22124]rc v). masses the quenching e\ufb00ect is no longer signi\ufb01cant at [2 \u22123]rc v. Second, for any given primary galaxy halo mass, the quenching is more e\ufb00ective when the ratio of secondary to primary stellar mass is smaller. That the impact of environmental e\ufb00ects increases with decreasing secondary to primary galaxy stellar mass ratio is perhaps not surprising and consistent with observations (e.g., Poggianti et al. 2009; Thomas et al. 2010; Wetzel et al. 2012), but at odds with the assumption of mass-independent environment quenching in empirical modeling (e.g., Peng et al. 2010). Our \ufb01nding that quenching is still e\ufb00ective down to at least halo mass range 1011 \u22121012 M\u2299for the primary is in agreement with observations (e.g., Wetzel et al. 2012). Mok et al. (2013), using deep GMOS-S spectroscopy for 11 galaxy groups at z = 0.8 \u22121, show that the strongest environmental dependence is observed in the fraction of passive galaxies, which make up only \u223c20 percent of the \ufb01eld in the mass range Mstar = 1010.3 \u22121011.0 M\u2299but are the dominant component of groups. If we take the radial range 3 \u22124rc v as the \u201c\ufb01eld\u201d, we see that the \u2013 36 \u2013 fraction of red galaxies is in the range 20 \u221230% (Figure 19), reaching 65 \u221290% within 2rc v, in agreement with Mok et al. (2013). In a large galaxy sample study of a z = 0.83 cluster, Patel et al. (2009) \ufb01nd that red galaxy fraction is 93 \u00b1 3% in the central region of the cluster and declines to a level of 64 \u00b1 3% at a projected cluster-centric radius of \u223c3Mpc. In the right column of Figure 19, for halos in the mass range of 1013\u221214 M\u2299, we see that within the virial radius the red fractions are in the range of 60 \u221290%, depending on the satellite to primary galaxy mass ratio, with the overall mean of red fraction within the virial radius in the range 80 \u221290%. The more central region has a red fraction higher than 80 \u221290%, consistent with their observation. Patel et al. (2009) also \ufb01nd that the environmental e\ufb00ect extends even beyond 3Mpc, which is about 3 virial radii for their cluster. From the right column in Figure 19 we see that red galaxies dominate up to 3 virial radii, in reasonable accord with observations. Some of our results are not necessarily the most straightforward to imagine physically in the absence of simulations and detailed analysis. For example, the interpretation by Presotto et al. (2012) that the rate of SF quenching is faster in groups than in the \ufb01eld may be interpreted, in a di\ufb00erent way, in the context of our results. The excess of quenched galaxies in group environments is larger than in less dense environments as seen in Figures (17,18), consistent with observations (Presotto et al. 2012). However, we show that the quenching time depends weakly on environment as shown in Figure 11. In other words, our simulations suggest the following physical picture: environment quenching of star formation in galaxies is more e\ufb03cient in more hostile environment (closer to a larger galaxy, higher density, high pressure, high entropy, etc), but not faster, for the most part. Given the unambiguous environmental e\ufb00ects on the relative distributions of galaxy colors, we ask the following reverse question: Can we decipher environmental e\ufb00ects on a set of blue galaxies alone across di\ufb00erent environments at any given epoch? Figure (20) shows the speci\ufb01c SFR (sSFR) distributions of blue galaxies as a function of the four environmental variables at z = 0.62. While one sees trends of the overall number of galaxies with respect to each of the environmental variables, as already shown in Figures (17,18), there is no strong visible trend of the mean value of sSFR with respect to environment for blue galaxies. To put it slightly di\ufb00erently, the variations of sSFR among blue galaxies at any given mass are su\ufb03ciently large and the quenching e\ufb00ects on galaxies at a given sSFR and stellar mass are su\ufb03ciently varied that at any environment the scatter in sSFR at a given stellar mass is larger than the di\ufb00erence in average sSFR. We attribute this result physically to the combined e\ufb00ects of substantial non-uniformity of the properties of blue galaxies prior to entering the environmental \u201cspheres\u201d of in\ufb02uence and substantial non-uniformity of the in\ufb02uence of the environment on galaxies illustrated in Figures (5 and 6). This result that the intrinsic properties of star-forming galaxies appear independent of environment is, however, in accord with observations (e.g., Ideue et al. 2012; Wijesinghe et al. 2012). \u2013 37 \u2013 0 1 2 3 \u22122 \u22121 0 log S300 (keV cm2) log sSFR (Gyr\u22121) blue galaxies \u22122 \u22121 0 1 2 3 4 \u22122 \u22121 0 log p300 (K cm\u22123) log sSFR (Gyr\u22121) blue galaxies 0 1 2 \u22122 \u22121 0 log 1+b2 log sSFR (Gyr\u22121) blue galaxies     M* = 3\u00d7 109 M* = 1010 M* = 1011 0 1 2 3 4 5 6 7 \u22122 \u22121 0 d/rv c log sSFR (Gyr\u22121) blue galaxies Fig. 20.\u2014 shows the speci\ufb01c SFR of blue galaxies at z = 0.62 as a function of each of the four environmental variables. Black circles are for central galaxies and red for satellites. The size of each circle indicates the stellar mass of a galaxy, as shown in the legend. The blue dots indicate median values. 4. Conclusions Utilizing ab initio Large-scale Adaptive-mesh-re\ufb01nement Omniscient Zoom-In cosmological hydrodynamic simulations (LAOZI Simulations) of the standard cold dark matter model, we perform a chronological and statistical study of formation and evolution of (1664, 367, 1296) (blue, green, red) galaxies of stellar mass 109.5 \u22121012.5 M\u2299at z = 0.62. The simulations have an ultra-high resolution of \u2264114pc/h with an additional calibration run of resolution 29pc/h. The soundness of treatment of relevant physical processes, especially the uncertain feedback processes from star formation, is checked and con\ufb01dence built by comparisons with a large set of independent observations over a range of scales and redshift. Here we examine some global trends of formation and evolution of galaxies, focusing on galaxy star formation quenching and color migration. We do not include AGN feedback, in part because of its large uncertainties and primarily because of our intention to focus on external e\ufb00ects. Our main \ufb01ndings may be summarized in several points. (1) Environment quenching is shown to be responsible for making the vast majority, if not all, of red galaxies. Two environmental conditions appear to be necessary in the making of a typical red galaxy: ram-pressure stripping and cold gas starvation. The ram-pressure stripping disconnects \u2013 38 \u2013 a galaxy from its large-scale cold gas reservoir, while existing cold gas in the central (\u223c10 kpc) region is una\ufb00ected by ram-pressure but consumed by diminishing SF with an exponential time of several hundred Myr. Subsequently, gas starvation in the high-velocity environment guards against further signi\ufb01cant SF, pushing it through the green valley to the red sequence. The total duration from the initial sharp drop of SFR to the time of entry into the red sequence is \u223c0.6 \u22123Gyr (see Eq 2 for a \ufb01tting formula) with the median of 1.2Gyr for red galaxies at z = 0.62. We suggest that adopting a spread in quenching time in the semi-analytic modeling may result in an improved treatment in that approach. (2) The radius of a galaxy\u2019s quenching sphere depends on properties of the infalling galaxy being quenched, causing large variations in the quenching time scales at a given radius and large variations in the quenching radius at a given mass of infalling galaxy. Nevertheless, the vast majority of red galaxies are found to be within three virial radii of a larger galaxy, at the onset of quenching when the speci\ufb01c star formation rate experiences the sharpest decline to fall below \u223c(10\u22122 \u221210\u22121)Gyr\u22121 (depending on the redshift when it occurs). The exponential decay time of SFR at the onset of quenching is, on average, about a factor of two shorter for events occurring within the virial radius of the quenching galaxy than for those outside the virial radius of the quenching galaxy, which may be evidence of enhanced quenching with the additional aid of tidal stripping when the onset of quenching takes place within the virial radius. However, it is stressed that the overall duration from the onset of quenching to the time entering the sequence does not depend much on environment. (3) Not all galaxies in the green valley migrate to the red sequence; (40%,40%,48%) of green valley galaxies of stellar mass > (3 \u00d7 109, 1010, 3 \u00d7 1010) M\u2299do not proceed to become red galaxies at z = 0.62 after having turned green for \u22652Gyrs. For those galaxies that are en route to the red sequence, the time spent in the green valley is brief, typically of 300Myr. (4) Throughout the quenching period and the ensuing period in the red sequence galaxies follow nearly vertical tracks in the color-stellar-mass diagram, which correspond most closely to \u201cC tracks\u201d proposed by Faber et al. (2007). In contrast, individual galaxies of all masses grow most of their stellar masses in the blue cloud, prior to the onset of quenching, and progressively more massive blue galaxies with already relatively old mean stellar ages continue to enter the red sequence. Consequently, correlations among observables of red galaxies such as the age-mass relation are largely inherited from their blue progenitors. The age-mass relation of simulated red galaxies is found to be in good agreement with observations. (5) While environmental e\ufb00ects are responsible for producing the environmental dependence of the color makeup of the galaxy population, the average properties (e.g., SFR) of blue galaxies as a sub-population display little dependence on environment, which is in agreement with observations. Overall, the excess (de\ufb01cit) of red (blue) galaxies occurs within about three virial radii, in good agreement with a wide range of observations. Our detailed examination suggests that the excess of quenched galaxies in progressively denser environment (groups, clusters, etc) is, for the most part, a result of quenching being more e\ufb03cient, not faster, on average, in denser environment. Physically, this comes about because most of the time it takes to drive a blue star-forming galaxy to the red sequence is spent during the starvation phase, not the initial gas removal phase by ram-pressure stripping that displays a stronger dependence on environment. \u2013 39 \u2013 I would like to thank Claire Lackner for providing the SQL based merger tree construction software, and Drs. John Wise, Matthew Turk and Sam Skillmans for help with analysis and visualization program yt (Turk et al. 2011). I would like to thank Michael Vogeley for a very careful reading of the manuscript, many colleagues for useful discussions, and an anonymous referee for a critical and constructive report. Computing resources were in part provided by the NASA HighEnd Computing (HEC) Program through the NASA Advanced Supercomputing (NAS) Division at Ames Research Center. This work is supported in part by grant NASA NNX11AI23G. The simulation data are available from the author upon request.",
                    "introduction": "The bimodal distribution of galaxy colors at low redshift is well established (e.g., Strateva et al. 2001; Blanton et al. 2003a; Kau\ufb00mann et al. 2003; Baldry et al. 2004). The \u201cblue cloud\u201d, 1Princeton University Observatory, Princeton, NJ 08544; cen@astro.princeton.edu arXiv:1311.5916v2  [astro-ph.CO]  15 Jan 2014 \u2013 2 \u2013 sometimes referred to as the \u201cstar formation sequence\u201d (Salim et al. 2007), is occupied by star- forming galaxies, while the \u201cred sequence\u201d galaxies appear to have little ongoing star formation (SF). It has been argued that this bimodality suggests that SF of the blue cloud galaxies en route to the red sequence must be turned o\ufb00promptly to prevent them from lingering in the green valley between the blue and red peaks. A number of physical mechanisms have been proposed to cause this apparent \u201cquenching\u201d of SF. Galaxy mergers have been suggested to trigger strong and rapid SF that subsequently drives gas away and shuts down further SF activities in a sudden fashion. However, recent observations show that galaxies in the green valley do not show merger signatures, perhaps disfavoring the merger scenario (e.g., Mendez et al. 2011). Feedback from active galactic nuclei (AGN) has also been suggested to provide quenching, but observational evidence for this scenario has been either inconclusive or at best circumstantial (e.g., Bundy et al. 2008; Santini et al. 2012; Bongiorno et al. 2012; Rosario et al. 2013). Some recent studies based on large data sets do not \ufb01nd evidence for AGN feedback playing a role in galaxy color migration (e.g., Zheng et al. 2007; Xue et al. 2010; Aird et al. 2012; Harrison et al. 2012; Swinbank et al. 2012; Mendel et al. 2013). External, environmental e\ufb00ects may have played an important role in shaping galaxy colors. High density environments are observed to be occupied primarily by early type (elliptical and S0) red galaxies - the \u201cdensity-morphology relation\u201d (e.g., Oemler 1974; Dressler 1980; Postman & Geller 1984) - with giant elliptical galaxies anchoring the centers of rich clusters of galaxies (e.g., Kormendy et al. 2009). This relation is consistent with the larger trend of the galaxy population appearing bluer in more underdense regions in the local universe (e.g., Goto et al. 2003; G\u00b4 omez et al. 2003; Tanaka et al. 2004; Rojas et al. 2004). Di\ufb00erent types of galaxies are seen to cluster di\ufb00erently and have di\ufb00erent environment-dependencies, in the same sense as the density-morphology relation (e.g., Davis & Geller 1976; Hogg et al. 2003; Balogh et al. 2004; Kau\ufb00mann et al. 2004; Park et al. 2007; Coil et al. 2008; Zehavi et al. 2011). Recent quantitative studies have yielded richer details on SF dependence on halo mass and environment, probing their relationships at higher redshifts. For example, using a large group catalog from the Sloan Digital Sky Survey (SDSS) Data Release 2, Weinmann et al. (2006) \ufb01nd that at \ufb01xed luminosity the fraction of early-type galaxies increases with increasing halo mass and this mass dependence is smooth and persists over the entire mass range probed without any break or feature at any mass-scale. From a spectral analysis of galaxies at z = 0.4\u22120.8 based on the ESO Distant Cluster Survey, Poggianti et al. (2009) \ufb01nd that the incidence of K+A galaxies increases strongly with increasing velocity dispersion of the environment from groups to clusters. McGee et al. (2011), examining the SF properties of group and \ufb01eld galaxies from SDSS at z \u223c0.08 and from ultraviolet imaging with GALEX at z \u223c0.4, \ufb01nd that the fraction of passive galaxies is higher in groups than the \ufb01eld at both redshifts, with the di\ufb00erence between the group and \ufb01eld growing with time and larger at low masses. With the NOAO Extremely Wide-Field Infrared Imager (NEWFIRM) Survey of the All-wavelength Extended Groth strip International Survey (AEGIS) and Cosmic Evolution Survey (COSMOS) \ufb01elds, Whitaker et al. (2011) show evidence for a bimodal color distribution between quiescent and star-forming galaxies that persists to z \u223c3. Presotto et al. (2012) study the evolution of galaxies located within groups using the group catalog obtained from zCOSMOS spectroscopic data and the complementary photometric data from the COSMOS \u2013 3 \u2013 survey at z = 0.2 \u22120.8 and \ufb01nd the rate of SF quenching to be faster in groups than in the \ufb01eld. Muzzin et al. (2012) analyze galaxy properties at z = 0.85 \u22121.20 using a spectroscopic sample of 797 cluster and \ufb01eld galaxies drawn from the Gemini Cluster Astrophysics Spectroscopic Survey, \ufb01nding that post starburst galaxies with M \u2217= 109.3\u221210.7 M\u2299are three times more common in high- density regions compared to low-density regions. Based on data from the zCOSMOS survey Tanaka et al. (2012) perform an environment study and \ufb01nd that quiescent galaxies prefer more massive systems at z = 0.5 \u22121. Rasmussen et al. (2012), analyzing GALEX imaging of a statistically representative sample of 23 galaxy groups at z \u223c0.06, suggest an average quenching timescale of \u22652Gyr. Mok et al. (2013), with deep GMOS-S spectroscopy for 11 galaxy groups at z = 0.8 \u22121, show that the strongest environmental dependence is observed in the fraction of passive galaxies, which make up only \u223c20 per cent of the \ufb01eld in the mass range Mstar = 1010.3\u22121011.0 M\u2299but are the dominant component of groups. Using SDSS (z \u223c0.1) and the All-Wavelength Extended Groth Strip International Survey (AEGIS; z \u223c1) data, Woo et al. (2013) \ufb01nd a strong environmental dependence of quenching in terms of halo mass and distance to the centrals at both redshifts. The widespread observational evidence of environment quenching is unsurprising theoretically. In regions of overdensity, whether around a large collapsed halo or unvirialized structure (e.g., a Zel\u2019dovich pancake or a \ufb01lament), gas is gravitationally shock heated when converging \ufb02ows meet. In regions \ufb01lled with hot shock-heated gas, multiple gasdynamical processes would occur. One of the most important gasdynamical processes is ram-pressure stripping of gas, when a galaxy moves through the ambient hot gas at a signi\ufb01cant speed, which includes, but is not limited to, the infall velocity of a satellite galaxy. The theoretical basis for the ram-pressure stripping process is laid down in the seminal work of Gunn & Gott (1972). Recent works with detailed simulations of this e\ufb00ect on galaxies (in non-cosmological settings) include those of Mori & Burkert (2000), Quilis et al. (2000), Kronberger et al. (2008), Bekki (2009) and Tonnesen & Bryan (2009). Even in the absence of ram-pressure stripping, ubiquitous supersonic and transonic motions of galaxies of complex acceleration patterns through ambient medium (intergalactic or circumgalactic medium) subject them to the Raleigh-Taylor and Richtmyer-Meshkov instabilities. Large shear velocities at the interfaces between galaxies and the ambient medium allow the Kelvin-Helmholtz (KH) instability to play an important role. When these processes work in tandem with ram-pressure displacements, the disruptive e\ufb00ects are ampli\ufb01ed. For example, the KH instability time scale is substantially shorter for a non-self-gravitating gas cloud (e.g., Murray et al. 1993) than for one sitting inside a virialized dark matter halo (e.g., Cen & Riquelme 2008). Another important process in hot environments is starvation of cold gas that is fuel for SF (e.g., Larson et al. 1980; Balogh et al. 2000; Dekel & Birnboim 2006). In regions with high- temperature and high-entropy cooling of hot gas is an ine\ufb03cient process for fueling SF, an important point noted long ago to account for the basic properties (mass, size) of galaxies (e.g., Binney 1977; Rees & Ostriker 1977; Silk 1977). This phenomenon may be understood by considering the dependence of cooling time on the entropy of the gas: the gas cooling time can be written \u2013 4 \u2013 as tcool(T, S) = S3/2 \u0014 3 2 \u0010 \u00b5e \u00b5 \u00112 kB T 1/2\u039b(T) \u0015 (Scannapieco & Oh 2004) 1. It follows that the minimum cooling time of a gas parcel just scales with S3/2. As a numerical example, for a gas parcel of entropy S = 109K cm2 (say, for temperature 107K and density 10\u22123cm\u22123) and metallicity 0.1 Z\u2299, its cooling time is no shorter than the Hubble time at z = 1 hence the gas can no longer cool e\ufb03ciently to fuel SF. It may be that the combination of cold gas removal and dispersal by ram-pressure stripping, hydrodynamic instabilities, and cold gas starvation, all of which are expected to become increasingly important in more massive environments, plays a primary role in driving the color migration from the blue cloud to the red sequence. In dense environments, gravitational tidal (stripping and shock) e\ufb00ects and relatively close \ufb02y-bys between galaxies (e.g., Moore et al. 1996) also become important. To understand the overall e\ufb00ect on SF quenching by these external processes in the context of the standard cold dark matter model, a realistic cosmological setting is imperative, in order to capture complex external processes that are likely intertwined with large variations of internal properties of galaxies. In this paper we perform ab initio Large-scale Adaptive-mesh-re\ufb01nement Omniscient Zoom-In cosmological hydrodynamic simulations, called LAOZI Simulations, to obtain a large sample of galaxies to, for the \ufb01rst time, perform a chronological and statistical investigation on a very large scale. The large simulated galaxy sample size and very high resolution of LAOZI simulations provide an unprecedented opportunity to undertake the study presented. Our study shares the spirit of the work by Feldmann et al. (2011), who examine the evolution of a dozen galaxies falling onto a forming group of galaxies, with a substantial improvement in the statistical treatment, the simulation resolution, the range of environment probed, and the analysis scope. Feedback from AGN is not included in this simulation, partly because of its large uncertainties and present lack of de\ufb01nitive driving sources and primarily due to our intention to focus on external e\ufb00ects. Internal e\ufb00ects due to SF are automatically included and we \ufb01nd no evidence that SF or merger triggered SF plays a primary role in quenching from our study. The outline of this paper is as follows. In \u00a72 we detail our simulations (\u00a72.1), method of making galaxy catalogs (\u00a72.2), construction of histories of galaxies (\u00a72.3), tests and validation of simulations (\u00a72.4) and the produced bimodal distribution of galaxies colors (\u00a72.5). Results are presented in \u00a73, organized in an approximately chronological order, starting with the ram-pressure stripping e\ufb00ects in \u00a73.1, followed by the ensuing period of gas starvation in hot environment in \u00a73.2. In \u00a73.3 we discuss stellar mass growth, evolution of stellar mass function of red galaxies and present galaxy color migration tracks. \u00a73.4 gives an example of consequences of the found color migration picture - galaxy age-mass relation. We present observable environmental dependence of galaxy makeup at z = 0.62 in \u00a73.5. Conclusions are given in \u00a74. 1 where kB is Boltzmann\u2019s constant, T temperature and \u039b cooling function, \u00b5 = 0.62 and \u00b5e = 1.18 for ionized gas that we are concerned with, S is the gas entropy de\ufb01ned as S \u2261 T n2/3 in units of K cm2 (n is gas number density). If one conservatively adopts the lowest value of the term inside the bracket at the cooling peak at temperature Tmin \u223c105.3K, it follows that the minimum cooling time of a gas parcel just scales with S3/2. \u2013 5 \u2013"
                },
                {
                    "url": "http://arxiv.org/abs/1311.1828v1",
                    "title": "Infrared Properties of z=7 Galaxies from Cosmological Simulations",
                    "abstract": "Three-dimensional panchromatic dust radiative transfer calculations are\nperformed on a set of 198 galaxies of stellar masses in the range\n5x10^8-3x10^10 Msun from a cosmological hydrodynamic simulation (resolved at\n29pc/h) at z=7. In a companion paper (Kimm & Cen), the stellar mass and UV\nluminosity functions, and UV-optical and FUV-NUV colors are shown to be in good\nagreement with observations, if an SMC-type dust extinction curve is adopted.\nHere we make useful predictions, self-consistently, of the infrared properties\nof these z=7 simulated galaxies that can be confronted with upcoming ALMA data.\nOur findings are as follows. (1) The effective radius in the rest-frame MIPS 70\nmicron band is in the range of 80-400pc proper for z=7 galaxies with\nL_FIR=10^{11.3-12}Lsun. (2) The median of the peak wavelength of the\nfar-infrared (FIR) spectral energy distribution is in the range of 45-60\nmicron, depending on the dust-to-metal ratio. (3) For star formation rate in\nthe range 3-100 Msun/yr the median FIR to bolometric luminosity ratio is\n60-90%. (4) The FIR luminosity function displays a power law in the high end\nwith a slope of -3.1 +- 0.4, instead of the usual exponential decline.",
                    "authors": "Renyue Cen, Taysun Kimm",
                    "published": "2013-11-07",
                    "updated": "2013-11-07",
                    "primary_cat": "astro-ph.CO",
                    "cats": [
                        "astro-ph.CO"
                    ],
                    "main_content": "2.1. Hydrocode and Simulation Parameters The cosmological simulation is performed with the Eulerian hydrodynamics code, enzo (Bryan 1999; O\u2019Shea et al. 2005; Joung et al. 2009). For more details on the simulation setup and implemented physics, the reader is referred to Cen (2012). We use the following cosmological parameters that are consistent with the WMAP7-normalized (Komatsu et al. 2010) \u039bCDM model: \u2126M = 0.28, \u2126b = 0.046, \u2126\u039b = 0.72, \u03c38 = 0.82, H0 = 100h km s\u22121Mpc\u22121 = 70 km s\u22121Mpc\u22121 and n = 0.96. These parameters are consistent with those from Planck first-year data (Planck Collaboration et al. 2013) if we average Planck derived H0 with SN Ia and HST based H0. First we ran a low resolution simulation with a periodic box of 120 h\u22121Mpc (comoving) on a side. We identified a region centered on a cluster of mass of \u223c3 \u00d7 1014 M\u2299at z = 0. We then resimulate with high resolution of the chosen region embedded in the outer 120h\u22121Mpc box to properly take into account the large-scale tidal field and appropriate boundary conditions at the surface of the refined region. The refined region has a comoving size of 21 \u00d7 24 \u00d7 20h\u22123Mpc3 and represents 1.8\u03c3 matter density fluctuation on that volume. The dark matter particle mass in the refined region is 1.3 \u00d7 107h\u22121 M\u2299. The refined region is surrounded by three layers (each of \u223c1h\u22121Mpc) of buffer zones with particle masses successively larger by a factor of 8 for each layer, which then connects with the outer root grid that has a dark matter particle mass 84 times that in the refined region. We choose the mesh refinement criterion such that the resolution is always better than 29h\u22121pc (physical), corresponding to a maximum mesh refinement level of 13 at z = 0. The simulations include a metagalactic UV background (Haardt & Madau 1996) where the cosmic reionization occurs at z = 9, and a model for shielding of UV radiation (Cen et al. 2005). They include metallicity-dependent radiative cooling (Cen et al. 1995). Our simulations also solve relevant gas chemistry chains for molecular hydrogen formation (Abel et al. 1997), molecular formation on dust grains (Joung et al. 2009), and metal cooling extended down to 10 K (Dalgarno & McCray 1972). Star particles are created in cells that satisfy a set of criteria for star formation proposed by Cen & Ostriker (1992). Each star particle is tagged with its initial mass, creation time, and metallicity; star particles typically have masses of \u223c106 M\u2299. Supernova feedback from star formation is modeled following Cen et al. (2005). Feedback energy and ejected metal-enriched mass are distributed into 27 local gas cells centered at the star particle in question, weighted by the specific volume of each cell. This is to mimic the physical process of supernova blastwave propagation that tends to channel energy, momentum and mass into the least dense regions (with the least resistance and cooling). The primary advantages of this supernova energy based feedback mechanism are three-fold. First, nature does drive winds in this way and energy input is realistic. Second, it has only one free parameter eSN, namely, the fraction of the rest mass energy of stars formed that is deposited as thermal energy on the cell scale at the location of supernovae. Third, the processes are treated physically, obeying their respective conservation laws (where they apply), allowing transport of metals, mass, energy and momentum to be treated self-consistently and taking into account relevant heating/cooling processes at all times. We allow the entire feedback processes to be hydrodynamically coupled to surroundings and subject to relevant physical processes, such as cooling and heating. The total amount of explosion \u2013 4 \u2013 kinetic energy from Type II supernovae for an amount of star formed M\u2217with a Chabrier initial mass function (IMF) is eSNM\u2217c2 (where c is the speed of light) with eSN = 6.6 \u00d7 10\u22126. Taking into account the contribution of prompt Type I supernovae, we use eSN = 1 \u00d7 10\u22125 in our simulations. Observations of local starburst galaxies indicate that nearly all of the star formation produced kinetic energy is used to power galactic superwinds (e.g., Heckman 2001). Supernova feedback is important primarily for regulating star formation and for transporting energy and metals into the intergalactic medium. The extremely inhomogeneous metal enrichment process demands that both metals and energy (and momentum) are correctly modeled so that they are transported in a physically sound (albeit still approximate at the current resolution) way. 2.2. Simulated Galaxy Catalogs We identify galaxies in our high resolution simulations using the HOP algorithm (Eisenstein & Hu 1999), operated on the stellar particles, which is tested to be robust and insensitive to speci\ufb01c choices of concerned parameters within reasonable ranges. Satellites within a galaxy are clearly identi\ufb01ed separately. The luminosity of each stellar particle at each of the Sloan Digital Sky Survey (SDSS) \ufb01ve bands is computed using the GISSEL stellar synthesis code (Bruzual & Charlot 2003), by supplying the formation time, metallicity and stellar mass. Collecting luminosity and other quantities of member stellar particles, gas cells and dark matter particles yields the following physical parameters for each galaxy: position, velocity, total mass, stellar mass, gas mass, mean formation time, mean stellar metallicity, mean gas metallicity, star formation rate, luminosities in \ufb01ve SDSS bands (and various colors) and others. 2.3. Three-Dimensiona Panchromatic Dust Radiative Transfer Calculations We post-process the simulated galaxy sample at z = 7 using a three-dimensional dust radiation transfer code, sunrise (Jonsson 2006; Jonsson et al. 2010). The main strength of the sunrise code is the use of a polychromatic algorithm to trace information in all wavelengths per ray, enabling us to compute the spectral energy distributions (SEDs) of each galaxy. It makes use of the standard dust cross-sections by Draine and collaborators (Weingartner & Draine 2001; Draine & Li 2007) to simulate absorption and multiple scattering by dust. Each stellar particle that is basically a coeval star cluster has three attributes mass (\u223c104\u22125 M\u2299), formation time and metallicity which are input to the code starburst99 (Leitherer et al. 1999), assuming a Kroupa initial mass function with an upper (lower) mass limit of 100 M\u2299(0.1 M\u2299). The output from starburst99 is the input stellar spectrum to sunrise. In order to take into account the immediate absorption and emission by birth clouds, which large-scale cosmological simulations cannot resolve, sunrise uses the spectra of Hii and photo-dissociation regions (PDRs) computed by photo-ionization code, mappingsiii (Dopita et al. 2005; Groves et al. 2008). This is done by replacing SEDs of star particles younger than 10 Myr with re-processed SEDs of a population with constant star formation for 10 Myr by mappingsiii (see Jonsson et al. 2010). The fraction of light travelled through the PDR is controlled by a parameter, fPDR, which we use fPDR = 0.2 following Jonsson et al. (2010). \u2013 5 \u2013 The metal mass in each simulation cell is followed hydrodynamically, including \ufb02ux, sources (from stellar feedback) and sinks (forming into new stars). The amount of dust is derived from the amount of metals in each hydro cell by using a dust-to-metal ratio (D/M). While the UV/optical properties depend sensitively on D/M, the FIR properties depends on D/M only weakly, as will be shown, making our predictions of FIR properties of z = 7 rather robust, except the peak wavelength of the FIR SED (see Figure 2 below). The dust temperature, emission, and dust opacity is obtained in a self-consistent fashion in SUNRISE by solving for the thermal equilibrium solution for dust grains at every location, where dust emission cooling is balanced by stellar radiative heating. This is achieved by iteration computationally. 3. Results 0.1 1.0 10.0 100.0 1000.0 \u03bb [\u00b5m] 1040 1041 1042 1043 1044 1045 1046 \u03bbL\u03bb [erg/s] log Mstar= 9.4 log Mstar=10.4 SMC.06_f0.0 SMC.4_f0.1 log mstar= 9.4 10.4 1kpc log MJy/sr -2.0 -1.5 -1.0 -0.5  0.0  0.5  1.0 Fig. 1.\u2014 Left panel: the rest-frame spectra (left panel) of two simulated galaxies of stellar masses of 109.4 M\u2299(dashed curves) and 1010.4 M\u2299(solid curves), respectively, at z = 7. The star formation rate (SFR) and speci\ufb01c SFR (sSFR) for the low and high mass galaxies are (94 M\u2299/yr, 3.7 Gyr\u22121) and (35 M\u2299/yr, 13 Gyr\u22121), respectively. For each galaxy we show two cases with two di\ufb00erent combinations of (D/M, fesc), (0.4,0.1) (red) and (0.06,0) (blue), both of which are found to reproduce the UV/optical properties of z = 7 galaxies (Kimm & Cen 2013). Right panel: restframe MIPS 70\u00b5m band images, smoothed with a Gaussian of FWHM=0.1kpc. The number in each panel indicates logarithmic stellar mass and white ticks in both panels are 1kpc proper. We \ufb01rst present in Figure 1 the SED in the rest-frame and rest-frame FIR images of two simulated galaxies of stellar masses of 109.4 M\u2299and 1010.4 M\u2299, respectively. For each galaxy we show two cases with two di\ufb00erent combinations of (D/M, fesc), (0.4,0.1) (red) and (0.06,0) (blue), which have been both found to reproduce the UV/optical properties of z = 7 galaxies (Kimm & Cen 2013). Three points are worth noting. First, the overall SED shares some of the properties of lower redshift starburst galaxies, in that the majority of the stellar radiation comes out in the FIR peak. Second, even though the two galaxies are in the category of starburst galaxies, the higher mass galaxy contains a signi\ufb01cant, evolved stellar population, as indicated by a strong Balmer break at \u223c0.37\u00b5m; the lower mass galaxy has a less prominent Balmer break, suggesting an overall \u2013 6 \u2013 30 40 50 60 70 10.5 11.0 11.5 12.0 log L8-1000\u00b5m [LO  \u2022 ] 30 40 50 60 70 \u03bbpeak [\u00b5m] 8.5 9.0 9.5 10.0 10.5 log Mstar [MO  \u2022 ] 30 40 50 60 70 \u03bbpeak [\u00b5m] SMC.06_f0.0 SMC.4_f0.1 Fig. 2.\u2014 shows the FIR peak wavelength \u03bbpeak of the SED of galaxies at z = 7 as a function of FIR luminosity (left panel) and stellar mass (right panel). Only galaxies with stellar masses Mstar \u22655\u00d7108M\u2299are shown. For each galaxy two cases are shown with two di\ufb00erent combinations of (D/M, fesc), (0.4,0.1) (red) and (0.06,0) (blue). The distributions of \u03bbpeak are shown on the right y-axis for the two cases. The histogram in the left panel is plotted using the sample with L8\u22121000\u00b5m \u22651011L\u2299over which our sample is more than 80% complete. The completeness is estimated as follows. At IR luminosity of \u22651011L\u2299we compute the fraction of galaxies with stellar masses larger than 5\u00d7108 M\u2299(which is our stellar mass threshold deemed reliably resolved), which is found to be 80%. younger population. The existence of an evolved population for z \u223c7 galaxies is consistent with observations (e.g., Labb\u00b4 e et al. 2010). It is likely that our simulation has underestimated the star formation rate at progressively higher redshift due to poorer resolutions for smaller objects at higher redshift, hence the evolved population. Third, the wavelength \u03bbpeak of the FIR peak at 45 \u221265\u00b5m suggests a relatively hot emitting dust, due to a combination of relatively high SFR and sub-kpc, compact sizes of the starbursting regions, seen in the images in the right panel. Figure 2 shows the FIR peak wavelength \u03bbpeak of the SED of the galaxies at z = 7 as a function of FIR luminosity (left panel) and stellar mass (right panel). For each galaxy two cases are shown with two di\ufb00erent combinations of (D/M, fesc), (0.4,0.1) (red) and (0.06,0) (blue). The distributions of \u03bbpeak are shown on the right y-axis for the two cases. Two points are noted. First, at the lower stellar mass (\u22641010 M\u2299) or lower FIR luminosity end (LFIR \u22641011.5 L\u2299), no strong correlation is found between either FIR luminosity or stellar mass and \u03bbpeak, whereas there is some hint that the highest FIR luminosity (LFIR \u22651011.5 L\u2299) or highest stellar mass (\u22651010 M\u2299) galaxies tend to occupy the low end of the \u03bbpeak distribution. Second, for a given simulated galaxy, post-processing it with di\ufb00erent dust-to-metal ratios D/M yields signi\ufb01cant di\ufb00erence in the \u03bbpeak distributions. For the lower D/M = 0.06 case, the median of the \u03bbpeak distribution is 43\u00b5m, compared to 61\u00b5m for the case with D/M = 0.4. This signi\ufb01cant dependence of \u03bbpeak on D/M may provide a probe \u2013 7 \u2013 of the latter, when the former is observationally obtained. The physical origin for this, in simple terms, is that a lower D/M value gives a lower dust opacity hence a higher interstellar radiation \ufb01eld, which in turn heats up the dust to a higher equilibrium temperature (balanced by emission cooling, primarily). -22 -21 -20 -19 -18 MUV 0.1 1.0 Reff,UV [kpc] Grazian+(12) Ono+(13) Simulations SMC.06 SMC.4 11.0 11.5 12.0 12.5 log L8-1000\u00b5m [LO  \u2022 ] 0.1 1.0 Reff,70\u00b5m [kpc] SMC.06_f0.0 SMC.4_f0.1 Fig. 3.\u2014 Left: FUV e\ufb00ective radius measured after smoothing with a Gaussian of FWHM=0.1 kpc as a function of GALEX FUV magnitude for simulated galaxies at z = 7. Included as black symbols are observational estimates by Grazian et al. (2012, circles) and Ono et al. (2012, triangles). Right: e\ufb00ective radius in FIR as a function of FIR luminosity for galaxies at z = 7. The e\ufb00ective radius is measured on restframe MIPS 70 \u00b5m band images after smoothing with a Gaussian of FWHM=0.1 kpc. The dotted line marks the e\ufb00ective resolution of our simulation (75 pc). The solid lines and error bars indicate the mean and standard deviation. We examine the sizes of simulated z = 7 galaxies. We \ufb01rst examine UV sizes. The left panel of Figure 3 shows the e\ufb00ective radius in GALEX FUV band as a function of FUV magnitude. We see that the simulated galaxies have somewhat smaller sizes than the observed counterparts in the rest-frame FUV band, although the trend that more UV luminous galaxies have larger sizes is in agreement with observations and there is signi\ufb01cant overalap between observations and our simulation. The red curve with fesc = 10% is actually computed not including the 10% directly escaped light, because we are unsure how to best model it without introducing some additional unchecked parameters. We now turn to FIR sizes of simulated z = 7 galaxies, shown in the right panel of Figure 3. What is striking is that the predicted sizes of z = 7 galaxies in the FIR band are very small, with e\ufb00ective radii being in the range of 80 \u2212500pc proper. The e\ufb00ective resolution of our simulation is 75pc [1.8 cells, see Cen (2013)], which is probably the cause of the size \ufb02oor seen. Thus, we expect the lower mass galaxies may have e\ufb00ective radii in FIR that are smaller than \u223c80pc. Nevertheless, we expect that the sizes in the range 100 \u2212500pc predicted to be real, to the extent that our simulation resolution is adeqaute for resolving them. Because the FIR emission is primarily a function of the metal density distribution in the simulated galaxies, they are much less prone to attenuation e\ufb00ects and hence are more robust. However, there are possible \u2013 8 \u2013 caveats that the reader should keep in mind. The central star formation may be dependent on feedback processes from star formation. Since the exact strength of stellar feedback depends on an array of factors that each have signi\ufb01cant uncertainties, including the initial stellar mass function (IMF), supernova feedback prescription used in the simulation, porosity of the interstellar medium in the simulation that may be underestimated, feedback from AGN that is not included, etc, our best estimate is that the sizes of the simulated galaxies may have been underestimated somewhat presently. A comparison between our simulated results and upcoming observations will thus shed useful light on both the cosmological model and astrophysics of galaxy formation at high redshift. 9 10 11 12 13 log \u03a3IR = LIR/(2\u03c0RIR 2  ) [LO  \u2022 kpc-2] -1 0 1 2 log SFR/Mstar [Gyr-1] Elbaz+(11) (0<z<2.5) compact SMC.4_f0.1 Fig. 4.\u2014 shows the sSFR as a function of FIR surface brightness (\u03a3IR) for simulated galaxies at z = 7 (circles). \u03a3IR is computed as L8\u22121000\u00b5m/2\u03c0R2 IR, where RIR is the e\ufb00ective radius in the restframe MIPS 70 \u00b5m band. Only one dust model is shown, because \u03a3IR is insensitive to details of the dust model. For comparisons, also shown as the shaded region is the star-forming sequence from the GOODS-Herschel sample at 0 < z < 2.5 (Elbaz et al. 2011). Another way to demonstrate the concentration of star formation in z = 7 galaxies is to plot the speci\ufb01c star formation rate as a function of FIR surface brightness, shown in Figure 4. Comparing to the galaxies in the star-forming sequence at moderate redshift (0 < z < 2.5) (Elbaz et al. 2011), it is evident that our simulated galaxies at z = 7 are substantially more star-bursting by a factor of 3 \u221220 at a \ufb01xed surface density. Elbaz et al. (2011) also de\ufb01nes a galaxy as \u201ccompact\u201d if the FIR surface brightness (\u03a3IR = LIR/2\u03c0R2 IR) is greater than 3 \u00d7 1010 L\u2299kpc\u22122. This roughly corresponds to galaxies emitting more than 60% of their 13.2 \u00b5m \ufb02ux in the unresolved central \u223c3 kpc2 region (see D\u00b4 \u0131az-Santos et al. 2010). According to the de\ufb01nition, the majority of the simulated galaxies will be classi\ufb01ed as compact galaxies. Having examined the SEDs and sizes, our attention is shifted to the FIR radiation output of z = 7 galaxies relative to their bolometric luminosities. Figure 5 shows FIR in the range 8\u20131000\u00b5m (left panel) and bolometric (right panel) luminosities of each galaxy at z = 7 as a function of the \u2013 9 \u2013 8.5 9.0 9.5 10.0 10.5 log Mstar [MO  \u2022 ] 10.0 10.5 11.0 11.5 12.0 12.5 log L8-1000\u00b5m [LO  \u2022 ] SMC.06_f0.0 SMC.4_f0.1 8.5 9.0 9.5 10.0 10.5 log Mstar [MO  \u2022 ] 10.0 10.5 11.0 11.5 12.0 12.5 log Lbol [LO  \u2022 ] SMC.06_f0.0 SMC.4_f0.1 Fig. 5.\u2014 shows FIR (left) and bolometric (right) luminosities in the range 8\u20131000\u00b5m of each galaxy at z = 7 as a function of the galaxy stellar mass, for two models with (D/M, fesc), (0.4,0.1) (red open circles) and (0.06,0) (blue open circles). Solid points with error bars represent the median and interquartile range. galaxy stellar mass, for two models with (D/M, fesc), (0.4,0.1) (red open circles) and (0.06,0) (blue open circles). Let us \ufb01rst study the right panel. It is evident that bolometric luminosity (i.e., SFR) scales with stellar mass substantially sublinearly, Lbol \u221dM \u03be star with \u03be \u223c0.6\u22120.8. We attribute this, primarily, to \u201cstochasticity\u201d of star formation, where galaxies with higher speci\ufb01c star formation are in some \u201cbursting periods\u201d, while those with relatively lower speci\ufb01c star formation rates presently are in relatively quiet \u201cpatches\u201d. This explanation is consistent with the \u223c0.5dex spread in the bolometric luminosity at a \ufb01xed stellar mass. The relation between FIR luminosity and stellar mass (left panel) is largely inherited from that of between bolometric luminosity and stellar mass (right panel), with a small correction due to a non-uniform ratio of FIR to bolometric luminosities, shown in Figure 6 below. If con\ufb01rmed by ALMA, this will provide signi\ufb01cant insight into the galaxy formation process at high redshift. The expectation is that, with time, galaxies will mature and become stellar mass dominated on the baryon budget, and as such, the overall stochasticity is expected to decline towards lower redshift, resulting in \u03be gradually approaching unity. Figure 6 shows the ratio of FIR luminosity in the range 8\u22121000\u00b5m to the bolometric luminosity for each galaxy as a function of stellar mass (left) and star formation rate (right), for two models with a dust-to-metal ratio (D/M) of 0.06 and 0.4. It is seen that there is a tendency for less massive galaxies or lower SFR galaxies to have lower median ratios. For galaxies with SFR= 3\u2212100 M\u2299/yr, it is found that the median FIR/bolometric luminosity ratio is in the range of 60\u221290%. For galaxies with stellar mass in the range of 109 \u22121010.5 M\u2299, the median FIR/bolometric luminosity ratio is predicted to be in the range of 80 \u221290%. We expect that targeted observations of current high redshift galaxies at z \u223c7 by ALMA should be able to verify these predictions. \u2013 10 \u2013 8.5 9.0 9.5 10.0 10.5 log Mstar [MO  \u2022 ] 0.0 0.2 0.4 0.6 0.8 1.0 L8-1000\u00b5m / Lbol SMC.06_f0.0 SMC.4_f0.1 0 1 2 log SFR [MO  \u2022 yr-1] 0.0 0.2 0.4 0.6 0.8 1.0 L8-1000\u00b5m / Lbol SMC.06_f0.0 SMC.4_f0.1 Fig. 6.\u2014 The ratio of FIR luminosity appearing in the range 8 \u22121000\u00b5m to the bolometric luminosity as a function of stellar mass (left) and star formation rate (right). Blue and red circles denote the model with a dust-to-metal ratio (D/M) of 0.06 and 0.4, respectively, as indicated in the legend. An SMC-type dust extinctin curve is used in both cases. Points with error bars represent median and interquartile range. Figure 7 shows the galaxy FIR luminosity function at z = 7. It is seen that the FIR luminosity function only depends weakly on the changes of dust properties; the two dust models that are found to be able to match UV/optical properties of galaxies at z = 7 are shown to give similar results. Interestingly, for the high end luminosity range probed, LFIR = 1011 \u22121012 L\u2299, there is no indication of an exponential drop that is normally the case for galaxy stellar mass function or UV/optical luminosity function at high redshift. We \ufb01nd that a power-law slope of \u22122.1 \u00b1 0.4 provides a good \ufb01t to our simulated FIR luminosity functions, where the uncertainty is measured by bootstrap resampling. This power-law shape is related to the stochasticity of star formation of z = 7 galaxies, as noted above, which will have signi\ufb01cant implications on small-scale power in the standard cold dark matter model as well as the consumption and thermodynamic state of the gas prior to star formation in galaxies at z = 7. It is expected that observing the UV selected high redshift galaxy candidates in the UDF by ALMA may be able to check this expected powerlaw slope. It is noted that, since the ratio of FIR to bolometric luminosity is close to unity (see Figure 6), this power-law behavior is rather robust to attentuation uncertainties that plague restframe UV luminosity functions, making FIR continuum observations by ALMA especially powerful. If veri\ufb01ed, we will learn a great deal of the mode of star formation in high-z galaxies: how bursty is star formation in high redshift galaxies and what is the dispersion in star formation rate at a \ufb01xed halo or stellar mass? \u2013 11 \u2013 10.5 11.0 11.5 12.0 12.5 log L8-1000\u00b5m [LO  \u2022 ] -5 -4 -3 -2 log dN(L) / Mpc3 / dlog L SMC.4_f0.1 SMC.06_f0.0 Fig. 7.\u2014 The infrared luminosity function at z = 7. Di\ufb00erent color-codings correspond to models with a di\ufb00erent assumption on D/M, as indicated in the legend. Solid lines display our reliable estimates for the number density, which can be directly compared to future observations. Other two bins below L8\u22121000\u00b5m = 1011L\u2299contain more than 20% of under-resolved galaxies of stellar mass Mstar < 2 \u00d7 108M\u2299. 1\u03c3 error bars shown are Poissonian. The simulated LFs can be \ufb01t by a power law [log dN \u221d(\u22122.1 \u00b1 0.4)d log L], shown as the gray line. 4. Conclusions We perform, in unprecedented details, three-dimensional panchromatic dust radiative transfer calculations on a set of 198 galaxies of stellar masses in the range 5 \u00d7 108 \u22123 \u00d7 1010 M\u2299resolved at 29h\u22121pc at z \u223c7 from an ab initio cosmological hydrodynamic simulation of the standard cold dark matter model. The soundness of treatment of relevant physical processes has been checked by comparing to a set of independent observations. In a companion paper (Kimm & Cen 2013) we show that the UV-optical properties, including stellar mass and luminosity functions, UV-optical and FUV-NUV colors, are in good agreement with observations, if an SMC-type dust extinction curve is adopted. In order to make further testable predictions of the same model, we present here, self-consistently, an additional set of infrared continuum properties of these z \u223c7 simulated galaxies, to be confronted with upcoming ALMA data. The main results may be summarized in \u2013 12 \u2013 four points. (1) The e\ufb00ective radius in the restframe MIPS70\u00b5m band is in the range of 80 \u2212400pc proper for z = 7 galaxies with LFIR = 1011.3\u221212 L\u2299, corresponding to an angular size of 0 \u2032\u2032.015 \u22120 \u2032\u2032.075, which may be resolvable by ALMA. The majority of the simulated galaxies would be classi\ufb01ed as compact starburst galaxies (Elbaz et al. 2011). The predicted size would be below the extrapolation from lower redshift evolution in rest-frame UV or visual band (e.g., Ferguson et al. 2004; Trujillo et al. 2006). (2) The median of the peak wavelength of the FIR SED is in the range of 45\u221260\u00b5m, depending on the dust-to-metal ratio, corresponding to observed wavelength of 360\u2212480\u00b5m, within the ALMA range. The peak wavelength found is comparable to local starburst galaxies, such as Arp 220 and NGC 6240. (3) For galaxies with SFR in the range 3\u2212100 M\u2299yr\u22121, the median FIR in the range 8\u20131000\u00b5m to bolometric luminosity ratio is 60 \u221290%. In other words, the SFR inferred based on the observed optical and UV luminosities is missing more than one half of the total SFR, on average. This is a new and key prediction that should be easily veri\ufb01able by upcoming ALMA observations, in conjunction with HST UDF data. (4) The FIR luminosity function displays a power law in the high end with a slope of -3.1\u00b10.4, instead of the usual exponential decline. A related result is that Lbol \u221dM \u03be star with \u03be \u223c0.6 \u22120.8, which is somewhat \ufb02atter than the corresponding relation at lower redshifts. Both results may be attributable to \u201cstochasticity\u201d and signi\ufb01cant dispersions in star formation at a given halo mass. Acknowledgements We would like to thank Bruce Draine, Simona Gallerani, Roberto Maiolino and John Wise for discussion, and an anonymous referee for a very useful constructive report. Computing resources were in part provided by the NASA HighEnd Computing (HEC) Program through the NASA Advanced Supercomputing (NAS) Division at Ames Research Center. The research is supported in part by NSF grant AST-1108700 and NASA grant NNX12AF91G. Some of our analysis is done using the YT toolkit (Turk et al. 2011).",
                    "introduction": "Did stars or quasars reionize the universe? We do not know that for sure, although there is a likelihood that stars most likely dominate the photoionization rate over quasars at z \u22656 (e.g., Faucher-Gigu` ere et al. 2008). While the \ufb01nal transition from an opaque to transparent universe for ionizing photons appears to occur at z \u223c6, as seen by the Sloan Digital Sky Survey (SDSS) quasar absorption spectrum observations (e.g., Fan et al. 2006), the reionization process may be quite complex and likely has started much earlier (z \u22659), as suggested by the high Thomson optical depth measured by the Wilkinson Microwave Anisotropy Probe (WMAP) observations (e.g., Hinshaw et al. 2012) and the Planck Surveyor (e.g., Planck Collaboration et al. 2013). To fundamentally answer the question of how the universe was reionized and what reionized it requires a satisfactory understanding of the formation of galaxies during the epoch of reionization. There have been rapid and remarkable advances on the observational front to address this question, with some of the recent observations penetrating well into the reionization era at z \u223c6\u22129 1Princeton University Observatory, Princeton, NJ 08544; cen@astro.princeton.edu arXiv:1311.1828v1  [astro-ph.CO]  7 Nov 2013 \u2013 2 \u2013 (e.g., Bouwens et al. 2010; Bunker et al. 2010; Yan et al. 2010; Stark et al. 2010; Labb\u00b4 e et al. 2010; Wilkins et al. 2011; McLure et al. 2011; Dunlop et al. 2012; Bouwens et al. 2012; Finkelstein et al. 2012; Dunlop et al. 2013). They have taught us three important things about the real universe. First, the observed faint end slope of the galaxy luminosity function (LF) is close to \u22122, indicating that fainter galaxies below the current detection limit likely make a signi\ufb01cant contribution to the overall ionizing photon budget. Second, it appears that star formation in these systems may have started much earlier (Labb\u00b4 e et al. 2010). Third, the stellar mass of detected galaxies is at or above 109 M\u2299, implying halo masses of \u22651010 M\u2299at the current detection limit. The standard cosmological constant-dominated cold dark matter model (LCDM) (e.g., Krauss & Turner 1995) predicts that the majority of stars at z = 6\u221210 are in small dwarf galaxies residing in halos of mass \u223c108 \u22121010 M\u2299(e.g., Wise & Cen 2009). Thus, it seems likely that the candidate galaxies that are currently detected in the Hubble Ultra Deep Field and Early Release Science (ERS) observations at z \u223c7 \u22128 may represent the high end of the galaxy mass spectrum. Can the multi-wavelength predictions of the standard cold dark matter model reproduce the observations? To answer this question, we have performed panchromatic (\u03bb = 0.1\u22121000\u00b5m) three- dimensional dust radiative transfer calculations on 198 galaxies of stellar mass 5\u00d7108 \u22123\u00d71010 M\u2299 obtained from an ab initio cosmological adaptive mesh re\ufb01nement hydrodynamic simulation with high resolution (29h\u22121pc). Three parameters are used in the radiative transfer calculation: the dust-to-metal ratio, the extinction curve, and the fraction of directly escaped light from stars (fesc). In Kimm & Cen (2013) we show that our stellar mass function is in broad agreement with Gonz\u00b4 alez et al. (2011), independent of the three parameters. We also show that our simulated galaxies can reasonably and simultaneously match the observed UV-optical color, UV spectral slope and the UV luminosity function, if fesc \u223c10% and a Small Magellanic Cloud (SMC)-type extinction curve is used. The conclusion that the model with fesc \u223c10% is favored over the model with much smaller fesc is encouraging based on independent considerations. Observations of cosmological reionization infer the Thomson optical depth \u03c4e = 0.089 \u00b1 0.014 (Hinshaw et al. 2012), indicating a reionization redshift of zre = 10.6 + 1.1 (assuming a sudden reionization picture). In order to reionize the universe at this redshift range by stellar sources, fesc \u226a10% would not be viable (e.g., Cen 2003). Moreover, detailed radiative transfer simulations with still higher resolutions indicate a porous interstellar medium, and fesc \u223c10% is within the range of predictions for galaxies at high redshift (e.g., Wise & Cen 2009; Razoumov & Sommer-Larsen 2010; Yajima et al. 2011). One interesting and perhaps not entirely expected property, according to the conventional wisdom, that comes from our calculations is that most of these simulated galaxies are heavily dust- attenuated with extinction of 1 \u2264AFUV \u22645. This indicates that a signi\ufb01cant amount of stellar radiation may be re-processed by dust and seen in the FIR. The questions are then: Does the star formation rate (SFR) inferred based on the observed optical and UV luminosities nearly account for the total SFR? What are their infrared properties that can be checked by upcoming ALMA observations (e.g., Carilli et al. 2008; Hodge et al. 2013)? This paper addresses these two questions. The outline of this paper is as follows. In \u00a72 we detail our simulations (\u00a72.1), method of making galaxy catalogs (\u00a72.2) and panchromatic three-dimensional dust radiative transfer method (\u00a72.3). Results are presented in \u00a73. Conclusions are given in \u00a74. \u2013 3 \u2013"
                },
                {
                    "url": "http://arxiv.org/abs/1304.3466v1",
                    "title": "Composition of Low Redshift Halo Gas",
                    "abstract": "Halo gas in low-z (z<0.5) >0.1L* galaxies in high-resolution, large-scale\ncosmological hydrodynamic simulations is examined with respect to three\ncomponents: (cold, warm, hot) with temperatures equal to (<10^5, 10^{5-6},\n>10^6)K, respectively. The warm component is compared, utilizing O VI\n\\lambda\\lambda 1032, 1038 absorption lines, to observations and agreement is\nfound with respect to the galaxy-O VI line correlation, the ratio of O VI line\nincidence rate in blue to red galaxies and the amount of O VI mass in\nstar-forming galaxies. A detailed account of the sources of warm halo gas\n(stellar feedback heating, gravitational shock heating and accretion from the\nintergalactic medium), inflowing and outflowing warm halo gas metallicity\ndisparities and their dependencies on galaxy types and environment is also\npresented. Having the warm component securely anchored, our simulations make\nthe following additional predictions. First, cold gas is the primary component\nin inner regions, with its mass comprising 50% of all gas within\ngalacto-centric radius r=(30,150)kpc in (red, blue) galaxies. Second, at\nr>(30,200)kpc in (red, blue) galaxies the hot component becomes the majority.\nThird, the warm component is a perpetual minority, with its contribution\npeaking at ~30% at r=100-300kpc in blue galaxies and never exceeding 5% in red\ngalaxies. The significant amount of cold gas in low-z early-type galaxies found\nin simulations, in agreement with recent observations (Thom et al.), is\nintriguing, so is the dominance of hot gas at large radii in blue galaxies.",
                    "authors": "Renyue Cen",
                    "published": "2013-04-11",
                    "updated": "2013-04-11",
                    "primary_cat": "astro-ph.CO",
                    "cats": [
                        "astro-ph.CO"
                    ],
                    "main_content": "2.1. Hydrocode and Simulation Parameters We perform cosmological simulations with the AMR Eulerian hydro code, Enzo (Bryan 1999; Bryan & Norman 1999; O\u2019Shea et al. 2005). The version we use is a \u201cbranch\u201d version (Joung et al. 2009), which includes a multi-tiered refinement method that allows for spatially varying maximum refinement levels, when desired. This Enzo version also includes metallicity-dependent radiative cooling extended down to 10 K, molecular formation on dust grains, photoelectric heating and other features that are different from or not in the public version of Enzo code. We use the following cosmological parameters that are consistent with the WMAP7-normalized (Komatsu et al. 2011) LCDM model: \u2126M = 0.28, \u2126b = 0.046, \u2126\u039b = 0.72, \u03c38 = 0.82, H0 = 100hkms\u22121Mpc\u22121 = 70kms\u22121Mpc\u22121 and n = 0.96. These parameters are also consistent with the latest Planck results (Planck Collaboration et al. 2013), if one adopts the Hubble constant that is the average between Planck value and those derived based on SNe Ia and HST key program (Riess et al. 2011; Freedman et al. 2012). We use the power spectrum transfer functions for cold dark matter particles and baryons using fitting formulae from Eisenstein & Hut (1998). We use the Enzo inits program to generate initial conditions. First we ran a low resolution simulation with a periodic box of 120 h\u22121Mpc on a side. We identified two regions separately, one centered on a cluster of mass of \u223c2 \u00d7 1014 M\u2299and the other centered on a void region at z = 0. We then resimulate each of the two regions separately with high resolution, but embedded in the outer 120h\u22121Mpc box to properly take into account large-scale tidal field and appropriate boundary conditions at the surface of the refined region. We name the simulation centered on the cluster \u201cC\u201d run and the one centered on the void \u201cV\u201d run. The refined region for \u201cC\u201d run has a size of 21 \u00d7 24 \u00d7 20h\u22123Mpc3 and that for \u201cV\u201d run is 31 \u00d7 31 \u00d7 35h\u22123Mpc3. At their respective volumes, they represent 1.8\u03c3 and \u22121.0\u03c3 fluctuations. The root grid has a size of 1283 with 1283 dark matter particles. The initial static grids in the two refined boxes correspond to a \u2212 dark matter particles. The initial static grids in the two refined boxes correspond to a 10243 grid on the outer box. The initial number of dark matter particles in the two refined boxes correspond to 10243 particles on the outer box. This translates to initial condition in the refined region having a mean interparticle-separation of 117h\u22121kpc comoving and dark matter particle mass of 1.07 \u00d7 108h\u22121 M\u2299. The refined region is surrounded by two layers (each of \u223c1h\u22121Mpc) of buffer zones with particle masses successively larger by a factor of 8 for each layer, which then connects with the outer root grid that has a dark matter particle \u2013 5 \u2013 mass 83 times that in the re\ufb01ned region. The initial density \ufb02uctuations are included up to the Nyquist frequency in the re\ufb01ned region. The surrounding volume outside the re\ufb01ned region is also followed hydrodynamically, which is important in order to properly capture matter and energy exchanges at the boundaries of the re\ufb01ned region. Because we still can not run a very large volume simulation with adequate resolution and physics, we choose these two runs of moderate volumes to represent two opposite environments that possibly bracket the universal average. We choose a varying mesh re\ufb01nement criterion scheme such that the resolution is always better than 460/h proper parsecs within the re\ufb01ned region, corresponding to a maximum mesh re\ufb01nement level of 9 above z = 3, of 10 at z = 1\u22123 and 11 at z = 0\u22121. The simulations include a metagalactic UV background (Haardt & Madau 2012), and a model for shielding of UV radiation by atoms (Cen et al. 2005). The simulations also include metallicity-dependent radiative cooling and heating (Cen et al. 1995). We clarify that our group has included metal cooling and metal heating (due to photoionization of metals) in all our studies since Cen et al. (1995) for the avoidance of doubt (e.g., Wiersma et al. 2009; Tepper-Garc\u00b4 \u0131a et al. 2011). Star particles are created in cells that satisfy a set of criteria for star formation proposed by Cen & Ostriker (1992). Each star particle is tagged with its initial mass, creation time, and metallicity; star particles typically have masses of \u223c105\u22126 M\u2299. Supernova feedback from star formation is modeled following Cen et al. (2005). Feedback energy and ejected metal-enriched mass are distributed into 27 local gas cells centered at the star particle in question, weighted by the speci\ufb01c volume of each cell (i.e., weighting is equal to the inverse of density), which is to mimic the physical process of supernova blastwave propagation that tends to channel energy, momentum and mass into the least dense regions (with the least resistance and cooling). We allow the whole feedback processes to be hydrodynamically coupled to surroundings and subject to relevant physical processes, such as cooling and heating, as in nature. The extremely inhomogeneous metal enrichment process demands that both metals and energy (and momentum) are correctly modeled so that they are transported into right directions in a physically sound (albeit still approximate at the current resolution) way, at least in a statistical sense. In our simulations metals are followed hydrodynamically by solving the metal density continuity equation with sources (from star formation feedback) and sinks (due to subsequent star formation). Thus, metal mixing and di\ufb00usion through advection, turbulence and other hydrodynamic processes are properly treated in our simulations. The primary advantages of this supernova energy based feedback mechanism are threefold. First, nature does drive winds in this way and energy input is realistic. Second, it has only one free parameter eSN, namely, the fraction of the rest mass energy of stars formed that is deposited as thermal energy on the cell scale at the location of supernovae. Third, the processes are treated physically, obeying their respective conservation laws (where \u2013 6 \u2013 they apply), allowing transport of metals, mass, energy and momentum to be treated selfconsistently and taking into account relevant heating/cooling processes at all times. We use eSN = 1 \u00d7 10\u22125 in these simulations. The total amount of explosion kinetic energy from Type II supernovae with a Chabrier IMF translates to eSN = 6.6 \u00d7 10\u22126. Observations of local starburst galaxies indicate that nearly all of the star formation produced kinetic energy (due to Type II supernovae) is used to power galactic superwinds (e.g., Heckman 2001). Given the uncertainties on the evolution of IMF with redshift (i.e., possibly more top heavy at higher redshift) and the fact that newly discovered prompt Type I supernovae contribute a comparable amount of energy compared to Type II supernovae, it seems that our adopted value for eSN is consistent with observations and physically realistic. The validity of this thermal energy-based feedback approach comes empirically. In Cen (2012b) the metal distribution in and around galaxies over a wide range of redshift (z = 0 \u22125) is shown to be in excellent agreement with respect to the properties of observed damped Ly\u03b1 systems (Rafelski et al. 2012), whereas in Cen (2012a) we further show that the properties of O VI absorption lines at low redshift, including their abundance, Doppler-column density distribution, temperature range, metallicity and coincidence between O VII and O VI lines, are all in good agreement with observations (Danforth & Shull 2008; Tripp et al. 2008; Yao et al. 2009). This is non-trivial by any means, because they require that the transport of metals and energy from galaxies to star formation sites to megaparsec scale be correctly modeled as a function of distance over the entire cosmic timeline, at least in a statistical sense. 2.2. Simulated Galaxy Catalogs We identify galaxies in our high resolution simulations using the HOP algorithm (Eisenstein & Hu 1999), operated on the stellar particles, which is tested to be robust and insensitive to speci\ufb01c choices of concerned parameters within reasonable ranges. Satellites within a galaxy are clearly identi\ufb01ed separately. The luminosity of each stellar particle at each of the Sloan Digital Sky Survey (SDSS) \ufb01ve bands is computed using the GISSEL (Galaxy Isochrone Synthesis Spectral Evolution Library) stellar synthesis code (Bruzual & Charlot 2003), by supplying the formation time, metallicity and stellar mass. Collecting luminosity and other quantities of member stellar particles, gas cells and dark matter particles yields the following physical parameters for each galaxy: position, velocity, total mass, stellar mass, gas mass, mean formation time, mean stellar metallicity, mean gas metallicity, star formation rate, luminosities in \ufb01ve SDSS bands (ugriz) and others. At a spatial resolution of proper 460pc/h with more than 2000 well resolved galaxies at z = 0, this simulated galaxy catalog presents an excellent (by far, the best available) tool to study circumgalactic medium around galaxies at low reshift. \u2013 7 \u2013 In some of the analysis we perform here we divide our simulated galaxy sample into two sets according to the galaxy color. We shall call galaxies with g \u2212r < 0.6 blue and those with g \u2212r > 0.6 red. It is found that g \u2212r = 0.6 is at the trough of the galaxy bimodal color distribution of our simulated galaxies (Cen 2011; Tonnesen & Cen 2012), which agrees well with that of observed low-z galaxies (e.g., Blanton et al. 2003). 2.3. Generation of Synthetic O VI Absorbers The photoionization code CLOUDY (Ferland et al. 1998) is used post-simulation to compute the abundance of O VI, adopting the shape of the UV background calculated by Haardt & Madau (2012) normalized by the intensity at 1 Ryd determined by Shull et al. (1999) and assuming ionization equilibrium. We generate synthetic absorption spectra given the density, temperature, metallicity and velocity \ufb01elds in simulations. Each absorption line is identi\ufb01ed by the velocity (or wavelength) interval between one downward-crossing and the next upward-crossing points at \ufb02ux equal to 0.99 (\ufb02ux equal to unity corresponds to an unabsorbed continuum \ufb02ux) in the spectra. We do not add instrumental and other noises to the synthetic spectra. Since the absorption lines in question are sparsely distributed in velocity space, their identi\ufb01cations have no signi\ufb01cant ambiguity. Column density, equivalent width, Doppler width, mean column density weighted velocity and physical space locations, mean column density weighted temperature, density and metallicity are computed for each line. We sample the C and V run, respectively, with 72, 000 and 168, 000 random lines of sight at z = 0, with a total pathlength of \u2206z \u223c2000. A total of \u223c30, 000 \u226550 mA O VI absorbers are identi\ufb01ed in the two volumes. While a detailed Voigt pro\ufb01le \ufb01tting of the \ufb02ux spectrum would have enabled closer comparisons with observations, simulations suggest that such an exercise does not necessarily provide a more clarifying physical understanding of the absorber properties, because bulk velocities are very important and velocity substructures within an absorber do not necessarily correspond to separate physical entities (Cen 2012a). 2.4. Averaging C and V Runs The C and V runs at z = 0 are used to obtain an \u201caverage\u201d of the universe. This cannot be done precisely without much larger simulation volumes, which is presently not feasible. Nevertheless, we make the following attempt to obtain an approximate average. The number density of galaxies with luminosity greater than 0.1L\u2217in SDSS r-band in the two runs is found to be 3.95 \u00d7 10\u22122h3Mpc\u22123 and 1.52 \u00d7 10\u22122h3Mpc\u22123, respectively, in the C and V box. We \ufb01x the weighting for C and V run for the purpose of averaging statistics of the C and V runs by requiring that the average density of galaxies with luminosity greater than 0.1L\u2217in SDSS r-band in the simulations to be equal to the observed global value of \u2013 8 \u2013 2.87 \u00d7 10\u22122h3Mpc\u22123 by SDSS (Blanton et al. 2003). In the results shown below we use this method to obtain averages of statistics, where doing so allows for some more quantitative comparisons with observed data. 3. Results 3.1. Galaxy-O VI Absorber Correlation at z = 0 \u22120.5 1 1.5 2 2.5 3 3.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 log rp (kpc) P(<rp)     W>50mA, >0.1L*, z=0\u22120.2 (full sim; 2m error) W>50mA, >0.1L*, z=0\u22120.2 (photoioniz; 2m error) Chen & Mulchaey (2009): z=0\u22120.5 (obs) Prochaska et al (2011): z=0\u22120.2 (obs) Tumlinson et al (2011): z=0.1\u22120.36 (obs) Fig. 1.\u2014 Cumulative probability distribution functions of \u226550 mA O VI absorbers of \ufb01nding \u22650.1L\u2217galaxies at z = 0\u22120.2 from simulations with 2\u03c3 errorbars (red solid curves). The distribution functions at z = 0\u22120.2 are obtained by averaging z = 0 and z = 0.2 results with equal weighting. Also shown as symbols are observations from Chen & Mulchaey (2009) (solid diamonds), Prochaska et al. (2011a) (open squares) and Tumlinson et al. (2011b) (solid dots). Because the impact parameter of Tumlinson et al. (2011b) samples reaches only 150kpc, we have normalized their data points by matching their rp = 150kpc point to the rp = 150kpc point of Prochaska et al. (2011a). The blue dashed curve is produced when only photoionized O VI lines with temperature T \u22643 \u00d7 104K in our simulations are used. The \u03c7 square per degree of freedom for the red solid curve using all observed data points is 1.2, whereas it is 7.6 for the blue dashed curve. Figure 1 shows the cumulative probability distribution functions of \u226550 mA O VI absorbers of \ufb01nding \u22650.1L\u2217galaxies at z = 0\u22120.2 from simulations as well as observations. \u2013 9 \u2013 We \ufb01nd good agreement between simulations and observations, quanti\ufb01ed by the \u03c7 square per degree of freedom of 1.2. In comparison, if using only the low temperature (T < 3 \u00d7 104K) O VI absorbers in the simulations, the cumulative probability is no longer in reasonable agreement with observations, with the \u03c7 square per degree of freedom equal to 7.6; this exercise, however, only serves as an illustration of what a photoionization dominated model may produce. It will be very interesting to make a similar calculation directly using SPH simulations that have predicted the dominance of photoionized O VI absorbers even for strong O VI absorbers as shown here (e.g., Oppenheimer et al. 2012). This signi\ufb01cant di\ufb00erence found with respect to the strong O VI absorber-galaxy cross correlations between the photoionization and collisional ionization dominated models stems from the relative di\ufb00erence in the locations of strong O VI absorbers in the two models. In the collisional ionization dominated model (Cen 2012a; Shull et al. 2011) the strong O VI absorbers are spatially closer to galaxies in order to have high enough temperature (hence high O VI abundance) and high enough density to make strong O VI absorbers, whereas in the photoionization dominated model (Tepper-Garc\u00b4 \u0131a et al. 2011; Oppenheimer et al. 2012) they have to be su\ufb03ciently far from galaxies to have low enough densities to be photoionized to O VI. Additional requirement in the latter for production of strong O VI absorbers is high metallicity (\u22650.1 Z\u2299) to yield high enough O VI columns, as found in SPH simulations (Tepper-Garc\u00b4 \u0131a et al. 2011; Oppenheimer et al. 2012). 3.2. O VI Absorbers Around Blue and Red Galaxies Observations have shown an interesting dichotomy of O VI incidence rate around blue and red galaxies. Figure 2 shows the cumulative probability distribution functions of NOVI > 1014 cm\u22122 O VI absorbers of \ufb01nding a (red, blue) galaxy of luminosity of \u22650.1L\u2217at z = 0.2 from simulations. In Figure 3 we show the ratio of the cumulative radial distribution per red galaxy to per blue galaxy of \u22650.1L\u2217at z = 0.2, compared to observations. It is seen in Figure 3 that in the r = 50\u2212300kpc range the ratio of incidence rate of strong O VI absorbers around red galaxies to that around blue galaxies is about 1:5, in quantitative agreement with observations. In the case with photoionized O VI absorbers only, the fraction of O VI absorbers around red galaxies is much lower and lies signi\ufb01cantly below the observational estimates, although the present small observational sample prevents from reaching strong statistical conclusions based on this ratio alone. We see in Figure 2 that statistical uncertainties of the radial probability distribution of simulated O VI absorbers are already very small due to a signi\ufb01cant number of simulated galaxies and a still larger number of simulated absorbers used. What limits the ability to make \ufb01rm statistical statements is the sample size of observational data. Hypothetically, if the mean remains the same, a factor of two smaller errorbars would render the photoioniza\u2013 10 \u2013 1 1.5 2 2.5 3 \u22123 \u22122 \u22121 0 log rp (kpc) log P(<rp)     N>1014, >0.1L* blue, full sample N>1014, >0.1L* red, full sample N>1014, >0.1L* blue, photo subsample N>1014, >0.1L* red, photo subsample Fig. 2.\u2014 The cumulative probability distribution functions of O VI absorbers with column density greater than 1014 cm\u22122 of \ufb01nding a (red, blue) galaxy of luminosity of \u22650.1L\u2217(in SDSS r-band) at z = 0.2 with (red dashed, blue solid) curves from simulations with 10\u03c3 errorbars. The (red dotted curve, blue dot-dashed curve) are the corresponding functions for the subset of O VI absorbers that have temperature T \u22643 \u00d7 104K in our simulations. tion dominated model inconsistent with observations at \u22652\u03c3 con\ufb01dence level, whereas our collisionally dominated model would be consistent with observations within 1\u03c3. 3.3. Physical Origin of O VI Absorbers We now turn to an analysis to give a physical description for the origin of O VI absorbers in the CGM, in the context of the cold dark matter based model. While this section is interesting on its own for physically understanding halo gas, the next section on halo gas mass decomposition is not predicated on it. First, we ask whether the warm gas traced by O VI absorbers requires signi\ufb01cant energy input to be sustained over the Hubble time. Figure 4 shows the metal mass in the warm gas (T = 105 \u2212106K) distributed in the density-metallicity phase space. We \u2013 11 \u2013 1 1.5 2 2.5 3 0 0.1 0.2 0.3 0.4 0.5 log rp (kpc) P(red)/P(blue)      full simulated sample NOVI>1014  photoionized subsample NOVI>1014 Tumlinson et al 2011 (z=0.1\u22120.36) Fig. 3.\u2014 The ratio of cumulative radial probability distribution function of O VI absorbers of equivalent width (W) greater than 50mA per red galaxy to that per blue galaxy of \u22650.1L\u2217 (in SDSS r-band) at redshift z = 0.2 from simulations (the black solid curve, 2\u03c3 errorbars). The same ratio for photoionized O VI absorbers (T \u22643 \u00d7 104K) only is shown as the green dashed curve. Also shown as an open circle is the observation by Tumlinson et al. (2011b). see that most of warm metals is concentrated in a small phase space region centered at (n, Z) = (10\u22125cm\u22123, 0.15 Z\u2299). We note that the amount of gas mass in the WHIM is 40% of total gas averaged over the simulation volumes, in agreement with previous simulations (e.g., Cen & Ostriker 1999; Dav\u00b4 e et al. 2001; Cen & Ostriker 2006) and other recent simulations (Smith et al. 2011; Dav\u00b4 e et al. 2010; Shen & Kelly 2010; Tornatore et al. 2010). For this gas we \ufb01nd that the cooling time is tcool = 6\u00d7108 yrs (assuming a temperature of 105.5K), shorter than the Hubble time by a factor \u226520. For the strong O VI absorbers considered here, the cooling time is still shorter. In other words, either (1) energy is supplied to sustain existing O VI gas or (2) new warm gas is accreted or (3) some hotter gas needs to continuously cool through the warm phase. Since O VI gas by itself does not de\ufb01ne a set of stable systems and is spatially well mixed or in close proximity with other phases of gas, this suggests that the O VI gas in halos is \u201ctransient\u201d in nature. \u2013 12 \u2013 Fig. 4.\u2014 shows the metal mass in the warm gas (T = 105 \u2212106K) distributed in the density-metallicity phase space. This is a good proxy for O VI bearing gas. The amount of gas mass in the WHIM is 40% of total gas in the simulation volume. We consider three sources of warm halo gas: mechanical feedback energy from stellar evolution, gravitational binding energy released from halo formation and interactions, and direct accretion from the IGM. This simpli\ufb01cation sets a framework to make a quantitative assessment of these three sources for warm gas that we now describe. We denote Fb and Fr as the O VI incidence rate (in some convenient units) per blue and red \u22650.1L\u2217galaxy due to star formation feedback energy heating, Gb and Gr as those due to gravitational heating, and Ab and Ar as those due to accreted gas from the IGM. It is useful to stress the distinction between G and A. A is gas directly accreted from IGM that is either already warm or heated up to be warm by compression upon accretion onto the halo. On the other hand, G is gas that is shock heated to the warm phase or to a hotter phase that cools back down to become \u2013 13 \u2013 0 1 2 3 5 6 7 8 9 10 11 12 13 log r (kpc) log gas mass (<r) (M\u2299)     T<105K, red >0.1L*, z=0.2 T=105\u22126K, red >0.1L*, z=0.2 T>106K, red >0.1L*, z=0.2 T<105K, blue >0.1L*, z=0.2 T=105\u22126K, blue >0.1L*, z=0.2 T>106K, blue >0.1L*, z=0.2 Tumlinson et al (2011) Thom et al (2012) Fig. 5.\u2014 shows the cumulative gas mass as a function of radius for cold (dashed curves), warm-hot (solid curves) and hot gas (dotted curves) around blue (blue curves) and red (red curves) galaxies at z = 0.2. Also shown the the black triangle is the lower limit from observations of Tumlinson et al. (2011a) for star forming galaxies. The horizontal blue and red dot-dashed lines are the amount of warm gas the respective star formation rate can possibly produce. Additional data point for cold (T < 105K) gas in early-type galaxies within 150kpc is also plotted as the the red square with the errorbars indicating an estimated vertical range from observations of Thom et al. (2012) based on 15 early-type galaxies. warm. Restricting our analysis to within a galactocentric radius of 150kpc and reading o\ufb00 numbers from the red curve in Figure 3, we obtain two relations: Fb + Gb + Ab = 5, Fr + Gr + Ar = 1. (1) An additional reasonable assumption is now made: feedback heating rate Sr (Sb) is proportional to average star formation rate SFRr (SFRb), which in turn is proportional to their respective gas accretion rate Ar (Ab). This assumption allows us to lump Fr and Ar (Fb and \u2013 14 \u2013 Ab): Sb = Fb + Ab = C \u00d7 SFRb Sr = Fr + Ar = C \u00d7 SFRr, (2) where C is a constant. We will return to determine Fr and Ar (Fb and Ab) separately later. Equation (1) is now simpli\ufb01ed to: Sb + Gb = 5, Sr + Gr = 1. (3) The ratio of SFRb to SFRr can be computed directly in the simulations, found to be 8.4. Rounding it down to 8 and combining it with Equation (2) give Sb/Sr = 8. (4) Lastly, a direct assessment of the relative strength of gravitational heating of warm gas in blue and red galaxies is obtained by making the following ansatz: the amount of hot T \u2265106K gas is proportional to the overall heating rate, to which the gravitational heating rate of warm gas is proportional. Figure 5 shows the gas mass of the three halo gas components interior to the radius shown in the x-axis. Within the galactocentric radius of 150kpc it is found that the amount of hot halo gas per red \u22650.1L\u2217galaxy is twice that of per blue \u22650.1L\u2217galaxy: Gr/Gb = 2. (5) Solving Equations (3,4,5) yields Sb = 24/5, Gb = 1/5; Sr = 3/5, Gr = 2/5. (6) The estimate given in Equations (5) is admittedly uncertain. Therefore, an estimate on how sensitively conclusions depend on it is instructive. We \ufb01nd that, if we had used Gr/Gb = 1 (instead of 2), we would have obtained Sb = 32/7, Gb = 3/7, Sr = 4/7, Gr = 3/7; had we used Gr/Gb = 1/2, we would have obtained Sb = 4, Gb = 1, Sr = 1/2, Gr = 1/2. Thus, a relatively robust conclusion for the sources of warm halo gas emerges: (1) for red \u22650.1L\u2217 galaxies (Fr + Ar) and Gr have the same magnitude, (2) for blue \u22650.1L\u2217galaxies (Fb + Ab) overwhelmingly dominates over Gb. It is prudent to have a consistency check for the conclusion that star formation feedback may dominate heating of warm gas that produces the observed O VI absorbers in blue galaxies. In Figure 5 the horizontal blue dot-dashed line is obtained by assuming a Chabrier-like \u2013 15 \u2013 IMF that is used in the simulations, which translates to 2/3\u00d710\u22125SFR\u00d7tcool\u00d7c2/(k105.5K), where c is speed of light and k Boltzmann constant; also assumed is that 2/3 of the initial supernova energy is converted to gas thermal energy, which is the asymptotic value for Sedov explosions, SFR the respective average star formation rate per \u22650.1L\u2217blue galaxy, tcool = 6 \u00d7 108yrs an estimated cooling time for warm halo gas. From this illustration we see that with about 20% e\ufb03ciency of heating warm gas, star formation feedback energy is already adequate for accounting for all the observed warm gas around blue galaxies. We therefore conclude that the required energy from star formation feedback to heat up the warm gas is available and our conclusions are self-consistent, even if the direct accretion contribution is zero, which we will show is not. Our results on warm gas mass are also in reasonable agreement with observations of Tumlinson et al. (2011a), so is the oxygen mass contained in the warm component, as shown in Figure 6. Let us now determine Fr and Ar (Fb and Ab) individually in the following way. We compute warm metal mass that have inward and outward radial velocities within a radial shell at r = [50, 150]kpc separately for all red > 0.1L\u2217galaxies and all blue > 0.1L\u2217galaxies, denoting in\ufb02ow warm metal mass as MZ(vr < 0) and out\ufb02ow warm metal mass as MZ(vr > 0), where vr is radial velocity of a gas element with positive being out\ufb02owing and negative being in\ufb02owing. We de\ufb01ne the in\ufb02ow warm metal fraction as fin \u2261MZ(vr < 0)/(MZ(vr < 0) + MZ(vr > 0)), which is listed as the \ufb01rst of the three elements in each entry in Table 1 under the column |vr| > 0 km/s. We also compute the mean metallicities (in solar units) for the in\ufb02ow and out\ufb02ow warm gas, which are the second and third of the three elements in each entry in Table 1. Four separated cases are given: (1) red galaxies in C run (C red), (2) red galaxies in V run (V red), (3) blue galaxies in C run (C blue), (4) blue galaxies in V run (V blue). In order to make sure that in\ufb02ow and out\ufb02ow are not confused with random motions of gas in a Maxwellian like distribution, we separately limit the magnitude of infall and out\ufb02ow radial velocities to greater than 100 km/s and 250 km/s, and listed the computed quantities under the third column |vr| > 100 km/s and the fourth column |vr| > 250 km/s, respectively. Table 1. Warm In\ufb02ow and Out\ufb02ow at r = [50 \u2212150]kpc Radial Shell |vr| > 0 km/s |vr| > 100 km/s |vr| > 250 km/s (fin, Zin/ Z\u2299, Zout/ Z\u2299) (fin, Zin/ Z\u2299, Zout/ Z\u2299) (fin, Zin/ Z\u2299, Zout/ Z\u2299) C red (58%, 0.27, 0.17) (58%, 0.29, 0.17) (59%, 0.31, 0.17) V red (51%, 0.21, 0.29) (61%, 0.18, 0.26) (65%, 0.11, 0.33) C blue (54%, 0.099, 0.10) (55%, 0.099, 0.10) (55%, 0.099, 0.10) V blue (52%, 0.10, 0.14) (52%, 0.09, 0.16) (46%, 0.08, 0.24) \u2013 16 \u2013 0 1 2 3 4 5 6 7 8 9 10 log r (kpc) log oxygen mass (<r) (M\u2299)      T<105K, red >0.1L*, z=0.2  T=105\u22126K, red >0.1L*, z=0.2  T>106K, red >0.1L*, z=0.2  T<105K, blue >0.1L*, z=0.2  T=105\u22126K, blue >0.1L*, z=0.2  T>106K, blue >0.1L*, z=0.2  Tumlinson et al 2011 Fig. 6.\u2014 shows the cumulative metal mass as a function of radius for cold (dashed curves), warm-hot (solid curves) and hot gas (dotted curves) around blue (blue curves) and red (red curves) galaxies at z = 0.2. It is interesting to \ufb01rst take a closer look at the di\ufb00erence in metallicities between in\ufb02ow and out\ufb02ow gas. The warm in\ufb02ow gas in red galaxies in the C run has consistently higher metallicity than warm out\ufb02ow gas, Zin = (0.27 \u22120.31) Z\u2299versus Zout = 0.17 Z\u2299. The opposite holds for red galaxies in the V run: Zin = (0.11 \u22120.21) Z\u2299versus Zout = (0.26 \u22120.33) Z\u2299. The warm in\ufb02ow gas in blue galaxies in the C run has about the same metallicity as warm out\ufb02ow gas at Z = (0.09 \u22120.1) Z\u2299. The warm in\ufb02ow gas in blue galaxies in the V run, on the other hand, has a substantially lower metallicity than the warm out\ufb02ow gas, Zin = (0.08 \u22120.10) Z\u2299versus Zout = (0.14 \u22120.24) Z\u2299. Except in the case of C blue, we note that the in\ufb02ow and out\ufb02ow gas has di\ufb00erent metallicities, with the di\ufb00erence being larger when a higher \ufb02ow velocitiy is imposed in the selection. This di\ufb00erence in metallicity demonstrates that the warm in\ufb02ows and out\ufb02ows are distinct dynamical entities, not random motions in a well-mixed gas, making our distinction of in\ufb02ows and out\ufb02ows physically meaningful. A physical explanation for the metallicity trends found can be made as follows. In low density environment (i.e., in the V run) circumgalactic medium has not been enriched to a high level and hot gas is not prevalent. As a result, warm (and possibly cold) in\ufb02ows of relatively low metallicities still exist at low redshift. The progression from blue to red galaxies in the V run re\ufb02ects a progression from very low density regions (i.e., true voids) to dense \ufb01laments and group environments, with higher metallicities for both \u2013 17 \u2013 in\ufb02ows and out\ufb02ows in the denser environments in the V run; but the di\ufb00erence between in\ufb02ow and out\ufb02ow metallicities remains. For red galaxies in high density environments (C run) the circumgalactic medium has been enriched to higher metallicities. Higher cooling rates of higher-metallicity gas in relatively hot environments preferentially produces highermetallicity warm gas that originates from hot gas and has now cooled to become warm gas. The blue galaxies in the C run are primarily in cosmic \ufb01laments and the metallicity of the in\ufb02ow gas is about 0.1 Z\u2299, which happens to coincide with the metallicity of the out\ufb02ow gas. One needs to realize that at the radial shell r = [50 \u2212150]kpc over which the tabulated quantities are computed, the out\ufb02ow gas originated in star forming regions has loaded a substantial amount of interstellar and circumgalactic medium in the propagation process. Let us now turn to the warm in\ufb02ow and out\ufb02ow metal mass. It appears that the fraction of in\ufb02ow warm metals (out of all warm metals) lies in a relatively narrow range fin = 45 \u221265%. For our present purpose we will just say Fr = Ar and Fb = Ab. Armed with these two relations our best estimates for various contributions to the observed warm halo metals, as a good proxy for the O VI absorption, can be summarized as follows. \u2022 For red \u22650.1L\u2217galaxies at z = 0.2 contributions to warm metals in the halo gas from star formation feedback (Fr), accretion of intergalactic medium (Ar) and gravitational shock heating (Gr) are (Fr, Ar, Gr) = (30%, 30%, 40%). \u2022 For blue \u22650.1L\u2217galaxies at z = 0.2 contributions to warm metals in the halo gas from the three sources are (Fb, Ab, Gb) = (48%, 48%, 4%). \u2022 Dependencies of warm halo gas metallicities on galaxy type and environment are complex but physically understandable. For red galaxies, the metallicity of in\ufb02owing warm gas increases with increasing environmental overdensity, whereas that of out\ufb02owing warm gas decreases with increasing environmental overdensity. For blue galaxies, the metallicity of in\ufb02owing warm gas depends very weakly on environmental overdensity, whereas that of out\ufb02owing warm gas decreases with increasing environmental overdensity. As a whole, the mean metallicity of warm halo gas in red galaxies is \u223c0.25 Z\u2299, while that of blue galaxies is \u223c0.11 Z\u2299. We suggest that these estimates of source fractions are not seriously in error on average, if one is satis\ufb01ed with an accuracy of a factor of two. The relative metallicity estimates should be quite robust with errors much smaller than a factor of two. It is stressed that these estimates are averaged over many red and blue galaxies and one is not expected to have been led to think that the correlations (such as between warm gas mass and SFR) hold strictly for individual galaxies. Rather, we expect large variations from galaxy to galaxy, even at a \ufb01xed star formation rate. Figure 7 makes this important point clear, which shows that, while there is a positive correlation between warm metal mass within 150kpc radius and SFR for galaxies with non-negligible SFR (i.e., appearing in the SFR range shown), a \u2013 18 \u2013 dispersion of \u223c1 dex in warm metal mass at a \ufb01xed SFR in the range of 0.1 \u2212100 M\u2299yr\u22121 exists. The goodness of the \ufb01t can be used as a way to rephrase this signi\ufb01cant dispersion. If one assumes that the errorbar size is each log mass determination for each shown galaxy is 1, one \ufb01nds that the chi-square per degree of the \ufb01tting line (green) is 0.80, indicating that the correlation between log MZ(T = 105\u22126K) and log SFR is only good to about 1 dex in warm metal gas mass. \u22123 \u22122 \u22121 0 1 2 3 4 5 6 7 8 9 log SFR (Msun/yr) log MZ(T=105\u22126) (Msun)     MZ(<150kpc) Fig. 7.\u2014 shows the metal mass in the warm gas MZ within a galactocentric radius of 150kpc as a function of the SFR of the galaxy at z = 0.2. Each red dot is a galaxy. The green curve shows the best linear regression, log MZ(T = 105\u22126K)/ M\u2299= 0.32 log SFR + 7.1, for the galaxies shown. 3.4. Composition of Low-z Halo Gas In Cen (2012a) we show that the properties of O VI absorption lines at low redshift, including their abundance, Doppler-column density distribution, temperature range, metallicity and coincidence between O VII and O VI lines, are all in good agreement with observations (Danforth & Shull 2008; Tripp et al. 2008; Yao et al. 2009). In the above we have shown that O VI-galaxies relations as well as oxygen mass in galaxies in the simulations are also in excellent agreement with observations. These tests together are non-trivial and lend us signi\ufb01cant con\ufb01dence to now examine the overall composition of halo gas at low-z. Figure 8 shows the di\ufb00erential (left panel) and cumulative (right panel) mass fractions of each gas component as a function of galactocentric distance for red (red curves) and blue \u2013 19 \u2013 0 1 2 3 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 log r (kpc) gas mass fractions (r) 0 1 2 3 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 log r (kpc) gas mass fractions (<r)     T<105K, red >0.1L*, z=0.2 T=105\u22126K, red >0.1L*, z=0.2 T>106K, red >0.1L*, z=0.2 T<105K, blue >0.1L*, z=0.2 T=105\u22126K, blue >0.1L*, z=0.2 T>106K, blue >0.1L*, z=0.2 Fig. 8.\u2014 shows the di\ufb00erential (left panel) and cumulative (right panel) gas mass fractions as a function of radius for cold (dashed curves), warm-hot (solid curves) and hot gas (dotted curves) around blue (blue curves) and red (red curves) > 0.1L\u2217galaxies at z = 0.2. 0 1 2 3 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 log r (kpc) metals mass fractions (<r) 0 1 2 3 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 log r (kpc) metals mass fractions (<r)     T<105K, red >0.1L*, z=0.2 T=105\u22126K, red >0.1L*, z=0.2 T>106K, red >0.1L*, z=0.2 T<105K, blue >0.1L*, z=0.2 T=105\u22126K, blue >0.1L*, z=0.2 T>106K, blue >0.1L*, z=0.2 Fig. 9.\u2014 shows the di\ufb00erential (left panel) and cumulative (right panel) gas metals mass fractions as a function of radius for cold (dashed curves), warm-hot (solid curves) and hot gas (dotted curves) around blue (blue curves) and red (red curves) galaxies at z = 0.2. (blue curves) galaxies. We note that the \ufb02uctuating behaviors (mostly in the di\ufb00erential functions on the left panel) are due to occasional dense cold clumps in neighboring galaxies. Overall, we see that within about (10,30)kpc for (red, blue) galaxies the cold (T < 105K) gas component completely dominates, making up about (80%, > 95%) of all gas at these radii. For both > 0.1L\u2217(red, blue) galaxies cold gas remains the major component up to r = (30, 150)kpc, within which its mass comprises 50% of all gas. At r > (30, 200)kpc for (red, blue) galaxies the hot (T > 106K) gas component dominates. The warm gas component, \u2013 20 \u2013 while having been extensively probed observationally, appears to be a minority in both red and blue galaxies at all radii. The warm component\u2019s contribution to the overall gas content reaches its peak value of \u223c30% at r = 100\u2212300kpc for blue galaxies, whereas in red galaxies it is negligible at r < 10kpc and hovers around 5% level at r = 30\u22121000kpc. The prevalence of cold gas at small radii in red (i.e., low star formation activities) galaxies is intriguing and perhaps surprising to some extent. Some recent observations indicate that early-type galaxies in the real universe do appear to contain a substantial amount of cold gas, consistent with our \ufb01ndings. For example, Thom et al. (2012) infer a mean mass of 109 \u22121011 M\u2299of gas with T < 105K at r < 150kpc based on a sample of 15 early-type galaxies at low redshift from COS observations, which is shown as the red square (its horizontal position is slightly shifted to the right for display clarity) in Figure 5. Their inferred range is in fact consistent with our computed value of \u223c6 \u00d7 1010 M\u2299of cold T < 105K gas for red > 0.1L\u2217galaxies shown as the red dashed curve in Figure 5. Figure 9 that is analogous to Figure 8 shows the corresponding distributions for metals mass fractions in the three components for red and blue galaxies. The overall trends are similar to those for total warm gas mass. We note one signi\ufb01cant di\ufb00erence here. The overall dominance of metals mass in cold gas extends further out radially for both red and blue galaxies, whereas the contributions to metal mass from the other two components are compensatorily reduced. For example, we \ufb01nd that the radius within which the cold mass component makes up 50% of total gas in (red, blue) galaxies is (40,150)kpc, where the radius within which the cold mass component makes up 50% of total gas metals in (red, blue) galaxies becomes (200,500)kpc. This is largely due to a signi\ufb01cantly higher metallicity of the cold component in both red and blue galaxies compared to the other two components, as shown in Figure 10. We also note from Figure 10 that the warm gas in red galaxies has a higher metallicity than in blue galaxies, as found earlier, with the mean metallicity (\u223c0.25 Z\u2299, \u223c0.11 Z\u2299) in (red, blue) galaxies within a radius of 150kpc. \u2013 21 \u2013 1 2 3 \u22122 \u22121 0 log r (kpc) [Z/H]     T<105K, red >0.1L*, z=0.2 T=105\u22126K, red >0.1L*, z=0.2 T>106K, red >0.1L*, z=0.2 T<105K, blue >0.1L*, z=0.2 T=105\u22126K, blue >0.1L*, z=0.2 T>106K, blue >0.1L*, z=0.2 Fig. 10.\u2014 shows as a function of radius the metallicity for cold (dashed curves), warm-hot (solid curves) and hot gas (dotted curves) around blue (blue curves) and red (red curves) galaxies at z = 0.2. 4. Conclusions The distribution and evolution of the intergalactic medium have largely been addressed by cosmological simulations (e.g., Cen & Ostriker 1999; Dav\u00b4 e et al. 2001; Cen & Chisari 2011; Cen 2012a). The global distribution and composition of halo gas in and around galaxies at low redshift (z < 0.5) are addressed here, utilizing state-of-the-art high-resolution (460h\u22121pc), large-scale cosmological hydrodynamic simulations with validated star formation and feedback prescriptions. We \ufb01nd that within about (10,30)kpc for (red, blue) > 0.1L\u2217galaxies the cold (T < 105K) gas component is the primary gas component making up about (80%, > 95%) of all gas. For both > 0.1L\u2217(red, blue) galaxies cold gas remains the major component up to r = (30, 150)kpc, within which its mass comprises 50% of all gas. At r > (30, 200)kpc for (red, blue) galaxies the hot (T > 106K) gas component dominates. The warm (T = 105 \u2212106K) gas component makes a minor contribution to the overall gas mass as well as gas metal mass in both red and blue galaxies. The warm component\u2019s contribution to the overall gas content reaches its peak value of \u223c30% at r = 100 \u2212300kpc for blue galaxies, whereas in red galaxies its contribution is negligible at r < 10kpc and capped at 5% level at r = 30 \u22121000kpc. Where comparisons with observations are possible, we \ufb01nd that the amount of warm gas and and oxygen mass in star forming galaxies are in agreement with observations (e.g., Tumlinson et al. 2011b), so is the amount of cold gas in early-type galaxies \u2013 22 \u2013 at low redshift (e.g., Thom et al. 2012). The presence of a signi\ufb01cant amount cold gas in red galaxies at low redshift is new and somewhat surprising. The nature of this cold gas and its role in star formation in red galaxies are not addressed in the present paper. This and signatures of the predicted dominance of hot gas in blue galaxies (as well as red galaxies) at large radii will be addressed elsewhere. In addition to the agreement between our simulations and observations with respect to the global O VI incidence rate (Cen 2012a), we show that our predicted correlations between galaxies and strong O VI absorbers of column density NOVI \u226514 cm\u22122 are in excellent agreement with observations with \u03c7 square per degree of freedom equal to 1.2. On the other hand, when we use only photoionized O VI absorbers (T < 3 \u00d7 104K) in the simulations, the comparisons between simulations and observations become substantially less favorable with \u03c7 square per degree of freedom equal to 7.6; the signi\ufb01cant disagreement stems from the photoionized O VI absorbers being too distant from galaxies. The O VI line incidence rate per \u22650.1L\u2217galaxy around blue (g \u2212r < 0.6) galaxies in our simulations is higher than that around \u22650.1L\u2217red (g \u2212r > 0.6) galaxies by a factor of \u223c4 at r \u2264100 \u2212300kpc, increasing to \u226510 at r \u226420kpc, in reasonable agreement with extant observations (e.g., Chen & Mulchaey 2009; Prochaska et al. 2011a), whereas in the photoionization dominated model the ratio is zero at r < 100 kpc. Thus, the cross correlations between galaxies and O VI lines provide powerful di\ufb00erentiation between collisional and photo ionization models, with collisional ionization dominance for strong (NOVI \u22651014cm\u22122) O VI absorbers being favored currently. The O VI-bearing halo gas (i.e., the warm component) is found to be \u201ctransient\u201d in nature and hence requires constant sources. We perform analysis to unravel the sources and their relations to galaxy formation. We \ufb01nd that, on average, to within a factor of two, contributions to warm metals in the halo gas from star formation feedback (Fr), accretion of intergalactic medium (Ar) and gravitational shock heating (Gr) are (Fr, Ar, Gr) = (30%, 30%, 40%) for red \u22650.1L\u2217galaxies at z = 0.2. For blue \u22650.1L\u2217galaxies at z = 0.2 contributions are (Fb, Ab, Gb) = (48%, 48%, 4%). For both red and blue galaxies, the amounts of warm gas in in\ufb02ows and out\ufb02ows are comparable. The mean metallicity of warm halo gas in (red, blue) galaxies is (\u223c0.25 Z\u2299, \u223c0.11 Z\u2299). Environmental dependence of O VI-bearing halo gas is as follows. In low density environments the metallicity of in\ufb02owing warm gas is substantially lower than that of out\ufb02owing warm gas; the opposite is true in high density environments. I would like to thank Dr. M.K.R. Joung for help on generating initial conditions for the simulations and running a portion of the simulations and Greg Bryan for help with Enzo code, Drs. John Wise and Matthew Turk for very useful help with analysis program yt(Turk et al. 2011), and an anonymous referee for constructive reports. Computing resources were in part \u2013 23 \u2013 provided by the NASA HighEnd Computing (HEC) Program through the NASA Advanced Supercomputing (NAS) Division at Ames Research Center. The research is supported in part by NASA grant NNX11AI23G.",
                    "introduction": "Galaxy formation and evolution is the central astrophysical problem in cosmology. The basic parameters of the cosmological framework - the standard cosmological constant- dominated cold dark matter (DM) model (LCDM) (e.g., Krauss & Turner 1995; Bahcall 1Department of Astrophysical Sciences, Princeton University, Peyton Hall, Ivy Lane, Princeton, NJ 08544; cen@astro.princeton.edu arXiv:1304.3466v1  [astro-ph.CO]  11 Apr 2013 \u2013 2 \u2013 et al. 1999) - are largely \ufb01xed to an accuracy of \u223c10% or better. The LCDM model is able to explain a variety of observations on scales greater than \u223c1Mpc, including high redshift supernovae (e.g., Perlmutter et al. 1998; Riess et al. 1998; Astier et al. 2006), the cosmic microwave background (e.g., Komatsu et al. 2011; Planck Collaboration et al. 2013), large- scale distribution of galaxies (e.g., Tegmark et al. 2004; Percival et al. 2007), X-ray cluster abundance (e.g., Allen et al. 2008) and Ly\u03b1 forest (e.g., Croft et al. 2002; Seljak et al. 2005). An important component of the astrophysical problem - gravitational formation and evolution of halos that host galaxies - is well understood, through N-body simulations (e.g., Jenkins et al. 2001; Bullock et al. 2001; Wechsler et al. 2002; Diemand et al. 2007) and analytic models (e.g., Bond et al. 1991; Lacey & Cole 1993; Sheth & Tormen 1999; Mo & White 2002; Cooray & Sheth 2002). The gastrophysics of galaxy formation and feedback, on the other hand, is far from being adequately understood. Alternative approaches that parameterize and then infer physical processes based on \ufb01nding best matches to observations, such as the semi-analytic methods (e.g., Somerville & Primack 1999; Benson et al. 2003) and the halo-occupation distribution (HOD) method (e.g., Berlind & Weinberg 2002; Zheng et al. 2007), have been successful but have limited predictive power. More importantly, in semi- analytic methods the treatment of galaxy formation is halo based and largely decoupled from that of the intergalactic medium, which in fact has dramatically evolved with time. At z = 2 \u22126 most of the baryons are found to be in the Ly\u03b1 forest, a relatively cold phase of temperature of \u223c104K, as indicated by both observations (e.g., Rauch et al. 1997) and simulations (e.g., Cen et al. 1994). By z = 0 most of the baryons in the intergalactic medium have been heated up, primarily by gravitational shocks, to temperatures that are broadly peaked at about 106K, the so-called Warm-Hot Intergalactic Medium (WHIM) (e.g., Cen & Ostriker 1999). The \u201cab initio\u201d, more predictive approach of direct cosmological hydrodynamic simulations, after having made steady progress (e.g., Evrard et al. 1994; Katz et al. 1996; Teyssier 2002; Kere\u02c7 s et al. 2005; Hopkins et al. 2006; Oppenheimer & Dav\u00b4 e 2006; Governato et al. 2007; Naab et al. 2007; Gnedin et al. 2008; Joung et al. 2009; Cen 2011), begin to be able to make statistically signi\ufb01cant and physically realistic characterizations of the simultaneous evolution of galaxies and the intergalactic medium. It is the aim of this writing to quantify the composition of the halo gas in low redshift galaxies, using state-of-the-art high resolution (460h\u22121pc), large-scale (thousands of galax- ies) cosmological hydrodynamic simulations with advanced treatments of star formation, feedback and microphysics. Our focus here is on gas that is in the immediate vicinities of galaxies, on galactocentric distances of 10 \u2212500kpc, where the exchanges of gas, metals, energy and momentum between galaxies and the intergalactic medium (IGM) primarily take place. We shall broadly term it \u201ccircumgalactic medium (CGM)\u201d or \u201chalo gas\u201d. Under- standing halo gas is necessary before a satisfactory theory of galaxy formation and evolution may be constructed. The present theoretical study is also strongly motivated observation- ally, in light of recent rapid accumulation of data by HST observations enabling detailed \u2013 3 \u2013 comparisons between galaxies and the warm component (T \u223c105 \u2212106K) of their CGM at low redshift (e.g., Chen & Mulchaey 2009; Prochaska et al. 2011b; Tumlinson et al. 2011a; Tripp et al. 2011). We shall dissect halo gas at low redshift (z < 0.5) into three components, (cold, warm, hot) gas with temperature (< 105, 105 \u2212106, > 106)K, respectively. A large portion of our presentation is spent on quantifying O VI \u03bb\u03bb1032, 1038 absorption lines and the overall properties of warm halo gas and comparing them to observations in as much detail as possible. Feedback processes, while being treated with increased physical sophistication, are still not based on \ufb01rst principles due primarily to resolution limitations in large-scale cosmological simulations. Thus, it is imperative that our simulations are well validated and anchored by requiring that some key and pertinent aspects of our simulations match relevant observations. The O VI line, when collisionally ionized, has its abundance peaked at a temperature of T = 105.3\u22125.7K and thus is an excellent proxy for the the warm gas. After validating our simulations with respect to the observed properties of O VI absorption lines, we present the overall composition of low redshift halo gas. We \ufb01nd that, for (red,blue) galaxies more luminous than 0.1L\u2217the cold gas of T < 105K, on average, dominates the halo gas budget within a radius of (30, 150)kpc. Beyond a radius of (30, 200)kpc for (red,blue) galaxies the hot gas of T > 106K dominates. The warm component remains a smallest minority at all radii, peaking at \u223c30% at \u223c100 \u2212300kpc for blue galaxies but never exceeding 5% for red galaxies. The following physical picture emerges for the physical nature of the warm gas com- ponent. The warm halo gas has a cooling time much shorter than the Hubble time and hence is \u201ctransient\u201d, with their presence requiring sources. To within a factor of two we \ufb01nd that, for low-z \u22650.1L\u2217red galaxies contributions to warm halo gas from star formation feedback (Fr), accretion of intergalactic medium (Ar) and gravitational shock heating (Gr) are (Fr, Ar, Gr) = (30%, 30%, 40%). For blue \u22650.1L\u2217galaxies contributions to warm halo gas from the three sources are (Fb, Ab, Gb) = (48%, 48%, 4%). The mean metallicity of warm halo gas in (red, blue) galaxies is (\u223c0.25 Z\u2299, \u223c0.11 Z\u2299). Environmental dependence of O VI-bearing halo gas is as follows. In low density environments the metallicity of in\ufb02owing warm gas is substantially lower than that of out\ufb02owing warm gas; the opposite is true in high density environments. The outline of this paper is as follows. In \u00a72.1 we detail simulation parameters and hy- drodynamics code, followed by a description of our method of making synthetic O VI spectra in \u00a72.2, which is followed by a description of how we average the two separate simulations C (cluster) and V (void) run in \u00a72.3. Results are presented in \u00a73. A detailed comparison of galaxy-O VI absorber correlation is computed and shown to match observations in \u00a73.1, followed in \u00a73.2 by an analysis of the ratio of O VI absorber incidence rates around blue and red galaxies that is found to be consistent with observations. A detailed examination of the \u2013 4 \u2013 physical origin and properties of the warm gas in low-z halo is given in \u00a73.3. The overall composition of low-z halo gas is given in \u00a73.4 and conclusions are summarized in \u00a74."
                },
                {
                    "url": "http://arxiv.org/abs/1210.3600v1",
                    "title": "Nature of Lyman Alpha Blobs: Powered by Extreme Starbursts",
                    "abstract": "We present a new model for the observed Lyman alpha blobs (LABs) within the\ncontext of the standard cold dark matter model. In this model, LABs are the\nmost massive halos with the strongest clustering (proto-clusters) undergoing\nextreme starbursts in the high-z universe. Aided by calculations of detailed\nradiative transfer of Lya photons through ultra-high resolution (159pc)\nlarge-scale (>30Mpc) adaptive mesh-refinement cosmological hydrodynamic\nsimulations with galaxy formation, this model is shown to be able to, for the\nfirst time, reproduce simultaneously the global Lya luminosity function and\nluminosity-size relation of the observed LABs. Physically, a combination of\ndust attenuation of Lya photons within galaxies, clustering of galaxies, and\ncomplex propagation of Lya photons through circumgalactic and intergalactic\nmedium gives rise to the large sizes and frequently irregular isophotal shapes\nof LABs that are observed. A generic and unique prediction of this model is\nthat there should be strong far-infrared (FIR) sources within each LAB, with\nthe most luminous FIR source likely representing the gravitational center of\nthe proto-cluster, not necessarily the apparent center of the Lya emission of\nthe LAB or the most luminous optical source. Upcoming ALMA observations should\nunambiguously test this prediction. If verified, LABs will provide very\nvaluable laboratories for studying formation of galaxies in the most overdense\nregions of the universe at a time when global star formation is most vigorous.",
                    "authors": "Renyue Cen, Zheng Zheng",
                    "published": "2012-10-12",
                    "updated": "2012-10-12",
                    "primary_cat": "astro-ph.CO",
                    "cats": [
                        "astro-ph.CO"
                    ],
                    "main_content": "2.1. Hydrocode and Simulation Parameters We perform cosmological simulations with the AMR Eulerian hydro code, Enzo (Bryan & Norman 1999; Joung et al. 2009). First we ran a low resolution simulation with a periodic box of 120 h\u22121Mpc (comoving) on a side. We identified a region centered on a cluster of mass of \u223c3 \u00d7 1014 M\u2299at z = 0. We then resimulate with high resolution of the chosen region embedded in the outer 120h\u22121Mpc box to properly take into account large-scale tidal field and appropriate boundary conditions at the surface of the refined region. The refined region has a comoving size of 21 \u00d7 24 \u00d7 20h\u22123Mpc3 and represents 1.8\u03c3 matter density fluctuation on that volume. The dark matter particle mass in the refined region is 1.3 \u00d7 107h\u22121 M\u2299. The refined region is surrounded by three layers (each of \u223c1h\u22121Mpc) of buffer zones with particle masses successively larger by a factor of 8 for each layer, which then connects with the outer root grid that has a dark matter particle mass 84 times that in the refined region. We choose the mesh refinement criterion such that the resolution is always better than 111h\u22121pc (physical), corresponding to a maximum mesh refinement level of 13 at z = 0. The simulations include a metagalactic UV background (Haardt & Madau 1996), and a model for shielding of UV radiation by neutral hydrogen (Cen et al. 2005). They include metallicity-dependent radiative cooling (Cen et al. 1995). Our simulations also solve relevant gas chemistry chains for molecular hydrogen formation (Abel et al. 1997), molecular formation on dust grains (Joung et al. 2009), and metal cooling extended down to 10 K (Dalgarno & McCray 1972). Star particles are created in cells that satisfy a set of criteria for star formation proposed by Cen & Ostriker (1992). Each star particle is tagged with its initial mass, creation time, and metallicity; star particles typically have masses of \u223c106 M\u2299. Supernova feedback from star formation is modeled following Cen et al. (2005). Feedback energy and ejected metal-enriched mass are distributed into 27 local gas cells centered at the star particle in question, weighted by the specific volume of each cell, which is to mimic the physical process of supernova blastwave propagation that tends to channel energy, momentum and mass into the least dense regions (with the least resistance and cooling). We allow the entire feedback processes to be hydrodynamically coupled to surroundings and subject to relevant physical processes, such as cooling and heating. The total amount of explosion kinetic energy from Type II supernovae for an amount of star formed M\u2217with a Chabrier initial mass function (IMF) is eSNM\u2217c2 (where c is the speed of light) with eSN = 6.6 \u00d7 10\u22126. Taking into account the contribution of prompt Type I supernovae, we use eSN = 1 \u00d7 10\u22125 in our simulations. Observations of local starburst galaxies indicate that nearly all of the star formation produced kinetic energy is used to power galactic superwinds (e.g., Heckman 2001). Supernova feedback is important primarily for regulating star formation and for transporting energy and metals into the intergalactic medium. The \u2013 6 \u2013 extremely inhomogeneous metal enrichment process demands that both metals and energy (and momentum) are correctly modeled so that they are transported in a physically sound (albeit still approximate at the current resolution) way. The kinematic properties traced by unsaturated metal lines in damped Lyman-alpha systems (DLAs) are extremely tough tests of the model, which is shown to agree well with observations (Cen 2012b). We use the following cosmological parameters that are consistent with the WMAP7normalized (Komatsu et al. 2010) \u039bCDM model: \u2126M = 0.28, \u2126b = 0.046, \u2126\u039b = 0.72, \u03c38 = 0.82, H0 = 100h km s\u22121Mpc\u22121 = 70 km s\u22121Mpc\u22121 and n = 0.96. This simulation has been used (Cen 2011b) to quantify partitioning of stellar light into optical and infrared light, through ray tracing of continuum photons in a dusty medium that is based on selfconsistently computed metallicity and gas density distributions. We identify galaxies in our high resolution simulations using the HOP algorithm (Eisenstein & Hu 1999), operated on the stellar particles, which is tested to be robust and insensitive to speci\ufb01c choices of concerned parameters within reasonable ranges. Satellites within a galaxy are clearly identi\ufb01ed separately. The luminosity of each stellar particle at each of the Sloan Digital Sky Survey (SDSS) \ufb01ve bands is computed using the GISSEL stellar synthesis code (Bruzual & Charlot 2003), by supplying the formation time, metallicity and stellar mass. Collecting luminosity and other quantities of member stellar particles, gas cells and dark matter particles yields the following physical parameters for each galaxy: position, velocity, total mass, stellar mass, gas mass, mean formation time, mean stellar metallicity, mean gas metallicity, star formation rate, luminosities in \ufb01ve SDSS bands (and various colors) and others. At a spatial resolution of 159pc (physical) with nearly 5000 well resolved galaxies at z \u223c3, this simulated galaxy catalog presents an excellent (by far, the best available) tool to study galaxy formation and evolution. 2.2. Ly\u03b1 Radiative Transfer Calculation The AMR simulation resolution is 159pc at z = 3. For each galaxy we produce a cylinder of size (2Rvir)\u00d7(2Rvir)\u00d7(42Rvir) on a uniform grid of cell size 318pc, where Rvir is the virial radius of the host halo. The purpose of using the elongated geometry is to incorporate the line-of-sight structures. Subsequently, in our Ly\u03b1 radiative transfer calculation, the line-of-sight direction is set to be along the longest dimension of the cylinder. In each cell of a cylinder Ly\u03b1 photon emissivities are computed, separately from star formation and cooling radiation. The luminosity of Ly\u03b1 produced by star formation is computed as LLy\u03b1 = 1042[SFR/( M\u2299yr\u22121)] erg s\u22121 (Furlanetto et al. 2005), where SFR is the star formation rate in the cell. The Ly\u03b1 emission from cooling radiation is computed with the gas properties in the cell by following the rates of excitation and ionization. \u2013 7 \u2013 With Ly\u03b1 emissivity, neutral hydrogen density, temperature, and velocity in the simulations, a Monte Carlo code (Zheng & Miralda-Escud\u00b4 e 2002) is adopted to follow the Ly\u03b1 radiative transfer. The code has been recently used to study Ly\u03b1 emitting galaxies (Zheng et al. 2010, 2011a,b). In our radiative transfer calculation, the number of Ly\u03b1 photons drawn from a cell is proportional to the total Ly\u03b1 luminosity in the cell, with a minimum number of 1000, and each photon is given a weight in order to reproduce the luminosity of the cell. Ly\u03b1 photons associated with star formation and cooling radiation are tracked separately so that we can study their \ufb01nal spatial distributions. For each photon, the scattering with neutral hydrogen atoms and the subsequent changes in frequency, direction, and position are followed until it escapes from the simulation cylinder. More details about the code can be found in Zheng & Miralda-Escud\u00b4 e (2002) and Zheng et al. (2010). The pixel size of the Ly\u03b1 images from the radiative transfer calculation is chosen to be equal to 318pc, corresponding to 0.04\u2032\u2032. We smooth the Ly\u03b1 images with 2D Gaussian kernels to match the resolutions in Matsuda et al. (2011) for detecting and characterizing LABs from observation. In Matsuda et al. (2011), the area of an LAB is the isophotal area with a threshold surface brightness 1.4 \u00d7 10\u221218erg s\u22121cm\u22122arcsec\u22122 in the narrowband image smoothed to an e\ufb00ective seeing of FWHM 1.4\u2032\u2032 (slightly di\ufb00erent from Matsuda et al. 2004, where FWHM=1\u2032\u2032), while the Ly\u03b1 luminosity is computed with the isophotal aperture in the FWHM=1\u2032\u2032 image. We de\ufb01ne LABs in our model by applying a friends-of-friends algorithm to link the pixels above the threshold surface brightness in the computed Ly\u03b1 images, with the area and luminosity computed from smoothed images with FWHM=1.4\u2032\u2032 and FWHM=1\u2032\u2032, respectively. 3. Results The SBM model that we study here in great detail may appear at odds with available observations at \ufb01rst sight. In particular, the LABs often lack close correspondence with galaxies in the overlapping \ufb01elds and their centers are often displaced from the brightest galaxies in the \ufb01elds. As we show below, these puzzling features are in fact exactly what are expected in the SBM model. The reasons are primarily three-fold. First, LABs universally arise in large halos with a signi\ufb01cant number of galaxies clustered around them. Second, dust attenuation renders the amount of Ly\u03b1 emission emerging from a galaxy dependent substantially sub-linearly on star formation rate. Third, the observed Ly\u03b1 emission, in both amount and three-dimensional (3D) location, originating from each galaxy depends on complex scattering processes subsequently. \u2013 8 \u2013 x (kpc) y (kpc)     0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 \u221220 \u221219 \u221218 \u221217 \u221216 \u221215 x (kpc) y (kpc)     0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 \u221220 \u221219 \u221218 \u221217 \u221216 \u221215 x (kpc) y (kpc)     0 50 100 150 200 250 300 0 50 100 150 200 250 300 \u221220 \u221219 \u221218 \u221217 \u221216 \u221215 x (kpc) y (kpc)     0 50 100 150 200 250 300 0 50 100 150 200 250 300 \u221220 \u221219 \u221218 \u221217 \u221216 \u221215 Fig. 1.\u2014 Two examples: left (a) and right (b) columns. See the caption below with columns (c) and (d). 3.1. E\ufb00ects Caused by Galaxy Clustering We \ufb01nd that large-scale structure and clustering of galaxies play a fundamental role in shaping all aspects of LABs, including two-dimensional line-of-sight velocity structure, line pro\ufb01le and Ly\u03b1 image in the sky plane. To illustrate this, Figure 1 shows Ly\u03b1 surface brightness maps (after the radiative transfer calculation) for four randomly selected galaxies with virial mass of the central galaxy exceeding 1012 M\u2299at z = 3.1. We \ufb01nd that Ly\u03b1 emission stemming from stellar radiation dominate over the gas cooling by about 10:1 to 4:1 in all relevant cases. We also \ufb01nd that the Ly\u03b1 emission due to gas cooling is at least as centrally concentrated as from the stellar emission for each galaxy. From this \ufb01gure it has become clear that large-scale structure and projection e\ufb00ects are instrumental to rendering \u2013 9 \u2013 x (kpc) y (kpc)     0 50 100 150 200 250 300 0 50 100 150 200 250 300 x (kpc) y (kpc)     0 50 100 150 200 250 300 0 50 100 150 200 250 300 \u221220 \u221219 \u221218 \u221217 \u221216 \u221215 \u221220 \u221219 \u221218 \u221217 \u221216 \u221215 x (kpc) y (kpc)     0 50 100 150 200 250 300 0 50 100 150 200 250 300 \u221220 \u221219 \u221218 \u221217 \u221216 \u221215 x (kpc) y (kpc)     0 50 100 150 200 250 300 0 50 100 150 200 250 300 \u221220 \u221219 \u221218 \u221217 \u221216 \u221215 Fig. 1.\u2014 Two more examples: left (c) and right (d) columns. The four columns (a,b,c,d) show the logarithm of Ly\u03b1 surface brightness maps (in units of erg s\u22121cm\u22122arcsec\u22122) for four randomly selected large galaxies of virial masses both exceeding 1012 M\u2299at z = 3.1 with the primary galaxy centered on their respective panel. For each column the bottom panel is obtained, if one only includes galaxies within \u00b1Rvir of the primary galaxy along the line of sight, where Rvir is the virial radius of the primary galaxy. The top panel is obtained, including all galaxies within \u00b110h\u22121Mpc comoving of the primary galaxy along the line of sight. The length shown is in physical kpc. The e\ufb00ects of dust and faint sources have not been included yet in these plots (see the text for more details). the appearance of LABs in all aspects (image as well as spectrum). One could see that, for example in the top-left panel of Figure 1, the approximately linear structure aligned in the direction of lower-left to upper-right is composed of three additional galaxies that are well outside the virial radius of the primary galaxy but from projected structures. At \u2013 10 \u2013 the 1.4\u00d710\u221218erg s\u22121cm\u22122arcsec\u22122 detection isophotal contours of Matsuda et al. (2004) and Matsuda et al. (2011) for LABs, the entire linear structure may be identi\ufb01ed as a single LAB. This rather random example is strikingly reminiscent of the observed LAB structures (e.g., Matsuda et al. 2009; Erb et al. 2011; Yang et al. 2011a). Interestingly, depending on which galaxy is brighter and located on the front or back, the overall Ly\u03b1 emission of the LAB may show a variety of line pro\ufb01les. For example, it could easily account for a broad/brighter blue side in the line pro\ufb01le, as noted by Saito et al. (2006) for some of the observed LABs, which was originally taken as supportive evidence for the gravitational cooling radiation model. Furthermore, it is not di\ufb03cult to envision that the overall velocity width of an LAB does not necessarily re\ufb02ect the virial velocity of a virialized system and may display a wide range from small (masked by caustics e\ufb00ect) to large (caused by either large virial velocities, infall velocities, or Hubble expansion). A detailed spectral analysis will be presented elsewhere. For the results shown in Figure 1 we have not included dust e\ufb00ect, contributions from small galaxies (Mh < 109.5 M\u2299) that are not properly captured in our simulation due to \ufb01nite resolution, and instrumental noise. We now describe how we include these important e\ufb00ects. 3.2. Taking into Account Faint, Under-resolved Sources Although the resolution of our simulations is high, it is still \ufb01nite and small sources are incomplete. We \ufb01nd that the star formation rate (SFR) function in the simulation \ufb02attens out at 3 M\u2299yr\u22121 toward lower SFR at z = 2 \u22123 (Cen 2011b), which likely means that sources with SFR< 3 M\u2299yr\u22121 are unresolved/under-resolved and hence incomplete in the simulations. Since these low SFR sources that cluster around large galaxies contribute to the Ly\u03b1 emission of LABs, it is necessary to include them in our modeling. For this purpose, we need to sample their SFR distribution and spatial distribution inside halos. First, we need to model the luminosity or SFR distribution of the faint, unresolved sources. In each LAB-hosting halo in the simulations, the number of (satellite) sources with SFR>3 M\u2299yr\u22121 is found to be proportional to the halo mass Mh. Observationally, the faint end slope \u03b1 of the UV luminosity function of star forming galaxies is \u223c\u22121.8 (e.g., Reddy & Steidel 2009). Given this faint end slope, the contribution due to faint, unresolved sources is weakly convergent. As a result, the overall contribution from faint sources do not strongly depend on the faint limit of the correction procedure. We \ufb01nd that the conditional SFR function \u03c6(L; Mh) of faint sources (SFR< 3 M\u2299yr\u22121) in halos can be modeled as \u03c6(L; Mh) = dN(Mh) dL = \u2212(\u03b1 + 1) Lth \u0012 L Lth \u0013\u03b1 Mh M1 , (1) where L represents the SFR and Lth = 3 M\u2299yr\u22121, \u03b1 = \u22121.8, and M1 = 1012 M\u2299. This conditional SFR function allows us to draw SFR for faint sources to be added in our model. \u2013 11 \u2013 We now turn to the spatial distribution of faint sources. In the simulation the spatial distribution (projected to the sky plane) of satellite sources in halos is found to closely follow a power-law with a slope of \u22122. This is in good agreement with the observed small scale slope of the projected two-point correlation function of LBGs (Ouchi et al. 2005). There is some direct observational evidence that there are faint UV sources distributed within the LAB radii. Matsuda et al. (2012) perform stacking analysis of z \u223c3.1 Ly\u03b1 emitters and protocluster LBGs, showing di\ufb00use Ly\u03b1 pro\ufb01le in the stacked Ly\u03b1 image. Interestingly, the pro\ufb01les in the stacked UV images appear to be extended to scales of tens of kpc (physical) for the most luminous Ly\u03b1 sources or for sources in protoclusters, suggesting contributions from faint, starforming galaxies. We add the contribution from faint sources to post-processed unsmoothed Ly\u03b1 images from radiative transfer modeling as follows. For each model LAB, we draw the number and SFRs of faint sources in the range of 0.01\u20133 M\u2299yr\u22121 based on the conditional SFR distribution in equation (1). Then we distribute them in the unsmoothed Ly\u03b1 image in a radial range of 0.01\u20131Rvir by following the power-law distribution with slope \u22122. The faint sources can be either added as point or extended sources in Ly\u03b1 emission. If added as point sources, they would be smoothed with a 2D Gaussian kernel of FWHM=1.4\u2032\u2032 or 1\u2032\u2032 when de\ufb01ning LAB size and luminosity. In our \ufb01ducial model, each faint source is added as an exponential disk with scale length of 3\u2032\u2032 to approximate the radiative transfer e\ufb00ect, which is consistent with the observed di\ufb00use emission pro\ufb01le of star-forming galaxies (Steidel et al. 2011). We \ufb01nd that our \ufb01nal conclusion does not sensitively depend on our choice of the faint source Ly\u03b1 pro\ufb01le. In Figure 2, panel (a) shows the surface brightness and the 1.4\u00d710\u221218erg s\u22121cm\u22122arcsec\u22122 isphotal contour for a model LAB without including the faint sources, while panel (b) is the case with faint sources. We see that the size of the LAB de\ufb01ned by the isophotal aperture does not change much. If the Ly\u03b1 emission of each faint sources is more concentrated, e.g., close to a point source in the unsmoothed image, the LAB size can increase a little bit. Therefore, in both panels (a) and (b), the size is mainly determined by the central bright source. However, as will be described in the next subsection, including the e\ufb00ect of dust extinction will suppress the contribution of the central source and relatively boost that of the faint sources in determining the LAB size. 3.3. Dust E\ufb00ect In the cases shown in Figure 1, the central galaxies each have SFR that exceeds 100 M\u2299yr\u22121 and is expected to be observed as a luminous infrared galaxy (LIRG) or ULIRG (Sanders & Mirabel 1996). This suggests that dust e\ufb00ects are important and have to be taken into account. \u2013 12 \u2013 Fig. 2.\u2014 An LAB under di\ufb00erent model assumptions. The model LAB shown in this example resides in the most massive host halo in our simulation (\u223c5 \u00d7 1012 M\u2299) at z = 3.1. The Ly\u03b1 images are smoothed to correspond to seeing of FWHM=1.4\u2032\u2032. In each panel, the black contour is the isophotal level of 1.4 \u00d7 10\u221218erg s\u22121cm\u22122arcsec\u22122, the surface brightness threshold used in observation to de\ufb01ne LABs (Matsuda et al. 2004, 2011). Panels (a)\u2013(d) enumerate the combinations of adding faint sources and extinction. Panel (a) is the initial case without faint sources and without extinction. Panel (d) corresponds to the case with faint sources added and with extinction considered, which we regard as the favored model. See the text for more details. In general, there are two types of e\ufb00ects of dust on Ly\u03b1 emission from star-forming galaxies. The \ufb01rst one is related to the production of Ly\u03b1 phtons. Dust attenuates ionizing photons in star-forming galaxies. Since Ly\u03b1 photons come from reprocessed ionizing photons, the attenuation by dust leads to a lower Ly\u03b1 luminosity in the \ufb01rst place. Second, after being produced, Ly\u03b1 photons can be absorbed by dust during propagation. A detailed investigation needs to account for both e\ufb00ects self-consistently, and we reserve that for a future study. In Cen (2011b) the dust obscuration/absorption is considered in a self-consistent way, with respect to luminosity functions observed in UV and FIR bands. The modelling uses detailed ray tracing with dust obscuration model based on that of our own Galaxy (Draine 2011) and extinction curve taken from Cardelli et al. (1989). While the simultaneous match of both UV and FIR luminosity functions at z = 2 without introducing additional free parameters is an important validation of the physical realm of our simulations, it is not necessarily directly extendable to the radiative transfer of Ly\u03b1 photons. Nevertheless, it is reasonable to adopt a simple optical depth approach as follows for our present purpose, normalized by relevant observations, as follows. For each galaxy we suppress the initial intrinsic Ly\u03b1 emission, by applying a mapping LLy\u03b1 to LLy\u03b1 exp [\u2212\u03c4(SFR)], where the \u201ce\ufb00ective\u201d optical depth \u03c4(SFR) is intended to account for extinction of Ly\u03b1 photons as a function of SFR. We stress that this method is approximate and its validation is only re\ufb02ected by the goodness of our model \ufb01tting the \u2013 13 \u2013 observed properties of LABs. We adopt \u03c4(SFR) = 0.2[SFR/( M\u2299yr\u22121)]0.6. In reality, in addition, it may be that there is a substantial scatter in \u03c4(SFR) at a \ufb01xed SFR. We ignore such complexities in this treatment. The adopted trend that higher SFR galaxies have larger optical depths is fully consistent with observations (e.g., Nilsson & M\u00f8ller 2009). At intrinsic SFR = 100 M\u2299yr\u22121 the escaped LLy\u03b1 luminosity is equivalent to SFR = 5 M\u2299yr\u22121, whereas at intrinsic SFR = 10 M\u2299yr\u22121 the escaped LLy\u03b1 luminosity is equivalent to SFR = 4.5 M\u2299yr\u22121. It is evident that the scaling of the emerging LLy\u03b1 luminosity on intrinsic SFR is substantially weakened with dust attenuation. In fact, it may be common that, due to dust e\ufb00ect, the optical luminosity of a galaxy does not necessarily positively correlate with its intrinsic SFR, or the most luminous source in Ly\u03b1 does not necessarily correspond to the highest SFR galaxy within an LAB. As a result, a variety of image appearance and mis-matches between the LAB centers and the most luminous galaxies detected in other bands may result, seemingly consistent with the anecdotal observational evidence mentioned in the introduction. The e\ufb00ect of dust on the surface brightness distribution for a model LAB is shown in panel (c) of Figure 2. Compared to panel (a), which is the model without dust e\ufb00ect, we see that surface brightness of the central source is substantially reduced and the isophotal area for the threshold 1.4\u00d710\u221218erg s\u22121cm\u22122arcsec\u22122 also reduces. The case in panel (c) does not include the contribution from faint sources. In general, taking into account dust e\ufb00ect in our Ly\u03b1 radiative transfer calculation, the central galaxies tend to make reduced (absolutely and relative to other smaller nearby galaxies) contributions to the Ly\u03b1 surface brightness maps and in fact the center of each LAB may or may not coincide with the primary galaxy that would likely be a ULIRG in these cases, which is again reminiscent of some observed LABs. In the next subsection, we describe the modeling results of combining all the above e\ufb00ects. 3.4. Final LABs with All E\ufb00ects Included By accounting for the line-of-sight structures, the unresolved faint sources, and the dust e\ufb00ect, we \ufb01nd that the observed properties of LABs can be reasonably reproduced by our model. In panel (d) of Figure 2, we add the faint sources and apply the dust e\ufb00ect. Compared with the case in panel (c), where no faint sources are added, the isophotal area increases. The central source has a substantially reduced surface brightness because of extinction. There appears to be another source near the central source, which corresponds to a source of lower SFR seen in panel (a) but with lower extinction than the central source. From Figure 2, we see that the overall e\ufb00ect is that dust helps reduce the central surface brightness and faint sources help somewhat enlarge the isophotal area. \u2013 14 \u2013 Fig. 3.\u2014 Model predictions under di\ufb00erent assumptions along with observed properties of LABs. Top panels show luminosity and size relations and bottom panels cumulative luminosity functions. Panel (a) does not account for dust e\ufb00ect and contributions from faint galaxies under-resolved in our simulation. Panel (b) includes under-resolved sources. Observations are taken from Matsuda et al. (2004) (open squares) and Matsuda et al. (2011) supplemented with new unpublished data (open circles). Model predictions are shown as red points (top panels) and curves (bottom panels). To test the model and see the e\ufb00ect of di\ufb00erent assumptions on extinction and faint sources, we compare the model predictions with observational properties of LABs, shown in Figure 3. In the top panels, we compare the luminosity-size relation de\ufb01ned by the isophot with surface brightness 1.4 \u00d7 10\u221218erg s\u22121cm\u22122arcsec\u22122. The observed data points are taken from Matsuda et al. (2004) (open squares) and Matsuda et al. (2011) (open circles), which has been supplemented with new, yet unpublished data (Matsuda 2012, private communications). Note that the isophotal area is de\ufb01ned with FWHM=1\u2032\u2032 and 1.4\u2032\u2032 images in Matsuda \u2013 15 \u2013 Fig. 3.\u2014 Continued. Panel (c) only includes the dust extinction e\ufb00ect. Panel (d) includes both the dust extinction and the faint sources. The blue dots and blue curve in panel (d) is our realization of the global LF by using the LLy\u03b1 \u2212Mh relation from our model and the analytic halo mass function. et al. (2004) and Matsuda et al. (2011), respectively. This may partly explain that the LAB sizes are somewhat larger with the Matsuda et al. (2011) data points. However, the di\ufb00erence is not substantial. Our model data points follow Matsuda et al. (2011) in de\ufb01ning the luminosity and size. In the bottom panels of Figure 3, we show the cumulative Ly\u03b1 luminosity function or abundance of LABs. The data points from Matsuda et al. (2004) and Matsuda et al. (2011) (supplemented with new unpublished data; Matsuda 2012, private communications) have a large o\ufb00set (\u223c1 dex at the luminous end) from each other, suggesting large sample variance. The survey volumes of Matsuda et al. (2004) and Matsuda et al. (2011) are 1.3 \u00d7 105Mpc3 \u2013 16 \u2013 and 1.6 \u00d7 106Mpc3, respectively. For comparison, the volume of our parent simulation from which we choose our LAB sample is only 3.06 \u00d7 104Mpc3, much smaller than the volume probed by observation. The red points in top panel (a) of Figure 3 come from our model without extinction and faint sources. Compared to the observational data, the model predicts more or less the correct slope in the luminosity-size relation. However, the overall relation has an o\ufb00set, which means that the model either overpredicts the luminosity or underpredicts the size, or both. From the bottom panel (a), the model greatly over-predicts the LAB abundance, showing as a vertical shift. But it can also be interpreted as an overprediction of the LAB luminosity, leading to a horizontal shift, which is more likely. Because the central sources are bright, adding faint sources only slightly changes the sizes, as shown in panel (b), which leads to little improvement in solving the mismatches in the luminosity-size relation and in the abundance. Once the dust extinction e\ufb00ect is introduced, the situation greatly improves. Panel (c) of Figure 3 shows the case with extinction but without adding faint sources. With the extinction included, the luminosity of the predicted LABs drops, and at the same time, the size becomes smaller. Now the model points agree well with observations at the lower end of the range of LAB luminosity (1042.6 \u22121043.3erg/s) and size (15-30 arcsec2), the predicted luminosity-size relation conforms to and extends the observed one to still lower luminosity and smaller size. The predicted abundance is much closer to the observed one, as well. Finally, panel (d) shows the case with both extinction and faint sources included. Adding faint sources helps enlarge the size of an LAB, because faint sources extends the isophot to larger radii. The luminosity also increases by including the contribution from faint sources. As a whole, the model data points appear to slide over the luminosity-size relation towards higher luminosity and larger size. The model luminosity-size relation, although still at the low luminosity end, is fully overlapped with the observed relation. The abundance at the high-luminosity end from the model is within the range probed by observation and shows a similar slope as that in Matsuda et al. (2004). The agreement of the luminosity function between simulations and Matsuda et al. (2004) is largely fortuitous, re\ufb02ecting that the overall bias of our simulation box over the underlying matter happens to be similar to that of the Matsuda et al. (2004) volume over matter, provided that the model universe is a reasonable statistical representation of the real universe. Limited by the simulation volume, we are not able to directly simulate the full range of the observed luminosity and size of LABs. Our model, however, reproduces the luminositysize relation and abundance in the low luminosity end. The most important ingredient in our model to achieve such an agreement with the observation is the dust extinction, which drives the apparent Ly\u03b1 luminosity down into the right range. Accounting for the contribution of faint, unresolved sources in the simulation also plays a role in further enhancing the sizes \u2013 17 \u2013 and, to a less extent, the luminosities of LABs. To rectify the lack of high luminosity, large size LABs in our simulations due to the limited simulation volume, we perform the following exercise. Figure 4 shows the Ly\u03b1 luminosity and LAB size as a function of halo mass from our model LABs in Figure 3(d). Both quantities correlate with halo mass, but there is a large scatter, which is caused by varying SFRs as well as di\ufb00erent environmental e\ufb00ects for halos of a given mass. The largest LABs fall into the range probed by the observational data and they reside in halos above 1012M\u2299. The model suggests that the vast majority of the observed LABs should reside in proto-clusters with the primary halos of mass above 1012M\u2299at z \u223c3 and on average larger LABs correspond to more massive halos. Note that the sources with halo mass below 1012M\u2299is highly incomplete here. Our results suggest an approximate relation between the halo mass of the central galaxy and the apparent Ly\u03b1 luminosity of the LAB: LLy\u03b1 = 1042.4 \u0012 Mh 1012 M\u2299 \u00131.15 erg s\u22121, (2) which is shown as the solid curve in the left panel of Figure 4. This relation should provide a self-consistency test of our model, when accurate halo masses hosting LABs or spatial clustering of LABs can be measured, interpreted in the context of the \u039bCDM clustering model. We also \ufb01nd that the area-halo mass relation: area = 5.0 \u0012 Mh 1012 M\u2299 \u00131.15 arcsec2, (3) shown as the solid curve in the right panel of Figure 4. Equations (2) and (3) lead to the following luminosity-size relation area = 5.0 \u0012 LLy\u03b1 1042.4erg s\u22121 \u0013 arcsec2, (4) which matches the observed one, nothing new in this except as a self-consistency check. By extrapolating the above relations (2,3) to higher halo mass and using the analytic halo mass function (Jenkins et al. 2001), we can obtain the global Ly\u03b1 LF expected from our model. In detail, we draw halo masses based on the analytic halo mass function. For each halo, we compute LLy\u03b1 from Equation (2). A scatter in log LLy\u03b1 is added following a Gaussian distribution with 1\u03c3 deviation of 0.28dex (indicated by the dotted lines in the left panel of Figure 4). Then Equation (4) is used to assign the area, and a Gaussian scatter of 0.11dex is added to approximately reproduce the scatter seen in the observed luminositysize relation. The implied scatter in the area-halo mass relation is the sum of the above two scatters in quadrature, i.e., about 0.30 dex, which is indicated by the dotted lines in the right panel of Figure 4. Finally, we adopt the same area cut (>15 arcsec2) used in observations (Matsuda et al. 2011) to de\ufb01ne LABs. \u2013 18 \u2013 Fig. 4.\u2014 Dependence of LAB luminosity and size on halo mass from the model. In each panel, the points are from our model LABs in the simulation. The solid and dotted lines show the relation and scatter we use to populate halos drawn from the analytic halo mass function to compute the expected global Ly\u03b1 LF of LABs. See the text for more details. Our computed global Ly\u03b1 LF of LABs is shown as the blue curve in the bottom panel (d). The agreement between our predicted global LF and that from the larger-survey-volume observations of Matsuda et al. (2011) is striking. Given still substantial uncertainties involved in our model assumptions, the precise agreement is not to be overstated. However, the fact that the relative displacement between LF from our simulated volume and global LF is in agreement with that between Matsuda et al. (2004) and Matsuda et al. (2011) is quite encouraging, recalling that we have no freedom to adjust any cosmological parameters. This is also indicative of the survey volume of Matsuda et al. (2011) having becoming a fair sample of the universe for LABs in question. The blue dots in top panel (d) show that the predicted luminosity-area relation is simultaneously in agreement with observations, now over the entire luminosity and size range, suggesting that our derived relations in Equations (2), (3), and (4) are statistically applicable to LABs of luminosities higher than those probed by the current simulations. 4. Conclusions and Discussions We present a new model, termed star-burst model (SBM), for the spatially extended (tens to hundreds of kiloparsecs) luminous (LLy\u03b1 \u22731043erg/s) Ly\u03b1 blobs. The SBM model is the \ufb01rst model to successfully reproduce both the global Ly\u03b1 luminosity function and \u2013 19 \u2013 the luminosity-size relation of the observed LABs (Matsuda et al. 2004, 2011). In the SBM model Ly\u03b1 emission from both stars and gravitational sources (such as gravitational binding energy released from structure collapse) is included, although it is found that the nebular Ly\u03b1 emission sourced by those other than stars, while signi\ufb01cant, is sub-dominant compared to stellar emission. It is also found that Ly\u03b1 emission originating from sources rather than stars is at least as centrally concentrated as that from stars within each galaxy. Our modeling is based on a high-resolution large-scale cosmological hydrodynamic simulation of structure formation, containing more than 3000 galaxies with halo mass Mh > 1010 M\u2299and more than 25 galaxies with Mh > 1012 M\u2299at z = 3.1, all resolved at a resolution of 159pc or better. Detailed 3D Ly\u03b1 radiative transfer calculation is applied to sub-volumes centered on each of the 40 most massive star-bursting galaxies in the simulation box with SFR = 10\u2212400 M\u2299yr\u22121. A self-consistent working model emerges, if proper dust attenuation trend is modeled in that Ly\u03b1 emission from higher SFR galaxies are more heavily attenuated by dust than lower SFR galaxies, which is empirically motivated by observations. For the results shown, we adopt an e\ufb00ective Ly\u03b1 optical depth \u03c4(SFR) = 0.2[SFR/( M\u2299yr\u22121)]0.6, which translates to escape fractions of (5%, 45%) for Ly\u03b1 photons at SFR = (100, 10) M\u2299yr\u22121, respectively. The dust attenuation model has two parameters, a normalization and a powerlaw index. The powerlaw index actually follows the slope of the metal column density dependence on SFR in the simulation. This thus leaves us with the normalization as the only free parameter. In practice, changing the powerlaw index does not sensitively change the results, as long as the normalization is adjusted such that the attenuation at high SFR end (\u223c100 M\u2299yr\u22121) is approximately the same as the adopted value, making the model rather robust. Also very encouraging is that the model is in broad agreeement with other observed properties of LABs, in addition to the simultaneous reproduction of the observed global Ly\u03b1 luminosity function and the luminosity-size relation aforenoted. Among them, we predict that LABs at high redshift correspond to proto-clusters containing the most massive galaxies/halos in the universe and ubiquitous strong infrared emitters, with the most luminous member galaxies mostly copious in FIR emission, fully consistent with extant observations (e.g., Geach et al. 2007; Bridge et al. 2012). It seems inevitable that some of the galaxies would contain active galactic nuclei (AGN) at the epoch of peak AGN formation in the universe (e.g., Geach et al. 2009). While it is straight-forward to include, the results shown do not include AGN, partly because, to the zero-th order, we may simply \u201cabsorb\u201d that by adjusting the dust attenuation e\ufb00ect and partly because observations indicate AGN contribution is subdominant (e.g., Webb et al. 2009; Colbert et al. 2011). The most massive halos in the standard cold dark matter universe also tend be the most strongly clustered in the universe, among all types of galaxies, and we predict that there should be numerous galaxies clustered around LABs (e.g., Uchimoto et al. 2008). \u2013 20 \u2013 Prescott et al. (2012) use high-resolution Hubble Space Telescope imaging to resolve galaxies within a giant LAB at z \u223c2.656. They \ufb01nd many compact, low-luminosity galaxies. Their observation becomes incomplete below \u223c0.1L\u2217, and with extrapolation there would be about 80 sources above 0.01L\u2217within a radius of 7\u2032\u2032. Their LAB has LLy\u03b1 = 1044erg s\u22121 and an isophotal area \u223c140 arcsec2, falling well onto the observed luminosity-size relation shown in Figure 3. Extrapolating from our model, the LAB is predicted to reside in a halo with mass of \u223c1013M\u2299(Fig. 4). The number of faint sources within 7\u2032\u2032 above 0.01L\u2217from our model would be about 100, in agreement with the observation. With the availability of ALMA, observers could make use of its superb capabilities to con\ufb01rm the generic prediction of this model that there should be FIR sources in each LAB with the most luminous FIR source likely representing the center of the proto-cluster. In combination with optical and other observations, this will potentially provide extremely useful information on the formation of galaxies in the most overdense regions of the universe when star formation is most vigorous and clusters have yet to be assembled. We highlight here that a potentially very discriminating signature of this model lies in the expected, signi\ufb01cant polarization strength of the Ly\u03b1 emission at large scales (\u223c10100kpc), which is not expected in some competing models for LABs, such as those sourcing primarily gravitational binding energy on large scales due to massive halo formation. We plan to quantify this signal with detailed polarization radiative transfer calculations of Ly\u03b1 photons. It is mentioned in passing that our model suggests the trends seen in LABs, in terms of the global Ly\u03b1 luminosity function and the luminosity-size relation of the observed LABs, are continuously extended to less luminous Ly\u03b1 emitters (LAEs). Consequently, we predict that LAEs, less luminous than LABs, have smaller sizes compared to those of LABs at a \ufb01xed isophotal level and should also be less strongly clustered than LABs, forming an extension of the observed LAB luminosity-size relation as well as the LAB luminosity and correlation functions. Finally, it is reassuring to note that the cosmological simulations themselves have already been subject to and passed a range of tests concerning a variety of observables of galaxies and the intergalactic medium, including properties of DLAs at z = 0 \u22124 (Cen 2012b), O VI absorbers in the circumgalactic and intergalactic medium in the local universe (Cen 2012a), global evolution of star formation rate density and cosmic downsizing of galaxies (Cen 2011a), galaxy luminosity functions from z = 0 to z = 3 (Cen 2011a,b), and properties of galaxy pairs as a function of environment in the low-z universe (Tonnesen & Cen 2012), among others. We would like to thank Dr. Yuichi Matsuda for kindly providing and allowing us to use new observational data before publication. Computing resources were in part provided by the \u2013 21 \u2013 NASA High-End Computing (HEC) Program through the NASA Advanced Supercomputing (NAS) Division at Ames Research Center. R.C. is supported in part by grant NNX11AI23G. Z.Z. is supported in part by NSF grant AST-1208891. The simulation data are available from the authors upon request.",
                    "introduction": "The physical origin of spatially extended (tens to hundreds of kiloparsecs) luminous (LLy\u03b1 \u22651043erg/s) Ly\u03b1 sources, also known as Ly\u03b1 blobs (LABs) \ufb01rst discovered more than 1Princeton University Observatory, Princeton, NJ 08544; cen@astro.princeton.edu 2University of Utah, Department of Physics and Astronomy, Salt Lake City, UT 84112; zhengzheng@astro.utah.edu arXiv:1210.3600v1  [astro-ph.CO]  12 Oct 2012 \u2013 2 \u2013 a decade ago (e.g., Francis et al. 1996; Fynbo et al. 1999; Keel et al. 1999; Steidel et al. 2000), remains a mystery. By now several tens of LABs have been found (e.g., Matsuda et al. 2004; Dey et al. 2005; Saito et al. 2006; Smith et al. 2009; Matsuda et al. 2011). One fact that has confused the matter considerably is that they appear to be associated with a very diverse galaxy population, including regular Lyman break galaxies (LBGs) (e.g., Matsuda et al. 2004), ultra-luminous infrared galaxies (ULIRGs) and sub-millimeter galaxies (SMGs) (e.g., Chapman et al. 2001; Geach et al. 2005, 2007; Matsuda et al. 2007; Yang et al. 2011b), unobscured (e.g., Bunker et al. 2003; Weidinger et al. 2004) and obscured quasars (e.g., Basu-Zych & Scharf 2004; Geach et al. 2007; Smith et al. 2009), or either starbursts or obscured quasars (e.g., Geach et al. 2009; Scarlata et al. 2009; Colbert et al. 2011). An overarching feature, however, is that the vast majority of them are associated with massive halos or rich large-scale structures that reside in dense parts of the Universe and will likely evolve to become rich clusters of galaxies by z = 0 (e.g., Steidel et al. 2000; Chapman et al. 2004; Matsuda et al. 2004; Palunas et al. 2004; Matsuda et al. 2006; Prescott et al. 2008; Matsuda et al. 2009; Yang et al. 2009; Webb et al. 2009; Weijmans et al. 2010; Matsuda et al. 2011; Erb et al. 2011; Yang et al. 2011a; Zafar et al. 2011). Another unifying feature is that LABs are strong infrared emitters. For instance, most of the 35 LABs with size > 30 kpc identi\ufb01ed by Matsuda et al. (2004) in the SSA 22 region have been detected in deep Spitzer observations (Webb et al. 2009). Many physical models of LABs have been proposed. A leading contender is the gravi- tational cooling radiation model in which gas that collapses inside a host dark matter halo releases a signi\ufb01cant fraction of its gravitational binding energy in Ly\u03b1 line emission (e.g., Haiman et al. 2000; Fardal et al. 2001; Birnboim & Dekel 2003; Dijkstra et al. 2006; Yang et al. 2006; Dijkstra & Loeb 2009; Goerdt et al. 2010; Faucher-Gigu` ere et al. 2010; Rosdahl & Blaizot 2012). The strongest observational support for this model comes from two LABs that appear not to be associated with any strong AGN/galaxy sources (Nilsson et al. 2006; Smith et al. 2008), although lack of sub-mm data in the case of Nilsson et al. (2006) and a loose constraint of \u2264550 M\u2299yr\u22121 (3\u03c3) in the case of Smith et al. (2008) both leave room to accommodate AGN/galaxies powered models. Another tentative support is claimed to come from the apparent positive correlation between velocity width (represented by the full width at half maximum, or FWHM, of the line) and Ly\u03b1 luminosity (Saito et al. 2008), although the observed correlation FWHM \u221dLLy\u03b1 appears to be much steeper than expected (approx- imately) FWHM \u221dLLy\u03b1 1/3 for virialized systems. Other models include photoionization of cold dense, spatially extended gas by obscured quasars (e.g., Haiman & Loeb 2001; Geach et al. 2009), by population III stars (e.g., Jimenez & Haiman 2006), or by spatially extended inverse Compton X-ray emission (e.g., Scharf et al. 2003), emission from dense, cold super- wind shells (e.g., Taniguchi & Shioya 2000; Ohyama et al. 2003; Mori et al. 2004; Wilman et al. 2005; Matsuda et al. 2007), or a combination of photoionization and gravitational cooling radiation (e.g., Furlanetto et al. 2005). \u2013 3 \u2013 The aim of this writing is, as a \ufb01rst step, to explore a simple star formation based model in su\ufb03cient details to access its physical plausibility and self-consistency, through detailed Ly\u03b1 radiative transfer calculations utilizing a large set of massive (\u22651012 M\u2299) starbursting galaxies from an ultra-high resolution (\u223c110h\u22121pc), cosmological, adaptive mesh re\ufb01nement (AMR) hydrodynamic simulation at z = 3.1. The most critical, basically the only major, free parameter in our model is the magnitude of dust attenuation. Adopting the observationally motivated trend that higher SFR galaxies have higher dust attenuation, with an overall normalization that seems plausible (e.g., we assume that \u223c5% of Ly\u03b1 photons escape a galaxy of SFR = 100 M\u2299yr\u22121), the model can successfully reproduce the global Ly\u03b1 luminosity function and the luminosity-size relation of LABs. To our knowledge this is the \ufb01rst model that is able to achieve this. The precise dependence of dust attenuation on SFR is not critical, within a reasonable range, and hence the results are robust. In this model we show that LABs at high redshift correspond to proto-clusters contain- ing the most massive galaxies/halos in the universe. Within each proto-cluster, all member galaxies contribute collectively to the overall Ly\u03b1 emission, giving rise to the diverse ge- ometries of the apparent contiguous large-area LAB emission, which is further enhanced by projection e\ufb00ects due to other galaxies that are not necessarily in strong gravitational interactions with the main galaxy (or galaxies), given the strong clustering environment of massive halos in a hierarchical universe. This prediction that LABs should correspond to the most overdense regions in the universe at high redshift is fully consistent with the observed universal association of LABs with high density peaks (see references above). The relative contribution to the overall Ly\u03b1 emission from each individual galaxy depends on a number of variables, including dust attenuation of Ly\u03b1 photons within the galaxy and propagation and di\ufb00usion processes through its complex circumgalactic medium and the intergalactic medium. Another major predictions of this model is that a large fraction of the stellar (and AGN) optical and ultraviolet (UV) radiation (including Ly\u03b1 photons) is reprocessed by dust and emerges as infrared (IR) radiation, consistent with observations of ubiquitous strong infrared emission from LABs. We should call this model simply \u201cstarburst model\u201d (SBM), encompassing those with or without contribution from central AGNs. This model automatically includes emission contribution from gravitational cooling radiation, which is found to be signi\ufb01cant but sub-dominant compared to stellar radiation. Interestingly, we also \ufb01nd that Ly\u03b1 emission originating from nebular emission (rather than the stellar emission), which includes contribution from gravitational binding energy due to halo collapse, is more centrally concentrated than that from stars. One potentially very important prediction is that in this model the Ly\u03b1 emission from photons that escape to us is expected to contain signi\ufb01cant polarization signals. Although polarization radiative transfer calculations will be performed to detail the polarization signal in a future study, we brie\ufb02y elaborate the essential physics and latest observational advances here. One may broadly \ufb01le all the proposed models into two classes in terms of the spatial \u2013 4 \u2013 distribution of the underlying energy source: central powering or in situ. Starburst galaxy and AGN powered models belong to the former, whereas gravitational cooling radiation model belongs to the latter. A smoking gun test between these two classes of models is the polarization signal of the Ly\u03b1 emission. In the case of a central powering source (not necessarily a point source) the Ly\u03b1 photons di\ufb00use out, spatially and in frequency, through optically thick medium and escape by a very large number of local resonant scatterings in the Ly\u03b1 line pro\ufb01le core and a relatively smaller number of scatterings in the damping wings with long \ufb02ights. Upon each scattering a Ly\u03b1 photon changes its direction, location and frequency, dependent upon the geometry, density and kinematics of the scattering neutral hydrogen atoms. In idealized models with central powering signi\ufb01cant linear polarizations of tens of percent on scales of tens to hundreds of kiloparsecs are predicted and the polar- ization signal strength increases with radius (e.g., Lee & Ahn 1998; Rybicki & Loeb 1999; Dijkstra & Loeb 2008). On the other hand, in situ radiation from the gravitational cooling model is not expected to have signi\ufb01cant polarizations (although detailed modeling will be needed to quantify this) or any systematic radial trend, because thermalized cooling gas from (likely) \ufb01laments will emit Ly\u03b1 photons that are either not scattered signi\ufb01cantly or have no preferential orientation or impact angle with respect to the scattering medium. An earlier attempt to measure polarization of LABd05 at z = 2.656 produced a null detection (Prescott et al. 2011). A more recent observation by Hayes et al. (2011), for the \ufb01rst time, detected a strong polarization signal tangentially oriented (almost forming a complete ring) from LAB1 at z = 3.05, whose strength increases with radius from the LAB center, a signature that is expected from central powering; they found the polarized fraction (P) of 20 percent at a radius of 45 kpc. Hayes et al. (2011) convincingly demonstrate their detection and, at the same time, explain the consistency of their result with the non- detection by Prescott et al. (2011), if the emission from LABd05 is in fact polarized, thanks to a signi\ufb01cant improvement in sensitivity and spatial resolution in Hayes et al. (2011). This latest discovery lends great support to models with central powering, including SBM, independent of other observational constraints that may or may not di\ufb00erentiate between the two classes of models or between models in each class. But we stress that detailed polarization calculations will be needed to enable statistical comparisons. The outline of this paper is as follows. In \u00a72.1 we detail simulation parameters and hydrodynamics code, followed by a description of our Ly\u03b1 radiative transfer method in \u00a72.2. Results are presented in \u00a73 with conclusions given in \u00a74. \u2013 5 \u2013"
                },
                {
                    "url": "http://arxiv.org/abs/1112.4527v2",
                    "title": "Coincidences between OVI and OVII Lines: Insights from High Resolution Simulations of the Warm-Hot Intergalactic Medium",
                    "abstract": "With high resolution (0.46kpc/h), adaptive mesh-refinement Eulerian\ncosmological hydrodynamic simulations we compute properties of O VI and O VII\nabsorbers from the warm-hot intergalactic medium (WHIM). Our new simulations\nare in broad agreement with previous simulations, with ~40% of the\nintergalactic medium being in the WHIM at z=0. It is found (1) The amount of\ngas in the WHIM at temperature below and above 10^6K is about equal within\nuncertainties. (1) Our simulations are in excellent agreement with observed\nproperties of O VI absorbers, with respect to the line incidence rate and\nDoppler width-column density relation. (2) Velocity structures within absorbing\nregions are a significant, and for large Doppler width clouds, a dominant\ncontributor to the Doppler widths of both O VI and O VII absorbers. A\nnon-negligible fraction (in number and mass) of O VI and O VII clouds can arise\nfrom gas of temperature lower than 10^5, until the Doppler width is well in\nexcess of 100km/s. (3) Strong O VI absorbers are predominantly collisionally\nionized. About (61%, 57%, 39%) of O VI absorbers in the column density ranges\nof log N(OVI) cm^2=(12.5-13,13-14,>14) have temperature lower than 10^5K. (4)\nQuantitative prediction is made for the presence of broad and shallow O VI\nlines, which current observations may have largely missed. Upcoming\nobservations by COS may be able to provide a test. (5) The reported 3 sigma\nupper limit on the mean column density of coincidental O VII lines at the\nlocation of detected O VI lines by Yao et al is above the predicted value by a\nfactor of 2.5-4. (6) The claimed observational detection of O VII lines by\nNicastro et al, if true, is 2 sigma above what our simulations predict.",
                    "authors": "Renyue Cen",
                    "published": "2011-12-19",
                    "updated": "2012-05-14",
                    "primary_cat": "astro-ph.CO",
                    "cats": [
                        "astro-ph.CO"
                    ],
                    "main_content": "2.1. Hydrocode and Simulation Parameters We perform cosmological simulations with the AMR Eulerian hydro code, Enzo (Bryan 1999; Bryan & Norman 1999; O\u2019Shea et al. 2005; Joung et al. 2009). First we ran a low resolution simulation with a periodic box of 120 h\u22121Mpc on a side. We identified two regions separately, one centered on a cluster of mass of \u223c2 \u00d7 1014 M\u2299and the other centered on a void region at z = 0. We then resimulate each of the two regions separately with high resolution, but embedded in the outer 120h\u22121Mpc box to properly take into account largescale tidal field and appropriate boundary conditions at the surface of the refined region. We name the simulation centered on the cluster \u201cC\u201d run and the one centered on the void \u201cV\u201d run. The refined region for \u201cC\u201d run has a size of 21\u00d724\u00d720h\u22123Mpc3 and that for \u201cV\u201d run is 31\u00d731\u00d735h\u22123Mpc3. At their respective volumes, they represent 1.8\u03c3 and \u22121.0\u03c3 fluctuations. The root grid has a size of 1283 with 1283 dark matter particles. The initial static grids in the two refined boxes correspond to a 10243 grid on the outer box. The initial number of dark matter particles in the two refined boxes correspond to 10243 particles on the outer box. This translates to initial condition in the refined region having a mean interparticle-separation of 117h\u22121kpc comoving and dark matter particle mass of 1.07 \u00d7 108h\u22121 M\u2299. The refined region is surrounded by two layers (each of \u223c1h\u22121Mpc) of buffer zones with particle masses successively larger by a factor of 8 for each layer, which then connects with the outer root grid that has a dark matter particle mass 83 times that in the refined region. The initial density fluctuations are included up to the Nyquist frequency in the refined region. The surrounding volume outside the refined region is aso followed hydrodynamically, which is important in order to properly capture matter and energy exchanges at the boundaries of the refined region. Because we still can not run a very large volume simulation with adequate resolution and physics, we choose these two runs of moderate volumes to represent two opposite environments that possibly bracket the average. We choose the mesh refinement criterion such that the resolution is always better than 460h\u22121pc physical, corresponding to a maximum mesh refinement level of 11 at z = 0. The simulations include a metagalactic UV background (Haardt & Madau 2012), and a model for shielding of UV radiation by neutral hydrogen (Cen et al. 2005). The simulations also include metallicity-dependent radiative cooling and heating (Cen et al. 1995). We clarify that our group has included metal cooling and metal heating (due to photoionization of metals) in all our studies since Cen et al. (1995), contrary to some claims (e.g., Wiersma et al. 2009; Tepper-Garc\u00b4 \u0131a et al. 2011). Star particles are created in cells that satisfy a set of criteria for star formation proposed by Cen & Ostriker (1992). Each star particle is tagged with its initial mass, creation time, and metallicity; star particles typically have masses of \u223c106 M\u2299. \u2013 6 \u2013 Supernova feedback from star formation is modeled following Cen et al. (2005). Feedback energy and ejected metal-enriched mass are distributed into 27 local gas cells centered at the star particle in question, weighted by the speci\ufb01c volume of each cell (i.e., weighting is equal to the inverse of density), which is to mimic the physical process of supernova blastwave propagation that tends to channel energy, momentum and mass into the least dense regions (with the least resistance and cooling). We allow the whole feedback processes to be hydrodynamically coupled to surroundings and subject to relevant physical processes, such as cooling and heating, as in nature. The extremely inhomogeneous metal enrichment process demands that both metals and energy (and momentum) are correctly modeled so that they are transported into right directions in a physically sound (albeit still approximate at the current resolution) way, at least in a statistical sense. The primary advantages of this supernova energy based feedback mechanism are threefold. First, nature does drive winds in this way and energy input is realistic. Second, it has only one free parameter eSN, namely, the fraction of the rest mass energy of stars formed that is deposited as thermal energy on the cell scale at the location of supernovae. Third, the processes are treated physically, obeying their respective conservation laws (where they apply), allowing transport of metals, mass, energy and momentum to be treated selfconsistently and taking into account relevant heating/cooling processes at all times. We use eSN = 1\u00d710\u22125 in these simulations. The total amount of explosion kinetic energy from Type II supernovae with a Chabrier IMF translates to eSN = 6.6 \u00d7 10\u22126. Observations of local starburst galaxies indicate that nearly all of the star formation produced kinetic energy (due to Type II supernovae) is used to power galactic superwinds (e.g., Heckman 2001). Given the uncertainties on the evolution of IMF with redshift (i.e., possibly more top heavy at higher redshift) and the fact that newly discovered prompt Type I supernovae contribute a comparable amount of energy compared to Type II supernovae, it seems that our adopted value for eSN is consistent with observations and within physical plausibility. Test of the success of this feedback approach comes empirically. As we show in Cen (2012), the metal distribution in and around galaxies over a wide range of redshift is in good agreement with respect to the properties of observed damped Ly\u03b1 systems; this is a non-trivial success and provides strong validation of the simulations. We will provide additional validation of the simulations in \u00a73.1. To better understand di\ufb00erences in results between AMR and SPH simulations that we will discuss later, we note here that the evolution of metals in the two types of simulations is treated rather di\ufb00erently. In AMR simulations metals are followed hydrodynamically by solving the metal density continuity equation with sources (from star formation feedback) and sinks (due to subsequent star formation), whereas in SPH simulations of WHIM one does not separately solve the metal density continuity equation. Thus, metal mixing and di\ufb00usion through advection, turbulence and other hydrodynamic processes are properly captured in AMR simulations. While some SPH simulations have implemented metal di\ufb00usion schemes \u2013 7 \u2013 Fig. 1.\u2014 Top-left and bottom-left panels show the gas density and density-weighted temperature projection of a portion of the re\ufb01nement box of the C run of size (18h\u22121Mpc)3. Top-right and bottom-right panels show the gas density and density-weighted temperature projection of a portion of the re\ufb01nement box of the V run of size (30h\u22121Mpc)3. that are motivated by some subgrid turbulence model as a remedy parameterized to roughly match results from hydrodynamic simulations (e.g., Shen et al. 2010), most SPH simulations of WHIM obtain gas metallicities based on kernel-smoothed metal masses of feedback SPH particles that are assigned at birth and un-evolved (e.g., Tepper-Garc\u00b4 \u0131a et al. 2011; Oppenheimer & Dav\u00b4 e 2009; Oppenheimer et al. 2012). In the simulations of Oppenheimer et al. (2012) \u201cfeedback\u201d SPH particles with initially given metal masses are launched (in random directions) to be transported ballistically to su\ufb03ciently large distance (\u223c10kpc), after allowance for some period of hydrodynamic de-coupling between the feedback SPH particles and other neighboring SPH particles. Once some of the feedback parameters are \ufb01xed, this approach produces de\ufb01nitive predictions with respect to various aspects of stellar and IGM \u2013 8 \u2013 metallicity and others (e.g., Springel & Hernquist 2003; Oppenheimer & Dav\u00b4 e 2009; Tornatore et al. 2010; Dav\u00b4 e et al. 2011b,a; Oppenheimer et al. 2012). It is likely that mixing of metals on small to intermediate scales (\u223c1\u2212100kpc) in SPH simulations (e.g., Oppenheimer et al. 2012; Tepper-Garc\u00b4 \u0131a et al. 2011) is probably substantially underestimated. This signi\ufb01cant di\ufb00erence in the treatment of metal evolution may have contributed, in a large part, to some discrepancies between SPH and AMR hydrodynamic simulations, as we will discuss later. We use the following cosmological parameters that are consistent with the WMAP7normalized (Komatsu et al. 2010) LCDM model: \u2126M = 0.28, \u2126b = 0.046, \u2126\u039b = 0.72, \u03c38 = 0.82, H0 = 100hkms\u22121Mpc\u22121 = 70kms\u22121Mpc\u22121 and n = 0.96. Figure 1 shows the density and temperature \ufb01elds of the two simulations. The environmental contrast between the two simulations is evident. We also note that there is substantial overlap visually between the two simulations in that both cover the \u201c\ufb01eld\u201d environment, which we have shown quantitatively in Tonnesen & Cen (2011). In other words, these two simulations cover two extreme environments voids and clusters with substantial overlap of intermediate environment that facilitates possible averaging of some computed quantities, with proper normalizations by independent observational constraints. 2.2. Generation of Synthetic O VI and O VII Absorption Lines The photoionization code CLOUDY (Ferland et al. 1998) is used post-simulation to compute the abundance of O VI and O VII, adopting the shape of the UV background calculated by Haardt & Madau (2012) normalized by the intensity at 1 Ryd determined by Shull et al. (1999) and assuming ionization equilibrium. We generate synthetic absorption spectra using a code similar to that used in our earlier papers (e.g., Cen et al. 1994, 2001; Cen & Fang 2006), given the density, temperature, metallicity and velocity \ufb01elds from simulations. Each absorption line is identi\ufb01ed by the interval between one downward and the next upward crossing in the synthetic \ufb02ux spectrum without noise at a \ufb02ux equal to 0.99 (\ufb02ux equal to unity corresponds to an unabsorbed continuum). Since the absorption lines in question are sparsely distributed in velocity space, their identi\ufb01cations have no signi\ufb01cant ambiguity. Column density, equivalent width, Doppler width, mean column density weighted velocity and physical space locations, mean column density weighted temperature, density and metallicity are computed for each line. We sample the C and V run, respectively, with 72, 000 and 168, 000 random lines of sight at z = 0, with a total pathlength of \u2206z \u223c2000. While a detailed Voigt pro\ufb01le \ufb01tting of the \ufb02ux spectrum would have enabled closer comparisons with observations, simulations suggest that such an exercise does not necessarily provide a more clarifying physical understanding of \u2013 9 \u2013 200 400 600 0 0.2 0.4 0.6 0.8 1 v (km/s) flux 200 400 600 \u22121 0 1 2 v (km/s) log overdensity  200 400 600 \u2212400 \u2212300 \u2212200 \u2212100 0 100 v (km/s) vp (km/s) 200 400 600 3 4 5 6 7 v (km/s) log T (K) 0 200 400 600 800 \u22123 \u22122 \u22121 0 v (km/s) [Z/H] 200 400 600 0 0.2 0.4 0.6 0.8 1 v (km/s) flux 200 400 600 \u22121 0 1 v (km/s) log overdensity  200 400 600 \u2212300 \u2212200 \u2212100 0 100 200 300 v (km/s) vp (km/s) 200 400 600 3 4 5 6 7 v (km/s) log T (K) 0 200 400 600 800 \u22123 \u22122 \u22121 0 v (km/s) [Z/H] Fig. 2.\u2014 shows \ufb02ux spectra of two separate O VI lines and physical conditions. The left and right cases have column densities of log N(OVI)cm2 = 14.48 and 14.30, respectively. The \ufb01ve panels from top to bottom are: \ufb02ux, gas overdensity, proper peculiar velocity, temperature and metallicity in solar units. While the x-axis for the top panel is the Hubble velocity, the x-axis for the bottom four panels is physical distance that is multiplied by the Hubble constant. the absorber properties, because bulk velocities are very important (see Figure 6 below) and velocity substructures within an absorber do not necessarily correspond to separate physical entities. A small number of simulated spectra may not serve to illustrate the extreme rich and complex physics involved. It may even be misleading in the sense that any statistical conclusions drawn based on anecdotal evidence could be substantially wrong. Thus, we will present two absorption spectrum segments merely only for the purpose of illustration. Figure 2 shows two O VI lines and their associated physical environment. 2.3. Averaging C and V Runs The C and V runs at z = 0 are used to obtain an \u201caverage\u201d of the universe. This cannot be done precisely without much larger simulation volumes, which is presently not feasible. Nevertheless, it is still possible to obtain an approximate average. Since the WHIM is mostly closely associated with groups and clusters of galaxies, we will use X-ray clusters \u2013 10 \u2013 3 4 5 6 7 8 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 log T (K) CDF(>T)     All IGM at z=0 Only WHIM with log T=5\u22127 at z=0 Fig. 3.\u2014 shows the cumulative probability distribution function (CDF) of the IGM at z = 0 as a function of gas temperature (black dashed curve) and that of the WHIM only in the temperature range T = 105 \u2212107K (red solid curve); stars are not included. as an appropriate \u201cnormalization\u201d anchor point. We normalize averaging weightings of the C and V runs by requiring that the fraction of hot gas with temperature T \u2265107K is consistent with the observed value of \u223c15% of baryons at z = 0 (Bahcall 2011). Note that small variations on the adopted X-ray gas fraction do not cause large changes in most of the results. For comparative measures such as the coincidence rates between O VI and O VII absorbers, the dependence on the normalization procedure is still weaker. The results are shown in Figure 3, which shows the temperature distribution of entire IGM and WHIM at z = 0. In agreement with previous simulations (e.g., Cen & Ostriker 1999; Dav\u00b4 e et al. 2001; Cen & Ostriker 2006), we \ufb01nd that \u223c40% of the IGM at z = 0 is in WHIM. This is compared to 35-40% in Smith et al. (2011), 24% in Dav\u00b4 e et al. (2010) (limited to overdensities outside halos), 40% in Shen et al. (2010) and 40% and 50% in Tornatore et al. (2010) in their wind and black hole feedback models, respectievely. In simulations of Cen et al. (1995); Cen & Ostriker (1999); Cen et al. (2001); Cen & Ostriker (2006); Cen & Chisari (2011), Wiersma et al. (2009); Tepper-Garc\u00b4 \u0131a et al. (2011), Shen et al. (2010) and Shull et al. (2011), in additional to radiative processes of a primordial gas, both metal cooling (due to collisional excitation and recombination) and metal heating (due to photo-ionization heating of metal species) in the presence of UV-X-ray background are included, whereas in Oppenheimer & Dav\u00b4 e (2009), Oppenheimer et al. (2012) and Tornatore et al. (2010) only metal cooling is included. Tepper-Garc\u00b4 \u0131a et al. (2011) suggest that the relatively overall low fraction of \u2013 11 \u2013 WHIM in the latter (25%) versus higher fraction in the former (35-50%) may be accounted by the di\ufb00erence in the treatment of metal heating; we concur with their explanation for at least part of the di\ufb00erence. All these simulations have a box size of \u223c50h\u22121Mpc, which still su\ufb00ers from signi\ufb01cant cosmic variance: Dav\u00b4 e et al. (2001) show that WHIM fraction increases from 37% to 42% from a box size of 50h\u22121Mpc to 100h\u22121Mpc in two Eulerian simulations. The amplitude of power spectrum has a similar e\ufb00ect and may be able to, at least in part, account for some of the di\ufb00erences among the simulations; \u03c38 = (0.82, 0.82, 0.74, 0.77, 0.80, 0.82) in [this work, Shull et al. (2011), Tepper-Garc\u00b4 \u0131a et al. (2011), Shen et al. (2010), Tornatore et al. (2010), Oppenheimer et al. (2012)]. Gravitational collapse of longer waves powers heating of the IGM at later times. We suggest that the peak of WHIM fraction at z \u223c0.5 found in the 25h\u22121Mpc simulation boxes in Smith et al. (2011) is because of the small box size; in other words, available, reduced gravitational heat input in the absence of breaking density waves of lengths longer than 25h\u22121Mpc at z \u22640.5 fails to balance the cooling due to (primarily) universal expansion and (in part) radiative cooling. This explanation is supported by the behavior of their simulation boxes of size 50\u22121Mpc at low redshift (z \u22640.5). Figure 3 shows that within the WHIM temperature range, roughly equal amounts are at T = 105 \u2212106K and T = 106 \u2212107K. 3. Results 3.1. Simulation Validation with Properties of O VI Absorbers The present simulations have been shown to produce the metal distribution in and around galaxies over a wide range of redshift (z = 0 \u22124) that is in good agreement with respect to the properties of observed damped Ly\u03b1 systems (Cen 2012). Here we provide additional, more pertinent validation with respect to O VI absorbers in the IGM at z = 0. The top panel of Figure 4 shows a scatter plot of simulated O VI absorbers (red pluses) in the Doppler width (b)-O VI column density [N(OVI)] plane, compared to observations. The agreement is excellent in that the observed O VI absorbers occupy a region that overlaps with the simulated one. It is intriguing to note that the simulations predict a large number of large b, low N(OVI) (i.e., broad and shallow) absorbers in the region b > 31(N(OVI)/1014cm\u22122)0.4km/s, corresponding to the upper left corner to the green dashed line, where there is no observed O VI absorber. This green dashed line, however, has no physical meaning to the best of our knowledge. The blue solid line of unity logarithmic slope has a clear physical origin, which is a requirement for the decrement at the \ufb02ux trough of the weaker of the O VI doublet to be 4%: b = 25(N(OVI)/1013cm\u22122) km/s. Current observational data are heterogeneous with varying qualities. Thus, the blue solid line is a much simpli\ufb01ed characterization of the complex situation. Nevertheless, one could understand the desert of observed O VI absorbers in the upper left corner to the blue solid line, thanks to the di\ufb03culty of identifying broad \u2013 12 \u2013 and shallow lines in existing observations. We attribute the \u201cmissing\u201d observed O VI lines in the upper right corner between the blue solid line and the green dashed line, in part, to the observational procedure of Voigt pro\ufb01le \ufb01tting that may break up some large b lines into separate, narrower components, whereas no such procedure is performed in the presented simulation results. Ongoing and upcoming observations by the Cosmic Origins Spectrograph (COS) (e.g., Froning & Green 2009; Shull 2009; Green et al. 2012) will be able to substantially improve in sensitivity and thus likely be able to detect a sizeable number of O VI lines in the upper left corner to the blue solid line. Quantitative distribution functions of b parameter will be shown in Figure 10 later, for which COS may provide a strong test. The bottom panel of Figure 4 shows a scatter plot of simulated O VII absorbers (red pluses); because there is no data to compare to, we only note that the positive correlation between b and N(OVI) is stronger for O VII lines than for O VI lines, in part due to less important contribution to the O VII lines from photoionization and in part due to positive correlation between density and velocity dispersion. Figure 5 shows O VI line density as a function of column density. The agreement between simulations and observations of Danforth & Shull (2008) is excellent over the entire column density, N(OVI) \u223c1013 \u22121015cm\u22122, where comparison can be made. The simulation results are up to a factor of \u223c2 below the observational results of Tripp et al. (2008) in the column density range N(OVI) \u223c1013.7 \u22121014.5cm\u22122. Some of the disagrement is due to di\ufb00erent treatments in de\ufb01ning lines in that we do not perform Voigt pro\ufb01le \ufb01tting thus deblending of non-gaussian pro\ufb01les into multiple components, where the observational groups do and di\ufb00erent groups often impose di\ufb00erent, subjective criteria of choosing the \u201cgoodness\u201d of the \ufb01t. The down turn of line density towards lower column densities from N(OVI) \u223c1013.9cm\u22122 from Tripp et al. (2008) as well as the lower values in the column density range N(OVI) \u223c1013.2 \u22121013.7cm\u22122 of Danforth & Shull (2008) may be related to the \u201cmissing\u201d broad and shallow lines, as indicated in the top panel of Figure 4. It is noted that the observed line density at N(OVI) \u223c1013cm\u22122 of the Danforth & Shull (2008) data displays an upturn and lies on top of the simulated curve. Closer examination reveals that this is due to the presence of two relatively broad absorbers at N(OVI) \u223c1013cm\u22122 and b \u223c30 km/s. We expect that the upcoming COS observations will substantially raise the line density at N(OVI) \u22641013.5cm\u22122. \u2013 13 \u2013 12 13 14 15 0.5 1 1.5 2 log N(OVI) (cm\u22122) log b (km/s)     simulation obs: Danforth et al 2008 obs: Tripp et al 2008 13 14 15 16 0.5 1 1.5 2 log N(OVII) (cm\u22122) log b (km/s) Fig. 4.\u2014 Top panel shows a scatter plot of simulated O VI absorbers (red pluses) in the b-N(OVI) plane. Also shown as black dots and blue triangles are the observations from Danforth & Shull (2008) and Tripp et al. (2008), respectively. The green dashed line of slope 4/10 is only intended to guide the eye to suggest that there appears to be a desert of observed O VI absorbers in the upper left corner. The blue solid line of unity logarithmic slope is a requirement for the decrement at the \ufb02ux trough of the weaker of the O VI doublet to be 4%: b = 25(N(OVI)/1013cm\u22122) km/s. Bottom panel shows the same for the O VII absorbers. \u2013 14 \u2013 10 12 10 13 10 14 10 15 10 \u22121 10 0 10 1 10 2 N(OVI) (cm\u22122) dn/dz/per unit log N(OVI)     total T>105K T<105K obs: Danforth & Shull 2008 obs: Tripp et al. 2008 Fig. 5.\u2014 shows the O VI line density as a function of column density, de\ufb01ned to be the number of lines per unit redshift per unit logarithmic interval of the column density. The red solid dots, green squares and blue triangles are the total, collisionally ionized and photoionized absorbers, respectively. Also shown as black open circles and stars are the observations from Danforth & Shull (2008) and Tripp et al. (2008), respectively. These results show that our simulation results are realistic with respect to the abundance of O VI lines in the CGM and IGM. This is a substantial validation of the simulations, when considered in conjunction with the success of the simulations with respect to the damped Ly\u03b1 systems (Cen 2012). The damped Ly\u03b1 systems primarily originate in gas within the virial radii of galaxies, whereas the O VI absorbers examined here extend well into the IGM, some reaching as far as the mean density of the universe (see Figure 7 below). In combination, they require the simulations to have substantially correctly modeled the propagation of initial metal-enriched blastwaves from sub-kpc scales to hundreds of kiloparsecs as well as other complex thermodynamics, at least in a statistical sense. Since O VII absorbers arise in regions in-between, this gives us con\ufb01dence that O VII lines are also modeled correctly and the comparisons that we will make between O VI and O VII lines are meaningful. \u2013 15 \u2013 4 5 6 7 0 10 20 30 40 50 60 70 80 90 100 150 log T (K) b (km/s)     EW(1032)>100mA EW(1032)=30\u2212100mA thermal broadening only obs: Tripp et al 2008 4 5 6 7 0 10 20 30 40 50 60 70 80 90 100 150 200 log T (K) b (km/s)     EW(OVII)>2mA EW(OVII)=0.5\u22122mA thermal broadening only Fig. 6.\u2014 shows absorbers in the b\u2212T plane for O VI line (top panel) and O VII line (bottom panel). Within each panel, we have broken up the absorbers into strong ones (blue squares) and weak ones (red circles). Only thermally broadened lines should follow the indicated solid green curve (Eq. 1). Also shown as right-pointing triangles are observed data of Tripp et al. (2008) based on a joint analysis of Ly\u03b1 and O VI lines; the location of each triangle is the best estimate of the temperature and the rightmost tip of the attached line to each triangle represents a 3\u03c3 upper limit. \u2013 16 \u2013 0 1 2 3 4 4 5 6 7 log b log T (K)     log N(O VI)>14 log N(O VI)=13\u221214 0 1 2 3 4 4 5 6 7 log b log T (K)     log N(O VII)>15 log N(O VII)=14\u221215 Fig. 7.\u2014 shows absorbers in the temperature-density plane for O VI line (top panel) and O VII line (bottom panel). Within each panel, we have broken up the absorbers into strong ones (blue squares) and weak ones (red circles). \u2013 17 \u2013 3.2. Physical Properties of O VI and O VII Lines In this subsection we will present physical properties of both O VI and O VII absorbers and relationships between them. For most of the \ufb01gures below we will show results in pairs, one for O VI and the other for O VII, to facilitate comparisons. Figure 6 shows absorbers in the b \u2212T plane for O VI (top panel) and O VII absorbers (bottom panel). For thermal broadening only absorbers the b \u2212T relation would follow the solid green curve obeying this formula: b(O) = 10.16(T/105K)1/2 km/s. (1) It is abundantly clear from Figure 6 that b is a poor indicator of absorber gas temperature. Bulk velocity structures within each absorbing line are important. For O VI lines of equivalent width greater than 100mA, it appears that bulk velocity structures are dominant over thermal broadening at all temperatures. No line is seen to lie below the green curve, as expected. All of the observationally derived temperature limits shown, based on a joint analysis of line pro\ufb01les of well-matched coincidental Ly\u03b1 and O VI lines by Tripp et al. (2008), are seen to be fully consistent with our simulation results. It is noted that velocity structures in unvirialized regions typically do not have gaussian distributions (in 1-d). Caustic-like velocity structures are frequently seen that are reminiscent of structure collapse along one dimension (e.g., Zeldovich pancake or \ufb01laments); for anecdotal evidence see Figure 2. Thus, we caution that temperatures derived on the grounds of gaussian velocity pro\ufb01le (e.g., Tripp et al. 2008) may be uncertain. A more detailed analysis will be performed elsewhere. The situations with respect to O VII absorbers are similar to O VI absorbers. Figure 7 shows absorbers in the temperature-density plane for O VI (top panel) and O VII absorbers (bottom panel). In the top panel we see that strong O VI absorbers with N(OVI)\u22651014cm\u22122 have a large concentration at (\u03b4, T)= (10 \u2212300, \u223c105.5K) that corresponds to collisional ionization dominated O VI population, consistent with Figure 5. For weaker absorbers with N(OVI)= 1013\u221214cm\u22122 we see that those with temperature above and those below 105K are roughly equal, consistent with Figure 5; the density distributions for the two subsets are rather di\ufb00erent: for the lower-temperature (T< 105K) subset the gas density is concentrated around \u03b4 \u223c10 that is photoionization dominated, whereas for the higher-temperature (T> 105K) subset the gas density is substantially spread out over \u03b4 \u223c 3\u22123000, which are mostly collisional ionization dominated. Finally, we note that still weaker lines with N(OVI)< 1013cm\u22122, not shown here, are mostly photoionization dominated, as indicated in Figure 5. In the bottom panel we see that strong O VII absorbers with N(OVI)\u2265 1015cm\u22122 are predominantly collisionally ionized at T \u223c105.5 \u2212106.5K and \u03b4 \u223c10 \u22121000, with a small fraction of lines concentrated at an overdensity of \u223c3 \u221220 and temperatures below 105.5K. For weaker absorbers with N(OVII)= 1014\u221215cm\u22122 collisionally ionized ones at temperatures greater than 105.5K and those photoionized at lower temperatures are roughly \u2013 18 \u2013 4 5 6 7 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 log T (K) CDF(>T)     log N(OVI)=12.5\u221213 log N(OVI)=13\u221214 log N(OVI)>14 OVI fraction with collisional ionization 4 5 6 7 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 log T (K) CDF(>T)     log N(OVII)=13\u221214 log N(OVII)=14\u221215 log N(OVII)>15 OVII fraction w/ coll ionization Fig. 8.\u2014 shows the cumulative probability distribution functions as a function of absorber temperature for three subsets of O VI line with column densities of log N(OVI)cm2 = (12.5\u2212 13, 13 \u221214, > 14) (top panel) and O VII line of log N(OVI)cm2 = (13 \u221214, 14 \u221215, > 15) (bottom panel). The blue dot-dashed curve in the top (bottom) panel shows the O VI (O VII) fraction as a function of gas temperature in the absence of photoionization. \u2013 19 \u2013 comparable in numbers, consistent with Figure 14 below. Our results for O VI lines is broadly consistent with (Shull et al. 2011). Shull et al. (2011) \ufb01nd a bimodal distribution of O VI absorbers, one concentrating at (\u03b4, T)=(\u223c10, 104.5K) and the other at (\u03b4, T)=(\u223c100, 105.5K) (see their Figures 4,5). Figure 8 shows the cumulative probability distribution functions as a function of absorber temperature for three subsets of O VI lines with column densities of log N(OVI)cm2 = (12.5\u221213, 13\u221214, > 14) (top panel) and O VII line of log N(OVI)cm2 = (13\u221214, 14\u221215, > 15) (bottom panel). We \ufb01nd that (39%, 43%, 61%) of O VI absorbers in the column density ranges of log N(OVI)cm2 = (12.5 \u221213, 13 \u221214, > 14) have temperature greater than 105K, (25%, 39%, 73%) of O VII absorbers in the column density ranges of log N(OVI)cm2 = (13 \u221214, 14 \u221215, > 15) have temperature greater than 105K. Our \ufb01ndings are in broad agreement with previous results obtained by our group (e.g., Cen et al. 2001; Cen & Ostriker 2006; Cen & Chisari 2011) and some other groups (e.g., Tepper-Garc\u00b4 \u0131a et al. 2011; Shull et al. 2011), but in substantial disaccord with results of Oppenheimer & Dav\u00b4 e (2009) and Oppenheimer et al. (2012) who \ufb01nd that photo-ionized O VI lines with temperature lower than 105K make up the vast majority of O VI lines across the column density range log N(OVI)cm2 = 12.5 \u221215. Given the di\ufb00erences in simulation codes and in treatment of feedback processes, we cannot completely ascertain the exact cause for the di\ufb00erent results. Nevertheless, the explanation given by Oppenheimer et al. (2012) that the lack of metal mixing in their SPH simulations plays an important role in contributing to the di\ufb00erence is further elaborated here. Oppenheimer et al. (2012) \ufb01nd a large fraction of metal-carrying feedback SPH particles wound up in low density regions that have relatively high metallicity (\u223c1 Z\u2299) and low temperature (T \u223c104K). As a result, they \ufb01nd low-density, high-metallicity and lowtemperature photo-ionized O VI absorbers to dominate the overall O VI absorber population in their SPH simulations. According to Tepper-Garc\u00b4 \u0131a et al. (2011), they repeat simulations with the same feedback model used in Oppenheimer & Dav\u00b4 e (2009) and Oppenheimer et al. (2012) but with metal heating included, and are unable to reproduce the dominance of lowtemperature photoionized O VI absorbers seen in the latter. This leads them to conclude that lack of metal heating, in the presence of high-metallicity feedback SPH particles, is the cause of the dominance of low-density, high-metallicity and low-temperature photo-ionized O VI absorbers found in Oppenheimer & Dav\u00b4 e (2009) and Oppenheimer et al. (2012). We suggest that this overcooling problem may have been exacerbated by lack of metal mixing. Consistent with this conjecture, while Tepper-Garc\u00b4 \u0131a et al. (2011) su\ufb00er less severely from the metal overcooling problem (because of metal heating), the median metallicity of their O VI absorbers is still \u223c0.6 Z\u2299, substantially higher than that of our O VI absorbers, Z \u223c0.03 \u22120.3 Z\u2299, even though their overall abundance of O VI absorbers is lower than observed by a factor of \u223c2. This noticeable di\ufb00erence in metallicity may be rooted in lack of metal mixing in theirs. \u2013 20 \u2013 As we will show later (see Figure 13 below), the metallicity of simulated O VI in our simulations appears to better match observations. Despite that, it is desirable to directly probe the physical nature of O VI absorbers to test models by di\ufb00erent simulation groups. One major di\ufb00erence between SPH simulations (e.g., Tepper-Garc\u00b4 \u0131a et al. 2011; Oppenheimer et al. 2012) and AMR simulations (e.g., Smith et al. 2011, and this work) is that the former predict metallicity distributions that are peaked at (0.6\u22121) Z\u2299compared to peaks of \u223c(0.05\u22120.2) Z\u2299 in the latter. In addition, in the latter positive correlations between metallicity and O VI column density and between metallicity and temperature are expected, whereas in the former the opposite or little correlation seems to be true. Therefore, direct measurements of O VI metallicity and correlations between metallicity and other physical quantities would provide a good discriminator. Putting di\ufb00erences between SPH simulations of WHIM by di\ufb00erent groups aside, what is in common among them is the dominance of low-density (\u03b4 \u2264100) O VI absorbers at all column densities. In the AMR simulations it is found that the collisionally ionized O VI absorbers, with density broadly peaked at \u03b4 \u223c100, dominate (by 2 to 1) over photoionized O VI absorbers for N(OV) \u22651014cm\u22122 population. Given these signi\ufb01cant di\ufb00erences between SPH and AMR simulations, we suggest a new test, namely, the cross-correlation function between galaxies and strong [N(O VI) \u22651014cm\u22122] O VI absorbers. Available observations appear to point to strong correlations at relatively small scales \u2264300 \u2212700kpc between luminous galaxies (\u22650.1L\u2217) and N(OV) \u22651013.2\u221213.8cm\u22122 O VI absorbers at z = 0 \u22120.5 (e.g., Stocke et al. 2006; Chen & Mulchaey 2009; Prochaska et al. 2011). We expect AMR simulated O VI absorbers to show stronger small-scale crosscorrelations with galaxies than SPH simulated O VI absorbers thanks to the predicted dominance of O VI absorbers in low density (but higher metallicity) regions in the latter that are at larger distances from galaxies. When an adequate observational sample of Ne VIII absorbers becomes available, galaxy-Ne VIII may provide a still more sensitive test between photoionization models suggested by some SPH simulations and AMR simulations, because the N VIII line needs a still higher temperature to collisionally ionize and hence the contrast is still higher between the simulations. However, the shorter wavelengths of the Ne VIII lines at 770\u02da A and 780\u02da A require galaxies at z > 0.47 to shift into the HST (COS or STIS) observable band, for which current galaxy surveys will only be able to probe most luminous galaxies (L > L\u2217). Detailed calculations and comparisons to observations will be needed to ascertain these expectations to nail down their physical nature and to constrain feedback models. The rapid rise in the cummulative fraction in the temperature range log T = 5.5\u00b10.1 in the top panel of Figure 8 re\ufb02ects the concentration of collisionally ionized O VI lines in that temperature range, supported the blue dot-dashed curve showing the collisional ionization fraction of O VI as a function of temperature. This feature is most prominent in the high column density O VI population with log N(OVI)cm2 > 14 (green dashed curve), simply stating the fact that collisional ionization is dominant in high column density O VI lines. \u2013 21 \u2013 For O VII there is a similar feature except that it is substantially broader at log T = 6.0\u00b10.4, which is consistent with the ionization fraction of O VII as a function of temperature in the collisional ionization dominated regime, shown as the blue dot-dashed curve in the bottom panel of Figure 8. For O VI lines with column density in the range log N(OVI)cm2 = 12.5\u221214 we see a relative dearth of absorbers in the temperature range log T = 4.8 \u22125.4, a regime where neither collisional ionization nor photoionization is e\ufb00ective due to structured multiphase medium (i.e., positive correlation between density and temperature in this regime, see Figure 17 below); at still lower temperature log T < 4.8 (and low density due to the positive correlation), the curve displays a rapid ascent due to its entry into the photoionization dominated regime. Analogous behaviors and explanations can be said for O VII absorbers. We see earlier in Figure 6 that b is not a good indicator of the temperature of absorbing gas. It is thus useful to quantify the fraction of absorbers at a given b whose temperature is in the WHIM regime. Figure 9 shows the fraction of O VI (top panel) and O VII (bottom panel) absorbers that is in WHIM temperature range of 105\u2212107K as a function of b. Broadly speaking, above the threshold (thermally broadened Doppler width of 10.16km/s for a gas at temperature of 105K), the WHIM fraction is dominant at \u226550% for both O VI and O VII lines, but only close to 100% when b is well in excess of 100km/s. This again indicates the origin of the O VI absorbing gas whose random motions are far from completely thermalized, consistent with its (mostly) intergalactic nature. The approximate \ufb01tting curve (blue curve) for the column density weighted hisotogram for O VI shown in Figure 9 can be formulated as the following equation: f(OVI) = 0.20 for b < 10 km/s = 0.0026(b \u221210) + 0.6 for b = 10 \u2212160 km/s = 1 for b > 160 km/s (2) As already indicated in Figure 4 that a substantial fraction of broad but shallow absorbers may be missing in current observational data, here we quantify it further. Figure 10 shows four cumulative probability distribution functions as a function of b for four subsets of O VI (top panel) and O VII (bottom panel) lines of di\ufb00ering column densities. To give some quantitative numbers, (15%, 20%, 26%, 39%) of O VI absorbers with log N(O VI) = (12.5 \u2212 13, 13 \u221213.5, 13.5 \u221214, > 14) have b > 40 km/s; the fractions drop to (1%, 2%, 4%, 7%) for b > 80 km/s. Similarly, (17%, 46%, 77%, 88%) of O VII absorbers with log N(O VI) = (13\u2212 14, 14 \u221215, 15 \u221216, > 16) have b > 40 km/s, with (2%, 9%, 29%, 30%) having b > 80 km/s. With COS observations of substantially higher sensitivities, broad O VI lines are begun to be detected (Savage et al. 2010). A direct, statistical comparison between simulation \u2013 22 \u2013 0 50 100 150 200 250 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 b (km/s) fraction of O VI lines in WHIM     # weighted N(OVI) weighted thermal broadening with 105K 0 50 100 150 200 250 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 b (km/s) fraction of O VII lines in WHIM     # weighted N (OVII) weighted Fig. 9.\u2014 shows the fraction of O VI (top panel) and O VII (bottom panel) absorbers that is in WHIM temperature range of 105 \u2212107K as a function of b. The red and green histograms are number and column density weighted, respectively, including only lines with column density above 1013cm\u22122 in the case of O VI and 1014cm\u22122 for O VII. The vertical black line indicates b for a purely thermally broadened line at a temperature of 105K. The approximate \ufb01tting curve indicated by blue dashed line is given in Equation (2). \u2013 23 \u2013 0 25 50 75 100 125 150 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 b (km/s) CDF(>b)     log N(OVI)=12.5\u221213 log N(OVI)=13\u221213.5 log N(OVI)=13.5\u221214 log N(OVI)>14 0 25 50 75 100 125 150 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 b (km/s) CDF(>b)     log N(OVII)=13\u221214 log N(OVII)=14\u221215 log N(OVII)=15\u221216 log N(OVII)>16 Fig. 10.\u2014 Top panel shows four cumulative probability distribution functions as a function of b for four subsets of O VI lines in the four column density ranges: log N(OVI)cm2 = 12.5\u221213 (black dotted curve), log N(OVI)cm2 = 13\u221213.5 (red solid curve), log N(OVI)cm2 = 13.5 \u221214 (green dashed curve) and log N(OVI)cm2 > 14 (blue dot-dashed curve). Bottom panel shows four cumulative probability distribution functions as a function of b for four subsets of O VII lines in the four column density ranges: log N(OVI)cm2 = 13 \u221214 (black dotted curve), log N(OVI)cm2 = 14 \u221215 (red solid curve), log N(OVI)cm2 = 15 \u221216 (green dashed curve) and log N(OVI)cm2 > 16 (blue dot-dashed curve). \u2013 24 \u2013 results found here and observations will be possible in the near future. It will be extremely interesting to see if there is indeed a large population of broad but shallow O VI lines still missing. That is also important, because, if that is veri\ufb01ed, one will have more con\ufb01dence on the results for O VII lines, which suggest that the O VII lines may be substantially broader than a typical thermally broadened width of 40 \u221250 km/s. Additional useful information is properties of other lines, including Ly\u03b1, which we will present in a subsequent paper. Since the expected b of O VII lines is still substantially smaller than spectral resolution of Chandra and XMM-Newton X-ray instruments, it does not make much di\ufb00erence for extant observations. However, it should be taken into consideration in designing future X-ray telescopes to probe WHIM in absorption or emission (e.g., Yao et al. 2012). Figure 11 shows absorbers in the metallicity-overdensity plane. The apparent anticorrelation between metallicity and overdensity with a log slope of approximately \u22121 for the mostly collisional ionization dominated population (red circles) is simply due to the fact that the absorbers near the chosen column density cuto\ufb00dominate the numbers and that collisional ionization rate is density independent. Similarly, the apparent anti-correlation between metallicity and overdensity with a log slope of approximately \u22122 for the mostly photoionization dominated population (blue squares) is due to the fact that photo-ionization fraction is proportional to density. So one should not be misled to believe that there is an anti-correlation between gas metallicity and overdensity in general; the opposite is in fact true (see Figure 18 below). In Figure 12 we project two subsets of absorbers onto the metallicity-b plane. Because of complex behaviors seen in Figure 11 and the additional role played by complex temperature and velocity distributions, one may not be surprised to see the large dispersions in metallicity at a given b. The metallicity distribution is seen to be, to zero-order within the large dispersions, nearly independent of b. When metallicity of O VI and O VII absorbers can be measured directly in the future, this prediction may be tested. No further detailed information on this shall be given here due to its still more futuristic nature in terms of observability, except noting that the weak trends can be understood and these trends are dependent upon the column density cuts. Figure 13 shows the mean metallicity as a function of column density for O VI (red circles) and O VII absorbers (blue squares). We see that a substantial dispersion of about 0.51 dex is present for all column density bins. The mean metallicity for O VI lines increases by 0.9 dex from [Z/H] \u223c\u22121.3 at N(OVI) = 1013cm\u22122 to [Z/H] \u223c\u22120.4 at N(OVI) = 1015cm\u22122. For O VII lines the mean metallicity increases by 0.4 dex from [Z/H] \u223c\u22121.1 at 1014cm\u22122 to [Z/H] \u223c\u22120.7 at 1016cm\u22122. The trend of increasing metallicity with increasing column density is consistent with the overall trend that higher density regions, on average, have higher metallicity, at least in the density range of interest here (see Figure 11 below). It is noted that the mean metallicity for O VII absorbers is, on average, lower than that for O VI lines at a \ufb01xed column density for the respective ions. This and some other relative behaviors between O VI and O VII seen in Figure 13 merely re\ufb02ect the facts (1) that the \u2013 25 \u2013 product of oscillator strength and restframe wavelength of O VII line is about a factor of 10 lower than that of O VI, (2) the peak collisional ionization fraction for O VII is about a factor of 5 higher than that of O VI, and (3) the peak width for collisional ionization temperature for O VII is larger by a factor of \u223c3 than that of O VI (see Figure 8). Examination of the C+P (collisional + photoionization) model with distributed feedback (which is closest to our feedback model) in Figure 17 of Smith et al. (2011) reveals that the average metallicity increases from \u223c\u22121.0 to \u223c0.0 for NOVI from 1012cm\u22122 to 1015cm\u22122, which should be compared to an increase of metallicity from \u223c\u22121.5 to \u223c\u22120.5. Thus, our results are in good agreement with Smith et al. (2011) except that their metallicity is uniformly higher by a factor of \u223c3. While there are substantial disagreements among the SPH and AMR simulations with respect to the metallicity of O VI absorbers, it is fair to say that a median value of 0.1\u22121 Z\u2299 encompasses them. Given that, some quantitative physical considerations are useful here. The cooling time for gas of \u03b4 = 100, T = 105.5K and Z = 0.1 Z\u2299at z = 0 is \u223c0.05tH (tH is the Hubble time at z = 0) (this already takes into account metal heating by the X-ray background; it should be noted that the X-ray background at z \u223c0 is still quite uncertain (e.g., Shull et al. 2011)). This indicates that the O VI-bearing gas of T \u223c105.5K and \u03b4 \u2265100, in the absence of other balancing heating processes, can only spend a small fraction of a Hubble time at the temperature for optimal O VI production via collisional ionization. This has two implications. First, O VI absorbers at \u03b4 \u2265100 \u00d7 (Z/0.1 Z\u2299)\u22121 is transient in nature and their appearance requires either constant heating of colder gas or higher temperature gas cooling through. Which process is more responsible for O VI production will be investigated in a future study. Second, the metal cooling that is linearly proportional to gas metallicity may give rise to an interesting \u201cselection e\ufb00ect\u201d, where high metallicity O VI gas in dense regions, having shorter cooling time than lower metallicity O VI gas of the same density, would preferentially remove itself from being O VI productive by cooling, leaving behind only lower metallicity gas at O VI-bearing temperatures. We suggest that this selection e\ufb00ect may have contributed to a much reduced proportion of collisionally ionized O VI lines in SPH simulations that lack adequate metal mixing; in other words, dense metal \u201cbullets\u201d of SPH particles either cools very quickly to \u223c104K or they have reached regions of su\ufb03ciently low density before that happens. The results of Oppenheimer et al. (2012) appear to suggest, in the context of this scenario, that the feedback metal-bearing SPH particles have cooled to \u223c104K, before they can reach low density regions to avoid severe cooling, thus resulting in high-metallicity, low-density, photoionized O VI lines when they eventually wind up in low density regions. An analogous situation occurs in Tepper-Garc\u00b4 \u0131a et al. (2011) SPH simulations but with two signi\ufb01cant di\ufb00erences from those of Oppenheimer et al. (2012): (1) in the former the inclusion of metal heating (due to photoionization of metal species) keeps the corresponding SPH particles at a higher temperature \ufb02oor (\u223c104.5\u22125K barring adiabatic cooling) than in the latter, and (2) \u201csmoothed\u201d metallicity used in the former to compute \u2013 26 \u2013 metal cooling/heating rates has reduced the metal cooling e\ufb00ects (which still dominate over metal heating at T \u2265105K) compared to the case without such smoothing in the latter. 0 1 2 3 4 \u22123 \u22122 \u22121 0 [Z/H] (OVI)     N(OVI)=1013\u221214cm\u22122 & T>105K N(OVI)=1013\u221214cm\u22122 & T<105K 0 1 2 3 4 \u22123 \u22122 \u22121 0     N(OVI)>1014cm\u22122 & T>105K N(OVI)>1014cm\u22122 & T<105K 0 1 2 3 4 \u22123 \u22122 \u22121 0 log b [Z/H] (OVII)     N(OVII)=1014\u221215cm\u22122 & T>105K N(OVII)=1014\u221215cm\u22122 & T<105K 0 1 2 3 4 \u22123 \u22122 \u22121 0 log b     N(OVII)>1015cm\u22122 & T>105K N(OVII)>1015cm\u22122 & T<105K Fig. 11.\u2014 shows absorbers in the metallicity-overdensity plane for O VI line with N(OVI) = 1013\u221214cm\u22122 (top left panel) and N(OVI) > 1014cm\u22122 (top right panel. The bottom two panels show O OVII line with N(OVII) = 1014\u221215cm\u22122 (bottom left panel) and N(OVII) > 1015cm\u22122 (bottom right panel). Within each panel, we have broken up the absorbers into two subsets using temperature: T > 105K (red circles) and T < 105K (blue squares). 3.3. Coincidence Between O VI and O VII Lines In \u00a73.1 we show that some of the primary observable properties of simulated O VI lines, including line incidence rate, are in excellent agreement with observations. In \u00a73.2 we have shown various physical properties underlying the observables of both lines. Before presenting quantitative coincidence rates between O VI and O VII lines, it is useful to further check \u2013 27 \u2013 0 50 100 150 200 250 \u22121.5 \u22121 \u22120.5 0 b (km/s) <[Z/H]>     N(OVI)\u2212weighted mean metallicity of lines w/ T>105K and log N(OVI)>13 N(OVI)\u2212weighted mean metallicity of lines w/ T<105K and log N(OVI)>13 0 50 100 150 200 250 \u22121.5 \u22121 \u22120.5 0 b (km/s) <[Z/H]>     N(OVII)\u2212weighted mean metallicity of lines w/ T>105K and log N(OVII)>14 N(OVII)\u2212weighted mean metallicity of lines w/ T<105K and log N(OVII)>14 Fig. 12.\u2014 shows the mean absorber metallicity as a function of b for O VI line with column density above 1013cm\u22122 (top panel) and O VII line with column density above 1014cm\u22122 (bottom panel). Within each panel, we have broken up the absorbers into two subsets using temperature: T > 105K (blue squares) and T < 105K (red circles). 12 13 14 15 16 17 \u22122 \u22121.5 \u22121 \u22120.5 0 log N(X) (cm\u22122) <[Z/H]>     X=O VI X=O VII O VI: obs of Danforth & Shull (2008) O VI: obs of Lacki & Charlton (2010) Fig. 13.\u2014 shows the mean metallicity as a function of column density for O VI (red open circles) and O VII (blue open squares) lines. Also shown as solid symbols are observational data. It is likely that the observational errorbars are underestimated. \u2013 28 \u2013 10 13 10 14 10 15 10 16 10 \u22121 10 0 10 1 10 2 N(OVII) (cm\u22122) dn/dz [>N(OVII)]     O VII: total O VII: T>10 5K O VII: T<10 5K Nicastro et al (2005) Fig. 14.\u2014 shows the cumulative O VII line density as a function of column density, de\ufb01ned to be the number of lines per unit redshift at the column density greater than the value at the x-axis. The red solid dots, green squares and blue triangles are the total, collisionally ionized and photo-ionized lines, respectively. Also shown as a black open circle is the observation of Nicastro et al. (2005a) with 1\u03c3 errorbar. Note that the quantify shown in the y-axis of Figure 5 is di\ufb00erential, not cumulative density. the O VII line incidence rate to assess the self-consistency of our simulations with extant observations. Figure 14 shows the cumulative O VII line density as a function of column density. We also show the implied observed line density, under the assumption that the detection reported by Nicastro et al. (2005a) is true. We see that the claimed observational detection is about 2\u03c3 above or a factor of \u223c7 higher than our predicted central value at the column density \u22657 \u00d7 1014cm\u22122. Our model is clearly in a more comfortable situation, if the claimed observational detection turns out to be negative. As discussed in the introduction the detection reported by Nicastro et al. (2005a) is presently controversial. This highlights the urgent need of higher sensitivity X-ray observations of this or other viable targets that could potentially place strong constraints on the model. We now turn to the coincidences between O VI and O VII lines. The top panel of \u2013 29 \u2013 Figure 15 shows the cumulative probability distribution functions as a function of velocity displacement of having a coincidental O VII line above the indicated equivalent width for an O VI line of a given equivalent width. We see that O VI lines of equivalent width in the range 50 \u2212200mA have (38%, 31%, 10%) probability of \ufb01nding an O VII line with equivalent width greater than (0.1, 0.5, 2)mA within a velocity displacement of 150 km/s. The vast majority of coincidental O VII lines for O VI lines for those equivalent widths in question are concentrated within a velocity displacement of \u226450 km/s and more than 50% at \u226425 km/s. The bottom panel of Figure 15 shows the cumulative probability distribution functions as a function of velocity displacement of having a coincidental O VI line above the indicated equivalent width for an O VII line of a given equivalent width. It is seen that for O VII lines of equivalent width in the range 2\u22124mA have a 17\u221227% probability of \ufb01nding an O VI line with equivalent width in the range 5 \u2212100mA within a velocity displacement of 150 km/s. Likewise, the vast majority of coincidental O VI lines for O VII lines for those equivalent widths in question are concentrated within a velocity displacement of \u226450 km/s and more than 80% at \u226425 km/s. The results shown in Figure 15 presently can not be compared to observations, because there is no de\ufb01nitive detection of O VII absorbers, although there are many detected O VI absorbers. Thus, we use the stacking method of Yao et al. (2009) to enable a direct comparison with available observations. The top panel of Figure 16 shows the expected mean O VII column density at the location of detected O VI lines of column density indicated by the x-axis, compared to the 3\u03c3 upper limits from observations of Yao et al. (2009) shown as black triangles. We see that the non-detection of O VII lines, or more precisely, a 3\u03c3 upper limit on the mean column of O VII lines for detected O VI lines of column density in the range log N(OVI)cm2 = 13.6 \u221214.1, is fully consistent with our simulations. The reported 3\u03c3 upper limit is above the expected value by a factor of 2.5 \u22124. This suggests that a factor of \u223c10 increase in sample size or sensitivity will be able to yield a de\ufb01nitive detection of O VII column density using the stacking technique even without detection of individual O VII absorbers. The bottom panel of Figure 16 shows the expected mean O VI column density at the location of detected O VII lines of column density indicated by the x-axis. It is evident from Figures 15,16 that O VI and O VII lines are coincidental only in a limited sense. We attribute the limited coincidence of O VII lines for O VI lines primarily to two situations for O VI producing regions. A line of sight that intersects an O VI producing region does not necessarily intersect a strong O VII producing region along the same line of sight, either because the temperature of the overall region does not reach a high enough value to be strong O VII bearing, or because the intersected O VI region is laterally an outskirt of an onion-like structure where the more central, higher temperature, O VII region makes up a smaller cross section. The former case should be ubiquitous, because weaker gravitational \u2013 30 \u2013 shocks that produce regions of temperature, say, 105.5K are more volume \ufb01lling than stronger gravitational shocks giving rise to regions of temperature, say, 106.0K. In addition, feedback shocks from star formation tend to be weaker than required to collisionally produce O VII at the spatial scales of interest here. In other words, one expects to see many O VI-bearing regions that have no associated O VII-bearing sub-regions. The latter case where hotter but smaller regions are surrounded by cooler regions is expected to arise naturally around large virialized systems such as groups and clusters of galaxies. A more quantitative but still intuitive physical check of the obtained results is not straight-forward, without performing a much more detailed study of individual physical regions that produce O VI and O VII absorbers. We shall reserve such a study for the future. The situation of coincidental O VI lines for given O VII lines might appear to be less ambiguous at \ufb01rst sight in the sense that the hotter central, O VII-producing regions should be surrounded by cooler regions and thus one might expect that the line of sight that intersects a strongly O VII-producing region should automatically intersect cooler regions that would show up as O VI absorbers. While it is true that a hot region is in general surrounded by cooler regions, it is not necessarily true that a hot 106K, O VII-bearing gas is surrounded by signi\ufb01cant 105.5K, O VI-bearing gas. For example, one may have a post-shock region of temperature 106K that is surrounded only by pre-shocked gas that is much colder than 105.5K. We note that for a gas of \u03b4 = 100, T = 106K and Z = 0.3 Z\u2299at z = 0, its cooling time is tcool \u223c0.5tH (tH is the Hubble time at z = 0). This means that O VII-bearing WHIM gas at \u03b4 \u2264100, which has been heated up by shocks to T \u2265106K, is unlikely to cool to T \u223c105.5K to become O VI rich gas. On the other hand, the cooling time for gas of \u03b4 = 100, T = 105.5K and Z = 0.1 Z\u2299at z = 0 is \u223c0.05tH, as noted earlier. Thus, it is physically possible that sharp interfaces between hot (T \u2265106K) and cold T \u2264105K gas develop. The simulations do not include thermal conduction, which can be shown to be unimportant here. The electron mean free path (mfp) is 0.44(T/106K)2(\u03b4/100)\u22121kpc, adopting the standard Spitzer value. The likely presence of magnetic \ufb01elds (not treated here) would further reduce the mfp by an order of magnitude (e.g., Cowie & McKee 1977). Thus, thermal conduction is insigni\ufb01cant and multi-phase media is expected to exist. \u2013 31 \u2013 0 25 50 75 100 125 150 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 6 v (km/s) CDF(O7 | O6, >6 v)     P[finding EW>2mA O7 line given EW=50\u2212200mA O6 line] P[finding EW>0.5mA O7 line given EW=50\u2212200mA O6 line] P[finding EW>0.1mA O7 line given EW=50\u2212200mA O6 line] 0 25 50 75 100 125 150 0 0.05 0.1 0.15 0.2 0.25 0.3 6 v (km/s) CDF(O6 | O7, >6 v)     P[finding EW>100mA O6 line given EW=2\u22124mA O7 line] P[finding EW>25mA O6 line given EW=2\u22124mA O7 line] P[finding EW>5mA O6 line given EW=2\u22124mA O7 line] Fig. 15.\u2014 Top panel shows the cumulative probability distribution functions as a function of velocity displacement of having a coincidental O VII line above the indicated equivalent width for an O VI line of a given equivalent width. Bottom panel shows the cumulative probability distribution functions as a function of velocity displacement of having a coincidental O VI line above the indicated equivalent width for an O VII line of a given equivalent width. \u2013 32 \u2013 12 13 14 15 13 13.5 14 14.5 15 log N(OVI) (cm\u22122) log <N(OVII)> (cm\u22122)     sim 3\u001f upper limit (Yao et al 2009) 14 15 16 12.5 13 13.5 14 log N(OVII) (cm\u22122) log <N(OVI)> (cm\u22122)     sim limit case: assuming polytropic gas limit case: assuming only hot gas at T>=106K Fig. 16.\u2014 The top panel shows the expected mean O VII column density at the location of detected O VI lines of column density indicated by the x-axis. Also shown as black triangles are 3\u03c3 upper limits from observations of Yao et al. (2009). The bottom panel shows the expected mean O VI column density at the location of detected O VII lines of column density indicated by the x-axis. The solid and dashed straight lines are possible limit cases based on simple physical considerations. \u2013 33 \u2013 Equipped with this information and adopting the simpler implied geometry allows for a simple physical check of the results in the bottom panel of Figure 16, as follows. We will take two separate approaches to estimate this. The \ufb01rst approach assumes a polytropic gas in the temperature range relevant for O VI and O VII collisional ionization. In the top panel of Figure 17 we show the entire temperature-overdensity phase diagram for the re\ufb01ned region in the C run. Note that the gas density reaches about 1 billion times the mean gas density, corresponding to \u223c100cm\u22123, i.e., star formation regions. For the regions of present relevance, the density range is about 10 \u2212300 times the mean density, illustrated by the upper part of the red tornado-like region near the middle of the plot. It is useful to note that for this density range, the gas mass is dominated by gas in the temperature range of 105 \u2212107K, i.e., WHIM. Because of this reason, it is a valid exercise to compute the mean pressure as a function of overdensity, at least for the density range relevant for WHIM, shown in the bottom panel of Figure 17. We see that for the WHIM overdensity range of 10 \u2212300, the adiabatic index 5/3, shown as the dashed line, provides an excellent approximation for the polytropic index of the gas. It is also necessary to have a relation between gas metallicity as a function of gas overdensity, shown in Figure 18. We only note that the metallicity is generally an increasing function with density above one tenth of the mean density, that the sharp rise of metallicity below one tenth of the mean density is due to metal-enrich galactic winds escaping into the low density regions, and that for our present purpose concerning the WHIM overdensity range of 10 \u2212300 the metallicity roughly goes as Z \u221d\u03b40.4, as indicated by the dashed line. Given the information in Figures 17, 18 we can now proceed to estimate the expected O VI column at a given O VII column density, i.e., < N(OVI) > / < N(OVII) >, assuming both are dominated by collisional ionization. The O VI column density may be roughly approximated as < N(OVI) >\u221df(OVI)\u2206log T(OVI)\u03c1(OVI)Z(OVI)L(OVI), where f(OVI) = 0.22 at log T(OVI)/K = 5.5, \u2206log T(OVI) = 0.2, \u03c1(OVI), Z(OVI) and L(OVI) are the peak collisional ionization fraction for O VI, the FWHM of the logarithmic temperature of the collisional ionization peak (see the blue curve in the top panel of Figures 8), the density of the O VI absorbing gas, the metallicity of the O VI absorbing gas and the physical thickness of the O VI absorbing gas, respectively. We have an exactly analagous relation for O VII, with f(OVII) = 1, log T(OVII) = 6, \u2206log T(OVII) = 0.7. With an additional assumption that the characteristic thickness at a given density goes as L(OVI) \u221d\u03c1(OVI)1/3 (i.e., mass distribution across log density is roughly uniform), we can now evaluate the column density ratio < N(OVI) > < N(OVII) > = f(OVI) f(OVII) \u2206log T(OVI) \u2206log T(OVII) \u03c1(OVI) \u03c1(OVII) Z(OVI) Z(OVII) L(OVI) L(OVII) = f(OVI) f(OVII) \u2206log T(OVI) \u2206log T(OVII) \u0012 T(OVI) T(OVII) \u0013(2/3+\u03b1)/(\u03b3\u22121) = 0.015, (3) \u2013 34 \u2013 10 \u22122 10 0 10 2 10 4 10 6 10 8 10 \u221222 10 \u221220 10 \u221218 10 \u221216 10 \u221214 10 \u221212 10 \u221210 10 \u22128 b pressure (erg/cm3)     simulation p=n5/3 Fig. 17.\u2014 Top panel shows mass weighted phase diagram in the temperature-overdensity plane for the re\ufb01ned region in the C run. The bottom panel shows the mean pressure as a function of overdensity averaged over all cells in the regions in the C run. The black dashed line indicates the slope for polytropic gas of index 5/3 (i.e., the adiabatic index), which provides a good approximation to the simulation in the overdensity range 10 \u2212300 that is most pertinent to the absorbing WHIM in O VI and O VII. \u2013 35 \u2013 where \u03b1 = 0.4 and \u03b3 = 5/3 are used, as indicated in Figures 18 and Figures 17, respectively. This resulting ratio is shown as the solid line in the bottom panel of Figure 16, which we expect to an approximate upper limit of the true ratio, since it implies the presence of O VI-bearing gas for every O VII line. 10 \u22122 10 0 10 2 10 4 10 6 10 8 \u22123 \u22122 \u22121 0 1 2 b [Z/H]     <[Z/H]> log(dispersion in linear Z) [Z/H]=0.4log(b) Fig. 18.\u2014 shows the mean gas metallicity (red solid curve) as a function of overdensity averaged over all cells in the re\ufb01ned region of the C run. Also shown as the green dotted curve is the logarithm of the dispersion in Z (linear metallicity). The black dashed line indicates the logarithmic slope of 0.4, which provides a good approximation to the simulation in the overdensity range 10 \u22121000 relevant to absorbing WHIM in O VI and O VII. Our second approach likely gives an approximate lower bound on < N(OVI) > / < N(OVII) >. We assume that the O VII-bearing gas is at the peak temperature of 106K and is surrounded by gas that has a temperature that is much lower than 105.5K (neglecting photoionization for the moment), in which case the coincidental O VI line is produced by the same temperature gas that produces the O VII line, giving < N(OVI) > < N(OVII) > = f(OVI)(T = 106K) f(OVII)(T = 106K) = 0.0035, (4) which is shown as the dashed line in the bottom panel of Figure 16. Admittedly, our approaches to estimate the column density ratios are quite simplistic. Nevertheless, we think \u2013 36 \u2013 they capture some of the essential underlying relationships between O VI-bearing gas and O VII-bearing gas in the collisional ionization dominated regime and it is reassuring that they are consistent with detailed calculations. Note that at N(OVII) < 1015cm\u22122 photoionization becomes important, especially for related O VI lines, hence our simple physical illustration breaks down in that regime. 4. Conclusions Utilizing high resolution (0.46h\u22121kpc), adaptive mesh-re\ufb01nement Eulerian cosmological hydrodynamic simulations we examine properties of O VI and O VII absorbers in the warmhot intergalactic medium (WHIM) at z = 0, along with a physical examination. We \ufb01nd that our new high resolution simulations are in broad agreement with all other simulations with respect to the thermal distribution of baryons in the present universe. In particular, we \ufb01nd that about 40% of the intergalactic medium is in the WHIM. We \ufb01nd that our simulations are in excellent agreement with observed properties of O VI absorbers, including line incidence rate, Doppler width-column density relation, and consistent with observed Doppler width-temperature relation. Physical properties of O VI and O VII absorbers are given, including inter-relations between metallicity, temperature, density, Doppler width, to facilitate a coherent understanding. We highlight some of the important or new \ufb01ndings. (1) We \ufb01nd that strong O VI absorbers are predominantly collisionally ionized, whereas for weaker absorbers the contributions from photoionization become progressively more important. We \ufb01nd that (39%, 43%, 61%) of O VI absorbers in the column density ranges of log N(OVI)cm2 = (12.5 \u221213, 13 \u221214, > 14) have temperature greater than 105K. This may be contrasted with the results of Oppenheimer & Dav\u00b4 e (2009) where low temperature (\u223c104K), high metallicity, photoionized O VI absorbers dominate even at high column densities (log N(OVI)cm2 > 14). We concur that lack of metal mixing in SPH simulations, which in turn causes overcooling of high-metallicity feedback SPH particles, most severely in high density regions, may be able to account for the discrepancy. We suggest that cross correlations between strong [N(OVI) \u22651014cm\u22122] O VI absorbers and galaxies on \u223c100kpc scales may be able to di\ufb00erentiate between the models. (2) Velocity structures within absorbing regions are a signi\ufb01cant, and for large Doppler width clouds, a dominant contributor to the Doppler widths of both O VI and O VII absorbers. Doppler width is thus a poor indicator of temperature. (3) Quantitative prediction is made for the presence of broad and shallow O VI lines, which current observations have largely failed to detect. Upcoming observations by COS may be able to provide a test. (4) The coincidence rates between O VI and O VII lines are found to be small, for \u2013 37 \u2013 which physical explanations are given. We \ufb01nd that the reported 3\u03c3 upper limit on the mean column density of coincidental O VII lines at the location of detected O VI lines by Yao et al. (2009) is above the predicted value by a factor of 2.5 \u22124, implying that a factor of \u223c10 increase in sample size or sensitivity will be able to yield a de\ufb01nitive detection of O VII column density using the stacking technique even without detection of individual O VII absorbers. (5) We show that, if the previously claimed observational detection of O VII lines by Nicastro et al. (2005a) is true, our predicted O VII line density is 2\u03c3 below that. This shows that higher sensitivity X-ray observations of this or other viable targets will be very useful to potentially place strong constraints on the model. I would like to thank Dr. M.K.R. Joung for help on generating initial conditions for the simulations and running a portion of the simulations and Greg Bryan for help with Enzo code. I would like to thank the referee Mike Shull for critical and constructive reports. I would like to thank Dr. Edward Jenkins for a careful reading of the manuscript and helpful discussion, Dr. Charles Danforth for kindly providing the observational data and useful discussion, Dr. Jeremiah P. Ostriker for useful discussion and Drs. John Wise, Matthew Turk and Cameron Hummels for help with visualization program yt (Turk et al. 2011). Computing resources were in part provided by the NASA HighEnd Computing (HEC) Program through the NASA Advanced Supercomputing (NAS) Division at Ames Research Center. This work is supported in part by grants NNX08AH31G and NAS8-03060. The simulation data are available from the author upon request.",
                    "introduction": "Physical understanding of the thermodynamic evolution of the intergalactic medium (IGM) has been substantially improved with the aid of ab initio cosmological hydrodynamic simulations. One of the most robust predictions is that 40\u221250% of all baryons in the present universe is in the WHIM of temperature 105 \u2212107K and overdensity 10 \u2212300 (e.g., Cen & 1Princeton University Observatory, Princeton, NJ 08544; cen@astro.princeton.edu arXiv:1112.4527v2  [astro-ph.CO]  14 May 2012 \u2013 2 \u2013 Ostriker 1999; Dav\u00b4 e et al. 2001). The predicted WHIM provides an attractive solution to the long standing missing baryons problem (Persic & Salucci 1992; Fukugita et al. 1998). Let us \ufb01rst clarify the nomenclature of several related gas phases. The intra-group and intra-cluster medium (ICM) is de\ufb01ned to be gas within these virialized regions (i.e., overdensity > 100). The high density portion (overdensity \u2265500) of the ICM has traditionally been detected in X-ray emission; thermal Sunyaev-Zeldovich e\ufb00ect and more sensitive X-ray measurements can now probe ICM to about the virial radius. The circumgalactic medium (CGM) is usually de\ufb01ned to be gas that embeds the stellar components in galactic halos and may be made up of gases of a wide range of temperatures (104 \u2212107K) and densities. It is likely, at least for large galaxies, that a signi\ufb01cant fraction of the CGM falls into the same temperature range of the WHIM. Of particular interest is some of the CGM that has been heated up by star formation feedback shocks to the WHIM temperature range (e.g., Cen & Ostriker 2006; Cen & Chisari 2011). In the present analysis we de\ufb01ne WHIM as gas of temperature 105 \u2212107K with no density limits. Most of the WHIM gas is truly intergalactic with overdensity < 100 (see Figure 7) and mostly easily probed in absorption. The reality of the WHIM, at least its low temperature (T \u2264106K) portion, has now been fairly convincingly con\ufb01rmed by a number of observations in the FUV portion of QSO spectra from HST and FUSE, through the O VI \u03bb\u03bb1032, 1038 absorption lines that peak at T \u223c3\u00d7105K when collisionally ionized (e.g., Tripp et al. 2000; Tripp & Savage 2000; Oegerle et al. 2000; Savage et al. 2002; Prochaska et al. 2004; Sembach et al. 2004; Danforth & Shull 2005; Danforth et al. 2006; Danforth & Shull 2008; Tripp et al. 2008; Thom & Chen 2008a,b; Cooksey et al. 2008) and Ne VIII \u03bb\u03bb770, 780 absorption lines that peak at T \u223c7 \u00d7 105K in collisional ionization equilibrium (Savage et al. 2005, 2006; Narayanan et al. 2009, 2011; Tripp et al. 2011) as well as broad Ly\u03b1 absorption lines (BLAs) (Danforth et al. 2010; Savage et al. 2011a,b). In agreement with simulations, the part of WHIM detected in O VI absorption is estimated to constitute about 20-30% of total WHIM. The detection of Ne VIII lines along at least some of the sight lines with O VI detection provides unambiguous evidence for the WHIM origin, instead of lower temperature, photoionized gas, under physically plausible and observationally constrained situations. X-ray observations performed to search for X-ray absorption of the higher temperature portion (T \u2265106K) of the WHIM associated with known massive clusters have also been successful. An XMM-Newton RGS spectrum of quasar LBQS 1228+1116 revealed a feature at the Virgo redshifted position of O VIII Ly\u03b1 at the 95% con\ufb01dence level (Fujimoto et al. 2004). Using XMM-Newton RGS observations of an AGN behind the Coma Cluster, the Seyfert 1 X Comae, Takei et al. (2007) claimed to have detected WHIM associated with the Coma cluster. Through the Sculptor Wall Buote et al. (2009) and Fang et al. (2010) have detected WHIM O VII absorption at a column greater than 1016cm\u22122. There is evidence of detection in soft X-ray emission along the \ufb01lament connecting clusters A222 and A223 at z = 0.21 that may be associated with the dense and hot portion of the WHIM (Werner et al. \u2013 3 \u2013 2008). However, the search for X-ray absorption of WHIM along random lines of sight turns out to be elusive. Early pioneering observations (Fang et al. 2001, 2002, S5 0836+710, PKS 2149-306, PKS 2155-304) gave the \ufb01rst O VII detection (O VIII for PKS 2155-304), which has not been convincingly con\ufb01rmed subsequently (Cagnoni et al. 2004; Williams et al. 2007; Fang et al. 2007). Mathur et al. (2003) performed a dedicated deep observation (470 ks) with the Chandra LETGS of the quasar H 1821+643, which has several con\ufb01rmed intervening O V I absorbers, but found no signi\ufb01cant (>> 2\u03c3) X-ray absorption lines at the redshifts of the O V I systems. Nicastro et al. (2005a,b) embarked on a campaign to observe Mrk 421 during its periodic X-ray outbursts with the Chandra LETGS with a total of more than 7 million continuum counts and presented evidence for the detection of two intervening absorption systems at z = 0.011 and z = 0.027. But the spectrum of the same source observed with the XMM-Newton RGS did not show these absorption lines (Rasmussen et al. 2007), despite higher signal-to-noise and comparable spectral resolution. Kaastra et al. (2006) and Yao et al. (2012) reanalyzed the Chandra LETGS data and were in agreement with Rasmussen et al. (2007). The detection of O VII lines may also be at odds with recent BLA measurements (Danforth et al. 2011), under simplistic assumptions about the nature of the absorbing medium. However, it has been argued that the reported XMM-Newton upper limits and the Chandra measurements may be consistent with one another, when taking into consideration certain instrumental characteristics of the XMM-Newton GRS (Williams et al. 2006). Moreover, an analysis of the two candidate X-ray absorbers at z = 0.011 and z = 0.027 yields intriguing evidence of two large-scale \ufb01laments at the respective redshifts, one of which has only 5 \u221210% probability of occurring by chance (Williams et al. 2010). Observations of 1ES 1028+511 at z = 0.361 by Steenbrugge et al. (2006) yield no convincing evidence for X-ray WHIM absorption. What is perceived to be more disconcerting is the lack of detection of O VII absorbers at the redshifts of detected O VI absorbers along some random lines of sight. This is because, overall, the O VII line is predicted to be the most abundant and anecdotal evidence suggests substantial coincidence between O VI and O VII (e.g., Cen & Fang 2006). A statistically signi\ufb01cant upper limit placed on the mean column density of O VII absorbers at the locations of a sizeable set of detected O VI absorbers using stacking techniques by Yao et al. (2009) prompts them to call into question the very existence of the high temperature (T \u2265106K) portion of the WHIM, although the limited sensitivity and spectral resolution of the current X-ray observations may render any such conclusions less than de\ufb01nite. Therefore, at this juncture, it is pressing to statistically address this lack of signi\ufb01cant coincidence between O VI and O VII absorbers and other issues theoretically, through higher resolution simulations that are necessary in order to well resolve the interfaces of multi-phase media. This is the primary purpose of this paper. We use two simulations of high resolution \u2013 4 \u2013 of 0.46h\u22121kpc and box size of 20\u221230h\u22121Mpc to perform much more detailed characterization of O VI and O VII lines to properly compare to extant observations. This high resolution is to be compared with 83h\u22121kpc resolution in our previous simulations (Cen & Ostriker 2006; Cen & Fang 2006), 25 \u221249h\u22121kpc resolution in Smith et al. (2011) and Shull et al. (2011), 1.25 \u22122.5h\u22121kpc in Oppenheimer et al. (2012) and 1.25 \u22122.5h\u22121kpc in Tepper-Garc\u00b4 \u0131a et al. (2011), resolves the Jeans scale of WHIM by 2-3 orders of magnitude and interfaces between gas phases of di\ufb00erent temperatures in a multi-phase medium. It is useful to distinguish, in the case of SPH simulations, between the gravity force resolution and the resolution of the hydrodynamics solver, with the latter being worse than the former by a factor of order a few. It is also useful to keep in mind the initial cell size or interparticle separation, because in both SPH and adaptive mesh re\ufb01nement (AMR) simulations not all regions are resolved by the maximum resolution. Calling this \u201cmean region resolution\u201d \u2206root, \u2206root = (117, 25\u221249, 125, 195)h\u22121kpc for [this paper, Smith et al. (2011), Oppenheimer et al. (2012), Tepper-Garc\u00b4 \u0131a et al. (2011)]. We note that a region of overdensity \u03b4 is approximately resolved at a resolution of C\u2206root\u03b4\u22121/3 (up to a pre-speci\ufb01ed highest resolution), where the pre-factor C is about unity for AMR simulations and \u223c2 for SPH simulations. Using Lagrangian SPH or AMR approaches becomes necessary for regions \u03b4 \u2265300, because simulations of a similar resolution with the uni-grid method become increasingly impractical (largely due to limitations of computer memory). A more important advantage with very high resolution simulations has to do with the need to resolve galaxies, which in turn allows for a more self- consistent treatment of the feedback processes from star formation, namely, the temporal and spatial distribution of metals and energy deposition rates to the CGM and IGM and their e\ufb00ects on subsequent star formation. Our new simulations, in agreement with earlier \ufb01ndings, rea\ufb03rm quantitatively the existence of WHIM and furthermore show that the properties of the WHIM with respect to O VI line and O VI-O VII relations are fully consistent with observations. In particular, the observed upper limit of the mean coincidental O VII column density of detected O VI absorbers is higher than what is predicted by the simulations by a factor of \u223c2.5 \u22124. Higher sensitivity X-ray observations or a larger sample by a factor of \u223c10 should test this prediction de\ufb01nitively. The outline of this paper is as follows. In \u00a72.1 we detail simulation parameters and hydrodynamics code, followed by a description of our method of making synthetic O VI and O VII spectra in \u00a72.2, which is followed by a description of how we average the two separate simulations C (cluster) and V (void) run in \u00a72.3. Results are presented in \u00a73. In \u00a73.1 we present some observables for O VI to compare to observations to provide additional validation of the simulations. In \u00a73.2 we dissect the simulations to provide a physical analysis of the O VI and O VII absorbers. In \u00a73.3 results on the coincidences between O VI and O VII lines are given. Conclusions are summarized in \u00a74. \u2013 5 \u2013"
                },
                {
                    "url": "http://arxiv.org/abs/1111.0707v1",
                    "title": "Inconsequence of Galaxy Major Mergers in Driving Star Formation at z>1: Insights from Cosmological Simulations",
                    "abstract": "Utilizing a high-resolution (114 pc/h) adaptive mesh-refinement cosmological\ngalaxy formation simulation of the standard cold dark matter model with a large\n(2000-3000 galaxies with stellar mass greater than 1e9 Msun) statistical\nsample, we examine the role of major mergers in driving star formation at z>1\nin a cosmological setting, after validating that some of the key properties of\nsimulated galaxies are in reasonable agreement with observations, including\nluminosity functions, SF history, effective sizes and damped Lyman alpha\nsystems. We find that major mergers have a relatively modest effect on star\nformation, in marked contrast to previous idealized merger simulations of disk\ngalaxies that show up to two orders of magnitude increase in star formation\nrate. At z=2.4-3.7, major mergers tend to increase the specific star formation\nrate by 10-25% for galaxies in the entire stellar mass range 10^9-10^12 Msun\nprobed. Their effect appears to increase with decreasing redshift, but is\ncapped at 60% at z=1.4-2.4. Two factors may account for this modest effect.\nFirst, SFR of galaxies not in major mergers are much higher at z>1 than local\ndisk galaxy counterparts. Second, most galaxies at z>1 have small sizes and\ncontain massive dense bulges, which suppress the merger induced structural\neffects and gas inflow enhancement. Various other predictions are also made\nthat will provide verifiable tests of the model.",
                    "authors": "Renyue Cen",
                    "published": "2011-11-03",
                    "updated": "2011-11-03",
                    "primary_cat": "astro-ph.CO",
                    "cats": [
                        "astro-ph.CO"
                    ],
                    "main_content": "2.1. Hydrocode and Simulation Parameters We perform cosmological simulations with the adaptive mesh refinement (AMR) Eulerian hydro code, Enzo (Bryan & Norman 1999; Joung et al. 2009). First we ran a low resolution simulation with a periodic box of 120 h\u22121Mpc on a side. We identified a region centered on a cluster of mass of \u223c2 \u00d7 1014 M\u2299at z = 0. We then resimulate with high resolution of the chosen region embedded in the outer 120h\u22121Mpc box to properly take into account large-scale tidal field and appropriate boundary conditions at the surface of the refined region. This simulation box is the same region as the \u201cC\u201d run in (Cen 2011b). The refined region for \u201cC\u201d run has a size of 21 \u00d7 24 \u00d7 20h\u22123Mpc3. The initial condition in the refined region has a mean interparticle-separation of 58h\u22121kpc comoving, dark matter particle mass of 1.3 \u00d7 107h\u22121 M\u2299. The refined region is surrounded by three layers (each of \u223c1h\u22121Mpc) of buffer zones with particle masses successively larger by a factor of 8 for each layer, which then connects with the outer root grid that has a dark matter particle mass 84 times that in the refined region. We choose the mesh refinement criterion such that the resolution is always better than 114h\u22121pc physical, corresponding to a maximum mesh refinement level of 13 at z = 0. The simulation includes a metagalactic UV background (Haardt & Madau 1996), and a model for shielding of UV radiation by neutral hydrogen (Cen et al. 2005). They also include metallicity-dependent radiative cooling (Cen et al. 1995). Our simulation also solves relevant gas chemistry chains for molecular hydrogen formation (Abel et al. 1997), molecular formation on dust grains (Joung et al. 2009) and metal cooling extended down to 10 K (Dalgarno & McCray 1972). Star particles are created in cells that satisfy a set of criteria for star formation proposed by Cen & Ostriker (1992). Each star particle is tagged with its initial mass, creation time, and metallicity; star particles typically have masses of \u223c106 M\u2299. Supernova feedback from star formation is modeled following Cen et al. (2005). Feedback energy and ejected metal-enriched mass are distributed into 27 local gas cells centered at the star particle in question, weighted by the specific volume of each cell, which is to mimic the physical process of supernova blastwave propagation that tends to channel energy, momentum and mass into the least dense regions (with the least resistance and cooling). We allow the entire feedback processes to be hydrodynamically coupled to surroundings and subject to relevant physical processes, such as cooling and heating. The total amount of explosion kinetic energy from Type II supernovae for an amount of star formed M\u2217with a Chabrier IMF is eSNM\u2217c2 (where c is the speed of light) with eSN = 6.6 \u00d7 10\u22126. Taking into account the contribution of prompt Type I supernovae, we use eSN = 1 \u00d7 10\u22125 in our simulation. Observations of local starburst galaxies indicate that nearly all of the star formation produced kinetic energy is used to power galactic superwinds (e.g., Heckman 2001). \u2013 4 \u2013 Supernova feedback is important primarily for regulating star formation and for transporting energy and metals into the intergalactic medium. The extremely inhomogeneous metal enrichment process demands that both metals and energy (and momentum) are correctly modeled so that they are transported in a physically sound (albeit still approximate at the current resolution) way. The kinematic properties traced by unsaturated metal lines in DLAs are extremely tough tests of the model, which is shown to agree well with observations (Cen 2010). As we will show below, the properties of galaxies produced in the simulation resemble well observed galaxies, within the limitations of \ufb01nite resolution. We use the following cosmological parameters that are consistent with the WMAP7normalized (Komatsu et al. 2010) LCDM model: \u2126M = 0.28, \u2126b = 0.046, \u2126\u039b = 0.72, \u03c38 = 0.82, H0 = 100hkms\u22121Mpc\u22121 = 70kms\u22121Mpc\u22121 and n = 0.96. 2.2. Simulated Galaxy Catalogs We identify galaxies in our high resolution simulation using the HOP algorithm (Eisenstein & Hu 1999), operated on the stellar particles, which is tested to be robust and insensitive to speci\ufb01c choices of concerned parameters within reasonable ranges. Satellites within a galaxy are clearly identi\ufb01ed separately. The luminosity of each stellar particle at each of the Sloan Digital Sky Survey (SDSS) \ufb01ve bands is computed using the GISSEL stellar synthesis code (Bruzual & Charlot 2003), by supplying the formation time, metallicity and stellar particle mass. Collecting luminosity and other quantities of member stellar particles, gas cells and dark matter particles yields the following physical parameters for each galaxy: position, velocity, total mass, stellar mass, gas mass, mean formation time, mean stellar metallicity, mean gas metallicity, star formation rate, luminosities in \ufb01ve SDSS bands (and various colors) and others. We create catalogs of galaxies from z = 1.4 to z = 3.7 with an increment of \u2206z = 0.05. We track the merger history of each galaxy in this redshift span. There are two di\ufb00erent ways to de\ufb01ne major mergers. First, a theoretical one where we identify the merger time as that when two galaxies with a stellar mass ratio greater than 1/3 are fully integrated into one with no identi\ufb01able separate stellar peaks. Second, an observational one where a major merger is de\ufb01ned to be that where a galaxy has a neighbor galaxy with a stellar mass greater than 1/3 its mass at a lateral distance smaller than 40kpc proper. Both will be used in subsequent analysis. It is useful to state that the observationally-oriented de\ufb01nition does not always lead to a true merger of the usual sense, because either the two galaxies are a projected pair, or their merging time scale is much longer than the relevant dynamic time or the time before something else will have happened to the two concerned galaxies. Some informative comparisons or distinctions between the two will be made, when useful. We \ufb01nd that there are about 2000-3000 galaxies with stellar mass greater than 109 M\u2299maximally resolved at \u2013 5 \u2013 better than 114h\u22121pc at each redshift snapshot in the range z = 1.4 \u22123.7, providing us with unprecedented statistical power. In Cen (2011b) we show that galaxy luminosity functions for both UV and FIR selected galaxies can be self-consistently produced by the simulation. This, in combination with other, independent tests of the simulation, including the properties of the damped Lyman alpha systems (Cen 2010), strongly indicates a range of applicability of our simulation to complex systems, including galaxies at sub-kpc ISM scales. This validation of the simulation results is critical and allows us, with signi\ufb01cant con\ufb01dence, to perform the particular analysis here with respect to e\ufb00ects of major mergers. 3. Results 9 9.5 10 10.5 11 11.5 12 12.5 0 0.5 1 1.5 2 2.5 3 log SFR (Msun/yr)     not MM; z=1.40 \u2212 2.40 9 9.5 10 10.5 11 11.5 12 12.5 0 0.5 1 1.5 2 2.5 3     not MM; z=2.40 \u2212 3.70 9 9.5 10 10.5 11 11.5 12 12.5 0 0.5 1 1.5 2 2.5 3 log SFR (Msun/yr) log Mstellar (Msun)     MM; z=1.40\u22122.70 9 9.5 10 10.5 11 11.5 12 12.5 0 0.5 1 1.5 2 2.5 3 log Mstellar (Msun)     MM; z=2.40\u22123.70 Fig. 1.\u2014 places each galaxy as a plus symbol in the SFR-stellar mass plane for non major merger galaxies in the redshift range z = 1.4\u22122.4 (top left panel) and z = 2.4\u22123.7 (top right panel). The corresponding ones for galaxies with major mergers are shown in the bottom panels. Here we adopt the observationally oriented de\ufb01nition of major mergers, i.e., pairs of stellar mass ratio greater than 1/3 and projected separation less than 40kpc. Only a small percentage of randomly selected galaxies is shown. Figure 1 shows scatter plots between SFR and stellar mass for galaxies that do not have ongoing major mergers (top two panels), compared to those that are ongoing major mergers (bottom two panels). Under visual inspection we see that there is no major discernible di\ufb00erence between galaxies that do and do not experience major mergers in the redshift \u2013 6 \u2013 range examined for the entire range of stellar mass or SFR. It is noticeable that the number of galaxies that are major mergers is a minor fraction of all galaxies at any stellar mass or SFR. 9 10 11 12 0 0.1 0.2 0.3 0.4 log Mstar (Msun) fraction with apparent major mergers     z=1.4\u22122.4 statistical errors 9 10 11 12 0 0.1 0.2 0.3 0.4 log Mstar (Msun)     z=2.4\u22123.7 statistical errors Fig. 2.\u2014 shows the fraction of galaxies that are in major merger as a function of stellar mass (red histograms) at z = 1.4 \u22122.4 (left panel) and z = 2.4 \u22123.7 (right panel). The statistical errors are shown as green histograms. We use the observationally oriented de\ufb01nition of major mergers, i.e., pairs of stellar mass ratio greater than 1/3 and projected separation less than 40kpc. Figure 2 shows the fraction of galaxies that are in major merger as a function of stellar mass with the observational de\ufb01nition. We note that the major merger fraction at the low steller mass (< 1011 M\u2299) is substantially overestimated due to the adopted de\ufb01nition, because many satellite galaxies within the virial radius of large galaxies are \u201cmis-identi\ufb01ed\u201d as major mergers in this case. In fact, many of these satellite galaxies do not ever merge with one another directly in a binary fashion, as will be shown below in Figure 3. The fraction of major mergers at the high stellar mass end does not signi\ufb01cantly su\ufb00er from this \u201cprojection\u201d e\ufb00ect. We see that for galaxies with stellar mass in the range 1011 \u22121012 M\u2299 major merger galaxies make up about 10 \u221220% of all galaxies in that mass range. The results on major merger fractions shown in Figure 2 (and Figure 4 below) are based on the observational de\ufb01nition of major mergers. It is useful to distinguish that from the theoretical one, where the latter is based on the actual merger events rather than pairs within some projected distance. Figure 3 shows the theoretical merger rate, de\ufb01ned to be the number of major mergers per unit redshift, as a function of galaxy stellar mass for galaxies \u2013 7 \u2013 10 11 12 \u22122 \u22121.5 \u22121 \u22120.5 0 log Mstar (Msun) log # of major merger per unit redshift     z=1.4 \u2212 2.4 z=2.4 \u2212 3.7 polynomial fit Fig. 3.\u2014 shows the merger rate (=number of major mergers per unit redshift) as a function of galaxy stellar mass for galaxies at z = 1.4 (red dots) and z = 2.4 (green squares). Here a merger is more physically based de\ufb01nition, an event where two galaxies of the stellar mass ratio greater than 1/3 physically merge. at z = 1.4 (red dots) and z = 2.4 (green squares), respectively. We see that the actual merger rate is roughly constant at \u223c0.3 \u22120.5 per unit redshift for the stellar mass range Mstar = 1010.5 \u22121012 M\u2299. At Mstar > 1012 M\u2299there is hint for a signi\ufb01cant upturn in merger rate, albeit with less statistical certainty due to a small number of such massive galaxies in the simulation. Nevertheless, such an upturn would be consistent with the expectation that the central cD galaxies may experience more major mergers due to dynamical inspiral of satellites. This is also consistent with the apparent di\ufb00erence seen in Figure 3 between galaxies at z = 1.4 \u22122.4 (red) and galaxies at z = 2.4 \u22123.7 (green) in that the upturn is absent in the higher redshift range, because of the absence of large galaxies at that redshift range in the given simulation box. If the simulation box were large enough to contain cD-like galaxies at that higher-redshift range, we expect to see the same upturn. The downturn at Mstar < 1010.5 M\u2299of the merger rate is still more dramatic. We see a decrease of merger rate by a factor of \u223c10 from Mstar = 1010.5 M\u2299to Mstar = 109.5 M\u2299. This should be compared to about a factor of 1.2\u22121.7 drop seen in Figure 2 across the mass range. This shows that the vast majority of galaxies of mass Mstar \u22641010 M\u2299that are seen in close proximity (< 40 kpc) with other galaxies of comparable masses are in fact do not end up in binary major mergers. In Cen (2011b) we show that the simulation reproduces observed luminosity functions in the concerned redshift range, indicating that the simulation is \u201ccomplete\u201d down to about a galaxy stellar mass of \u223c109 M\u2299. Thus, the results for the range of galaxy stellar mass shown here is reliable. A plausible physical explanation for the sharp downturn at the low mass end may be that most satellite galaxies just zoom around \u2013 8 \u2013 and never merge with their fellow satellite galaxies rather they dynamically spiral in to merge with the primary galaxy or remain as satellites. A more detailed study focused on the demographics of mass accretion, including mergers, will be presented elsewhere. Here we present a third-order polynomial \ufb01t to the major merger rate, R, de\ufb01ned to be the number of major mergers per unit redshift: log R = 0.34(log Mstar \u221211)3 \u22120.21(log Mstar \u221211)2 \u22120.013(log Mstar \u221211) \u22120.33, (1) shown as the solid black curve in Figure 3, where Mstar is in solar masses. 0 0.5 1 1.5 2 2.5 3 0 0.1 0.2 0.3 0.4 log SFR (Msun yr\u22121) fraction with apparent major mergers     z=1.4\u22122.4 statistical errors 0 0.5 1 1.5 2 2.5 3 0 0.1 0.2 0.3 0.4 log SFR (Msun yr\u22121)     z=2.4\u22123.7 statistical errors Fig. 4.\u2014 shows the fraction of galaxies that are in major merger as a function of SFR (red histograms) at z = 1.4\u22122.4 (left panel) and z = 2.4\u22123.7 (right panel). The statistical errors are shown as green histograms. We use the observationally oriented de\ufb01nition of major mergers, i.e., pairs of stellar mass ratio greater than 1/3 and projected separation less than 40kpc. Figure 4 shows the fraction of galaxies that are in major merger as a function of SFR. Similar to Figure 2, the actual major merger fraction at the low SFR end shown is overestimated, given the observational de\ufb01nition used. The major merger rate at the high SFR end, at SFR\u2265200 M\u2299yr\u22121, is less a\ufb00ected and the simulation shows that one should expect to see 10 \u221240% of these high SFR galaxies to be in apparent major mergers. This fraction is consistent with the observed upper bound of 57% (8/14) for the submillimeter galaxy (SMGs) sample of Tacconi et al. (2006) at z = 2 \u22123.4 that show a double-peaked pro\ufb01le in the CO 3-2/4-3 emission. Of this observed fraction of SMGs in major mergers, a fraction of it may be due to orbital motion of emitting gas in a disk con\ufb01guration or some other con\ufb01gurations instead of major mergers. We predict that, when high spatial resolution become available with the upcoming ALMA mission, the fraction due to major mergers should be in the range 10 \u221240%, if our model is correct. For star-forming galaxies of SFR\u2264200 M\u2299yr\u22121 \u2013 9 \u2013 at z = 1.4 \u22123.7, we also predict that the major merger fraction should fall in the range of 15 \u221235%. Recall that here we use the observationally oriented de\ufb01nition of major mergers, i.e., pairs of stellar mass ratio greater than 1/3 and projected separation less than 40kpc. To provide further tests of our model predictions, Figure 5 shows the probability distribution functions (PDFs) of the projected separation (rp) of major mergers at z = 1.4 \u22122.4 (top panels) and z = 2.4 \u22123.7 (bottom panels) for two subgroups of galaxies of SFR= 10 \u2212100 M\u2299yr\u22121 (left panels) and SFR> 100 M\u2299yr\u22121 (right panels), respectively. We \ufb01nd that the PDFs are reasonably \ufb01t with a single cored powerlaw of the following form: PDF(rp)drp \u221d(rc + rp)\u22123/4drp, (2) where the projected separation rp and core size rc are in physical kpc. The black curves shown in Figure 5 have rc = 1, although it is not stringently constrained. The simple powerlaw \ufb01ts are quite good, in contrast to gaussian or exponential forms that are found to provide poor \ufb01ts. The found slope of \u22123/4 in the PDF suggests that the three-dimensional distribution around each star-forming galaxy of other galaxies of comparable SFR approximately follows a powerlaw of a slope of \u22122.75. Details of this and other related clustering issues of galaxies will be presented elsewhere. 0 5 10 20 30 40 0 100 200 rp (kpc) PDF     SFR=10\u2212100 Msun/yr @z=1.4\u22122.4 statistical errors fit: PDF(rp)=1/(1+rp)3/4 0 5 10 20 30 40 0 5 10 15 20 rp (kpc) PDF     SFR>100 Msun/yr @z=1.4\u22122.4 statistical errors fit: PDF(rp)=1/(1+rp)3/4 0 5 10 20 30 40 0 100 200 300 400 500 rp (kpc) PDF     SFR=10\u2212100 Msun/yr @z=2.4\u22123.7 statistical errors fit: PDF(rp)=1/(1+rp)3/4 0 5 10 20 30 40 0 5 10 15 rp (kpc) PDF     SFR>100 Msun/yr @z=2.4\u22123.7 statistical errors fit: PDF(rp)=1/(1+rp)3/4 Fig. 5.\u2014 shows the probability distribution functions (PDF) of the projected separation (rp) of major mergers at z = 1.4 \u22122.4 (two upper panels) and z = 2.4 \u22123.7 (two bottom panels), respectively. The left panels are for star-forming galaxies of SFR= 10\u2212100 M\u2299yr\u22121 and the right panels for star-forming galaxies of SFR> 100 M\u2299yr\u22121. The red histograms are the PDFs and the green histograms the statistical errors at each bin. The black curves show a power \ufb01t described by Eq 2. The top panel of Figure 6 shows the meean SFR as a function of galaxy stellar mass, separately, for galaxies that are in major mergers and galaxies that are not in major mergers. \u2013 10 \u2013 9 10 11 12 0 1 2 3 log Mstar (Msun) log SFR (Msun yr\u22121)     non MM, z=1.4\u22122.4 MM, z=1.4\u22122.4 non MM, z=2.4\u22123.7 MM, z=2.4\u22123.7 non MM, z=1.4\u22122.4 fit MM, z=1.4\u22122.4 fit non MM, z=2.4\u22123.7 fit MM, z=2.4\u22123.7 fit 9 10 11 12 \u221210 0 10 20 30 40 50 60 70 log Mstar (Msun) % boost in SFR by MM     z=1.4\u22122.4 z=2.4\u22123.7 Fig. 6.\u2014 Top panel: the mean SFR of galaxies at a given stellar mass for galaxies that are in major mergers (red solid dots) and not in major mergers (red open dots) at z = 1.4 \u22122.4. The corresponding ones at z = 2.4 \u22123.7 are shown in green squares. The errorbars show the dispersion around the mean. The thin and thick dashed curves are the best second-order polynomial \ufb01ts to the non major mergers and major mergers, respectively, at z = 1.4 \u22122.4. The thin and thick solid curves are the best second-order polynomial \ufb01ts to the non major mergers and major mergers, respectively, at z = 2.4 \u22123.7. We use the observationally oriented de\ufb01nition of major mergers, i.e., pairs of stellar mass ratio greater than 1/3 and separation less than 40kpc. Bottom panel: the ratio of \ufb01tted curves to the major merger and non-major-merger minus one for z = 1.4 \u22122.4 (red solid curve) and z = 2.4 \u22123.7 (green dashed curve), respectively. Visually the ratio of the \ufb01tted curves and the actual computed data points display comparable amplitudes. The ratio of \ufb01tted curves for the galaxies with major mergers and those without major mergers minus one are shown in the bottom panel for z = 1.4 \u22122.4 (red solid curve) and z = 2.4 \u22123.7 (green dashed curve). We see that major mergers appear to experience very modest boost in SFR for galaxies at z = 2.4\u22123.7, at about 10\u221225% for the entire stellar mass range Mstar = 109 \u22121012 M\u2299probed. The overall strength of the boost due to major mergers appear to increase with decreasing redshift, when one compares the values at z = 1.4 \u22122.4 to those at z = 2.4 \u22123.7, but remains at less than 60% across the entire mass range. It also appears that there may be a trend of a relatively larger boost of SFR due to major mergers for lower mass galaxies than for larger mass galaxies at z = 1.4 \u22122.4. But we caution that the results in the bottom panel are somewhat sensitive to the exact \ufb01ts; given that the \ufb01ts do not exactly reproduce all the data points, one should be careful to not take the exact curves of the \ufb01ts too literally. In any case, it is abundantly clear that we do not see very large increase in SFR of a factor of two orders of magnitude that are found in simulations of isolated major gas-rich spiral galaxy mergers (e.g., Mihos & Hernquist 1996). In Figure 6 the modest boost in SFR due to major mergers is computed using the \u2013 11 \u2013 \u22120.5 \u22120.4 \u22120.3 \u22120.2 \u22120.1 0 0.1 0.2 0.3 0.4 0.5 0 1 2 3 \u2206 z log SFR (Msun/yr)     SFR=1\u22123.2; z=2.4\u22123.7 SFR=3.2\u221210; z=2.4\u22123.7 SFR=10\u221232; z=2.4\u22123.7 SFR=32\u2212100; z=2.4\u22123.7 SFR=100\u2212320; z=2.4\u22123.7 SFR=1\u22123.2; z=1.4\u22122.4 SFR=3.2\u221210; z=1.4\u22122.4 SFR=10\u221232; z=1.4\u22122.4 SFR=32\u2212100; z=1.4\u22122.4 SFR=100\u2212320; z=1.4\u22122.4 Fig. 7.\u2014 shows the history of the mean SFR as a function of time redshift \u2206z for \ufb01ve di\ufb00erent subsets of galaxies with SFR at \u2206z = 0.05 (i.e., prior to the merger event) equal to 1 \u22123.2, 3.2 \u221210, 10 \u221232 and 32 \u2212100, 100 \u2212320 M\u2299yr\u22121, respectively, separately for galaxies in the redshift range z = 1.4 \u22122.4 and z = 2.4 \u22123.7. Dispersions on the means are shown as well. observationally oriented de\ufb01nition of major mergers, i.e., pairs of stellar mass ratio greater than 1/3 and projected separation less than 40kpc. We now compute a similar quantity using the theoretical de\ufb01nition of major mergers where we identify the merger time as that when two galaxies are fully integrated into one with no identi\ufb01able separate stellar peaks. We follow the history of each galaxy and \u201cstack\u201d all major merger events centered at \u2206z = 0. Figure 7 shows the mean SFR history for galaxies at \ufb01ve given ranges of SFR, measured at \u2206z = 0.05 (using a di\ufb00erent redshift, say, \u2206z = 0.10 or 0.15, makes no material di\ufb00erence in the results). In a fashion that is consistent with the \ufb01ndings shown in Figure 6, we do not \ufb01nd any dramatic boost of SFR at the merger redshift and at |\u2206z| \u22640.5 for galaxies at SFR\u2264100 M\u2299yr\u22121 in the redshift range z = 1.4 \u22123.7. The 1\u03c3 dispersion about the mean is about 1.5 \u22123, roughly consistent with the range of SFR for each subset at \u2206z = 0.05, \u2013 12 \u2013 with a tendency that the dispersion is larger for lower SFR subsets. For the subset with the largest SFR (\u2265100 M\u2299yr\u22121), however, there is a visually noticeable jump in SFR by a factor of \u223c2 \u22125 from \u2206z > 0.2 to \u2206z < 0.2, hinting an intriguing possibility that a major merger event, not necessarily the \ufb01nal major merger moment, serves to \u201ctrigger\u201d a very high SFR event. In other words, it suggests that some very high SFR galaxies, such as ULIRGs or SMGs, may be initially triggered by some major merger events. At the same time results in Figure 7 also suggest that the very high SFR (\u2265100 M\u2299yr\u22121) galaxies remain at the elevated and upward trend for SFR following the merger event for a long period of time (\u2206z \u223c1) that is much longer than the typical merger time scale. This has profound implications for the nature of ULIRGs and SMGs that will be addressed elsewhere. 4. Physical Explanation of the Results Both external gravitational and internal gravitational and hydrodynamic torques may drive gas inward. Externally, the tidal \ufb01eld from a companion during a galaxy merger, major or minor, gives rise to a non-axisymmetric gravitational potential. This induces a response of the disk material (Toomre & Toomre 1972), in particular its cold gas, stronger for prograde mergers. More broadly, tidal \ufb01elds from interacting galaxies, which are not necessarily merging with one another, may drive gas inward. Internally, non-axisymmetric gravitational potentials, notably those sustained by stellar bars that are produced by secular evolution of su\ufb03ciently cold stellar disks under certain conditions or from other interactions, such as mergers, can also drive gas inward. A thorough study of torques due to gravitational and hydrodynamic processes to isolate the primary physical mechanisms governing the gas in\ufb02ows in a cosmological setting will be performed in a larger study. Here we provide some physical insight for the results found, relying mainly on circumstantial but strong evidence. Anecdotal evidence and visual examination of some galaxies suggest that chaotic gas in\ufb02ows often result in mis-alignments of newly formed stellar disks with previous stellar disk/non-spherical bulges, and the orbital planes of infalling satellite stellar or gas clumps do not always have a \ufb01xed orientation. These processes cumulatively may be thought to create stellar distributions in the central regions that are dynamically hot, which, in turn, provides conditions that are unfavorable to secular formation of stellar bars. We check if this indeed is the case. The left panel of Figure 8 shows axial ratios c/b versus b/a, where c < b < a are the semi-axes of an ellipsoid approximating the stellar distribution within re for galaxies with SFR \u226510 M\u2299yr\u22121 with major mergers (solid dots) and without (open circles) at z = 2. We see that the stellar distribution within re typically resembles an oblate spheroid with the half-height approximately equal to one half of that of the disk radius or more. For such hot stellar systems no barlike equilibria exist and no strong stellar bars would form \u2013 13 \u2013 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 b/a(stars) c/b(stars)     C S B B B B B B B B B B B B B B B B F MM, z=2 non MM, z=2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 b/a(SFR) c/b(SFR5) Fig. 8.\u2014 Left panel: shows axial ratios c/b versus b/a, where c < b < a are the semi-axes of an ellipsoid approximating the stellar distribution within re for galaxies with SFR \u226510 M\u2299yr\u22121 with major mergers (solid dots) and those without (open circles) at z = 2. The symbol size in both panels is linearly proportional to the logrithm of its SFR. Several special locations are indicated by special letters: \u201cB\u201d for thin bars of various thickness, \u201cS\u201d for sphere, \u201cC\u201d for \ufb02at circular disk and \u201cF\u201d for American football. Right panel: shows the same but for SFR density distribution within the radius of 50% SFR. secularly (e.g., Ostriker & Peebles 1973). Indeed, we do not \ufb01nd any instance of thin stellar bars that would occupy locations near the left y-axis; the one instance seen is in fact a close merging pair, which, when approximated as an ellipsoid by our code, shows up as a thin bar. The right panel of Figure 8 shows the same for SFR density, which shows that ongoing star formation in the central region for the majority of galaxies at z \u22651 takes place on a relatively thin disk of typical height-to-radius ratio of 0.1 \u22120.3, with some ratios reaching as low as 0.03, approaching our resolution limit of \u223c100pc. It is clear, however, the relatively thick stellar bulges seen in the left panel of Figure 8 are very well resolved and little a\ufb00ected by resolution e\ufb00ects. The number of stellar particles within re for mass in the range 109 \u22121012 M\u2299are typically N \u223c103.5 \u2212106.5 and the two-body relaxation time is roughly tr \u2248(N/50)tc (e.g., Steinmetz & White 1997), where tc is the orbital period at re. For a galaxy with Mstar = 1010 M\u2299(N \u223c104.2 within re) and re \u223c0.5kpc (see Figure 11 below) the relaxation heating time is estimated to be \u223c1 \u00d7 1010yr. A typical galaxy with Mstar = 1010 M\u2299corresponds to SFR \u223c10 M\u2299/yr at the relevant redshift range. Thus, we expect the two-body relaxation heating to be completely negligible for galaxies with SFR \u226510 M\u2299/yr. This shows that the dynamically hot state of the central stellar bulges of the simulated galaxies is unlikely caused by numerical e\ufb00ects. In the left panel of Figure 8 we do not see signi\ufb01cant di\ufb00erence between galaxies with major mergers and those without, indicating that major mergers do not appear to enhance formation of structures that resemble bars; this issue will be further examined below. In the absence of strong stellar bars, can signi\ufb01cant gas in\ufb02ows still exist? Figure 9 shows the gas depletion time in central regions at r < 1kpc (left panel) and over the entire galaxy within the virial radius (right panel) for all galaxies with SFR \u226510 M\u2299yr\u22121. The right panel indicates that the gas depletion time over the entire galaxy is longer than its \u2013 14 \u2013 9 10 11 12 5 6 7 8 9 10 log Mstar (Msun) log gas depletion time (r<1kpc)     MM with rp<3kpc, z=2 MM with rp>3kpc, z=2 non MM, z=2 9 10 11 12 5 6 7 8 9 10 log Mstar (Msun) log gas depletion time (r<rv)     MM with rp<3kpc, z=2 MM with rp>3kpc, z=2 non MM, z=2 depletion time equal to tH depletion time equal to tdyn at rv Fig. 9.\u2014 Left panel: gas depletion time within the central 1kpc region of galaxies at z = 2 with SFR \u2265 10 M\u2299yr\u22121. Three types of galaxies are shown using di\ufb00erent symbols: galaxies that are not undergoing major mergers are open circles, galaxies in major mergers with projected separation between the two galaxies less than 3kpc as squares and greater than 3kpc as triangles. Right panel: gas depletion time over the entire galaxy within the virial radius. The symbol size is linearly proportional to the logrithm of SFR. The thin and thick horizontal lines correspond to the Hubble time and dynamical time at virial radius at z = 2, respectively. Here the observational de\ufb01nition of major mergers is used. dynamic time and comparable to the Hubble time. The gas depletion time in the central 1kpc region, however, is shorter at \u2264100Myrs. The gas depletion time in the central region spans a wide range, 0.1 \u2212100Myrs, and there is no discernible di\ufb00erence between galaxies in major mergers (solid symbols) and those that are not (open symbols). Furthermore, there is no visible dependence of the depletion time in the central region on the separation of the two merging galaxies for those that are in major mergers. Examination of SF histories of individual galaxies indicate that the SFR are relatively steady and their durations are on the order of Hubble time, i.e., much longer than the gas depletion time scales of the central regions but comparable to the gas depletion time scales within the virial radii shown in Figure 9 (Figure 6 shows that for galaxies with mergers within \u2206z = 0.5). This suggests that, irrespective of being in major mergers or not, gas in\ufb02ows to the central regions appear to be ubiquitous; in other words, galaxies that are not in major mergers appear to be able to channel a su\ufb03cient amount of gas to fuel the star formation on time scales that are much longer than the gas depletion times in the central regions. The disparity in the gas depletion time scales of the central regions and between those and the overall star formation durations strongly imply that gas in\ufb02ows, in general, are not smooth but in the form of clumps falling \u2013 15 \u2013 9 10 11 12 \u22122 \u22121 0 1 log Mstar (Msun) [Z/H] (gas) (<1kpc)     MM with rp<3kpc, z=2 MM with rp>3kpc, z=2 non MM, z=2 \u22120.5 0 0.5 \u22122 \u22121 0 1 [Z/H] (gas) (<3kpc) [Z/H] (gas) (<1kpc)     MM with rp<3kpc, z=2 MM with rp>3kpc, z=2 non MM, z=2 Z(<1kpc)=Z(<3kpc) Fig. 10.\u2014 Left panel: the mean gas metallicity within the central 1kpc region as a function of galaxy stellar mass for galaxies with SFR \u226510 M\u2299yr\u22121. Three types of galaxies are shown using di\ufb00erent symbols: galaxies that are not undergoing major mergers are open circles, galaxies in major mergers with projected separation between the two galaxies less than 3kpc as squares and greater than 3kpc as triangles. Right panel: the mean gas metallicity within the central 1kpc region as a function of the mean gas metallicity within the central 3kpc region galaxy stellar mass for galaxies with SFR \u226510 M\u2299yr\u22121. The symbol size in both panels is linearly proportional to the logrithm of its SFR. in intermittently. To further demonstrate that gas in\ufb02ows towards the central regions are generally not caused by central non-spherical gravitational perturbations, the left panel of Figure 10 shows the mean gas metallicity in the central 1kpc region and the right panel shows the mean gas metallicity in the central 1kpc region as a function of the mean gas metallicity in the central 3kpc region, comparing galaxies with and without major mergers. From both panels we see that there is no visible di\ufb00erence in the metallicity of gas in the central regions between galaxies that are in major mergers and those that are not. It is seen that there is a relatively large span of mean gas metallicity in the central 1kpc region, from \u223c\u22121.5 to \u223c0.5 for both types of galaxies, while the range shrinks to about \u22120.5 to 0.5 within 3kpc for both types of galaxies. If non-spherical gravitational perturbations in the central regions were responsible for driving gas inward, they would be most e\ufb00ective for the gas in the immediate neighborhood. Consequently, if the central 1kpc region were just fed by gas driven inward from the immediate surroundings by internal non-spherical gravitational perturbations within, one would expect to see a higher gas metallicity in the central 1kpc than in the central 3kpc, since star formation rate is super-linear on gas density (the SchmidtKennicutt law) hence SFR density stronger in the 1kpc central region than in the 3kpc central region per unit gas. This expectation is not universally borne out for all galaxies in the simulation; on the contrary, the majority of galaxies lie below the Z(< 1kpc) = Z(< 3kpc) line, and there exists low mean metallicity (Z < \u22120.5) gas in the central 1kpc that is not seen in the mean metallicity within the central 3kpc. This is unambiguous evidence that a \u2013 16 \u2013 signi\ufb01cant amount of gas in\ufb02ow is directly \u201cparachuted in\u201d (e.g., dynamical friction inspiral of gas clumps with or without dark matter halos, or infalling satellites on nearly radial orbits) or \u201cchannelled in\u201d (e.g., clumpy cold streams) from large scales, not smooth gas from regions that immediately surround it, at least for a large fraction of galaxies. This is consistent with the implied intermittency of fueling seen in Figure 9. In any event, the results indicate that major mergers do not appear to form a distinct set of galaxies with respective to gas metallicity in the central regions. 10 10 10 11 10 12 0.1 0.2 0.3 0.5 1 2 3 5 7 10 Mstar (Msun) re (kpc)     MM, z=2.0 non MM, z=2.0 obs z=1.5\u22122.5 (Buitrago et al 2008) 10 10 10 11 10 12 50 70 100 200 300 500 700 1000 Mstar (Msun) me (km/s)     MM, z=2.0 non MM, z=2.0 van Dokkum et al 2009, z=2.2 van de Sande et al 2011, z=1.8 Cappellari et al 2009, z~1.7 Onodera et al 2010, z=1.8 Fig. 11.\u2014 Left panel: the e\ufb00ective radii of galaxies in restframe V band (observed H band) versus the stellar masses for galaxies with major mergers (solid dots) and those without (open circles) at z = 2. Also shown as solid diamonds are the observations of Buitrago et al. (2008) for the subset of galaxies at z = 1.5 \u22122.5 observed in H band. The symbol size in the left panel is linearly proportional to the logrithm of SFR. Right panel: the relation between velocity dispersion (y axis) and dynamical mass (x axis) at re. The black diamond, star, square and triangle symbols with cross errorbars are the observational data for galaxies in the range range z = 17 \u22122.2 from van Dokkum et al. (2009), van de Sande et al. (2011), Cappellari et al. (2009) and Onodera et al. (2010), respectively. The symbol size in the right panel is linearly proportional to the SFR. Mihos & Hernquist (1996) show that galaxy structure plays a dominant role in regulating gas in\ufb02ows, which they \ufb01nd are generally driven by gravitational torques from the host galaxy, rather than the companion, in their major merger simulations. The lack of any signi\ufb01cant merger induced e\ufb00ects appear at odds with their simulations at \ufb01rst instance. We attribute the di\ufb00erence primarily to the di\ufb00erence in the physical properties of galaxies between merger simulations and those in present cosmological simulation at z > 1. Speci\ufb01cally, as we will show shortly, most of galaxies in our simulation appear to have massive stellar bulges, whereas merger simulations with dramatic in\ufb02ows seen during mergers start with pre-merger disk galaxies without massive stellar bulges. In fact, a subset of simulations by Mihos & Hernquist (1996) where the per-merger galaxies have massive stellar bulges has already provided insight for the above apparent discrepancy: they note that dense bulges act to \u2013 17 \u2013 stabilize galaxies against bar modes and have much diminished in\ufb02ow enhancement. In the left panel of Figure 11 we show the e\ufb00ective stellar radii in restframe V band of galaxies with SFR \u226510 M\u2299yr\u22121 at z = 2, compared to observed galaxies also in restframe V band (observed H band). We see that the e\ufb00ective radii of most simulated galaxies at z = 2 are in the range of 0.5 \u22122kpc for galaxies of stellar mass \u22651011 M\u2299, consistent with previous results (Joung et al. 2009; Naab et al. 2009), and are in reasonable agreement with observations. No dust obscuration is applied in the calculation so the computed radii are likely lower limits; if we had taken dust obscuration into account, we expect the agreement would still be better. The right panel of Figure 11 shows the 1-d velocity dispersion at the e\ufb00ective stellar radius as a a function of stellar mass and we \ufb01nd that within the uncertainties the simulation results are in agreement with the observations, indicative of a self-consistency of the simulation results. The observed high value of central velocity dispersion (van Dokkum et al. 2009) was somewhat surprising initially based on an extrapolation of local elliptical galaxy properties, but now that additional observations have con\ufb01rmed the earlier discovery and our simulations indicate that this is in fact in line with the theoretical expectation based on the cold dark matter model. There is one exception (Onodera et al. 2010) that shows a lower central velocity dispersion; our current statistics are insu\ufb03cient to gauge this against our model one way or another. Although the simulation results and observations are statistically consistent with one another, enlarging both the simulation size and observed galaxy sample size may provide very useful constraints on physical processes that govern the formation of the bulges. If pressed, one might incline to conclude that there is a slight hint that the simulated galaxies are slightly smaller than the handful of observed galaxies, although the observed ones overlap and are statistically consistent with the simulated range in terms of velocity dispersion at a \ufb01xed stellar mass. Nonetheless, three e\ufb00ects may have caused slight overestimation of the velocity dispersions of simulated galaxies. First, no dust obscuration e\ufb00ect is taken into account. Second, no observational beam smearing e\ufb00ect is taken into account. Third, the simulated galaxies at a \ufb01xed stellar mass have a range in SFR, whereas the observed galaxies shown are thought to be quiescent; one might think that gas loss from aging or dying stars acts in the direction of enlarging stellar cores with aging stellar population due to adiabatic expansion related to mass loss that is known to be substantial. To be prudent and conservative, we have purposely plotted the symbol size in the right panel of Figure 11 to be linearly proportional to the SFR to see if there is noticeable trend in SFR with core size/velocity dispersion. We see one case, the green solid dot at (1.3 \u00d7 1011 M\u2299,150km/s), that has a SFR that may be a factor of a few higher than typical galaxies at around that mass. However, we also see galaxies to have higher SFR even though having much higher velocity dispersions, with or without major mergers. In any case, it appears that some of the noticeably high SFR galaxies are consistent with being randomly distributed with respect to \u03c3e. Thus, we conclude that there is no dramatic trend of SFR with \u2013 18 \u2013 respect to \u03c3e at a \ufb01xed stellar mass in the range of \u03c3e that overlaps with observed values, save the one noted exceptions that is presently di\ufb03cult to gauge statistically. This check suggests that our results are not hinged on our modeling of the size of the central stellar bulges being perfectly correct and are thus robust to possible small variations. Taking the evidence presented in the preceding four \ufb01gures together a consistent physical picture emerges: \u2022 Gravitational or hydrodynamic torques stemming from scales larger than the central regions containing most of the stars in the primary galaxy may play a fundamental role in transporting the necessary amount of gas to fuel the star formation in the central regions. \u2022 A large portion of often metal-poor gas from large scales is directly transported into the central regions, possibly in the form of dynamical friction inspiraling gas clumps, infalling satellites on nearly radial orbits, or clumpy cold streams from large scales in an intermittent fashion. \u2022 Signi\ufb01cant gas in\ufb02ows, not necessarily requiring major mergers, allow for formation of dense, compact, not-so-\ufb02at stellar bulges that are stable to bar formation. \u2022 Major mergers of galaxies, most of which have dense bulges, do not dramatically enhance gas in\ufb02ows and SFR or cause signi\ufb01cant di\ufb00erences in gas properties in the central regions for galaxies at z \u22651, in accord with earlier major mergers simulations of disk galaxies with massive bulges. 5. Conclusions With high resolution and a physically sound treatment of relevant physical processes, our state-of-the-art, adaptive mesh-re\ufb01nement Eulerian cosmological hydrodynamic simulations have reproduced well some key observables of the galaxy population as a whole (Cen 2010, 2011a,b), including galaxy luminosity functions at z = 0 \u22123, galaxy color distribution at z = 0, the entire star formation history, and properties of damped Lyman alpha systems that we have so far examined. Here we study how major mergers a\ufb00ect star formation. The simulation contains about 2000\u22123000 galaxies with stellar masses in the range 109\u22121012 M\u2299 and resolved at better than 114h\u22121pc at z = 1.4 \u22123.7, providing a good statistical sample to examine major mergers for a wide of range of galaxies in mass and SFR. The most signi\ufb01cant \ufb01nding is that major mergers, on average, do not result in two orders of magnitude boost in SFR, as found in simulations of major mergers of gas-rich disk galaxies with idealized initial conditions. Rather, for the redshift range examined, z = 1.4 \u22123.7, major mergers give rise to an average boost 0 \u221260% in speci\ufb01c SFR for SFR in range of 1 \u22121000 M\u2299/yr examined. Two physical factors of cosmological origin that are not taken into account in isolated merger simulations may be responsible for the di\ufb00erence. \u2013 19 \u2013 First, the central regions (\u223c1kpc) of galaxies at z > 1, in the absence of major mergers, are being fed, in an intermittent fashion, with signi\ufb01cant gas in\ufb02ows. As a result, galaxies without major mergers at z > 1 have much higher SFR than their lower redshift counterparts, a fact that is known observationally. We demonstrate that, at least for a signi\ufb01cant fraction of galaxies, gas in\ufb02ows to the central regions, often quite metal poor, originate from large scales (not smooth gas from the regions immediately surrounding the central region) possibly in the form of dynamical friction inspiraling gas clumps, infalling satellites on nearly radial orbits, or clumpy cold streams from large scales. We suggest that gravitational or hydrodynamic torques stemming from scales larger than the central regions play a fundamental role in transporting the necessary amount of gas to fuel the star formation in the central regions. How this is achieved physically and which processes are most important are some of the very important issues that will be investigated in a future study. Second, the large in\ufb02ows of gas in galaxies with or without major mergers produce compact, dense stellar cores/bulges with high velocity dispersions that are in agreement with observations and stable to bar formation. The dense massive stellar bulges signi\ufb01cantly diminish the importance of the major mergers induced, additional gas in\ufb02ows for galaxies at z \u22651, in good agreement with earlier major mergers simulations of disk galaxies with massive bulges. This result implies that a substantial revision of the current theoretical framework for galaxy formation is necessary, since some of the major foundational elements in our interpretation of galaxy properties hinge on the requirements/beliefs that major mergers are responsible for some of the extreme galaxy formation events, including high luminosity galaxies, such as starbursting galaxies, ULIRGs and SMGs, and formation of supermassive black holes. Some additional results found that may also be interesting are: \u2022 10 \u221220% of galaxies with stellar mass greater than 1011 M\u2299are in major mergers at any time from z = 1 \u22124. \u2022 The merger rate per unit redshift is roughly constant at \u223c0.4 for galaxies in the stellar mass range of 1010.7 \u22121011.7 M\u2299with an upturn and a dramatic downturn above and below that mass range, respectively, for the redshift range z \u223c1 \u22124. A \ufb01tting formula is provided in Eq 1. \u2022 For galaxies with SFR greater than 200 M\u2299/yr we predict that about 10\u221240% should be seen in major mergers at z = 1 \u22124. This predicted fraction is somewhat lower than what current spectral observations suggest (e.g., 57%; Tacconi et al. 2006) but can be directly tested with high resolution imaging with ALMA. \u2022 It is predicted that the cumulative probability distribution function of major merging \u2013 20 \u2013 galaxies within a projected separation rp goes approximately as rp1/4 for galaxies with SFR\u2265 10 M\u2299/yr (for rp greater than a few kpc). We expect that ALMA may be able to provide a direct measurement to test this. Computing resources were in part provided by the NASA HighEnd Computing (HEC) Program through the NASA Advanced Supercomputing (NAS) Division at Ames Research Center. This work is supported in part by grants NAS8-03060 and NNX11AI23G.",
                    "introduction": "Simulations of major gas-rich disk galaxy mergers have provided quantitative insights to gas in\ufb02ows and central starbursts under idealized conditions (e.g., Barnes & Hernquist 1996; Mihos & Hernquist 1996; Hopkins et al. 2006). These simulations have laid the foundation of the theoretical framework for almost all contemporary mainstream interpretations of ob- served extreme starbursting galaxies, namely, the ultraluminous infrared galaxies (ULIRGs), 1Princeton University Observatory, Princeton, NJ 08544; cen@astro.princeton.edu arXiv:1111.0707v1  [astro-ph.CO]  3 Nov 2011 \u2013 2 \u2013 as well as of the formation of supermassive black holes (e.g., Di Matteo et al. 2005). This framework is appealing, because almost all observed ULIRGs in the local universe either are directly seen merging or apparently show signs of mergers (at least some signi\ufb01cant interac- tions) (e.g., Joseph & Wright 1985; Sanders et al. 1988; Duc et al. 1997; Lutz et al. 1998) and at least some luminous quasars live in galaxies under strong interactions (e.g., Bahcall et al. 1997). What is known but not su\ufb03ciently stressed in the relevant context is that the local universe is very di\ufb00erent from the younger one at z > 1 when star formation was much more intensive. As an example, a typical Lyman Break Galaxy (LBG) several times less massive than our own Galaxy has a star-formation rate (SFR) that is about ten times that of the Galaxy (e.g., Steidel et al. 2003). Moreover, minor mergers and close interactions between galaxies are expected to be much more frequent at high redshift that, cumulatively, may have important e\ufb00ects. Furthermore, there are signi\ufb01cant structural di\ufb00erences between local galaxies and those at high redshift in that high redshift galaxies are more compact in size and the majority of massive quiescent galaxies that have been measured appear to have dense bulges (e.g., Lowenthal et al. 1997; Daddi et al. 2005; Trujillo et al. 2006b,a; Toft et al. 2007; Longhetti et al. 2007; Buitrago et al. 2008; Cimatti et al. 2008; van Dokkum et al. 2009; Cappellari et al. 2009; van de Sande et al. 2011). Therefore, our current physical interpretation of extreme galaxy events that is obtained based on linking local observations with substantially idealized major galaxy merger simulations may not pertain to the high redshift universe in general. In this work we examine theoretically, in a cosmological setting, the role of major mergers in driving star formation in the redshift range z > 1, utilizing a large-scale high-resolution galaxy formation simulation. At each redshift from z = 1.4 to z = 3.7 the simulation contains 2000 \u22123000 galaxies with stellar mass greater than 109 M\u2299resolved at better than 114h\u22121pc. Detailed merger histories of galaxies are tracked and (binary) major mergers, de\ufb01ned to be those of stellar mass ratios greater than 1/3, are examined in comparison to those that do not experience major mergers. We \ufb01nd that for galaxies with SFR in the range 1 \u22121000 M\u2299/yr and the stellar mass range Mstar = 109 \u22121012 M\u2299examined, major mergers, on average, yield a modest, fractional boost of 0 \u221260% in speci\ufb01c SFR; we do not \ufb01nd two orders of magnitude increase in SFR found in previous merger simulations of disk galaxies (e.g., Mihos & Hernquist 1996). We show that the properties of simulated galaxies are in reasonable agreement with observations and give a physical explanation of the results. Additional predictions are provided to further test the model. The outline of this paper is as follows. In \u00a72 we detail our simulation (\u00a72.1) and galaxy catalogs (\u00a72.2). Results are presented in \u00a73, followed by \u00a74 that gives a physical explanation of the results. Conclusions are given in \u00a75. \u2013 3 \u2013"
                },
                {
                    "url": "http://arxiv.org/abs/1110.5645v1",
                    "title": "Far-Infrared Properties of Lyman Break Galaxies from Cosmological Simulations",
                    "abstract": "Utilizing state-of-the-art, adaptive mesh-refinement cosmological\nhydrodynamic simulations with ultra-high resolution (114h-1pc) and large sample\nsize (>3300 galaxies of stellar mass >10^9Msun), we show how the stellar light\nof Lyman Break Galaxies at z=2 is distributed between optical/ultra-violet (UV)\nand far-infrared (FIR) bands. With a single scalar parameter for dust\nobscuration we can simultaneously reproduce the observed UV luminosity function\nfor the entire range (3-100 Msun/yr) and extant FIR luminosity function at the\nbright end (>20Msun/yr). We quantify that galaxies more massive or having\nhigher SFR tend to have larger amounts of dust obscuration mostly due to a\ntrend in column density and in a minor part due to a mass (or SFR)-metallicity\nrelation. It is predicted that the FIR luminosity function in the range\nSFR=1-100Msun/yr is a powerlaw with a slope about -1.7. We further predict that\nthere is a \"galaxy desert\" at SFR(FIR) < 0.02 (SFR(UV)/10Msun/yr)^2.1 Msun/yr\nin the SFR(UV)-SFR(FIR) plane. Detailed distributions of SFR(FIR) at a fixed\nSFR(UV) are presented. Upcoming observations by ALMA should test this model. If\nconfirmed, it validates the predictions of the standard cold dark matter model\nand has important implications on the intrinsic SFR function of galaxies at\nhigh redshift.",
                    "authors": "Renyue Cen",
                    "published": "2011-10-25",
                    "updated": "2011-10-25",
                    "primary_cat": "astro-ph.CO",
                    "cats": [
                        "astro-ph.CO"
                    ],
                    "main_content": "2.1. Hydrocode and Simulation Parameters We perform cosmological simulations with the adaptive mesh refinement (AMR) Eulerian hydro code, Enzo (Bryan & Norman 1999; Joung et al. 2009). First we ran a low resolution simulation with a periodic box of 120 h\u22121Mpc on a side. We identified a region centered on a cluster of mass of \u223c2 \u00d7 1014 M\u2299at z = 0 and then resimulate it with high resolution, embedded in the outer 120h\u22121Mpc box. The refined region for \u201cC\u201d run has a size of 21 \u00d7 24 \u00d7 20h\u22123Mpc3 and represents 1.8\u03c3 fluctuation on that volume. The dark matter particle mass in the refined region is 1.3 \u00d7 107h\u22121 M\u2299. The refined region is surrounded by three layers (each of \u223c1h\u22121Mpc) of buffer zones with particle masses successively larger by a factor of 8 for each layer, which then connects with the outer root grid that has a dark matter particle mass 84 times that in the refined region. We choose the mesh refinement criterion such that the resolution is always better than 114h\u22121pc physical, corresponding to a maximum mesh refinement level of 13 at z = 0. The simulations include a metagalactic UV background (Haardt & Madau 1996), a model for shielding of UV radiation by neutral hydrogen (Cen et al. 2005), metallicity-dependent radiative cooling (Cen et al. 1995) extended down to 10 K (Dalgarno & McCray 1972) and all relevant gas chemistry chains for molecular hydrogen formation (Abel et al. 1997), including molecular formation on dust grains (Joung et al. 2009). Star particles are created in cells that satisfy a set of criteria for star formation proposed by Cen & Ostriker (1992). Supernova feedback from star formation is modeled following Cen et al. (2005). We allow the entire feedback processes to be hydrodynamically coupled to surroundings and subject to relevant physical processes, such as cooling and heating. See Cen (2010) for all other simulation details and physical treatments. We use the following cosmological parameters that are consistent with the WMAP7-normalized (Komatsu et al. 2010) LCDM model: \u2126M = 0.28, \u2126b = 0.046, \u2126\u039b = 0.72, \u03c38 = 0.82, H0 = 100hkms\u22121Mpc\u22121 = 70kms\u22121Mpc\u22121 and n = 0.96. 2.2. Simulated Galaxy Catalogs We identify galaxies in our high resolution simulations using the HOP algorithm (Eisenstein & Hu 1999), operated on the stellar particles, which is tested to be robust. Satellites within a galaxy are clearly identified separately. The luminosity of each stellar particle at each of the Sloan \u2013 3 \u2013 Digital Sky Survey (SDSS) \ufb01ve bands is computed using the GISSEL stellar synthesis code (Bruzual & Charlot 2003), by supplying the formation time, metallicity and stellar mass. Collecting luminosity and other quantities of member stellar particles, gas cells and dark matter particles yields the following physical parameters for each galaxy: position, velocity, total mass, stellar mass, gas mass, mean formation time, mean stellar metallicity, mean gas metallicity, star formation rate, luminosities in \ufb01ve SDSS bands (and various colors) and others. At a spatial resolution of 109pc with nearly 5000 well resolved galaxies at z = 2, this simulated galaxy catalog presents an excellent tool to study galaxy formation and evolution. 2.3. Modeling Dust Obscuration A fully self-consistent modeling would be di\ufb03cult, given our lack of knowledge of the distribution of dust and its properties. Here we take a simpli\ufb01ed approach. Given the 3-d distribution of gas with varying metallicity and stellar particles distributed within it, the observed SFR at a rest-frame UV wavelength \u03bb for the galaxy is computed as SFRUV,\u03bb = X i sfri(1 \u2212e\u2212\u03c4\u03bb(\u20d7 ri\u2192obs)), (1) where \u03c4\u03bb(\u20d7 r \u2192obs) is the extinction optical depth at some UV wavelength \u03bb for an individual stellar particle i of star formation rate sfri in the galaxy from its individual location \u20d7 ri to the observer: \u03c4\u03bb(\u20d7 r \u2192obs) = (A\u2032 V /1.086)f\u03b2\u03bb \u00af Zi(\u20d7 r \u2192obs)NH,i(\u20d7 r \u2192obs), (2) where A\u2032 V = 5.3 \u00d7 10\u221222 is visual extinction AV per unit hydrogen column density per unit solar metallicity for RV = 3.1 (Draine 2011) and \u03b2\u03bb \u2261A\u03bb/AV (a \ufb01tting function) is taken from Cardelli et al. (1989); \u00af Zi(\u20d7 r \u2192obs) is the column density-weighted mean metallicity of gas obscuring the stellar particle i in solar units and NH,i(\u20d7 r \u2192obs) is the integrated hydrogen column density from the stellar particle i to the observer. Note that in Equation (1) the calculation is based on 3-d distributions of stellar particles that each are subject to their own integrated optical depth and the sum is over all the memeber stellar particles, typically of number 105 \u2212106 for a galaxy of stellar mass 1011 M\u2299. In Equation (2) f is a dimensionless parameter that we will adjust such that the simulated LBG UV luminosity function matches observations; f should be of order unity, if dust properties for galaxies at z \u223c2 are not drastically di\ufb00erent from those derived locally and our galaxy formation model is realistic. As we will see below, the required value of f is indeed close to unity with an adopted extinction law that is also close to those derived locally. Thus, the dust extinction of SFR at a speci\ufb01c UV band is a good proxy of the overall extinction of SFR in the optical-to-UV regime. We will use the 1700\u02da A band for subsequent analysis. The portion of the SFR that \u2013 4 \u2013 does not escape in UV/optical is assumed to be converted to FIR SFR: SFRFIR = X i sfri \u2212SFRUV,\u03bb. (3) For each galaxy we place 95 random observers in its sky at in\ufb01nity for results presented in the next section. This sampling is adequate and results are converged statistically. 3. Results 0 0.5 1 1.5 2 2.5 3 \u22125 \u22124 \u22123 \u22122 \u22121 log SFR (Msun/yr) log n(>SFR) (Mpc\u22123)     z=2.0 all galaxies z=2.0 UV\u2212selected z=2.0 FIR\u2212selected powerlaw slope \u22120.7 z=1.9\u22122.7 UV obs (Reddy & Steidel 2009) z=2 LIRG and ULIRG obs (Caputi etal 2007) 0 0.5 1 1.5 2 2.5 3 \u22125 \u22124 \u22123 \u22122 \u22121 log SFR (Msun/yr) log n(>SFR) (Mpc\u22123)     all galaxies 8 subboxes 0 0.5 1 1.5 2 2.5 3 \u22122 \u22121 0 log SFR (Msun/yr) log SFR density (>SFR) (Msun yr\u22121Mpc\u22123)     obs (Hopkins & Beacoms 2007) Fig. 1.\u2014 Top panel: cumulative total SFR function at z = 2 (red circles), cumulative UV and FIR SFR functions in blue squares and magenta stars, respectively. Black diamonds are LBG observations z = 1.9 \u22122.7 from Reddy & Steidel (2009); two green triangles are LIRG and ULIRG observational data from Caputi et al. (2007). We convert to SFR of observational data from MAB(1700\u02da A) using the standard conversion formula, SFR = 6.1 \u00d7 10\u2212[8+0.4MAB(1700\u02da A)] M\u2299/yr (Kennicutt 1998) in the AB magnitude system (Oke 1974). Solid magenta line indicates a powerlaw slope of \u22120.7 (corresponding to a slope of \u22121.7 for the di\ufb00erential SFRFIR function). Thin solid black line indicates a powerlaw slope of \u22121 (corresponding to a slope of \u22122 for the di\ufb00erential function). The three thin curves of color red, blue and magenta, respectively, correspond their thick counterparts but from a lower resolution simulation with four times poorer spatial and eight times poorer mass resolutions. Bottom left panel: the eight green curves represent the cumulative total SFR function in the eight octant volumes; the average of the green curves is the redshift circles (also shown in the top panel). Bottom right panel: Cumulative light densities for total (red circles), UV galaxies (blue squares) and FIR galaxies (magenta stars), respectively, at z = 2. Also show as a black diamond is the observed data at z = 2 compiled by Hopkins & Beacom (2006) with 1\u03c3 errorbar. The top panel of Figure 1 shows the SFR functions for total SFR, UV and FIR selected galaxies, respectively. We have adjusted the parameter f in Equation 2 to be f = 1.4 to \u2013 5 \u2013 arrive at the excellent match between the computed UV SFR function and the observations at z \u223c2. We note that f could be 1 if one had adopted a slightly di\ufb00erent Rv (Cardelli et al. 1989). In any case, the results with f = 1 with Rv = 3.1 di\ufb00er only slightly from the case with f = 1.4 shown here and UV SFR function in that case is consistent with the observations within the errorbars. This also suggests that our overall results are robust and insensitive to small variations of uncertain parameters for the dust model within a reasonable range. It also implies that dust properties at z \u223c2 are not signi\ufb01cantly di\ufb00erent from those of local dust. After matching the observed UV SFR function, we see that the predicted FIR SFR function agrees remarkably well with the observed LIRG and ULIRG data at z = 2 (top panel). As a consistency check, we show in the bottom right panel of Figure 1 the cumulative SFR density at z = 2. Here we see both the UV SFR density and FIR SFR density agree well with observations. We see that, while the directly observed UV SFR density should be roughly equal to the directly observed FIR SFR density, at face value, the UV SFR density is somewhat higher than FIR SFR density. Our results suggest that galaxies with higher SFR tend to have relatively larger obscuration in UV/optical than galaxies with lower SFR, resulting in a steepening UV luminosity function at the luminous end. The underlying cause will be discussed in Figure 4. Our previous studies (Cen 2010, 2011) indicate that the \u201cC\u201d run used is positively biased over the cosmic mean by a factor of \u223c2. Taking that into account, we \ufb01nd that the simulated SFR function as well SFR density becomes too low compared to observed ones. A plausible adjustment is to the stellar IMF. The results shown above uses an top-heavy IMF that produces twice the UV light output per unit SFR than the standard Salpeter function. This provides intriguing evidence for top-heavy IMF at high redshift, consistent with other independent considerations (e.g., Baugh et al. 2005; Dav\u00b4 e 2008; van Dokkum 2008). The abundance of massive, rare objects is expected to depend on box size as well as the overdensity of the environment. We assess this e\ufb00ect as follows. We divide the simulation box into eight equal-volume octants and compute the SFR function for each of the eight octants. The results for the eight SFR functions are shown as green curves in the bottom left panel of Figure 1. We note two points here. First, at SFR \u226430 M\u2299/yr the SFR function is very well converged and does not appear to sensitively depend on environment. Second, substantial variations are visible at SFR \u2265100 M\u2299/yr, which suggests that the abundance of galaxies with SFR higher than 100 M\u2299/yr depends sensitively on density environment and our positively biased simulation box likely has produced some over-abundance of galaxies with SFR \u2265100 M\u2299/yr relative to galaxies with SFR \u2264100 M\u2299/yr; the computed UV SFR at SFR \u2265100 M\u2299/yr in this simulation lies above the observed points is thus not inconsistent. A comparison between the thin and thick curves in the top panel of Figure 1 indicates that the resolutions achieved in the higher resolution run is required in order to provide an \u2013 6 \u2013 adequate match to observations. The lower (four times spatially and eight times in mass) resolution simulation of the same volume su\ufb00ers from the two shortcomings. First, there is a slight overproduction of the highest SFR (\u2265200 M\u2299yr\u22121) galaxies in the lower resolution simulation, which is due to a combination of slight overmerging and higher gas reservoir in the lower resolution run. Second, there is a signi\ufb01cant underproduction of lower SFR (\u2264200 M\u2299yr\u22121) galaxies in the lower resolution simulation due to lower resolution. Taking into account these two e\ufb00ects, the results can be understood and our main predictions on the faint slope and galaxy desert (see below) remain robust. Our model makes several predictions. The \ufb01rst is that the di\ufb00erential FIR SFR function displays a nearly perfect powerlaw of slope about \u22121.7 below SFRFIR \u223c100 M\u2299/yr at z = 2. We attribute this outcome to a combination of three physical factors: (1) the intrinsic di\ufb00erential SFR function is steeper than than \u22121.7 but close to \u22122, as indicated by the thin black line in the top panel of Figure 1; (2) on averagge, higher SFR galaxies have higher dust optical depth (as discussed in detail in Figure 4 below) that tends to \ufb02atten the FIR SFR function; (3) there is a signi\ufb01cant dispersion of SFRFIR at a \ufb01xed intrinsic SFR (see Figure 2 below) that also smoothes and \ufb02attens the FIR SFR function. This predictions can be tested by ALMA observations, and if con\ufb01rmed, will provide evidence that the intrinsic SFR function is close to a powerlaw with a slope that is steeper than \u22121.7 in the SFR range 10 \u2212300 M\u2299yr\u22121. We attribute this behavior to a large dispersion of SFR at a \ufb01xed halo mass but will address it in more detail separately. Given this slope, most of the FIR light is concentrated at the bright end. In terms of cumulative galaxy number density we \ufb01nd that UV and FIR selected samples are expected to have comparable abundances at SFR \u226520 \u221240 M\u2299/yr. In terms of cumulative SFR density we \ufb01nd that FIR selected galaxies with SFR \u226510 M\u2299/yr dominate over UV selected galaxies with SFR \u226510 M\u2299/yr; the reverse is true at SFR < 10 M\u2299/yr. Reading directly from simulations we \ufb01nd that FIR selected galaxies with FIR SFR \u226510 M\u2299/yr contain 78% of total FIR light density, whereas UV selected galaxies with UV SFR \u226510 M\u2299/yr contain only 50% (the actual number may be still lower, since our simulations likely have underestimated the number density of galaxies below SFR \u22643 M\u2299/yr, below which a \ufb02attening of the UV SFR function is seen in the top panel of Figure 1). Note that while a Schechter function normally \ufb01ts halo functions well, it does not provide an adequate \ufb01t to the FIR SFR function, due to large dispersions of SFR at \ufb01xed halo masses mentioned above. Our results suggest that the observed UV-selected LBGs detected at SFR \u2265a few M\u2299/yr at z = 2 \u22123 can account for the bulk of the FIR background at z \u223c2 \u22123, consistent with earlier independent observational assessments (e.g., Smail et al. 1999; Adelberger & Steidel 2000; Chapman & Casey 2009). Needless to say, our model implies that UV and FIR selected galaxies form a complementary pair of populations that are drawn from the same underlying general galaxy \u2013 7 \u2013 population. This point has been noted by others (e.g., Sawicki & Yee 1998; Meurer et al. 1999; Shapley et al. 2001; Papovich et al. 2001; Calzetti 2001). 0 1 2 3 \u22121 0 1 2 3 log SFRUV (Msun/yr) log SFRFIR (Msun/yr)     Galaxy Desert SFRFIR=0.02 (SFRUV/10)2.1 Fig. 2.\u2014 each dot is a galaxy in the plane of UV and FIR detected SFR at z = 2. The solid line is SFRFIR = 0.02[SFRUV/10 M\u2299yr\u22121]2.1 M\u2299yr\u22121. Figure 2 shows a scatter plot of galaxies in the SFRUV \u2212SFRFIR plane. We see a nearly complete empty space at the lower right corner of the plot, with SFRFIR < 0.02[SFRUV/10 M\u2299yr\u22121]2.1 M\u2299yr\u22121, which we shall call the \u201cgalaxy desert\u201d. The physical reason for this nearly complete absence of galaxies with high UV SFR and low FIR SFR rate is that the dust optical depth of galaxies increases with SFR. This second prediction of our model should be testable by ALMA observations. Figure 3 dissects the information contained in Figure 2 further and shows a set of Table 1. Parameters for gaussians in Figure 3 with log SFRUV being the variable SFRUV( M\u2299/yr) mean dispersion 3-10 -0.84 1.0 10-30 0.030 0.98 30-100 0.85 0.76 100-300 1.7 0.72 \u2013 8 \u2013 \u22124 \u22123 \u22122 \u22121 0 1 2 0 0.2 0.4 log SFR(FIR) PDF     \u22123 \u22122 \u22121 0 1 2 3 0 0.2 0.4 0.6 log SFR(FIR) PDF     \u22122 \u22121 0 1 2 3 0 0.2 0.4 0.6 log SFR(FIR) PDF     0 1 2 3 0 0.2 0.4 0.6 0.8 1 1.2 1.4 log SFR(FIR) PDF     SFR(UV)=3\u221210 SFR(UV)=10\u221230 SFR(UV)=30\u2212100 SFR(UV)=100\u2212300 Fig. 3.\u2014 shows four distributions of FIR SFR for LBG galaxies at each of the four UV SFR values of 3 \u221210 M\u2299/yr (top left), 10 \u221230 M\u2299/yr (top right), 30 \u2212100 M\u2299/yr (bottom left) and 100 \u2212300 M\u2299/yr (bottom right), respectively, at z = 2. Each black curve is a gaussian \ufb01t with its parameters listed in Table 1. distributions of SFRFIR at a given range of SFRUV. We see that for LBGs with SFRUV = 10\u2212 100 M\u2299/yr, the distributions are well \ufb01tted by gaussians (the black curves) using log SFRUV as the variable. In the lowest SFRUV (SFRUV = 3 \u221210 M\u2299/yr) we see a slight tendency of the SFRFIR distribution to skew towards the low SFRFIR end, indicative of increasingly diminishing dust obscuration for galaxies with low SFR. In the highest SFRUV (SFRUV = 100 \u2212300 M\u2299/yr), the SFRFIR distribution is signi\ufb01cantly skewed to the high SFRFIR end for the same physical reason. We list the parameters of the best gaussian \ufb01t of SFRFIR distributions for all SFRUV bins in Table 1. These predictions should be veri\ufb01able by ALMA observations. Finally, we examine the underlying cause of the generally di\ufb00erential rate of dust obscuration seen in prior \ufb01gures where higher SFR galaxies are more dust obscured. Figure 4 shows gas metallicity and gas column density as a function of stellar mass and total SFR, respectively. Examination of the top left panel of Figure 4 indicates that in the stellar mass range Mstar \u22651010 M\u2299there is a positive correlation between gas metallicity and stellar mass, in agreement with the observed, so-called mass-metallicity relation at z \u223c2 of Erb et al. (2006). While this is not the focus of our study here, the agreement is quite \u2013 9 \u2013 9 10 11 12 \u22121 0 1 log Mstar (Msun) [Z/H]     SFR > 10 Msun/yr SFR < 10 Msun/yr Erb et al 2006 9 10 11 12 20 21 22 23 log Mstar (Msun) log NH (cm\u22122)     SFR > 10 Msun/yr SFR < 10 Msun/yr 1 2 3 \u22121 0 1 log total SFR (Msun/yr) [Z/H] 1 2 3 20 21 22 23 log total SFR (Msun/yr) log NH (cm\u22122) Fig. 4.\u2014 Top left panel: column density weighted gas metallicity averaged over the entire galaxy as a function of stellar mass. Shown in black diamond is observations from Erb et al. (2006) at z \u223c2. Top right panel: column density weighted gas metallicity averaged over the entire galaxy as a function of SFR. Bottom left panel: radially integrated total column density as a function of stellar mass. Bottom right panel: radially integrated total column density as a function of SFR. In all the panels red symbols have SFR greater than 10 M\u2299/yr and green symbols less than 10 M\u2299/yr. remarkable but consistent with the agreement that is found between simulations and observations with respect to the metallicity distribution of damped Lyman alpha systems in an earlier study (Cen 2010). A comparison between the two top and two bottom panels of Figure 4 clearly indicates that the correlation between column density and stellar mass or SFR is about three times stronger than that between gas metallicity and stellar mass or SFR. This suggests that the general trend of larger dust obscuration for larger stellar mass or SFR is mostly due to a trend in column density in the same sense, but positively aided by a mass (or SFR)-metallicity trend. This overall trend gives an integral constraint on the total optical depth. The actual distribution of dust optical depth at a given galaxy mass (or SFR) or even for a given galaxy viewed at di\ufb00erent angels has large dispersions due to the clumpy distribution of gas with varying metallicity, resulting in a wide FIR SFR distribution within a narrow UV SFR range, as quanti\ufb01ed in Figure 3. \u2013 10 \u2013 4. Conclusions Using state-of-the-art, adaptive mesh-re\ufb01nement Eulerian cosmological hydrodynamic simulations with high resolution (114h\u22121pc), large sample size (\u22653300 galaxies of stellar mass \u2265109 M\u2299) and a physically sound treatment of relevant processes, we examine the properties of LBGs at z = 2 with respect to their partitioning of UV and FIR light. Using a single scalar parameter that relates the amount of dust obscuration to the product of hydrogen column density and gas metallicity to model dust obscuration along each line of sight (i.e., a dust extinction law derived in our local universe), we \ufb01nd that the observed UV luminosity function for the entire range and FIR luminosity function at the bright end can be simultaneously reproduced. Our theoretical modeling a\ufb03rms the aesthetically appealing picture where UV and FIR selected galaxies at z \u223c2 are drawn from the same general galaxy population. The observationally di\ufb00erent manifestations are merely due to the known fact that each galaxy is seen through its own unique set of dust screens at a given viewing angle. Star forming galaxies that are more massive or have higher SFR tend to have larger amounts of dust obscuration at high redshift. We predict that the FIR luminosity function in the range SFR = 1 \u2212100 M\u2299/yr is a powerlaw with a slope \u22121.7 with uncertainty of \u223c0.1. We further predict that there is a \u201cgalaxy desert\u201d at SFRFIR < 0.02(SFRUV/10 M\u2299yr\u22121)2.1 M\u2299yr\u22121 in the SFRUV \u2212SFRFIR plane. Detailed distributions of SFRFIR at an observed SFRUV are quanti\ufb01ed and can be used to further test the model. We expect that upcoming observations by ALMA should be able to test these predictions hence ultimately the standard cosmological model with respect to its properties on sub-megaparsec scales. If ALMA observations con\ufb01rms the predicted faint end slope of the FIR luminosity function, it would imply that the intrinsic SFR function of galaxies may be closer to a powerlaw of a slope at least as steep as \u22122 in the range SFR = 3 \u2212100 M\u2299than a Schechter function. I would like to thank Computing resources were in part provided by the NASA HighEnd Computing (HEC) Program through the NASA Advanced Supercomputing (NAS) Division at Ames Research Center. I thank an anonymous referee for a constructive report. This work is supported in part by grants NAS8-03060 and NNX11AI23G.",
                    "introduction": "The precise relation between optical/UV light detected and dust emission in the far infrared (FIR) of Lyman Break Galaxies (LBGs; Steidel et al. 2003) is di\ufb03cult to establish observationally, because of the faintness of the expected FIR luminosity (e.g., Ouchi et al. 1999; Adelberger & Steidel 2000). In this work we study this relation using direct simulations of galaxy formation in the standard cosmological constant-dominated cold dark matter model (LCDM; Komatsu et al. 2010) in light of the capabilities of the upcoming Atacama Large 1Princeton University Observatory, Princeton, NJ 08544; cen@astro.princeton.edu \u2013 2 \u2013 Millimeter Array (ALMA) mission. The outline of this paper is as follows. In \u00a72 we detail our simulations, method of making galaxy catalogs and a dust obscuration analysis method. Results are presented in \u00a73, followed by conclusions given in \u00a74."
                },
                {
                    "url": "http://arxiv.org/abs/1104.5046v1",
                    "title": "Environmentally Driven Global Evolution of Galaxies",
                    "abstract": "Utilizing high-resolution large-scale galaxy formation simulations of the\nstandard cold dark matter model, we examine global trends in the evolution of\ngalaxies due to gravitational shock heating by collapse of large halos and\nlarge-scale structure. We find two major global trends. (1) The mean specific\nstar formation rate (sSFR) at a given galaxy mass is a monotonically increasing\nfunction with increasing redshift. (2) The mean sSFR at a given redshift is a\nmonotonically increasing function of decreasing galaxy mass that steepens with\ndecreasing redshift. The general dimming trend with time merely reflects the\ngeneral decline of gas inflow rate with increasing time. The differential\nevolution of galaxies of different masses with redshift is a result of\ngravitational shock heating of gas due to formation of large halos (groups and\nclusters) and large-scale structure that move a progressively larger fraction\nof galaxies and their satellites into environments where gas has too high an\nentropy to cool to continue feeding resident galaxies. Overdense regions where\nlarger halos are preferentially located begin to be heated earlier and have\nhigher temperatures than lower density regions at any given time, causing sSFR\nof larger galaxies to fall below the general dimming trend at higher redshift\nthan less massive galaxies and galaxies with high sSFR to gradually shift to\nlower density environments at lower redshift. We find that several noted cosmic\ndownsizing phenomena are different manifestations of these general trends. We\nalso find that the great migration of galaxies from blue cloud to red sequence\nas well as color-density relation, among others, may arise naturally in this\npicture.",
                    "authors": "Renyue Cen",
                    "published": "2011-04-26",
                    "updated": "2011-04-26",
                    "primary_cat": "astro-ph.CO",
                    "cats": [
                        "astro-ph.CO",
                        "astro-ph.HE"
                    ],
                    "main_content": "2.1. Hydrocode and Simulation Parameters We perform cosmological simulations with the adaptive mesh refinement (AMR) Eulerian hydro code, Enzo (Bryan 1999; Bryan & Norman 1999; O\u2019Shea et al. 2004; Joung et al. 2009). First we ran a low resolution simulation with a periodic box of 120 h\u22121Mpc on a side. We identified two regions separately, one centered on a cluster of mass of \u223c2 \u00d7 1014 M\u2299and the other centered on a void region at z = 0. We then resimulate each of the two regions separately with high resolution, but embedded in the outer 120h\u22121Mpc box to properly take into account large-scale tidal field and appropriate boundary conditions at the surface of the refined region. We name the simulation centered on the cluster \u201cC\u201d run and the one centered on the void \u201cV\u201d run. The refined region for \u201cC\u201d run has a size of 21 \u00d7 24 \u00d7 20h\u22123Mpc3 and that for \u201cV\u201d run is 31 \u00d7 31 \u00d7 35h\u22123Mpc3. At their respective volumes, they represent 1.8\u03c3 and \u22121.0\u03c3 fluctuations. The initial condition in the refined region has a mean interparticleseparation of 117h\u22121kpc comoving, dark matter particle mass of 1.07 \u00d7 108h\u22121 M\u2299. The refined region is surrounded by two layers (each of \u223c1h\u22121Mpc) of buffer zones with particle masses successively larger by a factor of 8 for each layer, which then connects with the outer root grid that has a dark matter particle mass 83 times that in the refined region. Because \u2013 4 \u2013 we still can not run a very large volume simulation with adequate resolution and physics, we choose these two runs to represent two opposite environments that possibly bracket the average. As we have shown in Cen (2010), these two runs indeed bracket all compared observables of DLAs and tests show good numerical convergence. We choose the mesh re\ufb01nement criterion such that the resolution is always better than 460h\u22121pc physical, corresponding to a maximum mesh re\ufb01nement level of 11 at z = 0. The simulations include a metagalactic UV background (Haardt & Madau 1996), and a model for shielding of UV radiation by neutral hydrogen (Cen et al. 2005). They also include metallicity-dependent radiative cooling (Cen et al. 1995). Star particles are created in cells that satisfy a set of criteria for star formation proposed by Cen & Ostriker (1992). Each star particle is tagged with its initial mass, creation time, and metallicity; star particles typically have masses of \u223c106 M\u2299. Supernova feedback from star formation is modeled following Cen et al. (2005). Feedback energy and ejected metal-enriched mass are distributed into 27 local gas cells centered at the star particle in question, weighted by the speci\ufb01c volume of each cell, which is to mimic the physical process of supernova blastwave propagation that tends to channel energy, momentum and mass into the least dense regions (with the least resistance and cooling). We allow the entire feedback processes to be hydrodynamically coupled to surroundings and subject to relevant physical processes, such as cooling and heating. The total amount of explosion kinetic energy from Type II supernovae for an amount of star formed M\u2217with a Chabrier IMF is eSNM\u2217c2 (where c is the speed of light) with eGSW = 6.6\u00d710\u22126. Taking into account the contribution of prompt Type I supernovae, we use eSN = 1\u00d710\u22125 in our simulations. Observations of local starburst galaxies indicate that nearly all of the star formation produced kinetic energy is used to power GSW (e.g., Heckman 2001). Supernova feedback is important primarily for regulating star formation and for transporting energy and metals into the intergalactic medium. The extremely inhomogeneous metal enrichment process demands that both metals and energy (and momentum) are correctly modeled so that they are transported in a physically sound (albeit still approximate at the current resolution) way. The kinematic properties traced by unsaturated metal lines in DLAs are extremely tough tests of the model, which is shown to agree well with observations (Cen 2010). As we will show below, the properties of galaxies produced in the simulations resemble well observed galaxies, within the limitations of \ufb01nite resolution. In order not to mingle too many di\ufb00erent e\ufb00ects, we do not include any feedback e\ufb00ect from AGN, which is often invoked to suppress star formation by cooling from hot atmosphere in large galaxies. We will see later that this omission may have caused larger galaxies to be somewhat overluminous. We use the following cosmological parameters that are consistent with the WMAP7normalized (Komatsu et al. 2010) LCDM model: \u2126M = 0.28, \u2126b = 0.046, \u2126\u039b = 0.72, \u03c38 = 0.82, H0 = 100hkms\u22121Mpc\u22121 = 70kms\u22121Mpc\u22121 and n = 0.96. \u2013 5 \u2013 2.2. Simulated Galaxy Catalogs We identify galaxies in our high resolution simulations using the HOP algorithm (Eisenstein & Hu 1999), operated on the stellar particles, which is tested to be robust and insensitive to speci\ufb01c choices of concerned parameters within reasonable ranges. Satellites within a galaxy are clearly identi\ufb01ed separately. The luminosity of each stellar particle at each of the Sloan Digital Sky Survey (SDSS) \ufb01ve bands is computed using the GISSEL stellar synthesis code (Bruzual & Charlot 2003), by supplying the formation time, metallicity and stellar mass. Collecting luminosity and other quantities of member stellar particles, gas cells and dark matter particles yields the following physical parameters for each galaxy: position, velocity, total mass, stellar mass, gas mass, mean formation time, mean stellar metallicity, mean gas metallicity, star formation rate, luminosities in \ufb01ve SDSS bands (and various colors) and others. For each galaxy we also compute its intermediate-scale environmental overdensity, de\ufb01ned to be the dark matter density, smoothed by a Gaussian function of radius 2h\u22121Mpc comoving, divided by the global mean dark matter density. We choose this smoothing scale, because it encloses a mass of 1.3\u00d71013h\u22121 M\u2299, whose gas at virial radius shock heated to the virial temperature approximately corresponds to the critical entropy Scrit that is a weak function of redshift. The relevance of Scrit will be explained in \u00a73.2. In addition, we compute the mean gas entropy of each galaxy at its virial radius, de\ufb01ned as < S >= P Tn1/3dV/ P ndV , where the two sums are over the radial range (0.9 \u22121.1)rv (rv is the virial radius). We also compute various \ufb02uxes across the virial radius for each galaxy, including total gas mass \ufb02ux, cold mass \ufb02ux. 3. Results 3.1. Validating Simulated Galaxies This is \ufb01rst-in-its-class kind of galaxy formation simulations that includes sophisticated physical treatment, su\ufb03cient resolution, and in a perhaps ground breaking fashion, a large enough sample covering the entire redshift range to statistically address relevant questions. In Cen (2010) we presented a detailed examination of the DLAs and found that the simulations, for the \ufb01rst time, are able to match all observed properties of DLAs, including abundance, size, metallicity and kinematics. The broad agreement between simulations and observations suggests that our treatment of feedback processes (including metal enrichment and transport) is realistic; other simulations that do not include these detailed treatment (such as metal transport) do not provide as good agreement with observations as ours especially with respect to kinematics (that depends quite sensitively on metallicity distribution). Nevertheless, as with any simulation, there are limitations. As such, it is prudent to examine \u2013 6 \u2013 the basic properties of galaxies themselves in the simulations to gauge how realistically we can reproduce observations. 0 1 2 3 4 5 6 \u22123 \u22122 \u22121 0 z log SFR density (Msun/yr/Mpc3)     SFRD (C) SFRD (V) average SFRD Hopkins & Beacom (2006) Brinchmann et al (2004) Seymour et al (2008) Karim et al (2011) Bouwens et al (2007) Reddy & Steidel (2009) Fig. 1.\u2014 shows the evolution SFR density. Also shown as the grey shaded region is the observations compiled by Hopkins & Beacom (2006), as blue points and mageneta circles two more recent observations using radio techniques from Karim et al. (2011) (2\u03c3 errorbars) and Seymour et al. (2008) (1\u03c3 errorbars), as black asterisk the local SDSS data from Brinchmann et al. (2004) (1\u03c3 errorbars), as two black hexagons from Reddy & Steidel (2009) (1\u03c3 errorbars), and as open blue squares from Bouwens et al. (2007) (1\u03c3 errorbars). The blue curve is an average of the two runs. Figure 1 shows the SFR density history from z = 0 to z = 6. We see that for the entire redshift range the SF histories from C and V runs bracket the observations, suggesting that the SFR histories in the simulations are consistent with the observations. It is probably true that the global average lies between these two runs. However, the weightings of two runs for averaging are likely complicated, because di\ufb00erent properties of galaxies of di\ufb00erent masses depend on large-scale environments in a non-trivial fashion. For brevity, we use the constraints from the observed SFRD history to obtain our \u201cbest\u201d weightings for C and V run; we \ufb01nd that a weighting for the C run equal to (1 + z)/(7 + z) (with one minus that for the V run) to \ufb01t the redshift range of interest here, with the obtained average SFR density shown as the blue curve in Figure 1. In some of the subsequent \ufb01gures, we use the same weightings to average over some quantities of the two runs, when such an exercise is preferential. Figure 2 shows the SDSS restframe g \u2212r color distribution of galaxies at z = 0, 1.0, 1.6. The averaged color distribution at each redshift is obtained by the same weighting scheme normalized to the SFR density evolution in Figure 1. We see that the simulations can reproduce the observerd bimodality well at z = 0 (Blanton et al. 2003a); varying the weightings \u2013 7 \u2013 0 0.2 0.4 0.6 0.8 1 0 0.1 g \u2212 r PDF     z=0.0 z=1.0 z=1.6 Blanton et al 2003 Fig. 2.\u2014 shows the SDSS restframe g \u2212r color distributions of simulated galaxies (number weighted) with stellar mass greater than 109 M\u2299at z = 0, 1, 1.6 (red, green and blue, respectively). Also show as the black curve is the corresponding SDSS observations at z = 0.1 from Blanton et al. (2003a). of the two runs in averaging within any reasonable range does not alter the bimodal nature of the distribution. There is a hint that our simulated galaxies may be slightly too blue (by \u223c0.05 mag), which may in part due to the omission of type Ia supernova feedback on a longer time scale (\u223c1Gyr) in the present simulations (we include feedback from SNe II and prompt SNe Ia). Our future simulations including SNe Ia should verify this. There is evidence that the color bimodality persists at least to z \u223c1 but becomes largely absent by z = 1.6, consistent with observations (e.g., Weiner et al. 2005; Franzetti et al. 2007; Cirasuolo et al. 2007). Figure 3 shows the SDSS g band galaxy luminosity function at z = 0. Within the uncertainties the simulations agree reasonably well with observations, except at the high luminosity end where simulations overproduce luminous galaxies. This is a well-known problem in simulations that do not include some strong feedback in large galaxies. AGN feedback has been invoked to suppress star formation due to cooling o\ufb00of hot gas in large galaxies (e.g., Croton et al. 2006; Bower et al. 2006). If we apply a similar AGN feedback prescription as in Croton et al. (2006) by suppressing star formation post-simulation by a factor of f \u22611/(1+(Mh/1.0\u00d71013 M\u2299)2/3), where we use Mh = Mstar/0.4 for satellite galaxies whose halos can no longer be unambiguously delineated (while stellar identi\ufb01es remain intact), we obtain the result shown as the thick solid curve in Figure 3 that is in good agreement with observations. There is indication that at Mg > \u221219, we underproduce small galaxies, which \u2013 8 \u2013 \u221223 \u221222 \u221221 \u221220 \u221219 \u22125 \u22124 \u22123 \u22122 absolute r magnitude log r band LF (1/Mpc3/mag)     z=0 (uncorrected for AGN feedback) z=0 (corrected for AGN feedback) Blanton et al 2003 Fig. 3.\u2014 shows the SDSS g band galaxy luminosity function at z = 0. The thin dotted curve is directly from averaging over C and V run, whereas the thick solid curve is obtained after correcting for AGN feedback. Also shown as the thick dashed curve is the Schechter \ufb01t to the SDSS data (Blanton et al. 2003b). is probably a result of resolution e\ufb00ect. For the results that we present subsequently, these \u201cdefects\u201d do not materially alter any conclusions that we draw, because we are mostly interested in evolution of galaxies segregatd in mass and in environments, which do not depend strongly on precise abundances of galaxies. Figure 4 shows the rest-frame UV (at 1700\u02da A) luminosity functions at several redshifts, along with UV and IR (ULIRG and LIRG) observational data, to check if the reasonable agreement between simulations and observations found at lower redshift (Figure 2 and Figure 3) extend to higher redshifts. We convert SFR of each simulated galaxy to MAB(1700\u02da A) using the standard conversion formula, SFR = 6.1 \u00d7 10\u2212[8+0.4MAB(1700\u02da A)] M\u2299/yr (Kennicutt 1998) in combination with the AB magnitude system (Oke 1974). We see that the simulations agree well with the UV observations for MAB(1700\u02da A) > \u221222, within the uncertainties. A signi\ufb01cant portion of the disagreement between simulations and UV data at MAB(1700\u02da A) < \u221222 is removed when the abundance of ULIRGs is taken into account, and the simulations become approximately in agreement with observations within the errors at MAB(1700\u02da A) < \u221222. The faint end slope of the UV luminosity functions appear to be steeper than \u03b1 = \u22121.5 and about \u03b1 = \u22121.8 to \u22121.7, consistent with observations (e.g., Yan & Windhorst 2004; Bouwens et al. 2007; Reddy & Steidel 2009). In summary, our simulations produce properties of galaxies are in good agreement with a variety of observations that allow us now to examine their global evolutionary trends. \u2013 9 \u2013 \u221225 \u221224 \u221223 \u221222 \u221221 \u221220 \u221219 \u221218 \u22125 \u22124 \u22123 \u22122 MAB (1700) dn/dMAB(1700) (Mpc\u22123)     z=0 z=0.5 z=1.0 z=1.6 z=2.5 z=3.1 z=5.0 z=1.9\u22122.7 UV (Reddy & Steidel 2009) z=2.7\u22123.4 UV (Reddy & Steidel 2009) z=2 LIRG and ULIRG (Caputi etal 2007) \u001f = \u22121.5 \u001f = \u22121.7 Fig. 4.\u2014 shows the rest-frame UV (at 1700\u02da A) luminosity functions at z = 0, 0.5, 1.0, 1.6, 2.5, 3.1, 5 with 1\u03c3 Poisson errorbars indicated on the z = 1 curve. The UV observational data are from Reddy & Steidel (2009): solid diamonds at z = 1.9\u22122.7 and open diamonds at z = 2.7\u22123.4. Also shown as two solid dots are observed LIRG and ULIRG data from Caputi et al. (2007). The ULRIG and LIRG data points are shown, if they were not reprocessed through dust, to account for the fact that we do not process stellar light through dust grains. The dotted and dashed straight lines indicate the faint end slope of the luminosity function at \u03b1 = \u22121.5 and \u22121.7, respectively. 3.2. Global Trends of Galaxy Formation and Evolution Figure 5 shows the cumulative light density distribution in rest-frame SDSS z band as a function of absolute z magnitude from redshift z = 0 to z = 3.1. The fact that the redshift z = 0 values of the two runs bracket the SDSS data at redshift z \u223c0.1 is self-consistent. We did not average the two runs in this case, because there is a substantial mismatch between the two at z < \u221225, because the abundance of these most luminous galaxies, at the exponential tail, depends more strongly on large-scale environmental density. We see that from z = 0 (red circles) to z = 1.6 (black triangles) there is a trend that light density increases with increasing redshift, in accord with the same trend for SFR density seen in Figure 1. It is also seen that the percentage contribution to the light density of galaxies at the most luminous end as well as the luminosity of the most luminous galaxies increases with increasing redshift from z = 0 to z = 1.6. This particular manifestation is in excellent agreement with the apparent downsizing phenomenon \ufb01rst pointed out by Cowie et al. (1996, see Figures 6, 20, 24 therein). As we will show later, the underlying reason for this apparent downsizing phenomenon is simply that the luminosity function in rest-frame z (or in restframe K-band, as shown in Cowie et al. (1996)) becomes brighter with increasing redshift from z = 0 to z \u223c1.6, but the brightening is across the entire spectrum of galaxy masses. \u2013 10 \u2013 \u221229 \u221228 \u221227 \u221226 \u221225 \u221224 \u221223 \u221222 \u221221 \u221220 \u221219 7 7.5 8 8.5 9 9.5 absolute z magnitude log light density (>z) (Lsun/Mpc3)     redshift=0 (C) redshift=0.5 (C) redshift=1.0 (C) redshift=1.6 (C) redshift=2.5 (C) redshift=3.1 (C) redshift=0 (V) redshift=0.5 (V) redshift=1.0 (V) redshift=1.6 (V) redshift=2.5 (V) redshift=3.1 (V) Blanton et al 2003 Fig. 5.\u2014 shows the cumulative light density distribution in rest-frame SDSS z band as a function of absolute z magnitude at redshifts z = (0, 0.5, 1.0, 1.6, 2.5, 3.1) for both C and V runs. Also shown as the horizontal dashed line is the value from SDSS data at z \u223c0.1 (Blanton et al. 2003b). Similar redshift trends are seen in other SDSS broad bands. However, the brightening for galaxies of di\ufb00erent masses, i.e., sSFR, displays an important di\ufb00erential, where sSFR as a function of stellar mass has a negative slope that steepens with decreasing redshift, as shown in Figure 6 next. Figure 6 shows the distribution of galaxies in the sSFR-Mstar plane at z = (0, 0.5, 1.6, 3.1), where each galaxy is also encoded with the average gas entropy at its virial radius a higher entropy corresponds to a larger circle. The physical importance of gas entropy will become apparent later. The horizontal line in each panel indicates the value of sSFR at which the galaxy would double its stellar mass in one concurrent Hubble time. We see that at z = 3.1 (bottom right panel) most galaxies lie above the horizontal line and sSFR is nearly independent of stellar mass, indicating that all galaxies at this redshift are growing at a similar and rapid pace. As we will show later (see Figure 12), the cold gas in\ufb02ow rate signi\ufb01cantly exceeds SFR, indicating that SF is demand based and self-regulated. Comparison of the four panels clearly shows that a progressively larger fraction of galaxies of all masses downcross the horizontal line with decreasing redshift, with larger galaxies starting that migration earlier and generally at a faster pace than less massive galaxies. It is quite visible that the downcrossing of galaxies over the horizontal line is accompanied by orders of magnitude increase in gas entropy at the virial radii of these galaxies, i.e., circles get much larger moving downward. It is seen that some galaxies of all masses from C run occupy the lower quarter of the lower redshift (upper left and upper right) panels that have the lowest sSFR and largest entropies (large circles); these are galaxies in high entropy cluster environments. The negative slope \u2013 11 \u2013 9 10 11 12 \u221213 \u221212 \u221211 \u221210 \u22129 \u22128 sSFR (yr\u22121)     z=0.0 (C) z=0.0 (V) doubling in tH 9 10 11 12 \u221213 \u221212 \u221211 \u221210 \u22129 \u22128     z=0.5 (C) z=0.5 (V) doubling in tH 9 10 11 12 \u221213 \u221212 \u221211 \u221210 \u22129 \u22128 Mstar (Msun) sSFR (yr\u22121)     z=1.6 (C) z=1.6 (V) doubling in tH 9 10 11 12 \u221213 \u221212 \u221211 \u221210 \u22129 \u22128 Mstar (Msun)     z=3.1 (C) z=3.1 (V) doubling in tH Fig. 6.\u2014 shows a scatter plot of sSFR versus galaxy stellar mass at z = 0 (top left), z = 0.5 (top right), z = 1.6 (bottom left) and z = 3.1 (bottom right) for both C (red) and V (blue) run. Each circle is a galaxy from C (red) and V (blue) run with its size proportional to the logarithm of the gas entropy at its virial radius. The horizontal line in each panel indicates the sSFR value at which a galaxy would double its stellar mass in a Hubble time. of the sSFR as a function of stellar mass appears to steepen wth decreasing redshift, which will be quanti\ufb01ed in Figure 7. As a result, by z = 0, only a signi\ufb01cant fraction of galaxies of stellar mass less than \u223c1010 M\u2299can still double their mass in a Hubble time and they are mostly in the V run (i.e., not in overdense regions), while the vast majority of larger galaxies have lost that ability. A comparison of red (galaxies from C run) and blue circles (galaxies from V run) as well as substantial dispersions of sSFR at a \ufb01xed stellar mass within each run indicates that there are substantial variations among galaxies of a same mass starting at z = 1.6 that must depend on variables other than just the contemporary galaxy mass. As will be shown and discussed extensively subsequently, environmental dependence plays the most fundamental role in shaping the formation and evolution of galaxies, and we \ufb01nd that the gas entropy at the virial radius of each galaxy is a useful variable for understanding the underlying physical cause. Figure 7 shows the mean sSFR as a function of stellar mass at redshifts z = (0, 0.5, 1.6, 1.9, 4.0). We see that simulations show a trend of steepening slope with decreasing redshift, visually noticed in Figure 6 above, which is generally consistent with observations. The agreement of sSFR between our simulations and IR-UV observations of Martin et al. (2007) at z = 0 \u22121 is good within uncertainties. Currently, the uncertainties in the observed data are still quite substantial, especially at higher redshifts, as evidenced by the di\ufb00erences among the shown observations of Elbaz et al. (2007), Oliver et al. (2010) and Karim et al. (2011) and others \u2013 12 \u2013 9 10 11 12 13 \u221212 \u221211 \u221210 \u22129 log Mstar (Msun) log sSFR (yr\u22121)     z=0.0 z=0.5 z=1.0 z=1.9 z=4.0 z=0.1,0.5,1.0 (Martin et al 2007) z=1 (\u22120.1) (Elbaz et al 2007) z=0\u22121.6 (\u22120.35) (Karim et al 2011) z=0 (\u22120.52) to z=2 (\u22120.24) (Oliver et al 2010) Fig. 7.\u2014 shows the average sSFR as a function of stellar mass at redshifts z = (0, 0.5, 1.6, 1.9, 4.0) for both C (solid symbols) and V run (open symbols) with 1\u03c3 Poisson errorbars. The IR-to-UV observational data points are from Martin et al. (2007) (red, blue and green asterisks for z = 0.1, z = 0.5 and z = 1, respectively) are shown exactly as observed, from FIR observations of Elbaz et al. (2007) as the cyan line at z = 1 of log SFR \u2212logMstar slope of \u22120.1, from radio observations of Oliver et al. (2010) as two magenta lines are shown from z = 0 of slope \u22120.52 to z \u223c2 of slope \u22120.24, and from radio observations of Karim et al. (2011) as the dashed cyan for the slope range at z = 0 \u22121.6 of slope \u22120.35. (not shown here). Nonetheless, there is clear evidence of a negative slope of sSFR as a function of stellar mass that gradually \ufb02attens with increasing redshift, in both our simulations and these observations. In Figure 8 we plot the maximum and mean SFR as a function of stellar mass for seven di\ufb00erent redshifts z = (0, 0.5, 1.0, 1.6, 2.5, 3.1, 4.0) for both C (left panel) and V (right panel) runs. One striking result that is best seen in this plot is that the maximum SFR of galaxies at a given mass increases with increasing redshift up to zmax = 1.6 \u22123.1. Beyond zmax, that uptrend for maximum SFR at a \ufb01xed mass stops and appears to become static. Interestingly, the mean SFR at a \ufb01xed mass continues to increase up to the highest redshift shown and the ratio of maximum SFR to mean SFR at a \ufb01xed mass continues to shrink, reaching a value of 1 \u22123 in the range z = 2 \u22124, suggesting that at high redshift galaxy formation becomes more \u201cuniform\u201d. The second striking result is that the curves are nearly parallel to one another in the C run, suggesting that SFR of galaxies of di\ufb00erent masses evolve with redshift at similar rates. This point was noted earlier observationally, \ufb01rst by Zheng et al. (2007) (see their Figures 1,2). As shown in Figure 7, the rate of change of sSFR for galaxies of di\ufb00erent mass galaxies is, however, not exactly constant across the mass spectrum. We see very clearly here by comparing the two panels in Figure 8 that this di\ufb00erential at low \u2013 13 \u2013 8 9 10 11 12 13 \u22122 \u22121 0 1 2 3 log Mstar (Msun) log SFR(max) and SFR(mean) (Msun/yr)     SFR = Mstar 3/4 SFR(max) z=0 (C) SFR(max) z=0.5 (C) SFR(max) z=1.6 (C) SFR(max) z=3.1 (C) SFR(max) z=4.0 (C) SFR(mean) z=0 (C) SFR(mean) z=0.5 (C) SFR(mean) z=1.6 (C) SFR(mean) z=3.1 (C) SFR(mean) z=4.0 (C) 8 9 10 11 12 13 \u22122 \u22121 0 1 2 3 log Mstar (Msun) log SFR(max) and SFR(mean) (Msun/yr)     SFR = Mstar 3/4 SFR(max) z=0 (V) SFR(max) z=0.5 (V) SFR(max) z=1.6 (V) SFR(max) z=3.1 (V) SFR(max) z=4.0 (V) SFR(mean) z=0 (V) SFR(mean) z=0.5 (V) SFR(mean) z=1.6 (V) SFR(mean) z=3.1 (V) SFR(mean) z=4.0 (V) Fig. 8.\u2014 shows maximum (solid symbols) and mean SFR (open symbols) as a function of stellar mass at redshifts z = (0, 0.5, 1.0, 1.6, 2.5, 3.1) for both C (left) and V (right) run. The dashed magenta line has a slope of 3/4; it is not a \ufb01t to the curves but to guide the eye to see the general trend. redshift can be attributed, to a large degree, to less massive galaxies in the V run, i.e., in low density environment, that refuse to join the dimming trend of galaxies in high density environment. The physical reason for this will be made clear in \u00a73.2. We note that beyond zmax the mass at the high end is truncated at progressively smaller values with increasing redshift. This sharp cuto\ufb00at the high end may be somewhat arti\ufb01cial due to the limited simulation box size we have, but largely re\ufb02ects the hierarchical nature of growth of dark matter halos in the standard cold dark matter model. As we have shown earlier in Figure 1 and Figure 5 the SFR density and light density peak at z \u223c1.5 \u2212 2, this suggests, in combination with what is seen in Figure 8, that the growth of halos with time dominates over the downsizing trend of SFR down to z = 1.5 \u22122 from high redshift. Thereafter, gastrophysical processes that act upon galaxies at z < 1.5 \u22122 cause galaxy formation and evolution to deviate from the track of continued hierarchical buildup of Table 1. SFR evolution as a function of stellar mass, \ufb01tted in the form log SFR/( M\u2299yr\u22121) = a(1 + z)b row 1: stellar mass range; row 2: a; row 3: b. Stellar Mass 109 \u22121010 M\u2299 1010 \u22121011 M\u2299 1011 \u22121012 M\u2299 a -0.59 -0.018 0.80 b 1.9 2.1 2.4 \u2013 14 \u2013 0 1 2 3 4 \u22121 0 1 2 z log <SFR> (Msun/yr)     Mstar=109\u221210Msun (C) Mstar=109\u221210Msun (V) Mstar=1010\u221211Msun (C) Mstar=1010\u221211Msun (V) Mstar=1011\u221212Msun (C) Mstar=1011\u221212Msun (V) Mstar=109\u221210Msun (Martin et al 2007) Mstar=1010\u221211Msun (Martin et al 2007) Mstar=1011\u221212Msun (Martin et al 2007) Mstar=109\u221210Msun (Zheng et al 2007) Mstar=1010\u221211Msun (Zheng et al 2007) Mstar=1011\u221212Msun (Zheng et al 2007) Fig. 9.\u2014 shows the mean SFR for galaxies of stellar mass in three bins, 109 \u22121010 (red circles), 1010 \u22121011 (green squares) and 1011 \u22121012 M\u2299i (blue triangles), as a function of redshift. The solid symbols are from C run and open symbols from V run. The overplotted black curves are 1st order polynomial \ufb01ts to the three mass bins, averaged over C and V run curves. Also shown as hexagons and diamonds are observations from Martin et al. (2007) and Zheng et al. (2007), respectively. dark matter halos, resulting in a trend where the total luminosity density and SFR density decreases with time and di\ufb00erential evolution of galaxies with di\ufb00erent masses. Finally, in Figure 9, we show the redshift evolution of SFR for galaxies in three stellar mass bins: 109 \u22121010 (red circles), 1010 \u22121011 (green squares) and 1011 \u22121012 M\u2299(blue triangles). The observational data are still relatively uncertain at higher redshift bins for the low-mass galaxies, as indicated by the di\ufb00erence between di\ufb00erent observational determinations. The agreement between simulations and observations are reasonable, especially for the highest mass bin. To best gauge the evolution at low redshift, we decide to \ufb01t the simulated results using 1st order polynomial \ufb01ts using only the points at z < 2, although higher (e.g., 2nd) order polynomial \ufb01ts signi\ufb01cantly improve the goodness of the \ufb01ts at z \u22652. The best \ufb01t parameters are tabulated in Table 1. It is evident from the \ufb01tting parameters that higher-mass galaxies su\ufb00er a steeper drop in SFR in the range z = 0 \u22122 than lower-mass galaxies. This illustrates clearly the di\ufb00erential evolution of sSFR or SFR with redshift for galaxies of di\ufb00erent masses. \u2013 15 \u2013 3.3. Physical Origin: Gravitational Heating of External Gas We now perform a detailed analysis of the physical conditions of galaxies to understand the cause of the trend of cosmic dimming and its di\ufb00erential nature found in \u00a73.2. A useful starting point may be to quantify the evolution of the amount of gas that can cool to feed galaxies. The amount of gas that can cool depends on density, temperature, metallicity as well as what happens to the gas subsequently, such as shocks, compression, etc. It is therefore highly desirable to project the multidimensional parameter space to as a low dimension space as possible. Gas entropy provides an excellent variable to characterize gas cooling properties. As \ufb01rst insightfully noted by Scannapieco & Oh (2004), the cooling time of any parcel of gas has a minimum value that only depends on the entropy of the gas. Following them we write the gas cooling time in the following form: tcool = (3/2)nkBT n2 e\u039b(T) = S3/2 \" 3 2 \u0012\u00b5e \u00b5 \u00132 kB T 1/2\u039b(T) # , (1) where n and ne is total and electron density, respectively; kB is the Boltzmann\u2019s constant, T temperature and \u039b cooling function; \u00b5 = 0.62 and \u00b5e = 1.18 for ionized gas that we are concerned with; S is the gas entropy de\ufb01ned as S \u2261 T n2/3, (2) in units of K cm2. At a \ufb01xed S the cooling time is inversely proportional to T 1/2\u039b(T). The cooling function \u039b(T) depends on the gas metallicity, which is found in our simulations to be almost universal at a value of \u223c0.1 Z\u2299for gas at virial radii at the redshifts we are interested in here. Adopting a metallicity of 0.1 Z\u2299the term T 1/2\u039b(T) has a minimum at Tmin \u223c2.3 \u00d7 105K (we note that reasonable variations in metallicity, say, to 0.3 Z\u2299from 0.1 Z\u2299, does not materially impact our arguments). Therefore, if tcool(Tmin) > tH, the gas can never cool in a Hubble time, because (1) entropy is a non-decreasing quantity in the absence of cooling and (2) cooling will be insigni\ufb01cant within tH given the initial requirement. Subsequent adiabatic compression or expansion does not alter its fate. Any additional input of entropy, e.g., by shocks, would increase the entropy and make it more di\ufb03cult to cool. Thus, there is a critical value of entropy Scrit for any gas above which gas can no longer cool. The following \ufb01tting formula provides a \ufb01t to computed critical entropy Scrit for gas metallicity of 0.1 Z\u2299with an accuracy of a few percent over the entire redshift range z = 0\u22127: log[Scrit/(K cm2)] = 9.183 \u22120.167z + 0.0092z2. (3) In Figure 10 we place each galaxy in the entropy-overdensity parameter plane at four redshifts (z = 0, 0.5, 1.6, 3.1). The overdensity is de\ufb01ned to be the dark matter density, smoothed by a Gaussian function of radius 2h\u22121Mpc comoving, divided by the global mean \u2013 16 \u2013 \u22120.5 0 0.5 1 1.5 7 8 9 10 11 12 log S (K cm2)     z=0.0 (C) z=0.0 (V) tcool = tH \u22120.5 0 0.5 1 1.5 7 8 9 10 11 12     z=0.5 (C) z=0.5 (V) tcool = tH \u22120.4 \u22120.2 0 0.2 0.4 0.6 0.8 1 6 7 8 9 10 11 log overdensity log S (K cm2)     z=1.6 (C) z=1.6 (V) tcool = tH \u22120.2 0 0.2 0.4 0.6 6 7 8 9 10 11 log overdensity     z=3.1 (C) z=3.1 (V) tcool = tH Fig. 10.\u2014 shows local mean gas entropy at virial radius as a function of local overdensity smoothed by a Gaussian window of radius 2h\u22121Mpc comoving at redshifts z = 0 (top left), z = 0.5 (top right), z = 1.6 (bottom left) and z = 3.1 (bottom right). Each circle is a galaxy from C (red) and V (blue) run with its size linearly proportional to the inverse of the logarithm of its sSFR; smaller circles correspond to higher sSFR in this representation. Also shown as the horizontal bar is the critical entropy Scrit where cooling time is equal to the Hubble time. dark matter density. We see that at z = 3.1 the entropy of almost all galaxies is located below the critical entropy line, indicating that no signi\ufb01cant amount of gas at the virial radius has been heated. One should note that, once a gas element has upcrossed the critical entropy Scrit, it will not fall back below it again. Therefore, for most galaxies, the moment that it upcrosses Scrit marks the beginning of the cold gas starvation phase, because galaxies tend to move to higher density, higher entropy regions with time. The size of each circle in Figure 10 is linearly proportional to the inverse of the logarithm of the sSFR of each galaxy. We see that galaxies above the Scrit line have dramatically larger circles, i.e., having lower sSFR. It is also interesting to see that galaxies that upcross the Scrit line do so only in overdense region (smoothed by a Gaussian radius of 2h\u22121Mpc). This is clear and powerful evidence that the di\ufb00erential dimming of galaxies is caused by heating of gas in overdense regions; in other words, galaxy formation and long-term evolution are determined by external supply of cold gas, which in turn depends on overdensity on intermediate scales (\u223c1Mpc) that dictate the entropy of shock heated gas. To help further understant this, in Figure 11, we plot the galaxies in the entropy-halo mass parameter plane at four redshifts. Also shown as the dashed green line in each panel \u2013 17 \u2013 10 11 12 13 6 7 8 9 10 11 12 log <S> (K cm2)     z=0.0 (C) z=0.0 (V) tcool = tH at halo virial temperature 10 11 12 13 6 7 8 9 10 11 12     z=0.5 (C) z=0.5 (V) tcool = tH at halo virial temperature 10 11 12 13 6 7 8 9 10 11 12 log Mhalo (Msun) log <S> (K cm2)     z=1.6 (C) z=1.6 (V) tcool = tH at halo virial temperature 10 11 12 13 6 7 8 9 10 11 12 log Mhalo (Msun)     z=3.1 (C) z=3.1 (V) tcool = tH at halo virial temperature Fig. 11.\u2014 shows local mean gas entropy at virial radius as a function of halo mass at redshifts z = 0 (top left), z = 0.5 (top right), z = 1.6 (bottom left) and z = 3.1 (bottom right). Each circle is a galaxy from C (red) and V (blue) run with its size proportional to the logarithm of the local overdensity smoothed by a Gaussian window of radius 0.5h\u22121Mpc comoving. Also shown as the horizontal bar is the critical entropy Scrit where cooling time is equal to the Hubble time. The inclined line indicates the gas entropy at virial radius if the temperature is exactly equal to the virial temperature of the halo. is the gas entropy at virial radius, if the temperature is heated up to the virial temperature of the host halo itself. One notices that at z = 3.1 when no galaxies more massive than \u223c5 \u00d7 1012 M\u2299has formed, virial heating due to formation of halos is insu\ufb03cient to upcross the entropy barrier. This is the redshift range where an ample amount of cold gas is available to feed galaxy formation, resulting in sSFR that is very weakly mass-dependent and galaxy formation in the \u201cupsizing\u201d domain, in concert with the hierarchical buildup of dark matter halos. At lower redshifts, formation of larger halos more massive than \u223c1 \u00d7 1013 M\u2299(i.e., groups and clusters) as well as collapse of larger waves due to formation of large-scale structures (\ufb01laments and walls) raise a progressively larger fraction of regions to higher entropy than Scrit. This causes a dichotomy in the entropy distribution, especially at the low halo mass end (\u22641011 M\u2299) as follows. There is a branch of low-mass galaxies in low density environments, as evidenced by their small circle sizes, which are located along or below the green line in Figure 11 and have entropies comparable to or lower than what is produced due to adiabatic shock heating accompanying the formation of the halos themselves. These small galaxies correspond to galaxies in the upper left corner in Figure 6 that are still able \u2013 18 \u2013 to double their mass in a Hubble time. Then there is another branch of small galaxies that lie above the Scrit line and are in overdense regions, as evidenced by their large circle sizes. These small galaxies are red and dead, correspond to dwarf galaxies in heated \ufb01laments and group/cluster environments. Generally, the gas entropy of galaxies above the green dashed line is higher than what virial shock heating due to the formation of the halo itself produces; therefore, all these galaxies above the green line are in essence \u201csatellite\u201d galaxies within a large halo (such as a group or cluster) or, if one were to generalize it, \u201csatellite\u201d galaxies in a gravitational shock heated region due to collapse of large-scale structure (\ufb01laments or pancakes), not necessarily virialized. The concentration of galaxies with entropy along the green line is due to virial shock heating of halo itself, i.e., the primary galaxy. It is striking that even at z = 0 there is only a very handful of (blue circle) galaxies with mass greater than 1012 M\u2299that lie above the Scrit from the V run. Taken together, this is unequivocal evidence that it is the external gas heating that drives the gas supply hence star formation and galaxy evolution; the absence of such heating in the V run has allowed galaxies there to remain active in star formation at present. 0 1 2 3 4 \u221211 \u221210 \u22129 \u22128 z log specific cold gas flow rates and sSFR (yr\u22121)     sSFR, Ms=109\u22121010 (C) sSFR, Ms=109\u22121010 (V) specificc cold inflow rate, Ms=109\u22121010 (C) specificc cold inflow rate, Ms=109\u22121010 (V) sSFR, Ms=1010\u22121011 (C) sSFR, Ms=1010\u22121011 (V) specificc cold inflow rate, Ms=1010\u22121011 (C) specificc cold inflow rate, Ms=1010\u22121011 (V) a simple universal scaling Fig. 12.\u2014 shows the mean speci\ufb01c cold gas in\ufb02ow rate (de\ufb01ned to be the cold gas in\ufb02ow rate per unit stellar mass) and mean sSFR for galaxies in two di\ufb00erent stellar mass bins for C and V run. The cold gas is de\ufb01ned to be that with cooling time less than the dynamic time of the galaxy. Also shown as solid green curve is the general scaling of gas in\ufb02ow rate, which is assumed to be proportional to 4\u03c0r2 v(z)vv(z)\u03c13(z), where rv, vv and \u03c1(z) are redshift-dependent virial radius, virial velocity and mean gas density. Figure 12 shows the mean speci\ufb01c cold gas in\ufb02ow rate (de\ufb01ned to be the cold gas in\ufb02ow rate per unit stellar mass and cold gas is de\ufb01ned to be gas that has a cooling time less than the galaxy dynamical time at the virial radius) and mean sSFR for galaxies in two di\ufb00erent \u2013 19 \u2013 stellar mass bins for C and V run. Several points are worth noting. First, we see that the cold gas in\ufb02ow rates are generally higher than star formation rates, suggesting self-regulation of star formation, mostly due to feedback from star formation. Second, the ratio of cold gas in\ufb02ow rate to SFR decreases with decreasing redshift, pointing to a gradual transition of SF regimes from gas demand based at high redshift to gas supply based at low redshift. Third, the rough similarity between the evolution of the gas in\ufb02ow rate based on a simple scaling and the actual computed rates suggests the bulk of the cosmic dimming trend with decreasing redshift can be attributed to the decrease of mean density of the universe with increasing time and the evolution of the Hubble constant (or density parameter). Finally, the gravitational heating e\ufb00ects add a di\ufb00erentiating process on top of this general dimming trend, evident here by the di\ufb00erent steepening with decreasing redshift of the speci\ufb01c gas in\ufb02ow rates and SFR at lower redshifts among galaxies of di\ufb00erent masses and galaxies in di\ufb00erent environments (C versus V run). 7 8 9 10 11 0 0.2 0.4 0.6 0.8 1 overdense region g \u2212 r     z=0.0 (C) z=0.0 (V) tcool = tH 7 8 9 10 11 0 0.2 0.4 0.6 0.8 1 overdense region     z=0.5 (C) z=0.5 (V) tcool = tH 7 8 9 10 0 0.2 0.4 0.6 0.8 1 overdense region log <S> (K cm2) g \u2212 r     z=1.6 (C) z=1.6 (V) tcool = tH 7 8 9 0 0.2 0.4 0.6 0.8 1 log <S> (K cm2)     z=3.1 (C) z=3.1 (V) tcool = tH Fig. 13.\u2014 shows SDSS g-r color of galaxies as a function of local mean gas entropy at the virial radius at z = 0 (top left), z = 0.5 (top right), z = 1.6 (bottom left) and z = 3.1 (bottom right). The galaxies in C run are shown in red and those in V run in blue. The size of each circle is proportional to the logarithm of the galaxy stellar mass. Also shown as the vertical line is the critical entropy Scrit where cooling time is equal to the Hubble time. Finally, in Figure 13, we place galaxies in the color-entropy plane. Four things are immediately noticeable. First, the vast majority of galaxies are blue (in color, not the color of the plotted circles) and there is no strong evidence of bimodality in color at z \u22651.6. Second, at z = 0\u22120.5, almost all galaxies in the V run occupy the blue peak at g \u2212r \u223c0.2\u22120.6 with very few in the red peak. Third, the vast majority of galaxies on the left side of the critical \u2013 20 \u2013 entropy line are in the blue cloud, as they should. Fourth, there is a signi\ufb01cant number of galaxies on the right side of the critical entropy line that appear blue and have masses covering a comparable range compared to those in the red sequence. Thus, Figure 13 gives a physical underpinning for the well-known color-magnitude diagram of galaxies (e.g., Baldry et al. 2004). The existence of the cold-gas-starved yet blue galaxies indicates that external gas heating is the driving force to cause these blue galaxies to migrate upward in Figure 13 to ultimately join the red sequence. The fact that many galaxies in the V run, although having higher sSFR than those in the C run (see Figures 6, Figures 9, Figure 10 and Figure 12), both remain blue (as they should, given the high sSFR) and have low entropies suggest that SF is not the primary driver for the color migration. Internal driver, such as feedback from starbursts or AGN, may play a role in quenching star formation in a small fraction of galaxies that experience immense starbursts (e.g., caused by major mergers); but the situation is unclear at present. 3.4. Predictions Several manifestations of downsizing trends should by now be understood, including (1) the epoch of major stellar mass buildup in massive galaxies is substantially earlier than the epoch of mass buildup in low-mass galaxies, (2) the SF and stellar mass buildup are accelerated in overdense regions compared to less overdense regions, (3) massive galaxies are on average older than less massive galaxies, (4) galaxies of all masses, on average, get bluer with increasing redshift, (5) galaxy self metal enrichment shifts from high-mass galaxies at high redshift to lower-mass galaxies at lower redshift, all in broad agreement with a variety of observations (e.g., Kodama et al. 2004; P\u00b4 erez-Gonz\u00b4 alez et al. 2005; Bundy et al. 2006; Noeske et al. 2007; Zheng et al. 2007; Martin et al. 2007; Tresse et al. 2007; Buat et al. 2007; Lehmer et al. 2008; Mobasher et al. 2009; Hartley et al. 2010; Cirasuolo et al. 2010; Karim et al. 2011; Pilyugin & Thuan 2011). This model provide a coherent and uni\ufb01ed physical interpretation. Many other general trends in galaxy formation and evolution that this model would predict have already been con\ufb01rmed by observations, including (1) the galaxy color-environment relation (e.g., Blanton et al. 2005), (2) galaxy star formation as a function of environment, speci\ufb01cally the dramatic transition at a few cluster virial radii that mark location of virial shocks (e.g., G\u00b4 omez et al. 2003), (3) the trend of galaxies having higher sSFR and becoming bluer towards voids from cluster environments (e.g., Kau\ufb00mann et al. 2004; Rojas et al. 2004, 2005), (4) redder galaxies have stronger correlation functions than blue galaxies, irrespective of their luminosities (e.g., Zehavi et al. 2005). Several additional relatively robust trends may be predicted: (1) the faint end slope of the galaxy luminosity function should approach the Press-Schechter value of \u223c\u22122.0 at \u2013 21 \u2013 high redshift z \u22656, subject to uncertain e\ufb00ects of cosmological reionization. (2) Crosscorrelation between CMB Sunyaev-Zeldovich y maps and density of red galaxies is expected to be positive and the opposite is true for that between y maps and density of blue galaxies. (3) Correlations (galaxy-galaxy lensing) between background galaxy shapes and foreground red galaxies should be systematically stronger than between background galaxy shapes and foreground blue galaxies. 4. Conclusions With high resolution and a physically sound treatment of relevant physical processes, our state-of-the-art, adaptive mesh-re\ufb01nement Eulerian cosmological hydrodynamic simulations reproduce reasonably well some key observables of galaxies as a whole, including luminosity function, color distribution and star formation history. This allows us to examine, in addition, with con\ufb01dence, some global trends of formation and evolution of galaxies. Several \ufb01ndings are interesting and new. (1) The overall dimming trend of galaxies of all masses is largely attributable to the evolution of mean cosmic gas density and density parameter. (2) Gravitational shock heating due to formation of halos and large-scale structure adds a di\ufb00erential layer on top of this general global dimming trend. (3) As a result, the mean sSFR is a monotonically increasing function of redshift at a given galaxy mass. (4) The mean sSFR is a monotonically decreasing function of galaxy mass at a given redshift and steepens with decreasing redshift, which overwhelmed the continued hierarchical growth of halos at low redshift range z = 0 \u22122 and is the underlying physical driver for some apparent \u201canti-hierarchical\u201d manifestations of some galaxy properties. (5) The SFR function is a convolution of sSFR and galaxy mass function it increases from z = 0 to z \u223c2 and thereafter decreases towards (i.e., an upsizing trend) higher redshift. (6) Although the buildup of dark matter mass and stellar mass are not necessarily exactly parallel to one another, the overall trend for both is still hierarchical. The underlying physical cause Trend (2) above is as follows. With time, more regions are heated to higher temperatures due to formation of large halos (such as groups and clusters) and large-scale structures that result in a progressively larger fraction of halos inhabiting in regions where gas has too high an entropy to cool to continue feeding the residing galaxies. Thus, overdense regions enter the cold gas starvation phase earlier than lower density regions. Because larger halos tend to reside in more overdense regions than smaller halos, the net di\ufb00erential e\ufb00ects are that larger galaxies fall below the general dimming trend at higher redshift than less massive galaxies, the sSFR as a function of galaxy mass steepens with time and galaxies with the high sSFR gradually shift to lower density environments. By z = 0, galaxies with high sSFR (such that they may be categorized as blue) have almost entirely left the cluster environments and can be found in \ufb01elds and voids. Thus, the processes that \u2013 22 \u2013 drive galaxy evolution are mostly external at z \u22642, due to gravitational heating of either its own halo formation, or formation of the primary galaxy or group/cluster halo in the case of a satellite galaxy, or collapse of embedding large-scale structures such as \ufb01laments or Zeldovich pancakes, which at low redshift correspond to the cosmic web of warm-hot intergalactic medium (e.g., Cen & Ostriker 1999). We also \ufb01nd that the cold gas starvation due to gravitational heating provides a viable physical mechanism to explain the observed migration of galaxies to the red sequence from the blue cloud as well as many other phenomena, such as the observed color-density relation, the trend of galaxies becoming bluer in lower density environment, and others. Several predictions are made in \u00a73.4. As a site note, these \ufb01ndings may imply that the concept of two modes of gas accretion onto galaxies (e.g., Kere\u02c7 s et al. 2005; Dekel & Birnboim 2006), while very useful to crystallize some aspects of galaxy formation, may need to be mended to be globally applicable, because the amount of cold as well as hot gas around a galaxy depends on both its mass and its external environment (and perhaps its own history). For example, a small galaxy in a cluster environment would have a very di\ufb00erent mix of cold and hot gas components from a galaxy of the same mass in a void environment, with the latter having a much larger cold gas fraction than the former. We further note that galaxy formation recipes, such as those used in semi-analytic modeling, may need to include the important external e\ufb00ects found here to be physically realistic. In essence, realistic treatments of galaxy formation have to be multivariant, not just dependent on the contemporary halo mass. I would like to thank Dr. M.K.R. Joung for help on generating initial conditions for the simulations and running a portion of the simulations and Greg Bryan and John Wise for help with Enzo code. I would like to thank Dr. D. Christopher Martin for kindly providing plotting data for observations. Computing resources were in part provided by the NASA HighEnd Computing (HEC) Program through the NASA Advanced Supercomputing (NAS) Division at Ames Research Center. This work is supported in part by grants NNX08AH31G and NAS8-03060. The simulation data are available from the author upon request.",
                    "introduction": "The intriguing phenomenon of the so-called cosmic downsizing (e.g., Cowie et al. 1996) has had practioners of the cold dark matter cosmogony perplexed. Innovative astrophysical 1Princeton University Observatory, Princeton, NJ 08544; cen@astro.princeton.edu arXiv:1104.5046v1  [astro-ph.CO]  26 Apr 2011 \u2013 2 \u2013 ideas have been proposed to introduce scales in the growth of galaxies within the context of hierarchical formation of dark matter halos in the standard cosmological constant-dominated cold dark matter model (LCDM) (Komatsu et al. 2010). Successful models have been con- structed, for example, semi-analytically by incorporating possible AGN feedback (e.g., Cro- ton et al. 2006; Bower et al. 2006). In this work we investigate the nature of cosmic downsizing in the LCDM model by performing and analyzing high-resolution large-scale hydrodynamic galaxy formation simu- lations, including feedback from star formation and proper treatment of gravitational heating due to collapse of large-scale structure. Our simulations reproduce well observations that galaxies of higher star formation (SF) rates (SFR) contribute progressively more to the over- all SFR density towards higher redshift (e.g., Cowie et al. 1996). We \ufb01nd that this cosmic downsizing phenomenon is part of a fundamental and universal trend that the sSFR, on average, is a monotonic function of galaxy halo (or stellar) mass with lower-mass galaxies having higher sSFR. As a result, on average, the stellar mass doubling time is a monotoni- cally decreasing function with decreasing stellar mass at any redshift and for more massive galaxies that upcrosses the Hubble time earlier than less massive galaxies. The sSFR of galaxies of all masses, on average, display a monotonic and mass-dependent rate of increase with redshift. In this sense, we see primarily a trend of \u201cdi\ufb00erential galaxy dimming\u201d from high redshift to z = 0. Although the sSFR trend continues to the highest redshift we have examined, the SFR density that is a convolution of these trends and halo abundance evolu- tion in the cold dark matter model displays a maximum at z = 1.5 \u22122. Related, within the simulation volume and density \ufb02uctuations that we probe, we also see an \u201cupsizing\u201d trend at z \u22652 in that the maximum SFR of galaxies decreases towards still higher redshift, probably re\ufb02ecting the tenet of the standard cold dark matter model of hierarchical buildup of dark matter halos where the abundance of large, star-forming halos start to drop o\ufb00exponentially. We examine the underlying physical cause for these distinct trends. We \ufb01nd that at high redshift (z \u22652) SF is largely gas demand limited, where there is su\ufb03cient supply of cold gas for galaxies to double its stellar mass within a Hubble time and SF is mostly regulated by its own e\ufb03ciency, due to feedback e\ufb00ects from star formation. At z \u22642 SF gradually moves to the regime of being supply limited, dependent on environments, as the supply rate of cold gas decreases, due to a combination of primarily two factors. First, the overall decrease of density [\u221d(1 + z)3] causes the gas in\ufb02ow rate to decline with decreasing redshift. Second, the overall heating of cosmic gas due to formation of large halos (such as groups and clusters) and large-scale structures causes a progressively larger fraction of halos to inhabit in regions where gas has too high an entropy to cool to continue feeding the residing galaxies. The combined e\ufb00ect is di\ufb00erential in that overdense regions are heated earlier and to higher temperatures than lower density regions at any given time. Because larger halos tend to reside, in both a relative and absolute sense, in more overdense regions than smaller halos, the net di\ufb00erential e\ufb00ects are that larger galaxies fall below the general \u2013 3 \u2013 dimming trend at higher redshift than less massive galaxies, the sSFR as a function of galaxy mass steepens with time and galaxies with the high sSFR gradually shift to lower density environments. We do include supernova feedback in the simulations and \ufb01nd that galactic winds are strong for starburst galaxies, strongest at z \u22652 when SF activities are most vigorous and are stronger in less massive galaxies than in large galaxies. But it appears that the stellar feedback processes do not drive any noticeable trend of the sort presented here, although they are important in self-regulating star formation at high redshift when gas supply rate is high. We also \ufb01nd that the cold gas starvation due to gravitational heating provides a natural mechanism to explain the observed migration of galaxies to the red sequence from the blue cloud as well as many other phenomena, such as the observed color-density relation, the trend of galaxies becoming bluer in lower density environment, and others. The outline of this paper is as follows. In \u00a72 we detail our simulations, method of making galaxy catalogs and analysis methods. Results are presented in \u00a73. In \u00a73.1 we compare some basic galaxy observables to observations. In \u00a73.2 we present detailed results and compare to observations. We then examine and understand physical processes that are primarily responsible for the results obtained in \u00a73.3, followed by predictions of the model in \u00a73.4. Conclusions are given in \u00a74."
                },
                {
                    "url": "http://arxiv.org/abs/1102.0262v3",
                    "title": "Physics of Coevolution of Galaxies and Supermassive Black Holes",
                    "abstract": "A new model for coevolution of galaxies and supermassive black holes (SMBH)\nis presented that is physically based. The evolutionary track starts with an\nevent that triggers a significant starburst in the central region of a galaxy.\nIn this model, the main SMBH growth takes place in post-starburst phase fueled\nby recycled gas from inner bulge stars in a self-regulated fashion on a time\nscale that is substantially longer than 100Myrs and at a diminishing Eddington\nratio with time. We argue that the SMBH cannot gorge itself during the\nstarburst phase, despite the abundant supply of cold gas, because star\nformation is a preferred mode of gas consumption in such an environment than\naccretion to the central SMBH. We also show that feedback from star formation\nis at least as strong as that from AGN and thus, if star formation is in need\nof being quenched, AGN feedback generally does not play the primary role. The\npredicted relation between SMBH mass and bulge mass/velocity dispersion is\nconsistent with observations. A clear prediction is that early-type galaxy\nhosts of high Eddingtion rate AGNs are expected to be light-blue to green in\noptical color, gradually evolving to the red sequences with decreasing AGN\nluminosity. A suite of falsifiable predictions and implications with respect to\nrelationships between various types of galaxies and AGN, and others, are made.\nFor those where comparisons to extant observations are possible, the model\nappears to be in good standing.",
                    "authors": "Renyue Cen",
                    "published": "2011-02-01",
                    "updated": "2012-05-23",
                    "primary_cat": "astro-ph.CO",
                    "cats": [
                        "astro-ph.CO",
                        "astro-ph.GA",
                        "astro-ph.HE"
                    ],
                    "main_content": "While the subsequent sections of quantitative physical analysis are independent of statements made in this section, we shall argue for the assertion in the title of this section with logic, in hopes of being able to provide some conceptual clarity to the role of AGN feedback on star formation during the starburst phase. The starting point of the evolutionary sequence is a starburst. It may be triggered by a major merger of two gas-rich galaxies or by other significant events that channel a large amount of gas into the central region in a short period of time. Consider that an event causes a large amount of gas of mass Mgas to land in the central region. Physical processes then operate on the gas to produce a starburst, accompanied by some growth of the central SMBH, along with some associated feedback from both. Extreme events of this kind may be identified with observed Ultra-Luminous InfraRed Galaxies (ULIRGs) (e.g., Sanders et al. 1988) or Sub-Millimeter Galaxies (SMGs) (e.g., Chapman et al. 2005). Theoretical models (e.g, Silk & Rees 1998; Hopkins et al. 2006) have proposed that feedback from AGN is responsible for the regulation of SF and SMBH growth so as to produce the observed Magorrian et al. (1998) relation where the ratio of the final SMBH to bulge stellar mass is MBH : MBG \u223c2 : 1000. We shall now re-examine this case. Consider how the infallen gas may be partitioned. Mass conservation requires MBH + MBG + Mout = Mgas, where Mout is the amount of gas that is blown away from the bulge. Clearly, only a very small fraction of the initial gas Mgas can possibly end up in the central SMBH, i.e., fBH \u2261MBH/ Mgas \u226a1. Let us assume that the reason for a very small fBH is because the feedback from the central SMBH prevented its own further growth during this phase. Since SMBH masses are observed to span a very wide range, it must be that this purported SMBH feedback process that regulates its own growth is galaxy specific, i.e., dependent on at least some physical variables characterizing the galaxy. A usual and reasonable assumption (which we are not advocating at the moment) for that is that either the gravitational potential well of the bulge or of the total halo determines the final SMBH mass, in coordination with its feedback. Does SMBH feedback dominate that of starburst in terms of regulating both SMBH growth and starburst? While we will show later (in \u00a73) that the answer is largely no to regulating the starburst at least, we assume that the answer is yes to both for the sake of continuing the present thought experiment. The simplified sequence of events then plays out \u2013 5 \u2013 more or less as follows. The central SMBH accretes gas and builds up its feedback strength until its mass has reached the observed value, then blows away all the remaining gas and both SMBH accretion and SF stop abruptly. What might have happened to SF during all this time before the gas is blown away? There are three possible scenarios. Scenario #1, the SMBH accretion is so competitive and quick that most of the gas is blown away by the SMBH feedback before much SF has occured. That of course cannot have happened, because that would be inconsistent with the observed MBH \u2212MBG relation. Scenario #2, SF precedes at a pace that is in concert with the SMBH feedback such that by the time that MBH = 0.002( Mgas \u2212Mout), the amount of stars formed is equal to MBG = 0.998( Mgas \u2212Mout); the rest of gas of mass Mout got blown away by the feedback from the SMBH. This scenario is designed to match the observed MBH \u2212MBG relation. What remains undetermined is how large fout \u2261Mout/ Mgas is. Is it close to 1 or 0? In the case fout \u223c1, because (1 \u2212fout) is a small number, there is no particular preferred value for it. The potential well created by the eventual bulge stars would be much shallower than the original one already created by the residing gas. In other words, the SMBH only knew the potential well of the original gas and it would be rather arbitrary how much stars the SMBH decides to allow the bulge to have. If one argues that it is the potential well of the total halo mass that matters, the SMBH still did not know how to let SF take place at such a rate that we have the very tight observed MBH \u2212MBG relation for the bulge region. Thus, this case also appears to require much \ufb01ne tuning. Besides, if (1 \u2212fout) is too small, the bulge will be too small compared to what is observed. The opposite case with fout \u226a1 is at least substantially more stable, since a large fraction of the original gas has formed into stars before the remainder of the gas got blown away. In this case the SMBH would \u201cknow better\u201d the gravitational potential well eventually sustained by bulge stars, because it is not too far from that created by the initial gas. Then, how did the SMBH know when to blow away the remaining gas left over from SF and SMBH accretion? Should the SMBH blow away the gas when fout = 0.90 (an arbitrarily picked number for illustration purpose) or should it wait a bit longer to \ufb01nally blow away the gas when fout = 0.10? It may require more energy or momentum in the former than the latter; but that can readily be accommodated by a proportionally increased amount of gas accreted, in the vein of feedback from SMBH providing the required feedback energy or momentum. Since the amount of gas available before fout = 0.90 is blown away in this hypothetical case is capable of growing the SMBH to be 900 more massive than observed and the amount of time available (cosmological scale) is much longer than Salpeter time, there is no obvious reason why the SMBH cannot grow 10 times (or whatever factor) larger to blow away the gas when fout = 0.90 instead of when fout = 0.10. How the SMBH has communicated with the bulge to ration the gas consumption would be a mystery. Thus, even in this case with fout \u226a1, taking it as a given that the SMBH always stands ready to provide the necessary feedback, having SMBH feedback to regulate the overall SF in the bulge such that the ratio of the two matches \u2013 6 \u2013 the observation, again, requires a substantial amount of \ufb01ne tuning. Nevertheless, since it is reasonable to expect that the dependence of the outcome, such as the MBH \u2212MBG relation, on any proposed feedback processes (including those based on thermal energy deposition near the galaxy center) is likely a monotonic function of the adopted feedback strength, it should be expected that a solution be found such that the observed MBH \u2212MBG relation is obtained, for some chosen value of feedback strength, at least for some narrow range in MBG. But, until there is clear physical reason or direct observational evidence to support the chosen value of the feedback parameter which the solution sensitively depends on, such an approach remains to be re\ufb01ned. We will provide an alternative, signi\ufb01cantly less contrived, quantitative physical mechanism to circumvent this concern of \ufb01ne tuning. 3. Starburst Phase: Modest SMBH Growth and SF Shutdown by Stars We have argued in the previous section that AGN feedback cannot logically play the leading role in regulating SF, in the sense that while some feedback from the SMBH can certainly a\ufb00ect its surrounding gas, there is no particular reason why this could provide a quite precise (within a factor of a few) rationing mechanism during the starburst phase so as to produce the observed relation between the two. We shall now argue for Scenario #3: during the starburst phase the SF is self-regulated and self-limited, while SMBH growth is modest, does not need regulation and does not provide signi\ufb01cant feedback to star formation. We now give a physical reason for why, even though there is a very large supply of gas in the bulge region during the starburst phase, the SMBH growth is modest. We will make three simplifying assumptions to present trackable illustration without loss of generality. We assume (1) for the regions of interest a geometrically thin Keplerian disc dominated by the SMBH gravity (at least at the radii of interest here) is in a steady state, meaning the accretion rate (Frank et al. 1992): \u02d9 M = 3\u03c0\u03bd\u03a3g \u0002 1 \u2212(rin/r)1/2\u0003\u22121 \u22483\u03c0\u03bd\u03a3g (1) is constant in radius r and time, where \u03a3g is gas mass surface density and \u03bd is viscocity; the last equality is valid because the radii of interest here are much larger than the radius of the inner disc rin; note that it is inevitable to form a disk in the central given the rapid cooling and \ufb01nite angular momentum; (2) we adopt the \u03b1-disc viscosity (Shakura & Sunyaev 1973): \u03bd = \u03b1c2 s\u2126\u22121, (2) where \u03b1 is a dimensionless viscosity constant for which magnetorotational instability process (Balbus & Hawley 1991) provides a physical and magnitude-wise relevant value; cs is sound speed and \u2126is angular velocity (equal to epicyclic frequency for Keplerian disc). The Toomre \u2013 7 \u2013 Q parameter of the gas disc can be obtained from Equations (1,2): Q \u2261 cs\u2126 \u03c0G\u03a3g = 1 31/2\u03c03/2\u03b11/2   \u02d9 M MBH !1/2   G\u22121/4 MBH 5/4 \u03a33/2 g r9/4 ! (3) where G is gravitational constant. The slope of the surface brightness pro\ufb01les of the inner region of the observed powerlaw elliptical galaxies, which are assumed to be the product of the starbursts resulting from the gas-rich galaxy mergers, has a value concentrated in the range \u22121.0 to \u22120.5 (e.g., Faber et al. 1997; Kormendy et al. 2009), reproduced in merger simulations (e.g., Hopkins et al. 2009). Presumably the initial gas density pro\ufb01le is similar to the \ufb01nal observed stellar density pro\ufb01le in the inner regions. For ease of algebraic manipulations, we assume (3) the de Vaucouleur mass surface density pro\ufb01le (with a halfmass radius re) but with the inner region at r \u2264rp \u22610.07re modi\ufb01ed to be a Mestel disc as: \u03a3g(r) = \u03a30 \u0012 r r0 \u0013\u22121 for r \u2264rp, (4) where \u03a30 is the normalizing surface density at some radius r0; we will only be dealing with region r \u2264rp; the notional nuclear velocity dispersion of the system without the central SMBH at r \u2264rp is related to \u03a30 and r0 by \u03c32 n = \u03c0G\u03a30r0. (5) Subsequent results do not sensitively depend on the exact slope. The total mass of such a hybrid pro\ufb01le is equivalent to a truncated isothermal sphere with a truncation radius of 2re and velocity dispersion on galactic scales of \u03c3g such that \u03c3n = 1.55\u03c3g. (6) Since the dynamical time, say at 1kpc for a 200 km/s bulge being only 5 \u00d7 106yr, is much shorter than the Salpeter time, it is appropriate to assume that the gas disc is assembled instantaneously with respect to accretion to the SMBH when infalling gas lands on the disc. Combining Equations (3,4,5,6) we rewrite Q as Q = 0.32\u03b1\u22121/2 0.01 \u03f5\u22121/2 0.1 l1/2 E M 5/4 8 \u03c3\u22123 200r\u22123/4 pc , (7) where \u03b10.01 = \u03b1/0.01, \u03f5 = 0.1\u03f50.1 is the SMBH radiative e\ufb03ciency, lE is Eddington ratio, M8 = MBH/108 M\u2299, \u03c3200 = \u03c3g/200 km/s, rpc = r/1pc. The value of \u03b1 is quite uncertain, possibly ranging from 10\u22124 to 1 (e.g., Hawley et al. 1995; Brandenburg et al. 1995; Stone et al. 1996; Armitage 1998; Gammie 2001; Fleming & Stone 2003; Fromang & Papaloizou 2007). Setting Q in Equation (7) to unity de\ufb01nes the disc stability radius rQ = 0.22\u03b1\u22122/3 0.01 \u03f5\u22122/3 0.1 l2/3 E M 5/3 8 \u03c3\u22124 200 pc (8) \u2013 8 \u2013 within which Q > 1 and disc is stable to gravitational fragmentation, and outside which Q < 1 and disc is subject to gravitational fragmentation to form stars, supported by both simulations (e.g., Gammie 2001; Rice et al. 2003) and circumstantial observational evidence of the existence of stellar disc at small Galactic radius (\u223c0.1pc) (e.g., Levin & Beloborodov 2003; Paumard et al. 2006). The demarcation value of Q between stability and fragmentation does not appear to be qualitatively di\ufb00erent even if the disc is under strong illumination (e.g., Johnson & Gammie 2003), as might happen to a nuclear gas disc in the starburst phase. The disc mass within rQ is MQ = 9.8 \u00d7 106\u03b1\u22122/3 0.01 \u03f5\u22122/3 0.1 l2/3 E M 5/3 8 \u03c3\u22122 200 M\u2299 (9) This is the accretable mass out of the entire bulge region (note that some of the outer regions are more random motion supported). This conclusion reached is in good agreement with Goodman (2003), who employs somewhat di\ufb00erent assumptions than in this study in that he assumes local energy balance, while we impose the observationally inferred inner density pro\ufb01le to be self-consistent; the good agreement suggests that this result is quite robust, insensitive to assumptions made. Taking cue from our own Galaxy, if we assume that the initial SMBH mass of the two merging spiral galaxies of mass \u223c1012 M\u2299each is 2.5 \u00d7 106 M\u2299, for a spiral galaxy of velocity dispersion of 200 km/s, we see that the amount of mass that could be readily accreted according to Equation (9) using M8 = 0.05 is 6.7 \u00d7 104\u03b1\u22122/3 0.01 \u03f5\u22122/3 0.1 l2/3 E M\u2299. Note that the \ufb01nal SMBH mass for such a system is \u223c1.3 \u00d7 108 M\u2299 (Tremaine et al. 2002), if we were to match the observations. It is possible that the mass accreted to the SMBH may be larger than that indicated by Equation (9) due to replenishment. Replenishment of low angular momentum gas during the starburst phase may be possible in two ways: (1) through orbital decay of outer disc gas or (2) direct infall of low-J gas from outer regions. We will show below that (1) does not signi\ufb01cantly increase the accretable mass. Process (2) is probably unavoidable to some extent but unlikely to be frequent enough to be signi\ufb01cant for the following reasons. All the low angular momentum infalling gas falls into the inner regions initially according to its respective speci\ufb01c angular momentum driven by the torque of the trigger event (e.g., merger or some other signi\ufb01cant torquing event). To replenish low angular momentum gas directly to the central region some frequent and signi\ufb01cant torquing events during the starburst phase are needed. It seems unlikely that such events will be frequent enough to be able to reach the observed \ufb01nal SMBH mass: about \u223c100 \u22121000 replenishments will be required. One might approximately equate the number of replenishment (i.e., signi\ufb01cant disturbance) to the number of generations of stars formed during the starburst phase (by assuming that each generation of star formation manages to redistribute the angular momentum of a signi\ufb01cant fraction of the gas), which is unlikely to be close to \u223c100 \u22121000. In summary, taking into account possible additional accretion due to some replenishment and giving the bene\ufb01t of the possibility of \u03b10.01 < 1, it seems improbable that the SMBH is able to acquire a mass during the starburst phase that would be much more than 10% of the \ufb01nal value. \u2013 9 \u2013 At r \u2265rQ, the disc is unstable to SF. For SF under the conditions relevant here both the dynamical and cooling time are short and do not constitute signi\ufb01cant bottleneck; if they were the only time scale bottleneck, SF would be too e\ufb03cient. A possible bottleneck for SF is the time scale to rid the cloud of the magnetic \ufb02ux (assuming the SF clouds are initially magnetically sub-critical). The main ionization source in the depth of molecular cloud cores is cosmic rays (CR). While the exact ionization rate by CR is unknown for other cosmic systems, we have some estimate of that for our own Galaxy, \u03b6CR,Gal = (2.6 \u00b1 1.8) \u00d7 10\u221217 s\u22121 (e.g., van der Tak & van Dishoeck 2000). If one assumes that the CR ionization rate in starburst is 100 times (modeling a typical ULIRG in this case) that of the Galactic value, considering that the SF rate in ULIRGs is 100 \u22121000 times the Galactic value occuring in a more compact region and that the CR in ULIRGs may be advected out via fast galactic winds (versus slow di\ufb00usion in the Galaxy), one may roughly estimate that the ambipolar di\ufb00usion time is 7 \u00d7 106yr at a density of n \u223c105 cm\u22123 using standard formulas for recombinations (e.g., McKee & Ostriker 2007). This estimate is, however, uncertain. We will again look to direct observations to have a better gauge. Gao & Solomon (2004) show, from HCN observations, that ULIRGs and LIRGs convert molecular gas at n \u22653 \u00d7 104 cm\u22123 at an e-folding time scale of tSF \u223c2Myr, consistent with the above rough estimate. It is clear that SF time scale is much shorter than the Salpeter time of 4.5\u00d7107\u03f50.1yr; in other words, when gas is dense and unstable, star formation competes favorably with the SMBH accretion with respect to gas consumption. Therefore, most of the gas at r \u2265rQ will be depleted by SF. When the density pro\ufb01le of the disc at r \u2265rQ steepens to be \u03a3g(r) = \u03a3Q(r/rQ)\u22125/2, where \u03a3Q is the gas surface density at \u223crQ, the disc at r \u2265rQ may become stable again. While continued accretion supplied by gas on the outer disc is likely, albeit at a much lower level, the mass integral is convergent and most of the mass of this outer disc is at rQ given the density slope, even if the entire outer disc at this time is accreted. Thus, it appears that the amount of gas that is actually accreted by the SMBH during the starburst phase is rather limited. This new and perhaps somewhat counter-intuitive conclusion is strongly supported by available observations of ULIRGs. This conclusion is also opposite to most models that rely on SMBH to provide the necessary feedback to regulate star formation (e.g, Silk & Rees 1998; Hopkins et al. 2006). Observational evidence is that the SMBHs in ULIRGs and SMGs appear to be signi\ufb01cantly smaller (an order of magnitude or more) than what the MBH \u2212MBG relation would suggest (e.g., Genzel et al. 1998; Ivison et al. 2000; Ptak et al. 2003; Ivison et al. 2004; Alexander et al. 2005a,b; Kawakatu et al. 2006; Alexander et al. 2008). Nonetheless, it is expected that the AGN contribution in ULIRGs should become relatively more important for larger more luminous galaxies (see Equation 9), consistent with observations (e.g., Lutz et al. 1998). Starbursts occuring on rotating nuclear disc/rings in ULIRGs are also supported by circumstantial observational evidence (e.g., Downes & Solomon 1998). The overall conclusion that the SMBH feedback has little e\ufb00ect on the amount of stars \u2013 10 \u2013 formed is in agreement with that of DeBuhr et al. (2010) who investigated the radiation pressure-regulated SMBH feedback in the starburst phase of the merger simulations utilizing a sub-grid model for SMBH accretion. One speci\ufb01c common outcome between our calculation and their simulation is that most of the gas formed into stars, regardless of the feedback strength. A notable di\ufb00erence between our calculation and theirs is that their simulation resolution, a gravitational softening length of 47 pc, is signi\ufb01cantly larger than rQ (Equation 8). As a result, it is possible that their simulations do not resolve small scale that separates stable accretion from unstable, fragmenting disc, which is crucial to our quantitative conclusion (note that they use the viscosity parameter \u03b1 = 0.05 \u22120.15 that is larger than our \ufb01ducial value of 0.01, which would yield a still smaller rQ, see Equation 9). Thanks to that di\ufb00erence, we were able to conclude that, even without considering any feedback from the central SMBH, the SMBH during the starburst phase does not grow to anywhere close the observed \ufb01nal mass, because star formation can more favorably deplete the gas that may otherwise accrete to the SMBH, whereas they \ufb01nd SMBH masses to be too large even with substantial feedback (note that they use 10 times L/c radiation pressure force assuming multiple scatterings of each converted FIR photon). It seems likely that their di\ufb00erent conclusion may be due to a much higher accretion rate at their resolution scale, which we argue does not re\ufb02ect the actual accretion onto the SMBH, but rather the disc is unstable at that scale and mostly forms stars. As we have noted in the previous paragraph, observations indicate that the SMBH masses in the starburst phase appear to be smaller than the \ufb01nal values seen in quiescent elliptical galaxies by an order of magnitude, consistent with our conclusion. Substantially higher resolution (a factor of \u223c100) simulations may be necessary in order to realistically and more accurately simulate the intricate competition between accretion and star formation. 4. A Comparison of Feedback Energetics Between Star Formation and SMBH Having shown the unlikelihood of substantially growing SMBH during the starburst phase, we now turn to a comparison of the energetics of SMBH and SF to show that, feedback from starburst itself should play the leading role in shutting down or quenching star formation, i.e., promptly sweeping away the \ufb01nal portion of the gas, where needed. To avoid any apparent bias against SMBH or a possibly circular looking argument by the assertion that most of the SMBH growth takes place in the post-starburst phase (as we will show in \u00a74), we shall for the moment generously assume that the entire SMBH growth occurs during the starburst phase, to maximize the energy output from the SMBH, when comparing the energetics from the SMBH and the starburst. In Table 1, under the assumptions that MBH : MBG = 2 : 1000, a Salpeter IMF for stars and a radiative e\ufb03ciency of SMBH accretion of 10%, energy output from both SF and SMBH in various forms are listed: (1) \u2013 11 \u2013 total radiation energy, (2) ionizing radiation, (3) X-ray radiation in 2 \u221210keV band, (4) mechanical energy, which is supernova explosion energy for SF and broad absorption line (BAL) out\ufb02ow for SMBH, respectively, and (5) radio jets. To obtain energy is ergs per Mstar formed, one just needs multiply each coe\ufb03cient in Table 1 by Mstarc2, where c is speed of light. The relevant references are Elvis et al. (1994) and Sazonov et al. (2004) for both \u03f5BH(LL) and \u03f5BH(2-10keV), Ranalli et al. (2003) for \u03f5\u2217(2-10keV), Moe et al. (2009) and Dunn et al. (2010) for \u03f5BH(BAL) and Allen et al. (2006) for \u03f5BH(jet) (if one uses energy seen in the most powerful radio jet lobes and assumes that they are produced by the most massive SMBH, a comparable value is obtained). The entry for the BAL energy is based on two cases and very uncertain, primarily due to lack of strong constraints on the location of the BAL and their covering factor. It is evident that aside from the energy in the form of radio jets and hard X-rays, SF is at least competitive compared to SMBH. Heating due to hard X-rays from SMBH via metal line or Compton heating a\ufb00ects only the very central region surrounding the SMBH, not over the entire galaxy (Ciotti & Ostriker 2007). Within the physical framework outlined here, most of the SMBH growth occurs post-starburst and radio jets occur at a still later stage in core elliptical galaxies, energy output (or momentum output derived from it) from SF in all relevant forms should dominate over that of SMBH. Our argument that radio jets occur at a later stage in galaxy evolution is not at present based on a physical model, but on empirical evidence. Observationally, it appears that all signi\ufb01cant radio jets are launched in elliptical galaxies that have \ufb02at cores (Balmaverde & Capetti 2006), with a very few exception that originated in disc galaxies (e.g., Evans et al. 1999; Ledlow et al. 2001) or S0\u2019s (e.g., V\u00b4 eron-Cetty & V\u00b4 eron 2001). But none has been associated with elliptical galaxies with an inner powerlaw brightness pro\ufb01le slope. It has been plausibly argued that powerlaw elliptical galaxies are produced by gas-rich mergers (we adopt this scenario where a powerlaw elliptical galaxy is produced following each major gas-rich merger triggered starburst) (e.g., Faber et al. 1997), whereas core elliptical galaxies are produced later by dry mergers of two elliptical galaxies where the \ufb02at core is carved out by the merger of the two SMBHs via Table 1. # Form SF SMBH (1) total radiation \u03f5\u2217(rad) = 7 \u00d7 10\u22123 \u03f5BH(rad) = 2 \u00d7 10\u22124 (2) ionizing radiation (\u226513.6eV) \u03f5\u2217(LL) = 1.4 \u00d7 10\u22124 \u03f5BH(LL) = 3 \u00d7 10\u22125 (3) X-ray (2 \u221210keV) \u03f5\u2217(2-10keV) = 9 \u00d7 10\u22128 \u03f5BH(2-10keV) = 5 \u00d7 10\u22126 (4) mechanical \u03f5\u2217(SN) = 1 \u00d7 10\u22125 \u03f5BH(BAL) = (0.2 \u22122.8) \u00d7 10\u22125 (5) radio jets \u03f5\u2217(jet) = 0 \u03f5BH(jet) = 4 \u00d7 10\u22125 \u2013 12 \u2013 dynamical friction (e.g., Milosavljevi\u00b4 c & Merritt 2001). Directly supporting this statement is the lack of radio jet in available observations of ULIRGs (e.g., Alexander et al. 2010), in agreement with other observations that indicate a signi\ufb01cant time-delay between starburst and radio activities (e.g., Emonts et al. 2006). An independent, additional argument comes from the fact that radio jets are highly collimated and, for the most powerful ones that are energetically relevant, they appear to dissipate most of the energy at scales larger than that of the bulge region, suggesting that, even if one were to ignore the previous timing argument, the e\ufb03ciency of heating by radio jets for the bulge region is likely low and at best non-uniform. Weaker radio feedback, observed almost exclusively in galaxies with an atmosphere of hot gas, may be able to steadily provide feedback energy but it is too weak to be energetically important. Besides, they appear to only operate in elliptical galaxies with hot atmospheres (e.g., Best et al. 2005). The amount of supernova explosion energy that couples to the surrounding medium is ESN = 1 \u00d7 10\u22125M\u2217c2, which is exactly equivalent to 5 \u00d7 10\u22123 MBHc2 used in the in\ufb02uential simulations of Hopkins et al. (2006) with thermal AGN feedback, assuming MBH : MBG = 2 : 1000. Because the energy output from supernovae is subject to less cooling than that from the AGN, since the former is at larger radii and lower densities than the latter, we expect that the amount of energy due to supernovae can at least as e\ufb00ectively as that proposed from AGN to drive the gas away. Thus, when most of the gas have formed into stars (i.e., the bulge is largely in place after \u223c107 \u2212108yr of starburst), the remaining gas should be blown away by collective supernova explosions and the starburst comes to a full stop, reminiscent of what is seen in the simulations of Hopkins et al. (2006) with AGN feedback. Detailed high-resolution simulations will be necessary, taking into account cooling and other physical processes, to ascertain the fraction of gas that is blown away. In short, the bulk of galactic winds is likely driven by stellar feedback from the starburst. Galactic winds are observed and casual connection between SF rate and wind \ufb02uxes has been \ufb01rmly established (e.g., Heckman 2001; Weiner et al. 2009), lending strong observational support for the argument. 5. Post-Starburst: Main Growth of SMBH with Self-Regulation The previous section ends when the starburst has swept away the remaining gas and ended itself. This section describes what happens next the post-starburst period, the initial period of which is also known as K+A galaxies. The newly minted (future) bulge enters its \u201cpassive\u201d evolutionary phase, as normally referred to. We would like to show that this is when most of the action for SMBH begins, fueled by recycled gas from aging low-to-intermediate mass stars. Since two-body relaxation time is much longer than the Hubble time, it is safe to assume that the stars formed in the inner region during the starburst phase remain roughly in place radially. Angular momentum \u2013 13 \u2013 relaxation may also be ignored for our purpose (e.g., Rauch & Tremaine 1996). However, the stellar distribution in the inner region that initially formed on a disc probably has vertically thickened substantially and we will assume that they no longer substantially contribute to local gravity on the gas disc (within the thickness of the assumed thin gas disc) subsequently formed from returned stellar gas. Because stars in the inner regions are already mostly rotationally supported, the shedded gas rains almost \u201cstraight down\u201d to land at a location that their speci\ufb01c angular momentum allows, to form a disc. Obviously, going out radially, the rotational support lessens and star formation may occur in a 3-d fashion. But that does not alter our argument about what happened at small radii. The orientation of the disc is approximately the same as the previous disc out of which stars in the inner regions were formed, since the overall angular momentum distribution of stars has not much changed in the absence of any subsequent intrusions. The most important di\ufb00erence of this new accretion disc, compared to the disc formed during the starburst phase, is that this new disc starts with almost no material and surface density increases with time gradually on the timescale of hundreds of megayears to gigayear. To have a better gauge how the results obtained depend on the assumed inner density slope, instead of assuming a Mestel disc as is done in \u00a73 here we present a more general case assuming the inner density pro\ufb01le of the form \u03a3g(r) = \u03a30 \u0012 r r0 \u0013\u2212n , (10) where n \u223c[0.5, 1] (e.g., Faber et al. 1997; Kormendy et al. 2009). For this case Equation (8) is modi\ufb01ed, taking into account the gradual change of the gas disc surface density with time, to be rQ = 1 (\u03c0(3\u03c0)1/2)4/3(3\u22122n)  \u02d9 M M !2/3(3\u22122n) (frecfg)\u22122/(3\u22122n)\u03b1\u22122/3(3\u22122n)G\u22121/3(3\u22122n)M 5/3(3\u22122n)\u03a3\u22122/(3\u22122n) 0 r\u22122n/(3\u22122n) 0 (11) where frec is the total fractional stellar mass that recycles back to ISM and fg(t) the fraction of recycled gas that has returned by time t (out of the fraction frec). The process of SMBH accretion in this case goes as follows. The SMBH will accrete all the gas within its Bondi radius rB over some period of time, as long as rQ \u2265rB, where rB is de\ufb01ned as rB \u2261G MBH \u03c32 n , (12) with \u03c3n being the velocity dispersion of the inner region of the bulge (r \u226420pc or so for MBH = 108 M\u2299). For the moment we ignore any feedback e\ufb00ect from the SMBH. Since rB grows with time and rQ decreases with time with increasing fg for r > rB that has been \u2013 14 \u2013 accumulating gas, the condition rQ \u2265rB may be violated at some time t, at which point the SMBH is cut o\ufb00gas supply at its Bondi radius and the SMBH will subsequently grow by consuming the \ufb01nal patch of gas on the disc within its Bondi radius. Before the condition rQ \u2265rB is reached, the recycled gas that has landed outside (time varying) rB continues to accumulate (some of the accumulated gas possibly forms stars). Using Equations (11,12) we \ufb01nd the turning point rQ = rB is reached when frecfg = 2 \u2212n 2 (13) with the disc mass within rQ = rB, i.e., SMBH mass, being MF = 3(2 \u2212n)3 8  \u02d9 M M !\u22121 \u03b1\u03c33 n G . (14) From Equation (13) we see that (2\u2212n)/(2frec) > 1 for n = [0.5\u22121]. Thus, we simply correct Equation (14) by a factor of 2frec/(2 \u2212n) to \ufb01nally arrive at MBH = 3(2 \u2212n)2 4  \u02d9 M M !\u22121 frec\u03b1\u03c33 n G = 1.9 \u00d7 108(2 \u2212n)2\u03b10.01l\u22121 E \u03f50.1 \u0012 \u03c3n 200 km/s \u00133 M\u2299, (15) with the radius when rQ = rB = rBQ being: rBQ = 34(2 \u2212n)3\u03b10.01l\u22121 E \u03f50.1 \u0012 \u03c3n 200 km/s \u0013 pc. (16) Equations (15, 16) suggest that the SMBH accreted the recycled gas at r \u226420( MBH/108 M\u2299) pc or so for lE \u223c1; it could be substantially larger for smaller lE. The reason that the accretable mass is so much larger during this period than the starburst phase is because the accretion disc in this period is replenished continuously at a moderate rate such that it is stable within a much large radius than the case of sturburst phase with a much thicker (surface density-wise) disk. Equation (15) resembles the observed MBH \u2212\u03c3 relation (Tremaine et al. 2002). We argue the resemblance is deceptive, in a general sense, because it hinges on a value of \u03b1 \u223c0.01 or so and lE \u223c1. As we mentioned earlier, the currently allowed value of \u03b1 could range from 10\u22124 to 1 and at the moment we do not know what value nature has picked to grow her SMBHs. In light of this situation, using Equation (15) to declare victory is premature. However, Equation (15) does suggest that there is enough material and time to grow the SMBH to the observed value during the post-starburst phase. This is in stark contrast with the starburst phase when there is not enough accretable matter even if one pushes the viscosity value to the limit (see Equation 9). \u2013 15 \u2013 7 8 9 10 6 7 8 9 10 log 0.002*MBG*(\u001f /200) (Msun km/s) log MBH (Msun)     Observation: Marconi & Hunt (2003) model prediction Fig. 1.\u2014 The circles are data from Marconi & Hunt (2003). The solid line is predicted by Equation 17 using A = 1 (see Equation 18). A scenario where the allowed range of viscosity value is limited to one side, i.e., \u03b1 is allowed to have values greater than say 0.01, is much less \ufb01ne tuned. In this case, some self-regulation for the SMBH growth will be necessary. This self-regulation for the SMBH growth is indeed achievable during the post-starburst phase, as we will now describe. The total amount of radial momentum that radiation pressure of the SMBH may exert on the surrounding gas is \u03f5c MBH (this is likely a lower bound, neglecting the possibility of multiple scatterings of photons in the optically thick regime). Equating \u03f5\u03b2c MBH to frec MBG(1\u2212f\u2217)vesc (that is the momentum of the driven-way gas escaping the galaxy) gives MBH MBG = frecvesc \u03f5\u03b2c (1 \u2212f\u2217) (1 + frecf\u2217) = A 2 1000\u03c3200, (17) where A is A = (fesc/0.15)(1 \u2212f\u2217) (1 + (frec/0.15)f\u2217)\u03b2\u03b7\u03f50.1 vesc 2\u03c3 , (18) where f\u2217is the fraction of recycled gas that subsequently re-formed into stars and vesc is escape velocity [for an isothermal sphere truncated at virial radius rv, vesc(r)/2\u03c3 = (1 + ln(1 + rv/r))1/2 at radius r]; \u03b2 is the fractional solid angle that absorbs the radiation from \u2013 16 \u2013 the SMBH; the term (1 + fescf\u2217) takes into account additional stars added to the bulge stellar mass formed from the recycled gas. Of the parameters in Equation 18, fesc = 0.15 is reasonable taking into account that about the half of mass return occuring at early times by type II supernovae can escape without additional aid; radiative e\ufb03ciency of \u03f5 = 0.1\u03f50.1 is consistent with observations (Yu & Tremaine 2002; Marconi et al. 2004); some fraction of the recycled gas forming into stars is probably unavoidable, since some gas with column density greater than Compton column will slip through radiation pressure (see discussion below); f\u2217also includes the (possibly very large) amount of gas at large radii that would not have accreted onto the SMBH in the \ufb01rst place even in the absence of any feedback (e.g., molecular clouds on the Galactic disk are not being fed to the Galactic center SMBH in a consistent fashion); the factor \u03b7 (greater than one) takes into account additional stars that are not formed from the starburst event. Overall, considering all these balancing factors, a value of A of order unity seems quite plausible. Figure 1 plots the relation between MBH and \u03c3 MBG predicted by Equation 17 using A = 1. It is clear that it provides a very good \ufb01t to the observed data. A similar scaling relation as Equation 17 was derived based on a di\ufb00erent, radio jet feedback mechanism (Soker & Meiron 2010). A similar scenario of linear momentum feedback from AGN radiation pressure has been considered by Silk & Nusser (2010) to possibly produce the observed MBH \u2212MBG relation during the starburst phase but they conclude that the radiation pressure is insu\ufb03cient by an order of magnitude to be able to blow the unwanted gas away. The magnitude of the radiation pressure and escape velocity requirement considered here are the same as theirs. The di\ufb00erence is that here the amount of gas that need to be regulated in the post-starburst phase is nearly a factor of 10 lower and further allowance for star formation from the recycled gas make possible that the radiation pressure from the central AGN may be adequate to self-regulate the SMBH growth so as not to overgrow it. We note that Equation 17 would work without much variation if the gas that is blown away is uniformly distributed. The recycled gas is expected to be non-uniform. Even if it were uniform initially, thermal instabilities likely make the distribution non-uniform. Given that, we elaborate further on Equations (17,18) and the physical processes of radiation pressure driven winds. Some distinction may be made between about 1/3 of the total solid angle where UV and other photons are directly seen from AGN and the other \u03b2 \u223c2/3 of the solid angle that has a nearly Compton thick or thicker obscuring screen, most of which probably stems from the so-called molecular torus (e.g., Risaliti et al. 1999). For every \u2206Macc of mass accreted, roughly \u03f5c/vesc\u2206Macc = 100\u03f50.1(vesc/300 km/s)\u22121\u2206Macc of mass that rain down by aging stars could be driven away by the radiation momentum from the AGN. In the 1/3 opening solid angle some portion of the radiation pressure driven winds will be accelerated to high velocities, perhaps in a fashion similar to what is seen in simulations (e.g., Kurosawa & Proga 2009), observationally manifested as broad emission or absorption lines as well as out\ufb02ows seen in narrow lines (e.g., Crenshaw et al. 2003; Greene et al. 2011). \u2013 17 \u2013 A signi\ufb01cant fraction of the material may be accumulated in the remaining \u03b2 \u223c2/3 of the solid angle (i.e., Type 2 AGNs), including recycled gas that comes from the other 1/3 solid angle that is too heavy to be accelerated away \u201con the \ufb02y\u201d by the radiation pressure. In this 2/3 of the solid angle, high velocity winds radially exterior to the molecular torus is unlikely given the heaviness (i.e., low opacity) of the molecular torus. We discuss some of the physics here. To gain a more quantitative understanding, a look at some observed properties of the torus is instructive. Ja\ufb00e et al. (2004) measured the radius and height of the molecular torus of NGC 1068 to be 1.7pc and 2.1pc, respectively. The mass of the SMBH in NGC 1068 is (8.3 \u00b1 0.3) \u00d7 106 M\u2299(e.g., Marconi & Hunt 2003). If we extrapolate to a 108 M\u2299SMBH assuming that the location and height of the molecular torus is proportional to the SMBH mass, we have a surface area of the torus equal to 3200 pc2 at a SMBH-centric radius of 20pc. If we assume that the column density of the molecular torus is 1024cm\u22122 (e.g., Risaliti et al. 1999), its total mass is then 2 \u00d7 107 M\u2299. The dynamical time at 20 pc is 105 yrs. A SMBH of mass 108 M\u2299accreting at Eddington rate would grow a mass of \u223c105 M\u2299in 105 yrs, while the overall rate of gas return would be \u223c2 \u00d7 107 M\u2299over the entire bulge during that period. Thus, the abundant gas supply rate suggests that the necessary (not su\ufb03cient) condition for a near \u201csteady\u201d state is met such that the molecular torus may be kept roughly invariant with time, with the rate of driven-away gas by radiation pressure plus that of gas forming into stars equal to the rate of gas return from aging stars. Given the short star-formation timescale of the very dense gas in the molecular torus, it would be unavoidable that star formation should occur there (as well as some regions exterior to it). This \u201clightens up\u201d the torus to the extent that it may be pushed away by the radiation pressure, when the condition that the deposited radiation momentum divided by the accumulated mass exceeds the escape velocity (assuming, in the absence of radiation pressure, the torus would just be in a bound circular orbit). In this sense the radiation momentum from the SMBH serves to retard gas supply to accretion from the torus to let SF take over to have it mostly depleted. In combination with the analysis in the preceding paragraph, it seems physically plausible that radiation pressure and depletion of gas by star formation is able to jointly reduce and regulate the amount of gas that feeds the central SMBH. Given that the overall margin, in an \u201con average\u201d sense, is quite thin (i.e., A \u223c1 in Equation 18), it is likely that there are signi\ufb01cant variations in A, perhaps up to a factor of a few. In the 1-d simulations of Ciotti & Ostriker (2007) for an elliptical galaxy, the SMBH growth appear to be intermittent. The intermittency in their simulations was caused by a hot X-ray heated bubble that prevents continued gas accretion, until it bursts, which is then followed by another accretion episode, and so on. We suggest that Rayleigh-Taylor instability on the shell enclosing the X-ray bubble may prevent the X-ray bubble from in\ufb02ating, as hinted by recent 2-d simulations of Novak et al. (2010). It it reasonable to assume that shell fragmentation in three-dimension is still more pronounced to allow continued de\ufb02ation \u2013 18 \u2013 of a notional X-ray bubble. Observationally, the lack of signi\ufb01cant X-ray emission from circumnuclear region in powerlaw elliptical galaxies host AGNs, which we argue are the post-starburst galaxies we consider here, supports the picture that the hot bubble is not robust (e.g., Pellegrini 2005). In the absence of a hot X-ray bubble guarding the SMBH, we suggest that the recycled gas from aging stars is able to reach the disc and the accretion, with self-regulation argued above, is quasi-steady without major \ufb02ares of magnitude seen in 1-d simulations. As we will show later, a steady declining accretion rate proportional to the gas return rate provides a much better match to at least two observations: (1) the observed early-type host galaxies of AGNs are mostly in the green valley of the galaxy color-luminosity diagram with a small fraction in the red sequence (\u00a75.2) (e.g., Salim et al. 2007; Silverman et al. 2008; Hickox et al. 2009; Schawinski et al. 2010), but very few in the blue cloud, which would have been the case if AGN \ufb02ares are accompanied by starbursts (Ciotti & Ostriker 2007); (2) the observed AGN accretion rate for early-type galaxies in the local universe displays a powerlaw distribution with the amplitude and decay rate (Kau\ufb00mann & Heckman 2009) that is expected from the non-\ufb02are scenario that is proposed here. This indicates that bursty AGN accretion, while quite possible and sometimes perhaps unavoidable, is probably not the dominant mode. It is currently a challenge but will be of great value to carry out 3-d high-resolution simulations to more accurately quantify this outcome. 6. Model Predictions and Discussion We have presented a physically motivated picture for the coevolution of galaxies and SMBH starting with a triggered starburst. Let us now summarize the entire evolution in \u00a75.1 and then give an incomplete list of implications and predictions in \u00a76.2-6.9 to be qualitatively compared/veri\ufb01ed with observations. 6.1. Three Distinct Periods of Coevolution of Galaxies and SMBH From the onset of a signi\ufb01cant central starburst to becoming a quiescent bulge there are three distinct periods, as summarized in Figure 2 for an example merger of two gas-rich spirals each of mass \u223c1012 M\u2299that eventually becomes a powerlaw elliptical galaxy of velocity dispersion of 200 km/s. We stress that the trigger event is not limited to major mergers. This three-stage scenario is not new and its successes with respect many observations have been discussed previously (e.g., Granato et al. 2004, 2006; Cirasuolo et al. 2005; Lapi et al. 2006; Lamastra et al. 2010). The new theoretical element here is the primary growth of SMBH in the post starburst phase, which is re\ufb02ected in the color and other properies of AGN hosts and we will show is in remarkable accord with latest observations, in contrast to the conventional scenario where SMBH growth primarily occurs during the starburst phase. \u2013 19 \u2013 The time boundaries between di\ufb00erence consecutive phases (three ovals) are approximate (uncertain to a factor of at least a few). Given the complexity and variety of starburst trigger events, one should expect signi\ufb01cant variations from case to case. The expected consequences or predictions of this model are in many ways di\ufb00erent from and often opposite to those of models that invoke AGN feedback to shut down both starburst and AGN activities (e.g, Silk & Rees 1998; Hopkins et al. 2006). A new and in some way perhaps the most fundamental \ufb01nding of this work is that the SMBH does not grow during the starburst phase as much as previously thought, required in AGN-feedback based models, despite the obvious condition that there is a lot of gas being \u201cjammed\u201d into the central region; this is di\ufb00erent from almost all previous work (e.g, Silk & Rees 1998; Hopkins et al. 2006; DeBuhr et al. 2010) that either need to advocate very strong SMBH feedback or appear to overgrow the SMBH. The idea of feeding the SMBH with recycled stellar material in the post-starburst phase is not new (e.g., Norman & Scoville 1988; Ciotti & Ostriker 2007) and we inherit most of the already known elements from prior work, including gas return rate and the likelihood of continued star formation. Our analysis shows the likelihood that the SMBH may be fed too much in the post-starburst period in the absence of feedback from the SMBH, in dramatic contrast with the starburst phase when SMBH feedback is insu\ufb03cient. While energy feedback from the SMBH certainly plays a role, we show that the more robust momentum feedback from SMBH radiation pressure can play a critical role in regulating SMBH growth, not necessarily only by blowing powerful winds, but rather, in combination, by also pushing away thus retarding accretion of unwanted (by SMBH) gas to be instead consumed by star formation. While our analysis may have captured some of the essential physics in terms of accretion and star formation demarcation, to more realistically model the complex accretion and star formation dynamics, much higher resolution 3-d radiation hydrodynamic simulations will be required and will be of tremendous value. The \u201csize\u201d of the starburst depends on the \u201csize\u201d of the triggering event, with at least some fraction of ULIRGs and SMGs due to major mergers of massive gas-rich gas. However, irrespective of the size of the starburst event, the time scales involved, being largely due to physics of stellar interior and accretion time scale, remain the same. (1) \u201cStarburst Period\u201d: this phase is triggered by some event. The SMBH grows modestly during this period to possibly attain a mass that is up to order ten percent of its \ufb01nal mass. This phase lasts about 107 \u2212108yrs for typical starbursts and the host galaxies during this phase are in the blue cloud in the luminosity-color diagram. The feedback energy/momentum from the starburst, i.e., supernovae, drives the last patch of gas away and shuts down star formation, if needed. In other words, the starburst is self-regulated, not by the central AGN during this period. (2) \u201cSMBH Prime Period\u201d: several hundred million years after the end of the starburst, aging low-to-intermediate mass stars, now in their post-main-sequence phases, start to return a \u2013 20 \u2013 substantial fraction of their stellar mass to the ISM. The SMBH accretion is fueled by this recycled gas lasting for order of gigayear. The growth of SMBH is self-regulated, readily provided by the radiation pressure from the AGN. The host galaxies during this period start out light-blue or in the \u201cgreen valley\u201d and migrate to the \u201cred sequence\u201d. Because the rate of gas return from stars diminishes with time and SMBH mass grows, the Eddington ratio of the SMBH decreases with time. The SMBH growth is synchronous with star formation from recycled gas during this period. The accompanying star formation rate may also be substantial but typically does not constitute a starburst during this period. The entire duration of this phase depends sensitively on the lower cuto\ufb00mass of the initial mass function (IMF) \u2013 a sensitive and powerful prediction of this model. (3) \u201cQuiescent Bulge\u201d: several gigayears after the end of the starburst the bulge is now truly red and dead gas return rate is now negligible so both accretion to the central SMBH and residual star formation have ceased. It is possible that a disk is grown later around the bulge. The feeding of the central SMBH in the bulge of spiral galaxy during this period is no longer by overhead material from aging stars, rather by occasional objects that happen to be on some plunging orbits to be disrupted by the SMBH and form a short-lived accretion disc. Candidate objects may include molecular clouds, some tidally disruptable stars or gas streams. Signi\ufb01cant disturbances or torques, such as minor mergers and galactic bars, could provide the necessary drivers for some more consistent accretion events. How is a red and dead bulge with a hot atmosphere able to remain star-formation-free? This is a major topic on its own right and beyond the scope of the current paper, but will be addressed in a future paper. 6.2. Some \u201cObvious\u201d Implications of the Model There are some unambiguous discriminating signatures of this model that already can be directly \u201cread o\ufb00\u201d Figure 2. We highlight several here. (1) Starburst and AGN growth are not coeval in this model. AGN does not regulate the starburst, consistent with observations (e.g., Schawinski et al. 2009; Kaviraj 2009). AGN activities is expected to outlive the starburst, in agreement with observations (e.g., Georgakakis et al. 2008). These predictions are opposite to those of models that invoke AGN feedback as the primary regulating agent. (2) The apparent requirement of a rapid migration of early-type galaxies from the blue cloud to the red sequence, in order to produce a bimodal distribution in color (e.g., Blanton et al. 2003), is primarily due to the prompt shutdown of SF by stars (i.e., supernovae) at the end of the starburst phase; there is no need to invoke other ingredients, consistent with observations (e.g., Kaviraj et al. 2010). Observationally, there is no evidence that the \u2013 21 \u2013 presence of an AGN is related to quenching of star formation or the color transformation of galaxies (e.g., Aird et al. 2012). This prediction is di\ufb00erent from that of models that invoke AGN feedback to quench star formation. (3) AGN activities in ongoing starburst galaxies, i.e., buried AGN activities, are not expected to be dominant in this model, in agreement with observations (e.g., Genzel et al. 1998; Ivison et al. 2000; Ptak et al. 2003; Ivison et al. 2004; Alexander et al. 2005a,b; Schweitzer et al. 2006; Kawakatu et al. 2006; Alexander et al. 2008; Veilleux et al. 2009). Note that the above statement is not inconsistent with AGN/QSOs being associated with galaxies in the process of merging, which may enhance accretion activities in the involved (yet to merge) galaxies (e.g, Bahcall et al. 1997; Hennawi et al. 2010; Smith et al. 2010). (4) The most luminous quasars that accrete with high Eddington ratios occur order of 100Myr after the end of the starburst. They may contain substantially more merger signatures, which appears to be indicated by observations (e.g., Bennert et al. 2008). If one were to identify a population in-between ULIRGs and more regular QSO hosts in terms of spectral properties, they should show some more signs of tidal interactions that are yet to fully settle since the starburst, also consistent with observations (e.g., Canalizo & Stockton 2001). (5) Low Eddington ratio AGNs that are expected to last order of Gyr are not expected to show a close linkage to major disturbances that trigger the starburst (e.g., mergers), since possible signatures of the trigger merger event have largely been erased over time, consistent with observations (e.g., Grogin et al. 2005; Cisternas et al. 2011). Thus, one does not expect to see merger signatures to be associated with moderate-luminosity AGNs, which is in contrast with AGN feedback based models where most of the moderate luminosity AGNs are expected to coincide with starburst. (6) While the green-valley morphologically early-type galaxies that host AGN is the evolutionary link between starburst galaxies (in the blue cloud) and the red elliptical galaxies (on the red sequence), it is useful to distinguish between them and the other class of green galaxies that simply continuously form a modest amount of stars (such as our own Galaxy). The former are chronologically immediate successors to starburst galaxies and should be in early-type galaxies, strongly supported by observations (e.g., Salim et al. 2007; Silverman et al. 2008; Hickox et al. 2009; Schawinski et al. 2010), whereas the latter are not a chronologically intermediate class between the blue cloud and the red sequence. The total green galaxy population will be the sum of these two di\ufb00erent morphological types, with some obvious implications, such as green galaxies having mixed morphological types with limited merger signatures, consistent with observations (e.g., Mendez et al. 2011). This prediction is in contrast with AGN feedback based models where most AGN hosts are expected to coincide with starburst and a small fraction, mostly the most luminous AGNs (occuring near the end of the starburst phase), is expected to have matured early-type morphologies. \u2013 22 \u2013 (7) While the early-type AGN host galaxies may have similar morphologies as and will eventually evolve to inactive elliptical galaxies, the former should have much bluer colors than the latter, consistent with observations (e.g., S\u00b4 anchez et al. 2004). The basic morphological properties of the host galaxies of the most luminous quasars, corresponding to the most massive SMBHs in the prime growth phase should resemble those of giant elliptical galaxies, consistent with observations (e.g., Dunlop et al. 2003). (8) Because of the expected rate of gas return (\u221dt\u22121.3 on gigayear scales) to which both SMBH accretion and star formation are proportional and because more powerful AGN accretion occurs closer in time to the preceding starburst, it is expected that more powerful AGNs are hosted by early-type galaxies with younger mean stellar ages, consistent with observations (e.g., Kau\ufb00mann et al. 2003; Jahnke et al. 2004). (9) The accompanying star formation rate of elliptical galaxies may be quite substantial, on the order of \u223c(5 \u221210)(M\u2217/1011 M\u2299)(t/1Gyr)\u22121.3 M\u2299yr\u22121. Thus, while most AGN host galaxies have left the blue cloud, a signi\ufb01cant fraction of them, especially those hosting luminous AGNs, should still have substantial SFR, consistent with observations (e.g., Silverman et al. 2009; Shi et al. 2009). It is expected that the incidence of star formation signatures (e.g., dust) in the nuclear region should correlate positively with AGN activities for elliptical galaxies, because the strengths of both are proportional to the gas return rate, consistent with observations (e.g., Sim\u02dc oes Lopes et al. 2007). These predictions are opposite to AGN feedback based models where star formation is expected to be completely quenched after AGN feedback clears the gas out. 6.3. Origin of Two AGN Accretion Regimes Kau\ufb00mann & Heckman (2009) presented an insightful observational result of two distinct regimes of black hole growth in nearby galaxies along with its apparent implications. They \ufb01nd that star-forming galaxies display a lognormal distribution of Eddington ratios; their interpretation is that in this regime accretion on to the SMBH is not limited by the supply of gas but by feedback processes that are intrinsic to the SMBH itself. Our model provides the following alternative interpretation for this phenomenon: this lognormal distribution merely re\ufb02ects two random processes at work: (1) the amount of gas that landed on the stable accretion disc to provide accretion to the SMBH during the starburst phase depends on many \u201crandom\u201d variables of the triggering event (in the case of a merger, such as merging orbit inclination, velocity, spin alignment, etc), and (2) observations catch a random moment during the accretion of this gas. Central theorem should then give rise to a lognormal distribution. Another class of possible triggering events for SMBH accretion in star-forming galaxies (e.g., dormant SMBH in the bulge of disk galaxies) is stochastic feeding due to some random events, which should also follow a lognormal distribution. \u2013 23 \u2013 Separately, they \ufb01nd that galaxies with old stellar populations is characterized by a power-law distribution function of Eddington ratios and the AGN accretion rate is about 0.3 \u22121% of the gas return gas from recycling. In our model the expect accretion rate is expected to be MBH/(frec MBG) = 1.3 \u00d7 10\u22122A\u03f5\u22121 0.1\u03c3200. This expected relation between SMBH accretion rate and gas return rate is remarkably close to their observed value. As Kau\ufb00mann & Heckman (2009) already pointed out, the powerlaw distribution is consistent with the recycling gas return rate \u221dt\u22121.3 (Mathews 1989). This is a strong support for the proposed model here. 6.4. Initial Mass Function and AGN Accretion History Because the least massive stars live the longest, the cuto\ufb00mass of the initial stellar mass function (IMF) plays an important role in shaping the evolution on longer time scales of \u22651Gyr. For example, a 0.92 M\u2299star (solar metallicity) has a lifetime of 10Gyr, whereas a 1.4 M\u2299only lives \u223c2Gyr. Thus, the duration of the \u201cSMBH Prime Period\u201d depends sensitively on the lower mass cuto\ufb00of the IMF. Figure 3 shows several cases of the evolution of the SMBH growth tracks. It shows that the evolution and duration of SMBH growth in the post-starburst phase depend sensitively on the low mass cuto\ufb00of the IMF. We see that for a cuto\ufb00mass of 0.92 M\u2299the SMBH spends about 100Myr accreting at Eddington limit when its mass is up to about 10% of its \ufb01nal mass and a signi\ufb01cant period (\u22651Gyr) at less than 1% of the Eddington rate, and most of the time at about 0.1% of the Eddington rate when its mass approaches its \ufb01nal mass. On the other hand, with a mass cuto\ufb00of 1.4 M\u2299 the entire SMBH accretion shortens to 2Gyr and does not extend below 10\u22122 Eddington rate. Since not all elliptical galaxies at present time are observed to accrete at 0.1% of the Eddington rate, this already suggests that a higher than 0.92 M\u2299cuto\ufb00mass in the IMF may be required. Presently there is circumstantial evidence for massive star formation in galactic centers, including our own Galaxy (e.g., Lu et al. 2009) and M31 (e.g., Bender et al. 2005). Given the very sensitive dependence of stellar lifetime on stellar mass, careful considerations along this line may prove to be very powerful in placing constraints on the low-mass cuto\ufb00in the IMF as well as testing this model. Detailed comparisons between theoretical prediction with observational data in terms of the AGN luminosity-mass plane (e.g., Steinhardt & Elvis 2010), the Eddington ratio range (e.g., Woo & Urry 2002), AGN ages at di\ufb00erent redshifts (e.g., Martini 2004) or at di\ufb00erent luminosities (e.g., Adelberger et al. 2005) should also prove very powerful in constraining the IMF. We note that our assumption used to derive the light curves in Figure 3 is extremely simplistic and therefore we do not expect that they provide satisfactory matches to observations. It is called for that additional ingredients be included to account for, e.g., variations in stellar distribution, possible variations of IMF as a function of local star formation conditions, dependence of initial seed SMBH mass on galaxy model, etc, in order to have a more encompassing analysis. We shall carry out a more detailed \u2013 24 \u2013 analysis with additional parameters in a future study, especially when measurements of both SMBH masses and accretion rates become signi\ufb01cantly more precise for a large sample of active galaxies. 6.5. Super-Solar Metallicity of Accreting Gas One clear implication is that the accretion gas, being shedded from aging stars, should be very metal rich with supersolar metallicity, in agreement with observations (e.g. Hamann & Ferland 1993), especially to explain super-solar N/He ratio (e.g., Hamann & Ferland 1999). This is because nitrogen is believed to be secondary nature, where its abundanace scales quadratically with metallicity. The recycled gas that is feeding the SMBH in our model \ufb01ts the bill most naturally. In addition, the metallicity of accretion gas is not expected to depend on redshift, being intrinsic to stellar evolution, consistent with all accreting gas being very metal rich at all redshifts, including the highest redshift SDSS quasars (e.g., Fan et al. 2006). 6.6. Relative Cosmic Evolution Between Starburst Galaxies and AGN Given the modest amount of time delay (several 100Myrs) between the starburst phase and the SMBH prime growth phase, it is unsurprising that one should expect to see nearly synchronous evolution between the starburst and SMBH growth on longer, cosmic time scales, consistent with observations (e.g., Boyle et al. 1988; Nandra et al. 2005). In the context of the observed cosmic downsizing phenomenon, the downsizing of galaxies (e.g., Cowie et al. 1996; Treu et al. 2005) should thus be closely followed by downsizing of AGNs (e.g., Barger et al. 2005; Hasinger et al. 2005). There is, however, a very important di\ufb00erence between the two classes in post peak activities, predicted in this model. For starburst the shutdown time scale is expected to be about \u223c100Myrs, whereas for moderateluminosity AGNs (i.e., Eddington ratio \u223c10\u22123) the decay time scale is of order of \u223c1Gyrs. With a deep AGN survey that is capable of subdividing early-type galaxies in terms of their masses, one should be able to di\ufb00erentiate between the downturn time of starburst galaxies and that of AGNs hosted by elliptical galaxies at a \ufb01xed mass. This prediction would be a strong di\ufb00erentiator between this model and AGN-based feedback models. \u2013 25 \u2013 6.7. AGN Broad Emission and Absorption Lines Some of the overhead material raining down onto SMBH accretion disc from recycled gas from aging low-to-intermediate mass stars provides the material observed as broad emission lines (BEL) and broad absorption lines (BAL). When some of this gas, probably in the form of some discrete clouds, reaches the inner region of the the SMBH (at r \u2264102rs, where rs is Schwarzschild radius), the clouds will be accelerated by radiation pressure, likely through some absorption lines, to velocities up to 0.1c. These clouds will be the observed BEL and BAL. The fact that only 15-20% of type I AGN to have BAL may be indicative of the discrete nature of the clouds, not unexpected from discrete stellar remnants or from cooling instabilities. An advantage of this overhead material is that it naturally provides gas clouds that are presumably to be some \u226550o o\ufb00the equatorial plane, in order not to be obscured by the molecular torus (there are of course BEL and BAL gas clouds at smaller angles but they are not seen directly). In this model we do not need any additional pressure force to lift the gas o\ufb00the accretion disc some of the raining down gas clouds from aging stars will be launched outwards before they reach the disc, physics of which is well known (e.g., Murray et al. 1995). 6.8. Evolution of SMBH Mass Relative to Bulge Mass Massive elliptical galaxies appear to have increased their masses by 30 \u2212100% in the last 7Gyr (e.g., Brown et al. 2008). The growth of the elliptical mass is not expected to be always accompanied by corresponding growth in the mass of the central SMBH. For example, merger of a spiral galaxy without a signi\ufb01cant SMBH and an elliptical galaxy would make the \ufb01nal SMBH appear less massive. Given the dependence of MBH/ MBG \u221d\u03c3 \u221d(1 + z)1/2 predicted in this model, we predict that the MBH/ MBG relation should evolve with redshift stronger than (1 + z)1/2 for quiescent elliptical galaxies. 6.9. On Relation between SMBHs and Pseudo-bulges It is useful to add a note on the di\ufb00erence between classic bulges and pseudo-bulges (Kormendy & Kennicutt 2004) with respect to the central SMBHs in this model. The relation derived, Equations (17, 18), that matches the observed MBH \u2212MBG relation is dependent on the abundant supply of recycled gas in the inner region. Given the su\ufb03cient gas supply from recycled gas, the feedback from the SMBH then can regulate its own growth. This essential ingredient of su\ufb03cient gas supply is consistent with the observed inner slope \u2013 26 \u2013 of classic bulges (e.g., Faber et al. 1997; Kormendy et al. 2009), as we have shown. The situation would be very di\ufb00erent, if star formation is not as centrally concentrated as in classic bulges, for example, in rings (Kormendy & Kennicutt 2004, and references therein) of high angular momentum with a hollow core. In this case, the amount of recycled gas raining down from the innermost region may depend on other unknown factors. For instance, if secular processes act promptly, compared to the time scales of stellar gas recycle (\u223c0.1 \u22121 Gyr), to be able to substantially \ufb01ll the central region with stars initially formed in outer regions, the SMBH may follow the track we described. If, on ther other hand, secular processes evolve on longer time scales, the recycled stellar gas would predominantly land in outer regions that do not e\ufb03ciently accrete to the SMBH, which would in turn not grow substantially. It would seem likely that there may be two trends for pseudo-bulges: (1) there will be large variations in MBH \u2212MBG relation and (2) SMBH masses may lie below that of the MBH \u2212MBG relation derived from inactive classic elliptical galaxies/bulges, both consistent with independent considerations in the context of hierarchical structure formation model (e.g., Shankar et al. 2012). Observations, while very challenging, may have already provided some hints of both (Greene et al. 2008). Moreover, we do not expect any discernible correlation between the SMBH and galaxy disk or dark matter halo, simply because the stars in disks do not a\ufb00ect SMBH growth and the overall dark matter halo, while indirectly a\ufb00ect the escape velocity that enters Equation (18), does not control the amount of gas that feeds the SMBH. This prediction is consistent with observations (e.g., Kormendy & Bender 2011). In addition, some stellar population in the outskirts (either on a disk or just at large radii of an elliptical galaxy) of AGN hosts may be unrelated to the preceding starburst and could be substantially di\ufb00erent from bulge stars (e.g., Nolan et al. 2001). \u2013 27 \u2013 Green Valley       Red Sequence Starburst  0                                           0.1                                         3                              10 gas blowout by supernovae & starburst ends        SMBH   Prime Growth       Quiescent      Elliptical self-regulated SMBH growth fueled by  recycled gas from aging bulge stars    gas return rate & SFR = t-1.3 5x106 1x107 1x108      200   gas-rich    merger Phases Blue Cloud Galaxy Color                                                               Time (Gyr)     SMBH Mass   Red Sequence depend on low mass cutof of IMF        SFR decreasing Eddington ratio About Gas may become a bulge with a newly grown spiral disk SMBH Physics SMBH growth limited to inner disc supply-based growth w/ regulation stochastic feed or by hot gas SF Physics self-regulated star formation/burst supply-based star formation no star formation in bulge Fig. 2.\u2014 shows the entire evolutionary process for an example merger of two gas-rich spirals of mass \u223c1012 M\u2299each that eventually produces a powerlaw elliptical galaxy of velocity dispersion of 200 km/s. This scenario is not limitd to merger events but encompasses any signi\ufb01cant event triggering a starburst. Note that the time boundaries between di\ufb00erence consecutive phases are approximate and uncertain to within a factor of a few. The numbers in brown indicate the BH masses and the numbers in red indicate SFR. These numbers are very approximate and given mainly for illustration purpose. Clearly, given the complexity, one should expect large variations from case to case. \u2013 28 \u2013 7 8 9 \u22124 \u22123 \u22122 \u22121 0 0.01 0.1 0.3 1 2 5 10 0.01 0.1 0.3 1 2 5 10 log MBH (Msun) log lE     Minit=10% Mfinal, mcut=0.92 Minit=1% Mfinal, mcut=0.92 7 8 9 \u22124 \u22123 \u22122 \u22121 0 0.01 0.1 0.3 1 2 0.01 0.1 0.3 1 2 log MBH (Msun) log lE     Minit=10% Mfinal, mcut=1.4 Minit=1% Mfinal, mcut=1.4 7 8 9 43 44 45 46 0.01 0.1 0.3 1 2 5 0.01 0.1 0.3 1 2 5 log MBH (Msun) log Lbol (erg/s)     Minit=10% Mfinal, mcut=0.92 Minit=1% Mfinal, mcut=0.92 7 8 9 43 44 45 46 0.01 0.1 0.3 1 2 0.01 0.1 0.3 1 2 log MBH (Msun) log Lbol (erg/s)     Minit=10% Mfinal, mcut=1.4 Minit=1% Mfinal, mcut=1.4 Fig. 3.\u2014 Top left panel: evolutionary growth tracks in the SMBH massEddington ratio plane of an example SMBH of \ufb01nal mass 109 M\u2299with two cases of seed black mass of 107 and 108 M\u2299, respectively. A low mass cuto\ufb00for the IMF of 0.92 M\u2299that has a turno\ufb00lifetime of 10 Gyr is assumed. We assume that the SMBH accretion rate is proportional to the recycle gas return rate of the form \u221dt\u22121.3 Ciotti et al. (1991) capped at the Eddington rate with a radiative e\ufb03ciency of \u03f5 = 0.1, starting 200Myrs after the end of the starburst. Also indicated along each track are the times in Gyrs elapsed since the start of the accretion. Top right panel: the case for a low mass cuto\ufb00for the IMF of 1.4 M\u2299that has a turno\ufb00lifetime of 2 Gyr. Bottom panels: tracks for the cases in top panels but in the SMBH mass-luminosity plane. \u2013 29 \u2013 7. Conclusions We have presented an alternative physical model that has the following characteristics for the coevolution of galaxy and SMBH. From the onset of a starburst to becoming a quiescent bulge (in the absence of any subsequent signi\ufb01cant burst event) there are three distinct periods: (1) \u201cStarburst Period\u201d: some signi\ufb01cant event induces a starburst that probably lasts about 107 \u2212108yrs. The SMBH grows modestly during this period to possibly attain a mass that is up to order ten percent of its \ufb01nal mass. The feedback energy/momentum from the starburst, i.e., supernovae, drives the last patch of gas away and shuts down star formation. (2) \u201cSMBH Prime Period\u201d: several hundred million years after the end of the starburst, aging low-to-intermediate mass stars, now in their post-main-sequence phases, start to return a substantial fraction of their stellar mass to the ISM. Because the rate of gas return from stars diminishes with time, the Eddington ratio of the SMBH decreases with time roughly as t\u22121.3. The SMBH growth is synchronous with star formation from recycled gas during this period. The accompanying star formation rate may also be substantial. The duration of this phase depends sensitively on the lower cuto\ufb00mass of the initial mass function (IMF). (3) \u201cQuiescent Bulge\u201d: on order of gigayear after the end of the starburst the elliptical galaxy is now truly red and dead gas return rate is now negligible so both accretion to the central SMBH and residual star formation have ceased. It is possible that a disk may grow around the bulge later. The feeding of the central SMBH in the bulge of spiral galaxy during this period is not by overhead material from aging stars, rather by occasional objects that happen to be on some plunging orbits to be disrupted by the SMBH and form a short-lived accretion disc. Candidate objects may include molecular clouds or tidally disrupted stars. In this model, the end of starburst precedes the onset of prime SMBH growth by order of 100Myr. Starburst is responsible for shutting down its own activities; AGN has little to do with it. AGN does provide self-regulation during its prime growth post-starburst period. An important feature of this model is that it is physically based and no signi\ufb01cant \ufb01ne tuning is required. The physical reason why the SMBH does not grow substantially in the starburst phase, although over-supplied with gas, is that only a very small central disc is gravitationally stable for gas accretion onto the SMBH, while all other regions are unstable and more conducive to star formation. The condition is just the opposite during the post-starburst phase where recycled gas dropout from aging stars returns slowly and can be more e\ufb00ectively accreted, so e\ufb00ective that self-regulation comes to play, energetically feasibly provided by the radiation pressure. Many comparisons between this physical model and extant observations are made and the model appears to be in very agreement with them, including the MBH \u2212MBG relation. \u2013 30 \u2013 This model predicts that the distribution of the Eddington ratio of AGNs in star-forming galaxies is lognormal, whereas that of AGNs in early type galaxies is a powerlaw, consistent with observations (Kau\ufb00mann & Heckman 2009). We predict that early-type galaxy hosts of high Eddingtion rate AGNs are expected to be light-blue to green in optical color, gradually evolving to the red sequences with decreasing AGN luminosity. I thank Jerry Ostriker for useful comments and discussion. I would also like to thank Greg Novak, Kevin Schawinski and Charles Steinhardt for useful discussion. I thank an anonymous referee for critical and constructive reports. This work is supported in part by grants NNX08AH31G and NNX11AI23G.",
                    "introduction": "The tight correlation between galactic center supermassive black hole (SMBH) mass ( MBH) and the bulge mass ( MBG) or velocity dispersion (\u03c3) in the nearby universe (e.g., Richstone et al. 1998; Ferrarese & Merritt 2000; Tremaine et al. 2002) strongly suggests coevolution of the two classes, at least over the Hubble time. In many semi-analytic calcu- lations one of the most adopted assumptions, to put it simply, is that active galactic nuclei 1Princeton University Observatory, Princeton, NJ 08544; cen@astro.princeton.edu arXiv:1102.0262v3  [astro-ph.CO]  23 May 2012 \u2013 2 \u2013 (AGN) feedback is able to prevent most of the gas from accreting onto the SMBHs and at the same time is able to \ufb01x most of the \u201cdefects\u201d of galaxy formation models such as the shape of the galaxy luminosity function and star formation (SF) history (e.g., Kau\ufb00mann & Haehnelt 2000; Croton et al. 2006; Somerville et al. 2008) with the underlying feedback physics pa- rameterized. The substantial success in explaining a variety of observations enjoyed by these semi-analytic models is indicative of the relevance of AGN feedback. Calculations of the coupled evolution of SMBHs and galaxies using three-dimensional hydrodynamic simula- tions deploy thermal energy feedback in regions signi\ufb01cantly outside of the Bondi radius of the putative SMBH that e\ufb00ectively couples to the surroundings to regulate the SF and eventually drive the gas away. These pioneering detailed simulations have provided much physical insight and appear to be remarkably successful in accounting for many intricate observables, including AGN light curves, Eddington ratio distributions and SMBH-bulge relation and its scatter, for certain chosen value of the feedback energy strength (e.g., Di Matteo et al. 2005; Hopkins et al. 2006). What is hitherto left open in these calculations is the physical origin of the adopted energy feedback. One concern is that the derived SMBH- bulge relation depends very sensitively on the adopted energy feedback parameter due to the strong radiative cooling (e.g., Silk & Nusser 2010; Choi & Ostriker 2011). Thus, it is prudent to seek underlying physical origins for these successful models and, before that is achieved, continue to explore alternative models. This paper synthesizes an alternative physical model largely based on known physics. Before describing our overall model, we shall \ufb01rst, in \u00a72, examine the plausibility of the fundamental claim that AGN feedback is primarily responsible for regulating not only SMBH growth but also SF. We argue that scenarios invoking AGN as the primary \u201cblowing machine\u201d during the intense starburst phase may logically require signi\ufb01cant \ufb01ne-tuning. We then describe the evolutionary path from a starburst to an elliptical galaxy, including the coupled evolution of star formation and SMBH growth in the ensuing two sections. In \u00a73, we show that growth of SMBH during the starburst phase is limited and consti- tutes a small fraction of the overall SMBH consumption. The physical reason is that this phase is over-supplied with gas such that only a very small central disc is gravitationally stable (Toomre parameter Q > 1) for gas accretion onto the SMBH, while all other regions are unstable and more conducive to star formation. Since the SF time scale is much shorter than the Salpeter accretion time scale, most of the gas forms into stars. The accreted mass during this phase is probably limited to a few percent of the \ufb01nal SMBH mass. In \u00a74, we point out that energy or momentum feedback from SF is at least as competitive as that from the AGN during the starburst phase. Therefore, SF is largely responsible for blowing most of the last patch of gas away to end the starburst phase. In short, during the starburst phase, the SMBH does not grow signi\ufb01cantly and does not play the leading role in quenching the star formation. \u2013 3 \u2013 In \u00a75, we show that most of the growth of the SMBH occurs in the ensuing post- starburst period, when the bulge/elliptical galaxy is largely in place and SF enters \u201cpassive\u201d evolution. The fuel for this primary growth phase is provided by the gas recycled back into the interstellar medium (ISM) from aging bulge stars, proposed earlier by Norman & Scoville (1988) in the context of a central stellar cluster and stressed recently by Ciotti & Ostriker (2007) in the context of elliptical galaxies. It provides a relatively \u201cdi\ufb00use\u201d (compared to the starburst phase) but steady gas supply that, we show, is ideal for feeding SMBH via an accretion disc. Meanwhile, SF is the dominant mode for gas consumption in the outer region because the accretion is unstable to fragmentation there, even in this phase. Self- regulation is at work for the growth of the SMBH during this period and is provided by much more robust (compared to energy feedback) radiation pressure induced momentum. The amplitude and slope of the resultant SMBH-bulge relation with this self-regulation is consistent with observations. In this model, the entire evolution from the onset of starburst, due to a gas-rich merger or some signi\ufb01cant event that drives a large amount of gas into the central region within a short period of time, to becoming a quiescent elliptical galaxy (or a bulge of a future spiral galaxy) consists of three distinct periods, as summarized in \u00a75.1 and in Figure 2: (1) \u201cStarburst Period\u201d: merger of two gas-rich spiral galaxies or some other signi\ufb01cant event induces a starburst that lasts about 107 \u2212108yrs. The SMBH grows modestly during this period. The feedback energy/momentum from the starburst, i.e., supernovae, drives the last patch of gas away and helps shut down star formation. (2) \u201cSMBH Prime Period\u201d: several hundred million years after the end of the starburst, aging low-to-intermediate mass stars, now in the form of red giants and other post-main-sequence states, start to return a substantial fraction of their stellar mass to the ISM. The SMBH accretion is mostly supply limited in most of this period, except during the \ufb01rst several hundred million years or so, and lasts for order of gigayear. Because the rate of gas return from stars diminishes with time, the Eddington ratio of the SMBH decreases with time and the SMBH spends most of the time during this period at low the Eddington ratio (\u226410\u22123). The SMBH growth is nearly synchronous with star formation from recycled gas during this period. The accompanying star formation rate is quite substantial, roughly \u223c(5 \u221210)(M\u2217/1011 M\u2299)(t/1Gyr)\u22121.3 M\u2299yr\u22121, where t is time in Gyr and M\u2217is stellar mass of the elliptical galaxy formed during the starburst (at t = 0). The duration of this phase depends sensitively on the lower cuto\ufb00mass of the initial mass function (IMF). (3) \u201cQuiescent Elliptical Galaxy\u201d: several gigayears after the end of the starburst the elliptical galaxy is now truly red and dead - gas return rate is now negligible so both accretion to the central SMBH and residual star formation have ceased. It is possible, at least for an elliptical galaxy that is not too massive (i.e., Mtot \u22641012 M\u2299), that it may grow a disk. The feeding of the central SMBH in the bulge of spiral galaxy during this period is no longer by aging stars, rather by occasional objects (molecular clouds, stars, etc) that happen to be on some plunging orbits due to secular or random events. \u2013 4 \u2013 We present some predictions and implications of this model in \u00a76.2-6.9, followed by conclusions in \u00a77. Where comparisons can be made between the predictions of the model and observations, they appear to be in good agreement. Some additional predictions could provide further tests of the model."
                },
                {
                    "url": "http://arxiv.org/abs/1010.5014v1",
                    "title": "The Nature of Damped Lyman Alpha Systems and Their Hosts in the Standard Cold Dark Matter Universe",
                    "abstract": "Using adaptive mesh-refinement cosmological hydrodynamic simulations with a\nphysically motivated supernova feedback prescription we show that the standard\ncold dark matter model can account for extant observed properties of damped\nLyman alpha systems (DLAs). We then examine the properties of DLA host\ngalaxies. We find: (1) While DLA hosts roughly trace the overall population of\ngalaxies at all redshifts, they are always gas rich. (2) The history of DLA\nevolution reflects primarily the evolution of the underlying cosmic density,\ngalaxy size and galaxy interactions. With higher density and more interactions\nat high redshift DLAs are larger in both absolute terms and in relative terms\nwith respect to virial radii of halos. (3) The variety of DLAs at high redshift\nis richer with a large contribution coming from galactic filaments, created\nthrough close galaxy interactions. The portion of gaseous disks of galaxies\nwhere most stars reside makes relatively small contribution to DLA incidence at\nz=3-4. (4) The vast majority of DLAs arise in halos of mass M_h=10^10-10^12\nMsun at z=1.6-4. At z=3-4, 20-30% of DLA hosts are Lyman Break Galaxies (LBGs).\n(5) Galactic winds play an indispensable role in shaping the kinematic\nproperties of DLAs. Specifically, the high velocity width DLAs are a mixture of\nthose arising in high mass, high velocity dispersion halos and those arising in\nsmaller mass systems where cold gas clouds are entrained to high velocities by\ngalactic winds. (6) In agreement with observations, we see a weak but\nnoticeable evolution in DLA metallicity. The metallicity distribution centers\nat [Z/H]=-1.5 to -1 at z=3-4, with the peak moving to [Z/H]=-0.75 at z=1.6 and\n[Z/H]=-0.5 by z=0. (7) The star formation rate of DLA hosts is concentrated in\nthe range 0.3-30Msun/yr at z=3-4, gradually shifting lower to peak at ~0.5-1\nMsun/yr by z=0.",
                    "authors": "Renyue Cen",
                    "published": "2010-10-24",
                    "updated": "2010-10-24",
                    "primary_cat": "astro-ph.CO",
                    "cats": [
                        "astro-ph.CO",
                        "astro-ph.GA"
                    ],
                    "main_content": "2.1. Hydrocode and Simulation Parameters We perform cosmological simulations with the adaptive mesh refinement (AMR) Eulerian hydro code, Enzo (Bryan 1999; Bryan & Norman 1999; O\u2019Shea et al. 2004; Joung et al. 2009). First we ran a low resolution simulation with a periodic box of 120 h\u22121Mpc on a side. We identified two regions separately, one centered on a cluster of mass of \u223c2 \u00d7 1014 M\u2299and the other centered on a void region at z = 0. We then resimulate each of the two regions separately with high resolution, but embedded in the outer 120h\u22121Mpc box to properly take into account large-scale tidal field and appropriate boundary conditions at the surface of the refined region. We name the simulation centered on the cluster \u201cC\u201d run and the one centered on the void \u201cV\u201d run. The refined region for \u201cC\u201d run has a size of 21 \u00d7 24 \u00d7 20h\u22123Mpc3 and that for \u201cV\u201d run is 31 \u00d7 31 \u00d7 35h\u22123Mpc3. At their respective volumes, they represent 1.8\u03c3 and \u22121.0\u03c3 fluctuations. The initial condition in the refined region has a mean interparticleseparation of 117h\u22121kpc comoving, dark matter particle mass of 1.07 \u00d7 108h\u22121 M\u2299. The refined region is surrounded by two layers (each of \u223c1h\u22121Mpc) of buffer zones with particle masses successively larger by a factor of 8 for each layer, which then connects with the outer root grid that has a dark matter particle mass 83 times that in the refined region. Because we still can not run a very large volume simulation with adequate resolution and physics, we choose these two runs to represent two opposite environments that possibly bracket the average. At redshift z > 1.6, as we will show, the average properties of most quantities concerning DLAs in \u201cC\u201d and \u201cV\u201d runs are not very different, although the abundances of DLAs in the two runs are already very different. It is only at lower redshift where we see significant divergence of some quantities of DLAs between the two runs, presumably due to different dynamic evolutions in the two runs. We choose the mesh refinement criterion such that the resolution is always better than 460h\u22121pc physical, corresponding to a maximum mesh refinement level of 11 at z = 0. We also ran an additional simulation for \u201cC\u201d run with a factor of two lower resolution to assess the convergence of the results which we name \u201cC/2\u201d run and, as we will show in the Appendix, the convergence is excellent for all quantities examined here. The simulations include a metagalactic UV background (Haardt & Madau 1996), and a model for shielding of UV radiation by neutral hydrogen (Cen et al. 2005). They also include metallicity-dependent radiative cooling (Cen et al. 1995). Star particles are created in cells that satisfy a set of criteria for star formation proposed by Cen & Ostriker (1992). Each star particle is tagged with its initial mass, creation time, and metallicity; star particles typically have masses of \u223c106 M\u2299. Supernova feedback from star formation is modeled following Cen et al. (2005). Feedback energy and ejected metal-enriched mass are distributed into 27 local gas cells centered \u2013 5 \u2013 at the star particle in question, weighted by the speci\ufb01c volume of each cell, which is to mimic the physical process of supernova blastwave propagation that tends to channel energy, momentum and mass into the least dense regions (with the least resistance and cooling). We allow the whole feedback processes to be hydrodynamically coupled to surroundings and subject to relevant physical processes, such as cooling and heating, as in nature. As we will show later, the extremely inhomogeneous metal enrichment process demands that both metals and energy (and momentum) are correctly modeled so that they are transported into right directions in a physically sound (albeit still approximate at the current resolution) way. The primary advantages of this supernova energy based feedback mechanism are three-fold. First, nature does drive winds in this way and energy input is realistic. Second, it has only one free parameter eSN, namely, the fraction of the rest mass energy of stars formed that is deposited as thermal energy on the cell scale at the location of supernovae. Third, the processes are treated physically, obeying their respective conservation laws (where they apply), allowing transport of metals, mass, energy and momentum to be treated self-consistently and taking into account relevant heating/cooling processes at all times. We use eSN = 1 \u00d7 10\u22125 in these simulations. The total amount of explosion kinetic energy from Type II supernovae with a Chabrier IMF translates to eGSW = 6.6\u00d710\u22126. Observations of local starburst galaxies indicate that nearly all of the star formation produced kinetic energy (due to Type II supernovae) is used to power GSW (e.g., Heckman 2001). Given the uncertainties on the evolution of IMF with redshift (i.e., possibly more top heavy at higher redshift) and the fact that newly discovered prompt Type I supernovae contribute a comparable amount of energy compared to Type II supernovae, it seems that our adopted value for eSN is consistent with observations and within physical plausibility. We use the following cosmological parameters that are consistent with the WMAP7normalized (Komatsu et al. 2010) LCDM model: \u2126M = 0.28, \u2126b = 0.046, \u2126\u039b = 0.72, \u03c38 = 0.82, H0 = 100hkms\u22121Mpc\u22121 = 70kms\u22121Mpc\u22121 and n = 0.96. Convergence test of results are presented separately in Appendix A in order not to disrupt the \ufb02ow of the presentation in the results section. The tests show that our results are quite converged and should be robust at the accuracies concerned here, suggesting that our resolution has reached an adequate level for the present study. The reader may go to the Appendix any time to gauge the convergence of relevant computed quantities. The fact that most of the contributions to DLA incidence come from galaxies of mass \u223c1011 M\u2299that are well above our resolution, the results of our convergence tests are self-consistent. 2.2. Simulated Galaxy Catalogs We identify galaxies in our high resolution simulations using the HOP algorithm (Eisenstein & Hu 1999), operated on the stellar particles, which is tested to be robust and insen\u2013 6 \u2013 sitive to speci\ufb01c choices of concerned parameters within reasonable ranges. Satellites within a galaxy are clearly identi\ufb01ed separately. The luminosity of each stellar particle at each of the Sloan Digital Sky Survey (SDSS) \ufb01ve bands is computed using the GISSEL stellar synthesis code (Bruzual & Charlot 2003), by supplying the formation time, metallicity and stellar mass. Collecting luminosity and other quantities of member stellar particles, gas cells and dark matter particles yields the following physical parameters for each galaxy: position, velocity, total mass, stellar mass, gas mass, mean formation time, mean stellar metallicity, mean gas metallicity, star formation rate, luminosities in \ufb01ve SDSS bands (and various colors) and others. 2.3. Simulated Damped Lyman Alpha System Samples While our simulations also solve relevant gas chemistry chains for molecular hydrogen formation (Abel et al. 1997), molecular formation on dust grains (Joung et al. 2009) and metal cooling extended down to 10 K (Dalgarno & McCray 1972), at the resolution of the simulations, molecular clouds are not properly modeled. To correct for that, we use the Hidaka & Sofue (2002) observation that at nc = 5HI/cm3 H2 fraction is about 50% and then implement the following prescription to remove neutral gas in extrapolated high density regions and put it in H2 phase. In detail, we assume that the density pro\ufb01le is isothermal below our resolution, which would translate the fraction of mass in H2 is min(1, 0.5(nc/nres)\u22121/2). Thus, we post-process the neutral neutral density in the simulation by the following transformation: nHI(after) = nHI(before)(1\u2212min(1, 0.5(nc/nHI(before))\u22121/2)), where nHI(before) is the HI density directly from the simulation, and nHI(after) is that after this processing step. A very precise choice of the parameter in the above equation is unimportant; changing 0.5 to 1.0 makes marginally noticeable di\ufb00erences in the results. The primary e\ufb00ect of doing this is to remove very high HI column DLAs and causes the HI column density distribution function to steepen at NHI \u226522.5, in agreement with observations. In addition, because of that, the total amount of neutral gas in DLAs also become convergent and more stable. After the above post-process step, we shoot rays through the entire re\ufb01ned region of each simulation along all three orthogonal directions using a cell size of 0.915h\u22121kpc comoving. In practice, this is done piece-wise, one small volume of the simulation box at a time, due to limited computer memory. The spectral bin size is 3km/s. All physical e\ufb00ects are taken into account, including temperature broadening and peculiar velocities. Both intrinsic Lorentzian line pro\ufb01le and Doppler broadening are taken into account for both Ly\u03b1 and Si II \u03bb1808 line, although, in practice, for DLAs, Doppler broadening is important for Si II \u03bb1808 line and Lorentzian pro\ufb01le for Ly\u03b1 line. All relevant atomic data are taken from Morton (2003). A DLA is de\ufb01ned, as usual, a system with HI column larger than 1020.3cm\u22122. We assume that the fractional abundance of Si II is equal to fractional abundance of HI. Since, as we will see \u2013 7 \u2013 later, the HI regions of DLAs are \u201cpeaky\u201d with well-de\ufb01ned line-of-sight boundaries and since DLAs are very optically opaque to ionizing photons, any re\ufb01ned treatment of radiative selfshielding etc is unlikely to have any signi\ufb01cant e\ufb00ect. Note that we have already included a crude self-shielding method during the simulation, which should work well for optically opaque regions. As a side, one numerical point to note is that, because of the very large dynamic range of both line cross sections as a function of frequency shift from the line center and the delta function like cross section shapes in the line core regions, the convolution operations involved in the detailed calculations of optical depths require at least 64\u2212bits precision for \ufb02oating point numbers. For each DLA, we compute the HI column weighted metallicity, register its position relative to the center of the primary galaxy (i.e, the impact parameter), and for DLAs that are physically connected by at least one cell side in projection we merge them and in the end compute projected area A of each connected region to de\ufb01ne it size rDLA = (A/\u03c0)1/2. For each galaxy we also register the maximum velocity width v90,max among its associated DLAs. We are able to identify more than one million DLAs through ray tracing at each redshift examined in each of the runs. So the statistical errors are very small for each speci\ufb01c run at any redshift. But that does not speak to cosmic variance and as we shall show later, cosmic variance is indeed quite large concerning quantities that directly or indirectly pertain to the number density of DLAs. Other quantities, such as size, metallicity, kinematic properties, etc., however, appear to depend weakly on environments and their variances are small. A DLA \u201cbelongs\u201d to the largest galaxy in the region, within whose virial radius the DLA lies. For example, a DLA that is physically more closely located to a satellite galaxy that in turn is within the virial radius of a larger galaxy is said to belong to that larger galaxy. 2.4. Kinematic Measures for Si II Line We do not add instrumental noise to the simulated spectra, but we adopt the same observational procedure to compute the kinematic measures for the Si II absorption lines. For all relevant measures for the Si II line, we follow identically the procedures and de\ufb01nitions in Prochaska & Wolfe (1997). We generate synthetic spectra for both Ly\u03b1 and Si II line with 3km/s pixels and then smooth it with a 9-pixel boxcar averaging procedure. We de\ufb01ne the velocity width of a Si II absorption line associated with a DLA to be the velocity interval of 90% of the total optical depth, v90. For the three kinematic shape measures for Si II line we use all intensity troughs (optical depth peaks) without the 0.1 \u2264I(vpk)/\u00af I \u22640.6 constraint, where \u00af I is the continuum \ufb02ux, as re-emphasized by Prochaska & Wolfe (2010). The kinematic shape measures, fmm, fedg and f2pk, are de\ufb01ned exactly the same way as in Prochaska & Wolfe (1997). \u2013 8 \u2013 3. Results 3.1. A Garden Variety of DLAs y (kpc) pressure     0 10 20 30 40 50 60 70 0 10 20 30 40 50 3 3.5 4 4.5 5 y (kpc) atomic hydrogen density     0 10 20 30 40 50 60 70 0 10 20 30 40 50 \u22127 \u22126 \u22125 \u22124 \u22123 \u22122 \u22121 x (kpc) y (kpc) metallicity     0 10 20 30 40 50 60 70 0 10 20 30 40 50 \u22122 \u22121.5 \u22121 \u22120.5 0 temperature     0 10 20 30 40 50 60 70 0 10 20 30 40 50 3 4 5 6 7 baryon overdensity     0 10 20 30 40 50 60 70 0 10 20 30 40 50 0 1 2 3 4 5 x (kpc) stellar surface density     0 10 20 30 40 50 60 70 0 10 20 30 40 50 2 4 6 8 10 12 0 10 20 30 40 50 60 70 \u22125 \u22124 \u22123 \u22122 \u22121 0 1 nHI & nH,tot 0 10 20 30 40 50 60 70 \u22123 \u22122 \u22121 0 [Z/H] 0 10 20 30 40 50 60 70 \u2212800 \u2212600 \u2212400 \u2212200 0 x (kpc) vp (km/s) \u22124000 \u22122000 0 2000 4000 0 0.2 0.4 0.6 0.8 1 log N(HI)=21.7 log Mh=12.6 v90=129km/s fmm=0.02 fedge=0.12 f2pk=\u22120.81 FLya \u2212100 0 100 0 0.2 0.4 0.6 0.8 1 v(LOS) (km/s) FSi II Fig. 1.\u2014 Top left: temperature (K); middle left: atomic hydrogen density (cm\u22123); bottom left: metallicity (solar units); top middle: pressure (Kelvin cm\u22123); the above maps have a thickness of 1.3kpc. Middle middle: baryonic overdensity; bottom middle: SDSS U band luminosity surface density ( L\u2299/kpc2); these two maps are projected over the virial diameter of the galaxy. Included in pressure map is peculiar velocity \ufb01eld with 5kpc corresponding to 500km/s. The \ufb01ve panels on the right column, from top to bottom, are: atomic hydrogen density (cm\u22123; red solid curve) with total hydrogen density (dotted green curve), gas metallicity (solar units), LOS proper peculiar velocity, Ly\u03b1 \ufb02ux and \ufb01nally Si II \u03bb1808 \ufb02ux. The top three panels are plotted against physical distance, whereas the bottom two versus LOS velocity. Indicated in the second from bottom panel are properties of the DLA: log N(HI), log Mh, v90, fmm, fedg, f2pk. We \ufb01rst present a gallery of twelve DLAs at z = 3.1 (Figure 1-12) to show the richness of their physical properties. For each DLA six maps and \ufb01ve quantitative panels are displayed. In each of the six maps the line of sight (LOS) intercepting the DLA is shown as a white horizontal line and the exact location of the primary component of the DLA is at the intersection with another, white vertical line. In cases with multiple components along the LOS, the primary component coincides with the highest neutral density. Four of the maps top left (temperature in Kelvin), middle left (atomic hydrogen density in cm\u22123), bottom \u2013 9 \u2013 y (kpc) pressure     40 50 60 70 80 90 100 110 20 30 40 50 60 70 80 3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 y (kpc) atomic hydrogen density     40 50 60 70 80 90 100 110 20 30 40 50 60 70 80 \u22127 \u22126 \u22125 \u22124 \u22123 \u22122 x (kpc) y (kpc) metallicity     40 50 60 70 80 90 100 110 20 30 40 50 60 70 80 \u22122 \u22121.5 \u22121 \u22120.5 0 temperature     40 50 60 70 80 90 100 110 20 30 40 50 60 70 80 3 3.5 4 4.5 5 5.5 6 6.5 baryon overdensity     40 50 60 70 80 90 100 110 20 30 40 50 60 70 80 0 1 2 3 4 x (kpc) stellar surface density     40 50 60 70 80 90 100 110 20 30 40 50 60 70 80 2 4 6 8 10 0 10 20 30 40 50 60 70 80 90 100110120 \u22125 \u22124 \u22123 \u22122 nHI & nH,tot 0 10 20 30 40 50 60 70 80 90 100110120 \u22123 \u22122 \u22121 0 [Z/H] 0 10 20 30 40 50 60 70 80 90 100110120 \u2212200 0 200 x (kpc) vp (km/s) \u22124000 \u22122000 0 2000 4000 0 0.2 0.4 0.6 0.8 1 log N(HI)=20.5 log Mh=12.3 v90=219km/s fmm=0.18 fedge=0.15 f2pk=0.15 FLya \u2212200 \u2212100 0 100 0 0.2 0.4 0.6 0.8 1 v(LOS) (km/s) FSi II Fig. 2.\u2014 Top left: temperature (K); middle left: atomic hydrogen density (cm\u22123); bottom left: metallicity (solar units); top middle: pressure (Kelvin cm\u22123); the above maps have a thickness of 1.3kpc. Middle middle: baryonic overdensity; bottom middle: SDSS U band luminosity surface density ( L\u2299/kpc2); these two maps are projected over the virial diameter of the galaxy. Included in pressure map is peculiar velocity \ufb01eld with 5kpc corresponding to 500km/s. The \ufb01ve panels on the right column, from top to bottom, are: atomic hydrogen density (cm\u22123; red solid curve) with total hydrogen density (dotted green curve), gas metallicity (solar units), LOS proper peculiar velocity, Ly\u03b1 \ufb02ux and Si II \u03bb1808 \ufb02ux. The top three panels are plotted against physical distance, whereas the bottom two versus LOS velocity. Indicated in the second from bottom panel are properties of the DLA: log N(HI), log Mh, v90, fmm, fedg, f2pk. left (metallicity in solar units) and top middle (pressure in units of Kelvin cm\u22123) have a physical thickness of 1.3kpc. Also indicated in top middle (pressure) is the peculiar velocity \ufb01eld with a scaling of 5kpc corresponding to 500km/s. The remaining two maps middle middle (baryonic overdensity) and bottom middle (stellar surface density in M\u2299/kpc2) are projected over the entire galaxy of depth of order of the virial diameter of the primary galaxy. While these two projected maps give an overall indication of relative projected location of the DLA respect to the galaxy, the exact depth of the DLA inside the paper is, however, not shown. When we quote distance from the galaxy, we mean the projected distance on the paper plane. The \ufb01ve panels on the right column show various physical quantities along the line of \u2013 10 \u2013 y (kpc) pressure     20 30 40 50 60 70 30 40 50 60 70 80 3 3.1 3.2 3.3 3.4 3.5 3.6 y (kpc) atomic hydrogen density     20 30 40 50 60 70 30 40 50 60 70 80 \u22127 \u22126 \u22125 \u22124 \u22123 \u22122 \u22121 x (kpc) y (kpc) metallicity     20 30 40 50 60 70 30 40 50 60 70 80 \u22122 \u22121.5 \u22121 \u22120.5 0 temperature     20 30 40 50 60 70 30 40 50 60 70 80 3 3.5 4 4.5 5 5.5 6 6.5 baryon overdensity     20 30 40 50 60 70 30 40 50 60 70 80 0 1 2 3 4 5 x (kpc) stellar surface density     20 30 40 50 60 70 30 40 50 60 70 80 2 4 6 8 10 0 10 20 30 40 50 60 70 80 \u22124 \u22123 \u22122 \u22121 0 nHI & nH,tot 0 10 20 30 40 50 60 70 80 \u22123 \u22122 \u22121 0 [Z/H] 0 10 20 30 40 50 60 70 80 \u2212400 \u2212200 0 x (kpc) vp (km/s) \u22124000 \u22122000 0 2000 4000 0 0.2 0.4 0.6 0.8 1 log N(HI)=20.8 log Mh=11.9 v90=303km/s fmm=0.19 fedge=0.09 f2pk=\u22120.86 FLya \u2212400 \u2212300 \u2212200 \u2212100 0 100 0.96 0.97 0.98 0.99 1 v(LOS) (km/s) FSi II Fig. 3.\u2014 Top left: temperature (K); middle left: atomic hydrogen density (cm\u22123); bottom left: metallicity (solar units); top middle: pressure (Kelvin cm\u22123); the above maps have a thickness of 1.3kpc. Middle middle: baryonic overdensity; bottom middle: SDSS U band luminosity surface density ( L\u2299/kpc2); these two maps are projected over the virial diameter of the galaxy. Included in pressure map is peculiar velocity \ufb01eld with 5kpc corresponding to 500km/s. The \ufb01ve panels on the right column, from top to bottom, are: atomic hydrogen density (cm\u22123; red solid curve) with total hydrogen density (dotted green curve), gas metallicity (solar units), LOS proper peculiar velocity, Ly\u03b1 \ufb02ux and Si II \u03bb1808 \ufb02ux. The top three panels are plotted against physical distance, whereas the bottom two versus LOS velocity. Indicated in the second from bottom panel are properties of the DLA: log N(HI), log Mh, v90, fmm, fedg, f2pk. sight (i.e, along the white horizontal line shown in the maps on the left two columns). From top to bottom they are: atomic hydrogen density (in cm\u22123; red solid curve with a narrower shape) along with total hydrogen density (dotted green curve with a more extended shape), gas metallicity (in solar units), line-of-sight proper peculiar velocity (in km/s), Ly\u03b1 \ufb02ux and \ufb02ux for Si II \u03bb1808 line. The top three panels are plotted against physical distance, whereas the bottom two panels are plotted versus the LOS velocity. Also indicated in the Ly\u03b1 \ufb02ux panel (second from bottom) are several quantitative measures of the DLA, including the neutral hydrogen column density (log N(HI)), the halo mass of the primary galaxy in the system (log Mh), the velocity width of the associated Si II line (v90) and three kinetic measures of the Si II line, fmm, fedg, f2pk. We now describe in turn each of the twelve DLA examples. \u2013 11 \u2013 y (kpc) pressure     0 10 20 30 40 50 20 30 40 50 60 70 3 3.2 3.4 3.6 3.8 4 y (kpc) atomic hydrogen density     0 10 20 30 40 50 20 30 40 50 60 70 \u22127 \u22126 \u22125 \u22124 \u22123 \u22122 \u22121 x (kpc) y (kpc) metallicity     0 10 20 30 40 50 20 30 40 50 60 70 \u22122 \u22121.5 \u22121 \u22120.5 0 temperature     0 10 20 30 40 50 20 30 40 50 60 70 3 3.5 4 4.5 5 5.5 6 6.5 baryon overdensity     0 10 20 30 40 50 20 30 40 50 60 70 1 2 3 4 5 x (kpc) stellar surface density     0 10 20 30 40 50 20 30 40 50 60 70 2 4 6 8 10 12 0 10 20 30 40 50 60 70 \u22125 \u22124 \u22123 \u22122 \u22121 nHI & nH,tot 0 10 20 30 40 50 60 70 \u22123 \u22122 \u22121 0 [Z/H] 0 10 20 30 40 50 60 70 \u2212200 0 200 400 x (kpc) vp (km/s) \u22124000 \u22122000 0 2000 4000 0 0.2 0.4 0.6 0.8 1 log N(HI)=20.3 log Mh=11.9 v90=318km/s fmm=0.79 fedge=0.92 f2pk=0.92 FLya \u2212100 0 100 200 300 400 v(LOS) (km/s) FSi II Fig. 4.\u2014 Top left: temperature (K); middle left: atomic hydrogen density (cm\u22123); bottom left: metallicity (solar units); top middle: pressure (Kelvin cm\u22123); the above maps have a thickness of 1.3kpc. Middle middle: baryonic overdensity; bottom middle: SDSS U band luminosity surface density ( L\u2299/kpc2); these two maps are projected over the virial diameter of the galaxy. Included in pressure map is peculiar velocity \ufb01eld with 5kpc corresponding to 500km/s. The \ufb01ve panels on the right column, from top to bottom, are: atomic hydrogen density (cm\u22123; red solid curve) with total hydrogen density (dotted green curve), gas metallicity (solar units), LOS proper peculiar velocity, Ly\u03b1 \ufb02ux and Si II \u03bb1808 \ufb02ux. The top three panels are plotted against physical distance, whereas the bottom two versus LOS velocity. Indicated in the second from bottom panel are properties of the DLA: log N(HI), log Mh, v90, fmm, fedg, f2pk. Figure 1 shows a DLA produced by the LOS intersecting the tip of a long chimney at a distance of \u223c30kpc, The velocity structure suggests that it is still moving away (upwards) from the galaxy at a velocity of \u223c500km/s, likely caused by galactic winds. The metallicity at the interception is [Z/H] \u223c\u22121.5 but there are large gradients and variations of metallicity (we found that some other very nearby DLA systems intersecting di\ufb00erent parts of the chimney have metallicity [Z/H] < \u22123, not shown), suggesting very inhomogeneous enrichment process by galactic winds. While the primary galaxy has a mass of 4 \u00d7 1012 M\u2299, i.e., a 1-d velocity dispersion of 500km/s, the kinetic width of this line is only 129km/s with NHI = 21.7. Although the Ly\u03b1 \ufb02ux appears as a single component, as will be the case in all subsequent examples, the Si II absorption has several separate features, re\ufb02ecting the two-peak structure of the absorbing column and complex velocity structure within. We note \u2013 12 \u2013 that the nearby satellite galaxies may have triggered the starburst and the galactic winds. The responsible gas for this DLA is probably cooling and con\ufb01ned by external pressure likely due to thermal instability, as seen in the pressure panel. y (kpc) pressure     40 50 60 70 80 90 60 70 80 90 100 110 3 3.2 3.4 3.6 3.8 4 4.2 4.4 y (kpc) atomic hydrogen density     40 50 60 70 80 90 60 70 80 90 100 110 \u22127 \u22126 \u22125 \u22124 \u22123 \u22122 \u22121 x (kpc) y (kpc) metallicity     40 50 60 70 80 90 60 70 80 90 100 110 \u22122 \u22121.5 \u22121 \u22120.5 0 temperature     40 50 60 70 80 90 60 70 80 90 100 110 3 3.5 4 4.5 5 5.5 6 6.5 7 baryon overdensity     40 50 60 70 80 90 60 70 80 90 100 110 0 0.5 1 1.5 2 2.5 3 3.5 4 x (kpc) stellar surface density     40 50 60 70 80 90 60 70 80 90 100 110 2 4 6 8 10 0 10 20 30 40 50 60 70 80 90 100110120 \u22124 \u22123 \u22122 \u22121 0 nHI & nH,tot 0 10 20 30 40 50 60 70 80 90 100110120 \u22123 \u22122 \u22121 0 [Z/H] 0 10 20 30 40 50 60 70 80 90 100110120 \u2212400 \u2212200 0 200 400 x (kpc) vp (km/s) \u22124000 \u22122000 0 2000 4000 0 0.2 0.4 0.6 0.8 1 log N(HI)=21.4 log Mh=12.3 v90=420km/s fmm=0.39 fedge=0.47 f2pk=\u22120.74 FLya \u2212200 \u2212100 0 100 200 300 400 0 0.2 0.4 0.6 0.8 1 v(LOS) (km/s) FSi II Fig. 5.\u2014 Top left: temperature (K); middle left: atomic hydrogen density (cm\u22123); bottom left: metallicity (solar units); top middle: pressure (Kelvin cm\u22123); the above maps have a thickness of 1.3kpc. Middle middle: baryonic overdensity; bottom middle: SDSS U band luminosity surface density ( L\u2299/kpc2); these two maps are projected over the virial diameter of the galaxy. Included in pressure map is peculiar velocity \ufb01eld with 5kpc corresponding to 500km/s. The \ufb01ve panels on the right column, from top to bottom, are: atomic hydrogen density (cm\u22123; red solid curve) with total hydrogen density (dotted green curve), gas metallicity (solar units), LOS proper peculiar velocity, Ly\u03b1 \ufb02ux and Si II \u03bb1808 \ufb02ux. The top three panels are plotted against physical distance, whereas the bottom two versus LOS velocity. Indicated in the second from bottom panel are properties of the DLA: log N(HI), log Mh, v90, fmm, fedg, f2pk. In Figure 2 a DLA of width 219km/s is created jointly by two major components along the sightline, one at x \u223c70kpc of metallicity of [Z/H] \u223c[\u22121.0, \u22120.5] and size of \u223c20kpc at an impact parameter of \u223c30kpc and the other at x \u223c110kpc of metallicity of [Z/H] \u223c0.0 and size of \u223c30kpc. What is striking is many long gaseous structures in this galaxy. As we will see frequently, there are often long gaseous structures connected with galaxies that seem always coincidental with visible galaxy interactions of multiple galaxies or galaxies and satellites in close proximity. We shall call these features \u201cgalactic \ufb01laments\u201d hereafter. It seems likely that some of these galactic \ufb01laments are cold streams (Kere\u02c7 s et al. 2005; Dekel \u2013 13 \u2013 y (kpc)     10 20 30 40 10 20 30 40 3 3.5 4 4.5 5 5.5 6 6.5 y (kpc)     10 20 30 40 10 20 30 40 \u22127 \u22126 \u22125 \u22124 \u22123 \u22122 \u22121 0 1 x (kpc) y (kpc)     10 20 30 40 10 20 30 40 \u22122 \u22121.5 \u22121 \u22120.5 0     10 20 30 40 10 20 30 40 3 4 5 6 7     10 20 30 40 10 20 30 40 1 2 3 4 5 x (kpc)     10 20 30 40 10 20 30 40 2 4 6 8 10 0 10 20 30 40 50 60 70 \u22124 \u22123 \u22122 \u22121 0 nHI & nH,tot 0 10 20 30 40 50 60 70 \u22123 \u22122 \u22121 0 [Z/H] 0 10 20 30 40 50 60 70 \u2212200 0 200 400 x (kpc) vp (km/s) \u22124000 \u22122000 0 2000 4000 0 0.2 0.4 0.6 0.8 1 log N(HI)=21.5 log Mh=11.3 v90=510km/s fmm=0.59 fedge=0.95 f2pk=0.59 FLya \u2212200 0 200 400 0 0.2 0.4 0.6 0.8 1 v(LOS) (km/s) FSi II Fig. 6.\u2014 Top left: temperature (K); middle left: atomic hydrogen density (cm\u22123); bottom left: metallicity (solar units); top middle: pressure (Kelvin cm\u22123); the above maps have a thickness of 1.3kpc. Middle middle: baryonic overdensity; bottom middle: SDSS U band luminosity surface density ( L\u2299/kpc2); these two maps are projected over the virial diameter of the galaxy. Included in pressure map is peculiar velocity \ufb01eld with 5kpc corresponding to 500km/s. The \ufb01ve panels on the right column, from top to bottom, are: atomic hydrogen density (cm\u22123; red solid curve) with total hydrogen density (dotted green curve), gas metallicity (solar units), LOS proper peculiar velocity, Ly\u03b1 \ufb02ux and Si II \u03bb1808 \ufb02ux. The top three panels are plotted against physical distance, whereas the bottom two versus LOS velocity. Indicated in the second from bottom panel are properties of the DLA: log N(HI), log Mh, v90, fmm, fedg, f2pk. & Birnboim 2006). However, galactic \ufb01laments found in our simulations appear to be very rich in variety and disparate in metallicity (spanning 3 decades or more in metallicity). In other words, they are not necessarily primordial cold streams. In the case of this DLA, the \ufb01laments are likely made of gas pre-enriched, having cooled (as the pressure panel shows) and now rotating about the galaxy (roughly counter-clockwise). In contrast, note that the DLA in Figure 1 was still moving away from the galaxy. Like in Figure 1, the rich galactic \ufb01laments appear to be associated with signi\ufb01cant satellite structures in close proximity. The Si II absorption has several separate features, re\ufb02ecting the two separate physical components as well as substructures within each component. Figure 3 shows a DLA that is associated with a low metallicity ([Z/H] \u223c[\u22122.0, \u22121.5]) \u2013 14 \u2013 y (kpc) pressure     40 50 60 70 50 60 70 80 3 3.5 4 4.5 5 5.5 6 y (kpc) atomic hydrogen density     40 50 60 70 50 60 70 80 \u22127 \u22126 \u22125 \u22124 \u22123 \u22122 \u22121 0 x (kpc) y (kpc) metallicity     40 50 60 70 50 60 70 80 \u22122 \u22121.5 \u22121 \u22120.5 0 temperature     40 50 60 70 50 60 70 80 3 4 5 6 7 baryon overdensity     40 50 60 70 50 60 70 80 1 2 3 4 5 x (kpc) stellar surface density     40 50 60 70 50 60 70 80 2 4 6 8 10 12 0 10 20 30 40 50 60 70 80 90 100110120130 \u22124 \u22123 \u22122 \u22121 0 nHI & nH,tot 0 10 20 30 40 50 60 70 80 90 100110120130 \u22123 \u22122 \u22121 0 [Z/H] 0 10 20 30 40 50 60 70 80 90 100110120130 \u2212600 \u2212400 \u2212200 0 200 400 600 x (kpc) vp (km/s) \u22124000 \u22122000 0 2000 4000 0 0.2 0.4 0.6 0.8 1 log N(HI)=21.7 log Mh=12.5 v90=522km/s fmm=0.60 fedge=0.59 f2pk=\u22121.0 FLya \u2212100 0 100 200 300 400 500 0 0.2 0.4 0.6 0.8 1 v(LOS) (km/s) FSi II Fig. 7.\u2014 Top left: temperature (K); middle left: atomic hydrogen density (cm\u22123); bottom left: metallicity (solar units); top middle: pressure (Kelvin cm\u22123); the above maps have a thickness of 1.3kpc. Middle middle: baryonic overdensity; bottom middle: SDSS U band luminosity surface density ( L\u2299/kpc2); these two maps are projected over the virial diameter of the galaxy. Included in pressure map is peculiar velocity \ufb01eld with 5kpc corresponding to 500km/s. The \ufb01ve panels on the right column, from top to bottom, are: atomic hydrogen density (cm\u22123; red solid curve) with total hydrogen density (dotted green curve), gas metallicity (solar units), LOS proper peculiar velocity, Ly\u03b1 \ufb02ux and Si II \u03bb1808 \ufb02ux. The top three panels are plotted against physical distance, whereas the bottom two versus LOS velocity. Indicated in the second from bottom panel are properties of the DLA: log N(HI), log Mh, v90, fmm, fedg, f2pk. \ufb01lament that is feeding a small satellite, which in turn appears to be interacting and possibly feeding the primary galaxy at a projected distance of \u223c20kpc. This is yet another example of interacting galaxies producing rich gas-feeding \ufb01laments, as already seen in Figures 1 and 2. The relatively large width of 303km/s is produced by steep velocity gradient in the region from x \u223c45 to 50kpc. One could see that galactic winds are blowing to the upper left corner by the primary galaxy, whose starburst is likely triggered by the interaction. Figure 4 shows a DLA that is made up by several \ufb01laments at distances of 30 \u221240kpc from the galaxy. The metallicity of all the components is near solar, indicating that these are probably pre-enriched gas cooling due to thermal instability. The velocity structures show that they are falling back towards the galaxy, in a fashion perhaps similar to galactic \u2013 15 \u2013 y (kpc) pressure     0 10 20 30 40 50 10 20 30 40 50 3 3.2 3.4 3.6 3.8 y (kpc) atomic hydrogen density     0 10 20 30 40 50 10 20 30 40 50 \u22127 \u22126 \u22125 \u22124 \u22123 \u22122 \u22121 x (kpc) y (kpc) metallicity     0 10 20 30 40 50 10 20 30 40 50 \u22122 \u22121.5 \u22121 \u22120.5 0 temperature     0 10 20 30 40 50 10 20 30 40 50 3 3.5 4 4.5 5 5.5 6 6.5 baryon overdensity     0 10 20 30 40 50 10 20 30 40 50 0.5 1 1.5 2 2.5 3 3.5 4 x (kpc) stellar surface density     0 10 20 30 40 50 10 20 30 40 50 2 4 6 8 10 0 10 20 30 40 50 60 70 \u22125 \u22124 \u22123 \u22122 \u22121 nHI & nH,tot 0 10 20 30 40 50 60 70 \u22123 \u22122 \u22121 0 [Z/H] 0 10 20 30 40 50 60 70 200 400 600 x (kpc) vp (km/s) \u22124000 \u22122000 0 2000 4000 0 0.2 0.4 0.6 0.8 1 log N(HI)=20.4 log Mh=10.5 v90=306km/s fmm=0.78 fedge=0.87 f2pk=0.87 FLya 200 300 400 500 600 0.6 0.7 0.8 0.9 1 v(LOS) (km/s) FSi II Fig. 8.\u2014 Top left: temperature (K); middle left: atomic hydrogen density (cm\u22123); bottom left: metallicity (solar units); top middle: pressure (Kelvin cm\u22123); the above maps have a thickness of 1.3kpc. Middle middle: baryonic overdensity; bottom middle: SDSS U band luminosity surface density ( L\u2299/kpc2); these two maps are projected over the virial diameter of the galaxy. Included in pressure map is peculiar velocity \ufb01eld with 5kpc corresponding to 500km/s. The \ufb01ve panels on the right column, from top to bottom, are: atomic hydrogen density (cm\u22123; red solid curve) with total hydrogen density (dotted green curve), gas metallicity (solar units), LOS proper peculiar velocity, Ly\u03b1 \ufb02ux and Si II \u03bb1808 \ufb02ux. The top three panels are plotted against physical distance, whereas the bottom two versus LOS velocity. Indicated in the second from bottom panel are properties of the DLA: log N(HI), log Mh, v90, fmm, fedg, f2pk. fountains (Shapiro & Field 1976), on somewhat extended scales. Once again, it appears that galaxy-galaxy interactions may be responsible for the rich gas \ufb01laments, as seen in Figures 1, 2 and 3. There is evidence that winds are blowing upwards from the galaxy. Figure 5 shows another example of a DLA arising from a galaxy with a very rich \ufb01lament system due to galaxy interactions. The primary galaxy is the same as the one shown in Figure 2 and we are now looking at its south side. These \ufb01laments that are responsible for the neutral column of the DLA appear to have been enriched to a level of [Z/H] \u223c\u22121.0 and have cooled to low temperature. The large width of 420km/s is due to the multiple components spanning a spatial range of \u223c40kpc each of physical depth of several kpc and individual velocity width \u2264100km/s. Interestingly, for this DLA system, while most of \u2013 16 \u2013 y (kpc) pressure     0 10 20 30 40 50 60 10 20 30 40 50 60 3 3.5 4 4.5 5 5.5 y (kpc) atomic hydrogen density     0 10 20 30 40 50 60 10 20 30 40 50 60 \u22127 \u22126 \u22125 \u22124 \u22123 \u22122 \u22121 x (kpc) y (kpc) metallicity     0 10 20 30 40 50 60 10 20 30 40 50 60 \u22122 \u22121.5 \u22121 \u22120.5 0 temperature     0 10 20 30 40 50 60 10 20 30 40 50 60 3 4 5 6 7 baryon overdensity     0 10 20 30 40 50 60 10 20 30 40 50 60 1 2 3 4 5 x (kpc) stellar surface density     0 10 20 30 40 50 60 10 20 30 40 50 60 2 4 6 8 10 0 10 20 30 40 50 60 \u22125 \u22124 \u22123 \u22122 \u22121 0 nHI & nH,tot 0 10 20 30 40 50 60 \u22121 0 [Z/H] 0 10 20 30 40 50 60 \u22121000 \u2212800 \u2212600 \u2212400 \u2212200 0 200 400 x (kpc) vp (km/s) \u22124000 \u22122000 0 2000 4000 0 0.2 0.4 0.6 0.8 1 log N(HI)=21.4 log Mh=10.4 v90=516km/s fmm=0.19 fedge=0.49 f2pk=\u22120.51 FLya \u2212200 0 200 400 0 0.2 0.4 0.6 0.8 1 v(LOS) (km/s) FSi II Fig. 9.\u2014 Top left: temperature (K); middle left: atomic hydrogen density (cm\u22123); bottom left: metallicity (solar units); top middle: pressure (Kelvin cm\u22123); the above maps have a thickness of 1.3kpc. Middle middle: baryonic overdensity; bottom middle: SDSS U band luminosity surface density ( L\u2299/kpc2); these two maps are projected over the virial diameter of the galaxy. Included in pressure map is peculiar velocity \ufb01eld with 5kpc corresponding to 500km/s. The \ufb01ve panels on the right column, from top to bottom, are: atomic hydrogen density (cm\u22123; red solid curve) with total hydrogen density (dotted green curve), gas metallicity (solar units), LOS proper peculiar velocity, Ly\u03b1 \ufb02ux and Si II \u03bb1808 \ufb02ux. The top three panels are plotted against physical distance, whereas the bottom two versus LOS velocity. Indicated in the second from bottom panel are properties of the DLA: log N(HI), log Mh, v90, fmm, fedg, f2pk. the gas \ufb01laments are now falling back toward the galaxy (not necessarily radially), galactic winds are still blowing towards the upper right corner. Comparison of Figure 5 and Figure 2 indicates that the metallicity in the upper right quadrant of the galaxy is somewhat more metal enriched ([Z/H] \u223c0) than other regions ([Z/H] \u223c\u22121 or lower), consistent with the directions of ongoing galactic winds. This is strongly suggestive that metallicity enrichment process not only is episodic, multi-generational, anisotropic, but also in general possesses no parity. Figure 6 shows a DLA intercepting two \ufb01laments at a small inclined angle, giving rise to a broad physical extension of \u223c25kpc. All the visible \ufb01laments appear to run roughly topleft to bottom-right, whereas the metal enriched regions seem to spread out like a butter\ufb02y in \u2013 17 \u2013 y (kpc) pressure     0 10 20 30 40 50 60 0 10 20 30 40 50 60 3 3.2 3.4 3.6 3.8 y (kpc) atomic hydrogen density     0 10 20 30 40 50 60 0 10 20 30 40 50 60 \u22127 \u22126 \u22125 \u22124 \u22123 \u22122 \u22121 x (kpc) y (kpc) metallicity     0 10 20 30 40 50 60 0 10 20 30 40 50 60 \u22122 \u22121.5 \u22121 \u22120.5 0 temperature     0 10 20 30 40 50 60 0 10 20 30 40 50 60 3 3.5 4 4.5 5 5.5 6 6.5 baryon overdensity     0 10 20 30 40 50 60 0 10 20 30 40 50 60 0.5 1 1.5 2 2.5 3 3.5 4 x (kpc) stellar surface density     0 10 20 30 40 50 60 0 10 20 30 40 50 60 2 3 4 5 6 7 8 9 10 0 10 20 30 40 50 60 \u22125 \u22124 \u22123 \u22122 \u22121 nHI & nH,tot 0 10 20 30 40 50 60 \u22121 0 [Z/H] 0 10 20 30 40 50 60 \u2212200 0 200 400 600 x (kpc) vp (km/s) \u22124000 \u22122000 0 2000 4000 0 0.2 0.4 0.6 0.8 1 log N(HI)=20.4 log Mh=10.5 v90=501km/s fmm=0.79 fedge=0.79 f2pk=0.79 FLya \u2212200 \u2212100 0 100 200 300 400 500 0.97 0.98 0.99 1 v(LOS) (km/s) FSi II Fig. 10.\u2014 Top left: temperature (K); middle left: atomic hydrogen density (cm\u22123); bottom left: metallicity (solar units); top middle: pressure (Kelvin cm\u22123); the above maps have a thickness of 1.3kpc. Middle middle: baryonic overdensity; bottom middle: SDSS U band luminosity surface density ( L\u2299/kpc2); these two maps are projected over the virial diameter of the galaxy. Included in pressure map is peculiar velocity \ufb01eld with 5kpc corresponding to 500km/s. The \ufb01ve panels on the right column, from top to bottom, are: atomic hydrogen density (cm\u22123; red solid curve) with total hydrogen density (dotted green curve), gas metallicity (solar units), LOS proper peculiar velocity, Ly\u03b1 \ufb02ux and Si II \u03bb1808 \ufb02ux. The top three panels are plotted against physical distance, whereas the bottom two versus LOS velocity. Indicated in the second from bottom panel are properties of the DLA: log N(HI), log Mh, v90, fmm, fedg, f2pk. the direction roughly perpendicular to the \ufb01laments. This is the classic picture that galactic winds tend to blow in directions that are perpendicular to the \ufb01laments that are feeding the galaxy. The inner regions of the \ufb01laments appear to be less enriched ([Z/H] \u223c\u22122) than the outer regions of the \ufb01laments ([Z/H] \u223c[\u22120.5, 0]), strongly indicative of galactic winds tending to circumvent the denser \ufb01laments. The large width of 510km/s appears to be caused by oppositely moving (i.e., converging) \ufb02ows at x \u223c15 \u221240kpc, probably caused by the bipolar winds interacting with the complex \ufb01lament structures. This galaxy has a mass of 2 \u00d7 1011 M\u2299and we notice that most of its surrounding regions is relatively cold, whereas in Figures (1-5) we consistently see a hot atmosphere permeating the circumgalactic regions. The galaxies in Figures (1-5) all have mass \u22651012 M\u2299, consistent with the mass demarcation of cold and hot accretion modes (Kere\u02c7 s et al. 2005; Dekel & Birnboim 2006). \u2013 18 \u2013 y (kpc) pressure     0 10 20 30 40 50 60 10 20 30 40 50 60 3 3.5 4 4.5 5 y (kpc) atomic hydrogen density     0 10 20 30 40 50 60 10 20 30 40 50 60 \u22127 \u22126 \u22125 \u22124 \u22123 \u22122 \u22121 x (kpc) y (kpc) metallicity     0 10 20 30 40 50 60 10 20 30 40 50 60 \u22122 \u22121.5 \u22121 \u22120.5 0 temperature     0 10 20 30 40 50 60 10 20 30 40 50 60 3 4 5 6 7 baryon overdensity     0 10 20 30 40 50 60 10 20 30 40 50 60 0.5 1 1.5 2 2.5 3 3.5 4 x (kpc) stellar surface density     0 10 20 30 40 50 60 10 20 30 40 50 60 2 4 6 8 10 0 10 20 30 40 50 60 \u22125 \u22124 \u22123 \u22122 \u22121 0 nHI & nH,tot 0 10 20 30 40 50 60 \u22123 \u22122 \u22121 0 [Z/H] 0 10 20 30 40 50 60 \u2212200 0 200 400 600 x (kpc) vp (km/s) \u22124000 \u22122000 0 2000 4000 0 0.2 0.4 0.6 0.8 1 log N(HI)=21.6 log Mh=10.7 v90=501km/s fmm=0.0 fedge=0.2 f2pk=0.2 FLya \u2212200 0 200 400 0 0.2 0.4 0.6 0.8 1 v(LOS) (km/s) FSi II Fig. 11.\u2014 Top left: temperature (K); middle left: atomic hydrogen density (cm\u22123); bottom left: metallicity (solar units); top middle: pressure (Kelvin cm\u22123); the above maps have a thickness of 1.3kpc. Middle middle: baryonic overdensity; bottom middle: SDSS U band luminosity surface density ( L\u2299/kpc2); these two maps are projected over the virial diameter of the galaxy. Included in pressure map is peculiar velocity \ufb01eld with 5kpc corresponding to 500km/s. The \ufb01ve panels on the right column, from top to bottom, are: atomic hydrogen density (cm\u22123; red solid curve) with total hydrogen density (dotted green curve), gas metallicity (solar units), LOS proper peculiar velocity, Ly\u03b1 \ufb02ux and Si II \u03bb1808 \ufb02ux. The top three panels are plotted against physical distance, whereas the bottom two versus LOS velocity. Indicated in the second from bottom panel are properties of the DLA: log N(HI), log Mh, v90, fmm, fedg, f2pk. Nevertheless, the existence of cold galactic \ufb01laments seen in Figures (1-5) is consistent with the suggested cold mode of accretion of massive galaxies at high redshift (Dekel et al. 2009). Figure 7 shows a \u201cnormal\u201d DLA where a relatively quiet galactic disk is pierced edge-on. Its large width of 522km/s is simply due to the large halo that the galaxy is residing in of mass 3 \u00d7 1012 M\u2299(at z = 3.1). The surrounding environment seems relatively \u201cpristine\u201d with no widespread metal enrichment at a level of [Z/H] \u2265\u22121. However, the temperature panel indicates that there is a hot halo permeating the entire region and embedding and pressure-con\ufb01ning (see the pressure panel) the cold neutral clouds. It seems likely that this hot gaseous halo is produced by gravitational shocks rather than galactic wind shocks. There are several \ufb01laments attached to the galaxy. This is a good example of cold streams feeding \u2013 19 \u2013 y (kpc) pressure     0 10 20 30 40 50 60 70 0 10 20 30 40 50 3 4 5 6 7 y (kpc) atomic hydrogen density     0 10 20 30 40 50 60 70 0 10 20 30 40 50 \u22127 \u22126 \u22125 \u22124 \u22123 \u22122 \u22121 x (kpc) y (kpc) metallicity     0 10 20 30 40 50 60 70 0 10 20 30 40 50 \u22122 \u22121.5 \u22121 \u22120.5 0 temperature     0 10 20 30 40 50 60 70 0 10 20 30 40 50 3 4 5 6 7 baryon overdensity     0 10 20 30 40 50 60 70 0 10 20 30 40 50 0 1 2 3 4 5 x (kpc) stellar surface density     0 10 20 30 40 50 60 70 0 10 20 30 40 50 2 4 6 8 10 12 0 10 20 30 40 50 60 70 \u22125 \u22124 \u22123 \u22122 \u22121 0 nHI & nH,tot 0 10 20 30 40 50 60 70 \u22123 \u22122 \u22121 0 [Z/H] 0 10 20 30 40 50 60 70 \u2212200 0 200 400 x (kpc) vp (km/s) \u22124000 \u22122000 0 2000 4000 0 0.2 0.4 0.6 0.8 1 log N(HI)=21.3 log Mh=10.7 v90=504km/s fmm=0.38 fedge=0.96 f2pk=\u22121.0 FLya \u2212200 0 200 400 0 0.2 0.4 0.6 0.8 1 v(LOS) (km/s) FSi II Fig. 12.\u2014 Top left: temperature (K); middle left: atomic hydrogen density (cm\u22123); bottom left: metallicity (solar units); top middle: pressure (Kelvin cm\u22123); the above maps have a thickness of 1.3kpc. Middle middle: baryonic overdensity; bottom middle: SDSS U band luminosity surface density ( L\u2299/kpc2); these two maps are projected over the virial diameter of the galaxy. Included in pressure map is peculiar velocity \ufb01eld with 5kpc corresponding to 500km/s. The \ufb01ve panels on the right column, from top to bottom, are: atomic hydrogen density (cm\u22123; red solid curve) with total hydrogen density (dotted green curve), gas metallicity (solar units), LOS proper peculiar velocity, Ly\u03b1 \ufb02ux and Si II \u03bb1808 \ufb02ux. The top three panels are plotted against physical distance, whereas the bottom two versus LOS velocity. Indicated in the second from bottom panel are properties of the DLA: log N(HI), log Mh, v90, fmm, fedg, f2pk. a massive galaxy by penetrating a hot atmosphere. Figure 8 shows a DLA with a large velocity width arising from a relatively small galaxy of total mass 3 \u00d7 1010 M\u2299. The galactic winds are blowing in the north-east direction that entrain cold neutral clouds with it. The LOS of the DLA intercepts a high velocity component at x = 35 \u221255kpc. The combination of this high velocity component with the low velocity component at x \u223c0 produces the relatively large width of 306km/s. Note that an isotropic Maxwellian velocity distribution of dispersion equal to that of the halo velocity dispersion would only yield a width of v90 = 2.33vvir = 176km/s. Clearly, galactic winds are directly responsible for the large width of this DLA, by entraining cold gas clouds to a high velocity. Figure 9 shows another DLA produced by a small galaxy of mass 2 \u00d7 1010 M\u2299with a \u2013 20 \u2013 large velocity width. The galaxy system have multiple, interaction galaxies at close distances. The galactic winds are blowing primarily, in a bipolar fashion, in north-east and south-west direction, roughly perpendicular to the galactic disk, that entrain the cold neutral cloud at x \u223c40kpc to a broad velocity of vx = 0 \u2212400km/s relative to the galaxy itself. In combination with another complex structure at x = 45 \u221270kpc the galactic winds produce a very large width of 516km/s. Note that for this galaxy 2.33vvir = 160km/s. Figure 10 shows yet another DLA arising from a small galaxy but having a large velocity width of 501km/s. This is an interesting case where the galactic winds are blowing, by the primary galaxy, towards and passing through the satellite galaxy at (x, y) \u223c(40, 20)kpc in the north-east direction. The SDSS u band luminosity map suggests that the satellite galaxy itself is experiencing a starburst and likely blowing and enhancing the north-east/north winds. A very large positive velocity gradient in the positive x-direction (downstream) of \u223c700km/s over an LOS physical interval of \u2206x \u223c20kpc is produced, resulting in a very large width. Note that 2.33vvir = 162km/s for this galaxy. The entrained neutral gas cloud and its downstream appear to have escaped the metal enrichment by ongoing winds and remain at [Z/H] \u223c\u22121 \u201cshadowing\u201d e\ufb00ect due to dense clouds and \ufb01laments. Figure 11 shows another wide DLA from a small galaxy. For this DLA the majority of the column is due to the intersection with the disk of the galaxy, which would have produced a velocity width of \u223c200km/s on its own. The galactic winds blowing at the south-east direction entrain some cold clouds at x = 35 \u221245kpc to a velocity up to 500km/s. Together, a large width of 501km/s is produced. Given the small mass of the galaxy the surrounding regions are not embedded in a hot gravitationally shock heated atmosphere. There are some solid angles with low gas column that have been heated by galactic winds, probably triggered by the binary galaxy interaction, as can be seen by comparing temperature map and the density map. Note that 2.33vvir = 204km/s for this galaxy. Finally, Figure 12 shows the last example of a wide DLA from a small galaxy. Two galactic \ufb01laments make up this DLA, one at x \u223c10kpc and the other at x \u223c35kpc. The galactic system is a primary-satellite binary that is interacting, which has likely caused both to experience starbursts. The primary galaxy at (x, y) \u223c(23, 36)kpc is blowing bipolar galactic winds mainly in the north-south direction, whereas the satellite at (x, y) \u223c(35, 35)kpc is blowing bipolar galactic winds in the east-west direction. Together they produce a very complex, multi-stream velocity structure. The total velocity width of this DLA is 500km/s, although each of the two components individually has a velocity width of \u2264200km/s. Note that 2.33vvir = 200km/s for the primary galaxy. In summary, we see that DLAs arise in a wide variety of cold gas clouds, from galactic disks to cold streams to cooling gas from galactic winds to cold clouds entrained by hot galactic winds at a wide range of distances from galaxies, with a wide range of metallicity and in galaxies of all masses from 1010 \u221210\u221212.5 M\u2299at z \u223c3. Inspection of the gallery has \u2013 21 \u2013 already hinted that many large velocity width DLAs may be produced directly or indirectly by galactic winds. That is, directly by entraining cold gas clouds and compressing cold gas clouds with high pressure and indirectly by enhancing cooling and thermal instability with added metals and shock compression. In addition, the composite nature of many large width DLA systems should also help remove the perceived failure of the standard LCDM model with respect to producing large width systems (e.g., Prochaska & Wolfe 1997). Quantitative results later prove this is indeed the case. 3.2. Kinematic Velocity Width Distribution Functions 1.5 2 2.5 3 \u22127 \u22126 \u22125 \u22124 \u22123 log v90 (km/s) log d2nDLA/dXdv     z=1.6 (C) z=3.1 (C) z=4.0 (C) z=1.6 (V) z=3.1 (V) z=4.0 (V) Fig. 13.\u2014 Velocity distribution functions, de\ufb01ned to be the number of DLAs per unit width velocity per unit absorption length, at z = 1.6, 3.1, 4.0. Two sets of simulation results are shown, one for the \u201cC\u201d run (solid symbols) and \u201cV\u201d run (open symbols). The corresponding observational data for each of the individual redshifts (Prochaska et al. 2005) are shown as open squares, which span the redshift range of z = 1.7 \u22124.5. We now present more quantitative statistical results on the velocity width distribution functions of DLAs at several redshifts. Since the velocity structure in Ly\u03b1 \ufb02ux of a DLA is \u201cdamped\u201d and does not provide the kinematic information of the underlying physical cloud. Following Prochaska & Wolfe (1997), the velocity width, v90, is de\ufb01ned to be the velocity interval of 90% of the optical depth of the Si II \u03bb1808 absorption line associated with the DLA. Figure 13 shows the velocity width distribution at three redshifts (z = 1.6, 3.1, 4.0), \u2013 22 \u2013 covering most of the observed redshift range. We see a factor of \u223c10 variation from \u201cC\u201d to \u201cV\u201d run, indicating the need to have a larger statistical set of simulations covering, more densely, di\ufb00erent environments, before a more precise comparison can be made with observations. Insofaras the observed velocity width distribution function lies inbetween the two bracketing runs, \u201cC\u201d and \u201cV\u201d, and the shape of the functions are in excellent agreement with observations, including the high velocity tail (v90 \u2265300km/s), this should be considered a success for the LCDM model there is no lack of large width DLAs with v90 \u2265300km/s in the LCDM simulation. This conclusion is consistent with that of Hong et al. (2010), who studied this issue with a di\ufb00erent code and a di\ufb00erent feedback implementation. There is a signi\ufb01cant di\ufb00erence between our results and theirs in the that we \ufb01nd galactic winds are directly responsible for many of the large width DLAs, by entraining neutral dense clouds to large velocities. In addition, they conclude that a large halo mass (\u22651011 M\u2299) is a necessary condition for producing large velocity widths, while we \ufb01nd that a non-negligible fraction of large velocity width DLAs arise in halos less massive than 1011 M\u2299. 10 11 12 13 2 2.5 3 3.5 log Mhalo (Msun) log v90,max (km/s)     z=1.6 (C) v90,max=2.33vvir 10 11 12 13 2 2.5 3 3.5 log Mhalo (Msun) log v90,max (km/s)     z=3.1 (C) v90,max=2.33vvir 10 11 12 13 2 2.5 3 3.5 log Mhalo (Msun) log v90,max (km/s)     z=1.6 (V) v90,max=2.33vvir 10 11 12 13 2 2.5 3 3.5 log Mhalo (Msun) log v90,max (km/s)     z=3.1 (V) v90,max=2.33vvir Fig. 14.\u2014 The maximum v90 of all DLAs associated with each galaxy against the halo mass of the galaxy Mhalo for z = 1.6 and z = 3.1 for \u201cC\u201d and \u201cV\u201d run. The black line v90 = 2.33vvir is what v90 would be if the velocity distribution is an isotropic and Maxwellian distribution with its dispersion equal to vvir, and the Si II gas density is constant across the DLA. \u2013 23 \u2013 To help understand the large velocity width DLAs, we plot in Figure 14 the maximum v90 of all DLAs, v90,max, associated with each galaxy against the halo mass of the galaxy, Mhalo. The black line v90 = 2.33vvir is what v90 would be if the velocity distribution is an isotropic and Maxwellian distribution with its dispersion equal to vvir, and the Si II gas density is constant across the DLA. We see that the Maxwellian velocity distribution (the black line) approximately provides a lower bound to v90, although there is, unsurprisingly, some fraction of systems that lie below (see Figure 1 for an example). What is very interesting is that at z = 3.1 there is a large number of galaxies whose v90,max are substantially larger than what vvir could produce, i.e., \u201csuper-gravitational motion\u201d in the terminology of Hong et al. (2010). This super-gravitational motion is produced by galactic winds, as we have seen clearly in Figures 8, 9, 10, 11 and 12 in \u00a73.1. We also note that at z = 1.6 for both \u201cC\u201d and \u201cV\u201d run (and especially the \u201cC\u201d run), the correlation between v90 and vvir becomes substantially better with much reduced scatter, and the excess of DLAs with large v90/vvir is much removed. This is circumstantial but strong evidence that galactic winds are responsible for most of the large v90/vvir DLAs, because of higher star formation activities hence galactic winds at z = 3.1 than z = 1.6. Figure 16 below will further strengthen this point. It appears that the redshift evolution at a \ufb01xed environment is relatively mild in the redshift range z = 4.0 to z = 1.6. We speculate that the weak evolution of the velocity width distribution from z = 4.0 to z = 1.6 may be coincidental and attributable to two countering processes: growth of halo mass hence virial velocity with time and diminution of supergravitational motion produced by galactic winds with time (due to reduced star formation activities with time at z \u22642). This prediction of a weak evolution of velocity width distribution with redshift is veri\ufb01able with future larger DLA sample and is a powerful test for the non-gravitational origin of a large fraction of the large width systems. Figure 14 does not, however, fairly characterize the relative contribution of halos of di\ufb00erent masses to velocity width distribution function, because it does not specify the number of DLAs at a given halo mass. In Figure 15 we show the halo mass probability distribution function for DLAs above three velocity width cuts, v90 \u2265150, 300, 600km/s, respectively. We see a clear trend that larger halos make larger contribution to larger width DLAs, as one would have expected. For example, about one half of all DLAs with v90 \u2265 600km/s arise in halos of mass greater than 1012 M\u2299at z = 3.1, whereas that division line drops to 2 \u00d7 1011 M\u2299for v90 \u2265150km/s. It should be noted that the ratio of the virial velocity of a halo of mass 2 \u00d7 1011 M\u2299to that of 1012 M\u2299is 0.58, signi\ufb01cantly greater than 0.25 = 150/600, indicating an overweight of DLA cross-section by large galaxies. For moderate to large velocity width of v90 \u2265150km/s, halos of mass 1 \u00d7 1011 M\u2299dominate the contribution to DLA incidence, largely in agreement with Hong et al. (2010). Slightly at odds with Hong et al. (2010), however, we \ufb01nd a signi\ufb01cant fraction of these relative wide systems arising in galaxies of mass less than 1 \u00d7 1011 M\u2299: (24%, 18%, 12%) of DLAs with velocity width larger than (150, 300, 600)km/s are due to galaxies with mass less than 1 \u00d7 1011 M\u2299. \u2013 24 \u2013 9 10 11 12 13 0 0.1 0.2 0.3 log Mhalo (Msun) PDF     z=3.1 (C) v90>150km/s z=3.1 (C) v90>300km/s z=3.1 (C) v90>600km/s Fig. 15.\u2014 shows the DLA incidence weighted halo mass probability distribution function for DLAs above three velocity width cuts, v90 \u2265150, 300, 600km/s at z = 3.1 for the \u201cC\u201d run. Note that a DLA associated with a satellite galaxy or any gas cloud within the virial radius is given the halo mass of the primary galaxy. We note that our de\ufb01nition of associating DLAs with galaxies biases associating them to larger galaxies; Figure 3 gives an example, where the DLA is de\ufb01ned to arise from the larger galaxy of mass 8\u00d71011 M\u2299, even though it is more closely related to a much smaller satellite galaxy that is orbiting around the larger galaxy. Our results are perhaps unsurprising in the sense that one would have expected that galactic winds, when they are blowing, should be stronger, or at least not weaker, in dwarf starburst galaxies than larger galaxies thanks to shallow gravitational potential wells in the former, when cold gas is still abundant at high redshift. Both Figure 15 and gallery pictures in \u00a73.1 con\ufb01rm this point. Galactic winds, however, could be weaker in dwarf galaxies if star formation is inproportionally less vigorous. This may be the case at lower redshift, as shown in Figure 16. What is interesting, and further evidence, is that at z = 0 the dwarf galaxies in \u201cV\u201d run appear to have more super-gravitational motion than in the \u201cC\u201d run, simply because the former are gas richer and have higher star formation rate than the latter. Thus, it seems that galactic winds are a bivariate function of galaxy mass and star formation rate, in a fashion that is consistent with observations (e.g., Martin 2005). \u2013 25 \u2013 10 11 12 13 2 2.5 3 3.5 log Mhalo (Msun) log v90,max (km/s)     z=0 (C) v90,max=2.33vvir 10 11 12 13 2 2.5 3 3.5 log Mhalo (Msun) log v90,max (km/s)     z=0 (V) v90,max=2.33vvir Fig. 16.\u2014 The maximum v90 of all DLAs associated with each galaxy against the halo mass of the galaxy Mhalo at z = 0 for \u201cC\u201d and \u201cV\u201d run. The black line v90 = 2.33vvir is what v90 would be if the velocity distribution is an isotropic and Maxwellian distribution with its dispersion equal to vvir, and the Si II gas density is constant across the DLA. 3.3. Si II Line Pro\ufb01le Shape Measures Having found an overall good agreement with observations with respect to the velocity width distribution, we now turn to shape measures of Si II \u03bb1808 absorption line pro\ufb01le. Before comparing to observational data from Prochaska & Wolfe (1997), we shall \ufb01rst try to understand the relationship among the optical depth of a Si II line, HI column density metallicity and velocity width. Assuming that the optical depth pro\ufb01le of the Si II line is a simple top-hat (assuming a di\ufb00erent pro\ufb01le such as a gaussian makes no material di\ufb00erence for our purpose), it can be shown that \u03c4Si II = 0.01( NHI 2 \u00d7 1020 cm\u22122)( Z Z\u2299 )( v90 100 km/s)\u22121, (1) where Z is the metallicity of DLA in solar units. Left panel of Figure 17 shows v90 as a function of log NHI for Z = 0.1 Z\u2299. As expected, an increase in velocity width requires a corresponding increase in column density to produce a same optical depth. More important is that, quantitatively, in order to achieve an optical depth of 0.1, with a width v90 \u223c100km/s it requires a DLA column of \u223c2\u00d71022cm\u22122, if the DLA is composed of one single component with [Z/H] = \u22121. Since the abundance of DLAs with NHI \u22651022.5cm\u22122 declines rapidly (see Figure 21) but the abundance of Si II line peaks near v90 \u223c100km/s (Figure 13), this suggests that a signi\ufb01cant fraction of Si II lines must have multiple components. To quantitatively illustrate this, we de\ufb01ne a new simple two-component measure as follows. If there are at least two peaks in the optical depth pro\ufb01le that are separated by more than 0.5v90 and the ratio of the peak heights is greater than 1/15, we de\ufb01ne the DLA to be a two-component DLA. The ratio, 1/15, comes about such that the lower peak is guaranteed \u2013 26 \u2013 20 21 22 23 0 1 2 3 log NHI (cm\u00ef2) log v90 (km/s)     oSi II 1808=0.1 oSi II 1808=0.5 oSi II 1808=2.0 1 1.5 2 2.5 3 0 0.1 0.2 0.4 0.6 0.8 1 v90 (km/s) Two\u2212Peak %     two\u2212peak statistics Fig. 17.\u2014 Left panel: v90 as a function of log NHI assuming Z = 0.1 Z\u2299. Right panel: the percentage of DLAs that have multiple components, as a function of v90. to be included in the accounting of v90 interval, although changing it to say 1/10 makes no dramatic di\ufb00erence in the results. Note that DLAs with more than two components are included as two-component systems. Right panel of Figure 17 shows the percentage of two-component DLAs as a function of v90. In good agreement with the simple expectation, we see that at v90 = 100km/s, about 50% of DLAs have more than one component and that number increases to \u223c90% at v90 = 300km/s. This result is also consistent with the anecdotal evidence shown in the gallery examples in \u00a73.1, where most of large width DLAs contain more than one physical component. We now turn to the three kinematic shape measures de\ufb01ned in Prochaska & Wolfe (1997), fmm, fedg, f2pk, representing, respectively, measures of the symmetry, leading-edgeness and two-peakness of the pro\ufb01le of Si II \u03bb1808 absorption lines associated with DLAs (see the bottom right panels of the gallery pictures in \u00a73.1). Figures (18,19,20) show comparisons of simulation results with observations at three redshifts z = 1.6, z = 3.1 and z = 4.0. We see the overall agreement between simulations and observations is excellent, with K-S tests (indicated in the \ufb01gures) for both runs (\u201cC\u201d and \u201cV\u201d) at three compared redshifts (z = 1.6, 3.1, 4.0) all being at acceptable levels. Our results are in good agreement with one of the models with feedback in Hong et al. (2010), except for the case of f2pk: our simulations \ufb01nd acceptable K-S test values of 26-29%, 4-34% and 23-34% at z = 1.6, 3.1 and z = 4.0, respectively, whereas they \ufb01nd none of their models have probability higher than 5% at z = 3.1. We speculate that di\ufb00erence in the detailed treatments of metal transport process as well as feedback prescription between our simulations and theirs may have partly contributed to this di\ufb00erence; with detailed metal transport we \ufb01nd very inhomogeneous metallicity distributions across space and among DLAs in our simulations (see Figure 23 \u2013 27 \u2013 0 0.2 0.4 0.6 0.8 1 0 0.1 0.2 0.3 fmm PDF     0 0.2 0.4 0.6 0.8 1 0 0.1 0.2 0.3 fmm PDF     0 0.2 0.4 0.6 0.8 1 0 0.1 0.2 0.3 fmm PDF     0 0.2 0.4 0.6 0.8 1 0 0.1 0.2 0.3 fmm PDF     z=1.6 (C) p(K\u2212S)=0.18 z=1.2\u22122.0 (obs) z=3.1 (C) p(K\u2212S)=0.58 z=4.0 (C) p(K\u2212S)=0.27 z=3.8\u22124.2 (obs) z=1.6 (C) p(K\u2212S)=2E\u221289 z=3.1 (C) 0 0.2 0.4 0.6 0.8 1 0 0.1 0.2 0.3 fmm PDF     z=1.6 (V) p(K\u2212S)=0.16 z=1.2\u22122.0 (obs) 0 0.2 0.4 0.6 0.8 1 0 0.1 0.2 0.3 fmm PDF     z=3.1 (V) p(K\u2212S)=0.48 0 0.2 0.4 0.6 0.8 1 0 0.1 0.2 0.3 fmm PDF     z=4.0 (V) p(K\u2212S)=0.33 z=3.8\u22124.2 (obs) 0 0.2 0.4 0.6 0.8 1 0 0.1 0.2 0.3 fmm PDF     z=1.6 (V) p(K\u2212S)=2E\u221246 z=3.1 (V) Fig. 18.\u2014 Left set of four panels: fmm distributions for \u201cC\u201d run at redshift z = 1.6 (top left), z = 3.1 (top right) and z = 4.0 (bottom left). For z = 1.6 we compared to observed DLAs at the redshift range z = 1.2 \u22122.2; for z = 3.1 we compared to observed DLAs at z = 2.9 \u22123.3; for z = 4.0 we compared to observed DLAs at z = 3.8 \u22124.2. Observed sample is an updated version of Prochaska & Wolfe (1997), shown as the black histogram. Also shown in each K-S test probability that the two distributions (computed and observed) are drawn form the same underlying distribution. In the bottom right panel, we compare computed z = 1.6 and z = 3.1 distributions along with the K-S test probability to show a signi\ufb01cant evolution of this shape distribution function with redshift. Right set of four panels: fmm distributions for \u201cV\u201d run. below), whereas they assume a constant metallicity of [Z/H] = \u22121 for all DLAs. It is also noted that the metallicity distributions of our simulations at redshift range z = 1.6 \u22124.0 are in excellent agreement with observations (Figure 23). At the bottom-right panels of each four-panel set in Figures (18,19,20) we show a comparison between z = 1.6 and z = 3.1 distributions for each of the shape statistics and \ufb01nd that there is signi\ufb01cant evolution in all three shape measures. Current small observational sample does not allow for such a test. Our results demonstrate that the standard LCDM model, with a proper modeling of astrophysical processes, including galaxy formation and feedback in the forms of mechanical feedback and metal enrichment, can successfully produce Si II line shapes that are in good agreement with observations. \u2013 28 \u2013 0 0.2 0.4 0.6 0.8 1 0 0.1 0.2 0.3 fedg PDF     z=1.6 (C) p(K\u2212S)=0.37 z=1.2\u22122.0 (obs) 0 0.2 0.4 0.6 0.8 1 0 0.1 0.2 0.3 fedg PDF     z=3.1 (C) p(K\u2212S)=0.64 0 0.2 0.4 0.6 0.8 1 0 0.1 0.2 0.3 fedg PDF     z=4.0 (C) p(K\u2212S)=0.63 z=3.8\u22124.2 (obs) 0 0.2 0.4 0.6 0.8 1 0 0.1 0.2 0.3 fedg PDF     z=1.6 (C) p(K\u2212S)=3E\u2212120 z=3.1 (C) 0 0.2 0.4 0.6 0.8 1 0 0.1 0.2 0.3 fedg PDF     z=1.6 (V) p(K\u2212S)=0.29 z=1.2\u22122.0 (obs) 0 0.2 0.4 0.6 0.8 1 0 0.1 0.2 0.3 fedg PDF     z=3.1 (V) p(K\u2212S)=0.41 0 0.2 0.4 0.6 0.8 1 0 0.1 0.2 0.3 fedg PDF     z=4.0 (V) p(K\u2212S)=0.66 z=3.8\u22124.2 (obs) 0 0.2 0.4 0.6 0.8 1 0 0.1 0.2 0.3 fedg PDF     z=1.6 (V) p(K\u2212S)=3E\u221258 z=3.1 (V) Fig. 19.\u2014 Left set of four panels: fedg distributions for \u201cC\u201d run at redshift z = 1.6 (top left), z = 3.1 (top right) and z = 4.0 (bottom left). For z = 1.6 we compared to observed DLAs at the redshift range z = 1.2 \u22122.2; for z = 3.1 we compared to observed DLAs at z = 2.9 \u22123.3; for z = 4.0 we compared to observed DLAs at z = 3.8 \u22124.2. Observed sample is an updated version of Prochaska & Wolfe (1997), shown as the black histogram. Also shown in each K-S test probability that the two distributions (computed and observed) are drawn form the same underlying distribution. In the bottom right panel, we compare computed z = 1.6 and z = 3.1 distributions along with the K-S test probability to show a signi\ufb01cant evolution of this shape distribution function with redshift. Right set of four panels: fedg distributions for \u201cV\u201d run. 3.4. Column Density Distribution, Line Density and \u2126g(DLA) Evolution Let us now address the fundamentally important observable: the column density distribution of DLAs and its evolution. Figure 21 shows the column density distribution at several redshifts from z = 0 to z = 4. Where comparisons can be reliably made with observations, at z = 2.5, z = 3.1 and z = 4, we see that the overdense run \u201cC\u201d and underdense run \u201cV\u201d appropriately bracket the observational data in amplitude. Similar to the situation for the velocity distribution function (Figure 13), the strong environmental dependence of the column density distribution renders it impractical to make vigorous comparisons between the simulations and observations. Given that the amplitude of observed column density distribution lies between that of \u201cC\u201d and that of \u201cV\u201d run, and the shapes of both simulated functions are in reasonable agreement with observations we tentatively conclude that the standard LCDM model can reasonably reproduce the observed the column density distribution. Note that the shape at the highest column end depends on the treatment of high density regions, for which we have used an empirical relation. Ultimately, when pc resolution \u2013 29 \u2013 \u22121\u22120.8 \u22120.6 \u22120.4 \u22120.2 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 f2pk PDF     z=1.6 (C) p(K\u2212S)=0.26 z=1.2\u22122.0 (obs) \u22121\u22120.8 \u22120.6 \u22120.4 \u22120.2 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 f2pk PDF     z=3.1 (C) p(K\u2212S)=0.34 z=2.9\u22123.3 (obs) \u22121\u22120.8 \u22120.6 \u22120.4 \u22120.2 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 f2pk PDF     z=4.0 (C) p(K\u2212S)=0.34 z=3.8\u22124.2 (obs) \u22121\u22120.8 \u22120.6 \u22120.4 \u22120.2 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 f2pk PDF     z=1.6 (C) p(K\u2212S)=2E\u221237 z=3.1 (C) \u22121\u22120.8 \u22120.6 \u22120.4 \u22120.2 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 f2pk PDF     z=1.6 (V) p(K\u2212S)=0.29 z=1.2\u22122.0 (obs) \u22121\u22120.8 \u22120.6 \u22120.4 \u22120.2 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 f2pk PDF     z=3.1 (V) p(K\u2212S)=0.04 z=2.9\u22123.3 (obs) \u22121\u22120.8 \u22120.6 \u22120.4 \u22120.2 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 f2pk PDF     z=4.0 (V) p(K\u2212S)=0.23 z=3.8\u22124.2 (obs) \u22121\u22120.8 \u22120.6 \u22120.4 \u22120.2 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 f2pk PDF     z=1.6 (V) p(K\u2212S)=9E\u221216 z=3.1 (V) Fig. 20.\u2014 Left set of four panels: f2pk distributions for \u201cC\u201d run at redshift z = 1.6 (top left), z = 3.1 (top right) and z = 4.0 (bottom left). For z = 1.6 we compared to observed DLAs at the redshift range z = 1.2 \u22122.2; for z = 3.1 we compared to observed DLAs at z = 2.9 \u22123.3; for z = 4.0 we compared to observed DLAs at z = 3.8 \u22124.2. Observed sample is an updated version of Prochaska & Wolfe (1997), shown as the black histogram. Also shown in each K-S test probability that the two distributions (computed and observed) are drawn form the same underlying distribution. In the bottom right panel, we compare computed z = 1.6 and z = 3.1 distributions along with the K-S test probability to show a signi\ufb01cant evolution of this shape distribution function with redshift. Right set of four panels: f2pk distributions for \u201cV\u201d run. is reached, we can make more de\ufb01nitive tests. What is also interesting is that the variations between di\ufb00erent environments are larger than the redshift evolution of the column density distribution in each run. It is further noted that, seen in the lower-left panel of Figure 21, the evolution of the column density distribution in \u201cC\u201d and \u201cV\u201d run is di\ufb00erent. In \u201cC\u201d run, we see weak evolution from z = 4 to z = 1.6 and then a relatively large drop in amplitude at z = 0. In \u201cV\u201d run, on the other hand, we see practically little evolution from z = 3.1 to z = 0. This likely re\ufb02ects the dynamical stage of a simulated sample, where the \u201cC\u201d run is more dynamically advanced than the \u201cV\u201d at a same redshift, consistent with the behavior seen in Figure 25 below. Left panel of Figure 22 shows the redshift evolution of DLA line density, de\ufb01ned to be the number of DLAs per unit absorption length. Right panel of Figure 22 shows the redshift evolution of neutral gas density in DLAs. Inherited from the situation shown in Figure 21, there is a large variation of both plotted quantities between the two (\u201cC\u201d and \u201cV\u201d) runs. What is reassuring is that the observed data lie sensibly between results from these two \u2013 30 \u2013 20.3 21 21.5 22 22.5 \u221226 \u221225 \u221224 \u221223 \u221222 \u221221 log NHI (cm\u22122) fHI(N,X)     z=3.1 (C) z=3.1 (V) 20.3 21 21.5 22 22.5 \u221226 \u221225 \u221224 \u221223 \u221222 \u221221 log NHI (cm\u22122) fHI(N,X)     z=4.0 (C) z=4.0 (V) 20.3 21 21.5 22 22.5 \u221226 \u221225 \u221224 \u221223 \u221222 \u221221 log NHI (cm\u22122) fHI(N,X)     z=0.0 (C) z=1.6 (C) z=3.1 (C) z=4.0 (C) z=0.0 (V) z=1.6 (V) z=3.1 (V) z=4.0 (V) 20.3 21 21.5 22 22.5 \u221226 \u221225 \u221224 \u221223 \u221222 \u221221 log NHI (cm\u22122) fHI(N,X)     z=2.5 (C) z=2.5 (V) Fig. 21.\u2014 Column density distributions, de\ufb01ned to be the number of of DLAs per unit column density per unit absorption length, at z = 2.5 (lower right), at z = 3.1 (upper left), at z = 4.0 (upper right), separately, and together for z = 0, 1.6, 3.1, 4.0 (lower left). In each panel, two sets of simulation results are shown, one for the \u201cC\u201d run (solid dots) and \u201cV\u201d run (open circles). The corresponding observational data for each of the individual redshifts are an updated version with SDSS DR7 from Prochaska et al. (2005), shown as open squares. bracketing environments. If one assumes that the cosmic mean of each of the two plotted quantities should lie between \u201cC\u201d and \u201cV\u201d run, reading the range spanned by the two runs suggests that the LCDM model is likely to agree with observations to within a factor of \u223c2 with respect to both quantities, although what the overall temporal shape will look like is di\ufb03cult to guess. To \ufb01rmly quantify these important observables and to more precisely assess the agreement/disagreement between the predictions of the LCDM model and observations, a larger set of simulations sampling, more densely, di\ufb00erent environments in a statistically correct fashion will be necessary, so is a more accurate treatment of the transition from atomic to molecular hydrogen in very high density regions (that likely a\ufb00ects the shape at the high column density end). We reserve this for future work. \u2013 31 \u2013 0 1 2 3 4 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 z lDLA(X)     (C) (V) Prochaska et al (2005) Rao et al (2006) 0 1 2 3 4 0 1 2 3 4 5 z 1g DLA (x103)     (C) (V) Prochaska et al (2005) Rao et al (2006) Fig. 22.\u2014 Left panel: the redshift evolution of the DLA line density for the \u201cC\u201d run (solid dots) and \u201cV\u201d run (solid squares). The observational data at z > 2 are an updated version with SDSS DR7 from Prochaska et al. (2005), shown as open squares, the observational data at z < 2 are from Rao et al. (2006), shown as open circles. Right panel: the redshift evolution of the neutral gas density in DLAs for the \u201cC\u201d run (solid dots) and \u201cV\u201d run (solid squares). The observational data at z > 2 are an updated version with SDSS DR7 from Prochaska et al. (2005), shown as open squares, the observational data at z < 2 are from Rao et al. (2006), shown as open circles. 3.5. Metallicity Distribution and Evolution The current set of simulations is vastly superior to those used in our earlier work addressing the observed relatively weak but non-negligible evolution of DLA metallicity (Cen et al. 2003) and here we return to this critical issue. Figure 23 shows the DLA metallicity distributions at four redshift, z = 0, 1.6, 3.1, 4.0. For the three redshifts, z = 1.6, 3.1, 4.0, where comparisons can be made, we \ufb01nd that the agreement between simulations and observations at z = 1.6 to z = 0 is excellent, as K-S tests show. This is a non-trivial success, given that our feedback prescription has essentially one free parameter, that is, the supernova energy that is driving galactic winds transports energy, metals and mass throughout interstellar (ISM), circumgalactic (CGM) and intergalactic space (IGM). Furthermore, the absolute amount of metals is totally \ufb01xed by requiring that 25% of stellar mass with metallicity equal to 10 Z\u2299 returning to the ISM, CGM and IGM. The agreement indicates that our choices of both the supernova ejecta mass and its metallicity and the explosion energy, which are inspired by theories of stellar interior and direct observations, may provide a reasonable approximation of truth. We see that the peak of the DLA metallicity distribution evolves from [Z/H] = \u22121.5 \u2013 32 \u2013 \u22123 \u22122.5 \u22122 \u22121.5 \u22121 \u22120.5 0 0.5 0 0.1 0.2 0.3 0.4 [Z/H] PDF     \u22123 \u22122.5 \u22122 \u22121.5 \u22121 \u22120.5 0 0.5 0 0.1 0.2 0.3 0.4 [Z/H] PDF     \u22123 \u22122.5 \u22122 \u22121.5 \u22121 \u22120.5 0 0.5 0 0.1 0.2 0.3 0.4 [Z/H] PDF     \u22123 \u22122.5 \u22122 \u22121.5 \u22121 \u22120.5 0 0.5 0 0.1 0.2 0.3 0.4 [Z/H] PDF     z=0 (C) z=0 (V) z=1.6 (C) p(K\u2212S)=0.95 z=1.6 (V) p(K\u2212S)=0.83 z=1.2\u22122.0 (obs) z=3.1 (C) p(K\u2212S)=0.20 z=3.1 (V) p(K\u2212S)=0.25 z=2.9\u22123.3 (obs) z=4.0 (C) p(K\u2212S)=0.13 z=4.0 (V) p(K\u2212S)=0.40 z=3.8\u22124.2 (obs) Fig. 23.\u2014 shows the DLA metallicity distributions at four redshift, z = 0, 1.6, 3.1, 4.0 for both \u201cC\u201d (red histograms) and \u201cV\u201d (green histograms) run. The observational data are from Prochaska et al. (2005), shown as black histograms. Because there is non-negligible evolution, the comparisons between simulations at a given redshift are only made with observed DLAs within a narrow redshift window, as shown. Probabilities that simulated and observed samples are drawn from the same underlying distribution are indicated in each panel, separately for \u201cC\u201d and \u201cV\u201d run. at z = 3 \u22124, to [Z/H] = \u22120.75 at z = 1.6, and to [Z/H] = \u22120.5 at z = 0. Thus, both simulations and nature indicate that there is a weak but real evolution in DLA metallicity. What is also important to note is that, in agreement with observations, simulations indicate that the distribution of metallicity is very wide, spanning three or more decades at z \u2265 1.6 \u22124. This wide range re\ufb02ects the rich variety of neutral gas that composes the DLA population, from relatively pristine gas clouds falling onto or feeding galaxies, to metalenriched cold clouds that are falling back to (galactic fountain) or still moving away from (due to entrainment of galactic winds) galaxies, to cold neutral gas clouds in galactic disks. There is a metallicity \ufb02oor at [Z/H] \u223c\u22123 at z = 1.6 \u22124 and that \ufb02oor moves up to [Z/H] \u223c\u22121.5 by z = 0, consistent with observations (Prochaska et al. 2003). The distribution at z = 0 is signi\ufb01cantly narrower, partly re\ufb02ecting the overall enrichment of the IGM and partly due to much reduced variety of DLAs with galactic disks becoming a more dominant contributor to DLAs (see discussion below). \u2013 33 \u2013 Ellison et al. (2010) \ufb01nd that proximate DLAs (PDLAs), those within a velocity distance from the QSO \u2206v < 3000km/s, seem to have metallicity higher than the more widely studied, intervening DLAs. It seems conceivable that the total sample of PDLAs plus conventional (intervening) DLAs may somewhat shift the metallicity distribution to the right, perhaps bringing it to a still better agreement with our simulations. 1.5 2 2.5 3 \u22123 \u22122 \u22121 0 log v90 (km/s) PDF(>v90)     z=3.1 [Z/H]<\u22121 (C) z=2.5\u22123.7 [Z/H]<\u22121 (obs) z=3.1 [Z/H]>\u22121 (C) z=2.5\u22123.7 [Z/H]>\u22121 (obs) 1.5 2 2.5 3 \u22123 \u22122 \u22121 0 log v90 (km/s) PDF(>v90)     z=0 [Z/H]<\u22121 (C) z=0 [Z/H]>\u22121 (C) Fig. 24.\u2014 Left panel: shows the cumulative velocity width probability function for two subsets of the DLA sample, divided by DLA metallicity at [Z/H] = \u22121, at z = 3.1 from the \u201cC\u201d run; the results with \u201cV\u201d run, not shown, are nearly identical. The observational data is an updated version of Prochaska & Wolfe (1997), divided into two subsets such that the ratio of the number of DLAs in the two subsets is equal to that of the simulated sample to enable a fair comparison. The observed data points are slightly shifted to the right by a small amount for more clear reading. Right panel: z = 0 from the \u201cC\u201d run. Observations have found a strong positive correlation between galaxy mass and metallicity (e.g., Erb et al. 2006). We divide the simulated DLA sample at z = 3.1 into two subsets, one with metallicity less than [Z/H] = \u22121 and the other more than [Z/H] = \u22121. We then compute the velocity width functions separately for each subset, which are shown as solid dots (lower metallicity) and solid squares (higher metallicity) in the left panel of Figure 24. What we see is that there is a small excess of large velocity width DLAs for the higher metallicity subset compared to the lower metallicity one. This is of course in the sense that is consistent with the observed metallity-mass relation. However, current observational data sample is consistent with simulations, and the di\ufb00erence between the two simulated subsets and between the two observed subsets is statistically insigni\ufb01cant. A larger sample (by a factor of 4) may allow for a statistically signi\ufb01cant test. Do we expect a larger di\ufb00erence in the disk model (Wolfe et al. 1986; Prochaska & Wolfe 1997)? We do not have a straight answer to this question, without a very involved modeling. However, we we suggest that the picture we have presented, where DLAs arise from a variety of galactic systems, in a vari\u2013 34 \u2013 ety of locations of widely varying metallicity (see the gallery in \u00a73.1), would be consistent with the small di\ufb00erence found, because the velocity widths of large width DLAs do not strongly correlate with galaxy mass (see Figure 14). In other words, the observed correlation between metallicity and galaxy mass is largely washed out by DLAs that do not arise in disks and whose metallicity do not strongly correlate with galaxy mass. If one combines the information provided by Figure 15 and Figure 24, one may reach a similar conclusion. 0 0.2 0.4 0.6 0.8 1 1.5 2 2.5 0 0.1 0.2 log dDLA (kpc) PDF     z=0 (C) z=0 (V) 0 0.2 0.4 0.6 0.8 1 1.5 2 2.5 0 0.1 0.2 log dDLA (kpc) PDF     z=1.6 (C) z=1.6 (V) 0 0.2 0.4 0.6 0.8 1 1.5 2 2.5 0 0.1 0.2 log dDLA (kpc) PDF     z=3.1 (C) z=3.1 (V) 0 0.2 0.4 0.6 0.8 1 1.5 2 2.5 0 0.1 0.2 log dDLA (kpc) PDF     z=4.0 (C) z=4.0 (V) Fig. 25.\u2014 shows the distributions of distance of DLA from the center of galaxy (i.e., impact parameter) for \u201cC\u201d (red histograms) and \u201cV\u201d (green histograms) run at redshift z = 0 (top right), z = 1.6 (top left), z = 3.1 (bottom left) and z = 4.0 (bottom right). The implication may be that DLAs do not arise predominantly in gaseous disks of spiral galaxies at high redshift, in agreement with Maller et al. (2001) and Hong et al. (2010). We shall elaborate further on this signi\ufb01cant point. In Figure 25 we show the distribution of physical distance of DLAs from the galactic center (i.e., impact parameter) at four redshifts, z = 0, 1.6, 3.1, 4.0. Since we have shown in Figure 15 that DLA incidence contribution peaks at \u223c1011.5 M\u2299, let us make a simple estimate of their size at z \u223c3. As a reference, let us take the radius of Milky Way (MW) stellar disk to be 15kpc. Taking MW to z = 3 self-similarly would give a radius of 3.8kpc and for a 1011.5 M\u2299galaxy the stellar disk radius would be 2.5kpc at z = 3, corresponding to 0.40 in the shown x-axis. Observed large galaxies \u2013 35 \u2013 (of mass likely in the range \u223c1011 \u22121012 M\u2299) at z \u223c3 appear to have sizes of \u223c1 \u221210kpc (Lowenthal et al. 1997; Ferguson et al. 2004; Trujillo et al. 2006; Toft et al. 2007; Zirm et al. 2007; Buitrago et al. 2008), roughly consistent with the simple scaling. The distance distribution peaks at dDLA \u223c20 \u221230kpc at z = 3 \u22124, which is much larger than a few kpc of the observed (or expected based on z = 0 galaxies) stellar disk size at z \u223c3. It is noted that the virial radius of a Milky Way size galaxy is about \u223c50kpc at z = 3. Thus, these gaseous structures occur at about half the virial radius at z = 3, Thus, we conclude that at z = 3 \u22124 most of the DLAs do not arise from large galactic stellar disks. They appear to come from regions that are \u223c5 \u22128 larger than the stellar disks. The ubiquitous extended structures galactic \ufb01laments appear to be at the right distances of dDLA \u223c20 \u221230kpc, seen in the gallery examples in \u00a73.1. While the extremely close association of galactic \ufb01laments with galaxy interactions suggest that the host galaxies are likely experiencing starbursts, as seen in the gallery examples, the clouds that give rise to DLAs do not appear to have ongoing in situ star formation. Clearly, most DLAs do not arise in disks and most DLAs have low metallicities, as we have shown, are self-consistent. In other words, aside from those DLAs that arise from galactic disks and are metal rich, the metallicity of the vast majority of more metal poor DLAs do not appear to be forming stars. It may be that, if and when the gas in the galactic \ufb01laments forms stars, either they are destroyed by star formation feedback and remove themselves from the DLA category or they have already incorporated into disks of galaxies. We suggest that our model gives a natural explanation to the apparent puzzle of the lack of obvious star formation of gas-rich DLAs (Wolfe & Chen 2006). On the other hand, the inferred cooling rates of DLAs may be provided, in part, by radiative heating from the host galaxy (see Figure 31 below) and possibly in part by compression heating as we frequently see higher external pressure in \u00a73.1. Figure 26 shows the ratio of gas metallicity for DLAs at di\ufb00erent subset of DLAs with di\ufb00erent column density ranges to the mean metallicity of ongoing star-forming gas. It is clear that only the high end of the high column density range (NHI \u22651022cm\u22122) DLAs are forming stars; most of the DLAs have little star formation. Returning to Figure 25, at z = 1.6 there is a very interesting divergence between the two distributions for \u201cC\u201d and \u201cV\u201d run, where the distribution for \u201cC\u201d run peaks at dDLA \u223c 40kpc and for \u201cV\u201d run at dDLA \u223c10kpc. This is consistent with the expectation that the overdense region in the \u201cC\u201d run and the underdense region in the \u201cV\u201d run start to \u201cfeel\u201d the di\ufb00erence in their respective local large-scale density environment and evolve di\ufb00erently dynamically. That is, in \u201cC\u201d run gravitational shock heating due to large-scale structure formation begins to signi\ufb01cantly a\ufb00ect the cold gas in galaxies, whereas in \u201cV\u201d run the galaxies have not changed signi\ufb01cantly since z = 3 \u22124 except that they are now somewhat smaller due to lower gas density at lower redshift. By z = 0 the two distributions once again become nearly identical; this is rather intriguing and may re\ufb02ect the following physical picture: while galaxies in the \u201cV\u201d run has by now dynamically \u201ccaught up\u201d with the \ufb01eld \u2013 36 \u2013 \u22123 \u22122 \u22121 0 0 0.5 1 1.5 ZDLA/<ZSF> PDF     z=1.6 NHI=[20.3  21.0] (C) z=1.6 NHI=[21.0  21.8] (C) z=1.6 NHI=[21.8  22.5] (C) \u22123 \u22122 \u22121 0 0 0.5 1 1.5 ZDLA/<ZSF> PDF     z=0 NHI=[20.3  21.0] (C) z=0 NHI=[21.0  21.8] (C) z=0 NHI=[21.8  22.5] (C) \u22123 \u22122 \u22121 0 0 0.5 1 1.5 ZDLA/<ZSF> PDF     z=3.1 NHI=[20.3  21.0] (C) z=3.1 NHI=[21.0  21.8] (C) z=3.1 NHI=[21.8  22.5] (C) \u22123 \u22122 \u22121 0 0 0.5 1 1.5 ZDLA/<ZSF> PDF     z=4.0 NHI=[20.3  21.0] (C) z=4.0 NHI=[21.0  21.8] (C) z=4.0 NHI=[21.8  22.5] (C) \u22123 \u22122 \u22121 0 0 0.5 1 1.5 ZDLA/<ZSF> PDF     z=1.6 NHI=[20.3  21.0] (V) z=1.6 NHI=[21.0  21.8] (V) z=1.6 NHI=[21.8  22.5] (V) \u22123 \u22122 \u22121 0 0 0.5 1 1.5 ZDLA/<ZSF> PDF     z=0 NHI=[20.3  21.0] (V) z=0 NHI=[21.0  21.8] (V) z=0 NHI=[21.8  22.5] (V) \u22123 \u22122 \u22121 0 0 0.5 1 1.5 ZDLA/<ZSF> PDF     z=3.1 NHI=[20.3  21.0] (V) z=3.1 NHI=[21.0  21.8] (V) z=3.1 NHI=[21.8  22.5] (V) \u22123 \u22122 \u22121 0 0 0.5 1 1.5 ZDLA/<ZSF> PDF     z=4.0 NHI=[20.3  21.0] (V) z=4.0 NHI=[21.0  21.8] (V) z=4.0 NHI=[21.8  22.5] (V) Fig. 26.\u2014 shows the distribution of the ratio of gas metallicity for DLAs at di\ufb00erent column density ranges to the mean metallicity of ongoing star-forming gas in the \u201cC\u201d run (left set of four panels) at z = 0, 1.6, 3.1, 4.0 and in the \u201cV\u201d run (right set of four panels). We expect that gas that has the x-axis value close or greater than 0 may be forming stars. galaxies in the \u201cC\u201d run, giving rise to the similar gaussian-like distribution centered at dDLA = 10 kpc, the original gas-rich galaxies in the \u201cC\u201d run have fallen into the cluster, lost gas and \u201cdisappeared\u201d from the DLA population. While there is almost no DLA that is further away than 50kpc at z = 3\u22124, there is a second bump at dDLA = 100\u2212300kpc in the distribution for the \u201cC\u201d run at z = 0. This bump is likely due to gas rich satellite galaxies orbiting larger galaxies or small groups of mass 1012 \u22121013 M\u2299. Beyond dDLA = 300kpc, there is no DLA in the \u201cC\u201d run, which is due to gas-starvation of galaxies in still larger groups or clusters at z = 0. With direct inspection of simulation data we \ufb01nd that there is virtually no gas rich galaxies within the virial radius of the primary cluster in the \u201cC\u201d run. What is also interesting is that the peak distance of dDLA \u223c10kpc at z = 0 is totally consistent with the notion that gaseous disks of \ufb01eld galaxies, like the one in our own Galaxy, signi\ufb01cantly contribute to DLAs. Right panel of Figure 24 shows the velocity distributions of two subsets of DLAs, divided at metallicity at [Z/H] = \u22121 at z = 0. Here we see a very clear di\ufb00erence between the two distributions: the higher metallicity subset have large velocity widths, i.e., there is a strong positive correlation between metallicity and velocity width at z = 0. This supports the picture that a large fraction of DLAs arise in gaseous disks of large \ufb01eld galaxies. Most of the DLAs at z = 0 have a higher metallicity of [Z/H] \u2265\u22121.0 with the overall distribution peaking at [Z/H] = \u22120.5, also providing support for this picture. Therefore, by z = 0 the situation appears to have reversed: galactic disks of large galaxies make a major contribution to DLAs at z = 0. The fact that the peak distance has dropped \u2013 37 \u2013 from 30\u221240kpc at z = 3\u22124 to 10kpc at z = 0 is physically in partly due to a large decrease (a factor of \u223c100) in the mean gas density of the universe from z = 3 \u22124 to z = 0. 3.6. Size Distribution 0 0.2 0.4 0.6 0.8 1 1.5 0 0.1 0.2 0.3 log rDLA (kpc) PDF     z=0 single (C) z=0 total (C) 0 0.2 0.4 0.6 0.8 1 1.5 0 0.1 0.2 0.3 log rDLA (kpc) PDF     z=1.6 single (C) z=1.6 total (C) Cooke et al (2010) 0 0.2 0.4 0.6 0.8 1 1.5 0 0.1 0.2 0.3 log rDLA (kpc) PDF     z=3.1 single (C) z=3.1 total (C) Rauch et al (2008) 0 0.2 0.4 0.6 0.8 1 1.5 0 0.1 0.2 0.3 log rDLA (kpc) PDF     z=4.0 single (C) z=4.0 total (C) 0 0.2 0.4 0.6 0.8 1 1.5 0 0.1 0.2 0.3 log rDLA (kpc) PDF     z=0 single (V) z=0 total (V) 0 0.2 0.4 0.6 0.8 1 1.5 0 0.1 0.2 0.3 log rDLA (kpc) PDF     z=1.6 single (V) z=1.6 total (V) Cooke et al (2010) 0 0.2 0.4 0.6 0.8 1 1.5 0 0.1 0.2 0.3 log rDLA (kpc) PDF     z=3.1 single (V) z=3.1 total (V) Rauch et al (2008) 0 0.2 0.4 0.6 0.8 1 1.5 0 0.1 0.2 0.3 log rDLA (kpc) PDF     z=4.0 single (V) z=4.0 total (V) Fig. 27.\u2014 Left set of four panels: the DLA size distribution at redshift z = 0, 1.6, 3.1, 4.0 for \u201cC\u201d run. Each individual DLA size rDLA (see text for de\ufb01nition) is shown as red histograms, whereas the total DLA size of a galaxy rtot (see text for de\ufb01nition) is shown as green histograms. Right set of four panels: the DLA size distribution at redshift z = 0, 1.6, 3.1, 4.0 for \u201cV\u201d run. The observationally inferred DLA size, shown as an open square in both z = 1.6 panels, is from Cooke et al. (2010), and that shown as an open circle in both z = 3.1 panels is from Rauch et al. (2008) with the shown dispersion estimated by this author. Binary quasars, physical or lensed, provide an unique tool to probe the size of DLAs. Here we present our predictions of size distributions of DLAs in the LCDM model. As we have described in \u00a72.3, any cells (of size 0.915h\u22121kpc comoving) that are connected by one side in projection are merged into a \u201csingle isolated\u201d DLA. The area of each \u201cisolated\u201d DLA, A, is then used to de\ufb01ne the size (radius) of the DLA by rDLA = (A/\u03c0)1/2. The total area of all isolated DLA associated with a galaxy along three orthogonal directions (x, y, z), Ax, Ay and Az, are summed to obtain Atot = pA2 x + A2 y + A2 z and the total DLA size (radius) of the galaxy is de\ufb01ned to be rtot = (Atot/\u03c0)1/2. Note that, if DLAs arises from a thin disk, the Atot computed this way will be the exact size of the disk face on, regardless of its orientation. On the other hand, if each DLA cloud is a sphere, this method overestimate the size (area) by a factor of \u221a 3. Figure 27 shows the size (radius) distribution at redshift z = 0, 1.6, 3.1, 4.0 for individual \u2013 38 \u2013 10 14 10 15 10 16 10 17 10 18 10 19 10 20 1 3 10 30 50 100 NHI (cm\u22122) % (<NHI) z=1.6 (C) 10 14 10 15 10 16 10 17 10 18 10 19 10 20 1 3 10 30 50 100 NHI (cm\u22122) % (<NHI) z=0 (C) 10 14 10 15 10 16 10 17 10 18 10 19 10 20 1 3 10 30 50 100 NHI (cm\u22122) % (<NHI) z=4.0 (C) 10 14 10 15 10 16 10 17 10 18 10 19 10 20 1 3 10 30 50 100 NHI (cm\u22122) % (<NHI) z=3.1 (C) 10 14 10 15 10 16 10 17 10 18 10 19 10 20 1 3 10 30 50 100 NHI (cm\u22122) % (<NHI) z=1.6 (V) 10 14 10 15 10 16 10 17 10 18 10 19 10 20 1 3 10 30 50 100 NHI (cm\u22122) % (<NHI) z=0 (V) 10 14 10 15 10 16 10 17 10 18 10 19 10 20 1 3 10 30 50 100 NHI (cm\u22122) % (<NHI) z=4.0 (V) 10 14 10 15 10 16 10 17 10 18 10 19 10 20 1 3 10 30 50 100 NHI (cm\u22122) % (<NHI) z=3.1 (V) Fig. 28.\u2014 The probability of the second LOS having a HI column lower than the value shown in the x-axis, while the \ufb01rst LOS is known to have intercepted a DLA at projected separation of (30, 20, 10, 5, 3)kpc (\ufb01ve curves from top to bottom shown in each panel) at the redshift in question. The left set of four panels are at redshift z = 0, 1.6, 3.1, 4.0 for \u201cC\u201d run; the right set of four panels are for \u201cV\u201d run. DLA size and total DLA size of each galaxy. Figure 28 presents the size information in a di\ufb00erent way, where we show the probability that, for a random pair of sightlines separated by (30, 20, 10, 5, 3)kpc at the redshift in question, one sightline intercepts a DLA and the other intercepts a column density lower than shown in the x-axis. We see that, in the sense that is consistent with distance distributions shown in Figure 25, on average, individual DLA size as well as the total DLA size of galaxies are larger at high redshift than at lower redshift. The individual DLA size distribution appears to sharply peak at rDLA \u223c15kpc at z = 4, then move left to a broader peak at rDLA \u223c10kpc at z = 3.1, then sharpen somewhat to peak at rDLA \u223c5kpc at z = 1.6, and \ufb01nally move rightward slightly to peak at rDLA \u223c7kpc at z = 0 for the \u201cC\u201d run. The numbers for the \u201cV\u201d run are largely comparable to the \u201cC\u201d run: (15, 12, 4, 6)kpc at z = (4, 3.1, 1.6, 0), respectively. What is quite remarkable is that, at z = 1.6 where comparison can be made, the predicted size distribution and the available observation agree better than anyone would have expected. This is a testament to the success of the LCDM model and physical treatment of our simulations, especially considering other agreements that we have already found, for example, with respect to metallicity distribution, column density distribution, kinematics. Intriguingly, Rauch et al. (2008) \ufb01nd a new population of faint Lyman alpha emitters which they advocate may be the host galaxies of DLAs at z \u223c3. Their estimated size, based on observed Ly\u03b1 line emission pro\ufb01le, shown as the open circle in z = 3.1 panels of \u2013 39 \u2013 10 11 12 13 2 3 log Mhalo (Msun) log ADLA (kpc2)     z=3.1 (C) z=3.1 (V) rtot = 0.6 rvir 10 11 12 13 2 3 4 log Mhalo (Msun) log ADLA (kpc2)     z=0 (C) z=0 (V) rtot = 0.08 rvir Fig. 29.\u2014 Left panel: a scatter plot of DLA size of each galaxy against its halo mass at z = 3.1. Also shown as a black straight line is a proposed relation between the radius of DLA and virial radius of the halo that roughly goes through the median at z = 3.1: rDLA = 0.30rvir. Right panel: a scatter plot of DLA size of each galaxy against its halo mass at z = 0. Also shown as a black straight line is a linear relation between the radius of DLA and virial radius of the halo at z = 0: rDLA = 0.08rvir. Figure 27, would be consistent with our model, although the true nature of this population is relatively uncertain. Given the reasonable agreement in size, we will make some further speculation to gauge if our model can accommodate or explain this population as DLAs. One possible physical mechanism for the Ly\u03b1 emission of this population, if they are indeed DLA hosts, would be \ufb02uorescence due to ionizing photons from the host galaxies. Assuming that the distance of each DLA cloud from the host galaxy is 25kpc (Figure 25), the size of each DLA cloud is 8kpc (Figure 27) and the star formation rate of host galaxy is 10 M\u2299/yr (see Figure 31 below), then a typical expected star formation rate inferred from their \ufb02uorescence would be (82\u03c0)/(4\u03c0252) \u00d7 10 = 0.26 M\u2299/yr. This very rough estimate curiously falls within the range of 0.07 \u22121.5 M\u2299/yr estimated by Rauch et al. (2008) for the observed emitters if there are Ly\u03b1 emitters at z \u223c3. Now we make more direct comparisons between our model and available observed 18 pairs of QSOs (all lensed pairs/multiples except one real physical binary) at z \u223c1.6, given in Table 1. Columns 1-7 list parameters of each observed pair and columns 8-9 give the probability of each pair occurring the \u201cC\u201d [P(C))] and \u201cV\u201d [P(V)] run respectively at z = 1.6. We have made the following simpli\ufb01cation for computing the probability: we treat all DLA with NHI \u22652 \u00d7 1020cm\u22122 the same regardless of column density values and for non-DLA absorbers the probability that we present is the probability of having a column equal to or \u2013 40 \u2013 Table 1. Probability of observed QSO pairs column 1: QSO name; column 2: DLA redshift; column 3: pair name; column 4: separation of two images in the sky in arcseconds; column 5: physical separation of two sightlines at zabs; column 6: HI column density of the \ufb01rst sightline in units of 1020cm\u22122; column 7: HI column density of the second sightline in units of 1020cm\u22122; column 8: probability from \u201cC\u201d run; column 9: probability from \u201cV\u201d run. The observed data are taken from Table 1 of Cooke et al. (2010), which are all lensed binaries (or multiples). Note that the physical separations at the redshift of DLAs are computed correctly with the actual geometry of the lenses. We have also added in the last row the binary quasar LBQS1429-0053 taken from Monier et al. (2009). QSO zabs Pair \u03b8abs d (kpc) N1 N2 P(C) P(V) H1413+1143 1.440 B-A 0.753 3.13 60 9.0 0.84 0.80 B-D 0.967 4.02 60 0.25 0.11 0.13 B-C 1.359 5.65 60 0.20 0.17 0.21 A-D 1.118 4.64 9.0 0.25 0.13 0.16 A-C 0.872 3.62 9.0 0.20 0.093 0.11 D-C 0.893 3.71 0.25 0.20 0.097 0.12 H1413+1143 1.486 D-A 1.118 4.32 2.0 < 0.05 0.097 0.11 D-B 0.967 3.73 2.0 < 0.1 0.084 0.097 D-C 0.893 3.45 2.0 < 0.05 0.070 0.079 H1413+1143 1.662 B-A 0.753 2.17 6.0 1.5 0.92 0.89 B-C 1.359 3.91 6.0 0.6 0.13 0.17 B-D 0.967 2.78 6.0 0.3 0.064 0.078 A-C 0.872 2.51 1.5 0.6 0.058 0.074 A-D 1.118 3.22 1.5 0.3 0.086 0.11 C-D 0.893 2.57 0.6 0.3 0.052 0.063 HE1104-1805 1.662 A-B 3.0 4.47 6.3 < 0.013 0.10 0.11 UM673 1.6265 A-B 2.22 2.71 6.3 < 0.037 0.036 0.036 LBQS1429-0053 1.6616 A-B 5.1 43.9 3.0 0.1 0.051 0.050 \u2013 41 \u2013 less than the indicated value. We see from Table 1 that the the observed QSO pairs are all statistically consistent with our model at \u223c1.5\u03c3 level or better, entirely consistent with the agreement shown in Figure 27 between the computed size distribution and observationally inferred size, which is somewhat model dependent. Finally, in Figure 29, we plot the total DLA cross section of each galaxy (Atot) against its halo mass at z = 3.1 (left panel) and z = 0 (right panel). Also shown as the black line is a linear \ufb01t assuming that the e\ufb00ective radius rtot = (Atot/\u03c0)1/2 is proportional to the virial radius for simplicity. Note that a least-square linear \ufb01t is slightly \ufb02atter than the black curve. It is noted that there are a small fraction of galaxies that do not have signi\ufb01cant neutral gas thus do not show up in the plotted range. What is most striking is that, for gas rich galaxies that give rise to DLAs at z = 3.1, on average, the e\ufb00ective area that gives rise to DLAs occupies about 1/3 of the total area within the virial radius, i.e., rtot = 0.6rvir. By z = 0 the e\ufb00ective radius has much reduced to rtot = 0.08rvir, becoming comparable to the size of the stellar disk. The total DLA cross section as a function of halo mass is in agreement with Pontzen et al. (2008) within a factor of 3 (ours is higher than theirs). We note that the method we use to compute the total DLA cross section gives a correct value for the case of a thin disk but could overestimate it by a factor of \u221a 3 in the case of a sphere. Let us fast forward to Figure 30 and take a note that at z = 3.1 the typical halo mass for DLA incidence is Mh \u223c1011.5 having a virial radius of rvir = 37kpc, which then gives rtot = 22kpc (see above relation between rtot and rvir). From Figure 25 we see that the typical distance of DLA from galaxy center is dDLA \u223c25kpc, thus rtot \u223cdDLA. This near equality between the distance and size suggests that a large fraction of the sky seen by an object sitting in the galaxy, up to \u03c0r2 tot/4\u03c0d2 DLA \u223c20%, may be covered by DLAs! If that object is a QSO, the situation may be di\ufb00erent, because the QSO, with its intense radiation (and possibly other e\ufb00ects, such as winds), may have signi\ufb01cantly modi\ufb01ed its surroundings, including the nearby DLAs. Note that a QSO proximity radius is about 5 \u221210Mpc. The evidence we see in the gallery examples that the surge in DLA incidence of a galaxy seems always associated with starbursts and in gas-rich (probably) spiral like galaxies, whereas QSOs tend to reside in gas-poor elliptical galaxies. These two facts together suggest that it is not straight forward to estimate the fraction of QSOs that have this type of proximity DLAs. The situation for gamma-ray bursts (GRBs) may be relatively more straight forward to analyze, because GRBs are associated with star formation hence likely coincides with the surge in DLA cross section of interacting galaxies and because radiation from GRBs does not signi\ufb01cantly a\ufb00ect their surroundings at a distance of \u223c25kpc. Therefore, we suggest that at high redshift z \u22653, a signi\ufb01cant fraction (up to 20%) of GRBs, which depends on detailed geometry/orientation of DLA clouds, have associated DLAs with a typical velocity di\ufb00erence from its systemic redshift of \u2206v \u2264100km/s (see Figure 35 below for \u2206v). One complication factor is that some (or possibly most of) GRB-DLAs may be due to dense gas in the close vicinity of GRBs nearby DLAs. Since GRBs are thought to occur in star-forming regions, \u2013 42 \u2013 i.e., embedded in molecular clouds, one might expect to see a signicant amount of molecules associated with nearby DLAs and they should be dusty and relatively more metal enriched. However, if progenitors of GRBs are biased metal poor, such as preferred in the collapsar model (MacFadyen & Woosley 1999; Woosley & Heger 2006), then it may become more complicated, although latest observations seem to indicate otherwise (e.g., Levesque et al. 2010). Thus, we suggest that a subset of GRB-DLAs with little molecular hydrogen column density and being relatively metal poor and dust poor, such as those in Hjorth et al. (2003), Tumlinson et al. (2007) and Ledoux et al. (2009), may be identi\ufb01ed with circumgalactic DLAs proposed here. This fraction of GRBs with DLAs is, however, likely to decrease rapidly towards lower redshift because of (1) smaller rtot/dDLA ratio and (2) a smaller fraction of DLAs outside stellar disk. The unknown in the above estimate is the geometry of DLAs. We will reserve a detailed analysis of this issue for a future study. 3.7. Properties of DLA Host Galaxies So far we have presented our simulations and compare to observations of DLAs in many di\ufb00erent aspects. From these detailed comparisons we conclude that the model is consistent with all extant observations of DLAs, including kinematic properties, metallicity, column density distribution, line density and neutral hydrogen density, size distribution, and their evolution, wherever comparisons could be made. Proper modeling of galactic winds along with high numerical resolution seems to have contributed to the success. What is clear is that galactic winds play an indispensable role in alleviating previous tension between the LCDM model and observations, especially in producing large velocity width DLAs and disparate and low metallicities of DLA gas. We now examine the properties of DLA host galaxies. Figure 30 shows the DLA incidence as a function of the halo mass. We see that at redshift z = 0 \u22124 it appears that the DLA cross section of each galaxy is roughly proportional to the square of its virial radius, evidenced by the approximate agreement between the red and green histograms at z = 1.6, 3.1, 4.0. Thus our model makes this rather simple prediction: DLAs closely trace the overall population of galaxies at z = 0 \u22124, with a slight relative bias for lower mass galaxies for DLA hosts compared to the general galaxy population. The bias is more noticeable at z = 0. This is not to say that every galaxy has a DLA in it. Rather, this simply says that the portion of galaxies that give rise to DLAs at any particular time has statistically the same mass function as the galaxy population as a whole. At z = 1.6\u22124, the vast majority of DLAs arise in halos of mass Mh = 1010 \u22121012 M\u2299, as these galaxies dominate the overall population of galaxies. We expect the clustering of DLAs to be nearly identical to the overall population of galaxies at z \u22653 and gradually becomes relatively weaker compared to the galaxy population as a whole with time. \u2013 43 \u2013 10 11 12 13 14 0 0.1 0.2 log Mhalo (Msun) PDF     z=0 DLA hosts (C) z=0 all galaxies (C) 10 11 12 13 14 0 0.1 0.2 log Mhalo (Msun) PDF     z=1.6 DLA hosts (C) z=1.6 all galaxies (C) 10 11 12 13 0 0.1 0.2 log Mhalo (Msun) PDF     z=3.1 DLA hosts (C) z=3.1 all galaxies (C) 10 11 12 13 0 0.1 0.2 log Mhalo (Msun) PDF     z=4.0 DLA hosts (C) z=4.0 all galaxies (C) 10 11 12 13 0 0.1 0.2 log Mhalo (Msun) PDF     z=0 DLA hosts (V) z=0 all galaxies (V) 10 11 12 13 0 0.1 0.2 log Mhalo (Msun) PDF     z=1.6 DLA hosts (V) z=1.6 all galaxies (V) 10 11 12 13 0 0.1 0.2 log Mhalo (Msun) PDF     z=3.1 DLA hosts (V) z=3.1 all galaxies (V) 10 11 12 13 0 0.1 0.2 log Mhalo (Msun) PDF     z=4.0 DLA hosts (V) z=4.0 all galaxies (V) Fig. 30.\u2014 Left set of four panels: the DLA incidence distribution as a function of host dark matter halo mass (red histograms) at z = 0, 1.6, 3.1, 4.0 in the \u201cC\u201d run. Also shown as green histograms are notional distributions, if the total DLA cross section of a galaxy is proportional to its total mass to the two-third power, i.e., proportional to its virial radius squared. Right set of four panels: same for the \u201cV\u201d run. The open squares shown in the z = 1.6 and z = 3.1 panels are observationally inferred halo mass range for LBGs (Adelberger et al. 2005). Based on clustering analyses, the mass range of the observed LBGs is inferred to be 1011.2 \u22121011.8 M\u2299at z=2.9, 1011.8 \u22121012.2 M\u2299at z = 2.2, and 1011.9 \u22121012.3 M\u2299at z=1.7 (Adelberger et al. 2005). Comparing these observationally inferred ranges to the histograms in Figure 30 we \ufb01nd that 20 \u221230% of DLAs at z \u223c3 may be LBGs and the fraction drops to 10 \u221220% at z \u223c1.7. Schaye (2001) pointed out that, if DLAs have a radius of 27 kpc, LBGs could account for all the DLAs at z \u223c3. Working backwards, the estimated 20\u221230% of DLAs at z \u223c3 being LBGs would imply a DLA disk radius of 12\u221215kpc for LBGs, which is signi\ufb01cantly larger than the size of LBG stellar disks, suggesting that the distribution of neutral DLA gas is in a much more extended region than stellar disk, likely a combination of some extended gaseous disk and galactic \ufb01laments. While a signi\ufb01cant overlap between DLAs and LBGs is expected, the overall clustering of DLAs is expected to be comparable but slightly weaker than LBGs, since the median halo mass for DLA incidence distribution is slightly smaller than the typical LBG halo mass (more quantitative comparison will be performed in future work). M\u00f8ller et al. (2002) conclude that the properties of DLA hosts, including half-light radius, radial pro\ufb01le, optical to near-infrared color, morphology, Ly\u03b1 emission equivalent width, and Ly\u03b1 emission velocity structure, lie within the measured range for the general population of LBGs. Since those DLA hosts that are su\ufb03ciently luminous to be detected are large galaxies in the mass range of LBGs and because DLAs tend to arise in \u2013 44 \u2013 \u22122 \u22121 0 1 2 0 0.2 log SFR (Msun/yr) PDF     z=0 DLA hosts (C) z=0 all galaxies (C) \u22122 \u22121 0 1 2 0 0.1 0.2 log SFR (Msun/yr) PDF     z=1.6 DLA hosts (C) z=1.6 all galaxies (C) \u22122 \u22121 0 1 2 0 0.1 0.2 log SFR (Msun/yr) PDF     z=3.1 DLA hosts (C) z=3.1 all galaxies (C) \u22122 \u22121 0 1 2 0 0.1 0.2 log SFR (Msun/yr) PDF     z=4.0 DLA hosts (C) z=4.0 all galaxies (C) \u22122 \u22121 0 1 2 0 0.2 log SFR (Msun/yr) PDF     z=0 DLA hosts (V) z=0 all galaxies (V) \u22122 \u22121 0 1 2 0 0.1 0.2 log SFR (Msun/yr) PDF     z=1.6 DLA hosts (V) z=1.6 all galaxies (V) \u22122 \u22121 0 1 2 0 0.1 0.2 log SFR (Msun/yr) PDF     z=3.1 DLA hosts (V) z=3.1 all galaxies (V) \u22122 \u22121 0 1 2 0 0.1 0.2 log SFR (Msun/yr) PDF     z=4.0 DLA hosts (V) z=4.0 all galaxies (V) Fig. 31.\u2014 Left set of four panels: the DLA incidence distribution as a function of host star formation rate (red histograms) at z = 0, 1.6, 3.1, 4.0 in the \u201cC\u201d run. Also shown as green histograms are notional distributions, if the total DLA cross section of a galaxy is proportional to its stellar mass to the two-third power, i.e., proportional to its virial radius squared for a constant total mass to stellar mass ratio. Right set of four panels: same for the \u201cV\u201d run. gaseous galactic \ufb01laments of galaxies that experience starbursts (via galaxy interactions; see \u00a73.1), like LBGs, it is naturally expected in our model that they \ufb01nd similarity between their DLA hosts and LBGs. Of the remaining 70-80% that are not covered by LBGs at z = 3 \u22124, roughly 10-20% are due to more massive galaxies and 50-70% are from smaller galaxies. When systems become more dynamically advanced with time and large galaxies are no longer abundant with cold gas, a slightly more signi\ufb01cant shift occurs between DLA hosts and the overall population of galaxies at z = 0. At z = 0 we see that the contribution to DLA population is broadly peaked at Mh = 1012 M\u2299, whereas most of the sum of the square of virial radius is also broadly distributed but, unlike for DLA host, having a signi\ufb01cant contribution from halos of mass Mh = 1013\u221214 M\u2299, in the \u201cC\u201d run; For the \u201cV\u201d run most of DLAs are in halos of mass Mh = 1010\u221212 M\u2299, whereas most of the sum of the square of virial radius come from halos of mass Mh = 1011\u221213 M\u2299. Figure 31 shows the DLA incidence distribution as a function of host star formation rate (SFR) (red histograms) and the corresponding notional distribution if the total DLA cross section of a galaxy is proportional to its stellar mass to the two-third power. The relative distribution between the two seems complex and environment dependent. To zeroth order, DLA hosts roughly span the same SFR range of the general galaxy population and most of DLA hosts have SFR in excess of 0.1 M\u2299/yr at all redshifts. To \ufb01rst order, there is a bias for \u2013 45 \u2013 8 9 10 11 12 0 0.1 0.2 log MHI (Msun) PDF     z=0 (C) z=0 (V) 8 9 10 11 12 0 0.1 0.2 log MHI (Msun) PDF     z=1.6 (C) z=1.6 (V) 8 9 10 11 12 0 0.1 0.2 log MHI (Msun) PDF     z=3.1 (C) z=3.1 (V) 8 9 10 11 12 0 0.1 0.2 log MHI (Msun) PDF     z=4.0 (C) z=4.0 (V) Fig. 32.\u2014 show the DLA incidence distribution as a function of host HI mass for the \u201cC\u201d (red histograms) and \u201cV\u201d (green histograms) run, at z = 0, 1.6, 3.1, 4.0. DLA hosts to have slighly higher SFR at z = 3 \u22124 and slighly lower SFR at z = 0 than the general galaxy population. The most likely SFR rate for a typical DLA host falls in the range 0.3 \u221230 M\u2299/yr at z = 3 \u22124. LBGs lie at the upper end of this SFR range, consistent with the earlier \ufb01nding that 20-30% of DLAs overlap with LBGs. The peak in the distribution move to \u223c0.5 \u22121 M\u2299/yr by z = 0. It is beyond the scope of this study to investigate the cause for the preferred SFR range by DLAs at di\ufb00erent redshifts. We conjecture that the DLA incidence rate likely \u201csurges\u201d when mergers or other signi\ufb01cant interactions between galaxies produce the \ufb01laments seen in the gallery in \u00a73.1. These same interactions also cause the concerned galaxies to experience signi\ufb01cant star formation, plausibly falling into the found range above. The trend of moving to lower SFR galaxies at lower redshift is perhaps due to the transition from major mergers at high redshift (z = 3 \u22124) to minor mergers or smooth accretion and lack of cold gas in very large galaxies at z = 0. All evidence size (Figure 27), distance (Figure 25), metallicity (Figure 23) and now SFR (Figure 31) seems to point to the picture that by z = 0 most of DLS arise in disks of large galaxies of mass 1011 \u22121012.5 M\u2299that are relatively quiet. Figure 32 shows the DLA incidence distribution as a function of host HI mass. It is interesting that the HI mass appears to peak at 1010 M\u2299at all redshifts with 109 \u22121011 M\u2299 covering nearly all the contributions. There is a bias for DLA hosts to have slightly more gas rich than the general population of galaxies. Why the peak position of MHI does not \u2013 46 \u2013 \u22125 \u22124 \u22123 \u22122 \u22121 0 1 0 0.1 0.2 0.3 Mgas/Mstar PDF     z= 0 DLA hosts (C) z= 0 all galaxies (C) \u22125 \u22124 \u22123 \u22122 \u22121 0 1 0 0.1 0.2 0.3 Mgas/Mstar PDF     z=1.6 DLA hosts (C) z=1.6 all galaxies (C) \u22125 \u22124 \u22123 \u22122 \u22121 0 1 0 0.1 0.2 0.3 Mgas/Mstar PDF     z=3.1 DLA hosts (C) z=3.1 all galaxies (C) \u22125 \u22124 \u22123 \u22122 \u22121 0 1 0 0.1 0.2 0.3 Mgas/Mstar PDF     z=4.0 DLA hosts (C) z=4.0 all galaxies (C) \u22125 \u22124 \u22123 \u22122 \u22121 0 1 0 0.1 0.2 0.3 Mgas/Mstar PDF     z= 0 DLA hosts (V) z= 0 all galaxies (V) \u22125 \u22124 \u22123 \u22122 \u22121 0 1 0 0.1 0.2 0.3 Mgas/Mstar PDF     z=1.6 DLA hosts (V) z=1.6 all galaxies (V) \u22125 \u22124 \u22123 \u22122 \u22121 0 1 0 0.1 0.2 0.3 Mgas/Mstar PDF     z=3.1 DLA hosts (V) z=3.1 all galaxies (V) \u22125 \u22124 \u22123 \u22122 \u22121 0 1 0 0.1 0.2 0.3 Mgas/Mstar PDF     z=4.0 DLA hosts (V) z=4.0 all galaxies (V) Fig. 33.\u2014 Left set of four panels: the DLA incidence distribution as a function of host HI mass to stellar mass ratio at z = 0, 1.6, 3.1, 4.0 in the \u201cC\u201d run. Also shown as green histograms are notional distributions, if the total DLA cross section of a galaxy is proportional to its stellar mass to the two-third power, i.e., proportional to its virial radius squared for a constant total mass to stellar mass ratio. Right set of four panels: same for the \u201cV\u201d run. change with time is intriguing but not fully understood presently. Figure 33 shows the DLA incidence distribution as a function of host HI mass to stellar mass ratio. We see that at z = 3\u22124 the majority of galaxies are gas-rich (Mgas/Mstar \u22650.1) and DLA hosts very closely follow the general population of galaxies, consistent with what we saw in Figure 30. This statement remains true for the \u201cV\u201d run until z = 0, whereas for the regions that are more dynamically advanced, such as z = 0 in the \u201cC\u201d run, a signi\ufb01cant segregation is evident in that most of the galaxies are now gas poor (Mgas/Mstar \u22640.1) but majority of DLA hosts are still gas rich (Mgas/Mstar \u22650.1). Moreover, at z = 0 in \u201cC\u201d run, there is a population of old, red and \u201cdead\u201d galaxies with virtually no cold gas; these are likely galaxies in clusters of galaxies, which DLAs largely avoid. Figure 34 shows the DLA incidence distribution as a function of host SDSS g-r color. While the individual color of the simulated galaxies may not be totally consistent with observations due to its sensitivity to a relatively small variation in the amount of recent star formation that the simulation may not necessarily properly capture, a comparative statement is still valid statistically. We see that DLA hosts trace the general population of galaxies at z = 3\u22124 in all environments with a slight bias to a bluer color peaking sharply at g \u2212r \u223c0. At lower redshift DLA hosts become signi\ufb01cantly bluer than average galaxies by roughly \u2206(g \u2212r) \u223c0.3 \u22120.4 and they avoid the reddest galaxies that are presumably elliptical galaxies or galaxies in clusters of galaxies. \u2013 47 \u2013 \u22120.2 0 0.2 0.4 0.6 0.8 1 0 0.1 0.2 0.3 g \u2212 r PDF     z= 0 DLA hosts (C) z= 0 all galaxies (C) \u22120.2 0 0.2 0.4 0.6 0.8 1 0 0.1 0.2 0.3 g \u2212 r PDF     z=1.6 DLA hosts (C) z=1.6 all galaxies (C) \u22120.2 0 0.2 0.4 0.6 0.8 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 g \u2212 r PDF     z=3.1 DLA hosts (C) z=3.1 all galaxies (C) \u22120.2 0 0.2 0.4 0.6 0.8 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 g \u2212 r PDF     z=4.0 DLA hosts (C) z=4.0 all galaxies (C) \u22120.2 0 0.2 0.4 0.6 0.8 1 0 0.1 0.2 0.3 g \u2212 r PDF     z= 0 DLA hosts (V) z= 0 all galaxies (V) \u22120.2 0 0.2 0.4 0.6 0.8 1 0 0.1 0.2 0.3 g \u2212 r PDF     z=1.6 DLA hosts (V) z=1.6 all galaxies (V) \u22120.2 0 0.2 0.4 0.6 0.8 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 g \u2212 r PDF     z=3.1 DLA hosts (V) z=3.1 all galaxies (V) \u22120.2 0 0.2 0.4 0.6 0.8 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 g \u2212 r PDF     z=4.0 DLA hosts (V) z=4.0 all galaxies (V) Fig. 34.\u2014 Left set of four panels: the DLA incidence distribution as a function of host SDSS g-r color at z = 0, 1.6, 3.1, 4.0 in the \u201cC\u201d run. Also shown as green histograms are notional distributions, if the total DLA cross section of a galaxy is proportional to its stellar mass to the two-third power, i.e., proportional to its virial radius squared for a constant total mass to stellar mass ratio. Right set of four panels: same for the \u201cV\u201d run. Finally, in Figure 35 we show the distribution of the LOS velocity di\ufb00erence between the DLA and its host. We \ufb01nd the following exponential function provides an excellent \ufb01t, as shown in the \ufb01gure, while a gaussian fares much worse: PDF(vgal \u2212vDLA) = 1 2\u03c3 exp (\u2212|vgal \u2212vDLA|/\u03c3). (2) We \ufb01nd that the dispersion parameter \u03c3 only increases mildly with decreasing redshift from \u03c3 \u223c75 \u221290km/s at z = 3 \u22124 to \u223c90 \u2212110km/s at z = 0. The relatively small velocity dispersion and a symmetric distribution may make DLAs a useful proxy for the systemic velocity of host galaxies. This property may be utilized to measure galactic wind velocities, using a large statistical sample of DLA hosts with measured interstellar absorption lines, such as Na I line (e.g., Heckman et al. 2000). In summary, we show that, at z = 3 \u22124, DLA hosts approximately follow the general population of galaxies with respect to halo mass, star formation rate, HI mass, gas mass to stellar mass ratio, and color, with a small but noticeable tendency of being more gas rich, slightly smaller and bluer. It is seen that LBGs make up about 20-30% of the overall DLAs at z = 3\u22124 decreasing to 10\u221220% by z = 1.7. Of the remaining 70-80% that are not covered by LBGs at z = 3 \u22124, roughly 10-20% are due to galaxies more massive than LBGs and 50-70% are from smaller galaxies. The comparisons at lower redshifts become not as clean cut as at high redshift, but in a way that seems physically understandable. Speci\ufb01cally, at \u2013 48 \u2013 \u00ef500 \u00ef250 0 250 500 0 0.1 0.2 vgal \u00ef vDLA (km/s) PDF     z=0 (C) z=0 (V) m=114 km/s m=90 km/s \u00ef500 \u00ef250 0 250 500 0 0.1 0.2 vgal \u00ef vDLA (km/s) PDF     z=1.6 (C) z=1.6 (V) m=94 km/s m=85 km/s \u00ef500 \u00ef250 0 250 500 0 0.1 0.2 vgal \u00ef vDLA (km/s) PDF     z=3.1 (C) z=3.1 (V) m=93 km/s m=81 km/s \u00ef500 \u00ef250 0 250 500 0 0.1 0.2 vgal \u00ef vDLA (km/s) PDF     z=4.0 (C) z=4.0 (V) m=83 km/s m=74 km/s Fig. 35.\u2014 shows the distribution of the LOS velocity di\ufb00erence between the DLA and its host, for \u201cC\u201d (red histograms) and \u201cV\u201d (green histograms) run. As shown in blue (for \u201cC\u201d run) and black (for \u201cV\u201d run) are \ufb01ts to the histograms with the dispersion parameters \u03c3 indicated. lower redshifts, while the general population of galaxies gradually become less cold gas-rich, DLA hosts seem to \u201cpick out\u2019 those that are gas richer and bluer, but not necessarily of higher star formation rate. 4. Conclusions With high resolution, physically sound treatment of all relevant physical processes, our state-of-the-art, adaptive mesh-re\ufb01nement Eulerian cosmological hydrodynamic simulations can reproduce a whole array of observables of damped Lyman alpha systems, including the distributions of the following quantities and their evolution with redshift: column density, Si II \u03bb1808 absorption line velocity width, kinematic shape measures of the Si II line, metallicity, size, line density, HI mass density. This allows to examine, in addition, with signi\ufb01cant con\ufb01dence, the properties of DLA host galaxies. We are able to reach the following conclusions. (1) DLA hosts roughly trace the overall population of galaxies at all redshifts, with respect to halo mass, star formation rate, HI mass and color, with a noticeable tendency of being smaller and bluer, on average. The standout selection criterion seems being gas \u2013 49 \u2013 rich. Most of DLA hosts appear to have HI mass peaked at 1010 M\u2299at all redshifts with 109 \u22121011 M\u2299covering nearly all DLA hosts. The majority of DLA hosts are gas-rich (Mgas/Mstar \u22650.1) closely following the general population of galaxies at high redshift; by z = 0 most of the stars are in systems with (Mgas/Mstar \u22640.1), but majority of DLA hosts are still gas rich (Mgas/Mstar \u22650.1). (2) It seems that the history of DLA evolution is cosmological in nature and re\ufb02ects the underlying cosmic density evolution, galaxy evolution and galaxy interactions. With higher density and more interactions at high redshift DLAs are larger in both absolute terms and in relative terms with respect to virial radii of halos. At z = 3 \u22124 galactocentric distance of DLAs is, on average, 0.6rvir, whereas at z = 0 it decreases to 0.08rvir. The typical DLA impact parameter is d = 20 \u221230kpc at z = 3 \u22124 and 10kpc at z = 0. The typical size (radius) of individual DLAs is \u223c10kpc at z \u223c3 \u22124 dropping to \u223c5kpc at z \u223c1.6, in agreement with observations, then increasing to \u223c7kpc at z = 0. (3) The variety of DLAs at high redshift is richer with a large contribution coming from galactic \ufb01laments \ufb01lamentary gaseous structures sometimes extending to as far as virial radius that are created through close galaxy interactions. The portion of gaseous disks of galaxies where most stars reside makes relatively small contribution to DLA incidence at z = 3 \u22124. By z = 0 galaxy interactions have become rare, cosmic mean density has decreased dramatically, so what is left to contribute to DLA incidence is gas rich disks of galaxies in the mass range of 1010 \u22121012 M\u2299. (4) Galactic winds play an indispensable role in shaping the kinematic properties of DLAs. Speci\ufb01cally, the high velocity width DLAs are a mixture of those arising in high mass, high velocity dispersion halos and those arising in smaller mass systems where cold gas clouds are entrained to high velocities by galactic winds. Closer examination reveals that most of the large width DLAs are due to multiple physically distinct components of varying LOS velocities within a 100kpc separation (along the LOS). (5) Quantitatively, the vast majority of DLAs arise in halos of mass Mh = 1010\u22121012 M\u2299 at z = 1.6\u22124, as these galaxies dominate the overall population of galaxies then. At z = 3\u22124, 20-30% of DLA hosts are Lyman Break Galaxies (LBGs), 10-20% are due to galaxies more massive than LBGs and 50-70% are from smaller galaxies. The fraction of LBG DLA hosts drops to 10 \u221220% by z \u223c1.7. (6) In agreement with observations, we see a weak but noticeable evolution in DLA metallicity. The metallicity distribution centers at [Z/H] = \u22121.5 to \u22121 and spans more than three decades at z = 3 \u22124, with the peak moving to [Z/H] = \u22120.75 at z = 1.6 and [Z/H] = \u22120.5 by z = 0. The overall metallicity seems \ufb02oored at [Z/H] \u223c\u22123 at z = 1.6 \u22124 and at [Z/H] \u223c\u22121.5 at z = 0. When most of the DLA incidence is due to cold gas outside the stellar disks at high redshift, not only the metallicity is relatively low, but also there \u2013 50 \u2013 is little star formation within. This explains self-consistently their low metallicity and lack of star formation activity. If and when signi\ufb01cant internal star formation occurs, there are two possible scenarios. If that takes place outside galactic disk, the DLA will be destroyed and remove itself from the DLA category. If it takes place on galactic disk, the DLA will either be destroyed permanently, or temporarily and then cool back down to become a more metal-enriched one, after star formation has stopped. The former occurs predominantly at high redshift, which is why most of DLAs are metal poor. The latter occurs at low redshift, which explains the signi\ufb01cant increase of metallicity. (7) The star formation rate of DLA hosts is, however, quite strong, heavily concentrated in the range 0.3\u221230 M\u2299/yr at z = 3\u22124, gradually shifting lower to peak at \u223c0.5\u22121 M\u2299/yr by z = 0. The \ufb01nding that the typical size and galactocentric distance of DLAs are both large and comparable gives a moderate, \u201capparent\u201d star formation rate seen in Ly\u03b1 emission due to \ufb02uorescence of ionizing photons from the host galaxies. Both the size of Ly\u03b1 emission and the magnitude of this \ufb02uorescence is, curiously, consistent with the population of faint Ly\u03b1 emitters observed by Rauch et al. (2008), if they are at z \u223c3. (8) Finally, we suggest that a signi\ufb01cant fraction of sky seen by gamma-ray bursts should be covered by circumgalactic DLAs at high redshift (z \u22653). They may be identi\ufb01ed with those GRB-DLAs that have little H2 column densities and are relatively metal and dust poor. I would like to thank Dr. M.K.R. Joung for help on generating initial conditions for the simulations and running a portion of the simulations and Greg Bryan for help with Enzo code. I would like to thank Dr. Jason X. Prochaska and Dr. Andrew Pontzen for kindly providing the observational data, Dr. Sara L. Ellison for sending a paper draft before publication and for discussion, Dr. Edward Jenkins for discussion on atomic data. Computing resources were in part provided by the NASA HighEnd Computing (HEC) Program through the NASA Advanced Supercomputing (NAS) Division at Ames Research Center. This work is supported in part by grants NNX08AH31G and NAS8-03060. The simulation data are available from the author upon request.",
                    "introduction": "Damped Ly\u03b1 systems (DLAs) are fundamentally important, because they contain most of the neutral gas in the universe at all times since cosmological reionization (e.g., Storrie- Lombardi & Wolfe 2000; P\u00b4 eroux et al. 2003; Prochaska & Wolfe 2009). Molecular clouds, within which star formation takes place, likely condense out of cold dense neutral atomic gas contained in DLAs, evidenced by the fact that the neutral hydrogen (surface) density in DLAs and molecular hydrogen (surface) density in molecular clouds form a continuous sequence (e.g., Kennicutt 1998; Zwaan & Prochaska 2006). Therefore, DLAs likely hold key to understanding the fuel for and ultimately galaxy formation. A substantial amount of theoretical work has been devoted to studying the nature of DLAs (e.g., Gardner et al. 1997a; Gardner et al. 1997; Haehnelt et al. 1998; Gardner et al. 2001; Maller et al. 2001; Cen et al. 2003; Nagamine et al. 2004b,a, 2007; Razoumov et al. 2006, 2008; Pontzen et al. 2008; Tescari et al. 2009; Hong et al. 2010), since the pioneering investigation of Katz et al. (1996) in the context of the cold dark matter (CDM) cosmogony. A very interesting contrast is drawn between the observationally based inference of simple large disk galaxies possibly giving rise to DLAs (Wolfe et al. 1986; Prochaska & Wolfe 1997) and the more naturally expected hierarchical buildup of structures in the CDM cosmogony where galactic subunits may produce some of the observed kinematics of DLAs (Haehnelt et al. 1998). Clearly, the implications on the evolution of galaxies in the two scenarios are very di\ufb00erent. We have carried out a set of Eulerian adaptive mesh re\ufb01nement (AMR) simulations with a resolution of 0.65 kpc proper and a sample size of several thousand galaxies with mass \u22651010 M\u2299to statistically address the physical nature of DLAs in the current standard cosmological constant-dominated CDM model (LCDM) (Komatsu et al. 2010). Mechanical feedback from star formation driven by supernova explosions and stellar winds is modeled by a one-parameter prescription that is physically and energetically sound. Part of the motivation was to complement and cross-check studies to date that are largely based on smooth-particle-hydrodynamics (SPH) simulations. With the simulation set and detailed analysis performed here this study represents a signi\ufb01cant extension of previous works to si- multaneously subject the LCDM model to a wider and more complete range of comparisons with observations. We examine in detail the following properties of DLAs in a self-consistent fashion within the same model: DLA column density distribution evolution, line density evo- lution, metallicity distribution evolution, size distribution evolution, velocity width distri- bution evolution, kinematic structural parameters evolution, neutral mass content evolution and others. A gallery of DLAs is presented to obtain a visual understanding of the physi- cal richness of DLA systems, especially the e\ufb00ects of galactic winds and large-scale gaseous structures. In comparison to the recent work of Hong et al. (2010) we track the metallic- ity distribution and evolution explicitly and show that the metallicity distribution of DLAs is, in good agreement with observations, very wide, which itself calls for a self-consistent \u2013 3 \u2013 treatment of metals transport. In agreement with the conclusions of Hong et al. (2010), although not in the detailed process, we show that galactic winds are directly responsible for a large fraction of wide DLAs at high redshift, by entraining cold clouds to large velocities and causing large kinematic velocity widths. We \ufb01nd that the simulated Si II \u03bb1808 line velocity width, kinematic shape measures and DLA metallicity distributions that are all in excellent agreement with observations. Taking all together, we conclude that the standard LCDM model gives a satisfactory account of all properties of DLAs. Finally, we examine the properties of DLA hosts, including their mass, star formation rate, HI content, gas to stellar mass ratio and colors, and show that DLAs arise in a variety of galaxies and roughly trace the entire population of galaxies at any redshift. This may reconcile many apparently con\ufb02icting observational evidence of identifying DLAs with di\ufb00erent galaxy populations. Speci\ufb01cally, at z \u223c3 we show that 20 \u221230% of DLAs are Lyman Break Galaxies (LBGs) (Steidel et al. 1996), while the majority arise in smaller galaxies. The outline of this paper is as follows. In \u00a72 we detail our simulations, method of making galaxy catalogs, method of making DLA catalogs and procedure of de\ufb01ning Si II line pro\ufb01le shape measures. Results are presented in \u00a73. In \u00a73.1 we present a gallery of twelve DLAs. We give Si II line velocity width distribution functions in \u00a73.2, demonstrating excellent agreement between simulations and observations, particularly at high velocity width end. \u00a73.3 is devoted to the three kinematic measures of the Si II absorption line and we show the model produces results that are consistent with observations. Column density distribution and evolution, line density and neutral gas density evolution are described in \u00a73.4, where, while simulations are consistent with observations, we emphasize large cosmic variance from region to region with di\ufb00erent large-scale overdensities. The focus is shifted to metallicity distribution and evolution in \u00a73.5 and simulations are found to be in excellent agreement with observations where comparisons can be made. The next subsection \u00a73.6 performs a detailed analysis of the size of DLAs and \ufb01nds that the available observed QSO pairs with DLAs are in accord with the expectation of our model. Having found agreement between simulations and observations in all aspects pertinent to DLAs, we turn our attention to the properties of DLA hosts in \u00a73.7, where we show that DLAs, while slightly favoring galaxies that are more gas rich, less massive and bluer in color, and have higher HI mass and higher gas to stellar mass ratio, roughly trace the entire population of galaxies at all redshifts. Conclusions are given in \u00a74. \u2013 4 \u2013"
                },
                {
                    "url": "http://arxiv.org/abs/1007.0704v2",
                    "title": "The State of the Universe at z~6",
                    "abstract": "In the context stellar reionization in the standard cold dark matter model,\nwe analyze observations at z~6 and are able to draw three significant\nconclusions with respect to star formation and the state of the intergalactic\nmedium (IGM) at z~6. (1) An initial stellar mass function (IMF) more efficient,\nby a factor of 10-20, in producing ionizing photons than the standard Salpeter\nIMF is required at z~6. This may be achieved by having either (A) a\nmetal-enriched IMF with and a lower mass cutoff of >= 30Msun or (B) 2-4% of\nstellar mass being Population III massive metal-free stars at z~6. While there\nis no compelling physical reason or observational evidence to support (A), (B)\ncould be fulfilled plausibly by continued existence of some pockets of\nuncontaminated, metal-free gas for star formation. (2) The volume-weighted\nneutral fraction of the IGM of <f_HI>_V~ 10^-4 at z=5.8 inferred from the SDSS\nobservations of QSO absorption spectra provides enough information to ascertain\nthat reionization is basically complete with at most ~0.1-1% of IGM that is\nun-ionized at z=5.8. (3) Barring some extreme evolution of the IMF, the neutral\nfraction of the IGM is expected to rise quickly toward high redshift from the\npoint of HII bubble percolation, with the mean neutral fraction of the IGM\nexpected to reach 6-12% at z=6.5, 13-27% at z=7.7 and 22-38% at z=8.8.",
                    "authors": "Renyue Cen",
                    "published": "2010-07-05",
                    "updated": "2010-07-06",
                    "primary_cat": "astro-ph.CO",
                    "cats": [
                        "astro-ph.CO",
                        "astro-ph.HE"
                    ],
                    "main_content": "We use a semi-numerical method (Cen 2003) to explore the parameter space and compute the coupled thermal and reionization history with star formation of the universe. The reader is referred to \u00a74 of Cen (2003) for details. For a simple understanding the essential physics pertaining to reionization may be encapsulated into a single parameter, \u03b7, defined as cfR(z)\u03f5(z)mc2 \u03b7(z) \u2261c\u2217fescRh(z)\u03f5UV(z)mpc2 \u03b1(T)C(z)n0(1 + z)3h\u03bd0 c\u2217fescRh(z)\u03f5UV(z)mpc \u03b1(T)C(z)n0(1 + z)3h\u03bd0 , (1) where z is redshift, c\u2217the star formation efficiency (i.e., the ratio of the total amount of stars formed over the product of the halo mass and the cosmic baryon to total mass ratio), fesc the ionizing photon escape fraction, Rh(z) the total baryonic mass accretion rate of halos above the filter mass (i.e., those that are able to accrete gas) over the total baryonic mass in the universe, \u03f5UV(z) the ionizing photon production efficiency, defined to be the total emitted energy above hydrogen Lyman limit over the total rest mass energy of forming stars, mp proton mass, c speed of light, \u03b1(T) the case-B recombination coefficient, C(z) the clumping factor of the recombining IGM, n0 the mean hydrogen number density at z = 0 and h\u03bd0 hydrogen ionization potential. The numerator on the right hand side of Equation 1 is the rate of ionizing photons per baryon pumped into the IGM from stars, whereas the denominator is the destruction rate of Lyman limit photons per baryon due to case-B recombination. If \u03b7 < 1, the universe is opaque. When \u03b7 > 1 is sustained, the universe becomes fully reionized and a UV radiation background is built up with time with its amplitude determined by the balance between UV emissivity, recombination and universal expansion. If \u03b7 goes above unity at an earlier epoch and subsequently drops below unity, a double reionization would \u2013 3 \u2013 occur Cen (2003). Present calculations are done with the following updates of input physics. \u2022 We adopt the standard WMAP7-normalized (Komatsu et al. 2010) parameters for the cosmological constant dominated, \ufb02at cold dark matter model: \u2126M = 0.28, \u2126b = 0.046, \u2126\u039b = 0.72, \u03c38 = 0.81, H0 = 100hkms\u22121Mpc\u22121 = 70kms\u22121Mpc\u22121 and n = 0.96. \u2022 We replace the standard Press-Schechter formalism of spherical collapse model with the more accurate ellipsoidal collapse model (Sheth & Tormen 2002) to compute the halo formation rate Rh. \u2022 Latest ultra-high resolution (0.1pc) radiation hydrodynamic simulations indicate that c\u2217fesc \u223c0.02 \u22120.03 for atomic cooling halos and drops about two order of magnitude for minihalos, with fesc \u223c40 \u221280% (Wise & Cen 2009). Note that c\u2217fesc and \u03f5UV(z) are degenerate. Therefore, we adopt, conservatively, c\u2217fesc = 0.03 for the calculations presented here, which enables a \ufb01rm conclusion with respect to a required high value for \u03f5UV(z), as will be clear later. \u2022 We allow for an evolving IMF with redshift, parameterized by an evolving ionizing photon production e\ufb03ciency, \u03f5UV(z) = \u03f5UV,6( 1+z 7 )\u03b3, where \u03f5UV,6 is \u03f5UV(z) at z = 6. \u2022 The clumping factor, C(z), of the recombining IGM at z \u223c6 may be lower than previous estimates. We adopt the suggested range C6 = 3 \u22126 for the clumping factor at z = 6 based on recent calculations (Pawlik et al. 2009). In our semi-numerical method, the evolution of the clumping factor of the IGM is determined by one parameter, Ch, that takes into account the contribution of collapsed gas to the overall clumping factor: C(z) = \u03c6h(z)Ch + [1 \u2212\u03c6h(z)], where \u03c6h(z) is the fraction of mass in halos above the \ufb01lter mass (Gnedin 2000) that is followed self-consistently; we adjust Ch along with the other free parameter, \u03f5UV(z), until we obtain simultaneously a desired clumping factor at z = 6, C6, and that the universe completes reionization at exactly z = 5.8. We also examine a case where reionization ends at z = 6.8. Perhaps the most uncertain of the input physics on the list is \u03f5UV(z), which we now elaborate on. For a \ufb01ducial, non-evolving IMF case \u03f5UV(z) = \u03f5UV,6. For an evolving IMF, we take cue from recent development in the \ufb01eld of star formation at high redshift, in particular, on CMB-regulated star formation physical process (e.g., Larson 2005; Tumlinson 2007; Smith et al. 2009; Bailin et al. 2010; Schneider & Omukai 2010). Following Tumlinson (2007), the CMB-regulated Bonner-Ebert mass of a collapsing cloud evolves as MBE = 3.2[(1 + z)/7]1.7 M\u2299. Specifying lower mass cuto\ufb00(Mc) of a Salpeter IMF at z = 6 and assuming that evolves as Mc[(1 + z)/7]1.7, and using the Padova 0.02 Z\u2299track (Leitherer et al. 1999) to obtain \u03f5UV,6 and \u03f5UV(z = 9), we compute \u03b3 as a function of Mc, shown in Figure 1. Depending on the exact value of Mc, \u03b3 ranges from 0.6 to 1.25 for Mc = 1\u221220 M\u2299. \u2013 4 \u2013 1 2 3 4 5 6 7 8 10 13 15 20 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 M c \u03b1     \u03b5 UV(z)=\u03b5 UV,6[1+z)/7]\u03b1 Fig. 1.\u2014 The mean slope of the expected evolution \u03f5UV(z) = \u03f5UV,6( 1+z 7 )\u03b3 from z = 9 to z = 6 for an evolving IMF with a Salpeter slope and a varying lower mass cuto\ufb00at z = 6 shown at the x-axis. While it is uncertain, we identify MBE = 3.2 M\u2299at z = 6 with Mc, giving rise to \u03b3 = 0.84. In our subsequent analyses, we treat \u03b3 = 0 and \u03b3 = 0.84 as two limiting cases for the evolution of IMF. With c\u2217fesc = 0.03, \u03b3, C6 and the completion redshift of reionization zri being \ufb01xed, we can \ufb01nd a unique pair of values for Ch and \u03f5UV,6. Figure 2 shows the evolutionary histories of the fraction of the un-ionized IGM, x, for six models. A feature common in all six models is that x rapidly rises toward higher redshift from zri. Analysis of the SDSS observations of QSO absorption spectra suggests a transition to a (volume-weighted) neutral fraction \u27e8fHI\u27e9V \u226510\u22123 at z \u223c6.2 from \u27e8fHI\u27e9V \u223c10\u22124 at z = 5.8 (Fan et al. 2006). As we will show below, the observed \u27e8fHI\u27e9V \u223c10\u22124 at z = 5.8 indicates that the reionization is largely complete by z = 5.8. Thus, our models suggest that x is expected to reach 6 \u221212% at z = 6.5, 13 \u221227% at z = 7.7 and 22 \u221238% at z = 8.8. It is useful to have some simple physical understanding of the results. Star formation and reionization is somewhat self-regulated in that a higher star formation rate ionizes and heats up a larger fraction of the IGM that would tend to suppress gas accretion for further star formation, whereas cooling processes induce more star formation (Cen 2003). As the response time scale for this self-regulation is on the order of the halo dynamic time that is roughly 10% of the Hubble time, so if there is a protracted period during reionization, this argument suggests that it may only take place at a neutral fraction level of x \u226510% so as to allow star formation rate to be able to dynamically respond to reionization induced heating within a halo dynamical time. Once x has dropped signi\ufb01cantly below 10%, the \ufb01nal stage of reionization should be prompt, which is greatly conspired by the rapid increase of \u03b7(z) \u2013 5 \u2013 6 6.5 7 7.7 8.8 0.0001 0.02 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Redshift un\u2212ionized IGM fraction     \u03b3=0,C6=3,zri=5.8 \u03b3=0,C6=6,zri=5.8 \u03b3=0.84,C6=3,zri=5.8 \u03b3=0.84,C6=6,zri=5.8 \u03b3=0,C6=3,zri=6.8 \u03b3=0,C6=6,zri=6.8 Fig. 2.\u2014 The evolution of un-ionized fraction of the IGM, x, in six di\ufb00erent reionization models with speci\ufb01ed \u03f5UV(z), C6 and zri. toward the end of reionization (Equation 1). It can be shown that Rh \u221dexp(\u2212\u03b42 c/2\u03c32 M)(1+z), leading to \u03b7 \u221dexp(\u2212\u03b42 c/2\u03c32 M)(1+z)\u03b3\u22122C\u22121(z), where \u03c3M is the density variance on the mass scale of M \u223c109 M\u2299that can accrete photoheated gas and form stars (Gnedin 2000). By the end of reionization, about 1% of total mass turns out to have collapsed in these halos; in other words, the (star-forming) halo collapse rate is on the exponential rise when the universe becomes fully ionized. Since the evolution of C is much weaker than exponential (Pawlik et al. 2009), \u03b7(z) likely surpasses unity at zri in an \u201cexponential\u201d fashion from below. As a result, it takes signi\ufb01cantly less than x times Hubble time to reionize the last small x fraction of neutral IGM. These considerations are consistent with the rapid \ufb01nal reionization phase seen in Figure 2. The SDSS observations strongly suggest zri = 5.8 (Fan et al. 2006), after which the ionization state of the IGM is primarily determined, on the ionizing photon sink side, by LLS. We show here, from a somewhat di\ufb00erent angle, but in agreement with the conclusion of Fan et al. (2006), that reionization is largely complete by z = 5.8 (c.f., Mesinger 2009). The comoving mean free path (mfp) of Lyman limit photons, \u03bb, may be written as \u03bb\u22121 = \u03bb\u22121 LL + \u03bb\u22121 Lya + \u03bb\u22121 neu + \u03bb\u22121 other, (2) where \u03bbLL, \u03bbLya and \u03bbneu are comoving mfp due to LLS, Ly\u03b1 forest and un-ionized neutral IGM, respectively; \u03bbother is due to possible other sinks. Physically, LLS are in less ionized, overdense regions within the reionized portion of the universe that are individually opaque to Lyman limit photons; Ly\u03b1 forest is dominated by low density regions within the reionized \u2013 6 \u2013 portion of the IGM that individually are only partially opaque to Lyman limit photons; the un-ionized neutral IGM is the portion of the IGM that has not been engulfed by the reionization front. We conservatively assume \u03bbother = \u221e. Current large-scale cosmological reionization simulations do not provide su\ufb03ciently accurate results to constrain \u03bbLL due to lack of adequate resolution. An extrapolation (Gnedin & Fan 2006) of observations at lower redshift z = 0.4 \u22124.7 (Storrie-Lombardi et al. 1994) gives \u03bbLL \u223c22 \u221248 comoving Mpc/h at z \u223c5.8. We use \u03bbLL = 35 comoving Mpc/h in our calculations. The following three equations are used to compute the neutral fraction of a region, x\u03b4, at overdensity \u03b4 \u2261\u03c1b/\u27e8\u03c1b\u27e9, when the region is substantially ionized (i.e., x\u03b4 \u226a1): x\u03b4J\u03bd\u27e8\u03c3H\u27e9= \u03b4\u03b1(T)n0(1 + z)3, (3) where J\u03bd is the ionizing photon radiation intensity in units of cm\u22122 sec\u22121 and \u27e8\u03c3H\u27e9= 2.6 \u00d7 10\u221218cm2 is the spectrum-averaged photoionization cross section for a low-Z IMF ionizing spectrum at high-z. \u03a8 = C\u03b1(T)n0(1 + z)3, (4) where \u03a8 is mean ionizing photon emissivity per baryon. J\u03bd = \u03bb\u03a8n0(1 + z)2. (5) Equations 3,4,5, respectively, re\ufb02ect the local ionization balance (between photoionization and recombination) (3), global ionization balance (between mean emissivity and recombination) (4) and relationship between mean emissivity, ionizing photon intensity and mfp (5). Combining (3,4,5) we obtain x\u03b4 = \u03b4 \u03bbC\u27e8\u03c3H\u27e9n0(1 + z)3. (6) Thus, knowing C and \u03bb allows one to compute x\u03b4, which, when combined with the probability distribution function of \u03b4, PDF(\u03b4), can be used to compute the volume-weighted neutral fraction, \u27e8fHI\u27e9V : \u27e8fHI\u27e9V = Z \u221e 0 PDF(\u03b4)x\u03b4d\u03b4. (7) We use the density distribution, PDF(\u03b4), from one of the radiation-hydrodynamic simulations (Trac et al. 2008) where the universe completes reionization at z \u223c6, to compute \u27e8fHI\u27e9V at z = 5.8. A resolution of comoving 65kpc/h in the simulation is adequate for resolving the Jeans scale of photo-ionized gas. The mfp due to Ly\u03b1 forest can be computed as \u03bb\u22121 Lya = \u27e8fHI\u27e9V \u27e8\u03c3H\u27e9n0(1 + z)2/(1 + 1/e). (8) We use the same simulation to also compute \u03bbneu, simply by computing the average distance that a random ray can travel before it hits an un-ionized cell. We identify regions that have not been reionized and photon-heated with cells in the simulation box that have \u2013 7 \u2013 \u22123 \u22122 \u22121 0 0 1 2 log \u03bb (comoving Mpc/h)     \u03bb for C=3 \u03bb for C=6 \u03bb neu for C=3 \u03bb Lya for C=3 \u03bb LL \u22123 \u22122 \u22121 0 \u22125 \u22124 \u22123 \u22122 log x <fHI>V     <fHI>V @z=5.8 for C=3 <fHI>V @z=5.8 for C=6 obs: Fan et al 2006 Fig. 3.\u2014 Top panel shows the total comoving mean free path (mfp) \u03bb for two cases with C = 3 (solid squares) and C = 6 (stars) as well as \u03bbLL (open diamonds), \u03bbLya (open triangles) and \u03bbneu (open circles) for the case with C = 3, as a function of x at z = 5.8. Bottom panel shows the volume-weighted neutral fractions of the IGM, \u27e8fHI\u27e9V , as a function of x for the two cases with C = 3 (solid squares) and C = 6 (stars). Also shown as the shaded region is the total range of \u27e8fHI\u27e9V at z = 5.8 based on the SDSS QSO sample (Fan et al. 2006). neutral fraction greater than 0.99 and temperature lower than 103K; results are insensitive to reasonable variations of the parameters: changing 0.99 to 0.50 or 103K to 100K makes no visible di\ufb00erence in the results. Since, when scaled to x, the morphology of reionization does not vary strongly (e.g., Furlanetto et al. 2004), we use \u03bbneu(z) computed as a function of redshift from the simulation as \u03bbneu(x) as a function of x at z = 5.8. The detailed procedure to simultaneously compute \u03bb and \u27e8fHI\u27e9V is as follows. At a given value of x at z = 5.8, we know \u03bbneu(x) from simulations. Combining \u03bbneu(x) with an initial guess for \u03bbLya(x) and the adopted \u03bbLL gives \u03bb (Equation 1). With \u03bb and an assumed C we compute \u27e8fHI\u27e9V (Equations 6,7), which in turn yields a new value for \u03bbLya(x) (Equation 8). This procedure is iterated until we have a converged pair of \u03bbLya and \u27e8fHI\u27e9V . The results are shown in Figure 3, where the top panel shows the total comoving mfp for two cases with C = 3 and C = 6 as well as various components for the case with C = 3, and the bottom panel shows \u27e8fHI\u27e9V for two cases with C = 3 and C = 6 at z = 5.8 as well as the observationally inferred range at z = 5.8 (Fan et al. 2006). As it turns out, we see that the total \u03bb is primarily determined by \u2013 8 \u2013 \u03bbneu at x \u22650.01 and \u03bbLL at x \u22640.005, and Ly\u03b1 forest has secondary importance at all x. A comparison between the computed results and observations indicates that the un-ionized fraction x does not exceed 0.1 \u22121% at z = 5.8 and reionization is complete or largely complete by z = 5.8. In combination with our previous \ufb01nding of rapid reionization near zri, it suggests that zri = 5.8 or very near it. 0.1 1 5 15 30 50 100   1 2 3 4 5 6 7 8 9 10 \u22126 \u22125.5 \u22125 \u22124.5 \u22124 \u22123.5 \u22123 C6 log \u03b5 UV,6     Mc (M\u2299) \u03b5 UV\u221d (1+z)0,z ri=5.8 \u03b5 UV\u221d (1+z)0.84,z ri=5.8 \u03b5 UV\u221d (1+z)0,z ri=6.8 Salpeter (0.02Zsun) Pop III Fig. 4.\u2014 show the required ionizing photon production e\ufb03ciency at z = 6, \u03f5UV,6, as a function of IGM clumping factor at z = 6, C6, for several models. Also shown as stars are the expected \u03f5UV for Salpeter IMF (with 0.02 Z\u2299metallicity) (Leitherer et al. 1999) with the lower mass cuto\ufb00Mc indicated by the top x-axis. The diamonds are \u03f5UV for Pop III metal-free stars, again, with the lower mass cuto\ufb00Mc indicated by the top x-axis (Schaerer 2002). Finally, in Figure 4 we show the required ionizing photon production e\ufb03ciency at z = 6, \u03f5UV,6, as a function of C6, for several models. Several expected trends are noted. First, a higher C6 requires a higher \u03f56. Second, an earlier reionization requires a higher \u03f56. Third, a rising \u03f5UV with redshift lessens the required \u03f56 fractionally. What is most striking is that stars with the standard metal-enriched IMF and Mc = 1 M\u2299fall short of providing the required ionizing photons, by a factor of 10 \u221220 at z \u223c6. Having Mc \u223c5 M\u2299would help reduce the de\ufb01cit to a factor of 3 \u22126. Only with Mc \u223c30 M\u2299and C6 = 3, one is barely able to meet the requirement to reionize the universe at z \u223c6 by Population II stars. But such an extreme scenario with Mc \u226530 M\u2299may be disfavored by the existence of old stars in \u2013 9 \u2013 observed high-z galaxies (e.g., Mobasher et al. 2005) that need be less massive than \u223c10 M\u2299 to be long-lived. However, we note that Pop III metal-free stars (diamonds in Figure 4), thought to be more massive than 30 M\u2299(e.g., Abel et al. 2002; Bromm et al. 2002; McKee & Tan 2008), could provide ample ionizing photons. Unfortunately, normally, Pop III stars would not be expected to form at z \u223c6, had some earlier supernovae uniformly enriched the intergalactic medium. With gaseous low-temperature coolants, it is believed that the critical metallicity for transition from Pop III to Pop II IMF is Zcrit \u223c10\u22123.5 Z\u2299(e.g., Bromm et al. 2001; Bromm & Loeb 2003). If dust is formed in the Pop III.1 supernova ejecta, Schneider et al. (2006) argue that dust cooling may signi\ufb01cantly lower the critical transition metallicity to as low as Zcrit \u223c10\u22126 (e.f., Cherchne\ufb00& Dwek 2010). If a fraction 10\u22124 of baryons forms into Pop III stars and their supernovae uniformly enrich the IGM, the expected metallicity of the IGM will likely exceed Z \u223c10\u22123.5 Z\u2299(e.g., Fang & Cen 2004). Since a fraction of \u226510\u22124 of baryons needs to form into Pop III stars to reionize the universe, therefore, in the case of uniform IGM enrichment, the contribution of Pop III stars to ionizing photon budget at z \u223c6 is expected to have become negligible. In addition, a very small amount of metals (Z \u226410\u22123 Z\u2299) would change the internal dynamics of massive stars (core temperature, size, e\ufb00ective surface temperature, etc) and render them much less e\ufb03cient UV producers and notably di\ufb00erent from Pop III massive stars (e.g., Hirschi et al. 2008), as already hinted in Figure 4 between stars (Z = 0.02 Z\u2299) and diamonds (Pop III) at Mc \u223c30 M\u2299. We suggest that, if the metal enrichment process of gas, including IGM and gas in collapsed minihalos and other galaxies, is highly inhomogeneous, then it is possible that a small fraction of star-forming gas may have remained primordial to allow for Pop III star formation at z \u223c6. A signi\ufb01cant amount of gas in the central regions of non-starforming galaxies (e.g., Wyithe & Cen 2007; Cen & Riquelme 2008) as well as a fraction of IGM that has not been swept by galactic winds emanating from star-forming galaxies could remain uncontaminated. Cosmological simulations at lower redshift (z = 0\u22126) suggest that metal enrichment process of the IGM is indeed extremely inhomogeneous, leaving signi\ufb01cant pockets of metal-free gas even at z = 0 (e.g., Cen & Ostriker 1999; Aguirre et al. 2001; Oppenheimer & Dav\u00b4 e 2006; Cen & Chisari 2010). The common assumption is that earlier generations of stars not resolved in these simulations would have put in a metallicity-\ufb02oor in all regions. But this needs not be the case. Observationally, while the majority of local star formation has metallicity close to solar, relatively low-metallicity (1/30 of solar) star formation does occur occasionally (e.g., Izotov & Thuan 1999) and some of the observed local supernovae may be pair-instability supernovae (e.g., Smith et al. 2007; Gal-Yam et al. 2009) that may be due to metal-free progenitors (c.f., Smith et al. 2007; Langer et al. 2007; Woosley et al. 2007). At redshift z = 2 \u22123 the low density Ly\u03b1 forest, regions of density around and less than the global mean, appears to have not been enriched to a detectable level (\u226410\u22123.5 Z\u2299) (e.g., Lu et al. 1998). Therefore, it seems plausible that an increasing fraction \u2013 10 \u2013 of star-forming gas toward high redshift may be pristine, due to a combination of ine\ufb03cient and non-uniform mixing and a decreasingly amount of metals having been injected. From Figure 4 we see that what is minimally required in order to have enough ionizing photons at z \u223c6 is that about 2-4% of stars forming at z \u223c6 are Pop III stars and the remainder normal Pop II metal-enriched stars with a Salpeter-like IMF or other forms; the lower mass cuto\ufb00for the latter is unconstrained but Mc \u223c3 M\u2299or so is perhaps physically motivated and fully in line with other evidence that hints on an evolving IMF from redshift zero (e.g., van Dokkum 2008; Dav\u00b4 e 2008). With 2-4% being Pop III stars, Pop III stars\u2019 contribution to ionizing photons and FUV are dominant over the remaining normal stars, which would give rise to an \u201capparent\u201d, very low metallicity, top-heavy IMF for these high redshift galaxies. Interestingly, galaxies with such required properties a dust-free, very low metallicity, top-heavy IMF with a very high ionizing photon escape fraction of 40 \u221280% may have already been detected in the Hubble Ultra Deep Field (UDF) at z \u223c7 \u22128 (e.g., Bouwens et al. 2010). 3. Conclusions and Discussion We study the evolution of the IGM at z \u223c5.8 when universe \ufb01nally turns transparent in the context of stellar reionization in the standard cold dark matter model. Under the conservative assumption, c\u2217fesc = 0.03, that is based on recent calculations of ionizing photon escape fraction fesc and star formation e\ufb03ciency c\u2217, we \ufb01nd that metal-enriched Pop II stars with a normal IMF fail, by a factor of 10\u221220, to provide enough ionizing photons to reionize the universe at z \u223c6. Only under the scenario that the vast majority of Pop II stars are more massive than \u223c30 M\u2299one may be able to reionize the universe, if the clumping factor of the recombining IGM is \u22643 at z = 6. Perhaps the observed existence of high-z galaxies at z \u223c6 already rules out this scenario. Alternatively, we suggest that, if a mass fraction of 2 \u22124% of stars forming at z \u223c6 is massive Pop III metal-free stars, enough ionizing photons can be produced. Physically, this scenario can be plausibly accommodated by existence of a fraction of uncontaminated, metal-free gas at z \u223c6, due to non-uniform mixing of metals in the universe. The dominant contribution of UV light from these Pop III stars, likely being dust-free and expected very high ionizing photon escape fraction (40 \u221280%) would combine to make these galaxies look very blue, which would be consistent with recent observations of z = 7 \u22128 galaxies in the UDF. This hints exciting possibilities for JWST in detecting signatures of Pop III stars. Based on extant observations that the volume-weighted neutral fraction of the IGM is \u223c10\u22124 at z \u223c5.8, we conclude that the reionization is basically complete by z = 5.8 with no more than 0.1-1% of the IGM remaining neutral. In other words, zri = 5.8 or very near \u2013 11 \u2013 it, in agreement with earlier, independent analyses (Fan et al. 2006). With the complete percolation of HII bubbles occurring at z = 5.8, the mean neutral fraction of the IGM is expected to reach 6 \u221212% at z = 6.5, 13 \u221227% at z = 7.7 and 22 \u221238% at z = 8.8. Future measurements shall test this stellar reionization paradigm in the standard model. Finally, we mention the possibility of probing other physics with reionization. Signi\ufb01cant alteration of the properties of dark matter particles from \u201cvanilla cold\u201d may have substantial impact on the reionization process. Weakly interacting massive particle (WIMP) annihilation heating may a\ufb00ect the balance of cooling and heating processes and hence change the primordial star formation process, if dark matter particles are su\ufb03ciently cold to allow for very concentrated pro\ufb01les at stellar scales (e.g., Spolyar et al. 2008; Natarajan et al. 2009). Turning particles from \u201ccold\u201d to somewhat \u201cwarm\u201d may also have profound e\ufb00ects on reionization. Current astronomical observational constraints place a lower limit on dark matter particle mass mx in the neighborhood of 0.5 \u22121 keV (Narayanan et al. 2000; Barkana et al. 2001; Viel et al. 2005; Abazajian 2006). The smoothing scale, de\ufb01ned as the comoving halfwavelength of the mode for which the linear perturbation amplitude is suppressed by 2, is RS = 0.34(\u2126M 0.3 )0.15( h 0.7)1.3( mX keV)\u22121.15h\u22121 Mpc (Bode et al. 2001). For mX = (1, 10) keV, the mass smoothing scale is (1.2 \u00d7 1010, 4.3 \u00d7 106) M\u2299, respectively. Naturally, the formation epoch of Pop III star formation in a warm dark matter model of gravitino particle mass mx = 15 keV is found to be delayed relative to the case with cold dark matter by 108 yr or from z \u223c16 to z \u223c13 (O\u2019Shea & Norman 2006). Given that even mx = 15 keV has a signi\ufb01cant impact on Pop III star formation, it seems very promising that observations of high-z galaxies will place constraints on the nature of dark matter particles. With a dark matter particle mass of \u223c1 keV, minihalo formation would be largely suppressed and give rise to a very di\ufb00erent, \u201cfavorable\u201d scenario in which larger galaxies form stars out of primordial gas that may otherwise have been contaminated by star formation in minihalos. Thus, observations of reionization may provide a powerful probe of the physics of dark matter. This work is supported in part by grants NNG06GI09G and NNX08AH31G.",
                    "introduction": "How the universe becomes transparent at z \u223c5.8 is debated (Fan et al. 2006; Becker et al. 2007). Whether reionization is complete by z = 5 \u22126 has been questioned (Mesinger 2009). What kind of stars reionizes the universe at z \u223c6 remains less than certain. We ex- amine in greater detail this endgame to assess how reionization process may have proceeded approaching z \u223c5.8, how complete reionization is at z \u223c5.8 and what role Population III (Pop III) stars may have played in the \ufb01nal reionization phase at z \u223c6, in the context of stellar reionization in the standard cold dark matter model (Komatsu et al. 2010). We are 1Princeton University Observatory, Princeton, NJ 08544; cen@astro.princeton.edu arXiv:1007.0704v2  [astro-ph.CO]  6 Jul 2010 \u2013 2 \u2013 also motivated by the exciting possibility of being able to statistically measure the neutral fraction of the IGM at redshift above six in the coming years, as a variety of techniques are applied to larger samples that will become available. Those include methods based on (1) QSO Stromgren sphere measures (e.g., Wyithe & Loeb 2004; Mesinger et al. 2004), (2) mea- surements of damping wings of high redshift gamma-ray bursts (GRB) (e.g., Totani et al. 2006), (3) statistical analyses of high redshift Lyman alpha emitters from a variety of sur- veys (e.g., Malhotra & Rhoads 2004; Ouchi et al. 2007, 2008; Nilsson et al. 2007; Cuby et al. 2007; Stark et al. 2007; Willis et al. 2008; McMahon et al. 2008; Hibon et al. 2009). In ad- dition, polarization measurements of the cosmic microwave background (CMB) \ufb02uctuations by Planck satellite and others may provide some useful constraints (e.g., Kaplinghat et al. 2003). Finally, the James Webb Space Telescope (JWST) will likely be able to detect the bulk of dwarf galaxies of halo mass \u223c109 M\u2299that are believed to be primarily responsible for cosmological reionization at z \u223c6 (e.g., Stiavelli et al. 2004), especially if a signi\ufb01cant fraction of stars in them are active Pop III stars."
                },
                {
                    "url": "http://arxiv.org/abs/1005.1451v2",
                    "title": "Star Formation Feedback and Metal Enrichment History Of The Intergalactic Medium",
                    "abstract": "Using hydrodynamic simulations we compute the metal enrichment history of the\nintergalactic medium (IGM). We show that galactic superwind (GSW) feedback can\ntransport metals to the IGM and that the properties of simulated metal\nabsorbers match observations. The distance of influence of GSW is typically\nlimited to >0.5Mpc and within regions of overdensity >10. Most CIV and OVI\nabsorbers are located within shocked regions of elevated temperature\n(T>2x10^4K), overdensity (>10), and metallicity ([-2.5,-0.5]). OVI absorbers\nhave typically higher metallicity, lower density and higher temperature than\nCIV absorbers. For OVI absorbers collisional ionization dominates over the\nentire redshift range z=0-6, whereas for CIV absorbers the transition occurs at\nmoderate redshift z~3 from collisionally dominated to photoionization\ndominated. We find that the observed column density distributions for CIV and\nOVI in the range log N cm^2=12-15 are reasonably reproduced by the simulations.\nThe evolution of mass densities contained in CIV and OVI lines, Omega_CIV and\nOmega_OVI, is also in good agreement with observations, which shows a near\nconstancy at low redshifts and an exponential drop beyond redshift z=3-4. For\nboth CIV and OVI, most absorbers are transient and the amount of metals probed\nby CIV and OVI lines of column log N cm^2=12-15 is only ~2% of total metal\ndensity at any epoch. While gravitational shocks from large-scale structure\nformation dominate the energy budget (80-90%) for turning about 50% of IGM to\nthe warm-hot intergalactic medium (WHIM) by z=0, GSW feedback shocks are\nenergetically dominant over gravitational shocks at z > 1-2. Most of the\nso-called \"missing metals\" at z=2-3 are hidden in a warm-hot (T=10^{4.5-7}K)\ngaseous phase, heated up by GSW feedback shocks. Their mass distribution is\nbroadly peaked at $\\delta=1-10$ in the IGM, outside virialized halos.",
                    "authors": "Renyue Cen, Nora Elisa Chisari",
                    "published": "2010-05-10",
                    "updated": "2011-03-19",
                    "primary_cat": "astro-ph.CO",
                    "cats": [
                        "astro-ph.CO"
                    ],
                    "main_content": "2.1. The Hydrocode Numerical methods of the cosmological hydrodynamic code and input physical ingredients have been described in detail in an earlier paper (Cen et al. 2005). The simulation integrates five sets of equations simultaneously: the Euler equations for gas dynamics in comoving coordinates, time dependent rate equations for hydrogen and helium species, the Newtonian equations of motion for dynamics of collisionless (dark matter) particles, the Poisson equation for the gravitational potential field and the equation governing the evolution of the intergalactic ionizing radiation field, all in cosmological comoving coordinates. The gasdynamic equations are solved using a new, improved hydrodynamics code, \u201cCOSMO\u201d (Li et al. 2008) on a uniform mesh. The rate equations are treated using sub-cycles within a hydrodynamic time step due to the much shorter ionization time-scales (i.e., the rate equations are very \u201cstiff\u201d). Dark matter particles are advanced in time using the standard particlemesh (PM) with a leapfrog integrator. The Poisson equation is solved using the Fast Fourier Transform (FFT) method on the uniform mesh. The initial conditions adopted are those for Gaussian processes with the phases of the different waves being random and uncorrelated. The initial condition is generated by the COSMICS software package kindly provided by E. Bertschinger (2001). Cooling and heating processes due to all the principal line and continuum atomic processes for a plasma of primordial composition with additional metals ejected from star formation. Compton cooling due to the microwave background radiation field and Compton cooling/heating due to the X-ray and high energy background are computed. The cooling/heating due to metals is computed using a code based on the Raymond-Smith code assuming ionization equilibrium that takes into account the presence of a time-dependent UV/X-ray radiation background, which we have included in our simulations since Cen et al. (1995) and has now been performed by other investigators (e.g., Shen et al. 2010). We follow star formation using a well defined, Schmidt-Kennicutt-law-like prescription used by us in our previous work and similar to that of other investigators (e.g., Katz et al. 1996; Steinmetz 1996; Gnedin & Ostriker 1997). A stellar particle of mass m\u2217= c\u2217mgas\u2206t/t\u2217 is created (the same amount is removed from the gas mass in the cell), if the gas in a cell at any time meets the following three conditions simultaneously: (i) contracting flow, (ii) cooling time less than dynamic time, and (iii) Jeans unstable, where \u2206t is the time step, t\u2217= max(tdyn, 107yrs), tdyn = \ufffd 3\u03c0/(32G\u03c1tot) is the dynamical time of the cell, mgas is the baryonic gas mass in the cell and c\u2217= 0.03 is star formation efficiency (e.g., Krumholz & Tan 2007). Each stellar particle is given a number of other attributes at birth, including t\u2217= max(tdyn, 107yrs), tdyn = \ufffd 3\u03c0/(32G\u03c1tot) is the dynamical time of the cell, mgas is the baryonic gas mass in the cell and c\u2217= 0.03 is star formation efficiency (e.g., Krumholz & Tan 2007). Each stellar particle is given a number of other attributes at birth, including formation time ti, initial gas metallicity and the free-fall time in the birth cell tdyn. The typical mass of a stellar particle in the simulation is about 106M\u2299; in other words, these \u2013 5 \u2013 stellar particles are like coeval globular clusters. All variations of this commonly adopted star-formation algorithm essentially achieve the same goal: in any region where gas density exceeds the stellar density, gas is transformed to stars on a timescale longer than the local dynamical time and shorter than the Hubble time. Since these two time scales are widely separated, the e\ufb00ects, on the longer time scale, of changing the dimensionless numbers (here c\u2217) are minimal. Since nature does not provide us with examples of systems which violate this condition (systems which persist over many dynamical and cooling time scales in having more gas than stars), this commonly adopted algorithm should be adequate even though our understanding of star formation remains crude. Stellar particles are treated dynamically as collisionless particles subsequent to their birth. Feedback from star formation, the e\ufb00ects of the cumulative SN explosions known as Galactic Superwinds (GSW) and metal-enriched gas, will be described in more detail in the next subsection. While the code can self-consistently compute the ionizing UV-X-ray background using sources and sinks in the simulation, here we use the Haardt & Madau (1996) spectra for all runs such that we do not introduce additional variations due to otherwise varying UV backgrounds in the di\ufb00erent runs. However, a local optical depth approximation is adopted to crudely mimic the local shielding e\ufb00ects: each cubic cell is \ufb02agged with six hydrogen \u201coptical depths\u201d on the six faces, each equal to the product of neutral hydrogen density, hydrogen ionization cross section and scale height, and the appropriate mean from the six values is then calculated; analogous ones are computed for neutral helium and singly-ionized helium. In computing the local ionization and cooling/heating balance for each cell, self-shielding is taken into account to attenuate the external HM ionizing radiation \ufb01eld. Both these two shielding e\ufb00ects are essential in order to obtain self-consistent radiation background evolution and neutral hydrogen evolution. Table 1. Simulations Run Box (Mpc/h) Res (kpc/h) DM ( M\u2299) eGSW N 50 24 1.1 \u00d7 107 0 L 50 24 1.1 \u00d7 107 3 \u00d7 10\u22126 M 50 24 1.1 \u00d7 107 7 \u00d7 10\u22126 H 50 24 1.1 \u00d7 107 1 \u00d7 10\u22125 MR 50 48 8.8 \u00d7 107 7 \u00d7 10\u22126 \u2013 6 \u2013 2.2. Cosmological and Physical Parameters of the Simulations We have run a set of four new simulations of a WMAP5-normalized (Komatsu et al. 2009) cold dark matter model with a cosmological constant: \u2126M = 0.28, \u2126b = 0.046, \u2126\u039b = 0.72, \u03c38 = 0.82, H0 = 100hkms\u22121Mpc\u22121 = 70kms\u22121Mpc\u22121 and n = 0.96. The adopted box size is 50Mpc/h comoving and with 20483 cells of size 24kpc/h comoving; the dark matter particle mass and mean baryonic mass in a cell are equal to 1.1 \u00d7 107 M\u2299and 2.6 \u00d7 105 M\u2299, respectively. Some of the key parameters for the four simulations are summarized in Table 1. The only di\ufb00erence among the four main runs is the strength of the GSW feedback: (N) no GSW, (L) low GSW feedback, (M) moderate GSW feedback and (H) high GSW feedback. In the next subsection we will determine which feedback strength produces the star formation rate history that matches observations. We run an additional lower resolution simulation with 1024 cells a side, each of size 48kpc/h (run \u201cMR\u201d) to test convergence of results. When computing results using run \u201cMR\u201d, we multiply the metallicity of each cell in run \u201cMR\u201d by a constant factor such that its mean metallicity at any epoch match that of run \u201cM\u201d. We obtain an additional set of results by changing the amplitude of the UV background, run \u201cM2\u201d, where it is reduced to one half of that in \u201cM\u201d. 2.3. Mechanical Feedback from Star Formation It is well known that without impeding processes to counter the cooling and subsequent condensation of baryons, the stellar mass in the universe would be overproduced \u2013 the \u201covercooling\u201d problem (e.g., White & Frenk 1991; Cole 1991; Blanchard et al. 1992). Feedback from star formation is believed to play the essential role to prevent gas from overcooling. The key question is: Where does the feedback from SF throttle gas cooling and condensation? We consider three independent lines of evidence to address this question. First, while metals from supernovae ejecta can be accelerated to velocities exceeding the escape velocity, the whole interstellar gas is very di\ufb03cult to be blown away, even in starburst galaxies, based on simulations (e.g., Mac Low & Ferrara 1999), although their adopted feedback strength may be on the low side. Second, observed normal galaxies in the local universe tend to be relatively gas poor (e.g., Zhang et al. 2009). Their progeniors or their building blocks were presumably gas rich in the past when most of the star formation occurred. This implies that, once gas has collapsed, it would turn into stars on a time scale that is shorter than the Hubble time. Finally, if gas were able to collapse inside halos without hinderance, the observed soft X-ray background would be overproduced by more than an order of magnitude (Pen 1999; Wu et al. 2001). These three lines of evidence together suggest that feedback from star formation likely exerts its e\ufb00ect outside normal stellar disks, probably in regions that are tens to hundreds of kiloparsecs from halo centers, before too much gas has either \u2013 7 \u2013 been collected inside the virial radius or cooled and condensed onto the disk. It is currently di\ufb03cult to fully model GSW in a cosmological simulation, although signi\ufb01cant progress has been made to provide a better treatment of the multi-phase interstellar medium (e.g., Yepes et al. 1997; Springel & Hernquist 2003). It is likely that a combination of both high resolution and detailed multi-phase medium treatment (perhaps with the inclusion of magnetic \ufb01elds and cosmic rays) is a requisite for reproducing observations. Here we do not attempt to model the causes and generation of GSW, but, instead, to simply assume an input level of mass, energy and metals, and carefully compute the consequences of GSW on the surrounding medium and on subsequent galaxy formation. Our simulations have a resolution of 24kpc/h comoving (see Table 1), which may provide an adequate resolution for this purpose, given the aforementioned lines of evidence that feedback from star formation likely exerts most of its e\ufb00ects in regions on scales larger than tens of kiloparsecs. In our simulations, GSW energy and ejected metals are distributed into 27 local gas cells centered at the stellar particle in question, weighted by the speci\ufb01c volume of each cell (Cen et al. 2005). The temporal release of the feedback at time t has the following form, all being proportional to the local star formation rate: f(t, ti, tdyn) \u2261(1/tdyn)[(t \u2212 ti)/tdyn] exp[\u2212(t \u2212ti)/tdyn]. Within a time step dt, the released GSW energy and mass to the IGM from stars are eGSWf(t, ti, tdyn)m\u2217c2dt and emassf(t, ti, tdyn)m\u2217dt, respectively. We \ufb01x emass = 0.25, i.e., 25% of the stellar mass is recycled with the ejecta metallicity of 5 Z\u2299. Metals, collectively having the observed solar abundance pattern, are followed as a separate hydro variable (analogous to the total gas density or nuetral hydrogen, HeI density, HeII density) with the same hydrocode. We do not introduce any additional \u201cdi\ufb00usion\u201d process for the metals. We note that cooling process is never turned o\ufb00, before or after the deposition of thermal energy, and hydrodynamic coupling between ejected baryons and surrounding gas is not turned o\ufb00either, a departure from some of the previous simulations (e.g., Theuns et al. 2002a; Aguirre et al. 2005; Oppenheimer & Dav\u00b4 e 2006; Dalla Vecchia & Schaye 2008; Shen et al. 2010). This is physically made possible in part due to a deposition of energy at scales that are comparable or larger than the Sedov radius in our current simulations, thanks to our limited spatial resolution. The GSW strength is therefore controlled by one single adjustable parameter, eGSW. We normalize eGSW by the requirement that the computed star formation rate (SFR) history matches, as closely as possible, the observations over the redshift range z = 0 to z = 6 where comparisons can be made. Figure 1 shows the SFR history for the three runs with non-zero eGSW, (L,M,H). What is immediately evident is that the mechanical feedback strength from star formation has a dramatic e\ufb00ect on the overall SFR history, especially at low redshift (z \u22643). At the resolution of the simulation, run \u201cM\u201d provides the best and excellent match to observations, where run \u201cL\u201d and \u201cH\u201d, respectively, overand under-estimate the SFR at z < 2. At the time of this writing we prefer to avoid introducing additional ad \u2013 8 \u2013 0 1 2 3 4 5 6 7 \u22123 \u22122 \u22121 0 z log SFR (Msun yr\u22121 Mpc\u22123)     Run L Run M Run H MR Fig. 1.\u2014 Star formation rate density as a function of redshift for three models with di\ufb00ering feedback coe\ufb03cients eGSW = 7 \u00d7 10\u22126 (run \u201cM\u201d, thick solid curve), eGSW = 1 \u00d7 10\u22125 (run \u201cH\u201d, dot-dashed curve), eGSW = 3\u00d710\u22126 (run \u201cL\u201d, dashed curve), and run \u201cM2\u201d (thin solid curve), compared with observational data taken from (from low to high redshift): Heavens et al. (2004, 3 asterisks at z \u223c0), Nakamura et al. (2004, open inverted triangle at z = 0), Lilly et al. (1996, open circles), Norman et al. (2004, \ufb01lled triangles), Cowie et al. (1999, open diamonds), Gabasch et al. (2004, open squares), Reddy et al. (2005, cross at z = 2), Barger et al. (2000, open stars at z = 2 and 4.5), Steidel et al. (1999, \ufb01lled diamonds at z = 3, 4), Ouchi et al. (2004, \ufb01lled squares at z = 4, 4.7), Giavalisco et al. (2004, open triangles at z = 3\u22126), and Bouwens et al. (2005, \ufb01lled inverted triangle at z = 6). The data are converted to the values with the Chabrier IMF and common values are assumed for dust extinction for the UV data. hoc physics to remedy this and are instead content with the ballpark agreement at z > 3 between simulations and observations, given the large uncertainties in the observational data as evidenced by the large dispersion among di\ufb00erent observations. At redshift zero we \ufb01nd that the stellar densities in the three models (L,M,H) are \u2126\u2217= (0.011, 0.0048, 0.0030), which should be compared to the observed value of \u2126\u2217,obs = 0.0041 \u00b1 0.0006 (Cole et al. 2001). Our experiments indicate that, had we set eGSW = 0, the amount of stellar density \u2126\u2217at z = 0 would exceed 0.015, in serious disagreement with observations. In this respect model \u201cM\u201d also agrees better with observations. Our \ufb01ndings are in agreement with Springel & Hernquist (2003) and Oppenheimer & Dav\u00b4 e (2006) in that star formation rate history depends sensitively on the stellar feedback, but in disagreement with Shen et al. (2010) who \ufb01nd otherwise. All the subsequent results presented are based on run \u201cM\u201d. There is some indication that a model between \u201cM\u201d and \u201cL\u201d might provide a better match to the observations at low redshift (z < 1) if the compilation of Hopkins et al. (2006) is used. But we note that such a model may run into a worse agreement with observations with respect to \u2126\u2217at z = 0. Currently, it is di\ufb03cult to reconcile the observations of star formation rate \u2013 9 \u2013 history and \u2126\u2217at z = 0. One might appeal to an evolving IMF to provide an attractive reconcilation between the possible discrepancy (Dav\u00b4 e 2008). This is well beyond the scope of this investigation. In any case, a slight varied simulation, say, using an eGSW value between the \u201cM\u201d and \u201cL\u201d would give qualitatively comparable results. In order to test for numerical convergence we run one additional simulation, \u201cMR\u201d, which has the same parameters as run \u201cM\u201d but have half the resolution. To test the dependence of results on the extragalactic UV background we run our software pipeline through run \u201cM\u201d but with halving the amplitude of the UV background, called run \u201cM2\u201d. Fig. 2.\u2014 shows the mean \ufb02ux for Ly\u03b1 forest as a function of redshift. Our computed results are shown in asterisks. Diamonds correspond to mean transmitted \ufb02ux values for each quasar in the sample of McDonald et al. (2000), and triangles correspond to the mean \ufb02ux for the same observational data but binned in redshift intervals: [3.39, 4.43], [2.67, 3.39] and [2.09, 2.67]. It is prudent to make a self-consistency check for the value of eGSW that is empirically determined. The total amount of explosion kinetic energy from Type II supernovae with a Chabrier IMF translates to eGSW = 6.6 \u00d7 10\u22126. Observations of local sturburst galaxies indicate that nearly all of the star formation produced kinetic energy (due to Type II supernovae) is used to power GSW (e.g., Heckman 2001). Given the uncertainties on the evolution of IMF with redshift the fact that newly discovered prompt Type I supernovae contribute a comparable amount of energy compared to Type II supernovae, we argue that our adopted \u201cbest\u201d value of eGSW = 7 \u00d7 10\u22126 is consistent with observations and entirely within physical plausibility. \u2013 10 \u2013 2.4. Mock Spectra and Identi\ufb01cation of Absorption Lines The photoionization code CLOUDY (Ferland et al. 1998) is used post-simulation to compute the abundance of C IV and O VI , adopting the UV background calculated by Haardt & Madau (1996). For Ly\u03b1 absorption lines we use the computed neutral hydrogen density distribution directly from the simulation that was already using the Haardt & Madau (1996) UV background in the rate equations for hydrogen and helium species. We have checked that the radiation \ufb01eld is consistent with observations by comparing the simulated mean transmitted \ufb02ux as a function of redshift with observations. Figure 2 shows the mean transmitted Ly\u03b1 \ufb02ux as a function of redshift from the simulation in comparison with observations. We see the Ly\u03b1 forest produced in the LCDM model using the adopted UV background provides an adequate match to observations over most of the redshift range compared, z = 0 \u22124. At z \u22734, our results do not seem to coincide with observations. We attribute this to the UV background used: we have only considered a quasar background, while at these high redshifts the UV radiation coming from galaxies should have a signi\ufb01cant e\ufb00ect on the Ly\u03b1 forest. Nevertheless, we do not expect this to be an issue on the metal species considered in the following sections. These correspond to much higher energies than 1 ryd that are not a\ufb00ected by the UV contribution from galaxies to the ionizing radiation. We generate random synthetic absorption spectra for each of the three absorption lines by producing optical depth distribution along lines of sight parallel to one of the three axes of the simulation box, based on density, temperature and velocity distributions in the simulation (i.e., our calculations include redshift e\ufb00ects due to peculiar velocities and thermal broadening). The code used is similar to that used in our earlier papers (Cen et al. 1994, 2001). We identify each absorption line as a contiguous region in the \ufb02ux spectrum between a down-crossing point and an up-crossing point, both at a \ufb02ux equal to 0.85. Note that \ufb02ux equal to 1 corresponds to no absorption. For each identi\ufb01ed line we compute its equivalent width (EW), Doppler width (b), mean temperature (T), mean metallicity (Z) and mean gas overdensity (\u03b4), weighted by optically depth of each pixel. We do not attempt to perform Voigt pro\ufb01le \ufb01tting, a procedure often used to analyze observed spectra. Because of this, we tend to not generate some of the very low column lines that are purely an e\ufb00ect of pro\ufb01le \ufb01tting process. Also, precise comparison between our mock absorbers and observed ones is not possible for some quantities, such as Doppler width distributions. 3. Results 3.1. C IV \u03bb\u03bb1548, 1550 and O VI \u03bb\u03bb1032, 1038 absorption lines We begin with a visual examination of density, temperature and metallicity distribution of IGM at z = 2.6 and compare cases with and without star formation feedback, shown in \u2013 11 \u2013 x (Mpc/h) y (Mpc/h)     0 10 20 30 40 50 0 10 20 30 40 50 \u22121 \u22120.5 0 0.5 1 1.5 2 x (Mpc/h) y (Mpc/h)     38 40 42 44 46 48 50 38 40 42 44 46 48 50 \u22123 \u22122.5 \u22122 \u22121.5 \u22121 \u22120.5 0 x (Mpc/h) y (Mpc/h)     38 40 42 44 46 48 50 38 40 42 44 46 48 50 \u22121 \u22120.5 0 0.5 1 1.5 2 x (Mpc/h) y (Mpc/h)     38 40 42 44 46 48 50 38 40 42 44 46 48 50 3 3.5 4 4.5 5 5.5 6 6.5 7 x (Mpc/h) y (Mpc/h)     38 40 42 44 46 48 50 38 40 42 44 46 48 50 \u22121 \u22120.5 0 0.5 1 1.5 2 x (Mpc/h) y (Mpc/h)     38 40 42 44 46 48 50 38 40 42 44 46 48 50 3 3.5 4 4.5 5 5.5 6 6.5 7 Fig. 3.\u2014 The top-left panel shows a slice of gas surface density in units of the mean gas surface density at z = 2.6 of size 50 \u00d7 50(Mpc/h)2 comoving and a depth of 3.125Mpc/h comoving. The C IV absorption lines are indicated by black asterisks, produced by sampling the slice using 8000 random lines of sight. The O VI absorption lines are indicated by black circles. The top-right panel shows a zoom-in slice of the gas density of size 12.5 \u00d7 12.5(Mpc/h)2 comoving and a depth of 3.125Mpc/h comoving, corresponding to the lower right corner of the top-left panel, while the bottom two panels show the corresponding gas temperature in Kelvin and gas metallicity in solar units. \u2013 12 \u2013 Figure 3. Comparing the density structures in runs with (middle left panel) and without (bottom left panel) GSW we see that the e\ufb00ect of GSW on the overall appearance of largescale density structure is visually non-striking and the \ufb01lamentary skeleton of the large-scale density distribution remains intact. An important and visually discernible e\ufb00ect of GSW is to \u201csmooth\u201d out density concentrations in the dense (red) knots: the high density peaks (> 102; red regions) in the run without GSW are substantially higher than those with GSW; examples include the knots at (47, 41)Mpc/h, (45.5, 42.5)Mpc/h and (42, 40)Mpc/h. This e\ufb00ect is of course re\ufb02ective of the sensitivity on GSW of the SFR history, which in turn allowed the observations of SFR history to provide a powerful constraint on GSW, as shown earlier in Figure 1. The e\ufb00ect of GSW on low density (blue) regions seems small, likely because GSW do not reach there and/or become weak even if reaching there. The e\ufb00ect of the GSW on intermediate regions, a.k.a, \ufb01laments, is most easily seen by comparing the temperature distributions of the run with (middle right) and without (bottom right) GSW. We see that large-scale gravitational collapse induced shocks at this redshift tend to center on dense regions with a spatial extent that is not larger than about 100\u2212300kpc/h; these are virialization and infall shocks due to gravitational collapse of high density peaks. Some of the larger peaks are seen to be enclosed by shocks of temperature reaching or in excess of 107 K (note that the displayed picture is inevitably subject to smoothing by projection thus the higher temperature regions have their temperatures somewhat underestimated). Galaxies form in the center of the \ufb01lamentary structures where collapse of pancake structures occurs. Most of the shock heated volume from green (105K) to red (107K) are clearly caused by GSW, because they appear prominent only in the simulation with GSW. The GSW shock heated IGM seems to extend as far as \u223c0.5Mpc/h from galaxies. The temperature of this shock heated gas falls in the WHIM temperature range of 105 \u2212107 K; we will discuss this more quantitatively in \u00a73.2. Inspecting the temperature (middle right) and metal density (top right) distribution with GSW reveals that metal enriched regions, \u201cmetal bubbles\u201d, coincide with temperature bubbles. This indicates that GSW energy and metal deposition are tightly coupled. Most of the a\ufb00ected regions have a size of a few hundred kiloparsecs to about one megaparsec, suggesting that this is the range of in\ufb02uence of GSW in transporting most of the metals to the IGM. We now inspect visually typical physical locations of C IV and O VI absorption lines, shown as asterisks (C IV ) and circles (O VI ) in the top two rows in Figure 3. The interesting feature is that C IV and O VI absorbers tend to avoid \u201cvoids\u201d and are almost exclusively located around \ufb01lamentary structures with most of them seemingly residing in regions of an overdensity of \u223c3 \u221230; however, limited resolution of our simulation prevent us from reaching \ufb01rm conclusion on this at this time. For every C IV absorber that is produced, there is almost always an O VI absorber along the same line of sight. As we will see, all these paired-up C IV and O VI in fact arise from around the same regions in space. The converse \u2013 13 \u2013 is not necessarily true; a lower fraction of O VI absorbers do not have C IV counterparts within the depth of the projected slice of 3.125Mpc/h comoving and they tend to be located in regions that are slightly further away from high density peaks than those occupied by O VI lines with associated C IV lines. The vast majority of both C IV and O VI absorbers appear to be located in regions that have been swept by feedback shocks, as evidenced by the similarly looking shock heated temperature bubbles (middle right panel of Figure 3) and metal enriched bubbles emanating from collective supernovae in star-forming galaxies (upper right panel of Figure 3). The C IV and O VI lines, either collisionally ionized or photoionized, unequivocally stem from regions that are shock heated and metal enriched by feedback from star formation; this conclusion will be con\ufb01rmed quantitatively later. The typical metallicity and temperature of the C IV and O VI absorbers appear to be around [C/H] \u223c\u22122 and T \u223c104.5\u22125.5K. Typical Ly\u03b1 forest clouds have comparable densities but are at a signi\ufb01cantly lower temperature, T \u223c104K and a lower metallicity [C/H] \u223c\u22123. These properties indicate that, while most of the C IV and O VI absorption lines may have comparable overdensity compared to typical hydrogen Ly\u03b1 forestabsorption lines (NHI \u223c1013 \u22121015), the former are located in somewhat hotter regions with somewhat higher metallicity than the latter. Moreover, while many C IV and O VI lines often coincide along the same line of sight within a short distance, it will be shown that the actual gas properties of regions that produce them are signi\ufb01cantly di\ufb00erent. Let us now examine the physical properties of C IV and O VI absorbers in greater detail. Figures 4,5,6 show three random sightlines through the simulation box. In order to better see details we have concatenated all the zoomed-in regions around identi\ufb01ed C IV and O VI lines for each sightline to one panel, separated into columns. The left panels are for C IV lines and right for O VI lines. Several interesting properties of C IV and O VI absorbers may be gleaned. First, both C IV and O VI absorbers sit in regions with signi\ufb01cantly elevated temperature (i.e., > 2\u00d7104K) of widths of \u223c100km/s or larger, i.e., a few hundred physical kiloparsecs or larger, which are then connected with the general photo-ionized IGM of lower temperature of \u223c104K (2nd row from top in Figures 4,5,6). The density structures (top row in Figures 4,5,6) show that the densities in the regions of allevated temperatures span a wide range from \u03b4 \u223c0 to \u223c100 and there is no clear positive correlation between density and temperature (although there is a strong anti-correlation between them near density peaks). This suggests that the elevated temperatures in these regions are not caused by gravitational compression. It is also clearly seen that at the two locations demarcating each high temperature region, there is a shock-like density jump (of a factor of a few). A closer examination of the peculiar velocity structures (2nd panel from bottom in Figures 4,5,6) shows evidence of a double shock propagating outward, with the shock fronts coincidental with the temperature and density jump. Second, there is a tight correlation between gas temperature and gas metallicity (middle \u2013 14 \u2013 Fig. 4.\u2014 shows the physical properties of all C IV absorption lines (left) and O VI absorption lines (right) with column greater 1012cm\u22122 along a random line of sight of length equal to the simulation boxsize of 50\u22121Mpc at z = 2.6. Small regions around of all identi\ufb01ed C IV lines along each sightline are shown in separate columns. Aside from the \ufb02ux distribution shown at the bottom panel in velocity (Hubble) space, all other panels of physical variables are shown in real space. Each identi\ufb01ed C IV absorption line in the bottom panel is indicated by a shaded region with the value of the log of its column density. The corresponding physical location that produces the line is shown by a shaded vertical line with dark shades indicating larger contributions to the column of the line. \u2013 15 \u2013 Fig. 5.\u2014 this is similar to Figure 4 but for another random line of sight. \u2013 16 \u2013 Fig. 6.\u2014 this is similar to Figure 4 but for another random line of sight. \u2013 17 \u2013 row in Figures 4,5,6) in the sense that higher temperatures have higher metallicity and each region with elevated temperature is bordered by a synchronous drop in both temperature and metallicity on two sides. This is a strong indication that the elevated temperature is caused by a double shock originating from a alaxy or small group of galaxies due to GSW, which plays the double role of both shock heating the surrounding IGM and metal-enriching it. To reiterate this important point, C IV and O VI absorbers are located in regions that have been swept through by metal-enriched feedback shocks, which are still propagating outward and \u201cseparate\u201d the C IV and O VI absorbers from the general IGM of temperature T \u223c104K by about 100km/s or more. Because of the high temperatures probed by C IV and O VI lines, they are not in general correlated with Ly\u03b1 lines on scales \u2264100km/s. The latter probe typically lower temperatures. Overall, the locations of C IV and O VI lines are closely correlated. The overall spatial extent of O VI lines, in terms of their distance from galaxies, are somewhat larger than that of C IV lines, as seen in Figure 3 and Figures 4,5,6 and will be veri\ufb01ed by their origin being in somewhat lower density gas than C IV lines (see Figure 9 below). Third, many C IV absorbers appear to be paired up with O VI absorbers. For brevity, our convention is that we count absorption lines from left to right in each panel. For example, the \ufb01rst and fourth O VI lines in the right panel can be respectively paired up with the \ufb01rst and third C IV lines in the left panel of Figure 4; the \ufb01rst, third and fourth O VI lines in the right panel can be respectively paired up with the \ufb01rst, second and third C IV lines in the left panel of Figure 5; the second and \ufb01fth O VI lines in the right panel can be respectively paired up with the second and third C IV lines in the left panel of Figure 6. The O VI lines that appear together with C IV lines seem to have relatively low temperature (T \u223c104.5 \u2212105K), probably with a signi\ufb01cant photoionization component. Note that collisional ionization makes maximum contribution to O VI production at T = 105.5K, whereas for C IV this happens at T = 105.0K. Thus, it appears that relatively low-temperature O VI lines are often paired up with a C IV line, for which both photoionization and collisional ionization may be relevant. The excess of O VI lines compared to the number of C IV lines is likely due to the di\ufb00erence in the number of collisionally ionized cases for the two lines, given the di\ufb00erence in the optimal temperatures for collisional ionization for C IV and O VI lines. Note that with collisional ionization alone, the abundance of each species drops when the temperature moves away from the optimal temperature to either side (lower or higher) a factor of \u223c10 drop when temperature di\ufb00ers from the optical temperature by a factor of two. Roughly speaking, while the probability of an associated O VI line for a given C IV line is close to unity, the probability of an associated C IV line for a given O VI is somewhat lower. A more detailed study of this issue will be performed in sections to come. Finally, in Figure 7 we show a close-up view of several randomly chosen C IV lines. It is clear that the regions contributing to a C IV line tend to be centered or nearly centered on a local density peak along the line of sight, which almost always corresponds to a trough \u2013 18 \u2013 Fig. 7.\u2014 shows a close-up view of the region around each C IV line in real space, where the physical size along the line of sight has been translated to velocity using \u2206v = H(z)\u2206x. Each tickmark is 10 km/s. \u2013 19 \u2013 Fig. 8.\u2014 shows a close-up view of the region around each O VI line in real space, where the physical size along the line of sight has been translated to velocity using \u2206v = H(z)\u2206x. Each tickmark is 10 km/s. \u2013 20 \u2013 in temperature. It is also evident that the spatial extent of the C IV producing region is limited to about up to 10 km/s, corresponding to about comoving 100kpc/h, with some regions much narrower than that. As a consequence, even though the velocity gradients in the intermediate vicinities (i.e., the whole surrounding region of elevated temperature) of C IV -producing regions are often large (with dv/dr \u223ca few 100 km/s per comoving Mpc), the velocity gradients in the actual C IV -producing regions is smaller, which, in conjunction with the narrowness of the C IV -producing region, limits the velocity contribution to the Doppler width, as will be shown quantitatively later. Physically, this tells us that each C IV absorber tends to arise primarily from a narrow region in real space that have previously thermalized through feedback shocks, have cooled and are presently relatively quiescent. There does not appear to be a visible correlation between the LOS size of C IV lines and the column density; some of the high column C IV lines shown (the second and fourth panel from left) appear to come from very narrow regions of size \u226a100kpc comoving which appear to have very steep velocity gradients (for example, the fourth from left line with log of column equal 14.46). The C IV lines are mostly intergalactic in origin, not from inside galaxies. We next examine several randomly chosen O VI lines in close-up shown in Figure 8 and make detailed comparisons of the physical properties with C IV lines, when possible. We note three points. First, in Figures 4,5,6 we noted that most C IV lines (\u22651013.5) have associated O VI lines that have comparable column densities. This indicates that both C IV and O VI lines of relatively high column (\u22651013.5) tend to arise in regions in or near density peaks and temperature troughs. Second, a typical O VI line tends to have a lower column density due to a steeper column density distribution of O VI lines (see Figure 15 below). Third, O VI lines often lie in regions that are o\ufb00set from density peaks by \u223c10 \u2212100 km/s, and often these density peaks do not have corresponding temperature troughs. This is clear evidence that many, lower column O VI lines arise from regions that are not physically bound and instead they are mostly transient, stemming from density and temperature \ufb02uctuations in shock heated regions in the neighborhood of galaxies. It may be that the steeper column density distribution for O VI lines has its origin in the abundance of these more transient structures. The low density, shock heated regions may have temperatures that are too high to produce equally abundant C IV lines in conjunction with a lower abundance of carbon than oxygen. We now quantify the properties of C IV and O VI absorbers by di\ufb00erent projections through the multi-dimensional parameter space spanned by several fundamental physical variables. Figure 9 shows the distribution of gas overdensity for C IV (left) and O VI absorbers (right) at six di\ufb00erent redshifts, z = (0, 0.5, 1.5, 2.6, 4, 5). First, a comparison of the three histograms for three subsets of C IV and O VI absorbers in each panel indicates that higher column C IV and O VI absorbers are produced, on average, by higher density gas. Second, there is a clear trend that C IV absorbers trace increasingly more overdense regions with decreasing redshift. For example, while the location of the vast majority of \u2013 21 \u2013 Fig. 9.\u2014 Left panel shows the distribution of gas overdensity of regions that produce the CIV absorption lines at six di\ufb00erent redshifts, z = 0, 0.5, 1.5, 2.6, 4, 5, separately for three subsets of lines of column density in the range of logNC IV cm2=[12,13],[13,14],[14,15], respectively. Right panel shows the counterpart for O VI absorption lines. C IV absorbers with log(NC IV cm2) = [12, 13] appears to be outside virialized regions (i.e., overdensity less than about 100) at z > 2.6, a signi\ufb01cant fraction of them reside in virialized regions at z < 1.5; the same is true for higher column O VI absorbers. A comparison to O VI absorbers reveals a striking contrast: the vast majority of O VI absorbers with log(NC IV cm2) \u226414 are located outside virialized regions at all redshifts. In addition, typical O VI lines arise from somewhat lower density regions than C IV lines. For example, for O VI absorbers of log(NC IV cm2) = [12, 13], the typical overdensity peaks at \u03b4 \u223c5 for O VI absorbers versus \u223c10 for C IV lines at z = 2.6 \u22125, which jumps to \u03b4 \u223c10 for O VI absorbers versus \u223c50 for C IV absorbers at z = 1.5. A more quantitative analysis of the cross correlation between C IV and O VI absorption lines and galaxies will be presented in a later paper. Figure 10 shows the distribution of gas metallicity for C IV (left) and O VI absorbers (right) at six di\ufb00erent redshifts, z = (0, 0.5, 1.5, 2.6, 4, 5). We see that C IV absorption lines arise from gas with a wide range of metallicity from [C/H]=-3 to -0.5, peaked approximately around -2.5 to -1.5 at z > 0.5. At z > 2.6 the distribution for O VI lines is roughly like taking the left end of each corresponding C IV distribution and squeezing the whole distribution rightward by an amount of \u223c0.5 \u22121.0. So the metallicity distributions for O VI absorbers are generally cut o\ufb00at a higher metallicity than those for C IV absorbers at the low end by about 0.5 \u22121.0 and peak at a metallicity that is higher by this factor. The situation appears to start reversing at z = 1.5 such that at z < 0.5 the fraction of high metallicity C IV absorbers exceeds that of O VI absorbers. What is also interesting is that the typical metallicity of C IV and O VI lines displays a non-monotonic trend at a \ufb01xed column density. \u2013 22 \u2013 Fig. 10.\u2014 The left panel shows the distribution of gas metallicity in solar units of regions that produce the CIV absorption lines at six di\ufb00erent redshifts, z = 0, 0.5, 1.5, 2.6, 4, 5, separately for three subsets of lines of column density in the range of logNC IV cm2=[12,13],[13,14],[14,15], respectively. Right panel shows the counterpart for O VI absorption lines. For O VI absorbers, at z = 4\u22125 the metallicity of O VI lines with log(NO V I cm2) = [12, 14] peaks at [Z/ Z\u2299] = \u22121.5 to \u22121.0, which moves to a lower value of [Z/ Z\u2299] = \u22122.0 to \u22121.5 at z = 2.6, then slightly moves back up to [Z/ Z\u2299] \u223c\u22121.5 at z = (1.5, 0.5, 0). For comparison, the overall behavior for C IV lines is as follows: the metallicity of C IV lines with log(NC IV cm2) = [12, 14] peaks at Z = \u22122.0 to \u22121.5 at z = 5, at [Z/ Z\u2299] \u223c\u22122 at z = 4, followed by a very broad distribution peaking at Z = \u22122 to \u22121 at z = 1.5 to z = 2.6 with a larger fraction reaching a relatively high metallicity gas with [Z/ Z\u2299] > \u22121. The overall trend in metallicity evolution with redshift for the C IV and O VI absorbers could be understood as follows. Let us \ufb01rst note that the ionizing radiation background at z = 4, 5 is about (1/3, 1/30) of that z = 2.6, which in turn is larger than that at z = (1.5, 0.5, 0) by a factor of \u223c(2, 7, 30). At z = 4 \u22125 both C IV and O VI absorbers are predominantly collisionally ionized with the temperatures peaking at 105K and 105.5K, respectively, as shown below in Figure 11. These regions are relatively closer to galaxies, from which metal-carrying shocks originate and have relatively high metallicities. At lower redshift z = 2.6 larger regions around galaxies have been enriched with metals and the rise of the ionizing radiation background produces a large population of photoionized C IV and O VI lines at lower temperature and lower metallicity. Towards still lower redshift z < 1.5, the decrease of the mean gas density in the universe demands a rise in overdensity of the O VI -bearing gas in order to produce a comparable column density, causing a shift of these regions to be closer to galaxies where both metallicity and density are higher, seen in Figure 9. \u2013 23 \u2013 The combination of lower density (Figure 9) and higher metallicity (Figure 10) for the typical (low) column density O VI absorbers compared to C IV absorbers is reminiscent of metal-carrying shocks propagating through inhomogeneous medium, exactly the situation one would expect of the feedback shocks from galaxies entering the highly inhomogeneous IGM. Given the widespread steep density gradients (steeper than \u22122) in regions just outside the virial radius of galaxies, these shocks could not only heat up lower density regions to higher temperatures but also enrich them to higher metallicity. The feedback shocks generically propagate in a direction that has the least resistance and is roughly perpendicular to the orientation of a local \ufb01lament where a galaxy sits, as seen clearly in Figure 3 and shown previously (e.g., Theuns et al. 2002b; Cen et al. 2005). While higher density regions, on average, tend to have higher metallicity (as we will show later), the dispersion is su\ufb03ciently large that the reverse and other complex situations often occur in some local regions. This appears to be what is happening here, at least for some regions that manifest in C IV and O VI lines. Fig. 11.\u2014 Shows the distribution of gas temperature of regions that produce the C IV absorption lines at six di\ufb00erent redshifts, z = 0, 0.5, 1.5, 2.6, 4, 5, separately for three subsets of lines of column density in the range of logNC IV cm2=[12,13],[13,14],[14,15], respectively. Right panel shows the counterpart for O VI absorption lines. Figure 11 shows the distribution of gas temperature for C IV (left) and O VI (right) absorbers. We see that the temperatures of C IV absorbers at z = 5 and O VI absorbers at z = 4 \u22125 narrowly peak at 105K and 105.5K, respectively, suggesting that collisional ionization makes the dominant contribution to both species and the two types of absorbers arise from di\ufb00erent regions. The rapid drop in the amplitude of the UV radiation background beyond z = 3 and increase in gas density with (z + 1)3 is the primary reason for diminished component of photoionized C IV and O VI absorbers at these high redshifts. At redshift z < 2.6 the distributions for the two absorbers become progressively broader ranging from \u2013 24 \u2013 104.3K to 105.5K for C IV absorbers, and from 104.3K to 106K for O VI absorbers. Thus, at z < 2.6 both C IV and O VI absorbers are a mixture of photoionized and collisionally ionized ones. For both C IV and O VI lines, while the temperature distributions of O VI lines at z < 2.6 are broad, there is no signi\ufb01cant segregation in temperature of lines of di\ufb00erent column densities. Recall that there is a noticeable correlation between column density and overdensity for both O VI lines and C IV lines (Figure 9). This is likely indicative of complex, inhomogeneous nature of metal enrichment process around galaxies. Fig. 12.\u2014 The left panel shows the column density-weighted distribution of C IV lines in the overdensity-temperature plane at six di\ufb00erent redshifts, z = 0, 0.5, 1.5, 2.6, 4, 5. Right panel shows the counterpart for O VI absorption lines. Figure 12 displays the distribution of C IV (left) and O VI (right) absorbers in the overdensity-temperature plane at redshift z = 0, 0.5, 1.5, 3, 4, 5. We again see relatively narrow peaked temperature distribution at redshift z = 4 \u22125 for O VI absorbers, whereas at the same redshifts the C IV absorbers have a relatively broader temperature distribution. Towards lower redshift there appears to be a multi-modal distribution in temperature for C IV absorbers, with the lower temperature peak at T \u223c104.2\u22124.5K being progressively more important with decreasing redshift and becoming dominant by z = 0. The lower temperature peak is photoionized. At redshift z = 1.5 \u22122.6 a higher temperature peak at T \u223c104.5\u22124.8K is dominant, which is likely a mixture of collisional and photoionization. It is interesting to note that at z = 2.6 the radiation background is high enough to allow for the existence of a small peak at (\u03b4 \u2265200, T = 104.2K) for C IV absorbers, clearly arising from gas that is within virialized regions. At redshift z = 0 \u22120.5 the peak at T \u223c104.5\u22124.8K is still prominent. But, another peak at still higher temperature of T \u223c105.0\u22125.2K emerges, which is likely dominated by collisional ionization. Overall, the composition of C IV absorbers changes from being dominated by collisional ionization at z = 4 \u22125, through a mixture of collisional and photoionization at z = 1.5 \u22122.6, to being dominated by photoionization by z = 0. The distinct high temperature peak at T \u223c105K and density \u03b4 \u223c20 at z = 0 \u2013 25 \u2013 is rooted in the Warm-Hot Intergalactic Medium (WHIM; Cen & Ostriker (1999b); Dav\u00b4 e et al. (2001); Cen & Ostriker (2006)), where the intergalactic medium has been heated up by gravitational shocks due to the formation of the large-scale structure. A similar progression from mainly collisionally ionized to a mixture of collisional and photoionization for O VI absorbers is also seen. However, for O VI absorbers, the photoionization peak at T \u2264105K never dominates at any redshift. For both C IV and O VI absorbers there is no visible correlation between overdensity and temperature for O VI absorbers at all redshifts. For example, there is no evidence of these regions obeying the so-called equation of state (Hui & Gnedin 1997) that is applicable to low redshift Ly\u03b1 forest clouds. This just reinforces the statement that these regions are shock heated, in a dynamical state and perhaps transient, and do not resemble photo-heated Ly\u03b1 forest region. We have also plotted (not shown) the distribution of C IV and O VI absorbers in the overdensity-metallicity plane and \ufb01nd no visible correlation between them. Fig. 13.\u2014 Left panel shows the distribution of Doppler width of computed CIV absorption lines at six di\ufb00erent redshifts, z = 0, 0.5, 1.5, 2.6, 4, 5, separately for three subsets of lines of column density in the range of logNC IV cm2=[12,13],[13,14],[14,15], respectively. Right panel shows the distribution of the parameter \u03b7 at four di\ufb00erent redshifts, z = 1.5, 2.6, 4, 5, separately for three subsets of lines of column density in the range of logNC IV cm2=[12,13],[13,14],[14,15], respectively. We note that \u03b7 = 1 corresponds to a Doppler width that is 100% thermally broadened, whereas \u03b7 = 0 corresponds to a Doppler width that has no thermal contribution. The left panel of Figure 13 shows the distribution of Doppler width of computed C IV absorption lines. The Doppler width distributions generally peak at 10 \u221220km/s at all redshifts. Such a Doppler width peak is consistent with thermal broadening by gas temperature T \u223c104.5 \u2212105K as seen Figure 11. Because of the di\ufb00erent de\ufb01nition of absorption lines we use compared to Voigt pro\ufb01le \ufb01tting procedure for obtaining lines observationally, \u2013 26 \u2013 a direct comparison is not possible. Nonetheless, our results are consistent with the Doppler widths of the CIV absorber sample in Danforth & Shull (2008), the mean Doppler parameter at \u27e8z\u27e9= 0.06 is \u27e8bC IV \u27e9= 23 \u00b1 13, while for our whole sample at z = 0, the mean is \u27e8bC IV \u27e915.6\u00b17.1 (1\u03c3 interval). Comparisons to other samples, such as the one in Boksenberg et al. (2003), are di\ufb03cult. The reason for this is that it is common in observational investigations to \ufb01t a several number of components (with a Gaussian velocty distribution each) to each absorption line. This \u201ccomponent\u201d vs. \u201csystem\u201d de\ufb01nition makes comparisons between our work and observations subtle at least. Our de\ufb01nition of an absorber by establishing a \ufb02ux threshold more closely resembles the standard de\ufb01nition of a \u201csystem\u201d, and in general we limit our comparisons to observational samples of \u201csystems\u201d. Using this method, a large number of \u201ccomponentes\u201d might be \ufb01tted to one \u201csystem\u201d. In the sample of Boksenberg et al. (2003), this is as large as 32 components for one given system at z = 2.438; on average, there are 4.8 \u201ccomponents\u201d per \u201csystem\u201d in this sample ranging between 1.6 < z < 4.4. The right panel of Figure 13 characterizes the nature of the Doppler width of computed C IV absorption lines using parameter \u03b7 \u2261 q 2kT mionb2. It is indeed seen that most of the lower column density C IV absorbers with log(NC IV cm2) = [12, 13] are dominated by thermal broadening. However, for higher column C IV absorbers, there appears to be roughly equal contributions to the Doppler width from thermal broadening and bulk velocity broadening. What this suggests is that lower column C IV absorbers tend to lie in quiescent regions, whereas high column ones typically reside in regions with signi\ufb01cant velocity structures. This was seen earlier in Figures 4, 5, 6. Once again, it is important to stress that, even though the relative contribution to the line width from velocity structure is moderate for most C IV lines, the most likely physical explanation for the C IV producing regions is that they were shock heated by sweeping feedback shocks originating from nearby galaxies, have cooled to about 104.5 \u2212105K and perhaps somewhat compressed in the process. Most C IV lines are far from shock fronts, whose velocity structures would otherwise make the lines signi\ufb01cantly wider. Rauch et al. (1996) suggested that the quiescence of C IV lines may be due to the adiabatic compression of gas, which would not produce large velocity gradients. We show that this explanation may be incorrect given that most of the regions producing C IV lines at z > 2 lie outside virialized regions. Rather, the quiescence is due to a combination of two things: the thermalization of previous shocks that reduces the random velocities and velocity gradients, and the narrow range of the region in physical space that produces the C IV line, which limits the velocity di\ufb00erence. The left panel of Figure 14 shows the distribution of Doppler width of computed O VI absorption lines. For the OVI absorber sample of Danforth & Shull (2008), the mean Doppler parameter at \u27e8z\u27e9= 0.06 is \u27e8bO V I \u27e9= 30\u00b116, while for our whole sample at z = 0, the mean is \u27e8bO V I \u27e922 \u00b1 13 (1\u03c3 interval is quoted in both cases). In Thom & Chen (2008a), Voigt pro\ufb01le \ufb01tting yields a mean number of \u223c1.4 \u201ccomponents\u201d in 27 absorbers along 16 lines-of\u2013 27 \u2013 Fig. 14.\u2014 Left panel shows the distribution of Doppler width of computed O VI absorption lines at four di\ufb00erent redshifts, z = 1.5, 2.6, 4, 5, separately for three subsets of lines of column density in the range of logNO V I cm2=[12,13],[13,14],[14,15], respectively. Right panel shows the distribution of the parameter \u03b7 at four di\ufb00erent redshifts, z = 1.5, 2.6, 4, 5, separately for three subsets of lines of column density in the range of logNO V I cm2=[12,13],[13,14],[14,15], respectively. We note that \u03b7 = 1 corresponds to a Doppler width that is 100% thermally broadened, whereas \u03b7 = 0 corresponds to a Doppler width that has no thermal contribution. sight towards QSOs, with a mean redshift of \u223c0.25 and a corresponding Doppler width and 1\u03c3 of \u27e8bO V I \u27e9= 27\u00b117. Thus, within the errorbars our results agree with both observations. A comparison with C IV lines shown Figure 13 is instructive. First, while the distributions for C IV and O VI lines of logNO V I cm2=[12,13] peak at comparable b \u223c10 km/s at z = 1.5 and z = 2.6, suggesting limited velocity contribution to the widths of both lines, the distribution for O VI lines peaks at b \u223c20 km/s at z = 4 \u22125, signi\ufb01cantly higher than that of C IV lines at the same redshifts. This is indeed to be expected: the ratios of C IV and C (fC IV ) and of O VI and O (fO V I ) have a di\ufb00erent dependence on density and temperature. At these densities and high temperatures, fC IV increases with increasing density, whereas fO V I decreases with increasing density. So If you are looking for broad lines, you will in C IV have an advantage going to high-z (where physical gas densities are higher), but not in O VI . Second, it is clear that a signi\ufb01cant larger fraction of higher column O VI lines of logN cm2=[13,15] have larger Doppler width with b \u226540 km/s at all redshifts than C IV lines, suggesting that there are signi\ufb01cantly more O VI lines that C IV lines that are in dynamically hot regions, such as around shocks where velocity gradients are high. Since these dynamically hot regions likely also have higher temperatures, collisional ionization would make a larger contribution to O VI lines than C IV lines, consistent with our earlier statements. Third, let us take a close look at \u03b7 distribution for log(NO V I cm2)=[13,14] O VI lines and compare to that of C IV in Figure 13: for O VI lines it appears that the velocity contribution to the Doppler width is highest (i.e., lowest \u03b7) at z = 2.6, whereas for C IV lines \u2013 28 \u2013 that occurs at z = 4, suggesting that the fraction of C IV that are in dynamically hot regions peaks at a higher redshift than that for O VI lines. This is intriguing and likely due to a combination of several factors, including the evolution of the mixture of photoionized and collisionally ionized absorbers, evolution of metal enrichment and feedback shock strengths as a function of redshift. Potentially, useful and quantitative measures may be constructed to probe feedback processes using C IV , O VI and other lines jointly. Fig. 15.\u2014 Left panel: the computed column density distribution for the C IV absorption line at z = 2.5 for runs \u201cM\u201d (\ufb01lled black circles), \u201cMR\u201d (open circles) and \u201cM2\u201d (\ufb01lled grey circles). The solid line is the best power-law \ufb01t to our simulated results from run \u201cM\u201d performed for column densities in the range [13, 14.5]. The slope of the \ufb01t is \u22121.196 \u00b1 0.028. Diamonds are observational data from Songaila (2005) and Boksenberg et al. (2003) at a mean redshift of 2.7 and 2.6, respectively, corrected for our cosmology. Right panel: the computed column density distribution for the O VI absorption line at z = 2.5 is shown as the solid line, which is the best power-law \ufb01t to our simulated results, with slope \u22121.723\u00b10.075. The circles have the same meaning as in the left panel. The observational data are drawn from Carswell et al. (2002) (squares), Bergeron & Herbert-Fort (2005) (diamonds), and Simcoe et al. (2002)(triangles) corrected for our cosmology. 3.2. C IV And O VI Absorbers As Baryonic Matter Reservoirs Having gained a good understanding of the physical nature of C IV and O VI lines, we now turn to their overall column density distributions at z = 2.5, where observational data is most accurate, shown in Figure 15. For both C IV and O VI , the results obtained from runs \u201cM\u201d, \u201c\u2019MR\u2019 and \u201cM2\u201d show some small di\ufb00erence that is smaller than the magnitude of the di\ufb00erence between di\ufb00erent observational studies and comparable to the di\ufb00erence between simulations and observations. This shows that our simulations are reasonably converged and \u2013 29 \u2013 not too sensitive to a factor 2 or so variation in the strength of the UV backgrond. It is noted, however, that the convergence becomes much better for clouds with column density greater than 1013, indicating that our current simulation resolution probably still somewhat underestimates the abundance of clouds with columns smaller than that. The error bars are not visible for the simulated values because they lie within the symbols plotted. Overall, we \ufb01nd the agreement of the computed distributions from the simulation to the observed ones is at the level that we could have hoped for. We believe that di\ufb00erences may be contributable in part to cosmic variance, in part to our resolution at the lower column density (as evidenced by the noticeable \ufb02attening) and in part due to di\ufb00erent methods of identifying clouds (\ufb02ux thresholding in our case versus Voigt pro\ufb01le \ufb01tting in the observed results, with the latter often producing multiple components for a single physical system). Given the fact that our simulation has essentially only one free parameter (eGSW) that has already been signi\ufb01cantly constrained by the SFR history of the universe, it is really remarkable that we are able to match the observed column density distribution of both C IV and O VI lines to within a factor of 2-3. Since the regions probed by C IV lines and O VI lines are often physically di\ufb00erent and to some extent re\ufb02ect the di\ufb00erent stages of the evolution of the feedback shocks, the fair agreement between our simulations and observations suggests that our treatment of the feedback process provides a good approximation to what happens in nature in terms of heating and enriching the IGM, and it is indirect but strong evidence that feedback from star formation plays the central role in enriching the IGM with its energy and metals. No additional, signi\ufb01cantly energetic feedback from AGN seems required to account for the enrichment history of the IGM. Therefore, it is very encouraging to note that the overall picture of the process of star formation feedback may be jointly probed by C IV , O VI lines and other diagnostics. Detailed comparisons between simulations and observations in that regard would be the next logical step to further constrain theories of overall star formation in galaxies and feedback. In Figure 16, we show the evolution of the abundance of absorbers for di\ufb00erent subsets of column densities (top panels) and the evolution of log(f(N)) (bottom panels). The number of C IV absorbers per unit redshift pathlength decreases with increasing redshift at both the low redshift interval z \u223c0 \u22122 and the high redshift interval z > 4 but stays roughly constant in the redshift interval z \u223c2 \u22124. For O VI absorbers, the number of absorbers per unit redshift pathlength decreases monotonically with increasing redshift for absorbers with column densities in the intervals logNcm2 =[12,13],[13,14]. There are substantially fewer O VI absorbers in the high column density range and their number peaks around z \u223c1 \u22122. Comparing C IV and O VI absorbers at each column density interval, we see that at logNcm2 =[14,15] C IV and O VI absorbers have comparable numbers at z \u22651, but C IV absorbers outnumber O VI absorbers by z = 0 by a factor of a few, due to an upturn in C IV absorber number versus a downturn in O VI absorber number from z = 1 to z = 0. This is probably caused by a combination of the rapidly diminished star formation activity \u2013 30 \u2013 Fig. 16.\u2014 Top left panel: the evolution of the abundance of C IV absorbers separately for three subsets with column density in the range logNC IV cm2=[12,13],[13,14],[14,15], respectively. Top right panel: the same for O VI absorbers. Bottom left panel: column density distribution (logf(N)) for C IV absorbers at z = 0, 0.5, 1, 2.6, 4, 5. The results for our runs \u201cM\u201d (\ufb01lled black circles), \u201cMR\u201d (open circles) and \u201cM2\u201d (\ufb01lled grey circles) are shown. Open diamonds correspond to observations (Songaila 2001) corrected for our adopted cosmology, except at z=2.6, when they correspond to Songaila (2005). At z = 2.6 and z = 4, asterisks correspond to Boksenberg et al. (2003) for 3 and 1 sightline respectively in a 0.5 redshift interval around the mean redshift. At z = 0, the observational data correspond to Danforth & Shull (2008) (triangles) and Thom & Chen (2008a) (asterisks). Bottom right panel: logf(N) for O VI absorbers at z = 0, 0.5, 1, 2.6, 4, 5. Observational data is available at redshift z = 2.5: Carswell et al. (2002) (squares), Bergeron & Herbert-Fort (2005) (diamonds), and Simcoe et al. (2002)(triangles) corrected for our cosmology. At z = 0 we compare our results to Danforth & Shull (2008) (triangles). and a lower radiation background towards z = 0, which create an unfavorable condition for producing O VI absorbers in denser environments either collisionally or by photoionization. At logNcm2 = [12, 14] O VI absorbers outnumber C IV absorbers at all redshifts. From the lower panels we observe that the slope of log(f(N)) for C IV absorbers progressively becomes steeper at high redshifts. Our results seem to be consistent with observational results from Songaila (2005) and Boksenberg et al. (2003) at redshift z = 2.6 where observational data have the highest accuracy. We attribute the discrepancies at high column density between our simulations and observations to cosmic variance: the size of our box is not large enough to host the higher column density structures. At z = 4 \u22125 the agreement is not as good, where we produce a steeper slope for f(N) than observed; this is likely in part due to cosmic variance and in part due to an underestimated UV background used. \u2013 31 \u2013 What fraction of the metals in the IGM is directly seen in C IV and O VI absorbers? From the column density distribution of the absorbers, we can estimate the ion baryon density of the IGM. Two di\ufb00erent methods are typically used to do so. We can estimate \u2126ion from \u2126ion = H0mion c\u03c1c P i Ni,ion P \u2206X (1) where H0 is Hubble\u2019s constant today, mion is the mass of the considered ion, \u03c1c is the critical density, Nion is the absorber column density and P \u2206X accounts for the total redshift pathlength covered by the sample of sightlines. In a \ufb02at Friedmann universe, this quantity is given by X(z) = Z z 0 dz\u2032 (1 + z\u2032)2 [\u2126M(1 + z\u2032)3 + \u2126\u039b]1/2 (2) Another possibility is to construct the column density distribution per column density interval and unit \u2206X f(N) = P i Ni,ion \u2206N P \u2206X (3) where the sum in the numerator is carried on the column densities of the absorbers present in bin i and \u2206logN= 0.3 in our case. The distribution f(N) is typically \ufb01tted by a power-law f(N) = KN \u03b1. We can then obtain \u2126ion from the \ufb01t by \u2126ion = H0mion c\u03c1c Z Nmax Nmin Nf(N)dN (4) \u2126ion = 8\u03c0Gmion 3H0c K N \u03b1+2 \u03b1 + 2|Nmax Nmin (5) Following Becker et al. (2009) and Bergeron & Herbert-Fort (2005), we will integrate \u2126ion in the interval logN= [13, 15], but the \ufb01t will be performed in the interval logN= [13, 14.5] due to incompleteness of the sample at high values of N, as we have already mentioned. Figure 17 shows the evolution of the mass density contained in the C IV (left) and O VI (right) absorption lines, respectively. Considering the observational uncertainties and cosmic variance, it is very encouraging to see the excellent agreement between our simulated results and observations over the entire redshift range z \u223c2 \u22126, where comparisons may be made. As a new \ufb01nding from our simulation, we note that a signi\ufb01cant dispersion, i.e., cosmic variance, in \u2126CIV is expected for available data samples with limited size (i.e., pathlength). In the bottom panels of Figure 17 we show the expected distribution based on our simulations for various sample sizes. We \ufb01nd that with \u2206X = 30, the variance \u03c3 = 1.4 \u00d7 10\u22128 for C IV and 1.2 \u00d7 10\u22128 for O VI ; for \u2206X = 60, \u03c3 = 1.0 \u00d7 10\u22128 for C IV and 8.5 \u00d7 10\u22129 for O VI ; with \u2206X = 160, \u03c3 = 5.7 \u00d7 10\u22129 for C IV and 4.6 \u00d7 10\u22129 for O VI . Comparing C IV and O VI lines it is seen that the total amount of mass contained in the O VI line is comparable to that in the C IV line at all redshifts within a factor of 2 or so. Note that the size for \u2013 32 \u2013 Fig. 17.\u2014 Top left: redshift evolution of \u2126CIV from simulations: run \u201cM\u201d (\ufb01lled black circles), run \u201cMR\u201d (open circles) and run \u201cM2\u201d (\ufb01lled grey circles). Observational data are from Songaila (2005) (open diamonds), Becker et al. (2009) (arrows as limits), Pettini et al. (2003)(open triangle), Ryan-Weber et al. (2009) (\ufb01lled star), Boksenberg et al. (2003) (\ufb01lled upright triangles), Danforth & Shull (2008) (\ufb01lled downright triangle) and Simcoe (2006)(\ufb01lled square). The dashed curve is a simple physical model to explain the evolution of \u2126CIV (see text in \u00a73.2). Top right: redshift evolution of \u2126OVI. Observational data are from Carswell et al. (2002) (open square), Bergeron & Herbert-Fort (2005) (open diamond), Simcoe et al. (2002)(open triangle), Danforth & Shull (2008)(open star), Thom & Chen (2008b)(\ufb01lled triangle) and Frank et al. (2008) (lower limit, arrow). Bottom left: di\ufb00erent curves are the expected PDFs for \u2126CIV at z=2.6, based on our simulations, for observational samples of various sizes (i.e., \u2206X values). The solid vertical line indicates the median of the simulation results, whereas the vertical dashed line is Songaila (2005) value at z=2.5. Bottom right: the expected PDFs for \u2126OVI at z=2.6. The solid vertical line indicates the median of the simulation results, whereas the vertical dashed line is Simcoe et al. (2002) value at z=2.5. the observational sample of Songaila (2005) is \u2206X \u226420. Again, this suggests that some of the discrepancies between simulations and observations, and between observations may be accounted for by cosmic variance. For example, the slightly smaller value obtained from the observational sample of Songaila (2005) for \u2126CIV is statistically consistent with simulations within 0.5\u03c3; the slightly larger value obtained from the observational sample of Simcoe et al. (2002) for \u2126OVI is statistically consistent with simulations within 1\u03c3. In agreement with observations, the mass density contained in the C IV absorption line is, within a factor of two, constant from z = 1 to z = 4 and subsequently drops by a factor of \u223c(10, 20) by z = (5, 6). Some rather subtle di\ufb00erence between O VI and C IV lines may be noted. While the metal density contained in the C IV absorption line is nearly constant from z = 1 to z = 4, that plateau for the O VI line is attained only for z = 0\u22122. Because the \u2013 33 \u2013 total amount of metals in the IGM has increased signi\ufb01cantly in the redshift range z = 0\u22124, it seems that the near constancy of \u2126CIV at the redshift range z = 1 \u22124 and \u2126OVI at the redshift range z = 0\u22122 does not re\ufb02ect the amount of metals in the IGM, which has already been pointed out earlier by Oppenheimer & Dav\u00b4 e (2006). This probably re\ufb02ects a \u201cselection e\ufb00ect\u201d of C IV systems of the overall metals in the IGM, which may be due to a combination of several di\ufb00erent processes, including the evolution of the mean gas density as (1+z)3, the evolution of the overdensity of the regions that produce C IV lines, the density dependence of the IGM metallicity and its evolution, the evolution of the radiation background and hierarchical build-up hence gravitational shock heating of the large-scale structure. Our results contradict previous claims that observational data point towards a near constancy of \u2126CIV with redshift (e.g., Songaila 2001, 2005; Oppenheimer & Dav\u00b4 e 2006). However, more recent results have provided evidence of a downturn in \u2126CIV towards z \u223c6. Becker et al. (2009) \ufb01nd no C IV absorbers in 4 sightlines towards z \u223c6 QSOs. They set limits on \u2126CIV and attribute the downturn to a decline at least by a factor \u223c4.4 (to 95% con\ufb01dence) in the number of C IV absorbers at z = 5.3 \u22126 as compared to z = 2 \u22124.5. The decline shown in Figure 16 is higher, at least a factor of \u223c7 for low column densities absorbers. Ryan-Weber et al. (2009) perform the most extensive survey of intergalactic metals at z > 5, looking at the sightlines of 9 QSOs. They \ufb01nd evidence of a drop by a factor \u223c3.5 in the mass density of C IV from redshift z = 4.7 to z = 5.7. In comparison, we \ufb01nd a drop by a factor \u223c1.7 in \u2126CIV in the interval z = 5 \u22126. Fig. 18.\u2014 Left panel: the fraction of metals contained in C IV (circles) and O VI (squares) lines separately in terms of the overall amount of metals in the IGM at each redshift. Right panel: the fraction of metals contained in regions probed by C IV (circles) and O VI (squares) lines, respectively, in terms of the overall amount of metals in the IGM at each redshift. The second point, perhaps the most overlooked, is that the amount of metals contained in the C IV and O VI absorption line is a very small fraction of the overall metals. The left panel of Figure 18 shows the ratios of mass density measured in the C IV (diamonds) and \u2013 34 \u2013 Fig. 19.\u2014 shows the C IV ratio of nC IV /nC,tot (open circles) and the O VI ratio of nO V I /nO,tot (open squares) as a function of redshift. Note that at the optimal temperature with collisional ionization, fmax for C IV and O VI is 29% at log Tmax = 5.00 and 22% at log Tmax = 5.45, respectively (Sutherland & Dopita 1993). O VI lines (triangles) over the total amount of metals in the IGM as a function of redshift. We see that the amount of mass contained in the C IV line remains at \u223c0.13% within a dispersion of 40%, and at \u223c0.13% within a dispersion of 25% for the O VI line. In the right panel of Figure 18 we show the amount of metals probed by each line as a function of redshift. Here is how we compute the metals probed by each line and use C IV as an example. For each detected C IV line, a range of spatial locations (i.e., gas cells along the line of sight) contributes to its column density (see Figures 4,5,6). Roughly speaking, the amount of metals e\ufb00ectively probed by the C IV line will be larger than the metals directly seen in the C IV line by a factor of f = nC,tot/nCIV (a similar relation for the O VI line). This ratio f for the C IV and O VI line is shown in Figure 19. One point worth noting is that for C IV there is an upturn of f from \u223c0.1 at z < 2 towards high redshift, reaching again the same value at z = 6. This is caused from a transition from more collisionally dominated C IV absorber population at z > 4 to a more photoionization dominated one at intermediate redshifts. The trend for the O VI line is much less pronounced, indicative of a dominance of collisionally ionized O VI absorbers over the entire redshift range z = 0 \u22126, with a trend that it is more so at higher redshift. From the right panel of Figure 18 we see that, within a factor of 2, the amount of metals probed by either C IV or O VI line is roughtly 2%. Combining the fact that the majority of C IV -producing regions have not collapsed and virialized (see Figure 9) and a small fraction of all metals is probed by C IV and O VI lines at all redshifts, C IV and O VI absorbers are \u201ctransients\u201d; in other words, only a small fraction of metals in the IGM get \u201clit up\u201d as the C IV or O VI line at any given time. As we demonstrated earlier, these regions that produce C IV absorption lines have a set of properties that seem to be created by a combination of \u2013 35 \u2013 physical processes including feedback shock heating and radiative cooling (see Figures 4,5,6). These close observations suggest that only a fraction of metals at any given time that has recently passed through shocks and cooled to an appropriate temperature shows up as C IV absorption lines. In this sense, C IV absorption lines trace the current feedback processes from star formation and how the current feedback energy and metal-enriched gas interact with the surrounding IGM. Similar statements about the transient nature could be made for the O VI line, except that the O VI line corresponds to somewhat di\ufb00erent physical states of the shocked regions: they are slightly hotter in temperature and dynamically hotter. Third, returning to Figure 17, we would like to emphasize that, consistent with recent observations (e.g., Becker et al. 2009; Ryan-Weber et al. 2009), there is indeed a sharp drop in \u2126CIV from z = 3 to z = (4, 5, 6) by a factor of \u223c(2, 10, 20), respectively. This has less to do with the evolution of the total amount of metals produced, rather it is tracing the phase of C IV gas at any given time. At redshift z \u22653, C IV lines at di\ufb00erent redshifts appear to come from regions of comparable overdensity (see Figure 9) and comparable metallicity (see Figure 10). This allows us to test a very simple physical picture for the origin of C IV lines. They are produced by regions that were shock heated earlier by feedback shocks and have cooled to the temperature of T \u223c104.5 \u2212105K when they are seen, and the duration of each C IV line in this \u201cC IV phase\u201d would then be inversely proportional to the cooling time of the gas in this phase, which is proportional to \u039b\u22121(T, Z)(1 + z)\u22123(1 + \u03b4)\u22121, where \u039b(T, Z) is cooling function at temperature T and metallicity Z and the z-dependent term is due to density evolution with redshift. Then, the total amount of metals in C IV lines, \u2126CIV, will be proportional to \u02d9 Mstar(z)\u039b(T, Z)\u22121(1+z)\u22123(1+\u03b4)\u22121, where \u02d9 Mstar(z) is the star formation rate at z. Taking \u03b4, Z and T as roughly being constant (see Figures 9, 10, 11), we have \u2126CIV \u221d\u02d9 Mstar(z)(1 + z)\u22123, which is shown as the dashed curve on the left panel of Figure 17. It provides a reasonably good \ufb01t for the actual computed evolution of \u2126CIV. 3.3. Global Metal Enrichment of the IGM and Missing Metals We now turn to present a global metal enrichment history of the IGM to supplement what is captured by the C IV and O VI absorption lines. As in Cen & Ostriker (1999b), in our analysis we divide the IGM into three components by temperature: (1) T < 105 K cold-warm gas, which is in low density regions or cooling, star forming gas, (2) WHIM at 107 K> T > 105 K, (3) Hot X-ray emitting gas at T > 107K. One additional component (4) is the baryons that have left the IGM and been condensed into stellar objects, which we designate as \u201cstars\u201d. Figure 20 shows the evolution of these four components. The overall evolution of the four components are in good agreement with earlier \ufb01ndings (Cen & Ostriker 1999b; Dav\u00b4 e et al. 2001; Cen & Ostriker 2006) and relevant observations (e.g., Fukugita et al. 1998). In \u2013 36 \u2013 0 1 2 3 4 5 6 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Redshift Mass Fraction     T<105K T=105\u2212107K T>107K stars Fig. 20.\u2014 shows the evolution of baryons for the four mutually exclusive components: (1) T < 105 K cold-warm gas, (2) WHIM at 107 K> T > 105 K, (3) Hot X-ray emitting gas at T > 107K and (4) \u201cstars\u201d. particular, we see that 40 \u221250% of all baryons are in WHIM by the time z = 0, which is in excellent agreement with our previous \ufb01ndings (Cen & Ostriker 1999b; Dav\u00b4 e et al. 2001; Cen & Ostriker 2006). It is also noted that \u223c40% of the baryons at z = 0 reside in a relatively cool but di\ufb00use component with T < 105K (the triangles in Figure 20). It is likely that a signi\ufb01cant portion of this cool component at z = 0, in the form of Ly\u03b1 forest, is already seen by UV observations (e.g., Penton et al. 2004). As we noted earlier, the strength of feedback from star formation is chosen to match the observed overall star formation history. Each of the IGM components is composed of di\ufb00erent regions that have gone through distinct evolutionary paths and thus spans a wide range in density, shown in Figure 21. The distribution of the cold-warm component (triangles) is always peaked at the mean density at all redshifts, re\ufb02ecting the initial gaussian distribution of gas around the cosmic mean and indicating that the bulk of the IGM at mean density or lower has never been shock heated by either strong gravitational shocks or feedback shocks. The cold-warm gas extends to very high densities (\u2265105). It is interesting to note that the amount of cold-warm gas that could potentially feed the star formation, i.e., the cold-warm gas at density log \u03c1/\u27e8\u03c1\u27e9\u22652 \u22123, remains constant, within a factor of \u223c2, over the range redshift shown z = 0 \u22125. This is consistent with observations of the nearly non-evolving amount of gas probed by DLAs (e.g., P\u00b4 eroux et al. 2003; Zwaan et al. 2005; Rao et al. 2006; Prochaska & Wolfe 2009; Noterdaeme et al. 2009). The physical relation between this apparently non-evolving gas and the precipitous drop of star formation rate at z < 1 is currently unclear. The distribution of the WHIM also appears to peak at a constant overdensity of about 10 times the mean density. This is rather intriguing. In order to properly interpret this \u2013 37 \u2013 \u22123 \u22122 \u22121 0 1 2 3 4 5 6 3 4 5 6 7 8 9 log \u03c1/<\u03c1> log (dM/dlog \u03c1) z=0 \u22123 \u22122 \u22121 0 1 2 3 4 5 6 3 4 5 6 7 8 9 log \u03c1/<\u03c1> log (dM/dlog \u03c1) z=1     T<105K \u22123 \u22122 \u22121 0 1 2 3 4 5 6 3 4 5 6 7 8 9 log \u03c1/<\u03c1> log (dM/dlog \u03c1) z=3     T=105\u2212107K \u22123 \u22122 \u22121 0 1 2 3 4 5 6 3 4 5 6 7 8 9 log \u03c1/<\u03c1> log (dM/dlog \u03c1) z=5     T>107K Fig. 21.\u2014 shows the mass distribution of the three IGM components (1) cold-warm gas at T < 105 K, (2) WHIM at 107 K> T > 105 K, (3) Hot X-ray emitting gas at T > 107K as a function of overdensity at four di\ufb00erent redshifts z = 0, 1, 3, 5. Note that the area under each curve is proportional to the mass contained. interesting phenomenon it is useful to understand the heating sources of WHIM. There are two primary heating sources for WHIM: shocks due to the collapse of large-scale structure and GSW produced shocks. Earlier works have already shown that gravitational shock heating due to the formation of large-scale structure dominates the energy input for heating up and thus turning about 50% of the IGM into WHIM by z = 0 (Cen & Ostriker 1999b; Dav\u00b4 e et al. 2001; Cen & Ostriker 2006). It is, however, expected that heating due to hydrodynamic shocks emanating from galactic superwinds become increasingly more important at higher redshifts. This is because the amount of energy from gravitational collapse of large-scale structure as well as the resulting shock velocity decreases steeply towards higher redshift. The reason for this is simple: in the standard cosmological model the amount of power is peaked at a wavelength of \u223c300Mpc/h and drops steeply towards small scales. To quantify the relative contribution of GSW in turning the IGM into WHIM, we compare the simulation \u2013 38 \u2013 with GSW feedback to that without GSW feedback (run N in Table 1). Then, we make the simple assertion that the di\ufb00erence in the amount of WHIM between the two simulations is due to GSW. Figure 22 shows the fraction of WHIM that is produced (cumulatively) by GSW as a function of redshift. Consistent with previous results (Cen & Ostriker 1999b, 2006), the contribution from GSW to heating up WHIM by z = 0 is subdominant at 10 \u221220%. This relatively small contribution to WHIM from GSW can be understood based on simple energetics estimates. But we see the GSW fraction increases rapidly with increasing redshift. At redshift z = 1.5 the GSW fraction is about 50%, then reaching 70% at z = 3 and 95% at z = 5. Thus, we see the primary heating source of WHIM at z > 1.5 is GSW, whereas gravitational shocks due to structure formation are mostly responsible for heating the WHIM at z < 1.5. 0 1 2 3 4 5 6 0 10 20 30 40 50 60 70 80 90 100 Redshift WHIM fraction due to GSW (%) Fig. 22.\u2014 shows the (cumulative) fraction of WHIM that is produced by GSW as a function of redshift. From Figure 21 it seems clear that WHIM does not distinguish between gravitational shocks and feedback shocks. In both cases shocks have largely stopped at overdensity of about 10. Let us try to understand why that happened. First we note that the shocks originate approximately from the central regions of \ufb01laments, where pancakes collapse and shock for the case of gravitational shocks and galaxies are generally located for the case of GSW shocks. For gas shock heated to 105K the shock velocity is roughly 70 km/s. With that velocity the shock will be able to travel roughly 700(1 + z)\u22121kpc comoving over the Hubble time at any redshift. Therefore, one should expect to see shocks have reached a few hundred kpc comoving at any redshift, which are about one to a few times the virial \u2013 39 \u2013 radius of typical large galaxies, which in turn correspond an overdensity in the vicinity of 10 and are thus in good agreement with simulation results. Some shocks penetrate deeper into the IGM, especially along directions with lower densities and steeper density gradients, as seen in Figure 3; but the amount of mass e\ufb00ected in these low density regions is small, corresponding to the sharp drop of WHIM mass at the low density end (Figure 21). This last point is best corroborated by the distribution of the hot gas at high redshift (z = 3, 5), in the bottom two panels of Figure 21. There we see a small amount of hot gas heated up by GSW shocks is indeed produced in regions of density lower than the mean density and traces a larger amount of WHIM gas that is also produced there. At z \u22641, some comparable, small amount of hot gas is still produced at low density regions. But the vast majority of hot X-ray emitting gas is now residing in the deep potential wells of X-ray clusters of galaxies, when the cluster scale turns nonlinear and collapses. 0 1 2 3 4 5 6 0 10 20 30 40 50 60 Redshift Metals Mass Fraction (%)     T<3x104K T=3x104\u2212105K T=105\u2212107K T>107K in stars Fig. 23.\u2014 shows the evolution of fractions of all metals produced that are contained in each of the \ufb01ve components, as a function of redshift: (1C) T < 3 \u00d7 104 K cold gas, (1W) T = 3 \u00d7 104 \u2212105 K warm gas, (2) WHIM at 107 K> T > 105 K, (3) Hot X-ray emitting gas at T > 107K, (4) \u201cstars\u201d. Having obtained an overview of the thermal history of the IGM, we now turn to the metal story. We will \ufb01rst focus our attention on the WHIM here, because that is where most of the energy and metal exchanges between galaxies and the IGM take place, as shown in Figure 21. Observationally, integrating the observed star formation rate history from high redshift down to z = 2.5 suggests that the vast majority (possibly \u226580%) of cosmic metals at z \u223c2.5 appear to be missing (e.g., Pagel 1999; Pettini 1999). Note that this conclusion is insensitive to the choice of IMF, since both UV light and metals are, to zeroth order, produced by the same massive stars. Metals that have been accounted for in the estimates include those in stars of Lyman break galaxies (LBG), damped Lyman alpha systems (DLAs) and Ly\u03b1 forest, i.e., cold-warm gas and stars. Given the dominant heating of WHIM by \u2013 40 \u2013 GSW, one may immediately ask: Could a signi\ufb01cant fraction of metals that accompanies the GSW energy be heated up and in a phase like WHIM that is di\ufb00erent from those where metals have been inventoried? To better address this open question, we further break down the IGM component (1) (T < 105 K cold-warm gas) into two sub-components with (1C) (T < 3\u00d7104K cold gas) and (1W) (T = 3\u00d7104 \u2212105K warm gas). The purpose of this \ufb01ner division is to separate out the cold gas (1C), which can be more appropriately identi\ufb01ed with Ly\u03b1 forest clouds and DLAs. The results are shown in Figure 23. We see that about one third of all metals produced by z = 0 is locked up in stars, decreasing monotonically towards high redshift, dropping to about 10% by z = 5. The fraction of metals in the hot X-ray emitting component is at about 10% level at z = 0, plummeting to about 2% at z = 2 and slowly rising back to about 6% at z = 6. It is likely that the metal fraction in the hot X-ray component at z < 1 be somewhat underestimated given the relatively moderate simulation boxsize. The remaining metals are in the general photoionized Ly\u03b1 forest and the WHIM. At z = 6 the Ly\u03b1 forest (T < 3 \u00d7 104K, open triangles) contains about 43% of all metals, while WHIM (T = 105 \u2212107K, open circles), and warm IGM (T = 3 \u00d7 104 \u2212105K, solid triangles) contain 39% and 7%, respectively. But the fraction of metals in the Ly\u03b1 forest decreases steadily with time and becomes a minor component by z = 0 at < 3%. Most of the metals is seen to be contained in the WHIM at all times below redshift \ufb01ve at 50 \u221260%, peaking at \u223c60% at redshift z \u223c2. In total, the amount of metals contained in the IGM with temperature T > 3 \u00d7 104 constitutes about 2/3 of all metals produced by z = 2.5. Metals in this temperature range were not accounted for in the quoted observational inventory at z = 2.5. Thus, it seems probable that the missing metals problem at z = 2\u22123 can be largely recti\ufb01ed, if one counts the metals in the IGM at T > 3 \u00d7 104K. By now we have learned that a large amount of metals could be hidden in the WHIM of temperature 105 \u2212107K spanning a wide range in density. Since the metallicity is a strong function of density, it is still unclear the location of the WHIM that dominates the missing metals. Figure 24 shows the mean metallicity of the three IGM components as a function of overdensity at four di\ufb00erent redshifts. It is evident that within each IGM component there is a wide range in metallicity that is a non-trivial function of overdensity. Let us examine their behaviors in detail. For all three IGM components there is a strong correlation between the mean metallicity and overdensity at overdensity \u03b4 \u226510 and they converge at the highest density. While the metallicity of the cold-warm gas at the high density end remains at about solar at high density, its mean metallicity at the low overdensity drops rapidly with increasing redshift. For example, at \u03b4 = 10, the mean metallicity is (-2, -2.5, -3, -4) in solar units at z = (0, 1, 3, 5). One may notice that all three distributions exhibit a minimum metallicity at some intermediate density range, \u03b4 = 0.1 \u221210 for the cold warm-gas, \u03b4 = 10 for the WHIM and \u03b4 = 1 \u2212100 for hot gas (only at z = 0 \u22121). This is entirely in agreement with the physical picture that we described earlier for the GSW shock propagation through the IGM. \u2013 41 \u2013 \u22123 \u22122 \u22121 0 1 2 3 4 5 6 \u22123 \u22122.5 \u22122 \u22121.5 \u22121 \u22120.5 0 0.5 log \u03c1/<\u03c1> [Z/Zsun] z=0     T<105K T=105\u2212107K T>107K \u22123 \u22122 \u22121 0 1 2 3 4 5 6 \u22123 \u22122.5 \u22122 \u22121.5 \u22121 \u22120.5 0 0.5 log \u03c1/<\u03c1> [Z/Zsun] z=1 \u22123 \u22122 \u22121 0 1 2 3 4 5 6 \u22123.5 \u22123 \u22122.5 \u22122 \u22121.5 \u22121 \u22120.5 0 0.5 log \u03c1/<\u03c1> [Z/Zsun] z=3 \u22123 \u22122 \u22121 0 1 2 3 4 5 6 \u22123.5 \u22123 \u22122.5 \u22122 \u22121.5 \u22121 \u22120.5 0 0.5 log \u03c1/<\u03c1> [Z/Zsun] z=5 Fig. 24.\u2014 shows the metallicity of the three IGM components (1) cold-warm gas at T < 105 K, (2) WHIM at 107 K> T > 105 K, (3) Hot X-ray emitting gas at T > 107K as a function of overdensity at four di\ufb00erent redshifts z = 0, 1, 3, 5. Figure 24 con\ufb01rms that the transformation of cold gas to WHIM roughly stops at \u03b4 = 10. Additional metal-enriched gas is further transported along some directions, such as those perpendicular to the \ufb01laments, to very low density regions and enrich these regions to higher metallicity (due to a negligible amount of pre-existing gas there). The behavior of cold and hot components at the low density end can be understood in the same way as the WHIM. The metallicity of hot gas at the centers of clusters of galaxies (at overdensity \u03c1/\u27e8\u03c1\u27e9\u2265500) appear to stay in narrow range around [Z/ Z\u2299] \u223c\u22120.5 over the redshift range z = 0 \u22121, consistent with observations (e.g., Arnaud et al. 1994; Mushotzky et al. 1996; Tamura et al. 1996; Mushotzky & Loewenstein 1997). There is some indication of a still higher metallicity towards higher density regions, which may be in agreement with observations (e.g., Iwasawa et al. 2001). The metallicity of the WHIM at the peak of its mass distribution (\u03c1/\u27e8\u03c1\u27e9\u223c10) at z = 0 is [Z/ Z\u2299] \u223c\u22121, in good agreement with observations (e.g., Danforth & Shull 2005). We \ufb01nd that the following formula \ufb01ts well the metallicity of the WHIM as a function of overdensity \u03c1/\u27e8\u03c1\u27e9at the redshift range z = 0 \u22123: [Z/Z\u2299]WHIM = \u22121.2 \u22120.08z + (0.3 + 0.12z1/3)(log \u03c1/\u27e8\u03c1\u27e9\u22121), (6) which are shown as the straight lines in the three panels of Figure 24. \u2013 42 \u2013 \u22123 \u22122 \u22121 0 1 2 3 4 5 6 0 1 2 3 4 5 6 7 8 log \u03c1/<\u03c1> log (dMZ/dlog \u03c1) z=0     T<105K T=105\u2212107K T>107K \u22123 \u22122 \u22121 0 1 2 3 4 5 6 0 1 2 3 4 5 6 7 8 log \u03c1/<\u03c1> log (dMZ/dlog \u03c1) z=1 \u22123 \u22122 \u22121 0 1 2 3 4 5 6 0 1 2 3 4 5 6 7 8 log \u03c1/<\u03c1> log (dMZ/dlog \u03c1) z=3 \u22123 \u22122 \u22121 0 1 2 3 4 5 6 0 1 2 3 4 5 6 7 8 log \u03c1/<\u03c1> [Z/Zsun] z=5 Fig. 25.\u2014 shows the distributions of metals mass for the three IGM components (1) cold-warm gas at T < 105 K, (2) WHIM at 107 K> T > 105 K, (3) Hot X-ray emitting gas at T > 107K as a function of overdensity at four di\ufb00erent redshifts z = 0, 1, 3, 5. Note that the area under each curve is proportional to the metals mass contained. We now examine directly the distribution of metal mass as a function of density for each IGM component, shown in Figure 25. A very interesting result is that at high redshift (z = 3, 5) the metals mass in the WHIM tends to peak at a somewhat lower overdensity than that for the overall WHIM mass, thanks to the upturn of metallicity of the WHIM at low overdensity end. Speci\ufb01cally, at z = 3 \u22125 it appears that the metals mass peaks at \u03b4 \u223c2, whereas the total WHIM mass peaks at \u03b4 \u223c10. This trend is reversed at lower redshift; for example, at z = 0 the metals in WHIM is now broadly peaked at \u03b4 \u223c100, while the WHIM mass peaks at \u03b4 \u223c10. This reversal is likely due to accretion of metal-enriched gas onto high density regions during recent formation of large-scale structures. Quantitatively, we \ufb01nd that, at z = 2.5, only about 15% of the metals in warm and WHIM gas is located within virialized regions. About 73% of the metals in warm and WHIM gas resides in the IGM with \u03b4 = 1 \u2212100, with the remaining 12% in underdense regions. This con\ufb01rms an earlier expectation that some of the missing metals may be in the hot halos of galaxies (e.g., \u2013 43 \u2013 Pettini 1999; Ferrara et al. 2005); but that accounts for only a small fraction of the total missing metals. Combining with our earlier statements on missing metals at z = 2 \u22123, our \ufb01nding on missing metals is that most of the missing metals are in the warm and WHIM gas with moderate overdensity broadly distributed between \u03b4 \u223c1 \u221210. 0 1 2 3 4 5 6 \u22124 \u22123 \u22122 \u22121 0 Redshift [Z/Zsun] (25%, 50%, 75%)     \u03c1/<\u03c1>=1 \u03c1/<\u03c1>=10 \u03c1/<\u03c1>=100 \u03c1/<\u03c1>=1000 Fig. 26.\u2014 shows metallicity evolution as a function of redshift at four \ufb01xed densities, \u03c1/\u27e8\u03c1\u27e9= 1, 10, 100, 1000. For each density there are three curves, corresponding to (25%, 50%, 75%) percentiles. The open squares and open circles are the observed median metallicity evolution at overdensity equal to 10 and 1, respectively (Schaye et al. 2003). Note that the metallicity [Z/ Z\u2299] = \u22124 is a \ufb02oor value. Finally, our attention is turned to the cold-warm component, which displays a dramatic trough at the mean density. Physically, it suggests that GSW does not a\ufb00ect bulk of the IGM. Comparisons with observations are useful here to shed light on this dramatic behavior. We note that the mean metallicity at overdensity \u03c1/\u27e8\u03c1\u27e9< 10 drops quickly below [Z/ Z\u2299] = \u22123. The typical Ly\u03b1 forest clouds of column density 1013 \u22121014 cm\u22122 arise in these moderate density regions. Our simulations suggest that most of these clouds are not expected to be enriched to a level higher than [Z/ Z\u2299] = \u22123, which appear to be in agreement with direct metallicity measurements of Ly\u03b1 forest clouds (e.g., Tytler & Fan 1994; Lu et al. 1998). However, our results are at variance with recent measurements of metallicity in these moderate density regions using POD method in the sense that the observed metallicity seems to far exceed what we obtain in our simulations. To illustrate the disagreement we cast the information presented in Figures 21 and 24 into a di\ufb00erent form in Figure 26, where we show the evolution of metallicity as a function of redshift at four \ufb01xed densities, \u2013 44 \u2013 \u03c1/\u27e8\u03c1\u27e9= 1, 10, 100, 1000, for the ease of comparison. If one compares the middle solid square curve (the median metallicity at overdensity 10 from our simulations) and the open squares curve (the median metallicity at overdensity 10 from observations, Schaye et al. (2003)), the middle solid dots curve (the median metallicity at overdensity 1 from our simulations) and the open circles curve (the median metallicity at overdensity 1 from observations, Schaye et al. (2003)), the disagreement is clear and dramatic. We predict that the metallicity in regions with overdensity less than about 10 generally increases quite rapidly with decreasing redshift, whereas the observationally inferred trend goes in the opposite direction with a mild rate of change. Is our simulation incomplete or are the observations misinterpreted? Recall from Figure 9 that the typical overdensity for low column C IV lines is about 10, comparable to that of Ly\u03b1 forest clouds. But that is a mere coincidence: the two types of absorbers are generally not co-located in physical space. If we go back to Figures 4,5,6 and study the temperature (second rows) and metallicity (third row), we see there is a strong spatial correlation between temperature and metallicity; regions where a signi\ufb01cant amount of C IV reside tend to have an elevated temperature that exceeds 2\u00d7104K, whereas the metallicity in lower temperature regions, where HI reside in abundance to give rise Ly\u03b1 forest clouds, seems extremely low. As we noted earlier, the regions with elevated temperature and CIV lines have a width that corresponds to one to several hundred km/s. Interestingly, these regions also typically have peculiar velocities of several hundred km/s (fourth row from top of Figures 4,5,6). As a result, there should be some overlap in velocity space between some C IV lines and Ly\u03b1 forest lines, even when they are signi\ufb01cantly displaced in physical space. This overlap may \u201cdi\ufb00use\u201d, in velocity space, some of the metals in regions that producing C IV lines into the Ly\u03b1 forest lines, causing an apparent, moderate metallicity level in Ly\u03b1 forest, as inferred by Schaye et al. (2003)), when a method such as POD is employed. A closer look at the left panel of Figure 10 indicates that typical C IV absorbers show a decrease of metallicity with decreasing redshift in the range 2 \u22125: roughly [Z/ Z\u2299] = [\u22122.0, \u22121.5], [\u22122.3, 1.4], [\u22122.6, \u22121.5] at z = 5, 4, 2.6. This is in accord with the observed weak trend of increasing metallicity with increasing redshift, which otherwise is extremely di\ufb03cult to understand in the context of the standard cosmological model. Needless to say, the O VI lines located in regions that are spatially close to C IV lines will also \u201cdi\ufb00use\u201d into the Ly\u03b1 forest in velocity space. The fact that O VI lines tend to have a higher metallicity, about [Z/ Z\u2299] = 0.2 to 0.4, than the C IV lines over the redshift range of z \u223c2 \u22124 (comparing the left and right panels of Figure 10) and there are more O VI lines than C IV lines (comparing the left and right panels of Figure 10) would suggest that one may expect that the apparent oxygen abundance in the Ly\u03b1 forest inferred from POD should be higher than that of C IV lines. This is indeed the case: Aguirre et al. (2008) found that [O/C] = 0.66+0.06 \u22120.2 . We argue that this provides independent, supporting evidence for our explanation that is selfconsistent and physically plausible. Alternatively, the IGM may be enriched to the observed \u2013 45 \u2013 level by \ufb01rst generation, Pop III galaxies that are not properly captured in our simulations. To further test our \u201cdi\ufb00usion\u201d hypothesis, we have computed the cross-correlation between Ly\u03b1, C IV and O VI spectra and taken the mean along all lines of sight at z = 2.6 for two cases: run \u201cM\u201d of our simulations with and without the e\ufb00ect of peculiar velocities taken into account. We present in Figure 27 the following function: f(\u2206v) \u2261\u03bep,HI x ion(\u2206v) \u03be0,HI x ion(\u2206v) \u22121 (7) where \u03bep,HI x ion(v) is the cross-correlation function for the spectrum of HI and the corresponding ion averaged over all lines of sight and symmetrized for positive and negative velocity lags at z = 2.6. \u03be0,HI x ion(v) is the same function computed in the case where there are no peculiar velocities. Figure 27 shows that in the case of no peculiar velocity, the crosscorrelation between Ly\u03b1 and C IV , and Ly\u03b1 and O VI , is weaker than in the case where peculiar velocities are considered. This is compelling evidence that peculiar velocities e\ufb00ects could arti\ufb01cially di\ufb00use metals into the Ly\u03b1 forest. Fig. 27.\u2014 Comparison of the cross-correlation functions of C IV and O VI with and without peculiar velocities. The function plotted is f(\u2206v), de\ufb01ned in the text. Values greater than 0 imply there is a stronger correlation between the ion and the Ly\u03b1 spectrum in the case where peculiar velocities are taken into account. 4. Conclusions We have carried out the state-of-the-art cosmological hydrodynamic simulations of the standard cold dark matter model to investigate the process of metal enrichment of the intergalactic medium. Our simulations have substantially higher resolution than our previous simulations to address this problem. More importantly, we can now constrain the strength \u2013 46 \u2013 of the feedback process by matching the star formation history in our current simulation to the observed one in the range z = 0 \u22126. We \ufb01nd that our model reproduces the observed mean \ufb02ux of the Ly\u03b1 forest and the mass density of C IV and O VI absorbers. It is also in general consistent with observed physical properties of absorbers. This indicates that we can explain the metal enrichment of the IGM by considering star formation to be the main feedback mechanism, with no apparent need of signi\ufb01cant contribution from AGN in terms of additional energy. We conclude from our results that: (1) The overall star formation history depends rather sensitively on the feedback strength. This is likely due to GSW signi\ufb01cantly reducing the concentration of cold gas around halos. Nevertheless, GSW do not signi\ufb01cantly alter the overall large-scale \ufb01lamentary baryonic structure that follows the cosmic web of dark matter distribution. While GSW could travel far into low density regions sometimes, the amount of energy and metals that are deposited in underdense regions is very small. Most of the GSW energy and metals remain in regions of overdensity \u03b4 \u226510, with the distance of in\ufb02uence of GSW from galaxies limited to about \u22640.5Mpc. Metal bubbles blown by GSW coincide with temperatures bubbles, suggesting a tight coupling of energy and metal deposition, and they are terminated by shock fronts. (2) Both C IV and O VI absorbers are located in regions that have been swept by feedback shocks, of elevated temperature (T \u22652 \u00d7 104K), density (\u03b4 \u226510) and metallicity ([Z/ Z\u2299] = [\u22122.5, \u22120.5]), demarcated by a double shock propagating outwards, with O VI absorbers typically having a higher metallicity than C IV absorbers. Within these shocked regions, most of C IV absorbers tend to arise from moderate density peaks that are troughs in temperature and are thus relatively quiescent. The O VI absorbers are from regions that are dynamically hotter near shock fronts. There is a trend for the population of C IV and O VI absorbers to be more collisionally ionized at higher redshift; for O VI collisional ionization dominates over the entire redshift range z = 0 \u22126, whereas for C IV the transition occurs at moderate redshift z \u223c3 from collisionally dominated to photoionization dominated. (3) The evolution of the mass density contained in C IV and O VI lines, \u2126CIV is in good agreement with observations, with both the latest observations and simulations of \u2126CIV exhibiting an exponential drop beyond redshift z = 4; \u2126CIV drop exponentially beyond redshift z = 3; the near constancy of \u2126CIV at redshift z = 1\u22123 does not re\ufb02ect the evolution of the overall metal content in the IGM. In the case of \u2126OVI, we \ufb01nd a less good agreement between observations and out results. This might be in part due to cosmic variance. (4) Most of C IV and O VI absorbers, while clustered around galaxies, are transient and intergalactic in origin, produced by galactic superwinds in the process of transporting both energy and metals from galaxies into the IGM; the metal mass densities contained in C IV and O VI lines in the range log Ncm2 = 12\u221215 each constitutes \u223c0.1% of total metal density at all redshifts; the amount of metals probed by C IV and O VI lines in the range log Ncm2 = 12 \u221215 is \u223c1% of the total metal density at all redshifts. \u2013 47 \u2013 (5) While gravitational shocks from large-scale structure formation dominate the energy budget (80 \u221290%) for turning about 50% of IGM to the warm-hot intergalactic medium (WHIM) by z = 0, galactic superwind feedback shocks are energetically dominant over gravitational shocks at z \u22651 \u22122. (6) Most of the so-called \u201cmissing metals\u201d at z = 2 \u22123 are hidden in a warm-hot gaseous phase (T > 3 \u00d7 104K) that is heated up by star formation feedback shocks. Their mass distribution is broadly peaked at overdensity 1\u221210 in the IGM, outside virialized halos. Approximately (37, 46, 10, 7)% of the total metals at z = 0 are in (stars, WHIM, X-ray gas, cold gas); the distribution stands at (23, 57, 2, 18)% and (14, 51, 4, 31)% at z = 2 and z = 4, respectively. (7) The metallicity of the IGM with moderate overdensities (1 \u221210) that are probed by the Ly\u03b1 forest shows a rapid increase with decreasing redshift. We show that velocity \u201cdi\ufb00usion\u201d e\ufb00ect that arises from the peculiar velocities could enhance the \u201capparent\u201d metallicity of the Ly\u03b1 forest clouds, as supported by our cross-correlation analysis. Tentatively, we suggest that this may reconcile, at least in part, the discrepancy between our simulations and observations at z = 2 \u22124 based on pixel optical depth (POD) method. We are thankful to Ben Oppenheimer for useful conversations on the subject and an anonymous referee for a demanding but constructive report that helps signi\ufb01cantly improve the paper. Computing resources were in part provided by the NASA HighEnd Computing (HEC) Program through the NASA Advanced Supercomputing (NAS) Division at Ames Research Center. This work is supported in part by grants NNX08AH31G and NAS8-03060.",
                    "introduction": "One of the pillars of the Big Bang theory is its successful prediction of a primordial baryonic matter composition, made up of nearly one hundred percent hydrogen and helium with a trace amount of a few other light elements (e.g., Schramm & Turner 1998; Burles et al. 2001). The metals, nucleosynthesized in stars later, are found almost everywhere in the observable IGM, ranging from the metal-rich intracluster medium (e.g., Mushotzky & Loewenstein 1997) to moderately enriched damped Lyman systems (e.g., Pettini et al. 1997; Prochaska et al. 2003) to low metallicity Lyman alpha clouds (e.g., Schaye et al. 2003). When and where were the metals made and why are they distributed as observed? We address this fundamental question in the context of the standard cold dark matter cosmological model (Komatsu et al. 2009) using latest simulations. Our previous simulations (Cen & Ostriker 1999a; Cen et al. 2005) provided some of the earlier attempts to address this question with measured successes. In this investigation we use substantially better simulations to provide signi\ufb01cantly more constrained treatment of the feedback processes from star formation (SF) that drive energy and metals from supernovae into the IGM through galactic winds (e.g., Cen & Ostriker 1999a; Aguirre et al. 2001; Theuns et al. 2002b; Adelberger et al. 2003; Springel & Hernquist 2003). Metal-line absorption systems in QSO spectra are the primary probes of the metal enrichment of the IGM as well as in the vicinities of galaxies (e.g., Bahcall & Spitzer 1969). The most widely used metal lines include Mg II \u03bb\u03bb2796, 2803 doublet (e.g., Steidel & Sargent 1992), C IV \u03bb\u03bb1548, 1550 doublet (e.g., Young et al. 1982), and O VI \u03bb\u03bb1032, 1038 doublet (e.g., Simcoe et al. 2002). We here focus on the C IV and O VI absorption lines and the global evolution of metals in the IGM. We will limit our current investigation to the observationally accessible redshift range of z = 0\u22126, which in part is theoretically motivated simply because the theoretical uncertainties involving still earlier star formation are much larger. At z = 0 the O VI line (together with C VII and O VIII lines) provide vital information on the missing baryons (e.g., Mathur et al. 2003; Tripp et al. 2008; Danforth & Shull 2008; Nicastro et al. 2009), predicted to exist in a Warm-Hot Intergalactic Medium (WHIM) (Cen & Ostriker 1999a; Dav\u00b4 e et al. 2001). For a well understood sample of QSO absorption lines, one could derive the cosmological \u2013 3 \u2013 density contained in them (e.g., Cooksey et al. 2009). Early investigations indicate that \u2126CIV remains approximately constant in the redshift interval z \u223c1.5 \u22124 (Songaila 2001, 2005; Boksenberg et al. 2003). There have been recent e\ufb00orts to extend the measurements of \u2126CIV to z < 1.5 (Cooksey et al. 2009) and to z > 5 (Simcoe 2006; Ryan-Weber et al. 2006, 2009; D\u2019Odorico et al. 2009; Becker et al. 2009). Observations in these redshift ranges have been di\ufb03cult to carry out because C IV transition moves to the UV at low redshift and to the IR band at high redshift. D\u2019Odorico et al. (2009) \ufb01nd evidence of a rise in the C IV mass density for z < 2.5. Simcoe (2006) and Ryan-Weber et al. (2006) found evidence of C IV density at z \u223c6 being consistent with estimations at z \u223c2 \u22124.5. More recently, however, Becker et al. (2009) set upper limits for \u2126CIV at z \u223c5.3 and Ryan-Weber et al. (2009) observe a decline in intergalactic C IV approaching z = 6, which we will show are in good agreement with our simulations. The ionization potential of O VI and the relatively high oxygen abundance are very favorable for production of O VI absorbers in the IGM (e.g., Norris et al. 1983; Cha\ufb00ee et al. 1986). The rest wavelength of OVI (1032, 1037\u02da A) places it within the Ly-\u03b1 forest, which makes the identi\ufb01cations of these lines more complicated, although being a doublet helps signi\ufb01cantly. At z \u22652, however, O VI absorption can probe the metal content of the IGM in ways complementary to what is provided by C IV lines. For example, the O VI lines can probe IGM that is hotter than that probed by the C IV lines and can reach lower densities thank to higher abundance. There are now several observational studies at redshifts z = 2 \u22123 that describe the properties of O VI absorbers and attempt to estimate the O VI mass density, \u2126OVI (Carswell et al. 2002; Bergeron et al. 2002; Simcoe et al. 2004; Simcoe 2006; Frank et al. 2008; Danforth & Shull 2008; Tripp et al. 2008; Thom & Chen 2008b). At z \u223c2 \u22123 there is a missing metals problem: only 10-20% of the metals produced by all stars formed earlier have been identi\ufb01ed in stars of Lyman break galaxies (LBG), in damped Lyman alpha systems (DLAs) and Ly\u03b1 forest. The vast majority of the produced metals appear to be missing (e.g., Pettini 1999). The missing metals could be in hot gaseous halos of star-forming galaxies (Pettini 1999; Ferrara et al. 2005). We will show that most of the missing metals are in a warm-hot (T = 104.5\u22127K) but di\ufb00use IGM at z = 2 \u22123 of overdensities of \u223c10 that are outside of halos. The outline of this paper is as follows. In \u00a72 we detail our simulations and the procedure of normalizing the uncertain feedback processes from star formation. Results on the metal enrichment of the IGM are presented in \u00a73. In \u00a73.1 we give a full description of the properties of the C IV and O VI lines at z = 0 \u22126, followed \u00a73.2 discussing C IV and O VI absorbers as metals reservoirs. We devote \u00a73.3 to a general discussion of global distribution of metals, addressing several speci\ufb01c topics, including the metallicity of the moderate overdense regions at moderate redshift, the missing metals at z \u223c3. Conclusions are given in \u00a74. \u2013 4 \u2013"
                },
                {
                    "url": "http://arxiv.org/abs/0907.0735v3",
                    "title": "Probing the Epoch of Reionization with the Lyman Alpha Forest at z~4-5",
                    "abstract": "The inhomogeneous cosmological reionization process leaves tangible imprints\nin the intergalactic medium down to z=4-5. The Lyman-alpha forest flux power\nspectrum provides a potentially powerful probe of the epoch of reionization.\nWith the existing SDSS I/II quasar sample we show that two cosmological\nreionization scenarios, one completing reionization at z=6 and the other at\nz=9, can be distinguished at ~7 sigma level by utilizing Lyman alpha forest\nabsorption spectra at z=4.5+-0.5, in the absence of other physical processes\nthat may also affect the Lyman alpha flux power spectrum. The redshift range\nz=4-5 may provide the best window, because there is still enough transmitted\nflux and quasars to measure precise statistics of the flux fluctuations, and\nthe IGM still retains a significant amount of memory of reionization.",
                    "authors": "Renyue Cen, Patrick McDonald, Hy Trac, Abraham Loeb",
                    "published": "2009-07-04",
                    "updated": "2009-07-09",
                    "primary_cat": "astro-ph.CO",
                    "cats": [
                        "astro-ph.CO",
                        "astro-ph.GA"
                    ],
                    "main_content": "29 billion dark matter particles on an effective mesh with 11, 5203 cells in a comoving box of 100 h\u22121Mpc, yielding a particle mass resolution of 2.68 \u00d7 106 h\u22121M\u2299allowing us to resolve all atomic cooling dark matter halos. A total of N = 15363 gas cells of size 65kpc/h are used and we trace five frequency bins at > 13.6 eV with the ray-tracing code. The star formation rate is controlled by the halo formation history. We adjust the ionizing photon escape fraction to arrive at two models, where reionization is completed early (z \u223c9) and late (z \u223c6), respectively; note that the halo formation histories in the two models are identical. 3. RESULTS Previous studies (e.g., Furlanetto et al. 2004; Iliev et al. 2006; Lee et al. 2008) have shown that the reionization process proceeds in an inside-out fashion, where regions around high density peaks get reionized first. H II regions initially surround isolated galaxies that formed in high density peaks. With time these H II regions expand and lower density (void) regions are eventually engulfed by the expanding H II regions stemming from high density peaks. Consequently, the redshift of reionization of each individual spatial point, zreion, is highly correlated with the underlying large-scale density field, with the positive correlation extending down to scales \u223c 1 h\u22121Mpc, as we have shown earlier (Trac et al. 2008). Once an expanding region is photo-ionized and photo-heated, it would cool subsequently due to adiabatic expansion and other cooling processes (primarily Compton cooling at high redshift), countered by photoheating of residual recombining hydrogen atoms (on the time scale of recombination) (e.g., Theuns et al. 2002; Hui & Haiman 2003). As a result, the strong correlation between zreion and the underlying large-scale density is manifested in a strong anti-correlation between the temperature and the underlying large-scale density field. Specifically, different 2 Cen, McDonald, Trac, & Loeb Fig. 1.\u2014 Top panels show the log of the ratio of gas temperature from the simulation to that prescribed by a \ufb01xed EoS at z = 4, for the early (left) and late (right) reionization model, respectively. We use EoS formula T = T0(\u03c1/\u03c10)0.62, where T0 is the temperature at mean density \u03c10 in each model. The slice shown has a size (100 h\u22121Mpc)2 with a thickness equal to two hydro cells (130 h\u22121kpc). The distribution of \ufb02ux transmission, F(early)= exp(\u2212\u03c4(early)), for the late reionization model is shown in the bottom left. The \ufb02ux di\ufb00erence between the two models: F(late)\u2212F(early)= exp(\u2212\u03c4(late)) \u2212exp(\u2212\u03c4(early)) is shown in the bottom right panel. regions of the same low densities \u03b4 \u2264a few (without large-scale smoothing in this case) would display a large, long-range-correlated, dispersion in temperature, immediately following the completion of reionization (e.g., Trac et al. 2008). (Note that virialized regions are not a\ufb00ected and do not retain any information of reionization in this regard.) Both the anti-correlation between temperature and the underlying large-scale density and the consequent temperature dispersion at a \ufb01xed density weaken as time progresses and the temperature-density relation asymptotically approaches a so-called equation-of-state (EoS), a one-to-one mapping from IGM density to temperature (Hui & Gnedin 1997), with T = T0(\u03c1/\u03c10)0.62 in the latetime limit. However, at the redshift range z = 4.5 \u00b1 0.5, the IGM has not had enough time to have completely relaxed to this state prescribed by the EoS such that quantitatively signi\ufb01cant deviations from a deterministic EoS exist, if the universe was reionized, say, at zri \u223c6 \u22128. The deviations from a simple temperature-density relation are larger for smaller zri at a given observed redshift. In Fig. 1 we show the log of the ratio of gas temperature from the simulation to that prescribed by the asymptotic EoS at z = 4 in a slice of size (100 h\u22121Mpc)2 with a thickness equal to two hydro cells (130 h\u22121kpc), for the early (top left panel) and late (top right panel) reionization model, respectively. The \ufb01elds have been smoothed on cells of comoving length 130 h\u22121kpc. The small reddish/yellowish regions seen in the top left panel correspond to virialized regions, for which the plotted Imprint of Inhomogeneous Hydrogen Reionization 3 ratio does not contain useful information. But these regions show clearly the location of ionizing sources. We see striking di\ufb00erences in temperature distributions between the two reionization models with respect to their respective asymptotic EoS values. In the early reionization model (top left panel) most of the regions have blue color (i.e., the ratio equal to \u223c1) and appear to have mostly relaxed to the state predicted by the asymptotic EoS, while some low density regions in the voids still display yellowish color with a temperature that is higher than that of the asymptotic EoS by 30 \u221250%. On the other hand, in the late reionization simulation (top right panel), while regions just outside the shock-heated \ufb01laments and halos (bluish color) have largely relaxed to the asymptotic EoS, regions of comparable local densities in the voids are much hotter than that of the asymptotic EoS, by a factor of 1.5 \u22122.5. Because the neutral hydrogen fraction in regions of moderate density is determined by the balance between photoionization rate and recombination rate, the latter of which is a function of temperature, the two di\ufb00erent temperature distributions in the two reionization models result in di\ufb00erent large-scale neutral hydrogen distribution. In the bottom left panel of Fig 1 we show the expected \ufb02ux transmission, F(early)= exp(\u2212\u03c4(early)), for the early reionization model, where \u03c4(early) is the Ly\u03b1 optical depth computed based on the distribution of neutral hydrogen density, gas peculiar velocity and temperature at z = 4 in the early reionization model. In computing the neutral hydrogen fraction we have used a uniform background radiation \ufb01eld with its amplitude adjusted such that both models yield the same mean transmitted \ufb02ux of < F >= 0.43 at z = 4, as observed (Fan et al. 2006b). In the bottom right panel the \ufb02ux di\ufb00erence between the two models, F(late)\u2212F(early), is shown, where it is clearly seen that the transmitted Ly\u03b1 \ufb02ux is significantly a\ufb00ected by the temperature di\ufb00erence at z = 4, resulting in fractional di\ufb00erence in the transmitted \ufb02ux in the voids between the two models of \u223c15% (blue regions). Speci\ufb01cally, there is more transmitted \ufb02ux in the void regions in the late reionization model, compensated by comparably reduced transmitted \ufb02ux in high density regions. It is noted that, at z \u22654, the majority of transmitted Ly\u03b1 \ufb02ux comes from the lowest density regions of \u03b4 \u2264a few. Fig. 2 shows the ratio of \ufb02ux power spectrum in the late reionization model to that in the early reionization model at z = 4 (black solid) and z = 5 (black dashed). It appears that the large-scale anti-correlation between density and deviations from a single EoS in the late reionization model leads to a signi\ufb01cant amount of extra power in the \ufb02ux spectrum (speci\ufb01cally, relatively high temperatures in late-reionizing under-dense regions lead them to produce even less absorption than they otherwise would). The di\ufb00erence between the \ufb02ux power spectra of the two reionization models increases with scale, reaching 20% at k = 0.001(km/s)\u22121 at z = 4; the di\ufb00erence is still larger at z = 5 (\u223c30%), as expected, due to still larger di\ufb00erence in the temperature hence \ufb02ux transmission between the two reionization models. The black error bars indicate the statistical errors expected with the full SDSS I/II sample (completed, but not yet fully analyzed), With Fig. 2.\u2014 Black solid and dashed curves are the ratio of \ufb02ux power spectrum in the late reionization model to that in the early reionization model at z = 4 and z = 5, respectively. Also shown as the two green curves are the corresponding ratios produced by replacing the real temperature in each simulation by that prescribed by the EoS given density (the same EoS in both simulations). The black error bars are the error one can expect from the full SDSS I/II sample plus existing high resolution data. The error bars will be approximately uncorrelated. A formal analysis of the 16 data points indicates that the two reionization models can be di\ufb00erentiated at 7\u03c3 level. z \u223c4 SDSS I/II data plus existing high resolution data, one can distinguish formally between these two reionization models at 7\u03c3 level. However, we note that the statistical di\ufb00erences between the two models are unmarginalized, i.e., not taking into account other physical e\ufb00ects that a\ufb00ect the Ly\u03b1 \ufb02ux power spectrum determination (e.g, McDonald et al. 2005). Therefore, the quoted statistical signi\ufb01cance only serves as an indication of the potential power of this statistics. For comparison, the corresponding \ufb02ux power spectrum ratios at z = 4 and z = 5, if both models follow the same EoS (given density), are shown (green curves) in Fig. 2. In this case, aside from the relatively small di\ufb00erence on small scales due to cumulative dynamical a\ufb00ects on the gas density by the di\ufb00erence in the gas pressure histories, the two models have identical \ufb02ux power spectrum on large scales. This clearly demonstrates that the large di\ufb00erence in the \ufb02ux power spectra between the two reionization models (black curves in Fig. 2) is a result of large di\ufb00erences in the contemporaneous temperature distributions. 4. DISCUSSION This e\ufb00ect of inhomogeneous reionization on the \ufb02ux power spectrum was explored earlier by Lai et al. (2006) at z = 3, based on a semi-analytic model. Their focus is on z = 3 and found that, on large scales, k \u223c 0.001(km/s)\u22121, temperature \ufb02uctuations lead to an increase in the z \u223c3 \ufb02ux power spectrum by at most 10%. Our focus here is at higher redshifts z = 4 \u22125 and the e\ufb00ects, not surprisingly, are larger and potentially more 4 Cen, McDonald, Trac, & Loeb discriminating. A \ufb02uctuating radiation background, produced largely by radiation from sparsely distributed quasars but also by galaxies, can a\ufb00ect the \ufb02ux power spectrum (Meiksin & White 2004; Croft 2004; McDonald et al. 2005). Larger \ufb02uctuations in the radiation background give rise to larger amplitudes of the \ufb02ux power spectrum at large scales (e.g. McDonald et al. 2005, Figures 6,7 therein). This enhancement of the \ufb02ux power spectrum on large scales due to a \ufb02uctuating radiation background will be in addition to what is caused by the gas temperature \ufb02uctuations shown here, if QSOs were dominant. The radiation contribution from stars may be more dominant at the redshift range of concern here (e.g., Faucher-Giguere et al. 2009). Star formation is known to be biased and hence higher density regions, on average, tend to have higher radiation \ufb01eld than lower density regions. Thus, the two e\ufb00ects due to a \ufb02uctuating radiation background and an inhomogeneous reionization process may be partially degenerate or have a tendency to cancel each other\u2019s contribution, although there is a possibility that the radiation \ufb02uctuations may be relatively modest (e.g., Mesinger & Furlanetto 2009). A more careful modeling of the contribution from quasars as well as radiation sinks (such as Lyman limit systems) is required in a comprehensive modeling. The purpose of this Letter is to demonstrate that, if the e\ufb00ects on the Ly\u03b1 \ufb02ux power spectrum determination due to the epoch of reionization were the only relevant ones, then a precise measure of the \ufb02ux power spectrum with the full SDSS I/II data will be able to place a very tight constraint on the epoch of reionization. However, a detailed comparison between models and SDSS I/II observations requires a full analysis of all astrophysical/cosmological processes that may a\ufb00ect the determination of the \ufb02ux power spectrum and some of them may be degenerate to varying degrees (McDonald et al. 2005), including \ufb02uctuating radiation \ufb01eld, damped Ly\u03b1 systems, galaxy formation feedback, initial photoheating temperature (i.e., related to IMF of high redshift galaxies), X-ray heating, He II reionization, among others, before its statistical potential can be precisely marginalized and quanti\ufb01ed. We will perform such an analysis in a future study. 5. CONCLUSIONS Utilizing state-of-the-art radiative transfer hydrodynamic simulations of cosmological reionization, we put forth the point that the inhomogeneous reionization process imprints important and quantitatively signi\ufb01cant signatures in the intergalactic medium at z = 4.5 \u00b1 0.5 that can be probed by the Ly\u03b1 forest in the quasar absorption spectra. We illustrate that with Ly\u03b1 forest data at z = 4 \u22125 to be provided by the SDSS I/II full data sample, one may be able to distinguish between two cosmological epochs of reionization, one at z = 6 and the other z = 9 at 7\u03c3 level, if they were the only e\ufb00ects on the determination of the Ly\u03b1 \ufb02ux power spectrum. We thank J. Chang at NASA for invaluable supercomputing support. This work is supported in part by NASA grants NNG06GI09G and NNX08AH31G. Computing resources were in part provided by the NASA HighEnd Computing (HEC) Program through the NASA Advanced Supercomputing (NAS) Division at Ames Research Center. PM acknowledges support of the Beatrice D. Tremaine Fellowship. HT is supported by an Institute for Theory and Computation Fellowship.",
                    "introduction": "1. The history of cosmological reionization is presently primarily constrained by the cosmic microwave back- ground observations of WMAP (Wilkinson Microwave Anisotropy Probe) (Dunkley et al. 2009) and the SDSS (Sloan Digital Sky Survey) quasar absorption spectra. The former gives an integral constraint, strongly sug- gesting that cosmological reionization may well be un- derway at z \u223c12, while the latter provides a solid anchor point at z \u223c6 when the universe became largely trans- parent to Lyman limit photons (e.g., Fan et al. 2001; Becker et al. 2001; Cen & McDonald 2002; Fan et al. 2006b). At z \u22656.3 the lower bound on the neutral hydrogen fraction, x, of the IGM provided by SDSS observations is, however, fairly loose at x \u2265 0.01. Thus, exactly when most of the neutral hydrogen be- came reionized is yet unknown and there are many possible scenarios that could meet the current observa- tional constraints (e.g., Barkana & Loeb 2001; Cen 2003; Haiman & Holder 2003; Fan et al. 2006a; Wyithe & Cen 2007; Becker et al. 2007). The process of inhomogeneous cosmological reioniza- tion leaves quanti\ufb01able and signi\ufb01cant imprints on the thermal evolution of the IGM (Trac et al. 2008). In this Letter, we show that the Ly\u03b1 forest \ufb02ux spectrum at moderate redshift z = 4.5 \u00b1 0.5 sensitively depends on and hence provides a very powerful probe of the epoch of reionization. 2."
                }
            ],
            "Daniel Defelippis": [
                {
                    "url": "http://arxiv.org/abs/2403.14748v1",
                    "title": "The Effect of Cosmic Rays on the Observational Properties of the CGM",
                    "abstract": "The circumgalactic medium (CGM) contains information on the cumulative effect\nof galactic outflows over time, generally thought to be caused by feedback from\nstar formation and active galactic nuclei. Observations of such outflows via\nabsorption in CGM gas of quasar sightlines show a significant amount of cold\n($\\lesssim 10^4 \\; \\rm{K}$) gas which cosmological simulations struggle to\nreproduce. Here, we use the adaptive mesh refinement hydrodynamical code RAMSES\nto investigate the effect of cosmic rays (CR) on the cold gas content of the\nCGM using three zoom realizations of a $z=1$ star-forming galaxy with supernova\nmechanical feedback: one with no CR feedback (referred to as no-CR), one with a\nmedium CR diffusion coefficient $\\kappa = 10^{28} \\; \\rm{cm^{2}\\; s^{-1}}$\n(CR$-\\kappa_{\\rm med}$), and one with a high rate of diffusion of $\\kappa =\n3\\times10^{29} \\; \\rm{cm^{2}\\; s^{-1}}$ (CR$-\\kappa_{\\rm high}$). We find that,\nfor CR$-\\kappa_{\\rm med}$, the effects of CRs are largely confined to the\ngalaxy itself as CRs do not extend far into the CGM. However, for\nCR$-\\kappa_{\\rm high}$, the CGM temperature is lowered and the amount of\noutflowing gas is boosted. Our CR simulations fall short of the observed Mg II\ncovering fraction, a tracer of gas at temperatures $\\lesssim 10^4 \\; \\rm{K}$,\nbut the CR$-\\kappa_{\\rm high}$ simulation is more in agreement with covering\nfractions of C IV and O VI, which trace higher temperature gas.",
                    "authors": "Daniel DeFelippis, Fr\u00e9d\u00e9ric Bournaud, Nicolas F. Bouch\u00e9, Edouard Tollet, Marion Farcy, Maxime Rey, Joakim Rosdahl, J\u00e9r\u00e9my Blaizot",
                    "published": "2024-03-21",
                    "updated": "2024-03-21",
                    "primary_cat": "astro-ph.GA",
                    "cats": [
                        "astro-ph.GA"
                    ],
                    "main_content": "To study the effects of CRs on the CGM, we use cosmological zoom simulations, targeting a halo of interest and its environment with high resolution. For the simulations, we use the adaptive mesh refinement (AMR) code Ramses (Teyssier 2002). The positions of collisionless dark matter (DM) and stellar particles are evolved with a particlemesh solver, and cloud-in-cell interpolation is used to calculate their gravitational potential. Gas evolution is computed with either an HLLC Riemann solver (Toro et al. 1994) for runs without CRs, or an HLLD Riemann solver (Miyoshi & Kusano 2005) for runs with CRs. The anisotropic diffusion of the CR fluid along the magnetic field is performed with the methods described by Dubois & Commer\u00e7on (2016). To close the relation between gas internal energy and pressure, we assume an adiabatic index of \ud835\udefe= 5/3. We initialize magnetic fields by defining a uniform grid with 10243 cells and assigning random magnetic potentials to each cell interface, such that the magnetic field that arises from the curl of the potential is divergence-free. The six magnetic field components of each cell are normalized such that the initial magnetic field magnitude at a scale of 1 cMpc is \u224810\u221217 G. We choose a relatively weak initial magnetic field to better focus on the role of CR feedback alone on the CGM. The magnetic fields are then evolved using the MUSCL scheme MNRAS 000, 1\u201314 (2024) The Effect of Cosmic Rays on the CGM 3 (Teyssier et al. 2006). To identify DM haloes we use the Adaptahop halo finder in the most massive submaxima mode (Aubert et al. 2004; Tweed et al. 2009). A halo is defined as region satisfying the virial theorem that contains at least 20 DM particles and has a density 200 times the critical value. Initial conditions and refinement scheme We use the Music package (Hahn & Abel 2011) to generate cosmological initial conditions. Music allows refining of the DM mass resolution in a zoomed-in region of the simulation volume. We initially run a DM-only simulation with homogeneous resolution in a 30 cMpc/\u210ewide box to \ud835\udc67= 0. Then we select a target halo to be re-simulated up to \ud835\udc67= 1 with baryons and at a higher resolution. The criteria for our halo selection are as follows. (i) The target halo must have a \ud835\udc67= 0 halo mass close to \ud835\udc40target = 5 \u00d7 1011 M\u2299. The target mass is chosen to simulate a halo which would likely host a galaxy with a stellar mass of \u223c1010 \ud835\udc40\u2299at \ud835\udc67= 1, so as to be similar to galaxies from the MEGAFLOW survey (e.g. Zabl et al. 2019; Schroetter et al. 2021) 2. (ii) The target halo must not contain any massive substructures, and (iii) it must also not contain a neighboring halo more massive than 0.2 \u00d7 \ud835\udc40target within three virial radii of the target halo\u2019s centre. These last two criteria are to avoid re-simulating a very complex large-scale environment at a high resolution (and high computational cost). Music is then used to progressively define a zoom region in the initial conditions with a DM particle mass of 3.5 \u00d7 105 \ud835\udc40\u2299, corresponding to an effective fine resolution of 20483 DM particles. This is nested inside larger regions with progressively larger DM particle masses by a factor of 8 each time, up to a coarsest particle mass of 1.4\u00d7109 \ud835\udc40\u2299, corresponding to an effective coarse resolution of 1283 particles. The process of mapping out the zoomed region in the initial conditions is iterated until we confirm that the high-resolution zoomin region has no contamination from low-resolution DM particles out to 3\ud835\udc45vir from the centre of the targeted halo. All our production simulations use these same initial conditions and therefore model the evolution of the same galactic halo, albeit with different physics. The resolution of the gas and gravitational potential tracks that of the DM in the zoom-in scheme, with an effective resolution that goes from 1283 cells at the coarsest level, corresponding to a physical width of 350 ckpc, and progressively increasing to an effective base resolution of 20483 cells in the innermost zoomed-in region, corresponding to a physical width of 22 ckpc. Within this innermost region, we also allow for adaptive refinement to a minimum cell width of 40 pc (physical, not co-moving). A cell is split into 8 equal-size children cells if \ud835\udc40DM,cell + \ud835\udc40b,cell/ \ud835\udc53\ud835\udc4f> 8 \ud835\udc5adm, where \ud835\udc40DM,cell and \ud835\udc40b,cell are the total DM and baryonic (gas plus stars) masses in the cell and \ud835\udc53\ud835\udc4f= 0.154 is the baryon mass fraction, or if the cell width is larger than a quarter of the local Jeans length. In order to keep a roughly constant physical minimum cell width, within a factor of two, increasing maximum refinement levels are triggered with decreasing redshift. In our simulations, cell widths in the CGM generally range from \u22481 kpc in the inner region of the halo to \u22483 kpc in the outer region at the halo\u2019s virial radius. This is comparable to CGM resolutions achieved in simulations like TNG50 (see Figure 1 of Nelson et al. 2020), although existing simulations 2 In MEGAFLOW, the host galaxies associated with metal absorption lines have SFRs of 3-30 M\u2299yr\u22121 and \ud835\udc40\u2605of 109 \u22121010.5 M\u2299. We refer the reader to Bouch\u00e9 et al., in prep. for a more detailed presentation of the survey and observational strategy. that focus computational efforts on the CGM itself improve resolution in the inner and outer halo by factors of 2 \u221210 from our values (e.g. Hummels et al. 2019; Peeples et al. 2019; Suresh et al. 2019; van de Voort et al. 2019; Ramesh & Nelson 2024). Thermochemistry We use the standard equilibrium thermochemistry of Ramses. Equilibrium hydrogen and helium cooling rates, via collisional ionization, collisional excitation, recombination, dielectric recombination, bremsstrahlung, and Compton cooling off the Cosmic Microwave Background, are applied using the rates listed in Rosdahl et al. (2013). For photoionization heating, we assume a Haardt & Madau (1996) UV background with an exponential cutoff for gas densities above 10\u22122 cm\u22123 due to self-shielding. For \ud835\udc47> 104 K, the cooling contribution from metals is computed using tables generated with cloudy (Ferland et al. 1998, version 6.02), assuming photo-ionization equilibrium with a Haardt & Madau (1996) UV background. For \ud835\udc47\u2264104 K, we use the fine structure cooling rates from Rosen & Bregman (1995), allowing the gas to cool radiatively to a density-independent temperature floor of 15 K. We start all our simulations with an artificially non-zero gas metallicity of \ud835\udc4dinit = 6.4\u00d710\u22126 = 3.2\u00d710\u22124 \ud835\udc4d\u2299 (we assume a Solar metal mass fraction of \ud835\udc4d\u2299= 0.02). This artificially non-pristine initial metallicity compensates for our lack of molecular hydrogen cooling channels in metal-free gas, allowing the gas to cool below 104 K, and is calibrated so that the first stars form at redshift \ud835\udc67\u224815. Star formation Star formation is considered in cells where all the following criteria are met: the hydrogen gas density is > 10 cm\u22123, the local overdensity is > 200 times the cosmic mean, the local Jeans length is smaller than one cell width, and the gas is locally convergent, and at a local maximum density. Gas is converted into stars at a rate \u00a4 \ud835\udf0c\u2217= \ud835\udf16\u2217\ud835\udf0c/\ud835\udc61ff, (1) where \ud835\udc61ff is the free-fall time and \ud835\udf16\u2217is the efficiency of star formation, which depends on local estimates of the gas turbulence and virial parameter (for details see e.g. Trebitsch et al. 2017). To follow on average the rate of star formation given by (1), the stellar particles, each representing a stellar population, are created stochastically following a Poissonian distribution which provides the mass of the new stellar particle as an integer multiple of \ud835\udc5a\u2217= 400 M\u2299(see Rasera & Teyssier 2006), and hence the minimum mass of a stellar particle is \ud835\udc5a\u2217. Our simulations also include runaway stars with a kick velocity of 50 km s\u22121, but we expect these to have little to no impact on the properties of the CGM we study in later sections (see Rey 2022). Supernova feedback Supernova (SN) feedback is implemented with the mechanical feedback model described in Kimm & Cen (2014) and Kimm et al. (2015), where the SN energy is directly injected as momentum in the gas according to how well the Sedov phase is resolved. We assume four type II SN explosions per 100 \ud835\udc40\u2299of stellar mass formed. This is about four times larger than predicted by the Kroupa (2001) initial mass function and therefore likely unrealistic, but we do this, as in the SPHINX simulations (Rosdahl et al. 2022) to prevent overcooling and unnaturally rapid star formation. SN explosions, each releasing 1051 ergs, are sampled in each stellar particle between 3 and 50 Myrs MNRAS 000, 1\u201314 (2024) 4 D. DeFelippis et al. Name MHD \ud835\udf05 (cm2 s\u22121) no-CR No \u2013 CR\u2212\ud835\udf05med Yes 1028 CR\u2212\ud835\udf05high Yes 3 \u00d7 1029 Table 1. Key differences between the three simulations analysed in this paper. The columns are, from left to right, (1) the name of the run, (2) whether MHD (and therefore CRs) is used in the run, and (3) the numerical value of the CR diffusion coefficient, when relevant. of its lifetime (Kimm et al. 2015). Each particle returns on average 20% of its initial mass back to the gas, with a metal yield of 7.5%, roughly consistent with a Kroupa (2001) initial mass function. Cosmic ray feedback CRs are modelled as a relativistic fluid that propagates anisotropically along magnetic field lines following the advection-diffusion approximation developed by Dubois & Commer\u00e7on (2016); Dubois et al. (2019), and loses energy via cooling by hadronic and coulombic interactions (Guo & Oh 2008; Dashyan & Dubois 2020). This model has already been used in several works with Ramses (e.g. Dashyan & Dubois 2020; Farcy et al. 2022; Nu\u00f1ez-Casti\u00f1eyra et al. 2022; Martin-Alvarez et al. 2023). The CRs are tracked as a nonthermal pressure term \ud835\udc43CR = \ud835\udc52CR(\ud835\udefeCR \u22121), where \ud835\udc52CR is the CR energy density and \ud835\udefeCR = 4/3 is the associated adiabatic index. The CRs are injected via each SN explosion into the gas cell hosting the exploding stellar particle, reserving 10 percent of the SN energy in each explosion to CRs.3 We run simulations with two distinct values of the CR diffusion coefficient \ud835\udf05= 1028 cm2 s\u22121 and 3 \u00d7 1029 cm2 s\u22121 in the simulations labelled CR-\ud835\udf05med and CR-\ud835\udf05high, respectively. These two values are both within reasonable constraints from observations, particularly those from the Milky Way (Strong et al. 2007; Trotta et al. 2011) which generally favor a diffusion coefficient \u223c3 \u00d7 1028 cm2 s\u22121, and are considered to bracket regimes of slowlyand rapidly-diffusing CRs and how each of them affects the CGM (see e.g. Chan et al. 2019; Nu\u00f1ez-Casti\u00f1eyra et al. 2022). We also run a simulation without CR feedback (called no-CR), for a comparative study of their effects. The three simulations, identical except for the inclusion of MHD and CR feedback, are listed in Table 1. 3 RESULTS We begin with a general description of the properties of the galaxy and CGM for the three runs (Section 3.1). We then show more detailed results demonstrating the differences in baryonic content between the three runs, first for the stars and gas within the galaxy (Section 3.2), then for gas outflowing from the galaxy (Section 3.3), and finally for gas in the CGM (Section 3.4). In Section 3.5, we compare these simulations to CGM observations. 3 We do not lower the CR energy injection fraction to compensate for the \u201cboosted\u201d SN feedback as this would likely render any resulting CR feedback completely inefficient. A non-boosted SN rate would result in a higher starformation rate and potentially more cumulative CR energy injection, but measuring the size of this effect is outside the scope of this study. 8 4 0 4 8 y [kpc] no-CR CRmed CRhigh 8 4 0 4 8 y [kpc] 8 4 0 4 8 x [kpc] 8 4 0 4 8 y [kpc] 8 4 0 4 8 x [kpc] 8 4 0 4 8 x [kpc] 3 4 5 6 7 log T [K] -27 -25 -23 -21 log  [g cm 3] -4 -3 -2 log Z Figure 1. Face-on projections of density-weighted temperature (top row), density (middle row), and metallicity (bottom row) for the central galaxy at \ud835\udc67= 1. From left to right, we show the no-CR run, the CR\u2212\ud835\udf05med run, and the CR\u2212\ud835\udf05high run. 109 1010 Stellar Mass [M ] 100 101 SFR [M yr 1] no-CR CRmed CRhigh Boogaard+18 M.S. at z=1 Figure 2. Positions of the simulated galaxy, in relation to the \ud835\udc67= 1 starformation Main Sequence described in Boogaard et al. (2018), at specific times for the three different runs. The symbols show locations of the runs at redshifts \ud835\udc67= 4 (triangles), \ud835\udc67= 3 (diamonds), \ud835\udc67= 2 (circles), and \ud835\udc67= 1 (squares) at the endpoint of the simulation. The SFR has been averaged for \u00b1200 Myr around each redshift to account for its high variability. According to their mass and SFR evolution, the simulated galaxies were exactly on the Main Sequence between 1.3 and 1.7 Gyr before their final (\ud835\udc67= 1) position. 3.1 General properties We start by showing face-on projections of the gas in the central galaxy in each run in Figure 1. Qualitatively, the addition of CRs changes the appearance and extent of the central galaxy and inner CGM. With CRs, the cold (\u2272104 K) gas is both more extended radially and distributed more smoothly within the disc, especially for CR\u2212\ud835\udf05med, which also has a higher overall gas density, while the CR\u2212\ud835\udf05high gas density within the central galaxy is largely unchanged. In CR\u2212\ud835\udf05high, the central galaxy is also embedded in a somewhat MNRAS 000, 1\u201314 (2024) The Effect of Cosmic Rays on the CGM 5 90 60 30 0 30 60 90 no-CR CRmed CRhigh 90 60 30 0 30 60 90 z [kpc] 90 60 30 0 30 60 90 90 60 30 0 30 60 90 90 60 30 0 30 60 90 x [kpc] 90 60 30 0 30 60 90 104 105 106 107 Temperature [K] 10 28 10 27 10 26 10 25 10 24 10 23 Density [g cm 3] 10 5 10 4 10 3 Metallicity Figure 3. Density-weighted temperature, density, and metallicity projections for the three runs at \ud835\udc67= 1, viewed edge-on. higher metallicity environment compared to both other runs. Based on the morphology in Figure 1, for this paper we define the \u201cgalaxy\u201d as a cylindrical region surrounding the stellar disc with a radius 0.1 \ud835\udc45vir and a height 0.05 \ud835\udc45vir above and below the midplane of the disc. At \ud835\udc67= 1, the galaxy is a rotating gas disc \u223c10 \u221220 kpc across whose ISM is metal-rich and shows a substantial amount of structure. In Figure 2, we show the star formation rate (SFR) vs. stellar mass of the central galaxy in each run at a few selected redshifts and compare it to the observed star-formation Main Sequence of galaxies. We find that the galaxy is either slightly below (no-CR and CR\u2212\ud835\udf05med) or significantly below (CR\u2212\ud835\udf05high) the observed \ud835\udc67= 1 star-formation Main Sequence at the end of the simulations. At these later times, the no-CR and CR\u2212\ud835\udf05med runs have very similar stellar masses in their central galaxies, though the central galaxy in the CR\u2212\ud835\udf05high run is slightly less massive. We examine these differences in more detail in Section 3.2. In Figure 3, we show density-weighted edge-on projections of the main halo in each of the three runs out to its virial radius, which is \u2248100 kpc. In all three runs, we see the cold (\ud835\udc47\u2264104 \ud835\udc3e), dense, and metal-rich galaxy in the centre which is clearly distinct from the warmer, more diffuse, and lower metallicity CGM. However, closer inspection reveals differences between the three runs. In both the no-CR and CR\u2212\ud835\udf05med runs the CGM is dominated by relatively diffuse gas with a mean temperature of around 106 \ud835\udc3eapart from cold gas-dominated satellites. The typical temperature in the halo of the CR\u2212\ud835\udf05high run though is nearly 1 dex lower. This indicates that the mere addition of CRs in CR\u2212\ud835\udf05med is not enough to alter the phase of the CGM: a minimum level of diffusivity must be necessary for the CRs to be able to escape from the galaxy and influence the temperature of the surrounding medium. The gas density largely MNRAS 000, 1\u201314 (2024) 6 D. DeFelippis et al. follows the temperature projections: the densest gas within the galaxy and bound to satellites is also the coldest. Unlike the temperature, the gas density shows little variation between the three runs at any location in the halo, although the density distribution in the outer halo of the CR\u2212\ud835\udf05high run appears slightly less smooth than it does in the other two runs. Finally, we examine the metallicity of CGM gas in the bottom panels. Here, as in the temperature projections, we find that metallicity distributions of the no-CR and CR\u2212\ud835\udf05med runs are very similar, but the CR\u2212\ud835\udf05high run shows a dramatically higher metallicity throughout the entire CGM. 3.2 Star formation We start our more detailed investigation of the effects of CRs on the galaxy by examining their effect on the SFR over the entire length of each run, which we show in the top panel of Figure 4. The no-CR run is characterized by a SFR that varies between \u223c2 \u22128 \ud835\udc40\u2299yr\u22121 for most of its history, except for a \u22481 Gyr time period around \ud835\udc67\u22483 where the SFR jumps above 10 \ud835\udc40\u2299yr\u22121. The galaxy in this run is therefore unambiguously star-forming with a very bursty star-formation history. In the CR\u2212\ud835\udf05med run, the addition of CRs lowers the SFR at early times in the simulation, especially during the \u201cstarburst\u201d period around \ud835\udc67\u22483, but otherwise maintains the typical value and burstiness at later times. The CR\u2212\ud835\udf05high run behaves almost the same as the CR\u2212\ud835\udf05med run, though the typical SFR after the starburst period is lower and drops down below 2 \ud835\udc40\u2299yr\u22121 at the end of the simulation. This behavior is generally consistent with the effect of CRs found in previous works such as Hopkins et al. (2020), who find that higher values of CR diffusion more effectively suppress the SFR of MW-mass galaxies. In the lower panel of Figure 4, we plot the stellar and gas masses of the central galaxy in each run over time, which shows the cumulative effect of the star formation and accretion histories. As reflected in the SFRs, the no-CR run has the strongest period of growth from \ud835\udc67\u22484\u22123 before settling down slightly, while the two CR runs\u2019 stellar masses grow more steadily throughout the simulation and are consistently below the level of the no-CR run. By the end of the simulations, noCR has a factor of \u223c2 higher stellar mass than CR\u2212\ud835\udf05high, whereas CR\u2212\ud835\udf05med is only slightly less massive than no-CR. This factor of 2 difference appears to develop during the period of high star formation, and then it remains relatively constant afterwards. The gas mass in all three runs reaches a peak after \u22483 Gyr and then either fluctuates around that value as in the no-CR and CR\u2212\ud835\udf05med runs or slowly decreases with time as the CR\u2212\ud835\udf05high run does. 3.3 Outflows In this section, we examine the properties of outflowing gas and attempt to connect galactic outflows to star formation in the galaxy. We calculate the median outflow rate over the final five snapshots of the runs, representing a narrow redshift range of 1 < \ud835\udc67< 1.1. This is a large enough number of snapshots such that transitory features of the gas distribution (e.g. a short-lived tidal tail) will be removed, and a small enough number to also ensure that we do not include cosmological evolution in the median. In Figure 5, we show these median outflow rates (i.e. gas with a positive radial velocity) in radial bins around the central galaxy for the three runs, separated by temperature ranges that roughly correspond to commonly observed ions (Mgii, Civ, and Ovi). For the coldest gas, the three runs behave very similarly overall, with high outflow rates of \u223c10 \ud835\udc40\u2299yr\u22121 very close to the centre of the galaxy which quickly drop to below 0 2 4 6 8 10 12 14 16 SFR [M  yr 1] no-CR CRmed CRhigh 1 2 3 4 5 6 Time [Gyr] 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 Mass in the galaxy [1010 M ] stars gas 8 4 3 2 1.5 1 z Figure 4. Top: SFRs of the central galaxy (defined as a cylindrical region surrounding the stellar disc with a radius 0.1 \ud835\udc45vir and a height 0.05 \ud835\udc45vir above and below the midplane of the disc) as a function of time for the no-CR (blue), CR\u2212\ud835\udf05med (orange) and CR\u2212\ud835\udf05high (green) runs. CRs reduce the SFR most significantly in the first 2.5 Gyr of the runs. Bottom: stellar and gas mass in the central galaxy as a function of time for the same three runs. 0.1 \ud835\udc40\u2299yr\u22121 by 20 kpc. However, the slope of this outflow rate is noticeably shallower for the CR\u2212\ud835\udf05high run, resulting in values smaller than the other two runs within \u224810 kpc and larger than the other two runs at the very inner edge of the CGM. Above this radius, there is no appreciable outward-moving cold gas in any of the runs, except for that in a satellite galaxy with an overall positive radial velocity in the no-CR run. In the lower two panels, however, we see much more significant differences in the CR\u2212\ud835\udf05high run compared to the other two runs. For \u201cwarm\u201d gas, which has no substantial outflowing mass anywhere in the CGM for the no-CR and CR\u2212\ud835\udf05med runs, the CR\u2212\ud835\udf05high run shows an outflow rate of 0.2\u22120.9 \ud835\udc40\u2299yr\u22121 increasing with radius in the CGM. This is also seen in hotter gas, where the outflow rate in CR\u2212\ud835\udf05high reaches and maintains order unity by \u224830 kpc whereas both of the other runs remain below CR\u2212\ud835\udf05high and only approach it near the virial radius. We find (but do not show) that the gas velocities contributing to these outflow rates are typically small with median values up to 20 km s\u22121. In the CR\u2212\ud835\udf05high run, the amount of mass moving at all positive radial velocities is larger, including some material moving above 100 km s\u22121, at all radii in the halo, meaning that the larger outflow rates come from both more outflowing mass and faster outflowing mass. These strong CR-driven outflows in the CR\u2212\ud835\udf05high run also highlight the fact that its central galaxy\u2019s steadily declining gas mass in Figure 4 is due to gas expulsion via CR feedback rather than consumption by star formation. We note however that all radial velocity distributions have a negative median value, indicating that MNRAS 000, 1\u201314 (2024) The Effect of Cosmic Rays on the CGM 7 10 2 10 1 100 101 T < 104.5 K no-CR CRmed CRhigh 10 2 10 1 100 101 Median outflow rate [M yr 1] 104.75 K < T < 105.25 K 20 40 60 80 r [kpc] 10 2 10 1 100 101 105.25 K < T < 105.75 K Figure 5. Median outflow rates of five snapshots between redshifts 1 < \ud835\udc67< 1.1 of gas in spherical shells surrounding the central galaxy for the no-CR (thin lines), CR-\ud835\udf05med (medium lines) and CR-\ud835\udf05high (thick lines) runs. The gas is separated by temperature ranges roughly corresponding to gas observed in Mgii (top panel), Civ (middle panel), and Ovi (bottom panel). slow, steady accretion remains the dominant process occurring in the halo, even when CR feedback is operating. 3.4 CGM properties We now turn to the CGM itself and highlight similarities and differences between the three runs. In Figure 6, we show stacked massweighted temperature-number density phase diagrams for the CGM of the central galaxy in the three runs for the same narrow redshift range as Figure 5. In these phase diagrams, we have removed gas that is in the central galaxy as defined in Section 3.1 so as to only consider CGM gas. First, we see that the no-CR run contains a substantial amount of gas with \ud835\udc47< 104 \ud835\udc3ein the CGM whereas the two CR runs contain much less gas below this temperature. We see from the maps in Figure 3 that this is due to a combination of the dense tidal tails surrounding and directly connected to the galaxy and the more massive and numerous satellites found in the no-CR run. The same structures are significantly reduced in number and density for both of the CR runs. Thus, the CRs are likely able to help dissipate the very dense and cold gas found primarily in satellites and some tidal tails. Most of the CGM gas in all of the runs, however, is > 104 \ud835\udc3e. For the no-CR and CR\u2212\ud835\udf05med runs, the phase structure of this hotter diffuse gas is nearly identical. The peak of these temperature distributions is \u2248106 \ud835\udc3e, and the diffuse CGM component spans roughly 1.5 orders of magnitude in density. In the CR\u2212\ud835\udf05high run however, the diffuse CGM has a noticeably cooler average temperature: it is peaked at a lower temperature of \u2248105.5 \ud835\udc3eand the temperature distribution is noticeably wider, resulting in a more substantial amount of gas at temperatures between 104 and 105 \ud835\udc3ethan the other two runs have. This behavior is qualitatively similar to other recent studies of CRs, which generally find that the CGM is cooler when CR feedback is included (e.g. Ji et al. 2020; Farcy et al. 2022). We can understand the varying effects of the CR diffusion by examining the mean pressure profiles of CGM gas. As the initial magnetic fields in these simulations are very weak, the total pressure profiles should all be roughly equal due to hydrostatic pressure equilibrium. We indeed find this to be true outside of the galaxy for \ud835\udc5f> 10 kpc, but at smaller radius the CR\u2212\ud835\udf05med run has a higher total pressure by nearly an order of magnitude. To see why this is, we plot mean pressure profiles (the median profiles are almost identical) separated into thermal and non-thermal components in Figure 7. Compared to the no-CR run, the CR\u2212\ud835\udf05med run has a thermal pressure profile that is almost identical, likely because the similar cumulative star formation between the two runs released a similar amount of energy from supernovae. However, the CR\u2212\ud835\udf05med run\u2019s non-thermal pressure exceeds the thermal pressure within the galaxy by an order of magnitude, and is the source of the discrepancy in the total pressure profiles. While it is unrealistic for such a high non-thermal pressure to persist in the galaxy without first losing energy, it does not affect the CGM at all: beyond \u224815 kpc, the thermal pressure is completely dominant, as would be expected for CRs that remain largely trapped within the galaxy due to lower diffusivity. In the CR\u2212\ud835\udf05high run, however, the non-thermal pressure is the dominant source of pressure in the galaxy and the inner \u224840 kpc of the CGM. At larger radii, the thermal and CR pressures are comparable, thus allowing slightly colder gas not heated up from the surrounding thermal pressure to exist in the entire CGM and boosting the amount of outflowing gas seen in ions like Civ and Ovi as shown in Figure 5. This also explains why the CR\u2212\ud835\udf05med run\u2019s CGM has the same temperature as the no-CR run\u2019s CGM: trapped CRs only affect the properties of the ISM and largely leave the CGM unaffected. 3.5 Comparison to observations Having provided a description of the effects CRs have on our simulated galaxy and its CGM, we now seek to compare the CGM covering fractions to those observed in quasar absorption line studies, such as the MUSE GAs FLOw and Wind (MEGAFLOW) survey 4 for Mgii (Bouch\u00e9 et al. in prep.). In particular, Schroetter et al. (2021) investigated the Mgii (and Civ) covering fraction of star-forming galaxies at 1 < \ud835\udc67< 1.4 using \u223c100 Mg ii absorption lines (rest equivalent width \ud835\udc4a\ud835\udf062796 \ud835\udc5f > 0.5\u22120.8 \u00c5) and \u223c200 star-forming galaxies within 4 This survey was designed to study the CGM properties around star-forming galaxies using the Multi Unit Spectroscopic Explorer (MUSE, Bacon et al. 2010) spectrograph on the Very Large Telescope (VLT) towards two dozen quasar sight-lines (Bouch\u00e9 et al. in prep.). MNRAS 000, 1\u201314 (2024) 8 D. DeFelippis et al. 4 3 2 1 0 1 log n [cm 3] 2 3 4 5 6 7 log T [K] no-CR 4 3 2 1 0 1 log n [cm 3] CRmed 4 3 2 1 0 1 log n [cm 3] CRhigh 104 105 106 107 108 Mass [M ] Figure 6. Median temperature-number density phase diagrams of the central galaxies\u2019 CGM for the no-CR, CR\u2212\ud835\udf05med, and CR\u2212\ud835\udf05high runs for the five snapshots between redshifts 1 < \ud835\udc67< 1.1, where the ISM (i.e. all gas within the cylindrical region of the galaxy) has been removed. The colour shows the gas mass distribution. The red and blue curves on each panel are normalized probability density functions of the temperature (red) and density (blue) of the CGM gas. CRs almost completely remove gas below 104 K from the CGM, but only \ud835\udf05high noticeably changes the phase structure of the diffuse CGM. 101 102 r [kpc] 10 15 10 14 10 13 10 12 10 11 Pressure [dyn cm 2] no-CR CRmed CRhigh thermal CR Figure 7. Mean gas pressure vs. radius for the three runs at \ud835\udc67= 1. The no-CR run only has thermal pressure (solid lines) but the two runs with CRs additionally have non-thermal pressure (dashed lines). 250 kpc of the quasar sight-lines. In addition, we also use covering fractions for the higher ions Ovi from Kacprzak et al. (2015) and Tchernyshyov et al. (2023), whose host galaxies have a similar \ud835\udc40\u2605 of 1010 \u22121011 M\u2299and 0.1 \u2272\ud835\udc67\u22720.7, and Civ from Bordoloi et al. (2014), whose host galaxies have \ud835\udc40\u2605of 108.5 \u22121010 M\u2299and \ud835\udc67< 0.1. In order to compare our simulations to these quasar sightline observations, we use Trident (Hummels et al. 2017) to populate our simulations with specific ions using parameters derived from Cloudy (Ferland et al. 2013) ionization tables. For this paper, we focus on three ions commonly observed in absorption \u2013 Mgii, Civ, and Ovi \u2013 because they each trace a different temperature phase of the gas (\u2272104 \ud835\udc3e, \u2248104 \u2212105 \ud835\udc3e, and \u2248105.5 \ud835\udc3erespectively, from Tumlinson et al. 2017). In Figure 8, we show column density maps of these three ions for the three runs at \ud835\udc67= 1. We show the observational column density cutoffs for the three ions (Schroetter et al. 2021 for Mgii and Civ and Kacprzak et al. 2015 for Ovi) as coloured contours. First, we see that at distances > 25 kpc from the galaxy all three runs exhibit a CGM similarly devoid of Mgii except for the presence of satellites. This indicates that in addition to not changing the phase structure, neither run with CRs is any more effective than the default feedback model at pushing Mgii gas out of the galaxy to large distances in the CGM. Within < 25 kpc from the galaxy though, all three runs have different Mgii properties. In no-CR, Mgii traces the clear tidal tails seen in Figure 3 whereas in CR\u2212\ud835\udf05med those tidal tails are not cold or dense enough to absorb Mgii, and there is a sudden column density drop off at the edge of the disc. In CR\u2212\ud835\udf05high, small Mgii column densities extend slightly beyond the disc but they merely approach and do not exceed current observational column density limits from MEGAFLOW. Next, we examine the Civ distributions around the galaxy (middle row of Figure 8). For the no-CR run, most of the highest Civ column densities overlap with where the Mgii is (i.e. in satellites and tidal tails) but it extends beyond where the Mgii stops, indicating the cold structures are immediately surrounded by a warmer interface. This warmer and more diffuse gas is also being stripped from satellites further out in the CGM. In the CR\u2212\ud835\udf05med run, we again see an abrupt drop off at the edge of the disc similar to what is seen in no-CR and all of the Mgii maps, as well as a diffuse envelope being stripped from satellites in the same way. However, the CR\u2212\ud835\udf05high run shows a drastically different distribution of Civ with higher column densities (\u22731013 cm\u22122) out to 50 kpc and lower values (\u22721012 cm\u22122) that reach the virial radius and are close to volume-filling. Satellite galaxies do not stand out in this Civ map in the same way they do in no-CR and CR\u2212\ud835\udf05med, indicating that this phase of gas is found more in the diffuse \u201csmooth\u201d component of the CGM (as suggested by Figure 6) and is not merely a warm \u201cinterface\u201d between cold \ud835\udc47\u2272104 \ud835\udc3estructures and hot \ud835\udc47> 106 \ud835\udc3egas. Furthermore, the highest Civ column densities in this panel also trace regions of high metallicity seen in Figure 3. Finally in the bottom row of Figure 8, we show Ovi column densities. In all three runs, this phase of gas is volume-filling, although we again see a strong dichotomy between the CR\u2212\ud835\udf05high run and the other two runs. In the former, Ovi picks up high-metallicity gas at temperatures < 106 \ud835\udc3ethat is distributed throughout the halo as seen MNRAS 000, 1\u201314 (2024) The Effect of Cosmic Rays on the CGM 9 90 60 30 0 30 60 90 Mg II no-CR CRmed CRhigh 90 60 30 0 30 60 90 z [kpc] C IV 90 60 30 0 30 60 90 90 60 30 0 30 60 90 O VI 90 60 30 0 30 60 90 x [kpc] 90 60 30 0 30 60 90 1012 1013 1014 1015 Column density [cm 2] Figure 8. Column density maps of the central haloes in the no-CR (left), CR\u2212\ud835\udf05med (middle), and CR\u2212\ud835\udf05high (right) runs at \ud835\udc67= 1, viewed edge-on. Rows show Mgii (top), Civ (middle), and Ovi (bottom). Blue, green, and red contours highlight the minimum absorber column densities observed in recent surveys from MEGAFLOW (Schroetter et al. 2021) and Kacprzak et al. (2015). In all runs, nearly all Mgii is concentrated within the galaxy, satellites, or in tidal tails, and is rare in the CGM. Civ is slightly more extended in the CGM, especially in the CR\u2212\ud835\udf05high run, and Ovi is more volume-filling in all runs, but most significantly in CR\u2212\ud835\udf05high. in Figure 3, while in both of the latter, the highest Ovi column densities primarily overlap with satellites and tidal tails as is the case with both Mgii and Civ, and at all other locations in the halo Ovi has at least 1 dex smaller column densities. Now, we make an explicit comparison to observations by plotting the covering fraction of the different ions in the CGM of our runs. In Figure 9, we show Mgii, Civ, and Ovi covering fractions as a function of impact parameter for each run calculated using all 12-14 snapshots between \ud835\udc67= 1 and \ud835\udc67= 1.3. This large sample size serves two purposes: first, to increase the number of sightlines used in the calculation and reduce the effect of transient features in the CGM (as in previous figures), and second, to better represent the spread in absorber redshifts in \ud835\udc67\u223c1 surveys like MEGAFLOW. For each snapshot, we choose a random orientation of the halo and measure the column density of sightlines along that orientation with impact parameters as large as the virial radius. We define a sightline to be \u201ccovered\u201d if it exceeds the ion column density corresponding to an equivalent width threshold used by Schroetter et al. (2021) for Mgii and Civ and Kacprzak et al. (2015) for Ovi. This conversion from equivalent width to column density depends on the wavelength considered and assumes an optically thin regime (see Rey et al. 2023, in prep. for details) and results in minimum column densities of 1012.4 cm\u22122 for Mgii, 1013.4 cm\u22122 for Civ, and 1013.9 cm\u22122 for Ovi, all roughly corresponding to equivalent widths of 0.1 \u00c5. From the upper panel of Figure 9, it is clear that none of the runs produce nearly enough Mgii absorption in the CGM to be MNRAS 000, 1\u201314 (2024) 10 D. DeFelippis et al. consistent with observations from MEGAFLOW, as well as with similar observations from other recent Mgii surveys from Dutta et al. (2020) at 0.8 < \ud835\udc67< 1.5 and Huang et al. (2021) at 0.1 < \ud835\udc67< 0.5. Within the galaxy (< 10 kpc), the CR\u2212\ud835\udf05med run produces the highest Mgii covering fractions, boosting a bit the typical values seen in the no-CR run. The CR\u2212\ud835\udf05high run lowers the covering fraction at these impact parameters. All of the runs drop below a covering fraction of 50% by 10 kpc rather than at \u224850 kpc as in the observations. Outside of the galaxy, it is actually the no-CR run that has the highest overall covering fractions, largely coming from the high-column density tidal tails connected to the galaxy that are strongest in that run. However, all of the runs are very Mgii-deficient at these impact parameters. The middle panel shows covering fractions for Civ as well as comparable observations from Bordoloi et al. (2014) and MEGAFLOW (Schroetter et al. 2021). All three runs are better at matching observed Civ covering fractions from MEGAFLOW than they are at matching Mgii as a function of impact parameter. Within the galaxy, both runs with CRs show an enhancement of the covering fraction. Both noCR and CR\u2212\ud835\udf05med drop below 50% at impact parameters < 15 kpc, noticeably closer to the galaxy than both MEGAFLOW and Bordoloi et al. (2014), and in the CGM both of these runs are significantly below the observed covering fractions. The CR\u2212\ud835\udf05high run is different: it stays much closer to the observed values from MEGAFLOW until \u224840 kpc where it starts to fall short. However, it is still significantly below the lower-redshift observations from Bordoloi et al. (2014). Finally, we show the three runs\u2019 covering fractions for Ovi, as well as comparisons to recent observations from Kacprzak et al. (2015) and Tchernyshyov et al. (2023). As for Mgii, the no-CR and CR\u2212\ud835\udf05med runs fail to reproduce observable Ovi in the CGM. The CR\u2212\ud835\udf05high run is significantly closer to observations, though at nearly all impact parameters in the CGM that run still falls very short. Interestingly, within the galaxy, only the CR\u2212\ud835\udf05high run has enough Ovi to approach observed values of the covering fraction, likely indicative of the higher metallicity environment of the CR\u2212\ud835\udf05high run seen in Figure 1. As with Bordoloi et al. (2014), these two Ovi surveys are at lower redshifts than our fiducial simulation outputs. Running the simulations to a matching lower redshift could allow the CRs more time to diffuse out from the galaxy and affect the CGM, resulting in a better agreement between the covering fractions of Civ or Ovi. However, this is unlikely to occur as from redshifts \ud835\udc67= 1.3 to \ud835\udc67= 1 none of our simulated covering fractions consistently increase or decrease. 4 DISCUSSION In this section, we first consider the effect of varying the column density thresholds used in deriving covering fractions from our simulations, to determine how sensitive our observational comparison is to small (and large) adjustments to these values. Then, we discuss our results in the context of other recent studies on the effects CRs have on the CGM. 4.1 Column density cutoffs The main results of our comparison to observations in the previous section come from assuming particular column density thresholds for the different ions derived from recent observational studies and applying those to our simulations. These precise thresholds depend on specific properties of the surveys such as the length of observations, as well as the sensitivity of the actual instruments. We may therefore reach different conclusions if a deeper set of observations 101 102 0.2 0.4 0.6 0.8 1.0 fc(NMgII > 1012.4 cm 2) MEGAFLOW Dutta+20 Huang+21 101 102 0.2 0.4 0.6 0.8 1.0 fc(NCIV > 1013.4 cm 2) no-CR CRmed CRhigh MEGAFLOW Bordoloi+14 101 102 b [kpc] 0.2 0.4 0.6 0.8 1.0 fc(NOVI > 1013.9 cm 2) Tchernyshyov+23 Kacprzak+15 Figure 9. Mgii (top), Civ (middle), and Ovi (bottom) covering fractions as a function of impact parameter for the three runs, stacked for snapshots with 1 < \ud835\udc67< 1.3. The solid black line and shaded region shows fits and the 95% confidence region from MEGAFLOW (Schroetter et al. 2021) observations of Mgii and Civ (the 95% confidence region for Civ is comparable to that of Mgii), while the coloured markers and regions show Mgii observations from Dutta et al. (2020) and Huang et al. (2021), Civ observations from Bordoloi et al. (2014), and Ovi observations from Kacprzak et al. (2015) and Tchernyshyov et al. (2023). The horizontal gray dotted line in all panels shows a covering fraction of 50%. All runs, with or without CRs, fail to produce enough Mgii or Ovi in their CGM to match observations. However, CR\u2212\ud835\udf05high is effective at boosting the Civ closer to observed levels in the CGM. of any of these ions are used. To measure this possible effect, we vary the column density threshold used to derive covering fractions, thus mimicking the effect of observing the same object with different sensitivities or resolutions. We quantify this in Figure 10, by plotting the radius at which 50% of sightlines are higher than a series of thresholds for Mgii, Civ, and Ovi as a function of that column density threshold. We see that for Mgii, this radius shows little evolution over 4 dex in column density for all three runs, and reaches a maxiMNRAS 000, 1\u201314 (2024) The Effect of Cosmic Rays on the CGM 11 10 11 12 13 14 101 102 50% fcovering radius [kpc] Mg II no-CR CRmed CRhigh 11 12 13 14 15 log N [cm 2] C IV MEGAFLOW 12 13 14 15 O VI Kacprzak+15 0.001 0.01 0.1 1 0.001 0.01 0.1 1 EW [\u00c5] 0.001 0.01 0.1 1 Figure 10. Radius at which Mgii (left), Civ (middle), and Ovi (right) reach a 50% covering fraction depending on the column density threshold chosen. Conversions between equivalent width and column density are shown on the top and bottom axes. The two solid black markers represent the observations from MEGAFLOW (Schroetter et al. 2021) also shown in Figure 9, while the grey points with error bars in the left panel are from the most recent MEGAFLOW analysis by Cherrey et al. in prep.. The pink marker represents the covering radius for Ovi from Kacprzak et al. (2015). mum of only \u224815 kpc for a minimum column density of 1010 cm\u22122. This is substantially smaller than the corresponding radius of 52 kpc from the fit to the data from Schroetter et al. (2021), as well as the radii calculated by Cherrey et al. in prep. using multiple Mgii equivalent width cutoffs \u22641 \u00c5, indicating that the simulated covering fractions are consistently below observations and not sensitive at all to the precise choice of column density (or equivalent width) used to define observable Mgii in our simulations. Civ column densities span fewer orders of magnitude throughout the halo, so its 50% covering fraction radius shows a stronger trend with the column density threshold. Reducing the column density (or equivalent width) cutoff over a common observational range from \u22481 \u00c5 to \u22480.1 \u00c5 significantly increases the 50% covering fraction radius by at least half a dex. The CR\u2212\ud835\udf05high run in particular matches the the 50% covering fraction radius of MEGAFLOW very near the survey\u2019s minimum Civ column density of \u223c1013.4 cm\u22122, and these simulations suggest that more sensitive Civ observations would reveal higher covering fractions for that ion that extend to larger and larger radii. Finally, we see that like Civ, the extent of Ovi coverage is also very sensitive to the column density threshold. All three of our runs\u2019 50% covering fraction radii vary in a similar way with column density, and slightly more strongly than in the corresponding Civ panel. The CR\u2212\ud835\udf05high run in particular has a consistently larger 50% covering fraction radius at all considered column densities. The enhancement of Civ and Ovi in the CR\u2212\ud835\udf05high run at multiple column density thresholds compared to the other two runs shows that CRs can significantly contribute to the metal enrichment of the CGM and provide an environment favorable to certain ions, but only if they are able to escape the ISM so their pressure support becomes substantial at large distances. The reason Mgii behaves differently in Figure 10 is due to the lack of cold (\u2264104 K) gas in the CGM rather than a lack of metals, which itself comes from the loss of resolution of the coldest gas structures from the ISM to the CGM, resulting in very low Mgii column densities in the CGM. Simulations with increased CGM resolution such as Hummels et al. (2019) and van de Voort et al. (2019) suggest that the typical temperature of the CGM should be lower, and heavily favor the formation of low ions like Mgii. Thus, with significantly increased resolution in the CGM, we speculate that effective CR diffusion out of the ISM would produce a similar enhancement in the Mgii covering fraction as it currently does for Civ and Ovi. 4.2 Comparisons to recent work There have been many recent efforts in adding CRs to galaxy formation simulations, and we highlight some with direct connections to our analysis of galaxy and especially CGM gas properties here. Farcy et al. (2022) modelled a set of idealised galaxies using a similar CR feedback implementation, and we compare our results to the most massive galaxy from that study as it is most similar to our simulations. In the ISM, they also find that the gas density distribution is smoother and the SFR is reduced when CRs are included. However, the effect of different diffusion coefficients changes when the galaxies are modelled from cosmological initial conditions. In Farcy et al. (2022)\u2019s idealised galaxies, the largest reduction in the SFR occurs for lower stellar masses with \ud835\udf05= 1027 cm2 s\u22121, and as \ud835\udf05increases CRs are less effective at reducing the SFR. At higher stellar masses the SFR is essentially unaffected by CRs regardless of the choice of \ud835\udf05. In our simulations the trend with \ud835\udf05is different: we find that the higher diffusion in CR\u2212\ud835\udf05high results in a lower SFR over time than CR\u2212\ud835\udf05med. This is likely because our simulations have cosmological inflows which are slowed by CRs that diffuse out of the galaxy more effectively, thus reducing fuel for star formation. We also see a qualitatively similar result in the CGM: gas surrounding the idealised galaxies is cooler when CRs are included. This is driven entirely by the changing nature of the outflowing gas, which is dominated by both warm (104 \ud835\udc3e< \ud835\udc47< 105 \ud835\udc3e) and hot (\ud835\udc47> 105 \ud835\udc3e) gas with CRs, and only hot gas without CRs, when measured 10 kpc above the galaxy disc plane. However, in our cosmological simulations, we see that unless the CR diffusivity is high, gas at temperatures below 105 \ud835\udc3edo not extend very far into the CGM at all (see Figure 3). Furthermore, from Figure 5 we see that the highest outflow rates very close to the galaxy are in all cases dominated by cold (\ud835\udc47< 104.5 \ud835\udc3e) gas, but further out beyond 10 kpc only hot gas is outflowing. Unlike in Farcy et al. (2022), \ud835\udf05= 1028 cm2 s\u22121 as used in CR\u2212\ud835\udf05med results in very little outflow enhancement at any temperature, meaning that in a cosmological environment (i.e. with longer physical timescales MNRAS 000, 1\u201314 (2024) 12 D. DeFelippis et al. and large-scale inflows), a higher level of CR diffusivity is necessary to enhance the outflow rate to distances beyond 10 kpc. Rodr\u00edguez Montero et al. (2023) also study the effect of CR feedback on properties of the ISM and outflows using a Ramses simulation setup much more similar to ours: namely, a cosmological zoom-in simulation of a Milky Way-analogue evolved to \ud835\udc67= 1.5. They use a CR diffusion coefficient of 3 \u00d7 1028 cm2 s\u22121, which lies between our CR\u2212\ud835\udf05med and CR\u2212\ud835\udf05high, although they also include CR streaming. Though we focus our attention on circumgalactic gas, we still find many key consistencies in the effects CRs have on our simulated galaxies. For example, their CR simulation has an early reduction in the stellar mass that levels off to a factor of a few by the end of their simulation, much like what we see in Figure 4, although their inclusion of CR streaming has an impact on their star formation history that is not modelled in our analysis. CRs also smooth out the gas distribution in the disc. Furthermore, they find that CR-launched outflows are more dominated by \u201cwarm\u201d (104 \ud835\udc3e< \ud835\udc47< 105 \ud835\udc3e) gas than outflows without CRs. Particularly relevant to our work, they find that a non-thermal pressure gradient similar to what we find in Figure 7 further accelerates outflowing gas in the CGM of their simulation, demonstrating how CRs can redistribute gas on galactic and circumgalactic scales concurrently. There have also been many direct comparisons to CGM observations using various simulation codes such as Enzo, Gizmo and ChaNGa, which have found differing specific effects. While the overall temperatures of the CGM are cooler with CRs, the column density profiles of key ions do not always change in the same way. For example, in simulations from Salem et al. (2016), Ovi column densities are enhanced by nearly a factor of 100 when CRs are included in the physics model. Other studies have less drastic changes: in the inner regions of the CGM, Ji et al. (2020) finds an enhancement of the Ovi column density by a factor of \u22483 for halo masses comparable to ours. However, the simulations from Butsky et al. (2022) actually have lower Ovi column densities in the CGM with CRs than without. We speculate that this opposite effect observed in Butsky et al. (2022) originates from their \u201cblastwave\u201d supernova feedback model, in which cooling is temporarily disabled over some timescale. Rosdahl et al. (2017) showed that turning off cooling in supernova remnants tends to produce much cooler (i.e. Ovi-poorer) outflows than other supernova feedback models, so adding CRs may not boost Ovi column densities in the CGM. More intermediate ions like Siiii and Siiv are consistently enhanced in these simulations at levels currently probed by observations, but Mgii as measured by Ji et al. (2020) is only enhanced at column densities that are below current observational limits for radii outside the inner \u224830 kpc. Importantly, this indicates that highequivalent width Mgii observationssuchas thosefromMEGAFLOW are difficult to reproduce with CRs across multiple simulation codes. The simulations in these two studies use CR diffusion coefficients of 1 to a few \u00d7 1029 cm2 s\u22121, suggesting that higher values of diffusion are favored for matching CGM observations, especially at larger radii. The comparably high CR diffusion we use in our simulations is not enough to increase Mgii to the levels seen in large CGM absorption surveys, although as CR transport is fairly unconstrained the possibility of CR diffusion alone affecting the CGM at those levels cannot be ruled out. It is also likely that with higher resolution of the cold phase, CRs effect on Mgii in the CGM could be larger and bring the simulations closer to observations, even with the same CR diffusion coefficient. 5 CONCLUSIONS In this paper, we ran three Ramses simulations in order to understand the possible range of effects that CR feedback has on the CGM of galaxies. We evolved three realizations of the same galaxy from cosmological initial conditions to \ud835\udc67= 1 with no additional CR feedback (no-CR), CR feedback with a moderate value of 1028 cm2 s\u22121 for the CR diffusion coefficient (CR\u2212\ud835\udf05med), and CR feedback with a high value of 3 \u00d7 1029 cm2 s\u22121 for the CR diffusion coefficient (CR\u2212\ud835\udf05high). Our conclusions are as follows: (i) Over cosmological time, cosmic rays can smooth out the density distribution within the galaxy\u2019s ISM and expand the gas disc, though if the cosmic ray diffusion coefficient \ud835\udf05is large, this effect is minimal (Figure 1). (ii) As is the case for galaxies of a similar mass from other idealised and zoom-in simulations, cosmic rays lower the star formation rate, resulting in a slightly lower stellar mass by \ud835\udc67= 1 (Figure 4). (iii) The CR\u2212\ud835\udf05high run with a higher cosmic ray diffusion coefficient has a CGM that is cooler and, crucially, much richer in metals than either the no-CR run or the CR\u2212\ud835\udf05med run, indicating that the \u201csweet spot\u201d of CR diffusivity (see, e.g. Hopkins et al. 2020) necessary for CRs to affect the phase of the gas and the observability of metal ions beyond the immediate vicinity of the galaxy without completely decoupling the from the gas is at least 1029 cm2 s\u22121 (Figures 3 and 6). (iv) Cosmic rays with a high diffusion coefficient accelerate outflowing gas substantially further out into the CGM by enhancing such gas with temperatures \ud835\udc47\u2265105 \ud835\udc3eat distances above \u224820 kpc from the galaxy (Figure 5). (v) Cosmic ray pressure dominates but remains confined to the galaxy for smaller \ud835\udf05, but it dominates or is comparable to thermal pressure in the entire halo for larger \ud835\udf05, thus allowing more low temperature gas to exist throughout the halo (Figure 7). (vi) Cosmic rays do not significantly increase Mgii column densities anywhere in the halo, although they do restructure Mgii found near the galaxy-halo interface. The CR\u2212\ud835\udf05high run noticeably enhances ions found at higher temperatures (Civ and Ovi) throughout the halo (Figure 8). (vii) All three of our runs fail to match observed Mgii covering fractions in the CGM from multiple surveys at \ud835\udc67\u22481. The CR\u2212\ud835\udf05high run in particular actually lowers the Mgii covering fraction at all impact parameters. However, the same run increases the covering fraction of Civ and brings it more in line with MEGAFLOW observations (Figure 9). (viii) By reducing the column density threshold used to define the covering fraction, the \u201cobserved\u201d extent of Civ and Ovi moves outwards into the CGM, especially for the CR\u2212\ud835\udf05high run. This does not occur for Mgii because its spread in column densities between small and large radii is much bigger than the same spread for the other measured ions (Figure 10). With this work, we have studied how CR feedback can propagate out from the galaxy and affect the CGM differently depending on the CR diffusion coefficient. While the Mgii content of the CGM appears largely unaffected by the addition of CRs, the CGM as a whole and outflowing gas in particular have a lower temperature when CRs are able to effectively diffuse out from the galaxy. This diffusion is more relevant when modelling outflows with a cosmological zoom-in simulation rather than from an idealised galaxy without any inflows. We expect CR diffusion to be even more effective in future highresolution studies of the CGM where there will likely be a more prominent cold phase for CRs to influence. MNRAS 000, 1\u201314 (2024) The Effect of Cosmic Rays on the CGM 13 We note that the CRs in this study all propagate with a constant rate of diffusion. Recent work has focused on a more realistic treatment of CR transport by allowing \ud835\udf05to vary with gas properties (Farber et al. 2018; Semenov et al. 2021), or by modelling the CR spectrum which allows \ud835\udf05to vary with CR energy (Girichidis et al. 2022). Butsky et al. (2023) confirms that a constant \ud835\udf05cannot reproduce the observed complexity of the CGM of COS-Halos galaxies, showing that these more detailed models are indeed necessary for future work. Additionally, other CR transport methods we have not modelled such as streaming could significantly change how the energy from CRs affects the temperature and density structures found in the CGM (Butsky & Quinn 2018), and the evolution of the galaxy in general (Wiener et al. 2017). The importance of CR streaming relative to diffusion is an active area of study as well (e.g. Thomas et al. 2023). As work on this topic continues, we intend to further examine the possible constructive impact on CRs of other physical effects (e.g., radiative transfer) and sources of feedback (e.g., AGN) that are not included in our simulations, as this may help provide the physical coupling necessary to produce cold Mgii-bearing outflows that are found in observations. ACKNOWLEDGEMENTS We thank the anonymous referee for helpful comments that improved the paper. This work has been carried out thanks to the support of the ANR 3DGasFlows (ANR-17-CE31-0017). Simulations were run using the GENCI allocations A0070410560 from 2019 and A0070410560 from 2020, and they were stored and analysed on PSMN (P\u00f4le Scientifique de Mod\u00e9lisation Num\u00e9rique) of the ENS de Lyon. DATA AVAILABILITY The data generated and used in this article will be shared on reasonable request to the corresponding author.",
                    "introduction": "The diffuse gas surrounding galaxies (often referred to as the cir- cumgalactic medium, [CGM]) is made of several dynamical states (inflowing and outflow) and multiple phases (e.g. Tumlinson et al. 2017; Faucher-Gigu\u00e8re & Oh 2023). At any given time, gas inflowing (such as gas accretion from the cosmic web) and outflowing (such as galactic winds from supernovae and active galactic nuclei) occur in the CGM environment. Therefore, by studying the properties of a galaxy\u2019s CGM, it is possible to gain insights into these important processes of galaxy formation and evolution. Observationally, the CGM is best studied using absorption line spectroscopy of quasar sightlines passing near foreground galaxies. From these quasar spectra, it is possible to infer column densities and the kinematics of gas along the line of sight. This technique has been developed and utilized over many decades to produce a rich collection of CGM observations from dedicated surveys like COS- Halos (e.g. Burchett et al. 2019), KBSS (e.g. Turner et al. 2014), and MEGAFLOW (e.g Schroetter et al. 2016). Results from these observational efforts have concluded that the CGM is composed of many different gas phases that fall into one of two broad categories. First, a cold dense phase traced by ions such as Mgii and Siiii that has multiple kinematic components along most sightlines, suggesting \u2605E-mail: d.defelippis@columbia.edu a clumpy distribution within the CGM1, and second, a hot diffuse phase traced by ions such as Ovi and with broader absorption lines indicating a higher velocity dispersion and fewer spatially distinct clouds (e.g. Rudie et al. 2019). In order to understand the origins of and interplay between these different gas phases, it is necessary to model the CGM environment of galaxies with numerical simulations. In recent years, much progress has been made in simulating the CGM at many different scales, ranging from idealised simulations (e.g. Kopenhafer et al. 2023) to large cosmological simulations (e.g. Nelson et al. 2020). In all cases, it is necessary to model the effects of feedback from galaxies to produce a realistic CGM environment. Generally, modern simulations (e.g. Pillepich et al. 2018a) accom- plish this with feedback from two main sources: stars and active galactic nuclei (AGN). Stellar feedback usually consists of energy from supernovae explosions, as well as radiation pressure from mas- sive stars, and is capable of launching gas out of the galaxy where it can either exit the halo completely or reaccrete onto the galaxy at a later time, producing \u201cfountain flows\u201d (e.g. \u00dcbler et al. 2014; DeFelippis et al. 2017). AGN feedback is usually more dominant in massive galaxies, where supermassive black holes launch fast 1 This general characterization of the cold phase is somewhat redshift de- pendent: at low redshifts (\ud835\udc67\u22720.2) not considered in this paper, the inferred densities of the cold phase are significantly lower (see, e.g. Werk et al. 2014; McCourt et al. 2018). \u00a9 2024 The Authors arXiv:2403.14748v1  [astro-ph.GA]  21 Mar 2024 2 D. DeFelippis et al. intermittent jets from the centres of galaxies capable of drastically affecting the composition and kinematics of CGM gas over time (e.g. Obreja et al. 2023). With these two sources of feedback, modern cos- mological simulations such as the IllutrisTNG suite (Marinacci et al. 2018; Naiman et al. 2018; Nelson et al. 2018; Pillepich et al. 2018b; Springel et al. 2018; Nelson et al. 2019; Pillepich et al. 2019), EA- GLE (Schaye et al. 2015), and Horizon-AGN (Dubois et al. 2016) are capable of producing realistic populations of galaxies in terms of quantities like stellar mass, angular momentum, and overall shape. They are also capable of generating predictions for the mass content of the CGM and outflows (e.g. Davies et al. 2020; Mitchell et al. 2020), but these vary significantly depending on the galaxy forma- tion model used, and are not necessarily in agreement with CGM observations. One of the major difficulties cosmological simulations have with respect to CGM observations is related to the content of galactic outflows. Indeed, observations show that galactic outflows are mul- tiphase, consisting of gas at high temperatures of \ud835\udc47> 106 \ud835\udc3e(e.g. Chisholm et al. 2018; Veilleux et al. 2022) as well as low temper- atures of \ud835\udc47\u2272104 \ud835\udc3e(e.g. Schroetter et al. 2019; Zabl et al. 2020; Avery et al. 2022). However, simulations have historically struggled to produce lower temperature \u201ccold\u201d outflows and often require out- flows to be very fast and very hot in order to produce realistic galaxy populations, thus sacrificing the realism of the CGM and potentially altering the way in which the CGM and galaxy interact over longer Gyr timescales. Improvements in resolution and feedback models have reduced the gap between observed and simulated outflows (e.g. Nelson et al. 2019; Peeples et al. 2019), but it still remains very difficult for stellar and AGN feedback alone to generate substantial and consistent cold outflowing gas. A possible solution to this problem is to include in simulations other physically-motivated mechanisms by which gas can be expelled from the galaxy that might have been overlooked. A well-studied mechanism that has received much attention in recent years are cos- mic rays (CRs) from supernovae explosions. From observations of the Milky Way, energy from CRs is expected to be in equipartition with energy from other sources like gravity and turbulence (Boulares & Cox 1990) and to represent \u223c10% of all the energy released by supernovae (e.g. Morlino & Caprioli 2012), thus meaning it could significantly impact the dynamics of galaxies and the CGM. This is found to be the case: many recent studies have shown that the CGM in simulations of galaxies better reproduce absorption sightline obser- vations from surveys like COS-Halos (e.g. Werk et al. 2016) when CR feedback is implemented (Salem et al. 2016; Butsky & Quinn 2018; Ji et al. 2020; Butsky et al. 2022). In these works, the CGM tends to have lower average temperatures when CR feedback is included. In these recent studies, CRs have been implemented in a variety of different ways. Nearly all of them centre on how to treat the CR diffusion coefficient \ud835\udf05, which helps set the timescale needed for the energy from CRs to escape the location they are injected in (i.e., a supernova). This diffusion can occur isotropically or anisotropically from its source, at a constant or variable rate (e.g. Butsky et al. 2023), and at a single energy bin or along a spectrum of possible energies (e.g. Hopkins et al. 2021; Girichidis et al. 2022). CRs can also be transported by streaming along magnetic field lines rather than diffusion through the ambient medium (e.g. Wiener et al. 2017), or even a combination of both methods (e.g. Jiang & Oh 2018; Thomas & Pfrommer 2019; Hopkins et al. 2022). These choices result in differing galaxy properties, particularly on the cold gas content and velocity of emerging outflows, the amount of regulation of star formation, and the gas temperature and density structure of the interstellar medium (ISM) and CGM, so constraining the possible implementations of CRs in simulations is crucial. The numerical value of the diffusion coefficient \ud835\udf05has been shown to make a huge difference on the temperature distribution and outflow rates of gas, sometimes by orders of magnitude, by setting the rate of CR transport which itself determines the shape of the CR pressure gradient. While it is possible to loosely constrain the possible values of \ud835\udf05using gamma-ray luminosities from the Milky Way and local starburst galaxies (e.g. Chan et al. 2019; Nu\u00f1ez-Casti\u00f1eyra et al. 2022), the resulting properties of the CGM are different enough that they can be used to set boundaries on \ud835\udf05. Following several recent analyses (e.g. Girichidis et al. 2018; Jacob et al. 2018; Dashyan & Dubois 2020; Farcy et al. 2022; Girichidis et al. 2024), we seek to study the effect of varying the diffusion coefficient \ud835\udf05on the CGM by quantifying how the observable properties of the CGM, such as the covering fractions, change with \ud835\udf05. This will shed light on whether CR diffusion may be a key missing ingredient in galaxy formation models. In this paper, we study the effect CRs have on the CGM using cos- mological \u201czoom-in\u201d simulations. In particular, we study how CRs affect the CGM by comparing the covering fraction of metal lines to CGM absorption surveys such as the MEGAFLOW survey (Zabl et al. 2019; Schroetter et al. 2021). The structure of this paper is as follows. In Section 2, we detail the galaxy formation model and simulation setup of our analysis. In Section 3, we then present re- sults of our simulations showing the effect of CRs on the overall gas distribution in the halo (Section 3.1), properties of the galaxy (Sec- tion 3.2), properties of the CGM (Sections 3.3 and 3.4), and CGM observables (Section 3.5). In Section 4 we discuss the constraining power of CGM observations on our results and put our results in context of other recent work on CR feedback. Finally, we summarize our results and conclude in Section 5. Throughout this work we assume a \u039bCDM universe with dark energy fraction \u03a9\u039b = 0.6825, matter fraction \u03a9m = 0.3175, baryonic fraction \u03a9b = 0.049, Hubble constant H0 = 67.11 km s\u22121 Mpc\u22121, and amplitude of density fluctuations \ud835\udf0e8 = 0.83. These parameters are consistent with results from Planck Collaboration et al. (2014)."
                },
                {
                    "url": "http://arxiv.org/abs/2102.08383v2",
                    "title": "A Comparison of Circumgalactic MgII Absorption between the TNG50 Simulation and the MEGAFLOW Survey",
                    "abstract": "The circumgalactic medium (CGM) contains information on gas flows around\ngalaxies, such as accretion and supernova-driven winds, which are difficult to\nconstrain from observations alone. Here, we use the high-resolution TNG50\ncosmological magnetohydrodynamical simulation to study the properties and\nkinematics of the CGM around star-forming galaxies in\n$10^{11.5}-10^{12}\\;M_{\\odot}$ halos at $z\\simeq$ 1 using mock MgII absorption\nlines, which we generate by postprocessing halos to account for photoionization\nin the presence of a UV background. We find that the MgII gas is a very good\ntracer of the cold CGM, which is accreting inward at inflow velocities of up to\n50 km s$^{-1}$. For sight lines aligned with the galaxy's major axis, we find\nthat MgII absorption lines are kinematically shifted due to the cold CGM's\nsignificant corotation at speeds up to 50% of the virial velocity for impact\nparameters up to 60 kpc. We compare mock MgII spectra to observations from the\nMusE GAs FLow and Wind (MEGAFLOW) survey of strong MgII absorbers\n($\\rm{EW}^{2796\\r{A}}_{0}>0.5 \\; \\r{A}$). After matching the equivalent-width\n(EW) selection, we find that the mock MgII spectra reflect the diversity of\nobserved kinematics and EWs from MEGAFLOW, even though the sight lines probe a\nvery small fraction of the CGM. MgII absorption in higher-mass halos is\nstronger and broader than in lower-mass halos but has qualitatively similar\nkinematics. The median-specific angular momentum of the MgII CGM gas in TNG50\nis very similar to that of the entire CGM and only differs from non-CGM\ncomponents of the halo by normalization factors of $\\lesssim$ 1 dex.",
                    "authors": "Daniel DeFelippis, Nicolas F. Bouch\u00e9, Shy Genel, Greg L. Bryan, Dylan Nelson, Federico Marinacci, Lars Hernquist",
                    "published": "2021-02-16",
                    "updated": "2021-12-16",
                    "primary_cat": "astro-ph.GA",
                    "cats": [
                        "astro-ph.GA"
                    ],
                    "main_content": "Corresponding author: Daniel DeFelippis d.defelippis@columbia.edu pass through the local environment surrounding galaxies, often called the circumgalactic medium (CGM). The CGM might contain a substantial amount of angular momentum as shown by many studies of galaxy simulations (e.g., Stewart et al. 2011; Danovich et al. 2015; DeFelippis et al. 2020). As the gas accretes onto the galaxy, the angular momentum will flow inward too, meaning the CGM is a source not just of the mass of the disk, but its angular momentum as well. Not all gas surrounding galaxies is inflowing though: the CGM also contains outflowing gas ejected from the arXiv:2102.08383v2  [astro-ph.GA]  16 Dec 2021 2 DeFelippis et al. galaxy by feedback from supernovae and active galactic nuclei (AGN), which is capable of a\ufb00ecting the way in which CGM gas eventually joins the galaxy (DeFelippis et al. 2017). All of these physical processes occur concurrently and result in a multiphase environment shown in observations to have complex kinematics (see Tumlinson et al. 2017, and references therein). A large number of recent observations of the CGM have been accomplished through absorption line studies of background quasars through dedicated surveys (e.g., Liang & Chen 2014; Borthakur et al. 2015; Kacprzak et al. 2015). For instance, some surveys are constructed by cross-correlating quasar absorption lines with spectroscopic redshift surveys such as the Keck Baryonic Structure Survey (KBSS; Rakic et al. 2012; Rudie et al. 2012; Turner et al. 2014) or with photometric surveys like the Sloan Digital Sky Survey (SDSS; Huang et al. 2016; Lan & Mo 2018; Lan 2020). Other CGM surveys attempt to either match individual absorption lines to known galaxies (i.e., are \u201cgalaxy selected\u201d), like the COS-Halos (e.g., Tumlinson et al. 2011; Werk et al. 2013; Borthakur et al. 2016; Burchett et al. 2019), COS-LRG (Chen et al. 2018; Zahedy et al. 2019), and the lowredshift Keck surveys conducted at Keck Observatory (Ho et al. 2017; Martin et al. 2019), or match galaxies near known absorbers (i.e., \u201cabsorber selected\u201d) such as the MusE GAs FLOw and Wind survey (MEGAFLOW; Schroetter et al. 2016, 2019, 2021; Wendt et al. 2021; Zabl et al. 2019, 2020, 2021). In these surveys, there is generally only one quasar sight line per galaxy, but in certain rare cases it is possible to \ufb01nd multiple sight lines associated with a single galaxy through multiple quasars (Bowen et al. 2016), a single multiply lensed quasar (Chen et al. 2014; Zahedy et al. 2016; Kulkarni et al. 2019), an extended lensed quasar (Lopez et al. 2018), or even an extended background galaxy (Diamond-Stanic et al. 2016). The Mgii ion has been a focus of many recent surveys including the Mgii Absorber-Galaxy Catalog (MAGIICAT; Chen & Tinker 2008; Chen et al. 2010a; Nielsen et al. 2013b,a, 2015), the Magellan MagE Mgii (M3) Halo Project (Chen et al. 2010a,b; Huang et al. 2021), the MUSE Analysis of Gas around Galaxies Survey (MAGG; Dutta et al. 2020), the PRIsm MUlti-object Survey (PRIMUS; Coil et al. 2011; Rubin et al. 2018), and the aforementioned MEGAFLOW survey, as well as individual absorbers (e.g., Lopez et al. 2020). These studies belong to a long history of Mgii \u03bb2796 absorption line surveys (e.g., Bergeron & Boiss\u00b4 e 1991; Bergeron et al. 1992; Steidel & Sargent 1992), which unveiled the \ufb01rst galaxy\u2013absorber pairs at intermediate redshifts. Though not the focus of this paper, Mgii has also been seen in emission in extended structures around the galaxy and in the CGM (e.g., Rubin et al. 2011; Rickards Vaught et al. 2019; Rupke et al. 2019; Burchett et al. 2021; Zabl et al. 2021). Along with this wealth of Mgii observations, researchers in recent years have found Mgii kinematics to be correlated over large spatial scales. In particular, both Bordoloi et al. (2011) and Bouch\u00b4 e et al. (2012) found a strong dependence of Mgii absorption on azimuthal angle: speci\ufb01cally, more absorption near \u03c6 = 0\u25e6 and 90\u25e6and a lack of absorption near 45\u25e6. This type of absorption distribution is generally interpreted as bipolar out\ufb02ows along the minor axis and in\ufb02ows along the major axis. In this context, both galaxy-selected (e.g., Ho et al. 2017; Martin et al. 2019) and absorptionselected Mgii studies (e.g., Kacprzak et al. 2012; Bouch\u00b4 e et al. 2013, 2016; Zabl et al. 2019) have given support to the interpretation of accretion of gas from the CGM onto the galaxy. These Mgii studies show that when sight lines are located near the major axis of the galaxy there are clear signatures of corotating cold gas with respect to the galaxy kinematics. However, despite such extensive observational data, developing a general understanding of cold gas in the CGM from the Mgii line alone remains di\ufb03cult due to the limited spatial information provided by the observational technique (though IFU mapping of lensed arcs in e.g., Lopez et al. 2020, Mortensen et al. 2021, and Tejos et al. 2021 can improve this in the future), as well as the fact that Mgii gas may not be representative of the entire cold phase of the CGM. To study more physically fundamental properties of the CGM, it is therefore necessary to turn to galaxy simulations. In cosmological simulations (see Vogelsberger et al. 2020 for a review), the CGM has been notoriously di\ufb03cult to model accurately due to the need to resolve very small structures (e.g., Hummels et al. 2019; Peeples et al. 2019; Suresh et al. 2019; Corlies et al. 2020). Nonetheless, the CGM has been shown to preferentially align with and rotate in the same direction of the galaxy, especially near the galaxy\u2019s major axis (Stewart et al. 2013, 2017; Ho et al. 2019; DeFelippis et al. 2020), which is qualitatively consistent with observations in the same spatial region of the CGM (e.g., Zabl et al. 2019). However, this general qualitative agreement between simulations and observations is di\ufb03cult to put on \ufb01rm ground quantitatively due to the inherent di\ufb00erences between observations and simulations. In this paper, we analyze a set of halos from the TNG50 simulation (Nelson et al. 2019; Pillepich et al. 2019) using the Trident tool (Hummels et al. 2017) to model the ionization state of the CGM and then perCircumgalactic Mgii in TNG and MEGAFLOW 3 form a quantitative comparison of the kinematics of the cool (T \u22723 \u00d7 104 K) CGM traced by Mgii absorption to major-axis sight lines from the MEGAFLOW survey (Zabl et al. 2019) while attempting to match the observational selection criteria as described in Section 2. We note that our comparison to MEGAFLOW galaxies with stellar masses M\u2217\u223c1010 M\u2299is complementary to that of both Nelson et al. (2020), who study the origins of cold CGM gas of very massive galaxies (M\u2217> 1011 M\u2299), and Nelson et al. (2021), who study properties of extended Mgii emission in the CGM. The paper is organized as follows. In Section 2, we describe the TNG50 simulation and MEGAFLOW sample used in the comparison, and we outline the analysis pipeline used to generate mock observations. In Section 3, we describe our main results, \ufb01rst by comparing the simulated and real observations, then by analyzing the features of the simulation that give rise to the properties of the mock observations. In Section 4, we discuss the implications of our results for the role of the CGM in galaxy formation, and we summarize our \ufb01ndings in Section 5. 2. METHODS 2.1. Simulations We utilize the TNG50 simulation (Nelson et al. 2019; Pillepich et al. 2019), the highest-resolution version of the IllustrisTNG simulation suite (Marinacci et al. 2018; Naiman et al. 2018; Nelson et al. 2018; Pillepich et al. 2018; Springel et al. 2018), which is itself based on the original Illustris simulation (Vogelsberger et al. 2014a,b). TNG50 evolves a periodic \u2248(52 Mpc)3 box from cosmological initial conditions to z = 0 with the moving-mesh code Arepo (Springel 2010; Weinberger et al. 2020). It has a baryonic mass resolution of \u223c8.5\u00d7104 M\u2299per cell, which is a factor of \u224816 better than the resolution of TNG100. We discuss the e\ufb00ect of simulation resolution on our results later in Section 3. 2.2. Observational Data The MEGAFLOW survey (N. Bouch\u00b4 e et al., in preparation) consists of a sample of 79 Mgii \u03bb\u03bb2796, 2803 absorbers in 22 quasar lines of sight observed with the Multi-Unit Spectroscopic Explorer (MUSE; Bacon et al. 2006). The quasars were selected to have at least three Mgii absorbers from the Zhu & M\u00b4 enard (2013) SDSS catalog in the redshift range 0.4 < z < 1.4 such that the [Oii] \u03bb\u03bb3727, 3729 galaxy emission lines fell within the MUSE wavelength range (4800 \u22129300 \u02da A). A threshold on the rest-frame equivalent width of \u223c0.5 \u22120.8 \u02da A was also imposed on each absorber. 11.0 11.5 12.0 12.5 13.0 log Mvir [M ] 2.0 1.5 1.0 0.5 0.0 0.5 1.0 1.5 2.0 log SFR [M yr 1] 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 log M*  [M ] Figure 1. Star formation rate of the central galaxy vs. halo mass for all TNG50 halos between 1011 M\u2299and 1013 M\u2299at z = 1. Each point is colored by the stellar mass of the halo\u2019s central galaxy. Two thick vertical lines demarcate the halo mass range of the \ufb01ducial sample. For this paper, we focus on a preliminary subset of the MEGAFLOW sample of Mgii absorber\u2013galaxy pairs whose quasar location is positioned within 35\u25e6of the major axis of the host galaxy (Zabl et al. 2019). This subset consists of nine absorber\u2013galaxy pairs with redshifts 0.5 < z < 1.4 and impact parameters (b) ranging from 13 to 65 kpc with a mean of \u224834 kpc. Zabl et al. (2019) found that the Mgii gas in these absorbers show a strong preference for corotation with their corresponding host galaxies. The galaxies in Zabl et al. (2019) are both fairly isolated by having at most one companion within 100 kpc, and star forming with [Oii] \ufb02uxes fOii > 4 \u00d7 10\u221217 erg s\u22121 cm\u22122, i.e., star-formation rates \u2273 1 M\u2299yr\u22121. The galaxies have stellar masses M\u2217ranging from 109.3\u22121010.5 M\u2299and halo masses Mvir ranging from \u22481011.4 \u22121012.2 M\u2299, where Mvir is de\ufb01ned from the stellar mass\u2013halo mass relation from Behroozi et al. (2010). As Zabl et al. (2019) show, these halo masses generally match the Bryan & Norman (1998) de\ufb01nition of Mvir. 2.3. Sample selection and Forward Modeling Figure 1 shows the central galaxies\u2019 instantaneous star formation rates (SFR) and stellar masses of all TNG50 halos in and around the mass range of interest. Since we aim to compare the Mgii absorption properties of mock line-of-sight (LOS) observations through TNG50 halos to those of major-axis sight lines of the MEGAFLOW survey, we \ufb01rst select a sample of simulated halos at z = 1 in the mass range 1011.5 M\u2299< Mhalo < 1012 M\u2299 using the Bryan & Norman (1998) de\ufb01nition for Mhalo, which results in a sample of 495 halos. In the remainder of this paper, we will refer to this subsample as 4 DeFelippis et al. the \u201c\ufb01ducial\u201d sample. The chosen redshift is typical for the Zabl et al. (2019) sample, and the halo mass range covers the typical inferred virial masses of their halos. Nearly all of the halos in our \ufb01ducial sample host central galaxies with SFR \u22731 M\u2299yr\u22121 and stellar masses of \u223c1010 M\u2299, which is consistent with the MEGAFLOW subsample as described in Section 2.2. For each halo, we adjust all velocities to be in the center-of-mass frame of the stars in the central galaxy, and we rotate it so that the stellar speci\ufb01c angular momentum of the central galaxy points in the +z-direction (the xand y-directions are both arbitrary). With this geometry we then de\ufb01ne a sight line in the x \u2212z plane by the impact parameter b, the azimuthal angle \u03b1, and the inclination angle i, where b is the projected distance from the center of the galaxy in the y \u2212z plane (i.e., \u201csky\u201d plane), \u03b1 is the angle above the rotational plane of the galaxy, and i is the angle of the sight line with respect to the sky plane. In this setup, edge-on and face-on views have i = 90\u25e6and i = 0\u25e6, respectively (see Figure 1 of Zabl et al. 2019 for a sketch of the geometry described here). In order to mimic the observations of Zabl et al. (2019), we select sight lines through each halo at values of b ranging from 15 kpc to 60 kpc, \u03b1 = 5\u25e6and 25\u25e6, and at i = 60\u25e6, representing the average inclination angle of a random sight line. In order to generate observations of our TNG50 sample, we use the Trident package (Hummels et al. 2017), which calculates ionization parameters for outputs of galaxy simulations using properties of the simulated gas cells and Cloudy (Ferland et al. 2013) ionization tables. These tables take as input the gas temperature, density, metallicity, and cosmological redshift of each gas cell and provide ionization fractions and number densities of desired ions. We make use of the current development version of Trident1 (v1.3), which itself depends on the current development version of yt2 (v4.0). In this paper, we use a set of ion tables created assuming collisional ionization equilibrium, photoionization from a Faucher-Gigu` ere et al. (2009) UV background, and selfshielding of neutral hydrogen (for details see Emerick et al. 2019 and Li et al. 2021), as this was the background radiation model used to evolve the TNG50 simulation. We also use the elemental abundance of magnesium in each gas cell tracked by the simulation rather than assuming a constant solar abundance pattern throughout the halo to achieve greater self-consistency with TNG50. 1 http://trident-project.org 2 https://yt-project.org 5 4 3 2 1 0 log n [cm 3] 3 4 5 6 7 8 log T [K] 10 8 10 6 10 4 10 2 100 Mg II probability dex 2 Figure 2. Temperature\u2013number density phase diagram of a single TNG50 halo at z = 1, colored by the Mgii mass probability density per dex2. Contours show the distribution of all gas mass in the halo. We note, however, that our results are not particularly sensitive to either of these choices. Since our focus is on the Mgii \u03bb2796 line, we show in Figure 2 a temperature\u2013density phase diagram of the gas in one of the TNG50 halos from our sample, colored by the Mgii mass probability density. From this plot, it is clear that Mgii is mostly formed from the coldest (\u2272104.5 K) and densest (\u22730.01 cm\u22123) gas in the halo, though some Mgii mass exists at a larger range of temperatures and densities. However, contours showing the total gas mass demonstrate that despite this large range in temperature and density, essentially none of the diffuse \u201chot\u201d phase, comparable in mass to the cold phase, contributes to Mgii absorption. We also note here that for this analysis we are excluding star-forming gas as its temperature and density are de\ufb01ned using an e\ufb00ective equation of state (Springel & Hernquist 2003) and are therefore not analogous to the physical properties of non-star-forming gas. Properly modeling the physical properties of the star-forming gas (see Ramos Padilla et al. 2021 for an example of this technique) introduces a level of complexity not necessary for this analysis: we \ufb01nd that our results are not a\ufb00ected by the exclusion of this gas since our sight lines through the CGM rarely intersect any star-forming gas cells as most of them are within the galactic disk. 3. RESULTS We \ufb01rst present in Section 3.1 the results of directly comparing the Mgii properties of TNG50 and MEGAFLOW using the analysis described in Section 2. Then, we further analyze the 3D kinematic properties Circumgalactic Mgii in TNG and MEGAFLOW 5 halo 225 50 kpc 13 14 15 16 17 log Mg II column density [cm 2] halo 265 halo 271 halo 340 Figure 3. Mgii column density maps of four TNG50 halos from the \ufb01ducial halo mass bin of 1011.5 M\u2299< Mhalo < 1012 M\u2299at z = 1, aligned so the angular momentum vector of the stars in the central galaxy points along the vertical axis (i.e., edge-on). The lower limit of the color bar is chosen to approximate observational detection limits. The red circle in each panel is centered on the galaxy and has a radius of twice the galaxy\u2019s stellar half-mass\u2013radius, and the blue scale-bar shows a distance of 50 kpc on the maps. The complexity and diversity of Mgii structure in the CGM of similar-mass halos are evident even in this small sample. of the Mgii-bearing gas from TNG50 in Section 3.2 and consider evolution of Mgii absorption properties with halo mass and simulation resolution in Section 3.3. 3.1. Comparing TNG50 to MEGAFLOW In Figure 3, we show Mgii column density maps of a selection of TNG50 halos drawn from our \ufb01ducial sample at z = 1. The halos are aligned so that the angular momentum vector of the stars in the central galaxy points along the vertical axis; thus, the view is edge-on. The strongest Mgii columns are found within and very close to the galaxy, demarcated by a red circle with a radius of twice the galaxy\u2019s stellar half-mass\u2013radius (the same de\ufb01nition used in DeFelippis et al. 2020). Beyond the galaxy, Mgii gas consistently appears to both surround the galactic disk and be very clumpy, but the amount and morphology of such gas varies greatly. In particular, there is signi\ufb01cant variation with azimuthal angle: the highest Mgii columns generally appear in the plane of rotation, but strong columns can occur above and below the disk as well, such as in halo 265 (the bottom left panel of Figure 3). P\u00b4 eroux et al. (2020) found the CGM gas metallicity to vary with azimuthal angle, but interestingly, they found gas near the major axis to have lower than average metallicity in the halo, indicating that large Mgii columns do not necessarily correspond to metal-enriched gas. High Mgii columns are much less common in the outer halo (r \u227350 kpc), but the pres6 DeFelippis et al. 15 20 30 40 50 60 70 b [kpc] 0.05 0.1 0.2 0.5 1 2 3 EW0 [\u00c5] 11.5 < log Mhalo[M ] < 12 = 5 EW > 0.5 \u00c5 = 25 megaflow 0.0 0.2 0.4 0.6 0.8 1.0 strong absorber fraction Figure 4. Mean Mgii equivalent widths of halos in our \ufb01ducial sample vs. the impact parameter of sight lines through those halos. Black and red lines and corresponding shaded regions show the mean and \u00b11\u03c3 scatter of all halos and the subset of strong absorbers (EW0 > 0.5 \u02da A), respectively. Sight lines at a constant azimuth angle of \u03b1 = 5\u25e6and 25\u25e6 are shown with solid and dotted lines, respectively. Observations of individual accretion systems from Zabl et al. (2019) are shown as green squares. The fraction of strong absorbers as a function of impact parameter (blue) is shown with the right vertical axis. The cyan and orange dashed lines are log-linear \ufb01ts of z \u223c1 Mgii absorbers from Nielsen et al. (2013a) and Lundgren et al. (2021), respectively. ence of satellite galaxies can populate that region with Mgii gas, shown most clearly in halo 340 (the bottom right panel of Figure 3). Within our \ufb01ducial sample, it is evident that the distribution of Mgii varies drastically, presumably due to di\ufb00erent halo formation histories. Sight lines through di\ufb00erent halos will therefore likely produce di\ufb00erent absorption pro\ufb01les even for sight lines with identical geometries. This highlights the necessity of calculating population averages of Mgii properties from TNG50 to compare to MEGAFLOW. We begin such a comparison with Figure 4, which shows the average strength of Mgii absorption, represented as the rest-frame equivalent width (EW0) as a function of impact parameter (b) for our \ufb01ducial sample. In this plot, we make an important distinction between the entire \ufb01ducial sample, shown in black, and the subset of \u201cstrong absorbers\u201d in red. We de\ufb01ne strong absorbers as sight lines through a halo that produce an absorption spectrum with EW0 > 0.5 \u02da A (the same as in Zabl et al. 2019). It is this \u201cabsorber-selected\u201d subset of the \ufb01ducial sample that is most directly comparable to MEGAFLOW. For easier comparison to Figure 3, we \ufb01nd that sight lines with EW0 = 0.5 \u02da A have Mgii column densities ranging from \u22481013.5 \u22121014.5 cm\u22122, i.e., just above the lower limit of the color bar. At all impact parameters, the average rest-frame EW of the \u201call absorbers\u201d sample from TNG50 (black) is smaller than those of MEGAFLOW, as expected given the selection function. The di\ufb00erence ranges from a factor of only \u22483 at b \u226420 kpc to a factor of \u224830 at 60 kpc. If, instead, we compare the average EW0 of the strong absorber subset (EW0 > 0.5 \u02da A) from TNG50, which is the appropriate comparison to make, we \ufb01nd the mean shown in red. This is much more similar to the values from MEGAFLOW, especially for b \u226540 kpc, but it is still as much as a factor of \u22482 lower than the observed values at b \u226420 kpc. However, the limited size and large scatter of the MEGAFLOW points from Zabl et al. (2019) make it di\ufb03cult to assess the precise level of disagreement with TNG50. Sight lines at \u03b1 = 5\u25e6(solid) and \u03b1 = 25\u25e6(dotted) produce essentially identical equivalent widths over both the entire \ufb01ducial sample and the subset of strong absorbers. With the two additional dashed lines in Figure 4 we provide a point of comparison to larger samples of moderateredshift Mgii absorbers from Nielsen et al. (2013a) and Lundgren et al. (2021). Though both of these samples have a slightly smaller equivalent-width threshold than Zabl et al. (2019) (\u22480.2\u22120.3 \u02da A) and no selection based on the geometry of the sight line, they still bracket both the Zabl et al. (2019) absorbers and the strong absorbers from TNG50, indicating that these simulated Mgii EWs are also consistent with observed Mgii EWs in general, given the large scatter. The blue lines in Figure 4 show the fraction of all sight lines that host strong absorbers as a function of impact parameter. At sight lines very close to the galaxy (b = 15 kpc), strong absorbers are common and in fact represent a majority of all halos. However, by b = 20 kpc the strong absorber fraction drops below 50%, and at the largest impact parameters shown, the fraction is only \u22481%. Strong absorbers are slightly more common at \u03b1 = 5\u25e6compared to \u03b1 = 25\u25e6, which can be understood by noting that the sight lines with smaller \u03b1 pass through the disk midplane closer to the galaxy\u2019s center, where gas is generally denser. However, this difference in strong absorber fraction does not a\ufb00ect the measured equivalent widths, indicating that the TNG50 halos\u2019 agreement with MEGAFLOW for sight lines near the galaxies\u2019 major axes is not subject to the precise geometries of the sight lines. In Figure 5, we examine how Mgii EWs vary throughout the entire halo in TNG50, not just near the major axis, and we \ufb01nd a clear trend: at all impact parameters we study, the mean EW of a perfectly edge-on sight line decreases as the azimuth angle of that sight line \u03b1 increases. Sight lines near the minor axis (green) have Circumgalactic Mgii in TNG and MEGAFLOW 7 15 20 30 40 50 60 b [kpc] 10 2 10 1 100 strong absorber fraction i = 90  (edge-on) i = 60 = 5 = 45 = 85 Figure 5. Mgii covering fraction of our \ufb01ducial sample as a function of impact parameter for sight lines with \u03b1 = 5\u25e6 (blue), \u03b1 = 45\u25e6(orange), and \u03b1 = 85\u25e6(green). Solid and dashed lines show sight lines that are edge-on and inclined at i = 60\u25e6, respectively. EWs at least 0.35 dex smaller than sight lines near the major axis (blue), and sight lines between both axes (orange) have EWs between the values at both axes. This represents a disagreement between TNG50 and Mgii observations, which are generally observed to have a bimodal distribution of \u03b1 near 0\u25e6and 90\u25e6(Bordoloi et al. 2011; Bouch\u00b4 e et al. 2012; Kacprzak et al. 2012; Martin et al. 2019; Zabl et al. 2019; Lundgren et al. 2021). The distribution of \u03b1 in TNG50 is clearly peaked at small \u03b1, implying that TNG50 is not producing the same kind of Mgii that is inferred to be out\ufb02owing in observations. It is also clear that this azimuthal angle dependence is very sensitive to the inclination angle of the sight line because it nearly disappears when the sight lines are inclined at an angle of 60\u25e6with respect to the axis of rotation (dotted lines in Figure 5), as would be typical for observations. This sensitivity indicates that most Mgii absorption in TNG50 comes from a gas in the vicinity of the disk midplane, where we have already seen (Figure 4) that TNG50 is consistent with observations. Therefore, for the remainder of this paper we restrict our observational comparison to sight lines near the major axis. Having established the degree of consistency of Mgii equivalent widths, we now examine kinematic signatures of Mgii along sight lines in TNG50 and compare them to MEGAFLOW. In Figure 6, we explicitly draw the connection between the Mgii gas cells that contribute to the column densities seen in Figure 3 and the velocity spectrum created from a subset of those cells that intersect a sight line through the halo. In each row, we show two orientations of one of the four halos from Figure 3 overlaid with a sight line with b = 30 kpc, \u03b1 = 5\u25e6, and i = 60\u25e6, and the Mgii velocity spectrum generated from that sight line. From these few examples it is clear that the gas producing the Mgii absorption is generally not distributed uniformly along any sight line: it is usually concentrated in discrete clumps in regions of the sight line nearest to the galaxy. This is seen clearly in rows one, two, and four of Figure 6, where the majority of gas cells have positive LOS velocities (i.e., corotating with the galaxy) and produce distinct kinematic components in the spectrum that are often saturated. It is also notable that by comparing the spectra alone it is possible to distinguish morphological di\ufb00erences in the Mgii distribution between halos. The \ufb01rst two halos, for example, have a prominent Mgii disk that both spectra reveal to be primarily corotating. The halo in row three, however, does not have such a clear disk, and the spectrum is instead composed of a cluster of counter-rotating gas cells signi\ufb01cantly above the plane of the galaxy. The halo in row four has a spectrum with substantial corotating and counter-rotating components, which imply Mgii structure in between the ordered halos (rows one and two) and disordered ones (row three). With this small sample, we have demonstrated that the velocity spectrum, despite being composed of a very small fraction of all of the Mgii gas, is capable of re\ufb02ecting the potential diversity of Mgii gas kinematics in halos of similar mass, but is also fairly consistent between halos with similar morphologies. Later in the paper, we consider whether the Mgii gas re\ufb02ects the kinematics of other components of the CGM. From these results, we now compare stacked spectra from the \ufb01ducial sample to the stacked spectra presented in Zabl et al. (2019). Figure 7 shows stacked spectra for the entire TNG50 \ufb01ducial sample (black), TNG50 strong absorbers (red), and the absorbers from Zabl et al. (2019) (green). The two panels correspond to two di\ufb00erent impact parameters that allow a comparison between absorbers nearer to a galaxy and farther from a galaxy. In the left panel, showing stacked spectra at small impact parameters, there is a very clear kinematic picture. The strong absorber spectrum from TNG50 is symmetric, centered at \u22480.6Vvir, and has a with a full width at half maximum (FWHM) of 1.2Vvir, the same as the spectrum of Zabl et al. (2019). Thus, qualitatively, strong Mgii absorbers as a population generally have LOS velocities in the same direction as their corresponding galaxies\u2019 rotations. One slight di\ufb00erence with the stacked spectra for strong absorbers is that the TNG50 spectrum (red) is somewhat shallower than the observed spectrum (green). However, there is essentially no di\ufb00erence between TNG50 spectra generated from 8 DeFelippis et al. x y halo 225 x z 13 14 15 16 17 log Mg II column density [cm 2] 2.0 1.5 1.0 0.5 0.0 0.5 1.0 1.5 2.0 v/(vvirsin(i)) 0.0 0.2 0.4 0.6 0.8 1.0 b = 30,  = 5 , i = 60 x y halo 265 x z 13 14 15 16 17 log Mg II column density [cm 2] 2.0 1.5 1.0 0.5 0.0 0.5 1.0 1.5 2.0 v/(vvirsin(i)) 0.0 0.2 0.4 0.6 0.8 1.0 b = 30,  = 5 , i = 60 x y halo 271 x z 13 14 15 16 17 log Mg II column density [cm 2] 2.0 1.5 1.0 0.5 0.0 0.5 1.0 1.5 2.0 v/(vvirsin(i)) 0.0 0.2 0.4 0.6 0.8 1.0 b = 30,  = 5 , i = 60 x y halo 340 x z 13 14 15 16 17 log Mg II column density [cm 2] 2.0 1.5 1.0 0.5 0.0 0.5 1.0 1.5 2.0 v/(vvirsin(i)) 0.0 0.2 0.4 0.6 0.8 1.0 b = 30,  = 5 , i = 60 Figure 6. Each row contains two Mgii column density maps of a halo from Figure 3 projected along the vertical (left) and a horizontal (middle) axis. A sight line at b = 30 kpc, \u03b1 = 5\u25e6, and i = 60\u25e6is overlaid along with gas cells that intersect that sight line and have a Mgii column density of at least 1012 cm\u22122, which accounts for > 95% of the Mgii mass along those sight lines. The Mgii gas cells and the resulting \ufb02ux-normalized velocity spectrum (right) are colored by the velocity along the line of sight normalized by Vvir sin(i), where Vvir is the virial velocity of the halo. Dashed circles show twice each galaxy\u2019s stellar half-mass\u2013radius. Circumgalactic Mgii in TNG and MEGAFLOW 9 sight lines at the two azimuthal angles \u03b1 = 5\u25e6(solid line) and 25\u25e6(dotted line). In Figure 7 (left), the only di\ufb00erence between the full \ufb01ducial spectrum and the strong absorber-only spectrum is the depth, indicating that, as a population, strong absorbers are not kinematically distinct from absorbers in general at this impact parameter. The precise reason for the discrepancy in the depth is di\ufb03cult to determine, but it may be sensitive to certain parameters in the TNG physics model (e.g., metal loading of out\ufb02ows from supernovae). However, it could also be an effect of simulation resolution (see Section 3.3). So, while TNG50 potentially slightly underproduces the observed amount of Mgii gas at 20 kpc, it does possess average kinematics that are consistent with observations of the same region of the CGM. Figure 7 (right) compares the stacked spectra at a larger impact parameter (b = 40 kpc). The strong absorbers from TNG50 and MEGAFLOW (Zabl et al. 2019) are both shallower, wider (FWHMs of 1.3Vvir and 2Vvir respectively), no longer symmetric, and signi\ufb01cantly noisier, though both are still approximately centered at a velocity on the order of Vvir/2. At this impact parameter, the depths of the simulated strong absorber and observed spectra are consistent with each other. However, strong absorbers no longer kinematically resemble the full \ufb01ducial sample: in addition to being much rarer at 40 kpc than at 20 kpc, the strong absorbers have larger positive velocities, indicating that Mgii in this region is tracing atypically faster-moving gas. As was the case at 20 kpc, the di\ufb00erence in the spectra between the two azimuth angles is minor. We also note here, but do not show, that the shapes and depths of individual spectra from Zabl et al. (2019) match quite well with particular individual spectra from the much larger \ufb01ducial sample from TNG50 (examples of individual spectra from TNG50 are shown in Figure 6). 3.2. 3D Kinematics of Mgii in TNG50 In this section, we characterize the three-dimensional kinematics of the Mgii gas in TNG50 and its relation to the observed quantities we discussed in Section 3.1. We show average velocity pro\ufb01les of the halos in the \ufb01ducial sample in Figure 8. The top panel shows the azimuthal velocity component (v\u03c6) in spherical coordinates as a function of radius. We divide gas into cold and hot components based on a temperature threshold of 3 \u00d7 104 K, which is chosen to separate the cold and hot clusters seen in Figure 2, although the pro\ufb01les are not sensitive to the precise choice of temperature threshold. To understand the relationship of the hot and cold gas to Mgii-bearing material we also show the Mgii massweighted pro\ufb01les. First, we see that the Mgii gas and the cold gas have nearly identical v\u03c6 pro\ufb01les throughout the halo. In the innermost regions of the CGM (15 \u221220 kpc), the cold gas has a mean azimuthal velocity of 80 km s\u22121 (\u2248 0.6Vvir), while in the outermost regions (90 \u2212100 kpc), the mean azimuthal velocity decreases to 20 km s\u22121 (\u22480.15Vvir). At all radii, the \u00b11\u03c3 scatter is quite large (\u2248100 km s\u22121), though the standard errors on this and all other mean velocities in Figure 8 range from only 1 \u22123 km s\u22121. Though not explicitly shown, most of the cold and Mgii gas mass is closer to the major rather than the minor axis because the all-\u03b1 pro\ufb01les are much more similar to the \u03b1 < 45\u25e6(dashed) pro\ufb01les than the \u03b1 > 45\u25e6(dotted) pro\ufb01les. Hot gas has lower azimuthal velocities at all radii, a slightly shallower slope to its pro\ufb01le, and a smaller scatter in azimuthal velocity by a factor of \u22482 but is otherwise qualitatively similar to the cold and Mgii gas. This relationship between hot and cold gas is consistent with similar measurements of v\u03c6 made from TNG100 in DeFelippis et al. (2020). In the radial-velocity pro\ufb01les (Figure 8, bottom), we see a gulf between the velocities of the hot and cold gas develop within 90 kpc. Above this radius, the average radial velocities of all components of the gas converge to \u221220 km s\u22121 (\u22480.15Vvir), though the spread of radial velocities in this region of the CGM is very large, especially for cold gas (\u00b11\u03c3 scatter of 120 km s\u22121). Moving toward smaller radii, the cold gas in\ufb02ow velocities become larger, while hot gas in\ufb02ow velocities decrease and then switch to a net out\ufb02ow at 50 kpc. The Mgii gas still traces the cold gas, which reaches typical in\ufb02owing velocities of 45 \u221250 km s\u22121 in the inner CGM out to r = 40 kpc, where the spread in radial velocities is a factor of 2 smaller than in the outer halo. The geometry of accretion and out\ufb02ows is evident from this panel as well: hot gas has especially large mean out\ufb02owing velocities for \u03b1 > 45\u25e6while cold gas in the same region has a mean in\ufb02owing velocity in the inner halo and nearly no net radial motion in the outer halo. Most of the cold and Mgii gas mass is moving toward the galaxy in regions surrounding the major axis out to a substantial fraction of the virial radius. It is also clear that kinematically, Mgii gas in TNG50 is nearly identical to a simple cut on temperature and so is an excellent tracer of the kinematics of cold CGM gas. In the context of Section 3.1, these results indicate that mock Mgii spectra are representative of the entire cold phase of the CGM along the same sight lines. Finally, we examine the 3D velocities of the Mgii gas along our sight lines. In Figure 9, we plot stacked spec10 DeFelippis et al. 2.0 1.5 1.0 0.5 0.0 0.5 1.0 1.5 2.0 v/(vvirsin(i)) 0.2 0.4 0.6 0.8 1.0 b = 20 kpc all halos EW0 > 0.5\u00c5 megaflow  b < 30 kpc 2.0 1.5 1.0 0.5 0.0 0.5 1.0 1.5 2.0 v/(vvirsin(i)) 0.2 0.4 0.6 0.8 1.0 b = 40 kpc = 5 = 25 megaflow  b > 30 kpc Figure 7. The stacked Mgii velocity spectra for the full \ufb01ducial TNG50 sample (black) and the subset of strong absorbers (red) for sight lines with \u03b1 = 5\u25e6(solid) and 25\u25e6(dotted), and b = 20 kpc (left) and 40 kpc (right). Spectra are normalized by Vvir sin(i), where Vvir is the halo\u2019s virial velocity. The green line in each panel is the stacked spectrum of the four smallest (left) and largest (right) impact parameters from Zabl et al. (2019), and the green shaded region is an estimate of the error from bootstrapping. tra for Mgii using the three spherical velocity components individually (r, \u03b8, and \u03c6), and compare those to the spectrum generated with the full velocity of our \ufb01ducial sample of halos. Both the r and \u03b8 component spectra are centered at 0 km s\u22121, indicating that over the entire sample they do not contribute any net velocity shift to the gas along the sight lines. The spectrum of the \u03c6 component is remarkably similar to the spectrum of the entire velocity, both in terms of velocity shift and width. This means that for our \ufb01ducial sample, the shape of the stacked velocity spectrum along sight lines is completely determined by only the \u03c6 (i.e., rotational) component of the velocity along those sight lines. 3.3. E\ufb00ects of halo mass and resolution on Mgii in TNG50 We now describe how our main results vary with halo mass and mass resolution. To study the e\ufb00ect of halo mass, we consider two mass bins containing halos from TNG50 with 1011 M\u2299< Mhalo < 1011.5 M\u2299and 1012 M\u2299< Mhalo < 1012.5 M\u2299at z = 1, which are above and below the \ufb01ducial mass range and contain 1130 and 167 halos, respectively. As in Section 3.1 we calculate Mgii equivalent widths and generate velocity spectra that we show in Figure 10. For easier comparison, we also show the TNG50 \ufb01ducial sample. As shown in the left panel of Figure 10, at a given impact parameter, the shape of the equivalent-width distribution changes with halo mass: lower halo masses (cyan) are much more likely to host weak or nonabsorbers than higher halo masses (magenta), and they are much less likely to host strong absorbers. We \ufb01nd this trend to hold at all impact parameters studied in this paper. We can see the e\ufb00ect on observability with the vertical lines in this panel, which show the mean equivalent widths of the strong absorbers in each mass bin. Typical strong absorbers in the \ufb01ducial sample have only slightly larger equivalent widths than those those at lower halo masses, but are substantially weaker than the strong absorbers at higher halo masses. At larger impact parameters, the mean equivalent widths of all strong absorbers is \u22480.8 \u02da A, but they are exceedingly rare in lower-mass halos. Thus, the primary e\ufb00ects of increasing halo mass on strong absorbers are to increase their occurrence at all impact parameters, especially at large distances, and to increase the mean equivalent width of strong absorbers for halo masses \u22731012 M\u2299. We note that this result is qualitatively consistent with Chen et al. (2010b), who \ufb01nd a larger Mgii extent in the CGM of higher-mass galaxies. Also shown in the left panel of Figure 10 is the equivalent-width distribution of 4315 halos with the same mass as the \ufb01ducial sample from the TNG100 simulation, which has a lower baryonic mass resolution than TNG50 by a factor of \u223c16. Decreasing the simulation resolution lowers equivalent widths overall and steepens the distribution in the same way as decreasing the halo mass does, but the e\ufb00ect is weaker. The mean equivalent width of strong absorbers is largely una\ufb00ected by the change in resolution. In the right panel of Figure 10 we examine the e\ufb00ect of halo mass and resolution on the observed Mgii spectrum of strong absorbers. We note that the spectra of the entire samples, as in Figure 7, have the same shape Circumgalactic Mgii in TNG and MEGAFLOW 11 0.2 0.0 0.2 0.4 0.6 0.8 1.0 v /Vvir 20 40 60 80 100 25 0 25 50 75 100 125 phi velocity [km/s] Mg II T < 3 \u00d7 104 K T > 3 \u00d7 104 K 0.6 0.4 0.2 0.0 0.2 0.4 0.6 vr/Vvir 20 40 60 80 100 r [kpc] 75 50 25 0 25 50 75 radial velocity [km/s] all  > 45 < 45 Figure 8. Mean mass-weighted velocity pro\ufb01les of the spherical phi-component (v\u03c6, top) and r-component (vr, bottom) for cold gas (blue), hot gas (red), and Mgii gas (black) in spherical bins. Velocity is given in km s\u22121 and as a fraction of the virial velocity. A temperature of 3 \u00d7 104 K is used to separate \u201ccold\u201d and \u201chot\u201d gas. Pro\ufb01les are shown for gas in the entire halo (solid), gas with \u03b1 > 45\u25e6(dotted), and gas with \u03b1 < 45\u25e6(dashed). Shaded regions show the \u00b11\u03c3 scatter of the solid lines and are of similar size for all pro\ufb01les. and center as their corresponding strong absorber subset, but are substantially shallower. We also plot the real velocity rather than the normalized velocity to emphasize the di\ufb00erence in equivalent widths, which can be more easily read o\ufb00. We see that the \ufb01ducial and lower-mass bins have remarkably similar spectra: they are both symmetric and centered at moderate positive velocities. The spectrum of the higher-mass bin is markedly di\ufb00erent: it is much broader, asymmetric, and centered at a signi\ufb01cantly higher velocity. It still, however, shows a preference for Mgii gas to be corotating. We note that the difference between Figure 10 as shown and the corresponding velocity-normalized spectrum (not shown) is that the normalized higher-mass spectrum is compressed slightly and therefore appears more similar to the normalized \ufb01ducial spectrum. Additionally, while the lower-mass and \ufb01ducial spectra are both centered at \u22480.5Vvir, the 2.0 1.5 1.0 0.5 0.0 0.5 1.0 1.5 2.0 v/(vvirsin(i)) 0.4 0.5 0.6 0.7 0.8 0.9 1.0 b = 20,  = 5 , i = 60 vtot v vr v Figure 9. Stacked Mgii velocity spectra for the full \ufb01ducial TNG50 sample at a single sight line. The contributions of the three spherical components of velocity \u2013 vr (dotted red), v\u03c6 (dashed green), and v\u03b8 (dotted-dashed blue) \u2013 are shown, as well as the spectrum created from the total velocity (solid black). higher-mass spectra are peaked at \u2248Vvir. Higher halo masses (\u22731012 M\u2299) thus have substantially more Mgii absorption and more complex kinematic signatures than for the halo masses of the \ufb01ducial sample and lower. Finally, we consider the di\ufb00erence that resolution makes in the Mgii absorption spectrum. As was the case with equivalent widths, the di\ufb00erence caused by resolution is smaller than the di\ufb00erence caused by either increasing or decreasing the halo mass. Apart from a slight change in the depth of the spectrum, the kinematic properties of strong absorbers in TNG are essentially resolution independent (see solid vs. dotted curves in Figure 10 for TNG50 and TNG100, respectively). The e\ufb00ect of increasing the resolution of the simulation is therefore primarily to increase the occurrence of strong absorbers at a given halo mass. 4. DISCUSSION 4.1. The Role of Mgii in TNG We consider here the rami\ufb01cations of the detailed analysis of Mgii in TNG from Section 3. In Figure 8, we found that Mgii gas is very well approximated by a simple temperature cut. Therefore, we expect the angular momentum of cold gas in the CGM of TNG galaxies should be very similar to that of Mgii. DeFelippis et al. (2020) found cold CGM gas in halos of this mass range and redshift to have higher angular momentum when surrounding high-angular-momentum galaxies, meaning Mgii is likely tracing high-angular-momentum gas in the CGM of these halos. As the velocity spectrum\u2019s center and shape is almost completely set by the rotational ve12 DeFelippis et al. 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 EW0 [\u00c5] 10 3 10 2 10 1 100 101 b = 20 kpc,  = 5 , i = 60 200 100 0 100 200 v [km/s] 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 b = 20 kpc,  = 5 , i = 60 TNG50 fiducial TNG100 fiducial TNG50 lower mass TNG50 higher mass Figure 10. Left: rest-frame equivalent-width distribution of the TNG50 \ufb01ducial sample (solid black), lower-mass halos with 1011 M\u2299< Mhalo < 1011.5 M\u2299(cyan), higher-mass halos with 1012 M\u2299< Mhalo < 1012.5 M\u2299(magenta), and the same mass halos from TNG100 (dotted black) at the same sight line of b = 20 kpc, \u03b1 = 5\u25e6, and i = 60\u25e6. The mean EW0 of the strong absorbers in each halo mass bin is shown with a translucent vertical line of the same color. Right: stacked velocity spectra of the same halo samples with velocities in km s\u22121. locity component (see Figure 9), it should therefore be possible to use Mgii velocity spectra from sight lines near the major axis to estimate the angular momentum of cold gas in the CGM. In Section 3.3 we examined possible halo mass and resolution dependencies of our results with two main goals in mind: to establish any broad e\ufb00ects of the TNG feedback model on Mgii, and to determine to what extent the cosmological simulation can capture Mgii kinematics. Feedback is known to be important for regulating gas \ufb02ows into, out of, and around galaxies, and therefore could have observable signatures in the Mgii spectra, especially at di\ufb00erent halo masses. The results of the halo mass analysis suggest that for halos with masses between 1011 M\u2299and 1012 M\u2299, the physical mechanisms a\ufb00ecting their CGM are similar enough to result in Mgii spectra that essentially scale with the halo\u2019s virial velocity. This is presumably because feedback from supernovae is the dominant form of feedback that a\ufb00ects the CGM for all halo masses below \u223c1012 M\u2299and produces Mgii gas with similar kinematic signatures. For halos above 1012 M\u2299however, Mgii gas has stronger overall absorption, as re\ufb02ected by their \ufb02atter EW distribution, and substantially larger velocities and velocity dispersions, as re\ufb02ected by their very broad velocity spectra. This is likely due to the dominant form of feedback switching from stars to AGN around this halo mass. However, within the higher-mass sample, halos with larger black hole masses do not themselves have broader Mgii spectra, so there is probably a combination of e\ufb00ects that result in a noticeable di\ufb00erence in the properties of the spectrum at higher masses. Nelson et al. (2020) have recently used TNG50 to study the origin of cold Mgii gas in the CGM of very massive (M\u2217\u22731011 M\u2299) galaxies and found structures of size a few \u00d7102 pc that are su\ufb03cient to explain the observed covering fractions and LOS kinematics. They also note that while some fundamental properties like the number of cold gas clouds present in halos are not converged at TNG50\u2019s resolution, the total cold gas mass of such halos is converged in TNG50. This supports our \ufb01ndings that our kinematic results do not qualitatively change even going from TNG50 to TNG100, a factor of \u223c16 in mass resolution (Figure 10), because the majority of the Mgii mass is already in the halo by TNG50\u2019s resolution. We expect higher-resolution simulations to produce more strong absorbers at a given halo mass but the rotation of Mgii near the major axis appears to be a resolution-independent aspect of the CGM for MEGAFLOW analogs in the TNG simulations. Finally, in Figure 11, we show the speci\ufb01c angular momentum (j) of di\ufb00erent halo components as a function of stellar mass of their central galaxies, with the goal of contextualizing the angular momentum of Mgii gas (black line) in the CGM in relation to the rest of the gas in the CGM as well as to the other components of the halo. The slope of this j \u2212M\u2217relation for the stellar component of galaxies (purple line) is \u223c0.6 as generally observed (e.g., Fall & Romanowsky 2013), and all other components appear to have roughly equal slopes. Most interesting are the relative positions of the CGM and dark matter (orange line) on this plane. At a given stellar mass, all components of the CGM have a slightly higher typical j than that of the dark matter by Circumgalactic Mgii in TNG and MEGAFLOW 13 9.00 9.25 9.50 9.75 10.00 10.25 10.50 10.75 11.00 log Mstars 2.0 2.5 3.0 3.5 4.0 4.5 log j [km/s\u00d7kpc] cold CGM hot CGM MgII CGM stars dark matter megaflow fiducial sample Figure 11. Median-speci\ufb01c angular momentum vs. galactic stellar mass for the cold (blue), hot (red), and Mgii (black) CGM as de\ufb01ned in Figure 8, as well as the dark matter halo (dotted orange) and the stellar component of the galaxy (purple) at z = 1. Unlike previous \ufb01gures, medians are calculated using a sample of all halos containing central galaxies with stellar masses 109 M\u2299< M\u2217< 1011 M\u2299. Shaded regions show the 16th and 84th percentiles of the distributions of the Mgii gas (black), which is similar in size to all components except dark matter (orange), which has noticeably larger scatter. Black points show the Mgii speci\ufb01c angular momentum of the halo-mass-selected \ufb01ducial sample that is biased toward higher j for M\u2217\u2272109.75. Green squares show estimations for the speci\ufb01c angular momentum of the majoraxis absorbers using inferred rotational velocities from Zabl et al. (2019). \u223c0.2 dex. There are multiple potential reasons for this. First, galaxies can remove low-angular-momentum gas from the CGM by accreting it and using it to form stars. Second, feedback from stars and/or AGN can also eject low-angular-momentum gas from the halo completely. Finally, dark matter in the halo can transfer some of its angular momentum to the gas. Regardless, it is clear that Mgii traces the angular momentum of the both the cold and hot components of the CGM quite well. Also shown in Figure 11 are two sets of points representing Mgii gas in individual halos: the \ufb01ducial sample in black and the Zabl et al. (2019) sample in green, for which j was estimated using their derived rotational velocities. The two are not directly comparable since the points from Zabl et al. (2019) represent Mgii gas along a single sight line, yet they are still able to reproduce the scatter in this relation found in TNG50, though they are somewhat biased toward higher j. This bias is likely due to the selection in Zabl et al. (2019) of strong Mgii absorption near the major axis, which is where high-j cold gas tends to reside in the CGM as shown in DeFelippis et al. (2020). Nevertheless, from Figure 11 we can conclude that estimations of the angular momentum content of the CGM provided by single sight lines of Mgii can get within \u223c0.5 dex of typical values from TNG50 over a large range of galaxy masses. 4.2. Comparisons to Recent Work We now highlight results from previous work on Mgii absorption in observations and simulations in the context of our results. Observations of Mgii using sight lines near the major axis of galaxies have generally found that gas is corotating with the galaxy both for small impact parameters of < 15 kpc (e.g., Bouch\u00b4 e et al. 2016) and large impact parameters of > 50 kpc (e.g., Martin et al. 2019). Using a lensed system, Lopez et al. (2020) observed multiple sight lines of the same CGM and measured a decreasing Mgii rotation curve that is qualitatively similar to Figure 8. However, their absorption data only go out to \u224830 kpc. Our work suggests Mgii rotation curves should continue to decrease to at least 100 kpc, though based on the maps in Figure 3 the Mgii column densities at those distances are significantly below current observational limits. While this paper is focused on Mgii gas near the major axis, there are also recent results suggesting Mgii out\ufb02ows along the minor axis of galaxies with velocities > 100 km s\u22121 (e.g., Schroetter et al. 2019; Zabl et al. 2020). It is worth noting though that Mortensen et al. (2021) found a lensed system with Mgii on the geometric minor axis of the absorber galaxy with LOS velocities < 100 km s\u22121 and a large velocity dispersion, indicating that the kinematics of Mgii out\ufb02ows may vary signi\ufb01cantly. We showed in Figures 5 and 8 that Mgii absorption along the minor axis is weaker than along the major axis, and that there are no net Mgii out\ufb02ows along the minor axis in the TNG \ufb01ducial sample. This result appears to be discrepant with the previously cited observational papers, but we defer a detailed analysis to a future paper. Ho et al. (2020) recently studied similar aspects of Mgii absorption in the EAGLE simulation at z \u22480.3 and found results broadly consistent with ours. Specifically, they measure a rotating Mgii structure around star-forming galaxies as well as a lower detection fraction of Mgii near the minor axis. They also \ufb01nd that higher-mass galaxies host detectable (i.e., above a \ufb01xed column density) Mgii structures out to larger distances in the CGM, which we indirectly show with the EW distributions in Figure 10, where higher-mass halos have more strong absorbers. 5. SUMMARY We have simulated Mgii absorption in the CGM of halos from TNG50 comparable to the major-axis sight lines observed in the MEGAFLOW survey by Zabl et al. 14 DeFelippis et al. (2019) and compared absorption and kinematic properties of the two samples. We also examined the 3D kinematics of the Mgii in TNG50. Our conclusions are as follows: 1. The equivalent widths of absorber-selected halos (i.e., strong absorbers) from TNG50 match reasonably well with the equivalent widths of major-axis sight lines from Zabl et al. (2019) (Figure 4). 2. A majority of halos are strong absorbers at the smallest impact parameter studied (15 kpc), but the strong absorber fraction drops quickly as a function of distance (Figure 4). 3. The stacked velocity spectra of TNG50 strong absorbers match the stacked spectra of Zabl et al. (2019) very well, thus supporting the physical interpretation of corotation both below 30 kpc, where the spectra are strongly peaked near \u223c 0.5Vvir and symmetric, and above 30 kpc, where the spectra are similarly peaked but are much noisier, broader, and asymmetric (Figure 7). 4. In TNG50, Mgii gas has velocity pro\ufb01les nearly identical to gas below a temperature cuto\ufb00of 3 \u00d7 104 K, meaning Mgii absorption is a good proxy for cold gas kinematics in general. There is substantial rotation and typical in\ufb02ow velocities of up to 50 km s\u22121 out to \u223c40 kpc in the CGM (Figure 8). 5. The radial and polar velocity components by themselves do not cause any net velocity shift in the stacked spectrum, which implies that Mgii absorption kinematics alone cannot be used to measure typical in\ufb02ow speeds of rotating gas in the CGM. (Figure 9). 6. Mgii absorption strengths and spectra are stronger and broader for halos more massive than the \ufb01ducial sample of 1011.5 \u22121012 M\u2299halos but do not change very much for halos less massive than the \ufb01ducial sample. Lowering the resolution from TNG50 to TNG100 only modestly changes any of the Mgii kinematic properties (Figure 10). 7. The median-speci\ufb01c angular momentum of the Mgii component of the CGM as a function of galactic stellar mass is very similar to that of both cold and hot CGM gas, and it is larger than that of the dark matter halo and the stars in the galaxy by \u223c0.2 dex and \u223c0.8 dex, respectively. Estimates of the speci\ufb01c angular momentum of Mgii from the Zabl et al. (2019) data are also reasonably close to the values from TNG50 to within a factor of \u223c0.5 dex. (Figure 11). This work demonstrates that generating mock Mgii observations from TNG50 generates absorption spectra that are comparable to real data. In particular, our results are consistent with the emerging picture of rotating Mgii gas found in observations and also other simulations. In future work, we plan to widen our investigation to include other ions that trace warmer and more di\ufb00use gas, as well as follow gas at particular redshifts backward and forward through time to determine the stability of various ion structures and their role in transporting angular momentum to or from the galaxy. ACKNOWLEDGMENTS We thank Johannes Zabl, \u00b4 Edouard Tollet, Joakim Rosdahl, and J\u00b4 er\u00b4 emy Blaizot for insightful and useful discussions, as well as Cameron Hummels for assistance with Trident. We also thank the anonymous referee for helpful comments. D.D. acknowledges support from the Chateaubriand Fellowship of the O\ufb03ce for Science & Technology of the Embassy of France in the United States. N.B. acknowledges funding support from the French Agence National de la Recherche (ANR) grant \u201c3DGasFlows\u201d (ANR-17-CE31-0017). Flatiron Institute is supported by the Simons Foundation. G.L.B. acknowledges \ufb01nancial support from the NSF (grants AST-1615955, OAC-1835509) and computing support from NSF XSEDE. F.M. acknowledges support through the Program \u201cRita Levi Montalcini\u201d of the Italian MUR. Software: Trident (Hummels et al. 2017), yt (Turk et al. 2011), Cloudy (Ferland et al. 2013), NumPy (van der Walt et al. 2011), Matplotlib (Hunter 2007), and IPython (Perez & Granger 2007)",
                    "introduction": "1."
                },
                {
                    "url": "http://arxiv.org/abs/2004.07846v2",
                    "title": "The Angular Momentum of the Circumgalactic Medium in the TNG100 Simulation",
                    "abstract": "We present an analysis of the angular momentum content of the circumgalactic\nmedium (CGM) using TNG100, one of the flagship runs of the IllustrisTNG\nproject. We focus on Milky Way-mass halos ($\\sim 10^{12} \\; M_{\\odot}$) at\n$z=0$ but also analyze other masses and redshifts up to $z=5$. We find that the\nCGM angular momentum properties are strongly correlated with the stellar\nangular momentum of the corresponding galaxy: the CGM surrounding high-angular\nmomentum galaxies has a systematically higher angular momentum and is better\naligned to the rotational axis of the galaxy itself than the CGM surrounding\nlow-angular momentum galaxies. Both the hot and cold phases of the CGM show\nthis dichotomy, though it is stronger for colder gas. The CGM of high-angular\nmomentum galaxies is characterized by a large wedge of cold gas with rotational\nvelocities at least $\\sim1/2$ of the halo's virial velocity, extending out to\n$\\sim 1/2$ of the virial radius, and by biconical polar regions dominated by\nradial velocities suggestive of galactic fountains; both of these features are\nabsent from the CGM of low-angular momentum galaxies. These conclusions are\ngeneral to halo masses $\\lesssim 10^{12} \\; M_{\\odot}$ and for $z \\lesssim 2$,\nbut they do not apply for more massive halos or at the highest redshift\nstudied. By comparing simulations run with alterations to the fiducial feedback\nmodel, we identify the better alignment of the CGM to high-angular momentum\ngalaxies as a feedback-independent effect and the galactic winds as a dominant\ninfluence on the CGM's angular momentum.",
                    "authors": "Daniel DeFelippis, Shy Genel, Greg L. Bryan, Dylan Nelson, Annalisa Pillepich, Lars Hernquist",
                    "published": "2020-04-16",
                    "updated": "2020-05-20",
                    "primary_cat": "astro-ph.GA",
                    "cats": [
                        "astro-ph.GA"
                    ],
                    "main_content": "Corresponding author: Daniel DeFelippis d.defelippis@columbia.edu Angl\u00b4 es-Alc\u00b4 azar et al. 2017; Hafen et al. 2019) generally find many different origins and evolutionary histories of gas in the CGM, supporting this picture. Furthermore, the fact that galaxies and their CGM are physically connected to each other and exchange mass suggests that certain properties of the two may be, in general, correlated (see, e.g., Bland-Hawthorn et al. 2017). Similarly, the diversity of observed galaxies suggests that the CGM may be diverse as well, whether because accreting gas in the CGM affects the evolution of the galaxy, or gas ejected from the galaxy affects the evolution of the CGM. Observations of the CGM have generally supported these conclusions. Through studies of both small samples (e.g. Bouch\u00b4 e et al. 2016; Rahmani et al. 2018; Lochhaas et al. 2019; Martin et al. 2019b) and large samples (e.g. Bordoloi et al. 2014; Liang & Chen 2014; Turner et al. 2014; Werk et al. 2014; Kacprzak et al. 2015; Schroetter et al. 2016; Turner et al. 2017; McQuinn & Werk 2018; Burchett et al. 2019; Pointon et al. 2019) of absorption lines, as well as studies using emission lines (e.g. Martin et al. 2015, 2016), the CGM has arXiv:2004.07846v2  [astro-ph.GA]  20 May 2020 2 DeFelippis et al. been found to contain a mass of baryons comparable to that of its associated galaxy, composed of gas in many di\ufb00erent ionization and dynamical states, indicative of many channels of formation. Close to the plane of the galactic disk, the velocity of this material is often consistent with being corotating with the galaxy (\ufb01rst seen in Barcons et al. 1995; more recent works include Ho et al. 2017; Zabl et al. 2019). These observations are limited by the nature of the observational technique, which integrates gas absorption along line-of-sight \u201cpencil beams\u201d through the CGM and can combine gas at di\ufb00erent radii and in di\ufb00erent dynamical states (e.g. Kacprzak et al. 2019; Ng et al. 2019). Gravitational lensing can allow a quasar to probe multiple discrete locations (e.g. Chen et al. 2014) or a continuous region (e.g. Lopez et al. 2018, 2020) in the same CGM: such special cases are also consistent with corotation. However, in all of these cases, the real 3D motions of gas in the CGM are reduced to 1D line-of-sight velocities, meaning direct measurements of more fundamental vector quantities like angular momentum are very di\ufb03cult to achieve. Therefore, even though there is observational evidence for high-angular momentum gas in the Milky Way\u2019s (MW\u2019s) CGM (probed by quasar sightlines out to \u223c80 kpc into the halo in Hodges-Kluck et al. 2016) and in speci\ufb01c higher-redshift MW analogs (probed by Ly\u03b1 up to \u223c40 kpc from the galaxy in Prescott et al. 2015), the angular momentum of gas in the CGM is rarely directly studied. Angular momentum has long been considered an important quantity in galaxy structure and evolution. It is predicted theoretically to originate from tidal torquing by the cosmic web at high redshifts (Peebles 1969; Fall & Efstathiou 1980; Mo et al. 1998) and has been shown to strongly correlate with galaxy morphology, both in observations (Fall & Romanowsky 2013; Cortese et al. 2016; Swinbank et al. 2017) and in large cosmological simulations (Genel et al. 2015; Teklu et al. 2015; Zavala et al. 2016). Angular momentum contained in galaxies and halos has been measured in cosmological simulations including Illustris (Rodriguez-Gomez et al. 2017; Zjupa & Springel 2017) and EAGLE (e.g. Lagos et al. 2017; Stevens et al. 2017; Oppenheimer 2018), in zoomin simulations of individual halos (El-Badry et al. 2018; Garrison-Kimmel et al. 2018), and using analytic models (Pezzulli et al. 2017; Sormani et al. 2018). However, the nature of the relationship between the angular momentum of the galaxy and the angular momentum of the CGM is not yet clear. A well-established result from both zoom-in and largescale cosmological simulations is that galaxies can eject low-angular momentum gas into the CGM while also accreting higher-angular momentum gas from the CGM that eventually can form stars (Brook et al. 2011, 2012; \u00a8 Ubler et al. 2014; Christensen et al. 2016; DeFelippis et al. 2017; Grand et al. 2019). In particular, Brook et al. (2012) and DeFelippis et al. (2017) found that much of the gas that forms stars by z = 0 has been ejected into and reaccreted from the CGM successively, each time with incrementally more angular momentum. Other studies have found similar links that relate the misalignment of the galaxy and halo to properties of accreting gas (Ro\u02c7 skar et al. 2010), out\ufb02owing gas (Tenneti et al. 2017), and satellite galaxies (Shao et al. 2016) in the halo. Furthermore, Stewart et al. (2013) and Stewart et al. (2017) have found, using zoom-in simulations, that the CGM can develop a cold extended disk of high-angular momentum gas from cosmological accretion. These results all suggest that the CGM could generally be a source and reservoir not just of gas, in general, but of angular momentum for galaxies. To determine whether this is the case would require measuring the angular momentum in the CGM of a large sample of realistic galaxies, which has not yet been done for a large cosmological simulation. It is with this motivation in mind that we seek, as a \ufb01rst step, to characterize the angular momentum of the CGM for a large population of galaxies from the TNG100 simulation to determine what, if any, systematic properties appear. In Section 2, we describe the IllustrisTNG simulation suite and our angular momentum calculations in detail, as well as de\ufb01ne key properties of our CGM sample. In Section 3 we describe our main results. In Section 4, we discuss the implications and possible physical origins of our results, and we summarize in Section 5. We plan, in future papers, to follow up this theoretically based work in two ways: by determining to what extent our conclusions are supported by observations, and by tracing the overall and detailed evolution of gas throughout the CGM using the IllustrisTNG simulations. 2. METHODS 2.1. Simulations This work makes use of the TNG100 box of the IllustrisTNG simulation suite (Marinacci et al. 2018; Naiman et al. 2018; Nelson et al. 2018; Pillepich et al. 2018a; Springel et al. 2018), which utilizes the moving-mesh code Arepo (Springel 2010; Weinberger et al. 2019) to evolve a periodic \u2248(111 Mpc)3 box from cosmological initial conditions down to z = 0. It has a baryonic mass resolution of 1.4 \u00d7 106 M\u2299per cell. Two forms of feedback are included: (1) galactic winds launched using energy released from evolving stellar populations (Pillepich et al. 2018b), and (2) energy ejections from active galactic nuclei (AGNs) that occur in two modes corresponding to high and low accretion rates onto the black hole (Weinberger et al. 2017). IllustrisTNG is based on the original Illustris simulation suite (Vogelsberger et al. 2013, 2014a,b; Genel et al. 2014) and notably improves upon its feedback prescriptions to be more in line with the observational constraints for both high-mass (Nelson et al. 2018; Pillepich et al. 2018a) and low-mass (Pillepich et al. 2018b) galaxies. The Angular Momentum of the CGM in TNG100 3 2.2. Analysis Our halo selection is made based on the virial mass Mvir, calculated with a spherically averaged overdensity criterion (Bryan & Norman 1998) for objects identi\ufb01ed with the friends-of-friends algorithm (Davis et al. 1985). However, we wish to distinguish between the contribution of satellite galaxies and the contribution of the main central galaxy. Thus, for each halo, we select (i) gas cells from the central subhalo as calculated by the subfind algorithm (Springel et al. 2001), (ii) gas contained in satellite subhalos identi\ufb01ed by the same algorithm, and (iii) gas contained in the halo \u201cfuzz\u201d that is geometrically part of the halo but not bound to any subhalo. We then de\ufb01ne \u201csmooth\u201d gas as all gas bound to the central subhalo or part of the halo fuzz ((i)and (iii)) and satellite gas as all gas bound to satellite subhalos (ii). Finally, we de\ufb01ne the smooth (satellite) component of the CGM as all smooth (satellite) gas that is outside of a sphere centered on the most bound particle contained in the galaxy with radius equal to twice the stellar half-mass radius. The gas inside this sphere, though we do not consider it in this paper, we call the interstellar medium (ISM). Pillepich et al. (2019) found in TNG50 that the extent of the star-forming gas (i.e. gas with a number density n > 0.13 cm\u22123) relative to the stellar half-mass radius depends on both halo mass and redshift. We \ufb01nd this as well in TNG100, but the impact on the CGM mass is minimal: at z = 0, star-forming gas is on average < 2% of the CGM by mass for all halo masses considered in this paper, and it is < 10% for all z \u22642. We have also tried de\ufb01ning the CGM with other geometric and/or mass cuts but settled on twice the stellar half-mass radius due to its relative simplicity and so as to mimic how galaxy sizes are measured observationally with stellar light. Regardless, we generally \ufb01nd that our results are not sensitive to the precise de\ufb01nition we choose here. We also further divide the smooth CGM into \u201chot\u201d and \u201ccold\u201d phases based on a threshold at half the virial temperature, Tvir, de\ufb01ned as Tvir = \u03b3 \u22121 kB GMvir Rvir \u00b5 (1) where \u03b3 = 5/3, and \u00b5 is the mean molecular weight of the gas in the halo. For halos of masses \u223c1011 M\u2299, \u223c1012 M\u2299, and \u223c1013 M\u2299, Tvir has average values of \u2248 2\u00d7105 K, \u22488\u00d7105 K, and \u22484\u00d7106 K respectively, and the \u201ccold\u201d phase comprises on average \u224880%, \u224866%, and \u224850% of the total CGM gas mass, respectively. Note that by our de\ufb01nition, all gas is either hot or cold. We calculate the speci\ufb01c angular momentum of the CGM of a galaxy as follows: jCGM = 1 MCGM N X i=1 mi(ri \u2212rcenter) \u00d7 (vi \u2212vcom) (2) where the summations go over all gas cells included as part of the CGM or of one of its components, as appropriate. MCGM = PN i=1 mi is the total mass of that component, rcenter is the position of the most bound particle in the halo, and vcom is the center-of-mass velocity of the central galaxy, de\ufb01ned as the collection of all of the stars in the central subhalo. We also de\ufb01ne the misalignment angle of the CGM with respect to the galaxy as the angle between jCGM and the stellar speci\ufb01c angular momentum vector (j\u2217), where j\u2217is calculated as in Equation 2 but using the central galaxy\u2019s star particles. Following our previous analyses of baryonic angular momentum in the Illustris simulation (Genel et al. 2015; DeFelippis et al. 2017), we divide halos into two populations based on the stellar speci\ufb01c angular momentum magnitude (j\u2217) of the central galaxy (i.e. the central subfind subhalo). For the MW-mass scale, which is our focus, we select all halos with virial masses in the range 1011.75 < Mvir < 1012.25 M\u2299to have as large a sample of as possible. Rather than using the distribution of j\u2217alone, we \ufb01rst normalize j\u2217by M 2/3 vir and choose the upper and lower quartiles of the distribution of j\u2217M \u22122/3 vir , a quantity that is functionally similar to the traditional halo spin parameter \u03bb \u221djhaloM \u22122/3 vir . This is necessary for removing any lingering halo mass dependence and ensuring that the two populations have essentially the same mass distributions. We refer to the upper and lower quartiles de\ufb01ned above, which each contain 630 halos, as high-j\u2217and low-j\u2217respectively, and we show the full j\u2217distribution of our halo mass range and highlight the high-j\u2217and low-j\u2217samples in Figure 1. We note that the high-j\u2217sample has a lower median black hole mass and higher speci\ufb01c star-formation rate than the low-j\u2217sample by factors of \u22480.6 and \u22481.4, respectively. 3. RESULTS In this section, we present the results of our analysis technique as described in Section 2. We primarily focus on MW-mass halos at z = 0 (Section 3.1), and then expand our analysis to higher redshifts (Section 3.2) and other halo masses (Section 3.3). 3.1. MW-mass Halos at z = 0 We begin in Figure 2 by plotting the total speci\ufb01c angular momentum magnitude of the CGM against its misalignment angle relative to the stars for high-j\u2217and low-j\u2217MW-mass halos at z = 0 as de\ufb01ned in Section 2. We also distinguish between the smooth and satellite components as de\ufb01ned above. First, we consider the smooth component shown as the solid black triangles: we see that the entire smooth CGM of high-j\u2217galaxies (upward triangles) is very well aligned to the stars in the galaxy, with a median misalignment angle of only about 15\u25e6. Conversely, the smooth CGM of low-j\u2217galaxies (downward triangles) is much more poorly aligned, with a higher misalignment angle by \u223c40\u25e6, and a lower speci\ufb01c angular momentum magnitude, by about a factor of 4 DeFelippis et al. 1011.8 1011.9 1012 1012.1 1012.2 Mvir [M ] 10 30 100 300 1000 3000 j* [km/s\u00d7kpc] j* M2/3 vir high-j* low-j* 109.5 1010 1010.5 1011 M* [M ] Figure 1. Stellar speci\ufb01c angular momentum magnitude vs. the virial mass of TNG100 MW-mass halos at z = 0. The high-j\u2217and low-j\u2217galaxies as de\ufb01ned in Section 2 are shown as upward and downward facing triangles, and the two middle quartiles of the j\u2217distribution are shown as smaller circles. Each point is colored by the galaxy\u2019s stellar mass. The black dashed line indicates a power law in this plane with a slope of 2/3. 1.5. By comparing Figures 1 and 2, we can see that the CGM of high-j\u2217galaxies has a \u223c3\u22124 times higher speci\ufb01c angular momentum than that of the high-j\u2217galaxies themselves (namely their stellar component), while for low-j\u2217galaxies, this ratio is typically larger, \u223c10. Further, Figure 2 also shows the same quantities but now split into the hot and cold components of the smooth CGM. We see that the \u223c40\u25e6misalignment angle di\ufb00erence and factor of \u223c1.5 magnitude di\ufb00erence between high-j\u2217and low-j\u2217galaxies is present in each of the cold and hot gas components separately. In detail, the cold and hot components di\ufb00er (in a similar way for high-j\u2217and low-j\u2217galaxies) such that the cold component around both galaxy types has a slightly higher magnitude and is somewhat better aligned to the stars than the hot component. We found these results to be insensitive to temperature cuto\ufb00s anywhere between 0.1 and 1 Tvir. Next, we look at the satellite component. We note that, unlike for the smooth component, we do not de\ufb01ne a cuto\ufb00around the stellar disk of any satellite galaxy, as the entire satellite subhalo is part of the CGM of the central subhalo. Gas in satellites (empty triangles in Figure 2) has a much higher speci\ufb01c angular momentum than the smooth CGM\u2212about 0.5 dex for high-j\u2217 galaxies and 1 dex for low-j\u2217galaxies\u2212and both satellite components are less aligned to the stars than their corresponding smooth components are. However, on average, the smooth component contains an order-ofmagnitude more mass, which means the total angular 0 30 60 90 120 angle between CGM and stars [deg] 103 104 jCGM [km/s\u00d7kpc] high-j* low-j* smooth satellite cold hot Figure 2. Speci\ufb01c angular momentum magnitude vs. misalignment angle of CGM gas with respect to the stellar angular momentum axis for TNG100 MW-mass halos at z = 0. The median values are shown for all gas (black) around highj\u2217galaxies (upward pointing triangles) and low-j\u2217galaxies (downward pointing triangles). This is shown both for the smooth (i.e. non-satellite) component (solid, \ufb01lled triangles) and for satellites (dashed, empty triangles). The smooth component is further divided into cold (blue) and hot (red) components based on a temperature threshold of Tvir/2 for each halo. The ellipses surrounding each median point show the corresponding 1\u03c3 scatter of the covariance between the magnitude and misalignment. momentum contents of the smooth and satellite components are roughly equal. In comparing high-j\u2217and low-j\u2217galaxies, we see a smaller misalignment angle with respect to the stars for satellites around high-j\u2217galaxies, just like for the smooth component. But, unlike the smooth component, there is a larger magnitude around the low-j\u2217galaxies. However, there are reasons to believe the same highj\u2217/low-j\u2217split is not very meaningful for the satellite component. First, the mass fraction of the CGM in the satellite component is extremely variable: \u223c20% of MW-mass halos contain no satellite component to their CGM at all, and \u223c2/3 of them have less than 5% of their CGM mass contained in satellites; still, \u223c1% of halos actually have a majority of their CGM mass in satellites. Second, the scatter of the satellite component as shown in Figure 2 is quite large compared to that of the smooth component, especially in the misalignment angle. Third, the median misalignment between the satellite compoThe Angular Momentum of the CGM in TNG100 5 0 0.25 0.5 0.75 1 z/Rvir j 99 90 50 high-j* j z = j* 99 90 50 low-j* j high-j* low-j* difference 0 0.25 0.5 0.75 1 rxy/Rvir 0 0.25 0.5 0.75 z/Rvir 99 90 50 0 0.25 0.5 0.75 1 rxy/Rvir 99 90 50 0 0.25 0.5 0.75 1 rxy/Rvir 2 3 5 10 15 [103 km/s\u00d7kpc] 0 15 30 45 60 75 90 [deg] 3 2 1 0 1 2 3 [103 km/s\u00d7kpc] 45 30 15 0 15 30 45 [deg] 0 0.25 0.5 0.75 z/Rvir j z = jCGM high-j* low-j* difference 0 0.25 0.5 0.75 1 rxy/Rvir 0 0.25 0.5 0.75 z/Rvir Figure 3. Each panel shows mass-weighted spatial distributions of the cold CGM binned in height (y-axis) and cylindrical radius (x-axis) for TNG100 MW-mass halos at z = 0. The \ufb01rst three columns are computed with the z-axis pointing in the direction of the stellar angular momentum vector. The top row displays speci\ufb01c angular momentum magnitudes in units of 1000 km s\u22121 kpc and the bottom row displays misalignment angles in degrees. The \ufb01rst column shows the actual angular momentum magnitude and misalignment angle of the CGM around high-j\u2217galaxies, and the second column shows the same for the CGM around low-j\u2217galaxies. The third column is simply the di\ufb00erence between the \ufb01rst column and the second column. The \ufb01nal column is calculated in the same way as the third column but with the z-axis pointing in the direction of the total angular momentum vector of the CGM, rather than the stars. The black contours in each panel are isodensity contours of cold gas, labeled by the percentage of cold gas mass (50%, 90%, and 99%) they enclose. Rounder (\ufb02atter) contours therefore highlight more (less) spherically symmetric density pro\ufb01les. The white dashed triangle is meant to guide the eye by emphasizing the properties of the gas within a \u223c30\u25e6wedge centered on the plane perpendicular to the axis of rotation. nent and the smooth component (not shown) is nearly the same for high-j\u2217and low-j\u2217galaxies (30\u25e6and 40\u25e6, respectively) and is notably in between the medians of the high-j\u2217and low-j\u2217smooth component. These results indicate that the angular momentum found in satellites at z = 0 is generally associated with a small amount of mass at misalignment angles more related to the smooth component than to the galaxy. This can be understood as follows: at z = 0, the smooth component of the CGM is made up of accreted and ejected gas averaged over all cosmic time, while the satellite component is much more transient and subject to strong variations. In other words, the satellite component is tracing a much shorter timescale of accretion and is thus more weakly related to the angular momentum of the galaxy. Therefore, for the rest of this paper, we will focus on the smooth component of the CGM where there is more gas and where the split in high-j\u2217and low-j\u2217populations is strongest and more physically meaningful, presumably highlighting an important connection between the CGM and the galaxy. In particular, we want to identify the gas that could be driving the di\ufb00erence in the overall properties of the two populations. In Figure 3, we show the distribution of the average angular momentum magnitude (top row) and misalignment angle (bottom row) in di\ufb00erent spatial bins of the cold, smooth CGM component. Figure 4 shows the same quantities but for the hot, smooth component. Our goal in displaying the CGM this way is to understand which parts of the CGM are signi\ufb01cantly di\ufb00erent between high-j\u2217and low-j\u2217galaxies and, thus, where the overall angular momentum trends in Figure 2 come from. Before discussing the results, we provide two minor caveats. First, we only display properties of the gas out to a spherical radius of Rvir because past this boundary, we \ufb01nd all measured properties to be very noisy. Second, within Rvir, we only show averages in spatial bins where at least 50% of the halos have gas in that bin. Immediately evident in the \ufb01rst two columns of Figures 3 and 4, especially in Figure 3, is a high-angular momentum and well-aligned gaseous \u201cwedge\u201d centered on the galactic plane and extending to large radii in 6 DeFelippis et al. 0 0.25 0.5 0.75 1 z/Rvir j 99 90 50 high-j* j z = j* 99 90 50 low-j* j high-j* low-j* difference 0 0.25 0.5 0.75 1 rxy/Rvir 0 0.25 0.5 0.75 z/Rvir 99 90 50 0 0.25 0.5 0.75 1 rxy/Rvir 99 90 50 0 0.25 0.5 0.75 1 rxy/Rvir 2 3 5 10 15 [103 km/s\u00d7kpc] 0 15 30 45 60 75 90 [deg] 3 2 1 0 1 2 3 [103 km/s\u00d7kpc] 45 30 15 0 15 30 45 [deg] 0 0.25 0.5 0.75 z/Rvir j z = jCGM high-j* low-j* difference 0 0.25 0.5 0.75 1 rxy/Rvir 0 0.25 0.5 0.75 z/Rvir Figure 4. Each panel shows the mass-weighted spatial distributions of the hot CGM for TNG100 MW-mass halos at z = 0 and plots the same quantity as the corresponding panel in Figure 3. high-j\u2217galaxies that barely exists in low-j\u2217galaxies. To help guide the eye, such a wedge is outlined with dashed white lines in each panel of Figures 3 and 4. Such a feature is perhaps expected for cold gas, which is generally the more centrally concentrated (as shown by the black isodensity contours, which are labeled with the percentage of mass enclosed) and rotationally supported, but interestingly, the hot gas also shows this feature, albeit to a lesser extent in angular momentum magnitude. This can also be seen quantitatively in the third column, which is simply the di\ufb00erence between the \ufb01rst two columns: the CGM of high-j\u2217galaxies with respect to low-j\u2217galaxies has an angular momentum excess of as much as 3000 km s\u22121 kpc in cold gas and 1000 km s\u22121 kpc in hot gas within this wedge, and it is also \u224830\u25e6better aligned to the stars in this wedge, independent of temperature. Outside the wedge region, the differences between the CGM of high-j\u2217and low-j\u2217galaxies are much smaller. We comment here that the existence of this wedge demonstrates that the angular momentum distribution of the CGM is more cylindrically symmetric (i.e. symmetric with respect to the z-axis) than spherically symmetric in the halo, which Bullock et al. (2001) also found to be true for dark-matter-only simulations of comparable halos. Finally, we calculate the same spatial distributions for the CGM of high-j\u2217and low-j\u2217galaxies but with the zaxis set to the direction of jCGM rather than j\u2217. We note that the misalignment angle in this case is no longer between the CGM and the galaxy but between the local CGM and global CGM. We \ufb01nd that the CGM properties of high-j\u2217galaxies hardly change (as expected, since the galaxy and the CGM are rather well aligned, see Figure 2), but the CGM properties of low-j\u2217galaxies do, resulting in the di\ufb00erence maps shown in the fourth columns of both Figures 3 and 4. Compared to those in the third columns, the misalignment angle di\ufb00erence maps show much smaller values, meaning the local-toglobal CGM misalignment angles of the CGM of high-j\u2217 and low-j\u2217galaxies are similar. Therefore, large misalignment di\ufb00erences in the third columns of Figures 3 and 4 are due to the overall misalignment of the CGM of low-j\u2217galaxies to the galaxy, rather than the internal properties of the CGM around those galaxies. However, while the misalignment angle di\ufb00erence is signi\ufb01cantly lessened, the angular momentum magnitude di\ufb00erence hardly changes, and there is still a nonzero misalignment angle di\ufb00erence at rxy < 0.5Rvir and z < 0.5Rvir in both the hot and cold phases. We now seek to quantify the magnitude of the tangential (i.e. non-radial) velocities that contribute to the angular momentum magnitudes displayed so far. In Figure 5, we plot mass-weighted radial pro\ufb01les (in cylindrical shells) of the vector-summed spherical tangential velocity of the cold and hot components of the CGM. As we are interested here in the motion within the CGM, we align these pro\ufb01les to the CGM\u2019s total angular momentum vector (as in the rightmost columns of Figures 3 and 4). Note that this alignment choice does not a\ufb00ect the computation of the tangential velocity but merely the location at which that velocity is displayed in the pro\ufb01les. For radii \u22720.5Rvir, we see that cold gas and The Angular Momentum of the CGM in TNG100 7 0 25 50 75 100 125 150 175 200 vtangential [km/s] cold high-j* low-j* Vvir/2 0 0.2 0.4 0.6 0.8 1 rxy/Rvir 0 25 50 75 100 125 150 175 200 vtangential [km/s] hot 0.0 < z/Rvir < 0.1 0.1 < z/Rvir < 0.2 0.5 < z/Rvir < 0.6 Figure 5. Tangential velocity pro\ufb01les for cold (top panel) and hot (bottom panel) gas in the CGM of TNG100 MWmass halos at z = 0, aligned to the total angular momentum vector of the CGM. Each panel shows the CGM of high-j\u2217 (solid) and low-j\u2217(dotted) galaxies at three di\ufb00erent heights (blue, green, red). The colored shaded regions are the \u00b11\u03c3 scatter for the high-j\u2217pro\ufb01les and are of comparable size to those of of the low-j\u2217pro\ufb01les. The black shaded region shows the range of Vvir/2 for all halos, where Vvir = p GMvir/Rvir is the virial velocity. gas around high-j\u2217galaxies have higher tangential velocities than hot gas and gas around low-j\u2217galaxies, respectively. At larger radii however, the high-j\u2217and low-j\u2217samples are nearly identical, and the hot gas has slightly higher velocities. For both cold and hot components, the largest tangential velocities occur close to the galactic plane and within \u223c0.5Rvir, where they can exceed half the virial velocity of the halo. The tangential velocities fairly quickly drop o\ufb00with height and radius, reaching a value of \u224825 km s\u22121, independent of temperature, before they start to increase again in the outer halo, mostly for the hot gas. The tangential velocity as we have de\ufb01ned it contains rotation in two coordinates: the azimuthal coordinate \u03c6 and the polar coordinate \u03b8. We \ufb01nd (but do not show) that the shapes of the azimuthal velocity (v\u03c6) pro\ufb01les are almost identical to those of the tangential velocity pro\ufb01les in Figure 5 but reduced by \u223c10 \u221220 km s\u22121. However, the average polar velocity (v\u03b8) at all locations is 0 km s\u22121, meaning there is no coherent rotation in the \u03b8 direction at all. These results con\ufb01rm that the highangular momentum \u201cwedge\u201d we see in Figures 3 and 4 is associated with rotational velocities primarily in the azimuthal direction, which are a signi\ufb01cant fraction of the virial velocity of the halo in the inner CGM. 3.2. MW-mass Halos at z > 0 In this section, we extend our analysis to halos that have a z = 0 MW-mass at higher redshifts (and thus, a larger halo mass at z = 0) by applying the same galaxy selection criteria as described in Section 2 to redshifts z > 0. First, in Figure 6, we plot the same quantities as shown in Figure 2 but at redshifts from z = 0 to z = 5 for the hot and cold smooth components of the CGM separately. The thick opaque lines connecting the median high-j\u2217and low-j\u2217points at di\ufb00erent redshifts have similar slopes and lengths, both for hot gas and cold gas, thus indicating a remarkable consistency between magnitudes and alignments of high-j\u2217and low-j\u2217galaxies with redshift. The only signi\ufb01cant di\ufb00erence with redshift is the total magnitude of a given component of the gas, which increases over time at approximately similar rates for the upper and lower quartiles of the stellar speci\ufb01c angular momentum distribution. This is consistent with the expected growth of speci\ufb01c angular momentum with redshift at \ufb01xed mass1: j \u221d(1 + z)\u22121/2. There also appears to be a steady trend of decreasing misalignment angle for the cold CGM of high-j\u2217galaxies at z \u22721. However, broadly speaking, the total angular momentum properties of MW-mass halos are redshift independent, apart from the total angular momentum magnitudes themselves. In Figure 7, we show the angular momentum magnitude and misalignment angle di\ufb00erence maps for cold gas, analogous to those in the fourth column of Figure 3 (i.e. aligned to the total angular momentum vector of the CGM) but for higher redshifts; to ease comparison, the \ufb01rst column of Figure 7 is identical to the fourth column of Figure 3. We also normalize the angular momentum magnitude di\ufb00erence by (1 + z)\u22121/2 to remove the overall angular momentum growth from the di\ufb00erence plots. We immediately see that there are two key structural di\ufb00erences between the high-j\u2217and low-j\u2217galaxies that are redshift dependent. First, at very high redshifts (z = 5), the magnitude and misalignment angle di\ufb00erence structure is much noisier than at all other redshifts, indicating that the organized structure seen at z = 0 is the result of longer-term evolution. However, by z = 2, 1 Assuming a constant halo spin parameter \u03bb: j \u221d\u03bbRV \u221d R1/2 \u221d1/(1 + z)1/2. 8 DeFelippis et al. 0 30 60 90 angle between CGM and stars [deg] 500 1000 5000 jCGM [km/s\u00d7kpc] high-j* low-j* z = 0 z = 1 z = 2 z = 5 cold hot Figure 6. Speci\ufb01c angular momentum magnitude vs. misalignment to the stars for cold (blue) and hot (red) gas in high-j\u2217(upward pointing triangles) and low-j\u2217(downward pointing triangles) TNG100 MW-mass halos at z = 0 to z = 5. Ellipses show 1\u03c3 scatter of z = 0 galaxies (identical to those in Figure 2) and are of similar size at all redshifts. Opaque lines connect high-j\u2217and low-j\u2217points at four selected redshifts and demonstrate the persistence of the misalignment angle and magnitude di\ufb00erence over cosmic time. the basic aligned \u201cwedge\u201d structure is in place. Second, at redshifts z < 2, the area of the strongest magnitude di\ufb00erence seems to drift inward toward the galaxy from \u223cRvir at z = 1\u22122 to \u223cRvir/3 at z = 0. This is accompanied by the inward drift of the largest radius where the misalignment angle di\ufb00erence is negative, indicating a better intrinsic alignment around high-j\u2217galaxies. In examining the actual magnitude and misalignment angle values as a function of redshift, we \ufb01nd that for the cold gas, the magnitude of jCGM increases in the outer parts of the halo over time, but only in the CGM of high-j\u2217galaxies does the magnitude increase in the inner part of the halo, and this happens most dramatically after z = 1. Neither the high-j\u2217nor low-j\u2217misalignment angle pro\ufb01les change signi\ufb01cantly after z = 2. We also \ufb01nd the same features in the corresponding plots for hot gas, though the size of the magnitude e\ufb00ect is decreased. This potentially highlights a point in time at which angular momentum exchange between the galaxy and the CGM becomes particularly e\ufb00ective, presumably due to the emergence of fountain \ufb02ows, and high-j gas can exist nearer to the galaxy. 3.3. Other Halo Masses Next, we consider the role of halo mass in in\ufb02uencing the angular momentum structure of the CGM. Figure 8 displays the same cold and hot gas evolutionary tracks as shown in Figure 6 but now for \ufb01ve halo mass bins of width 0.5 dex centered on 1011 M\u2299, 1011.5 M\u2299, 1012 M\u2299, 1012.5 M\u2299, and 1013 M\u2299. Clearly, highermass halos have more angular momentum, consistent with the expected scaling of j \u221dM 2/3 vir , but the misalignment angle seems to be essentially independent of halo mass. As in Figure 6, the misalignment of the cold CGM of high-j\u2217galaxies decreases at z \u22721. We can also see evidence of two regimes of halo mass: one is Mhalo \u22721012 M\u2299(green, blue, and purple), for which all halos have a CGM with a higher-angular momentum magnitude and better alignment around high-j\u2217 galaxies compared to low-j\u2217ones. The other regime is Mhalo > 1012 M\u2299(orange, red). In these halos, the CGM angular momentum magnitude di\ufb00erence between high-j\u2217and low-j\u2217galaxies is consistent with zero, though the misalignment angle di\ufb00erence remains. The evolutionary tracks are also considerably more jagged. Additionally, for all galaxies, the misalignment di\ufb00erence between cold and hot gas increases toward lower halo masses at z = 0, possibly demonstrating less mixing between the phases due to the lower \u201chot\u201d (with respect to Tvir) gas mass fraction in the CGM of those lowestmass halos (\u224820%) compared to the highest-mass ones (\u224850%). In Figure 9, we show cold gas di\ufb00erence maps at z = 0 for the same \ufb01ve halo mass bins as in Figure 8, again, aligned to the total angular momentum vector of the CGM. First and foremost, we can clearly see the distinction between the \ufb01rst three columns and the last two: the lower-mass high-j\u2217halos have an excess angular momentum in the wedge de\ufb01ned earlier compared to the low-j\u2217halos and are similarly self-aligned. In the two highest-mass bins, the di\ufb00erence between the high-j\u2217and low-j\u2217is less clear. In examining each population by itself, we \ufb01nd that both contain a similarly sized excess in the wedge, but the structure outside the wedge is more complicated, sometimes resulting in an excess around the low-j\u2217galaxies (fourth column) and sometimes little organized structure at all (\ufb01fth column). The misalignment angle maps do not vary much with mass, consistent with the overall result from Figure 8. We \ufb01nd broadly similar results when we examine the hot gas (not shown), though the di\ufb00erence map in the largest halo mass bin shows a nearly uniform slight angular momentum magnitude excess and a misalignment angle di\ufb00erence of nearly 0\u25e6. This is presumably due to two related factors: (1) the dominance of black hole feedback over stellar feedback at higher halo masses, and (2) the resulting dearth of typical high-j\u2217spirals at halo masses \u223c1013 M\u2299that renders the high-j\u2217/low-j\u2217split of the galaxy population less physically meaningful (see, The Angular Momentum of the CGM in TNG100 9 0 0.25 0.5 0.75 1 z/Rvir z = 0 high-j* low-j* difference z = 1 z = 2 j z = 5 0 0.25 0.5 0.75 1 rxy/Rvir 0 0.25 0.5 0.75 z/Rvir 0 0.25 0.5 0.75 1 rxy/Rvir 0 0.25 0.5 0.75 1 rxy/Rvir 0 0.25 0.5 0.75 1 rxy/Rvir 3 2 1 0 1 2 3 [103 km/s\u00d7kpc\u00d7(1+z)1/2] 45 30 15 0 15 30 45 [deg] Figure 7. The di\ufb00erence between the mass-weighted spatial distributions of the cold CGM of high-j\u2217and low-j\u2217galaxies binned in height (y-axis) and cylindrical radius (x-axis; the same panels as the fourth column of Figure 3) for TNG100 MW-mass halos at z = 0, 1, 2, and 5, from left to right. The scale of the \ufb01rst row is normalized by (1 + z)\u22121/2 to account for overall growth of angular momentum with redshift. The corresponding evolution of the hot CGM is very similar. 0 30 60 90 angle between CGM and stars [deg] 102 103 104 jCGM [km/s\u00d7kpc] high-j* low-j* cold hot 1013 M 1012.5 M 1012 M 1011.5 M 1011 M Figure 8. Speci\ufb01c angular momentum magnitude vs. stellar misalignment angle for cold (solid, \ufb01lled triangles) and hot (dashed, empty triangles) gas in TNG100 halos of over two orders of magnitude in mass binned in \ufb01ve bins, each a di\ufb00erent color. The triangles show z = 0 values, and the lines show the population evolution within the bin up to z = 5. for example, Figure 2 of Genel et al. 2015, which shows this for the original Illustris simulation). What does seem clear though is that the angular momentum structure of MW-mass halos (which we found to be largely independent of redshift) is not unique to MW-mass halos and represents a typical structure for a wide range of halos up to \u223c1012 M\u2299. 4. DISCUSSION Having established the basic di\ufb00erences of the CGM angular momentum content between highand low-j\u2217 galaxies, we now explore what coherent velocities in the CGM and variations to the IllustrisTNG physics model can tell us about the source of these di\ufb00erences. We then place the results in this paper in the larger context of previous CGM-related angular momentum results. 4.1. Radial and Total Velocities In this section, we identify a clear distinction between hot and cold gas, which so far have appeared dynamically very similar, i.e., the distribution of radial velocities. In Figure 10 we show radial velocity maps of the cold CGM (top two panels) and the hot CGM (bottom two panels) for our main sample of interest (MW-mass halos at z = 0). For both high-j\u2217(left panels) and lowj\u2217(right panels) galaxies, the hot CGM is characterized by strongly out\ufb02owing gas in the polar regions and relatively weakly out\ufb02owing gas elsewhere. However, the cold gas shows a key di\ufb00erence between the two populations. While there is always in\ufb02owing cold gas at small heights above the galaxy as well as in the disk plane, only the CGM of high-j\u2217galaxies shows the presence of net out\ufb02owing cold gas in the polar region of the CGM. 10 DeFelippis et al. 0 0.25 0.5 0.75 1 z/Rvir [1010.75, 1011.25] high-j* low-j* difference [1011.25, 1011.75] [1011.75, 1012.25] [1012.25, 1012.75] j [1012.75, 1013.25] 0 0.25 0.5 0.75 1 rxy/Rvir 0 0.25 0.5 0.75 z/Rvir 0 0.25 0.5 0.75 1 rxy/Rvir 0 0.25 0.5 0.75 1 rxy/Rvir 0 0.25 0.5 0.75 1 rxy/Rvir 0 0.25 0.5 0.75 1 rxy/Rvir 3 2 1 0 1 2 3 [10 5 km/s\u00d7kpc\u00d7M 2/3] 45 30 15 0 15 30 45 [deg] Figure 9. The di\ufb00erence between the mass-weighted spatial distributions of the cold CGM of high-j\u2217and low-j\u2217galaxies binned in height (y-axis) and cylindrical radius (x-axis; the same panels as the fourth column of Figure 3) for the cold CGM of \ufb01ve di\ufb00erent TNG100 halo mass bins at z = 0, which are displayed on the top of each column in units of M\u2299. The scale of the \ufb01rst row is normalized by M 2/3 vir to account for the median halo mass in each bin. The corresponding plots for the hot CGM di\ufb00er slightly in the rightmost column but are otherwise very similar. This pattern of radial velocities is strongly suggestive of galactic fountains where gas in the CGM is continuously recycled, and it could potentially explain why the CGM of high-j\u2217galaxies is so much more aligned to their galaxies than are the CGM of low-j\u2217galaxies. We have found in previous work (DeFelippis et al. 2017) that the baryons locked in z = 0 stars in high-angular momentum disks (comparable to the high-j\u2217population in this paper) spend a signi\ufb01cant amount of time participating in galactic fountains, while stars in galaxies simulated without feedback end up with a few times lower angular momentum. We also found in that work that participation in the fountains increases the speci\ufb01c angular momentum of the gas, meaning the out\ufb02owing/in\ufb02owing pattern in the cold gas may be broadly tracing the angular momentum growth in the CGM. Slightly more subtly, the regions of the strongest radial in\ufb02ow also di\ufb00er between the CGM of high-j\u2217and low-j\u2217galaxies: the former has essentially no radial motion in the plane of the galaxy at < 0.2 Rvir, possibly indicative of the much stronger rotation there (see Figure 5). Evidently, low-j\u2217galaxies are associated with stronger net radial in\ufb02ows in their inner CGM. Further analysis of the mass (and angular momentum) participating in these radial \ufb02ows requires the use of tracer particles, which we defer to a later work. In Figure 11, we estimate the extent to which the gas is kinematically supported by coherent motion by plotting the average total \u201ccoherent\u201d velocity, de\ufb01ned as p v2 tan + v2 rad, where vtan is the tangential velocity shown in Figure 5 and vrad is the radial velocity shown in Figure 10. We see that total coherent velocity is always less than the circular velocity as a function of radius, except for cold gas within \u223c0.1 \u22120.2 Rvir of high-j\u2217 galaxies, indicating that the vast majority of the CGM is not completely kinematically supported by coherent motion. The remainder of the support must come from a combination of random motion (i.e. velocity dispersion) and pressure; however, the precise measurement of these other factors is outside of the scope of this paper. 4.2. Model Variations Next, we use some of the IllustrisTNG model variations described in Pillepich et al. (2018b) (each one a \u2248(37 Mpc)3 box with a baryonic mass resolution of 2.4 \u00d7 106 M\u2299per cell, comparable to TNG100) to investigate the sensitivity of the angular momentum of the CGM to changes in the IllustrisTNG physics model. These changes are summarized in Figure 12, which shows the same quantities as in Figures 2, 6, and 8 (i.e. CGM angular momentum magnitude and misalignment angle with respect to the stars). We focus on two types of variations: (1) those that change a property of the galactic wind, the dominant form of feedback for MW-mass halos, and (2) those that remove one or more physical processes completely. In each simulation, we perform the same halo selection, speci\ufb01c angular moThe Angular Momentum of the CGM in TNG100 11 0 0.25 0.5 0.75 1 z/Rvir vradial high-j* cold low-j* 0 0.25 0.5 0.75 1 rxy/Rvir 0 0.25 0.5 0.75 z/Rvir 0 0.25 0.5 0.75 1 rxy/Rvir hot 35 25 15 5 5 15 25 35 [km/s] 0 25 50 75 100 [km/s] Figure 10. Mass-weighted spatial distributions of the radial velocity of the cold (top row panels) and hot (bottom row panels) CGM of TNG100 MW-mass halos at z = 0, split into high-j\u2217(left panels) and low-j\u2217(right panels) populations as before. Mass contours are the same as the corresponding contours in Figures 3 and 4. mentum cut, and temperature separation as described in Section 2. Variations of the wind model change at least one of two quantities: the speed of the wind, and the mass loading (\u03b7) of the wind. The left column of Figure 12 shows the total magnitude and misalignment angle of three simulations with varying values of \u03b7 and \ufb01xed wind speed, both for cold (top panels) and hot gas (bottom panels). We see that increasing the mass loading does not change the angular momentum of the CGM very much compared to the \ufb01ducial properties, but reducing the mass loading drastically changes the properties around low-j\u2217galaxies by increasing their CGM\u2019s angular momentum to be greater than those around highj\u2217galaxies and signi\ufb01cantly worsening their alignment. The middle column panels show simulations where the wind speed is varied, and the mass loading is either kept at the \ufb01ducial value or varied in tandem with the wind speed so as to keep a \ufb01xed speci\ufb01c kinetic wind energy. The simulations with increased wind speed (whether or not \u03b7 is kept \ufb01xed) are also qualitatively similar to the \ufb01ducial model, while those with decreased wind speed have larger misalignment angles and higher-angular momentum magnitudes around low-j\u2217galaxies. 0 0.2 0.4 0.6 0.8 1 rxy/Rvir 0 25 50 75 100 125 150 175 200 vtot [km/s] high-j* low-j* 0.0 < z/Rvir < 0.1 0.5 < z/Rvir < 0.6 cold hot Vcirc Figure 11. Total coherent velocity pro\ufb01les for the cold (blue) and hot (red) CGM of TNG100 MW-mass halos at z = 0, split into high-j\u2217(solid) and low-j\u2217(dotted) populations as before. We show pro\ufb01les at a small (thick) and large (thin) height in the halo. The green dashed line is the circular velocity, Vcirc = p GM(< r)/r, where M(< r) is the total mass enclosed in the spherical radius r. The colored shaded regions are the \u00b11\u03c3 scatter for the two cold high-j\u2217pro\ufb01les and are of comparable size for all pro\ufb01les at a given height. Taken together, we \ufb01nd that the angular momentum magnitude of the CGM, and to a lesser extent, the misalignment angle, is sensitive to the strength of the wind but mostly only if the wind is \u201cweaker\u201d than the \ufb01ducial model. Stronger winds do not signi\ufb01cantly change the angular momentum of the CGM. These conclusions apply to both the cold and the hot phases of the CGM. It is important to note, however, that the di\ufb00erence in misalignment angle between high-j\u2217and low-j\u2217galaxies is a consistent feature of all of the simulations. A detailed or quantitative interpretation of these sensitivities is di\ufb03cult to achieve (see also Pillepich et al. 2018b), but we hypothesize in a general sense that the reason that weaker winds lead to worse galaxy-CGM alignments and to higher CGM speci\ufb01c angular momentum magnitudes is that the diminished wind feedback allows for more low-angular momentum gas to form stars and stay locked in the galaxy rather than return to the CGM and thereby lower the CGM angular momentum and \u201cmix\u201d it with that of the galaxy\u2019s. We also checked angular momentum properties for simulations with various aspects of the IllustrisTNG model removed completely: speci\ufb01cally, with no galactic winds, no metal cooling, and no black holes. We also checked a simulation that had all three of these mechanisms removed. The results, shown in the right column panels of Figure 12, indicate that removing only the winds has the greatest e\ufb00ect on the CGM\u2019s angu12 DeFelippis et al. 103 104 jCGM [km/s\u00d7kpc] cold high-j* low-j* TNG speed\u00d70.5, \u00d7 4 speed\u00d70.5,  fiducial 0 30 60 90 103 104 jCGM [km/s\u00d7kpc] hot \u00d7 0.5, speed fixed \u00d7 2, speed fixed \u00d7 4, speed fixed 0 30 60 90 angle between CGM and stars [deg] speed\u00d72, \u00d7 0.25 speed\u00d72,  fiducial 0 30 60 90 no mcooling no winds no BHs no mcooling, winds, BHs Figure 12. Speci\ufb01c angular momentum magnitude vs. misalignment to the stars of cold gas (top panels) and hot gas (bottom panels) in the CGM of MW-mass halos at z = 0 for variations of the IllustrisTNG feedback model. The colored lines connect the high-j\u2217(\ufb01lled triangles) and low-j\u2217(empty triangles) populations of each variation and emphasize that the qualitative misalignment angle di\ufb00erence between those two populations in the full TNG model (black) is also found in all other variations, with or without feedback. lar momentum by increasing its magnitude around all galaxies; removing black holes has negligible e\ufb00ects on the magnitude, but removing metal cooling slightly lowers the magnitude. In all cases, the misalignment angle di\ufb00erence between high-j\u2217and low-j\u2217galaxies remains. Interestingly, removing all three forms of feedback at once resulted in changes to the \ufb01ducial model smaller than when only one form was removed. There are many caveats to this analysis that make interpretation di\ufb03cult. As demonstrated previously (Pillepich et al. 2018b), di\ufb00erent forms of feedback often interact with each other in nonlinear ways, which is evident here in the third column of Figure 12: knowing how removing each individual form of feedback affects the CGM does not obviously inform how removing all three together a\ufb00ects the CGM. Additionally, any change to the \ufb01ducial model will in some way change galactic properties and could therefore a\ufb00ect the properties of galaxies classi\ufb01ed as high-j\u2217or low-j\u2217, not just their CGM. Other studies comparing simulations with di\ufb00erent subgrid models (Kau\ufb00mann et al. 2019) and including di\ufb00erent physics such as cosmic-rays (Buck et al. 2019) further demonstrate how sensitive properties of the CGM can be to the strength and implementation of various forms of feedback. Nevertheless, there are three clear conclusions we can draw from this analysis. First, median j and \u03b8 values for the CGM depend somewhat on the properties of the wind and the presence of feedback. Second, the high-j\u2217\u2212low-j\u2217di\ufb00erence in angular momentum magnitude is usually positive but can \ufb02ip sign if the feedback is weak enough. Finally, the high-j\u2217\u2212low-j\u2217di\ufb00erence in misalignment angle is always positive and, thus, is not driven by feedback. 4.3. Comparisons to Previous Work We highlight here important results from other recent studies of the CGM and whether or not our results are consistent with them. The main \ufb01nding by Stewart et al. (2017) was that the presence of high speci\ufb01c angular momentum gas in the halo (\u223c4 times larger than that of the dark matter) is independent of simulation code, suggesting that it is a fundamental characteristic of galaxy formation. Our results con\ufb01rm the presence of such gas in a large population of galaxies (compared to a single halo studied by Stewart et al. 2017), and we furthermore show that high-angular momentum galaxies have the highest angular momentum gas in their CGM. They also found that large-scale \ufb01lamentary in\ufb02ows resembling an extended cold disk can form around MWmass galaxies (strongly resembling the spatial pattern of cold gas we \ufb01nd in Figure 3) and that velocities of such gas can be as large as 1.5\u00d7 the virial velocity of the halo (\u223c250 km s\u22121). The tangential velocities of cold gas in TNG100 MW-mass halos are not generally that high (see top panel of Figure 5) but can exceed the virial velocity close to the disk. Other studies of simulated galaxies at high redshifts (e.g. Kimm et al. 2011; Danovich et al. 2015) have found that in\ufb02owing cold gas The Angular Momentum of the CGM in TNG100 13 streams can transport angular momentum through the halo toward the galaxy while maintaining its high spin with respect to the dark matter. While we only look at average velocity structures in TNG100 and do not follow individual gas streams, the radial velocity maps (Figure 10) nevertheless show that much of the cold rotating (and high-j) gas in the CGM has a net in\ufb02owing velocity out to nearly the virial radius at z = 0, perhaps suggesting it is indeed a source of the baryonic angular momentum of the galaxy. Recent work with EAGLE, another modern large-scale cosmological simulation, has also found evidence of rotation in the CGM. Oppenheimer (2018) measured the spin parameter of the hot halos of L\u2217galaxies and found that they are comparable to those of the cold gas, even though the hot gas is more spherically distributed. We also \ufb01nd a similar relationship between the cold and hot CGM and provide further support to the Oppenheimer (2018) conclusion that rotation in the CGM, especially in the inner parts, is a signi\ufb01cant deviation from hydrostatic equilibrium that models of the CGM should take into account. Ho et al. (2019) focus on the cold gas around a single EAGLE galaxy in a MW-mass halo and \ufb01nd corotating gas that would be detectable observationally at low azimuthal angles from the galaxy (\u227210\u25e6) and impact parameters \u227260 kpc (\u223c0.2 \u22120.3 Rvir for this halo mass). This is comparable to the region of the CGM in TNG100 MW-mass halos where cold gas is rotating near or above the virial velocity (see Figure 5). Ho et al. (2019) also measure typical in\ufb02ow speeds between 20 and 60 km s\u22121, which match fairly well with the net in\ufb02ow we measure in TNG100. They further \ufb01nd that gas tends to accrete anisotropically in structures that extend further in cylindrical radius than height, which is, again, qualitatively matched by our radial velocity maps. As a whole, we \ufb01nd signs for good agreement between the rotational properties of the CGM between the EAGLE and TNG100 simulations. We further demonstrate in this work that the hot and cold CGM components have similar angular momentum properties as well, though the cold CGM always has a higher magnitude than the hot CGM. This supports results from Danovich et al. (2015) who found that while cold and hot gas in their (smaller) sample of MW-mass halos at z > 1 have similarly shaped spin pro\ufb01les, the cold gas has a factor of \u223c2 higher spin than the hot gas. Rotation in the CGM is di\ufb03cult to measure observationally, but recent e\ufb00orts provide powerful evidence of its prevalence. Martin et al. (2019a) use 50 pairs of galaxies and quasar sightlines to measure Mg II absorption and \ufb01nd that it is preferentially located along both the major axis of the galaxy, consistent with corotation, and the minor axis, indicative of biconical out\ufb02ows. Zabl et al. (2019) use a smaller sample taken with the MUSE instrument on the Very Large Telescope and \ufb01nd similar results in Mg II, as well as inferred accretion rates consistent with simulations and previous observations of Mg II (e.g. Bouch\u00b4 e et al. 2012; Kacprzak et al. 2012; Bouch\u00b4 e et al. 2013). Hodges-Kluck et al. (2016) use Xray measurements of O VII to detect a rotating hot halo around the MW (though with a large misalignment angle) that contains as much angular momentum as the stars. Taken all together, these observational results are at least qualitatively consistent with our measurements of the CGM\u2019s angular momentum in TNG100. There are discrepancies though, such as the rotational velocity inferred by Hodges-Kluck et al. (2016) of \u223c180 km s\u22121, which is much larger than our measured hot gas rotational velocities in TNG100. However, a more careful comparison to observations is necessary to properly address this, which we defer to a future paper. 5. SUMMARY We have calculated and characterized the angular momentum of the CGM in the TNG100 simulation. We focus on the smooth CGM, namely halo gas excluding the ISM (i.e. outside twice the stellar half-mass radius of the galaxy) as well as satellites, and in particular on z = 0 MW-mass halos. Our main conclusions are as follows: 1. The total speci\ufb01c angular momentum of the smooth CGM around galaxies with high stellar spin (high-j\u2217) is systematically larger and better aligned to the stellar body of the galaxy than that of the CGM around low-j\u2217galaxies, both for hot and cold gas. The satellite component has a higher speci\ufb01c angular momentum but in general much less mass than the smooth component. 2. High-angular momentum cold gas around high-j\u2217 galaxies is distributed in a large structure that is well aligned with the galaxy plane (de\ufb01ned as the plane perpendicular to the galaxy angular momentum vector) and has an opening angle of \u223c30\u25e6. Low-j\u2217galaxies do not have such a structure in their CGM with respect to the galaxy. However, the spatial distributions of self-alignment of the cold CGM around high-j\u2217and low-j\u2217galaxies are very similar, indicating that the misalignment difference between the populations is largely due to an overall galaxy-CGM misalignment in the lowj\u2217case, rather than internal structural di\ufb00erences between the CGM of the two types of galaxies. 3. The spatial angular momentum distribution of the hot CGM is not structurally di\ufb00erent between the two galaxy populations, but the hot gas in the CGM of high-j\u2217galaxies is systematically better aligned and has a higher magnitude throughout the halo. Furthermore, the inner half of the hot CGM around high-j\u2217galaxies is dominated by rotation around the galaxy, but the outer half is dynamically very similar to the same area of the CGM of low-j\u2217galaxies. 14 DeFelippis et al. 4. These CGM characteristics are roughly independent of halo mass and redshift for halos with masses \u22721012 M\u2299, but for halo masses > 1012 M\u2299, the high-j\u2217\u2212low-j\u2217di\ufb00erence in magnitude is no longer positive, and the di\ufb00erence maps are much noisier. This is likely due to the increased in\ufb02uence of AGN feedback a\ufb00ecting the properties of galaxies and halos at these masses. 5. The CGM of high-j\u2217galaxies contains out\ufb02owing and accreting cold (relative to Tvir) gas characteristic of galactic fountains, whereas the CGM of low-j\u2217galaxies has no signi\ufb01cant cold out\ufb02ows. This points to stronger gas mixing and, thus, a stronger dynamical connection between the galaxy and the CGM of high-j\u2217galaxies. 6. The precise form and parameters of the galactic wind feedback model can a\ufb00ect the angular momentum properties of the CGM, but the misalignment angle di\ufb00erence between the CGM of highj\u2217and low-j\u2217galaxies is always present, suggesting its existence results from cosmic gas accretion and, thus, is a fundamental part of galaxy formation. We \ufb01nd our results to be qualitatively consistent with recent studies of rotation in the CGM, both for other simulations run with di\ufb00erent subgrid models (EAGLE) and observations using quasar sightlines. Future work is necessary to elucidate the origins of the angular momentum trends we see and whether they are primarily set by cosmic in\ufb02ows, feedback, or both in tandem. Nevertheless, the robustness of the trends across large ranges of halo mass and cosmic time emphasizes the important role the CGM\u2019s angular momentum has on galaxy evolution. We thank Nicolas Bouch\u00b4 e, Mary Putman, Ari Maller, Jolanta Zjupa, and Drummond Fielding for insightful and useful discussions. We also thank the anonymous referee for their helpful comments. Support for program numbers HST-AR-14565 and HST-AR-15022 was provided through a grant from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Incorporated, under NASA contract NAS5-26555. D.D. acknowledges support from the Chateaubriand Fellowship Program. G.L.B. acknowledges support from NSF grants AST-1615955 and OAC-1835509 and NASA grant NNX15AB20G. The Flatiron Institute is supported by the Simons Foundation. Software: NumPy (van der Walt et al. 2011), Matplotlib (Hunter 2007), and IPython (Perez & Granger 2007)",
                    "introduction": "1."
                },
                {
                    "url": "http://arxiv.org/abs/1906.05287v1",
                    "title": "A Correlated Search for Local Dwarf Galaxies in GALFA-HI and Pan-STARRS",
                    "abstract": "In recent years, ultrafaint dwarf (UFD) galaxies have been found through\nsystematic searches of large optical surveys. However, the existence of Leo T,\na nearby gas-rich dwarf, suggests that there could be other nearby UFDs that\nare optically obscured but have gas detectable at nonoptical wavelengths. With\nthis in mind, we perform a search of the full Galactic Arecibo $L-$band Feed\nArray HI (GALFA-HI) survey, a radio survey which covers one-third of the sky at\nvelocities $-650 < V_{\\rm{LSR}} < +650 \\; \\rm{km} \\; \\rm{s^{-1}}$, for neutral\nhydrogen sources. We are able to probe regions of the sky at lower Galactic\nlatitudes and smaller $|V_{LSR}|$ compared to previous explorations. We use the\nSource Finding Application (SoFiA) on GALFA-HI and select all sources with\nsimilar properties to Leo T and other local dwarf galaxies. We find 690 dwarf\ngalaxy candidates, one of which is particularly promising and likely a new\ngalaxy near the Galactic plane ($b=-8^{\\circ}$) that is comparable in velocity\nwidth and HI-flux to other recently discovered local volume galaxies. We find\nwe are sensitive to Leo T-like objects out to $1 \\; \\rm{Mpc}$ at velocities\nclear from background HI emission. We check each candidate's corresponding\noptical fields from Pan-STARRS and fit stars drawn from isochrones, but find no\nevidence of stellar populations. We thus find no other Leo T-like dwarfs within\n$500 \\; \\rm{kpc}$ of the Milky Way in the one-third of the sky covered by the\nGALFA-HI footprint and discuss our nondetection in a cosmological context.",
                    "authors": "Daniel DeFelippis, Mary Putman, Erik Tollerud",
                    "published": "2019-06-12",
                    "updated": "2019-06-12",
                    "primary_cat": "astro-ph.GA",
                    "cats": [
                        "astro-ph.GA"
                    ],
                    "main_content": "et al. 2019), but discrepancies between the observed MW environment and simulated environments still remain, especially in the local volume (Klypin et al. 2015). Based on SDSS data there are potentially hundreds of faint satellites that could be revealed by deeper surveys (Tollerud et al. 2008; Hargis et al. 2014). Though folding in data from the Dark Energy Survey lowers that estimate considerably (Newton et al. 2018), there may still be \u223c100 undiscovered satellites that are \u201cmissing\u201d simply due to the incompleteness of large sky surveys, a conclusion also supported by Fritz et al. (2018)\u2019s finding that there should be a population of undiscovered UFDs at the apocenter, thus illustrating the importance of looking for dwarfs in previously unsearched regions of the sky. Many such unsearched regions remain that way due to various observational difficulties. Areas covered by the Galactic plane are essentially opaque in optical wavelengths, and in velocity space, Galactic emission dominates at low velocities and complicates spectral follow-up at all wavelengths. Thus far, searches for dwarf galaxies have focused on observing their stellar light at high Galactic latitude, thus limiting the area surveyed both spatially and in distance, and biasing surveys toward those galaxies with significant stellar populations. arXiv:1906.05287v1  [astro-ph.GA]  12 Jun 2019 2 DEFELIPPIS ET AL. Though \ufb01rst detected optically, a UFD called Leo T has been found to have recent star formation from < 1 Gyr ago and a sizable reservoir of neutral hydrogen gas (HI) (Irwin et al. 2007; Weisz et al. 2014). Why Leo T even exists is still not clear, as most reionization models strip dwarfs of this mass of their gas and prevent them from accreting gas after z = 1 which would be necessary for recent star formation (e.g. Ricotti & Gnedin 2005; Ricotti et al. 2016). However, some models predict dwarfs could exist as gas-rich Leo Tlike objects if they evolved in relative isolation from the MW (Ricotti 2009). Such models thus imply there are dwarfs that can be detected by observing their gas rather than their stars, which would allow previously unobservable areas of the sky to be probed. If such dwarfs exist and have properties similar to Leo T (MHI \u223c4.1\u00d7105 M\u2299and w50 \u223c17 km s\u22121 from Adams & Oosterloo 2018), they should be detectable with high resolution and sensitivity by HI surveys within and beyond the Local Group. With this motivation in mind, this paper attempts to \ufb01nd and catalog new dwarf galaxy candidates from the full GALFA-HI survey, an HI survey that covers \u22481/3 of the sky at unprecedented spatial and velocity resolution (Peek et al. 2018). We subsequently correlate the candidates with the optical Pan-STARRS survey to investigate if they have a detectable stellar population. In Section 2 we describe the surveys and software used, and detail our analysis methodologies. In Section 3 we present a catalog of dwarf galaxy candidates from our analysis, which includes a very strong candidate galaxy in the Galactic plane, and in Section 4 we compare our catalog to other surveys of HI objects. Finally, we discuss the implications of our nondetections in Section 5, and summarize our results in Section 6. 2. METHODS 2.1. Surveys The Galactic Arecibo L\u2212band Feed Array HI (GALFA-HI) survey is a high spatial (4 arcmin) and spectral (0.74 km s\u22121, smoothed) resolution survey of HI in the MW environment. It comprises 225 data cubes with 1\u2032 pixels that cover declinations between \u22121\u25e6and 38\u25e6across all right ascensions, and covers velocities from \u2212650 < VLSR < +650 km s\u22121. The survey includes a wide range of Galactic latitudes and passes through the plane of the MW twice. We utilize GALFA-HI DR2 (Peek et al. 2018) for this study as it covers the complete 32% of the sky with relatively uniform coverage. Peek et al. (2018) quote a median root mean square (rms) noise of 0.15 K (16 mJy per beam), in a 1 km s\u22121 channel for DR2. We note that GALFA-HI DR1 (Peek et al. 2011) is deeper in some areas, but only covers approximately half the sky area in a nonuniform way. See Saul et al. (2012) for a compact cloud catalog using the DR1 data and Donovan Meyer et al. (2015) for an investigation of UV counterparts to these HI candidates. To correlate objects found in GALFA-HI with optical observations, we require an optical survey with an overlapping footprint. The Pan-STARRS survey \ufb01ts this need, as it covers all parts of the sky north of \u221230\u25e6decl. and thus fully contains the area covered by GALFA-HI. Pan-STARRS was run using the 1.8 m telescope at the University of Hawaii that mapped the sky in \ufb01ve optical and infrared bands: g,r,i,z, and y. For further details, see Chambers et al. (2016). 2.2. HI Source Finding We used the Source Finding Application (SoFiA) developed by Serra et al. (2015) to search through the entire GALFA-HI DR2 dataset for Leo T-like objects. SoFiA\u2019s user interface contains many optional input parameters and preprocessing choices. In this section, we enumerate the steps of our analysis before, during, and after running this program, along with our rationale. 1. We decided to search for sources only in velocity slices where the average brightness temperature was < 1 K, to avoid the brightest Galactic emission. For most data cubes this range was typically \u223c40 km s\u22121 wide centered around VLSR = 0 km s\u22121, but for some cubes at lower Galactic latitude the range was as high as 175 km s\u22121 (see Figure 1). In addition, we removed the Galactic background emission from each data cube by applying an unsharp mask to each velocity slice. Without doing this, SoFiA would often merge discrete HI blobs at low to moderate VLSR with the extended Galactic emission. After experimenting with various masks and \ufb01nding no major differences in the properties of the sources SoFiA detected, we chose a mask radius of r = 30 arcmin. This radius is both larger than the expected size of a candidate galaxy, and consistent with the smoothing box size chosen by Saul et al. (2012) for searching the GALFA-HI DR1 data. 2. When running SoFiA we turned on the noise scaling \ufb01lter which normalizes the input data cube by the local noise level in each velocity slice, thus preventing faint sources from being thrown out solely because they were being compared to a less noisy background. SoFiA measures local RMS noise by de\ufb01ning a box around each source, calculating the median absolute deviation of all pixels within that box that are not masked as part of the source, and multiplying by 1.4 under the assumption of Gaussian noise (T. Westmeier 2019, personal communication). The noise level varies across the sky, largely as a function of Galactic latitude; near the plane (|b| < 15\u25e6), the average RMS noise level SoFiA calculates near detected sources is 0.21 K, while far from the plane (b > 70\u25e6) it is 0.16 K. 3 25 50 75 100 125 150 175 Velocity Range [km/s] 0 10 20 30 40 Number of data cubes |b| > 15\u25e6 |b| < 15\u25e6 Figure 1. Distribution of Galactic emission region sizes in km s\u22121 with an average brightness temperature TB > 1 K for all 225 data cubes, separated into regions of high and low Galactic latitude (b). We chose 1 K as a compromise between being able to push to lower velocities and being able to distinguish extended Galactic emission from compact sources. 3. For the source \ufb01nding itself, we used the \u201cSmooth+Clip\u201d (S+C) \ufb01nder, which smooths the data cube with userinputted Gaussian kernels and then separates pixels that have a \ufb02ux greater than some thresholds relative to the noise level. Pixels that were \u22641 pixel apart in any dimension were merged into a single source. We chose a 4 pixel full width at half maximum (FWHM) for each spatial dimension to match the survey resolution, a 5, 10, 20, and 30 pixel (3.68, 7.36, 14.72, and 22.08 km s\u22121) FWHM for the velocity dimension to cover the potential ranges of velocity widths of yet undetected dwarf galaxies, and a 5\u03c3 \ufb02ux threshold to reduce the probability of detecting too many spurious sources. If a source was found in any applied smoothing \ufb01lter, it was then added to the catalog. 4. Once the source catalog for each cube was compiled, we removed previously known galaxies and then applied a series of cuts to remove any obviously spurious sources and tune our source list to most resemble dwarf galaxies. For reference, the properties of several recently discovered gaseous dwarf galaxies are shown in Table 1 (the de\ufb01nitions of the columns in the table are given in Section 3 except for M\u2217, the stellar mass in M\u2299, and D, the distance to the galaxy in Mpc). We set the minimum and maximum major axes of the ellipse \ufb01tted to the spatial extent of the source (called ell3s_maj in SoFiA) to 4 and 8 pixels, respectively; the minimum and maximum velocity widths (w50) to 10 and 50 km s\u22121, respectively; the maximum axis ratio of the source to 1.5; and the minimum integrated signal-to-noise ratio to 20. Table 1. Properties of Recently Detected Local Group Galaxies with HI Galaxy R.A. Decl. l b F HI MHI M\u2217 w50 VLSR D (J2000) (J2000) (\u25e6) (\u25e6) (Jy km s\u22121) (105 M\u2299) (105 M\u2299) (km s\u22121) (km s\u22121) (Mpc) Leo T 09h34m53. s4 17\u25e603\u203205\u2032\u2032 214.85 43.66 9.9 4.1 2.0 17 34 0.42 Leo P 10h21m45. s1 18\u25e605\u203217\u2032\u2032 219.65 54.43 1.3 8.1 5.6 24 261 1.62 Pisces A 00h14m46. s0 10\u25e648\u203247\u2032\u2032 108.52 -51.03 1.2 89 100 23 236 5.64 Pisces B 01h19m11. s7 11\u25e607\u203218\u2032\u2032 133.83 -51.16 1.6 300 316 43 611 8.89 NOTE\u2014 The Leo T data are from Adams & Oosterloo (2018), the Leo P data are from McQuinn et al. (2015), and the Pisces A and B data are from Tollerud et al. (2016). At the end of this process we were left with \u223c1000 HI sources. We did a \ufb01nal pruning of this source list by examining the moment maps and velocity spectra of each source by eye, and removing as candidates only those that were obviously artifacts or very close to the edge of their cube and were not already removed by the previous data cuts, or had irregular velocity spectra at high |VLSR|. This process resulted in a \ufb01nal list of 690 objects, the beginning of which is shown in Table 2. The entire list is provided in the online journal. 2.3. Optical Correlation We developed and tuned an algorithm to recognize the stellar population of Leo T and other local dwarf galaxies from Pan-STARRS data, and then applied it to our HI candidates. The algorithm works as follows. 4 DEFELIPPIS ET AL. 1. We draw a model population from a stellar isochrone of a given age and metallicity, downloaded from the CMD input form1 (Bressan et al. 2012; Chen et al. 2014, 2015; Tang et al. 2014). We chose from isochrones with ages of 0.5, 2, 5, and 10 Gyr and metallicities of [Fe/H] = \u22121, \u22121.5, and \u22122 to account for the large range of stellar properties of dwarfs. 2. We assign magnitudes to the model population by linearly interpolating the magnitudes and integrated IMF parameters of its isochrone, and then place it at a range of possible distances. 3. We assign magnitude and color errors based on the uncertainties provided by Pan-STARRS in the area around the source. 4. We compute the detection probability of the stars as a function of magnitude by binning the stars in the relevant Pan-STARRS \ufb01eld and \ufb01tting a power law. We then apply this detection probability to the model population. 5. We then compute the fraction of the model population that is within 1\u03c3 of a real star on both the magnitude and color axes. 6. To report a detection, we require a signi\ufb01cant peak in the overlapping fraction as a function of distance relative to a nearby control \ufb01eld. We tested this method on the resolved stellar population of the Draco Dwarf galaxy and easily recovered a distance within 10% of its measured distance of 76 kpc (McConnachie 2012). We were also able to detect Leo T with this method (Figure 2), though the measured distance is not very accurate. Of the three metallicities, the peak of the lowest metallicity isochrones (red lines) is closest to Leo T\u2019s known distance (420 kpc), but the width is large. This indicates that Leo T\u2019s distance is already approaching our algorithm\u2019s detection limit when used with Pan-STARRS and that beyond that limit, further analysis would be required to con\ufb01dently identify a stellar population. In addition to \ufb01tting to stellar isochrones, we also visually inspected Pan-STARRS images at each source\u2019s coordinates to identify any potential signs of a galaxy, because a galaxy\u2019s stars may be resolved or unresolved depending on its distance. We obtained uniformly scaled images by combining the y, i, and g \ufb01lters downloaded from the image cutout server2 with Astropy\u2019s make_lupton_rgb function (Astropy 1 http://stev.oapd.inaf.it/cgi-bin/cmd 2 http://ps1images.stsci.edu/cgi-bin/ps1cutouts 0 200 400 600 800 1000 Distance [kpc] 0.0 0.2 0.4 0.6 0.8 1.0 Overlapping Fraction 0 200 400 600 800 1000 Distance [kpc] 0.0 0.2 0.4 0.6 0.8 1.0 Overlapping Fraction [Fe/H] = \u22122.0 [Fe/H] = \u22121.5 [Fe/H] = \u22121.0 Figure 2. Fractions of model stellar populations that overlap with real stars in the Pan-STARRS \ufb01eld for Leo T, which is at a distance of \u223c420 kpc (left), and for the average of four control \ufb01elds 10 and 20 arcmin away on either side of Leo T at the same Galactic latitude (right). Solid and dashed lines are 10 and 5 Gyr isochrones, respectively. Figure 3. Leo P in Pan-STARRS (left) at a distance of 1.6 Mpc which represents what we would identify as a successful detection of diffuse blue light, compared to a nearby \ufb01eld without a galaxy (right). Both images are 2 arcmin across. Collaboration et al. 2018) to detect any potential stellar populations, which would show up as diffuse blue light. Figure 3 shows a successful detection of Leo P using this method at a distance of 1.6 Mpc (McQuinn et al. 2015). Pan-STARRS also reveals the HI discovered galaxies Pisces A and B at 5.6 and 8.9 Mpc (Tollerud et al. 2016), respectively, as diffuse blue light; however, the quality of the images varies for individual sources. Leo T\u2019s stellar population does not appear as diffuse light because it is much closer and resolved. 3. RESULTS 3.1. Catalog and Sample Properties There are 690 HI galaxy candidates that were also inspected for an optical component with Pan-STARRS. The \ufb01rst 10 candidates are shown in Table 2; the entire table can be found in the online journal. The table properties are as follows. 5 1. (Source ID) A string containing (1) the Galactic longitude, (2) the Galactic latitude (both in degrees), and (3) the VLSR velocity in km s\u22121. 2. (R.A. and Decl.) The R.A. (hours, minutes, and seconds) and decl. (degrees, arcminutes, and arcseconds) in J2000 coordinates of the source\u2019s \ufb02ux-weighted center (in other words, the \u201ccenter of \ufb02ux\u201d of all pixels de\ufb01ned to be part of the source). Previous work in the ALFALFA group has found the HI positions to be accurate to within 30 arcsec (Kent et al. 2008). 3. (Size) The major axis of the ellipse in arcmin \ufb01tted to all pixels in the source that are \u22653\u03c3 above the local noise level (called ell3s_maj in SoFiA). Every such pixel is given equal weight in this calculation. 4. (S/N) The signal-to-noise ratio integrated over the entire velocity spectrum. 5. (Fint) The \ufb02ux of the source integrated over the entire velocity spectrum in Jy km s\u22121. This was converted from the extracted SoFiA values in units of K channel using the following factor: Fint [Jy km s\u22121] Fint [K channel] = 2kB\u03b82 \u03bb2 21 cos(\u03b4)\u00d7 0.74 km s\u22121 channel \u00d71023, where \u03b8 = 1 arcmin in radians, \u03bb21 = 21.106 cm, and \u03b4 is the source\u2019s decl. 6. (TB) The peak brightness temperature in K (called f_peak, the peak \ufb02ux density in SoFiA). 7. (w50) The line width at 50% of the peak \ufb02ux density of the source in km s\u22121. 8. (VLSR) The local standard of rest velocity at the source\u2019s \ufb02ux-weighted center in km s\u22121. Table 2. Partial Source List Sorted by Increasing Galactic Longitude Source ID R.A. Decl. Size S/N F int TB w50 VLSR (l +b+VLSR) (h:m:s) (\u25e6:\u2032:\u2032\u2032) (arcmin) (Jy km s\u22121) (K) (km s\u22121) (km s\u22121) 000.12+75.05-034 13:44:18 18:25:34 5.0 44 0.83 0.59 18 -34 000.68+72.41-029 13:53:26 16:55:19 4.2 36 0.64 0.5 18 -29 001.51+59.47+015 14:35:36 09:02:07 5.0 40 1.31 1.03 20 15 002.70+70.81-035 14:00:19 16:27:45 5.2 64 1.41 0.81 12 -35 003.89+68.38-062 14:09:29 15:21:07 7.3 80 3.14 0.98 14 -62 004.01+54.40-050 14:54:58 06:54:13 6.1 69 3.17 1.05 21 -50 004.27+57.23-059 14:46:19 08:46:05 5.8 51 1.61 1.0 13 -59 004.43+41.74-050 15:35:23 -00:45:48 5.5 70 1.98 0.75 15 -50 004.46+58.24-068 14:43:19 09:27:47 4.8 38 0.93 0.83 12 -68 006.80+58.39-028 14:45:50 10:32:03 4.6 35 0.75 0.58 11 -28 NOTE\u2014 Uncertainty estimates for each column are given in Section 3.1. We now comment on the properties of our sample. In Figure 4 we see that sources are present over the entire DR2 \ufb01eld roughly uniformly, with a noticeable gap near R.A. \u2248180\u25e6 corresponding to the North Galactic Pole. Sources are also present over a wide range of Galactic latitudes, notably including close to the Galactic plane (|b| \u227215\u25e6). The variation of the local noise calculated by SoFiA when searching the data is clearly dependent on Galactic latitude (lower latitudes have systematically higher RMS values) which affects the detection limit, as discussed below. However, the distribution of the HI sources across position and velocity space shows that the noise variation is not signi\ufb01cantly dependent on velocity. A majority (\u224875%) of sources have |VLSR| < 100 km s\u22121, and we see structure at VLSR < \u2212200 km s\u22121 most likely associated with the Magellanic Stream. Figure 5 shows a series of properties of our detected sources. The top panel demonstrates that we are detecting objects within our desired angular size range roughly uniformly, with a slight bias to smaller objects. At a distance of 500 kpc, these sizes correspond to diameters of 0.6\u22121.2 kpc. The upper middle panel shows that our upper limit on the velocity width of 50 km s\u22121 was conservative; nearly all sources have a velocity width < 20 km s\u22121. The plot also implies that the population would continue to lower velocity widths if we did not apply a cut at w50 = 10 km s\u22121. In examining the ve6 DEFELIPPIS ET AL. 0 10 20 30 DEC [deg] 0 30 60 90 120 150 180 210 240 270 300 330 360 RA [deg] 400 200 0 200 400 VLSR [km/s] 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.10 0.15 0.20 0.25 0.30 0.35 rms [K] Figure 4. Top: R.A. and Decl. positions of each source. The regions within the dashed black lines correspond to the Galactic plane in between latitudes \u221215\u25e6and 15\u25e6. Bottom: local standard of rest velocity in km s\u22121 vs. R.A. for each source. Points are colored by their local RMS values calculated by SoFiA. The outlined square is the local volume candidate described in Section 3.4. locity distribution (lower middle panel) we \ufb01nd that there is an overall bias toward objects with negative velocities; the median value of VLSR is \u221246 km s\u22121. Fluxes range from 0.5 to 15.6 Jy km s\u22121, and we show the distribution of \ufb02uxes in the bottom panel of Figure 5. The \ufb02ux distribution turns over at 1.4 Jy km s\u22121, but we note that the variability of the RMS values shown in Figure 4 implies that this turnover is not constant across the entire GALFA-HI \ufb01eld. At lower Galactic latitudes, the mean noise level is \u2248 10% higher than the noise level outside of the plane. There are also known to be sources at lower \ufb02uxes than we detected in DR2 (see Saul et al. (2012) and Figure 7). We estimated errors on the properties derived by SoFiA using injected sources, described in Section 3.2. Position uncertainties were on the order of 15 arcsec (negligible compared to the beam size), and velocity uncertainties were on the order of 1 km s\u22121, or roughly 1-2 channel spacings. Fractional uncertainties were 2 \u22128% for size measurements, 5 \u221210% for w50 measurements, and 10 \u221220% for all other reported parameters, depending on both the distance and the velocity the injected sources were placed at. Sources at larger distances and lower velocities had higher fractional uncertainties by as much as a factor of 3. 3.2. HI Detection Limits We measure the value of the turnover in the \ufb02ux distribution to be 1.4 Jy km s\u22121. We convert this to a completeness limit estimate of Dmax = 1.74 \u00d7 \u0000MHI 106 M\u2299 \u00011/2 Mpc for an object with an HI-mass (MHI) in solar masses. For an object with an HI-mass comparable to Leo T, this distance limit is \u223c1.15 Mpc. If we compute Dmax for the galaxies in Table 1, we \ufb01nd that Pisces A, B, and Leo P are all very close to their edge of detectability, and only Leo T itself is comfortably detectable. SoFiA was indeed easily able to \ufb01nd Leo T in the DR2 data, but it was unable to \ufb01nd Pisces A, Pisces B, or Leo P. However, we were able to \ufb01nd Pisces A in the DR2 data cube by manually applying smoothing \ufb01lters. Due to the inherent variability of backgrounds and foregrounds across the \ufb01eld, we ran further tests to better quantify our estimated detection limits. We injected 3D Gaussian sources3 meant to replicate Leo T\u2019s accepted size and velocity width as found in Adams & Oosterloo (2018) (which are also consistent with the SoFiA-derived size and velocity width of 6.1 arcmin and 15 km s\u22121, respectively) into each cube with a peak \ufb02ux corresponding to Leo T\u2019s actual distance (0.42 Mpc) at three different velocities: high velocity (250 km s\u22121), a low velocity de\ufb01ned as 15 km s\u22121 greater than 3 Leo T\u2019s actual HI pro\ufb01les are not exactly Gaussian (Adams & Oosterloo 2018) so this assumption does lead to differences from Leo T\u2019s accepted mass and \ufb02ux by as much as a factor of 2. 7 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 Size [arcmin] 100 101 10 15 20 25 30 35 40 45 50 w50 [km/s] 100 101 102 400 300 200 100 0 100 200 300 VLSR [km/s] 100 101 102 100 101 Flux [Jy\u00d7km/s] 100 101 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Number of Sources Figure 5. Distributions of angular size (top) in arcmin, velocity width (upper middle) in km s\u22121, local standard of rest velocity (lower middle) in km s\u22121, and integrated \ufb02ux (bottom) in Jy km s\u22121. The dashed line in the bottom panel is the estimated turnover of the \ufb02ux distribution at 1.4 Jy km s\u22121. the boundary of the searched region de\ufb01ned in Section 2.2, and Leo T\u2019s velocity (from Table 1). For the purpose of this test, we de\ufb01ned a successful detection to be one where SoFiA pulled out the injected source at its given velocity (within 15 km s\u22121), position (within 5 arcmin), and derived a velocity width and size within our cuts used in Section 2.2. We recovered every injected source at high velocities, where Galactic emission is the weakest, and nearly every source at low velocities and Leo T velocities (97% and 82% respectively), the latter of which is lower because Leo T\u2019s velocity is often within the region of average Galactic emission > 1K which we purposely ignored. Nevertheless, we can con\ufb01dently say that SoFiA would successfully detect Leo T at its actual distance in the vast majority of our search area. We next wanted to determine how accurate our detection limit of Leo T-like objects was, based on our observed \ufb02ux distribution. To do this, we performed the same procedure as before with two alterations; we scaled the peak \ufb02ux of the injected source to a larger distance (from 0.5 to 1 Mpc) and we reduced the size of the injected source to better correspond to a more distant galaxy. At high velocities, the detection fraction dropped to its lowest value of 86% at 1 Mpc, but the Table 3. Detection Fraction of Sources Injected at or beyond a Distance of 500 kpc Mass (Leo T) Distance (Mpc) High-v Low-v Leo T-v 1 0.5 100% 76% 69% 1 0.75 99% 40% 45% 1 1 86% 11% 18% 2 1 100% 46% 50% 3 1 100% 68% 63% 10 1 100% 83% 76% NOTE\u2014 The HI mass of Leo T is 4.1\u00d7105 M\u2299. Detection fractions are colored and shaded by how far above (green) or below (red) 50% they are. difference at low and Leo T velocities is much more drastic, as shown in the \ufb01rst three rows of Table 3 (with Mass = 1 Leo T). Note, however, that a typical local group galaxy that is 1 Mpc away has a velocity closer to our high-velocity case than either of the lower-velocity cases. In other words, the region of distance-velocity space where our detection fraction is lowest also probably contains the smallest number of dwarf galaxies. We also tried reducing the injected sources\u2019 size, which results in a \u223c10% drop in the detection fraction at lower velocities compared to the same test without changing the size, meaning the dominant reason for the overall drop is the reduction in \ufb02ux caused by increasing distance. In the bottom three rows of Table 3 we inject sources with successively larger multiples of Leo T\u2019s mass to determine how complete we are out to 1 Mpc. We note that we would detect \u224850% of galaxies at lower velocities with only 2 times Leo T\u2019s mass, and \u224866% of those with 3 times Leo T\u2019s mass.4 The last row of 10 times Leo T\u2019s mass is an exception to the previous rows in that the size and w50 cuts we apply are the dominant cause for reduction in recovered sources in regions signi\ufb01cantly contaminated by Galactic emission at low velocities. Without the size and w50 cuts, the detection fractions are all > 92%. The higher level of background noise at low latitude causes SoFiA to chop off the outer regions of the object in its size calculation. Therefore our size cut may lead us to miss some dwarf galaxies with a range of HI masses at low latitudes and velocities. 3.3. Optical Results Using the algorithm de\ufb01ned in Section 2.3 we also attempted to \ufb01nd optical counterparts for all of our sources. 4 At 4 times Leo T\u2019s mass we naturally recover the same detection fractions as the \ufb01rst row of Table 3, because multiplying the mass of the third row by 4 is equivalent to halving the third row\u2019s distance in terms of HI \ufb02ux. 8 DEFELIPPIS ET AL. Table 4. HI properties of Local Volume candidate shown in Figure 6 Parameter LV Candidate Source ID (l +b+VLSR) 067.73-08.13+358 R.A. (J2000) 20h32m26s Decl. (J2000) 25\u25e659\u203246\u2032\u2032 Size (arcmin) 4.4 S/N 175 Fint (Jy km s\u22121) 4.97 TB (K) 1.44 w50 (km s\u22121) 49 VLSR (km s\u22121) 358 The vast majority of overlapping fractions were no larger than those of nearby control \ufb01elds, and the few that were larger were not at all comparable to the values seen in the left panel of Figure 2, indicating no resolvable stellar populations. We note that Leo T is already close to the edge of detectability in Pan-STARRS and it is only \u2248400 kpc away, so it is not necessarily surprising we were unable to see a stellar population in any of our HI sources of potentially comparable HI-masses out to 1 Mpc. We also checked the Pan-STARRS \ufb01elds visually, as described in Section 2.3, and found two potential sources with diffuse blue light (see Appendix), but otherwise nothing that indicated an unresolved stellar population similar to Leo P shown in Figure 3. 3.4. Local Volume Candidate In Table 4 we show the properties of a particularly unusual galaxy candidate that is very close to the Galactic plane (b = \u22128\u25e6) in the constellation Vulpecula. It is an outlier in our sample in many respects. As evident in Figure 4, it has the largest positive value of VLSR, and is the only object in our sample with VLSR > 300 km s\u22121. It has a much larger signalto-noise ratio than the typical value of \u224865 for our source list. Its velocity width is just below our cutoff at 50 km s\u22121 and at the tail end of the distribution of velocity widths which has a mean of \u224815 km s\u22121 (see Figure 5). We also note that it is in an area of the sky not covered by DR1 or ALFALFA. Figure 6, a velocity moment map of this source, shows evidence for a velocity gradient. Follow-up optical imaging suggests a faint optical counterpart, to be detailed in a forthcoming paper. 4. COMPARISON TO OTHER CATALOGS We \ufb01nd broad consistencies in the properties of our sources compared to the Compact Cloud Catalog based on GALFAHI\u2019s DR1 data (Saul et al. 2012) and objects in the ALFALFA survey (Haynes et al. 2018) categorized as high velocity 308\u25e6 308\u25e65' 308\u25e610' RA [deg] 25\u25e655' 26\u25e6 26\u25e65' DEC [deg] 340 345 350 355 360 365 370 VLSR [km/s] Figure 6. HI velocity map of the local volume candidate in (R.A., decl.) coordinates. Surrounding (unconnected) pixels have been masked out. The dashed line is Galactic latitude b = \u22128.13\u25e6. clouds (HVCs). For comparison to the ALFALFA catalog we used the \u03b1\u2212100 complete catalog available on their website5, which they state is not fully vetted but which contains Galactic sources not included in Haynes et al. (2018). We found sources in common between the surveys distributed uniformly across all areas of overlap on the sky. For a match, we required the difference in both R.A. and decl. to be < 5 arcmin, and the difference in the center of the velocity spectrum to be < 15 km s\u22121. We do not recover all sources from Saul et al. (2012) or ALFALFA (68 matching objects in the former, 47 matching objects in the latter) due to differing search parameter choices and catalog methods, survey depths, and ALFALFA\u2019s lower velocity resolution. Our skycoverage also for the \ufb01rst time includes the Galactic plane. Comparisons of the same distributions in Figure 5 for the compact cloud and ALFALFA catalogs are shown in Figure 7. Our velocity width distribution (top panel) does not extend over the same range as Saul et al. (2012)\u2019s because we cut off sources with w50 < 10 km s\u22121 and applied different masks when searching the data to focus on potential galaxy sources over clouds. Our sources extend over the velocity widths of both the cold (\u2206V < 15 km s\u22121) and warm (\u2206V > 15 km s\u22121) clouds de\ufb01ned by Saul et al. (2012). The difference between our catalog and the ALFALFA distribution also comes partially from the search masks we apply, but at the lower width end it is due to ALFALFA\u2019s much larger channel spacing of 5 km s\u22121. Our sources have cen5 http://egg.astro.cornell.edu/alfalfa/data/ 9 0 10 20 30 40 50 60 w50 [km/s] 100 101 102 Compact Cloud Catalog 400 200 0 200 400 VLSR [km/s] 100 101 102 ALFALFA 10-2 10-1 100 101 102 103 Total Flux [Jy\u00d7km/s] 100 101 102 SoFiA Candidates 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Number of Sources Figure 7. Distributions of velocity width (top) in km s\u22121, local standard of rest velocity (middle) in km s\u22121, and integrated \ufb02ux (bottom) in Jy km s\u22121 for our sources (solid blue), the Compact Cloud Catalog (dotted orange), and HVCs from ALFALFA (dashed green). The dashed black line in the bottom panel is the estimated turnover of our \ufb02ux distribution at 1.4 Jy km s\u22121, the same as in Figure 5. tral velocities (middle panel) that follow the distribution of Saul et al. (2012) very closely and have the same median VLSR \u2248\u221250 km s\u22121. The ALFALFA HVCs have more negative velocities (median VLSR \u2248\u2212300 km s\u22121) most likely due to their catalog capturing many large clouds, such as those associated with the Magellanic system. Saul et al. (2012)\u2019s \ufb02ux distribution is essentially identical to ours down to 1.4 Jy km s\u22121, though it continues to nearly two orders of magnitude fainter in \ufb02ux. This is to be expected as DR1 was deeper in some areas of the sky and therefore able to pick out fainter sources. The ALFALFA catalog has a similar turnover but includes many more sources at higher \ufb02uxes, again due to the lack of size or velocity width cuts. In Figure 8, we directly compare properties of our candidates, the Compact Cloud Catalog, and the four reference dwarf galaxies from Table 1. The left panel shows the HImasses of our candidates and objects in the Compact Cloud Catalog all placed at 1 Mpc. We see that both Leo T and Leo P have comparable HI-masses compared to the derived masses of our candidates if placed at 1 Mpc. Though the right panel implies dwarf galaxies are more likely to have large positive values of VLSR, Leo T\u2019s existence demonstrates that local dwarfs can also have low velocities. 5. DISCUSSION 5.1. Local Volume Candidate There is an observed dearth of MW satellites and local group galaxies at low Galactic latitudes (see Figure 1 of McConnachie 2012), presumably due to the dif\ufb01culties of detecting anything in the crowded Galactic plane. If con\ufb01rmed, our local volume candidate would begin to \ufb01ll in the spatial distribution of nearby dwarf galaxies in regions the Galactic plane obscures. Using the galaxy candidate\u2019s measured integrated \ufb02ux, we calculate it to have a HI-mass of 1.17 \u0000D 1 Mpc \u00012 \u00d7 106 M\u2299, where D is its as yet undetermined distance. It has a velocity width similar to Pisces B, which was also \ufb01rst discovered in GALFA data, and if it also has a similar HI-mass, its HI-\ufb02ux would place it at a distance of \u22485 Mpc (see Figure 8). This is also very close to the distance we derive assuming the candidate is in the Hubble \ufb02ow (D = VLSR/H0, where H0 = 70 km s\u22121 Mpc\u22121). Using an estimate of the dynamical mass, Mdyn = 6.2 \u00d7 103aW 2 50d (Equation (8) from Adams et al. (2013)), where a is the angular diameter in arcmin, W50 is the velocity width in km s\u22121, and d is the distance Mpc, we calculate a dynamical mass from our HI data of 6.5 \u0000D 1 Mpc \u0001 \u00d7107 M\u2299. If D = 5 Mpc, we derive an HI-mass-to-total mass ratio of 0.1. We defer further analysis of this object\u2019s physical properties to a future paper with optical follow-up, which will in particular allow us to measure its distance. However, we speculate here that it is very unlikely our candidate is as close as Leo T due to its large velocity, which is inconsistent with other known galaxies in the local group (McConnachie 2012), and the absence of a Leo T-like optical image from Pan-STARRS: thus, it is probably not a true Leo T analog. 5.2. Dwarf Galaxy Limits We discuss our limits on dwarf galaxy candidates in two regimes: a galactocentric distance < 500 kpc and a galactocentric distance > 500 kpc. We can place our strongest constraints on the existence of Leo T-like objects in the \ufb01rst regime, where both gas from GALFA-HI and resolved stellar populations in Pan-STARRS are detectable (see Section 2). The fact that we do not see stellar populations in any of our candidates shows that there are no other Leo T-like objects closer than 500 kpc within the GALFA-HI footprint, except possibly near the Galactic plane (where the stellar population would be indistinguishable from foreground stars) or near VLSR = 0 km s\u22121 (where we did not search to avoid bright Galactic emission). This nondetection is not completely surprising, as ram pressure stripping and other mechanisms near the MW (at \u223c250 kpc) are expected to deplete the gas in dwarfs that reside there (Grcevich & Putman 2009; Nichols & Bland-Hawthorn 2011; Spekkens et al. 2014; Emerick et al. 2016). Nevertheless, there remains a volume of \u22480.17 Mpc3 (the GALFA-HI sky out to 500 kpc) where we detect no additional Leo T-like objects. Our nondetection 10 DEFELIPPIS ET AL. 101 102 w50 [km/s] 105 106 107 MHI [M\u2299] SoFiA (1 Mpc) CCC (1 Mpc) L. V. Candidate (1 Mpc) L. V. Candidate (5 Mpc) 10 20 30 40 50 w50 [km/s] 400 200 0 200 400 600 VLSR [km/s] Leo T Leo P Pisces A Pisces B Figure 8. Left: HI-mass in M\u2299vs. velocity width (w50) in km s\u22121. The blue and orange points are our candidate sources and objects in the Compact Cloud Catalog, respectively. They are all placed at a constant distance (1 Mpc) to derive an HI-mass. The dashed line is the HI-mass corresponding to a \ufb02ux of 1.4 Jy km s\u22121, also at 1 Mpc. Right: local standard of rest velocity in km s\u22121 vs. w50 for our sources. Also shown in both panels are the four galaxies in Table 1, and our local volume candidate placed at a possible distance of 1 and 5 Mpc. within this distance is consistent with a reionization epoch during which gas is removed from dwarf galaxies in the local group with halo masses \u2272108.5 M\u2299(Tollerud & Peek 2018). In summary, an object like Leo T appears to be a rarity < 500 kpc from the MW in the GALFA-HI footprint (which covers one-third of the sky), rather than one of many such objects. At distances > 500 kpc, we are unable to detect resolved stellar populations in Pan-STARRS, and our ability to detect Leo T-mass objects is signi\ufb01cantly reduced at lower velocities. We can detect Leo T-like objects in HI at high velocities clear of background emission at 1 Mpc, but we only have that same level of completeness at low velocities for sources with 10 times Leo T\u2019s mass at 1 Mpc. More distant objects with larger stellar populations than Leo T can be detected as diffuse blue light in Pan-STARRS (e.g. as Leo P appears in Figure 3), and we inspected the data for these optical sources. Though we have not quanti\ufb01ed the distance range and stellar population detectable as diffuse blue light in Pan-STARRS, the lack of any visual detections is consistent with all of our candidates\u2019 stellar masses being less than Leo P\u2019s stellar mass of 5.6\u00d7105 M\u2299at a distance of 1.62 Mpc. Therefore, despite the fact that many of our candidates would be comparable in HI-mass to Leo P at distances \u22731 Mpc (see Figure 8), the general lack of diffuse blue light is not encouraging that a large number of these are new galaxies. It also remains possible that some of our candidates are dark matter halos that just contain HI, as gas-rich minihalos without stars are predicted to exist around the MW (Ricotti 2009). If we consider our results in the context of the missing satellites problem (Klypin et al. 1999) as well as more recent galaxy count mismatches in the local \ufb01eld (Klypin et al. 2015), we see that they support a model of strong and effective reionization that limits star formation in satellites at later times. However, the precise mechanism that operates during reionization is not yet clear. Both Brown et al. (2014) and Tollerud & Peek (2018) invoke reionization from massive stars in early galaxies to explain the current population of local dwarfs; the former by measuring ancient stellar populations, and the latter by setting a halo mass at which a dwarf cannot retain gas. Our lack of detections of Leo T-like objects strengthens this interpretation. We note though that when looking directly at star-formation histories, Weisz et al. (2014) could not conclusively determine the effect reionization had, if any, on local dwarfs, meaning more observations are necessary to be able to distinguish between reionization models. Finally, we consider what other classi\ufb01cations for our HI sources are possible besides small galaxies. In Figure 9, we compare our candidates to objects in the Compact Cloud Catalog of Saul et al. (2012). For the 68 matches between the two, we see a strong overlap between different types of clouds; our candidate list contains objects that overlap all types of HI sources identi\ufb01ed in Saul et al. (2012), including high-velocity clouds, cold and warm low-velocity clouds, and galaxy candidates far from known HI complexes. Therefore, a plausible scenario is that most of these HI sources are a heterogeneous mixture of nearby MW structures. However, we note that it is possible that galaxies sitting at the outskirts of the local group may have small velocities (like Leo T) and could have been identi\ufb01ed as a low-velocity cloud in Saul et al. (2012). 11 400 300 200 100 0 100 200 300 VLSR [km/s] 0 10 20 30 40 w50 [km/s] SoFiA HVCs GCs Q3 CLVCs WLVCs Figure 9. Velocity width vs. local standard of rest velocity for SoFiA candidates and Compact Cloud Catalog objects, the latter of which is separated into HVCs which are near known complexes and have |VLSR| > 90 km s\u22121, galaxy candidates (GCs) not near known complexes with |VLSR| > 90 km s\u22121, cold low-velocity clouds (CLVCs) with |VLSR| < 90 km s\u22121 and w50 < 15 km s\u22121, warm low-velocity clouds (WLVCs) with |VLSR| < 90 km s\u22121 and w50 > 15 km s\u22121, and Q3 WLVCs with 0 < VLSR < 90 km s\u22121, w50 > 15 km s\u22121, and 180\u25e6< l < 270\u25e6. 6. SUMMARY Using Data Release 2 of GALFA-HI we performed a search for new local dwarf galaxies. We found 690 candidates, among which is an extremely promising candidate in the Galactic plane that is likely within the local volume at VLSR = 358 km s\u22121. We quanti\ufb01ed our completeness by injecting Leo T-like sources into each GALFA-HI data cube and measuring the fraction of sources detected by SoFiA. We found we were complete out to 1 Mpc at high velocities and out to Leo T\u2019s distance at low velocities for Leo T-like dwarfs. We searched Pan-STARRS for resolved stellar populations and found none comparable to Leo T\u2019s, thus ruling out the existence of other Leo T-like dwarfs within the GALFAHI footprint at distances < 500 kpc, except possibly at the lowest Galactic latitudes and local standard of rest velocities. We also searched for unresolved stellar populations manifesting as diffuse blue light in Pan-STARRS images, but again found no evidence of any, which limits the number of more massive dwarfs in the vicinity of the local group. We conclude that our results are consistent with strong reionization effects on the evolution of dwarf galaxies. Finally, we highlight some of our strongest candidates for potential follow-up observations in the Appendix. We thank the entire GALFA team, and in particular Josh Peek, Yong Zheng, and Susan Clark for their help with the analysis of the GALFA-HI data and for useful discussions. We also thank Tobias Westmeier for assistance with interpreting the output from SoFiA, and the anonymous referee for helpful comments. M.E.P. acknowledges support from the National Science Foundation under grant No. AST-1410800. Software: This research made use of Astropy, a community-developed core Python package for Astronomy (Astropy Collaboration et al. 2018), the open-source software tools Numpy, Matplotlib, and IPython (Hunter 2007; Perez & Granger 2007; van der Walt et al. 2011), and the SoFiA source \ufb01nding pipeline (Serra et al. 2015).",
                    "introduction": "1."
                },
                {
                    "url": "http://arxiv.org/abs/1703.03806v2",
                    "title": "The Impact of Galactic Winds on the Angular Momentum of Disk Galaxies in the Illustris Simulation",
                    "abstract": "Observed galactic disks have specific angular momenta similar to expectations\nfor typical dark matter halos in $\\Lambda$CDM. Cosmological hydrodynamical\nsimulations have recently reproduced this similarity in large galaxy samples by\nincluding strong galactic winds, but the exact mechanism that achieves this is\nnot yet clear. Here we present an analysis of key aspects contributing to this\nrelation: angular momentum selection and evolution of Lagrangian mass elements\nas they accrete onto dark matter halos, condense into Milky Way-scale galaxies,\nand join the $z=0$ stellar phase. We contrast this evolution in the Illustris\nsimulation with that in a simulation without galactic winds, where the $z=0$\nangular momentum is $\\approx0.6$ dex lower. We find that winds induce\ndifferences between these simulations in several ways: increasing angular\nmomentum, preventing angular momentum loss, and causing $z=0$ stars to sample\nthe accretion-time angular momentum distribution of baryons in a biased way. In\nboth simulations, gas loses on average $\\approx0.4$ dex between accreting onto\nhalos and first accreting onto central galaxies. In Illustris, this is followed\nby $\\approx0.2$ dex gains in the `galactic wind fountain' and no further net\nevolution past the final accretion onto the galaxy. Without feedback, further\nlosses of $\\approx0.2$ dex occur in the gas phase inside the galaxies. An\nadditional $\\approx0.15$ dex difference arises from feedback preferentially\nselecting higher angular momentum gas at accretion by expelling gas that is\npoorly aligned. These and additional effects of similar magnitude are\ndiscussed, suggesting a complex origin of the similarity between the specific\nangular momenta of galactic disks and typical halos.",
                    "authors": "Daniel DeFelippis, Shy Genel, Greg Bryan, S. Michael Fall",
                    "published": "2017-03-10",
                    "updated": "2017-04-18",
                    "primary_cat": "astro-ph.GA",
                    "cats": [
                        "astro-ph.GA"
                    ],
                    "main_content": "connecting galaxies to dark matter halos, and with the properties of halos from theory or simulations, to make a statistical connection between the angular momentum contents of galaxies and those of halos. The conclusion from such exercises is that galactic disks have approximately the same values of specific angular momentum as do their host halos (e.g., Zavala et al. 2008; Soko\u0142owska et al. 2017). It is this fact that allows analytical and semi-analytical models that build upon \u039bCDM hierarchical formation to succeed in reproducing various disk galaxy scaling relations provided that they make a simple assumption: that the angular momentum obtained by dark matter halos from cosmological tidal torques is effectively \u2018retained\u2019 by the baryons that fall from the circumgalactic medium into the centers of those halos where they form the stellar bodies of galaxies (Fall & Efstathiou 1980; Mo et al. 1998). This simple assumption, \u2018angular momentum retention\u2019, has however historically not been born out in more detailed dynamical models, namely cosmological hydrodynamical simulations. In those simulations, baryons tended to lose the lion\u2019s share of the angular momentum they acquired in the intergalactic medium before virial collapse, resulting in unrealistically small galaxies (Navarro et al. 1995). Very recently, however, this situation has changed, with the advent of more accurate solvers (Sijacki et al. 2012), increased resolution (Governato et al. 2004), and the introduction of strong galactic winds in the models (Sommer-Larsen et al. 1999; Maller & Dekel 2002). A number of groups have managed to form galactic disks with realistic properties, including size and angular momentum content, in \u2018zoom-in\u2019 cosmological simulations (e.g. Grand et al. 2017). Moreover, with the increase in computing power, very recent simulations followed large cosmological volumes that contain up to hundreds of arXiv:1703.03806v2  [astro-ph.GA]  18 Apr 2017 2 DEFELIPPIS, D., ET AL. massive disk galaxies, and found realistic angular momentum contents not only in a handful of galaxies, but in galaxy populations (e.g. Teklu et al. 2015). In particular, they are able to reproduce the parallel scaling relations of angular momentum versus stellar mass displayed by observed early-type and latetype galaxies (Zavala et al. 2016). These advances open the door to detailed studies that will elucidate the nature of angular momentum evolution in a fully (hydro)dynamical cosmological context (e.g. Stevens et al. 2017; Lagos et al. 2017; Penoyre et al. 2017). In this paper we focus on the high degree of \u2018angular momentum retention\u2019 of galactic disks. The starting point for this study is the result of Genel et al. (2015) that: i) the population of late-type galaxies in the Illustris simulation has a similar mean angular momentum content to the mean of both their own dark matter halos and observed late-type galaxies, and ii) galactic angular momenta are lower by a factor of a few when galactic winds are turned off. The speci\ufb01c scope of this paper is to describe in what way the galactic winds in the Illustris simulation change the angular momentum evolution of the baryons that make up the stellar components of z = 0 late-type galaxies at the Milky Way mass scale. Several ways in which galactic winds may increase the \ufb01nal angular momentum content of a galaxy have been identi\ufb01ed in \u2018zoom-in\u2019 simulations. First, galactic winds in these simulations preferentially remove gas that has lower speci\ufb01c angular momentum than the mean, hence continuously increasing the mean speci\ufb01c angular momentum of the remaining gas, and consequentially of newly-born stars (Governato et al. 2010; Brook et al. 2011; Okamoto 2013; Agertz & Kravtsov 2016). Second, some fraction of the gas ejected into a galactic wind has been found to fall back to the galaxy (\u2018galactic/halo fountain\u2019) with higher angular momentum than that with which it left the galaxy (Brook et al. 2012; \u00dcbler et al. 2014; Christensen et al. 2016). Third, in the presence of feedback, galaxies are more gas rich than without feedback and hence baryons lose less angular momentum during galaxy mergers (Brook et al. 2004; Springel & Hernquist 2005; Robertson et al. 2006; Hopkins et al. 2009). The emerging picture from these works is qualitatively consistent, which is encouraging given that they were based on different hydrodynamics codes, feedback schemes, and mass scales. However, these differences, as well as the small number of isolated galaxies included in these analyses, imply that no comprehensive, detailed, and quantitatively consistent picture exists as of yet. The main focus of the present work is a quanti\ufb01cation of the changes that the angular momenta of baryons comprising the stars in late-type galaxies undergo between the time they entered their host halos and z = 0. We de\ufb01ne several distinct \u2018events\u2019 in the evolution of every baryonic mass element and divide this full time period into several intervals using these events. We then compare the angular momentum evolution during those intervals between the Illustris simulation and a similar simulation run without galactic winds. This study focuses on providing answers to \u2018When\u2019, \u2018Where\u2019, and \u2018How much\u2019, setting the stage for future studies of the \u2018How\u2019 and \u2018Why\u2019. With respect to the existing literature on this topic, the tools used in this work are unique in two aspects. First, it is based on a large population of simulated galaxies in a simulation that reproduces observed angular momentum relations (Genel et al. 2015) as well as many other properties of galaxy populations (Vogelsberger et al. 2014a; Genel et al. 2014; Torrey et al. 2014). Second, it employs a Lagrangian analysis in a simulation based on a mesh code, using tracer particles, while previous Lagrangian analyses on this topic have all been based on Smoothed Particle Hydrodynamics (SPH) (e.g. Zavala et al. 2016). This paper is organized as follows. In Section 2 we describe the simulations and our analysis methodologies. In Section 3 we present the evolution of angular momentum and contrast the two types of simulations, with and without galactic winds. Section 3.2 is the main results section and Fig. 3 presents its key plot. In Section 4 we discuss our results within a broader context and summarize them. 2. METHODS 2.1. Simulations We use the Illustris-2 simulation (Genel et al. 2014; Vogelsberger et al. 2014a,b) of a (106.5 Mpc)3 volume, as well as a \u2018No-Feedback\u2019 simulation of a (35.5 Mpc)3 volume, both evolved with a WMAP-9 \u039bCDM cosmology (Hinshaw et al. 2013) down to z = 0 using the moving-mesh code AREPO (Springel 2010). The former is initialized with 9103 dark matter and baryonic resolution elements, and the latter with 2563, implying that they have similar resolutions in space (\u223ckpc) and mass (\u223c(1\u22122)\u00d7107 M\u2299baryonic; \u223c(5\u221210)\u00d7107 M\u2299 for dark matter). Both simulations include gas cooling and stochastic star formation, but only Illustris-2 (hereafter \u2018Illustris\u2019) has feedback in the form of star formation-driven galactic winds, as well as black hole formation and evolution (Vogelsberger et al. 2013), rendering No-Feedback very similar to the simulations in Vogelsberger et al. (2012). For the purposes of this work, and in particular with regards to angular momentum, the results at this resolution level are converged well enough with respect to the higher-resolution Illustris-1 simulation and its no-feedback analogue (for detailed resolution studies see Vogelsberger et al. 2012, 2013; Genel et al. 2015). The implementation of galactic winds in Illustris closely follow the technique introduced in Springel & Hernquist (2003). Wind particles are launched stochastically directly from the star-forming gas with prescribed velocities and mass-loading factors that depend on the local dark matter velocity dispersion around the star-forming cells, which itself closely follows the local gravitational potential. The wind ejection velocities are set to be larger than the escape velocity from the galaxy but typically smaller than the escape velocity from the host halo, such that wind particles typically reach maximum distances that are comparable to but smaller than the virial radii of their host halos. The mass-loading factors are derived from the wind velocity such that the kinetic energy associated with the ejections per unit star-formation rate is a constant that corresponds to \u22483\u00d71051 erg per supernova. This results in mass-loading factors that are typically greater than unity, and on the order of 5 for galaxies around the Milky Way mass, as is commonly employed in cosmological simulations with comparable resolution to Illustris (Zahid et al. 2014)4. The wind particles are \ufb01rst decoupled from hydrodynamical forces and move ballistically to allow them to 4 These mass-loading factors are high compared to direct observational estimates, however they should not be compared at face value. Beyond the large uncertainties on observational mass-loading measurements, they are measured at a distance from the disk while the simulated mass-loading factors apply directly at the ejection from the disk. A robust comparison of massloading factors between simulations and observations is beyond the scope of this work. IMPACT OF GALACTIC WIND ON ANGULAR MOMENTUM 3 escape the galaxies, and are recoupled to the gas after either a short amount of time or when they reach a low density region. The direction of the momentum kick given to a wind particle is perpendicular to both the velocity and the acceleration of the star-forming cell from which it is launched with respect to the galaxy center. All these various aspects of the implementation and the numerical values of the adjustable parameters were set with the aim of approximately reproducing the stellar mass function of galaxies at z = 0 and the global history of cosmic star-formation density. No aspect of the angular momentum of galaxies was tuned for. Halos are found with the friends-of-friends algorithm (FOF, Davis et al. 1985). FOF halos may have general shapes and their boundaries roughly trace a constant density contour such that their mean density corresponds roughly to 200 times the mean cosmic matter density (for relations between halo definition and angular momentum, see e.g. Zjupa & Springel 2017). Galaxies are identi\ufb01ed using the SUBFIND algorithm (Springel et al. 2001). These are gravitationally bound objects constructed around density peaks. We de\ufb01ne a \u2018galaxy\u2019 as the collection of all stellar particles, as well as gas particles with a density above 0.13 cm\u22123 \u2013 referred to as \u2018star-forming gas\u2019, inside any given SUBFIND object. The data from each simulation include 136 snapshots and corresponding group catalogs, providing a time resolution of the order of 100 Myr. We utilize a Lagrangian point of view for the evolution of angular momentum, meaning that we are interested in the angular momentum histories of unique baryonic mass elements as they travel across cosmic time from the uniform initial conditions through the cosmic web into dark matter halos and \ufb01nally into the galaxies where they reside at the present epoch. To perform a Lagrangian analysis in a mesh-based code like AREPO requires using tracer particles, since the hydrodynamical cells represent a discretization of space, not of mass. These are implemented using the Monte Carlo method introduced in Genel et al. (2013), where each tracer belongs at any given time to a certain baryonic resolution element (including gas cells, stellar and black hole particles, as well as wind particles). These \u2018passive\u2019 tracers carry only their identity throughout the simulation, and no mass, however they do continuously record certain properties of the cells they belong to. For example, a property that we use in this work is the \u2018wind-counter\u2019 each tracer stores, which increases by unity every time that tracer is incorporated into the galactic wind. Following the Lagrangian evolution of the angular momentum of certain z = 0 galaxies means following back in time the tracers associated with the \u2018active\u2019 baryonic elements comprising those galaxies. 2.2. Analysis The main analysis tool we present in the next section is relationships between the angular momentum values of individual tracers at particular \u2018events\u2019 in their evolution history. Generally, for each tracer each of these events occurs at a different cosmic time. We make direct comparisons of identical event types between Illustris and No-Feedback, and also examine certain types of events that only occur in Illustris, namely those related to the galactic winds. The events are illustrated in Fig. 1 and de\ufb01ned as follows: (i) Accretion onto main halo: the snapshot when a tracer \ufb01rst becomes part of the FOF halo that is on the main progenitor branch of the FOF halo it ends up in at z = 0. (ii) First (last) star-forming gas: the snapshot when a tracer is \ufb01rst (last) recorded entering the star-forming gas phase, namely crossing from below a density threshold of 0.13 cm\u22123. (iii) First (last) ejection: the snapshot when a tracer is \ufb01rst (last) recorded switching from a gas cell to a wind particle (only de\ufb01ned for Illustris). (iv) Star-formation: the snapshot when a tracer is last recorded changing from a gas cell or wind particle to a stellar particle. (v) z = 0 star: the \ufb01nal snapshot in the simulation (de\ufb01ned only for tracers that belong to the stellar component at that time). All tracers that belong to a stellar particle at z = 0 are included in the analysis (which focuses our analysis on the stellar angular momentum), except those that join the central galaxy while already belonging to a star particle. This latter criterion excludes \u2018ex-situ\u2019 stars, which are not directly affected by the winds and are therefore left outside the scope of this paper. This removes 10% of the z = 0 stars in Illustris and 40% in No-Feedback. For those tracers that are included in the analysis, we exclude events \u2013 except accretion onto the halo \u2013 that occur while a tracer is contained in a satellite galaxy. This is because as the angular momentum of these tracers with respect to the main progenitor galaxy is dominated by the orbital angular momentum of the satellite and hence not meaningful for our purposes. In other words, the starting point for the events above in the time line of each tracer is the time it becomes part of the main progenitor halo. The \u2018accretion onto main halo\u2019 event is the exception, as it is considered also for tracers that accrete as part of a satellite. To calculate the speci\ufb01c angular momentum of a particle, we de\ufb01ne a center of rotation as the minimum of the potential well of its host galaxy (Genel et al. 2015). To do this at all simulation snapshots, we use the SUBLINK merger trees (Rodriguez-Gomez et al. 2015) to \ufb01nd the main progenitor branch of the z = 0 galaxy and calculate the angular momentum of all particles with respect to the main progenitor, regardless of whether the particles already belong to that main progenitor or are yet to be accreted onto it. We also de\ufb01ne the reference frame for the angular momentum calculation as having the velocity of the center of mass of the main progenitor, and speci\ufb01cally of all the stars and star-forming gas present in the main progenitor galaxy. Then, we calculate the speci\ufb01c angular momentum of a tracer particle i as follows: ji = (ri \u2212rminpot)\u00d7(vi \u2212vCOM). (1) To compute the total angular momentum of a galaxy we sum the angular momenta of the tracers associated with it5: jgal = 1 Ntr,gal Ntr,gal X i=1 ji. (2) As the angular momentum is a (pseudo-)vector, the magnitude of the sum and the sum of the magnitudes are different quantities, when looking at many tracers together. In the next 5 This is a simple rather than a weighted average because all tracer particles represent equal masses. It is not an exact value due to the Monte Carlo noise in the number of tracers per cell (see Genel et al. 2013), but for our galaxies of interest, with tens of thousands of resolution elements, this is an excellent approximation. 4 DEFELIPPIS, D., ET AL. Fig. 4 (i) (ii) (iii) (ii) Fig. 7 (v) (iv) z=0 Fig. 5 Dark Matter Halo Galactic Disk (iii) Fig. 8 Figure 1. A cartoon illustrating the various \u2018events\u2019 in the evolution of a tracer particle that are considered in this work. These are (i) halo accretion, (ii) \ufb01rst/last becoming part of the star-forming phase, (iii) \ufb01rst/last ejection into the wind, (iv) becoming part of the stellar phase, (v) z = 0. In addition, certain intervals between these events that are addressed by particular \ufb01gures are marked as such. section, we \ufb01nd both quantities to be informative, as well as the comparison between them. We de\ufb01ne the level of selfalignment of a population of tracers as the ratio of these quantities, A = |Pji| P|ji| . (3) If all vectors of a particular tracer population cancel each other out, the self-alignment is A = 0, while if they all have the same direction, the self-alignment equals A = 1. When calculating the vector sum across different galaxies, one has to take into account the fact that each galaxy is in general oriented in a different direction in the simulation box, such that simply summing different galaxies together will necessarily lead to a meaningless vector cancellation. Hence, for the purpose of summing up individual tracer vectors across many galaxies, each ji at any particular event is measured as in equation (1) but in a reference frame that is rotated such that the z axis points in the direction of jgal of the galaxy hosting the tracer at the time of that event. In order to focus the scope of the paper, we select central galaxies at the Milky Way mass scale, namely with virial masses (Bryan & Norman 1997) in the ranges 1012.1 < Mh[ M\u2299] < 1012.2 and 1011.65 < Mh[ M\u2299] < 1012.65 for Illustris and No-Feedback respectively. The mass range used for No-Feedback is larger, given its smaller cosmic volume, as these bins are chosen to follow an equal total number of tracers in each simulation, \u2248106. This selection results in 278 galaxies in Illustris and 140 galaxies in No-Feedback. In order to further narrow our focus to disk galaxies, we consider only the galaxies that are at the high-tail of the angular momentum distribution, which correspond to disks both from observations (Romanowsky & Fall 2012) and in Illustris (Genel et al. 2015). Speci\ufb01cally, we select the 25% of central galaxies with the highest stellar angular momentum at z = 0 in both simulations. 3. RESULTS 3.1. The overall picture from accretion onto halos to z = 0 In Fig. 2 we present the joint, two-dimensional distributions of the magnitudes of the speci\ufb01c angular momentum vectors of individual tracers at two distinct events, both for Illustris (left) and No-Feedback (middle). For each simulation, the tracers included in these distributions are all those that are part of the stellar component of z = 0 galaxies selected as described in Section 2. The vertical axes represent the angular momentum of each tracer at a \ufb01xed cosmological time, z = 0. The horizontal axes represent the angular momentum at the time of accretion onto the halo (which occurs in general at different times for different tracers). The striking difference between the two simulations on the vertical axis is in essence the result of Genel et al. (2015) that in a simulation without feedback, galaxies at z = 0 have \u22480.5 dex lower angular momentum content. This is the result that motivates this work. The difference between the two simulations on the horizontal axis is much milder. This suggests that most of the difference represented on the vertical axis develops in between these two events, namely inside halos, rather than before the accretion onto them. In Section 3.2 and the following \ufb01gures (as indicated in Fig. 1), we will break this typically long time interval IMPACT OF GALACTIC WIND ON ANGULAR MOMENTUM 5 between accretion onto the halo and z = 0 into sub-intervals and examine each of them separately, which will constitute the main results. The difference on the horizontal axis that represents the earliest event considered in our main analysis is not zero, and we will return to it in Section 3.3, but it is mild, representing a similar starting point to the main analysis between the two simulations. Examining each panel in Fig. 2 by itself, it is worth noting that in Illustris the magnitudes of speci\ufb01c angular momentum loss (around the peak of the distribution, where most tracers are located) between accretion and z = 0 range between \u22480\u22121 dex, and in No-Feedback the corresponding losses are \u22480.5 \u22122 dex. Put more precisely, we \ufb01nd that the sum of the angular momentum magnitudes at z = 0 is lower than the sum of angular momentum magnitudes at halo accretion time by 0.57 dex in Illustris and by as much as 1.04 dex in NoFeedback. Additionally, in both panels, the peak of the distribution occupies a locus that is signi\ufb01cantly shallower than the 1 : 1 relation. This means that gas accreted onto the halo with high angular momentum tends to lose by z = 0 a larger fraction of that angular momentum compared with gas that was accreted with lower angular momentum in the \ufb01rst place. The sum of vector magnitudes does not tell the full story, however. If instead we examine the magnitudes of the vector sums on each of the axes in Fig. 2, we \ufb01nd that the difference between z = 0 and halo accretion time is only 0.23 dex in Illustris and 0.65 dex in No-Feedback. That these numbers are smaller than the differences of the magnitude sums (0.57 dex and 1.04 dex respectively, as reported in the previous paragraph) means that the individual vectors are signi\ufb01cantly more aligned at z = 0 than at the halo accretion time. This by itself is easy to understand as a result of angular momentum cancellation. The angular momentum magnitudes of individual tracers drop by a combination of: (i) transport of angular momentum to other, potentially both baryonic and dark matter, components (which accounts for the decrease of the magnitude of the vector sum), and (ii) cancellation with other baryons that end up in the z = 0 galaxy but have been accreted with different angular momentum directions (which does not change the magnitude of the vector sum). To summarize, in terms of the magnitude of the total speci\ufb01c angular momentum vector, baryons experience a signi\ufb01cant angular momentum loss between the time when they are accreted onto halos and z = 0 in the no-feedback simulation (0.65 dex), an effective loss that is much smaller in the Illustris simulation (0.23 dex). In the following sub-section we break this difference to smaller intervals in order to gain insight into its nature and origin. 3.2. The evolution between various events Fig. 3 shows a quantitative summary of the results presented in this section for the convenience of the reader. The horizontal axis represents the sequence of events de\ufb01ned in Section 2.2 and Fig. 1, with the events discussed in Section 3.1 and Fig. 2 shown as the initial and \ufb01nal points. The vertical axis represents the difference in angular momenta, in logarithmic space, relative to the starting point of accretion onto the halo. The nearly-monotonic loss of mean angular momentum in No-Feedback (red) and non-monotonic evolution in Illustris (blue) are shown in more detail in the following Figs. 4 through 8. In Fig. 4 the horizontal axes show the same quantity as the horizontal axes in Fig. 2, namely the angular momentum at the time of halo accretion. The vertical axes show the angular momentum magnitude of each tracer at the time it \ufb01rst crosses the density threshold for star-formation, i.e. when it \ufb01rst becomes part of the star-forming phase, inside the main progenitor galaxy. This time interval represents the \ufb01rst \u2018halo crossing\u2019 from the outskirts to the central part of the halo, and is marked in green in Fig. 1. The difference between the two simulations is again signi\ufb01cant. In Illustris, there is a clear correlation between the angular momentum at the two events. From Fig. 4 we read off an approximately constant degree of loss of \u2248(0.5 \u00b1 0.2) dex, which amounts to an overall loss during this \ufb01rst passage through the halo of 0.68 dex in the magnitude sum and 0.37 dex in the magnitude of the vector sum (again indicating that some angular momentum cancellation occurs between the virial radius and the galaxy itself). In No-Feedback, on the other hand, the relation is much shallower than the 1 : 1 relation, amounting to an overall loss of 0.91 dex in the magnitude sum and 0.49 dex in the magnitude of the vector sum. That the difference between these two sum measures is larger in No-Feedback (0.91 \u22120.49 = 0.42 dex) than in Illustris (0.68 \u22120.37 = 0.31 dex) means that there is more angular momentum cancellation in No-Feedback. We \ufb01nd that this originates primarily in a lower level of self-alignment (see equation (3)) in No-Feedback at the time of halo accretion, Aacc No\u2212FB = 0.24 compared with Aacc Illustris = 0.36, rather than in self-alignment differences at the time of crossing the starformation threshold, ASF No\u2212FB = 0.62 and ASF Ill = 0.73. One might hypothesize that a lower level of self-alignment is a result of a wider distribution of accretion times in No-Feedback; however, the distribution of accretion times is similar between the two simulations (Fig. A1), implying a different origin. This is discussed further in Secion 3.3. To summarize the time interval shown in Fig. 4, in terms of the magnitude of the total speci\ufb01c angular momentum vector, the loss is rather large in both simulations and not dissimilar, namely 0.37 dex in Illustris and 0.49 dex in NoFeedback. Comparing these numbers to those quoted in Section 3.1 based on Fig. 2 (0.23 dex and 0.65 dex respectively), we conclude that losses during the \ufb01rst passage through the halo represent roughly three-quarters of the total loss experienced in No-Feedback by z = 0. In contrast, in Illustris we expect to \ufb01nd a time interval that occurs after the \ufb01rst crossing of the star-formation threshold during which almost half of the losses incurred before that crossing are counteracted. This is indeed shown in the next two \ufb01gures. Fig. 5 presents the joint angular momentum magnitude distribution at the last time, versus the \ufb01rst time, tracers join the star-forming phase in the main progenitor of their z = 0 galaxy, and is marked in red in Fig. 1. We begin with a discussion of Illustris, where this includes the full time a tracer is in the galactic fountain during which it typically goes out of the galaxy, and falls back in, several times (only \u224820% of the tracers join the star-forming phase only once). Fig. 5 shows that the angular momentum magnitude at the end of this cycle is typically higher than at its beginning, more so for tracers that have low angular momentum magnitudes at the \ufb01rst time they join the star-forming phase. Over the whole tracer population, the mean magnitude increase is 0.09 dex, and the magnitude of the vector sum increases by 0.16 dex. This latter gain undoes almost half of the loss that is incurred between halo accretion and arrival at the galaxy (Fig. 4(a)), and its origin will be discussed further in relation to Fig. 6. Before that, we discuss No-Feedback during the Fig. 5 in6 DEFELIPPIS, D., ET AL. 1.5 2.0 2.5 3.0 3.5 4.0 4.5 Accretion log10(j [kpc*km/s]) 2.0 2.5 3.0 3.5 4.0 4.5 z = 0 log10(j [kpc*km/s]) Illustris (a) 1.5 2.0 2.5 3.0 3.5 4.0 4.5 Accretion log10(j [kpc*km/s]) 2 . 0 2 . 5 3 . 0 3 . 5 4 . 0 4 . 5 No-Feedback 0.01 0.03 0.1 0.3 1 3 (b) 1.5 2.0 2.5 3.0 3.5 4.0 4.5  log10(j [kpc*km/s]) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Illustris No-Feedback x-axis y-axis (c) Figure 2. Joint (left and middle) and one-dimensional (right) probability distributions of angular momentum magnitudes of stellar tracers at z = 0 (vertical axes) and those same tracers as gas at their time of accretion onto the host halo (horizontal axes). The units indicated by the color bars are of probability per dex2. The diagonal dashed lines indicate the 1 : 1 relation. The cross indicates the median angular momentum at both events. In both simulations, an overall average loss of angular momentum is evident, but to a much larger degree in the simulation without feedback (0.65 dex; middle) than in Illustris (0.23 dex; left). Figure 3. The average angular momentum loss of tracers at events de\ufb01ned in Sec. 2.2 relative to their accretion value for Illustris (blue/cyan) and NoFeedback (red/pink). Solid lines in dark color show the magnitude of the vector sum, while dashed lines in light color show the mean magnitude. The dark-shaded regions are the 1\u03c3 spread of relative losses among different galaxies. The 1\u03c3 spreads of the relative losses of each individual tracer are \u223c1 dex and are not shown for clarity. terval. In contrast to Illustris, it shows some overall loss of 0.1 dex in both mean magnitude and the magnitude of the vector sum. It is important to remember that in No-Feedback, about half of the tracers actually never leave the star-forming phase after they join it, hence the \u2018\ufb01rst\u2019 and \u2018last\u2019 times they do so are in fact the same event. In Fig. 5 we do not show these tracers, which by de\ufb01nition would lie on the 1:1 line. For the No-Feedback tracers for which these are indeed distinct events, the physical reason is very different from the typical case in Illustris. In No-Feedback, a tracer may leave the star-forming phase primarily for \u2018dynamical\u2019 reasons, which occur naturally in the simulation and are not imposed as part of the sub-grid physics as is the case for wind ejections in Illustris. These dynamical reasons include for example tidal ejections during galaxy mergers and temporal density \ufb02uctuations around the star-formation density threshold due to weaker disturbances. The angular momentum loss occurring between these two events in No-Feedback is not negligible but is small compared to the losses incurred earlier and later, as shown in Figs. 4(b) and 7(b), respectively. Returning to Illustris, the period analyzed in Fig. 5(a) includes both times when the tracer is in the star-forming phase and times in which it is outside of the galaxy in the \u2018circumgalactic fountain\u2019. The latter can be further broken down into times when the tracer belongs to a collisionless \u2018wind particle\u2019 moving away from the galaxy, later times when it has recoupled to the normal gas phase and may be still moving away from the galaxy, and times when it is falling back toward the galaxy on its way to join the star-forming phase again. It is important to understand where the overall gains of 0.16 dex associated with this full period occur. Fig. 6 hence focuses on the last of possibly multiple \u2018circum-galactic cycles\u2019 that each tracer goes through. The horizontal axis of each panel represents the same event: the time just before the last ejection into a wind (marked as the \u2018later\u2019 (iii) in Fig. 1). The vertical axes show three subsequent events in chronological order: the very \ufb01rst snapshot after that same ejection event (Fig. 6(a)); the maximum angular momentum the tracer has during that cycle through the halo before coming back to the galaxy (Fig. 6(b)); and the \ufb01rst snapshot after the tracer returns to the galaxy (namely either in the star-forming phase or directly as a star; Fig. 6(c)). Fig. 6(a) shows that the angular momentum magnitudes of individual tracers increase between the two adjacent snapshots bracketing a wind ejection event. This is understandable, as a wind ejection implies an imposed momentum kick that increases the velocity of the tracer almost to the halo escape velocity. However, since these kicks are equally directed either \u2018upwards\u2019 or \u2018downwards\u2019 from the galaxy, they do not change the vector sum of the angular momentum of a population of ejected tracers. Indeed, we \ufb01nd that the vector sum between the two events shown in Fig. 6(a) changes by only 0.04 dex (and in fact in the opposite direction, i.e. it decreases). In other words, the momentum kicks associated with the wind ejection model itself do not change the overall angular momentum content of the tracers that enter the wind. However during the time tracers spend in the circumgalactic medium following their ejection (Fig. 6(b)), they gain IMPACT OF GALACTIC WIND ON ANGULAR MOMENTUM 7 1.5 2.0 2.5 3.0 3.5 4.0 4.5 Accretion log10(j [kpc*km/s]) 2.0 2.5 3.0 3.5 4.0 4.5 First SF-Gas log10(j [kpc*km/s]) Illustris (a) 1.5 2.0 2.5 3.0 3.5 4.0 4.5 Accretion log10(j [kpc*km/s]) 2 . 0 2 . 5 3 . 0 3 . 5 4 . 0 4 . 5 No-Feedback 0.01 0.03 0.1 0.3 1 3 (b) 1.5 2.0 2.5 3.0 3.5 4.0 4.5  log10(j [kpc*km/s]) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Illustris No-Feedback x-axis y-axis (c) Figure 4. Joint and one-dimensional probability distributions of angular momentum magnitudes of tracers as they \ufb01rst cross the star-formation density threshold (vertical axes) and at accretion onto the host halo (horizontal axes). The No-Feedback plot (middle) resembles its counterpart in Fig. 2 but translated up \u223c0.4 dex on the vertical axis, meaning that only a fraction of the loss seen in Fig. 2 occurs before crossing the star-formation density threshold. The positive slope in the Illustris plot (left), when compared to the \ufb02atter one in Fig. 2, indicates that tracers accreted with log( j) \u223c3.5 lose some angular momentum before crossing the star-formation density threshold and then re-gain it by z = 0, while tracers accreted with log(j) \u223c4 already have here their z = 0 value. 1.5 2.0 2.5 3.0 3.5 4.0 4.5 First SF-Gas log10(j [kpc*km/s]) 2.0 2.5 3.0 3.5 4.0 4.5 Last SF-Gas log10(j [kpc*km/s]) Illustris (a) 1.5 2.0 2.5 3.0 3.5 4.0 4.5 First SF-Gas log10(j [kpc*km/s]) 2 . 0 2 . 5 3 . 0 3 . 5 4 . 0 4 . 5 No-Feedback 0.01 0.03 0.1 0.3 1 3 (b) 1.5 2.0 2.5 3.0 3.5 4.0 4.5  log10(j [kpc*km/s]) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Illustris No-Feedback x-axis y-axis (c) Figure 5. Joint and one-dimensional probability distributions of angular momentum magnitudes of tracers as they \ufb01rst cross the star-formation density threshold (horizontal axes; the same quantity as on the vertical axes in Fig. 4) and at the last time they do so (vertical axes). In Illustris (left), gas with lower angular momentum at the \ufb01rst crossing preferentially gains more angular momentum between these two events, namely during its participation in the \u2018galactic wind fountain\u2019, compared with gas starting out with higher values. In No-Feedback (middle), there is a mild tendency to lose angular momentum between the two events, which however, in the absence of winds, do not represent a galactic fountain but instead \u2018dynamical ejections\u2019. signi\ufb01cant angular momentum. When each tracer is considered at the time its angular momentum magnitude is maximal between the ejection and the next time it appears in the central galaxy, the sum of magnitudes is 0.29 dex higher than it is right before the ejection, and the magnitude of the vector sum is 0.2 dex higher. The gains are particularly high for tracers that had lower angular momentum at the time they were ejected. Nevertheless, by the time tracers come back to the galaxy (Fig. 6(c)), they return with angular momentum magnitudes that are on average essentially identical to those they had before the ejection (within the error on the mean, \u223c0.01 dex, but some considerable spread), and a vector sum that is larger by 0.04 dex. In other words, a single cycle through the halo results in a net small degree of increased alignment between the tracers compared to the time before their ejection into the wind. Since in our galaxies of interest tracers go typically through several such cycles, this result ties well to the result discussed around Fig. 5(a) that the full baryonic cycle in Illustris induces a 0.16 dex increase in net angular momentum. Continuing forward in the tracers\u2019 evolution, Fig. 7 starts on the horizontal axes with the angular momentum at the last time tracers join the star-forming phase, and ends with the time they are converted to the stellar phase on the vertical axes. Namely, it pertains to evolution occurring within the galaxy, after all the evolution that occurs out in the halo. The two simulations again differ signi\ufb01cantly. Illustris shows a tight correlation around the identity relation between the angular momenta at these times. In contrast, No-Feedback shows clear losses amounting to 0.14 dex for both the sum of magnitudes and the magnitude of the vector sum. Since the time tracers spend in the star-forming gas phase before forming stars is not very different between the two simulations, this result indicates that the presence of the galactic winds is changing the structure of galaxies in such a way that prevents the torques that exist otherwise and lead to angular momen8 DEFELIPPIS, D., ET AL. tum loss of the star-forming gas. Finally in this sequence of events, we \ufb01nd the tightest correlation between the angular momentum tracers have at their time of star-formation and at z = 0, shown in Fig. 8. In Illustris, the stellar component experiences a minor gain of 0.03 dex in magnitude but essentially no change in the vector sum while in No-Feedback there is a small overall gain of 0.08 dex in both magnitude and vector sums. 3.3. The angular momentum selection bias at halo accretion After characterizing the angular momentum evolution inside halos, here we make several notes regarding the angular momentum differences between the simulations at the starting point of the preceding discussion, namely at the time baryons accrete onto the main progenitors of their z = 0 host halos. First, we make use of a third simulation, which we dub the \u2018Feedback\u2019 simulation, that has identical initial conditions to No-Feedback, but the same subgrid models and parameter choices as Illustris. The tracers in this simulation can be compared on a one-to-one basis with the tracers in the NoFeedback simulation, as they have the same initial conditions. From this \u2018Feedback\u2019 simulation, we select all z = 0 stars from halos within the same mass range used for No-Feedback in the preceding analysis, identify those same individual tracers in No-Feedback, and compare their angular momentum at accretion between the two simulations6. We \ufb01nd that both the vector and magnitude sums of the angular momentum at accretion of this identical set of tracers are equal between the two simulations. Namely, the addition of feedback does not modify the angular momentum value at halo accretion in Lagrangian space. This contrasts with a comparison made when in each simulation tracers are selected independently as in Section 2.2. Fig. 9 shows the angular momentum distributions of z = 0 stars at the time of accretion (solid), divided into the component that appears as gas in the main galaxy (dashed; the same as the distributions on the horizontal axes in Figs. 2 and 4) and the component that enters the main galaxy already as stars (dotted). While the gas-accreted distribution in No-Feedback (dashed red) is wider than the one in Illustris (dashed blue), they are peaked at the same value and have nearly identical magnitude sums. However, the vector sum of angular momentum in Illustris is 0.15 dex larger than that of No-Feedback, which re\ufb02ects different degrees of self-alignment at accretion, as already noted in Section 3.2 (Aacc No\u2212FB = 0.24, Aacc Ill = 0.36). These two results together imply that the galactic winds expel a fraction of the baryons and prevent them from becoming z = 0 stars in a way that \u2018selects\u2019 a more highly self-aligned set of gas tracers to end up as z = 0 stars. This is done however without changing the angular momentum of those \u2018selected\u2019 tracers at accretion. Finally, the dotted curves in Fig. 9 represent material that forms stars in satellites and is accreted onto the main galaxy in stellar form (stellar mergers). We see that in both simulations, these stars accrete with a higher angular momentum7, having distributions that peak at log j \u223c4.5. However, in Illustris this population only constitutes \u224810% of the z = 0 stars while in 6 For direct comparison of stellar angular momentum, we exclude any of those tracers that are not stars by z = 0 in No-Feedback, but this does not affect the numerical outcome. 7 We also \ufb01nd (but do not show) that the accretion times of the different types of particles in Fig. 9 are unaffected by feedback: in both simulations stars are accreted later, in a similar way. No-Feedback it constitutes nearly half of them. The suppression of stellar accretion by feedback hence has a substantial effect on the overall angular momentum distribution that the baryons making up the z = 0 galaxies have at their accretion time (solid). In this work we deliberately do not address the evolution of the stellar accretion inside the halo down to z = 0, as it would require a distinctively different analysis from the gas component that is the focus of this work. 4. DISCUSSION AND SUMMARY Combining measurements of the angular momentum content of galactic disks with simple models that match galaxies to dark matter halos suggests that the speci\ufb01c angular momentum of galactic disks of different masses is very close (within \u224820%) to the typical speci\ufb01c angular momentum of their host halo populations. The speci\ufb01c angular momentum content of a z = 0 galaxy and its relation to that of its host halo can be considered using the following independent \u2018bookkeeping\u2019 factors meant to separate physical effects: (i) The speci\ufb01c angular momentum content of dark matter accreted onto the halo, which integrated over cosmic time roughly gives the overall speci\ufb01c angular momentum of the z = 0 dark matter halo. (ii) The relation between the speci\ufb01c angular momentum of the baryons that accrete onto the halo along with the dark matter to that of the dark matter itself. (iii) The (possible) speci\ufb01c angular momentum bias between all the baryons ever accreted onto the halo and the subset that end up in the galaxy. (iv) The angular momentum evolution of those baryons that end up in the galaxy between the time they were accreted onto the halo and z = 0. As we now discuss, this work has bearing for all of these steps except the second one, and in particular for the last two steps, which are shown here to be signi\ufb01cantly affected by feedback processes. First, if galaxy speci\ufb01c angular momentum was equal to that of the halo and all other factors did not introduce any differences, one would expect high angular momentum galactic disks to reside in halos with spins that are themselves higher than average, by a magnitude on the order of the standard deviation of the halo spin distribution, \u22480.2\u22120.25 dex (e.g. Bett et al. 2007). This spread by itself would not suf\ufb01ce to explain the full range of speci\ufb01c angular momentum values of observed galaxies (Romanowsky & Fall 2012), but it does need to be taken into account when comparing a subset of the galaxy population, namely galactic disks, to the full population of halos. Indeed, several recent cosmological hydrodynamical simulations found correlations between the angular momentum of halos and the galaxies they host (Teklu et al. 2015; Rodriguez-Gomez et al. 2017; Grand et al. 2017). We \ufb01nd a closely related trend here by the fact that our main analysis is based on the galaxies at the top 25% of the speci\ufb01c angular momentum distribution, for which we \ufb01nd that at accretion, the vector sum is increased by 0.1 dex (0.18 dex) in Illustris (No-Feedback) with respect to the case of considering the full galaxy population. In other words, by selecting galaxies with high z = 0 speci\ufb01c angular momentum, we select host halos that accrete (at least baryons) with higher angular momentum than typical. This shift has bearings for the IMPACT OF GALACTIC WIND ON ANGULAR MOMENTUM 9 1.5 2.0 2.5 3.0 3.5 4.0 4.5 Pre-Ejection log10(j [kpc*km/s]) 2.0 2.5 3.0 3.5 4.0 4.5 Ejection log10(j [kpc*km/s]) Illustris (a) 1.5 2.0 2.5 3.0 3.5 4.0 4.5 Pre-Ejection log10(j [kpc*km/s]) 2.0 2.5 3.0 3.5 4.0 4.5 Maximum log10(j [kpc*km/s]) Illustris (b) 1.5 2.0 2.5 3.0 3.5 4.0 4.5 Pre-Ejection log10(j [kpc*km/s]) 2.0 2.5 3.0 3.5 4.0 4.5 End of Ejection log10(j [kpc*km/s]) Illustris 0.01 0.03 0.1 0.3 1 3 (c) Figure 6. Joint probability distributions of angular momentum magnitudes of tracers in Illustris immediately before they are last recorded ejected in the wind (horizontal axes) and at three subsequent times on the vertical axes: immediately after that ejection (left); the end of the ejection, de\ufb01ned as the snapshot before coming back to the star-forming phase (right); and the time with the largest recorded angular momentum in between these two times (middle). During the ejection, tracers tend to gain angular momentum, especially those that have a low value before ejection, but by the time they return to the galaxy, the angular momentum largely returns to its pre-ejection value. The same holds when examining the distributions before, during, and after the \ufb01rst ejection, though the spread is larger. 1.5 2.0 2.5 3.0 3.5 4.0 4.5 Last SF-Gas log10(j [kpc*km/s]) 2.0 2.5 3.0 3.5 4.0 4.5 Star Formation log10(j [kpc*km/s]) Illustris (a) 1.5 2.0 2.5 3.0 3.5 4.0 4.5 Last SF-Gas log10(j [kpc*km/s]) 2 . 0 2 . 5 3 . 0 3 . 5 4 . 0 4 . 5 No-Feedback 0.01 0.03 0.1 0.3 1 3 (b) 1.5 2.0 2.5 3.0 3.5 4.0 4.5  log10(j [kpc*km/s]) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Illustris No-Feedback x-axis y-axis (c) Figure 7. Joint and one-dimensional probability distributions of angular momentum magnitudes of tracers at the last time they cross the star-formation density threshold (horizontal axes; the same quantity as on the vertical axes in Fig. 5) and at the last time they are converted from the gas phase to the stellar component (vertical axes). More so than any other period, these events in Illustris (left) are strongly correlated, while the tracers in No-Feedback still lose angular momentum by as much as 0.5 dex during their time in the star-forming phase before they are converted to stars. overall picture in that a comparison of the angular momentum of galaxies at the top of the distribution to the typical angular momentum of halos includes a \u2018halo selection bias\u20198. Second, recent work suggests that the speci\ufb01c angular momentum of baryons at the time they accrete onto dark matter halos may be systematically higher than that of the dark matter accreted around the same time (Stewart et al. 2013; Danovich et al. 2015), by up to \u22480.2 dex. This has to do with the higher quadrupole moment of cold gas in cosmic web streams. These conclusions were however drawn from a small number of \u2018zoom-in\u2019 simulations and were mostly focused on z \u22731, hence the quantitative signi\ufb01cance of such an offset is 8 The choice of whether all or just the top 25% of galaxies are included does not, however, affect our conclusions regarding the angular momentum histories of baryons inside halos. Speci\ufb01cally, in Illustris the loss in the \ufb01rst interval (Fig. 4) is larger if the full population is selected (0.44 dex) compared to the case of our main analysis (0.37 dex), but the losses/gains in every subsequent interval remain unchanged. not yet clear. In this work we have not examined the angular momentum of the dark matter itself and therefore do not show evidence to this effect or to the contrary, however it is important to keep this possibility in mind when considering the full picture. Third, various effects can lead to a situation where the baryons that accrete over cosmic history onto the halo, with a distribution of angular momentum values, will not be sampled uniformly in angular momentum space in the galactic disks themselves. For example, gas accreted via cold streams, which has higher angular momentum at accretion, may be more likely to build the galaxy than hot gas accreted outside of streams (Stewart et al. 2013). On the other hand, if galaxies are preferentially made of baryons that cool from the inner regions of their halos, the baryons making up the galaxies will be negatively biased in angular momentum relative to the full halo (Fall 2002; Kassin et al. 2012). Another possibility, which is directly related to feedback and to the results 10 DEFELIPPIS, D., ET AL. 1.5 2.0 2.5 3.0 3.5 4.0 4.5 Star Formation log10(j [kpc*km/s]) 2.0 2.5 3.0 3.5 4.0 4.5 z = 0 log10(j [kpc*km/s]) Illustris (a) 1.5 2.0 2.5 3.0 3.5 4.0 4.5 Star Formation log10(j [kpc*km/s]) 2 . 0 2 . 5 3 . 0 3 . 5 4 . 0 4 . 5 No-Feedback 0.01 0.03 0.1 0.3 1 3 (b) 1.5 2.0 2.5 3.0 3.5 4.0 4.5  log10(j [kpc*km/s]) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Illustris No-Feedback x-axis y-axis (c) Figure 8. Joint and one-dimensional probability distributions of angular momentum magnitudes of tracers at the last time they are converted from the gas phase to the stellar component (horizontal axes; the same quantity as on the vertical axes in Fig. 7) and as stars at z = 0 (vertical axes). The two events are strongly correlated in both Illustris (left) and No-Feedback (middle), but the stellar component in No-Feedback experiences angular momentum gains of 0.08 dex compared to a negligible change in the stellar component of Illustris. 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Accretion log10(j [kpc*km/s]) 0 0.2 0.4 0.6 0.8 Illustris No-Feedback all gas stars Figure 9. Angular momentum magnitude probability density of tracers at their accretion time onto the main progenitor branch of their z = 0 halo. For each simulation, the full tracer population that are in z = 0 stars (solid) is split between those that were present at some point in the main galaxy as gas (dashed), and those that became a star already in a satellite galaxy and hence accreted to the main galaxy in stellar form (dotted). Stellar accretion typically has higher angular momentum, and it is far more signi\ufb01cant in No-Feedback (red) than in Illustris (blue). in this work, is a bias generated by timing differences. Mass accreted at earlier cosmic times has lower angular momentum than mass accreted at later times (as in the classical tidal torque theory). Combined with the higher ef\ufb01ciency of galactic winds at ejecting gas out of galaxies at higher redshifts, this means that early-accreting, low-angular momentum gas can be biased against making up the \ufb01nal z = 0 galaxy with respect to late-accreting, high-angular momentum gas (Binney et al. 2001; Brook et al. 2011). In this work we do not directly compare the baryons that do not make it to comprising the \ufb01nal z = 0 galaxy to those that do, but we do show that the Illustris feedback does not signi\ufb01cantly change the accretion time distribution of z = 0 stars, and also has a weak effect on the angular momentum of individual tracers at accretion. We \ufb01nd however that the total angular momentum vector at accretion of z = 0 stars that are accreted as gas is 0.15 dex higher in Illustris compared with No-Feedback, which requires further research. In addition, the fraction of z = 0 stars that were formed in satellites (\u2018ex-situ stars\u2019), which are accreted with high angular momentum, is suppressed by the galactic winds in Illustris, thereby generating a bias at accretion that has an opposite sign to the overall difference between the two simulations, giving an \u2018advantage\u2019 at accretion to the No-Feedback simulation. More research is needed to understand why the stellar accretion has higher angular momentum at accretion compared to gas that forms stars in-situ. One possibility is that it is related to the distinction between satellite and smooth accretion. Finally, there are a variety of processes that may give rise to a situation where the baryons comprising the stars in a z = 0 galaxy do not have the same angular momentum as they did when they entered the halo. Quanti\ufb01cation of this scenario is the main focus of this work. We divide the time period between accretion into the halo and z = 0 into several segments and reach the following \ufb01ndings, which are visually summarized in Fig. 3. \u2022 Between accretion onto the halo and reaching the galaxy itself, we \ufb01nd that in No-Feedback baryons lose 0.49 dex and in Illustris they lose 0.37 dex. Several processes probably operate during this period. Mutual torques between the dark matter and the gas due to their different spatial distributions can lead to angular momentum exchange from the former to the latter that results in the gas having an increase of \u22480.1 dex in speci\ufb01c angular momentum compared to the dark matter, as shown by Zjupa & Springel (2017) using an adiabatic cosmological simulation. On the other hand, in the realistic case when radiative cooling is included, mass accreted via satellites (both as gas and as stars) is expected to experience dynamical friction that deprives it of orbital angular momentum. Torques in the inner part of the halo between the galaxy itself, the in\ufb02owing gas and the hot halo gas can signi\ufb01cantly change the original angular momentum of all components (Ro\u0161kar et al. 2010; Danovich et al. 2015). Our results suggest that feedback has a minimal effect on these processes, IMPACT OF GALACTIC WIND ON ANGULAR MOMENTUM 11 at least in a combined sense. \u2022 During the galactic fountain, namely between the \ufb01rst time baryons become part of the galactic star-forming gas and the last time they do so, we \ufb01nd gains of \u22480.2 dex in the Illustris simulation. There is no true parallel to this time segment in the no-feedback simulation, since there are no galactic winds in that case. These gains in Illustris occur, in particular, to gas that initially has low angular momentum gas, as already seen in a handful of zoomed-in halos (Brook et al. 2012; \u00dcbler et al. 2014; Christensen et al. 2016) even though, unlike those studies, the winds in Illustris are decoupled from the hydrodynamics. This suggests that it is not the kick itself that imparts lasting angular momentum gains, but rather several other processes likely operating during this period that do so. Gas that is ejected into the galactic wind spends of order the halo dynamical time at distances that are typically of order half of the virial radius. During this time its angular momentum can be enhanced by both large-scale tidal torques and local angular momentum exchange with the ambient halo may also occur via both gravitational and gas pressure forces. \u2022 Between reaching the galaxy itself (crossing the starformation density threshold) for the last time and the actual star-formation time, we \ufb01nd that gas in Illustris on average does not lose any angular momentum, while in No-Feedback it loses on average as much as 0.14 dex. Several processes probably operate during this period. Various types of non-axisymmetric distributions, such as spiral features, bars, and clumps formed by dynamical instabilities inside galactic disks, can cause angular momentum to \ufb02ow out and mass to \ufb02ow in. Dynamical interactions during galaxy mergers can also induce signi\ufb01cant angular momentum losses. These interactions are expected to be stronger in No-Feedback because the low-mass galaxies that participate in mergers have much higher densities than those in Illustris, and indeed, our results show that these processes are strongly suppressed in the presence of galactic winds. \u2022 Of all the events we consider, the smallest changes in angular momentum content occur in the stellar phase, namely between the star-formation time and z = 0. In Illustris, the stellar phase changes its angular momentum by z = 0 by less than \u22480.03 dex. This is expected theoretically to be the case in the absence of bars, as the stellar component is dynamically hotter and nondissipative (e.g. Sellwood 2014). Our simulations are likely suppressing bar formation due to their limited resolution. Regardless, even in the presence of bars, where there is empirical indication for non-negligible secular evolution of angular momentum in disk galaxies (e.g. Foyle et al. 2010), angular momentum exchange from the stellar component to the dark matter is expected to be inef\ufb01cient (Valenzuela & Klypin 2003). In the No-Feedback case, there are actually small gains at a level of 0.08 dex. One possibility is that these stellar gains are obtained at the expense of the losses of gas component (Bournaud et al. 2005), which are indeed stronger in No-Feedback. Numerical work has shown in recent years that each of the \u2018bookkeeping\u2019 steps discussed in the beginning of this section potentially involves numerical factors with signi\ufb01cant deviations from unity. Our results are qualitatively consistent with that work discussed in Section 1, but demonstrating a true robustness to the hydrodynamics solver and input physics would require a direct code-to-code analysis. We show here that in the Illustris simulation, which reproduces the observed angular momentum of disk galaxies in 1012 M\u2299halos, the last of these bookkeeping items, namely the angular momentum evolution of baryons inside halos, is composed of losses and gains of different magnitudes. The overall result of an offset of \u223c20% between the angular momentum of galactic disks and of typical dark matter halos (Fall & Romanowsky 2013) is hence composed of a handful of numerical factors of \u22480.1\u22120.4 dex each, which have distinct natures and origins. Some of these act to increase the baryonic angular momentum with respect to the dark matter one, and some in the opposite direction. It therefore remains a pressing theoretical challenge to understand the underlying reason for which they \u2018conspire\u2019 to the simple and useful result of approximate \u2018angular momentum retention\u2019 in galactic disks. Future work will be required to clarify the physical processes and their relative roles in setting the angular momentum of disks: in other words, the \u2018How?\u2019 and \u2018Why?\u2019 presented in the Introduction. In particular it would be interesting to further investigate the lack of angular momentum loss of the star-forming gas phase in the Illustris simulation by better understanding the disk dynamics. Also important is to understand why and how (whether hydrodynamically or gravitationally) the low angular momentum gas gains angular momentum during wind ejections out in the halo (and what are the important effectors of torques and on which scales), while high angular momentum gas roughly maintains its angular momentum. In addition to new types of analysis, this will require smaller separation between snapshots than the full Illustris simulations currently provide. Additionally, it is necessary to further investigate the origins of self-alignment of the different baryonic components before accretion. The quantitative analysis of \u2019When\u2019, \u2019Where\u2019, and \u2019How much\u2019 presented here will serve as a starting point and guidance to these future studies. We thank Rachel Somerville, Ari Maller and Avishai Dekel for useful discussions, as well as Vicente Rodriguez-Gomez for generating merger trees. We also thank the anonymous referee for their helpful comments. Analysis of the simulations was performed on the Odyssey cluster supported by the FAS Science Division Research Computing Group at Harvard University. The Flatiron Institute is supported by the Simons Foundation. SG acknowledges support provided by NASA through Hubble Fellowship grant HST-HF251341.001-A awarded by the STScI, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS5-26555. GB acknowledges \ufb01nancial support from NASA grant NNX15AB20G and NSF grants AST-1312888 and AST-1615955. APPENDIX To further understand angular momentum differences between Illustris and No-Feedback, we examine the redshift distributions 12 DEFELIPPIS, D., ET AL. 0 1 2 6 z 0.0 0.2 0.4 0.6 0.8 1.0 Illustris accretion first SFgas last SFgas star formation (a) 0 1 2 6 z 0.0 0.2 0.4 0.6 0.8 1.0 No-Feedback (b) Figure A1. Cumulative redshift distributions of various events in Illustris (left) and No-Feedback (right) for z = 0 stars that accreted onto the main galaxy as gas (i.e., ignoring stellar accretion). The addition of feedback delays star formation but leaves the halo accretion times essentially unaffected. of the \u2018events\u2019 identi\ufb01ed in Section 2, which are shown in Fig. A1. Unsurprisingly, feedback delays the formation of stars in Illustris (blue) and introduces a signi\ufb01cant time lag between the \ufb01rst (yellow) and last (green) crossings of the star-formation density threshold. However, the distribution of halo accretion redshifts (red) is largely unaffected, indicating that while feedback changes the amount of time accreted gas spends in the halo before forming stars, it does not change the time at which gas is accreted in the \ufb01rst place.",
                    "introduction": "1. Understanding the origin of Hubble\u2019s tuning fork for galaxy morphological classi\ufb01cation is a holy grail of galaxy forma- tion research. It is now known that the morphological classi\ufb01- cation of a galaxy as an early-type or late-type is strongly cor- related with a basic dynamical quantity \u2013 its speci\ufb01c angular momentum content, namely angular momentum per unit stel- lar mass (Fall 1983; Romanowsky & Fall 2012; Obreschkow & Glazebrook 2014; Cortese et al. 2016). This quantity scales with galaxy stellar mass, with two nearly parallel re- lations existing for late-type galaxies and early-type galaxies, the former having approximately \ufb01ve times as much angu- lar momentum as the latter at a given stellar mass (Fall & Romanowsky 2013). In fact, the angular momentum of a galaxy may well be the more fundamental parameter that is actually driving its morphology. This possibility is receiv- ing increasing attention and scrutiny in recent years thanks to increasingly complete and accurate measurements of galaxy angular momentum content (e.g., Burkert et al. 2016; Contini et al. 2016; Swinbank et al. 2017; Harrison et al. 2017), which are much more laborious than those of galaxy morphology. Hence, understanding the origin of galaxy angular momen- tum will represent a major advance in our understanding of galaxy formation as a whole. The tight scaling relation between speci\ufb01c angular momen- tum and stellar mass can be combined with empirical models"
                }
            ],
            "Jeremiah P. Ostriker": [
                {
                    "url": "http://arxiv.org/abs/1904.10471v2",
                    "title": "MIND THE GAP: Is The Too Big To Fail Problem Resolved?",
                    "abstract": "The faintness of satellite systems in galaxy groups has contributed to the\nwidely discussed \"missing satellite\" and \"too big to fail\" issues. Using\ntechniques based on Tremaine & Richstone (1977), we show that there is no\nproblem with the luminosity function computed from modern codes per se, but\nthat the gap between first and second brightest systems is too big {\\it given}\nthe luminosity function, that the same large gap is found in modern, large\nscale baryonic $\\Lambda$CDM simulations such as EAGLE and IllustrisTNG, is even\ngreater in dark matter only simulations, and finally, that this is most likely\ndue to gravitationally induced merging caused by classical dynamical friction.\nQuantitatively the gap is larger in the computed simulations than in the\nrandomized ones by $1.79 \\pm 1.04$, $1.51 \\pm 0.93$, $3.43 \\pm 1.44$ and $3.33\n\\pm 1.35$ magnitudes in the EAGLE, IllustrisTNG, and dark matter only\nsimulations of EAGLE and IllustrisTNG respectively. Furthermore the anomalous\ngaps in the simulated systems are even larger than in the real data by over\nhalf a magnitude and are still larger in the dark matter only simulations.\nBriefly stated, $\\Lambda$CDM does not have a problem with an absence of \"too\nbig to fail\" galaxies. Statistically significant large gaps between first and\nsecond brightest galaxies are to be expected.",
                    "authors": "Jeremiah P. Ostriker, Ena Choi, Anthony Chow, Kundan Guha",
                    "published": "2019-04-23",
                    "updated": "2019-07-16",
                    "primary_cat": "astro-ph.GA",
                    "cats": [
                        "astro-ph.GA"
                    ],
                    "main_content": "detailed work done subsequently (e.g. Laporte et al. 2013; Liu et al. 2015; Zhao et al. 2015; Golden-Marx & Miller 2018). The first brightest system will grow via mergers and the effect is greatest in the smallest systems, since at fixed density the merger time scales inversely with the total cluster mass. This tends to balance the statistical expectation of more massive first brightest galaxies in more massive systems and produces a smaller variance \u03c3(M1) in the magnitude of first brightest galaxies than was expected. But the same merger process is most likely to consume the second brightest galaxy increasing the gap between the now brighter first brightest and the now fainter second brightest system. On average the gap M12 would thus grow as mergers proceeded and that growth was demonstrated in Ostriker & Hausman (1977) quantitatively. Sandage & Hardy (1973) commented that \u201cThe brighter the dominant galaxy becomes, the absolutely fainter will be the second and third ranked members. The rich are rich at the expense of the poor, progressively.\u201d Tremaine & Richstone (1977) invented the ingenious statistic, t1 (Equation 1), which quantified both changes described above and then showed mathematically that for galaxies picked randomly from general distribution functions the quantity t1 would be expected to be greater than unity. However, when they compared expectations with reality, using the data compiled by Sandage & Hardy (1973), they found the opposite to be true. In general t1 < 1 and discrepancy was greatest in the smallest groups. As early as Dressler (1978b), it was pointed out that \u201cthe statistical model, regardless of the form of the luminosity function cannot fulfill all requirements, hence a special process model seems required.\u201d He based his conclusion on the magnitudes of the M12, gap, the small value of \u03c3(M1) and the weak correlation between m1 and cluster richness. Tremaine & Richstone (1977), basing their analysis on the Sandage & Hardy (1973) cluster data, looking at groups with over 30 members found a variance in the V magnitude of first brightest systems which was only 0.035 \u00b1 0.002 and a value for t1 for these same systems t1 = 0.55 \u00b1 0.13 far below the expectation (given the luminosity function) of t1 > 1. For Gamma function, Schechter function and even double exponential functions the expected value is t1 \u223c1.3. Loh & Strauss (2006) examined 2099 deg2 of Sloan Digital Sky Survey (SDSS) data again looking for bright galaxies and searching in the redshift range 0.12 < z < 0.38 using the r band best for detecting luminous red galaxies. Again they found large gaps between first and second brightest systems with a characteristic value of \u27e8M12\u27e9\u223c0.8 mag, very similar to the value obtained by Tremaine & Richstone (1977), from the Sandage & Hardy (1973) data. Loh & Strauss (2006) data give a value for t1 = 0.75 \u00b1 0.12 for the richer clusters and t1 = 0.27 \u00b1 0.06 for the poorer systems consistent with Tremaine & Richstone (1977) and grossly inconsistent with the statistical expectation of t1 \u223c1.3. They again formed a gap of \u27e8M12\u27e9\u223c0.87 magnitude. Clearly the observed gaps are far bigger than what we would have expected from the Mind The Gap 3 12-24 25-49 50-74 75-150 Number of galaxy halos in group 0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 <M12> EAGLE simulation EAGLE randomized simulation Fig. 1.\u2014 M12 presented in EAGLE simulation (red) and in the \u2018randomized\u2019 data (blue). luminosity function, i.e., intermediate mass galaxies are missing, and the \ufb01rst brightest systems are more standardized than expected. There is a very relevant later paper by Shen et al. (2014) entitled \u201cThe Statistical Nature of the Brightest Group Galaxies\u201d which examines the problem from a different angle. They also compute the Tremaine-Richstone statistic and again \ufb01nd t1 signi\ufb01cantly less than unity for the large sample of groups that they study with typical observed values being 0.70 \u00b1 0.05. They attribute this to their \ufb01nding that the \ufb01rst brightest galaxies are \u2018too bright\u2019 and, when they correct down the brightness of these systems, they conclude that the gaps are close to expectations. But there is however a bit of circular reasoning involved in this explanation. They use the total luminosity of the systems to estimate the halo masses and then ask what is the expected luminosity of the \ufb01rst brightest system given that halo mass. But of course if the satellite systems are too faint, then the halo mass is underestimated and then the \u2018expected\u2019 luminosity of the \ufb01rst brightest system is found to be low and the observed BCG is consequently \u2018too bright\u2019. The TremaineRichstone criterion itself is not subject to this criticism. So, in sum, the Shen et al. (2014) paper agrees that the observed gaps are larger than statistically expected but can not make a clean argument as to how much of this is due to the BCG being brighter than expected or to the satellites being fainter than expected. In a related paper Lin et al. (2010) studying more massive groups had found the value t1 = 0.93 \u00b1 0.01, but do not draw a \ufb01rm conclusion as to the origin of the statistical anomaly. Notice that we have not discussed galaxy formation, feedback or any of the factors that determine the halo mass \u2013 galaxy mass relation. All of the discussion concerns the expectations of the properties of the two most massive systems in a group, given the luminosity (or mass) function. Thus, the too big gap \u2013 which can contribute to the \u201ctoo big to fail\u201d problems must be understood quite separately from the processes such as ef\ufb01ciency of star formation, feedback etc, that determine the overall luminosity function. 3. COSMOLOGICAL SIMULATIONS 12-24 25-49 50-74 75-150 Number of galaxy halos in group 25 24 23 22 21 <M1> EAGLE simulation EAGLE randomized simulation Fig. 2.\u2014 Average \ufb01rst-ranked r magnitude as a function of number of galaxy members in EAGLE simulation. These anomalies in the real world were observed long before there were detailed, physically based numerical simulations of galaxy formation with which to compare the strange results. The papers which have pointed out the \u201ctoo big to fail\u201d problem have not \u2013 so far as we are aware \u2013 compared expectations with cosmological simulations. Rather, they have asked, given the brightest galaxy in a group and its expected dark matter halo, what are the expected lower mass halos in the group and what galaxies are expected to live within them. For this they use the Schechter (1976) function giving the average mass distribution of dark matter halos on an equivalent statistical model. And the authors universally \ufb01nd that many intermediate mass galaxies are expected in the groups which are not there at a statistically signi\ufb01cant level: the missing systems are \u201ctoo big to fail\u201d. Let us see what the simulations tell us. We have looked at three sets: EAGLE simulation (Schaye et al. 2015), IllustrisTNG simulation (Pillepich et al. 2018b; Springel et al. 2018), and our own (Choi et al. 2017). The \ufb01rst two sets of simulations have had enough statistical power to determine if they can match the observed luminosity function for bright galaxies and numerous papers (e.g. Vogelsberger et al. 2014; Crain et al. 2015) detail their success. So, whether the CDM paradigm is right or wrong, the physical processes that they implement give them a luminosity function, above and below the L\u2217 break, which matches real data. We have looked at the publicly available output from these groups to see if their results do or do not match observations on statistical expectations with regard to the Tremaine & Richstone (1977) t1 statistics. We use r-band magnitudes throughout this study. 3.1. EAGLE simulation The EAGLE simulation is a publicly available (McAlpine et al. 2016) suite of cosmological hydrodynamical simulation (Schaye et al. 2015; Crain et al. 2015) It assumes a standard \u039b cold dark matter cosmology from the Planck-1 (Planck Collaboration et al. 2014), \u2126m = 1 \u2212\u2126\u039b = 0.307, \u2126b = 0.04825, h = 0.6777, \u03c38 = 0.8288, and nS = 0.9611. The simulation suite is run with a modi\ufb01ed version of the GADGET-3 Nbody Tree-PM smoothed particle hydrodynamics (SPH) 4 Ostriker et al. TABLE 1 EAGLE simulation galaxy number \u27e8mhalo,1\u27e9a \u27e8M1\u27e9 \u03c3(M1) \u27e8M12\u27e9 \u03c3(M12) t1 Number of groups 12-24 9.09 \u00d7 1012 -23.55 0.54 1.89 1.13 0.28 152 25-49 2.07 \u00d7 1013 -24.26 0.43 1.57 1.00 0.27 73 50-74 4.17 \u00d7 1013 -24.84 0.28 1.92 0.70 0.15 19 75-150 6.98 \u00d7 1013 -25.26 0.37 1.60 0.69 0.23 12 Mean 1.77 \u00d7 1013 -23.93 0.48 1.79 1.04 0.27 \u00b1 0.03 256 a Average halo mass of the \ufb01rst brightest galaxies in solar mass. TABLE 2 EAGLE \u2018randomized\u2019 simulation galaxy number \u27e8mhalo,1\u27e9 \u27e8M1\u27e9 \u03c3(M1) \u27e8M12\u27e9 \u03c3(M12) t1 Number of groups 12-24 3.27 \u00d7 1012 -22.01 1.33 1.22 1.04 1.09 152 25-49 4.35 \u00d7 1012 -22.52 1.16 0.79 0.69 1.46 73 50-74 1.08 \u00d7 1013 -22.40 0.82 0.89 0.54 0.92 19 75-150 9.91 \u00d7 1012 -23.39 0.77 0.73 0.46 1.06 12 Mean 4.45 \u00d7 1013 -22.38 1.15 1.10 0.86 1.06 \u00b1 0.06 256 12-24 25-49 50-74 75-150 Number of galaxy halos in group 0.0 0.5 1.0 1.5 2.0 2.5 <M12> Illustris simulation Illustris randomized simulation Fig. 3.\u2014 M12 presented in IllustrisTNG simulation (red) and in the \u2018randomized\u2019 data (blue). code (Springel 2005), and includes an updated formulation of SPH, new time stepping, and sub-grid physics (see Schaye et al. 2015, for details). In this study, we use RefL0100, which has a cosmological volume of (100 comoving Mpc)3 and a baryonic mass resolution of 1.81 \u00d7 106 M\u2299. We refer the readers to the introductory papers (Schaye et al. 2015; Crain et al. 2015) for a complete descriptions of sub-grid physics models. We bin EAGLE simulation results into di\ufb00erent size galaxy groups from smallest (12\u201324 objects) with stellar mass greater than 108 M\u2299to more massive systems with 75\u2013150 galaxies (See Table 1). The red lines in Figures 1 and 2 show the average magnitude gap between \ufb01rstbrightest and second-brightest galaxies, \u27e8M12\u27e9, in each group and brightness of the \ufb01rst brightest galaxy \u27e8M1\u27e9. Overall, simulated galaxies in EAGLE show \u223c1.7 magnitude gap between \ufb01rst and second brightest galaxies, which is similar to the gap reported by van den Bosch et al. (2007) with 2-degree Field Galaxy Redshift Survey data. Next, we put all groups in one bin and randomly re12-24 25-49 50-74 75-150 Number of galaxy halos in group 24.5 24.0 23.5 23.0 22.5 22.0 21.5 21.0 20.5 <M1> Illustris simulation Illustris randomized simulation Fig. 4.\u2014 Average \ufb01rst-ranked r magnitude as a function of number of galaxy members in IllustrisTNG simulation. populate each group from the collective bin, keeping the same number of galaxies, in each galaxy group or cluster (See Table 2). By construction, this keeps the overall luminosity function invariant. Then we recompute \u27e8M12\u27e9, \u27e8M1\u27e9and \u03c3(M1) for each of Figure 1 and 2. Note how the gap is systematically larger in the original (\u27e8M12\u27e9= 1.79) than in the randomized groups (\u27e8M12\u27e9= 1.10) and the \ufb01rst brightest galaxy is brighter by over a magnitudes in each original set of galaxy groups than in the randomized versions of the same objects. Somehow in each system the dominant member \u201cknows\u201d it is \ufb01rst and becomes more dominant. In Tables 1 and 2, we summarize these results and compute the Tremaine-Richstone parameter t1, statistic via Equation 1. We note that the simulated data in Table 1 shows very low values of t1, typically around 1/4, even lower than the real data analyzed by Tremaine & Richstone (1977) and Loh & Strauss (2006). So this \u201canomalous\u201d behavior is reproduced by the simulations which have larger than expected gaps and consequently could be accused of not having the expected second brightest Mind The Gap 5 TABLE 3 IllustrisTNG simulation galaxy number \u27e8mhalo,1\u27e9 \u27e8M1\u27e9 \u03c3(M1) \u27e8M12\u27e9 \u03c3(M12) t1 Number of groups 12-24 8.27 \u00d7 1012 -22.47 0.47 1.55 0.97 0.30 187 25-49 1.95 \u00d7 1013 -23.14 0.47 1.60 0.91 0.30 82 50-74 3.87 \u00d7 1013 -23.65 0.37 1.19 0.75 0.31 23 75-149 6.60 \u00d7 1013 -24.00 0.44 1.47 0.98 0.30 26 150> 1.85 \u00d7 1014 -24.76 0.44 1.04 0.81 0.42 14 Mean 2.63 \u00d7 1013 -22.93 0.46 1.51 0.93 0.31 \u00b1 0.02 332 TABLE 4 IllustrisTNG \u2018randomized\u2019 simulation galaxy number \u27e8mhalo,1\u27e9 \u27e8M1\u27e9 \u03c3(M1) \u27e8M12\u27e9 \u03c3(M12) t1 Number of groups 12-24 1.87 \u00d7 1012 -21.77 1.29 1.16 0.95 1.12 187 25-49 4.18 \u00d7 1012 -22.61 0.98 0.94 0.73 1.04 82 50-74 7.98 \u00d7 1012 -23.19 1.00 0.73 0.74 1.36 23 75-149 1.46 \u00d7 1013 -23.47 0.93 0.59 0.70 1.58 26 150> 6.59 \u00d7 1013 -23.84 0.65 0.45 0.34 1.45 14 Mean 7.79 \u00d7 1012 -22.30 1.14 1.00 0.84 1.17 \u00b1 0.16 332 galaxies. Then Table 2 shows the t1 statistic for the randomized data and \u2013 lo and behold \u2013 it exactly follows the statistical expectations with t1 \u22481.06 \u00b1 0.06. 3.2. IllustrisTNG simulation The IllustrisTNG simulation (Pillepich et al. 2018b; Nelson et al. 2018; Springel et al. 2018) is a publicly available suite of cosmological simulation (Nelson et al. 2015), an extension of the Illustris simulation (Genel et al. 2014; Vogelsberger et al. 2014; Sijacki et al. 2015). It adopts the Planck Collaboration XIII cosmological parameters (Planck Collaboration et al. 2016), with \u2126m = 1 \u2212\u2126\u039b = 0.3089, \u2126b = 0.0486, h = 0.6774, \u03c38 = 0.8159, and nS = 0.9667. The simulation is evolved with the AREPO moving-mesh code (Springel 2010), and employs a number of improvements of sub-grid physics models for stellar and AGN feedback, and black hole growth (Pillepich et al. 2018a; Weinberger et al. 2018). The adopted \ufb01ducial simulation we use in this paper (TNG-100) has a cosmological volume of (110.7 Mpc)3 and a baryonic mass resolution of 1.4 \u00d7 106 M\u2299. We refer the readers to the introductory papers of original Illustris (e.g. Genel et al. 2014) and IllustrisTNG (e.g. Pillepich et al. 2018b) for further details. Now we repeat the same exercise done previously with the EAGLE simulations using now the IllustrisTNG simulations, for the galaxies with stellar mass greater than 108 M\u2299. The results are shown in Figure 3 and 4 and summarized in Table 3 and 4. Again the published simulations show \u201ctoo big\u201d a gap and \u201ctoo bright\u201d \ufb01rst brightest galaxies and \u2013 correspondingly \u2013 the t1 statistic is smaller (t1 = 0.31 \u00b1 0.02) than statistically expected. In the randomized data t1 is again much higher (t1 = 1.17 \u00b1 0.16) and larger than unity. The gap is again larger by 0.51 in the initial \ufb01ducial data than in the randomized data. What is the cause of these fascinating results? We mentioned in the Introduction several possible physical e\ufb00ects that could do it: tidal stripping of satellites, feedback from the central galaxies removing cold gas from the Fig. 5.\u2014 Evolution of t1 parameter (t1 = \u03c3(M1)/\u27e8M12\u27e9) and the magnitude gap \u27e8M12\u27e9in Choi et al. (2017) simulation from z = 2 to 0. environments of satellite systems, ram pressure stripping and \ufb01nally merging. One could imagine complicated simulation tests where each of these e\ufb00ects was switched on or o\ufb00to determine its consequences for the statistical tests, but there is a far simpler approach that can be taken. All these \u2013 and many other \u201cbaryonic\u201d e\ufb00ects are missing in the preliminary dark matter only simulations that the EAGLE and Illustris group have performed. We will discuss this in Section 3.4. 3.3. Zoom-in simulation of galaxy-group size halos This time we study the evolution of the magnitude gap and t1 parameter in 30 massive halos with present-day halo masses of 1.4 \u00d7 1012 M\u2299\u2264Mvir \u22642.3 \u00d7 1013 M\u2299 in cosmological zoom-in hydrodynamic simulations. We 6 Ostriker et al. TABLE 5 EAGLE Dark Matter Only Simulation galaxy number \u27e8mhalo,1\u27e9 \u27e8M1\u27e9a \u03c3(M1) \u27e8M12\u27e9 \u03c3(M12) t1 Number of groups 12-24 1.09 \u00d7 1012 -25.92 0.66 3.43 1.44 0.19 1111 25-49 2.60 \u00d7 1012 -26.91 0.55 3.46 1.44 0.16 485 50-74 4.66 \u00d7 1012 -27.57 0.50 3.30 1.43 0.15 172 75-150 8.33 \u00d7 1012 -28.21 0.49 3.43 1.43 0.14 181 Mean 2.45 \u00d7 1012 -26.52 0.60 3.43 1.44 0.17 \u00b1 0.02 1949 a Note: we de\ufb01ne \u2018mass-magnitude\u2019 of dark matter halo mass as M = \u22122.5log(mhalo/ M\u2299) + 4 TABLE 6 EAGLE Dark Matter Only Simulation \u2018Randomized\u2019 galaxy number \u27e8mhalo,1\u27e9 \u27e8M1\u27e9a \u03c3(M1) \u27e8M12\u27e9 \u03c3(M12) t1 Number of groups 12-24 2.43 \u00d7 1011 -23.08 1.44 1.15 1.13 1.24 1111 25-49 4.73 \u00d7 1011 -24.96 1.43 1.18 1.11 1.21 485 50-74 7.55 \u00d7 1011 -24.53 1.41 1.11 1.09 1.27 172 75-150 1.49 \u00d7 1012 -25.27 1.35 1.12 1.04 1.20 181 Mean 4.60 \u00d7 1011 -23.77 1.58 1.34 1.24 1.18 \u00b1 0.06 1949 a Note: we de\ufb01ne \u2018mass-magnitude\u2019 of dark matter halo mass as M = \u22122.5log(mhalo/ M\u2299) + 4 TABLE 7 IllustrisTNG Dark Matter Only Simulation galaxy number \u27e8mhalo,1\u27e9 \u27e8M1\u27e9a \u03c3(M1) \u27e8M12\u27e9 \u03c3(M12) t1 Number of groups 12-24 1.86 \u00d7 1012 -25.69 0.67 3.36 1.36 0.20 840 25-49 4.18 \u00d7 1012 -26.63 0.56 3.27 1.37 0.17 388 50-74 7.98 \u00d7 1012 -27.37 0.44 3.47 1.19 0.13 145 75-149 1.46 \u00d7 1013 -28.03 0.42 3.49 1.34 0.12 118 150> 6.59 \u00d7 1013 -29.33 0.88 2.95 1.40 0.30 106 Mean 8.17 \u00d7 1012 -26.49 0.62 3.33 1.35 0.19 \u00b1 0.04 1597 a Note: we de\ufb01ne \u2018mass-magnitude\u2019 of dark matter halo mass as M = \u22122.5log(mhalo/ M\u2299) + 4 TABLE 8 IllustrisTNG Dark Matter Only Simulation \u2018Randomized\u2019 galaxy number \u27e8mhalo,1\u27e9 \u27e8M1\u27e9a \u03c3(M1) \u27e8M12\u27e9 \u03c3(M12) t1 Number of groups 12-24 2.50 \u00d7 1012 -23.45 2.10 1.71 1.66 1.23 840 25-49 3.47 \u00d7 1012 -24.92 2.06 1.89 1.70 1.09 388 50-74 6.83 \u00d7 1012 -25.67 1.80 1.59 1.46 1.14 145 75-149 1.38 \u00d7 1013 -26.58 1.61 1.49 1.20 1.08 118 150> 3.59 \u00d7 1013 -28.24 1.49 1.06 1.00 1.40 106 Mean 6.18 \u00d7 1012 -24.56 1.99 1.68 1.57 1.19 \u00b1 0.09 1597 a Note: we de\ufb01ne \u2018mass-magnitude\u2019 of dark matter halo mass as M = \u22122.5log(mhalo/ M\u2299) + 4 used two sets of 30 high-resolution zoom-in simulations from Choi et al. (2017) simulated with and without AGN feedback. The most massive and brightest central galaxies in these zoom-in simulations have stellar masses of 8.2 \u00d7 1010 M\u2299\u2264M\u2217\u22641.5 \u00d7 1012 M\u2299at z = 0. The physics implemented in the simulations includes star formation, mechanical supernova feedback, wind feedback from massive stars, AGB stars and metal cooling and di\ufb00usion. The AGN feedback model is adopted from (Choi et al. 2012, 2014) and consists of two main components: (1) mechanical feedback via high velocity broad absorption line winds, which deposits energy, mass and momentum into the adjacent gas, and (2) radiative feedback from X-ray radiation of the accreting black holes via the photoionization and the Compton heating following Sazonov et al. (2004). The simulation set used in this section is presented in Choi et al. (2017), and we refer the reader to this paper for further details. In Figure 5, we show the evolution of t1 parameter and the r-band magnitude gap between \ufb01rstand secondbrightest galaxies \u27e8M12\u27e9from z = 2 to z = 0 for two sets of zoom-in simulations, run with and without the AGN feedback. We have almost constant t1 parameter from z = 2 to z = 0, in both simulations with and Mind The Gap 7 TABLE 9 Summary of observation and simulations \u27e8M12\u27e9 t1 Tremaine & Richstone (1977) Analysis\u2217 0.80 \u00b1 0.71 0.45 Loh & Strauss (2006) Analysis\u2217\u2217 0.88 \u00b1 0.07 0.34 \u00b1 0.02 EAGLE \u039bCDM galaxy simulation 1.79 \u00b1 1.04 0.27 \u00b1 0.03 IllustrisTNG \u039bCDM galaxy simulation 1.51 \u00b1 0.93 0.31 \u00b1 0.02 Choi et al. (2017) galaxy simulation 2.57 \u00b1 1.00 0.21 \u00b1 0.14 EAGLE \u039bCDM dark matter only simulation 3.43 \u00b1 1.44 0.17 \u00b1 0.02 IllustrisTNG \u039bCDM dark matter only simulation 3.33 \u00b1 1.35 0.19 \u00b1 0.04 \u2217Sandage & Hardy (1973) data \u2217\u2217SDSS data from Abazajian et al. (2003) without AGN feedback, and a mild increase of \u27e8M12\u27e9 with time from z = 2 to z = 0 in simulations without AGN feedback, implying some brightening of the \ufb01rst ranked galaxy compared with the second ranked galaxy over time. Also, as expected AGN activity does tend to strip satellite systems (Dashyan et al. 2019; Shen et al. 2019) increasing the gap and further decreasing t1, but these real e\ufb00ects are not the dominant ones. Instead, an excess and prolonged star formation in \ufb01rst-ranked galaxies shows a dominant e\ufb00ect, showing an increase in \u27e8M12\u27e9with time. However, we see that for all three \ufb01ducial sets of simulations presented in 3.1, 3.2, and 3.3, the t1 statistic is similar, t1 \u223c0.3, and it is even below the value found in the observational data. 3.4. Dark matter only simulation We show in Figures 6 and 7 and in Tables 5 and 6 the results from the EAGLE dark matter only simulations. The results show that the typical gap in mass (expressed in magnitudes) even larger than in the far more complicated full baryonic simulations and the values of t1 even smaller (t1 = 0.16\u00b10.02). As noted earlier a piece of this e\ufb00ect is due to de\ufb01nitions, not physics: matter tidally torn o\ufb00subhalos is, by de\ufb01nition, added to the parent halos, increasing the gaps. But it is unlikely that this accounts for the whole e\ufb00ect. Therefore whatever physical processes produce the large gaps seem to be even stronger in purely gravitational simulations. We also show the randomized dark matter simulations as red lines in Figure 6 and 7, giving the value of t1 in Table 6. These completely match the Tremaine & Richstone (1977) statistical expectations. The gap is larger in the original data than in the randomized data in these dark matter simulations by 2.11\u00b11.91 magnitudes, even larger than in the galaxy simulations. The results from IllustrisTNG dark matter only simulations are summarized in Tables 7 and 8. Again, we have a large gap between \ufb01rst and second massive systems, and the gap is much larger in the original data than in the randomized data. These results provide dramatic evidence that whatever causes the large gap (\u201ctoo big to fail\u201d) in observed phenomenon is gravitational/dynamical in origin, since it is stronger in the dark matter only simulations than in either the real or simulated works. Merging is a plausible explanation but more work would need to be done to prove this. 4. CONCLUSION 12-24 25-49 50-74 75-150 Number of galaxy halos in group 1 0 1 2 3 4 5 <M12> EAGLE simulation EAGLE randomized simulation Fig. 6.\u2014 M12 presented in EAGLE dark matter only simulation (red) and in the \u2018randomized\u2019 data (blue). 12-24 25-49 50-74 75-150 Number of galaxy halos in group 29 28 27 26 25 24 23 22 <M1> EAGLE simulation EAGLE randomized simulation Fig. 7.\u2014 Average \ufb01rst-ranked magnitude proxy of the dark matter mass as a function of number of galaxy members in EAGLE dark matter only simulation. We summarize the real data and the \u039bCDM simulations in Table 9. We see that the \u27e8M12\u27e9gaps are actually larger in the \u039bCDM simulations than in observed data and the anomalous t1 statistic is as low in the simulated data as in the real data. The dark matter only simulations are even more extreme. First it is clear that modern simulations by active groups do not have a \u201ctoo big to fail\u201d problem. The 8 Ostriker et al. 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 t1 EAGLE fiduciary simulation EAGLE dark-matter-only simulation 0.0 1.5 3.0 4.5 6.0 7.5 9.0 10.5 lookback time (Gyr) 5 4 3 2 1 0 <M12> 0.0 0.11 0.24 0.41 0.62 0.9 1.31 1.98 redshift 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 5 4 3 2 1 0 Fig. 8.\u2014 Evolution of t1 parameter (t1 = \u03c3(M1)/\u27e8M12\u27e9) and the magnitude gap \u27e8M12\u27e9in EAGLE simulation from z = 2 to 0. gaps M12 in their simulated groups are large and the t1 statistics derived from their simulations can be even lower than those seen in real observational data. This is good news. Standard CDM simulations do not have a too big to fail problem. Second, when their data in randomized \u2013 keeping the luminosity function constant \u2013 the gaps disappear and the data satis\ufb01es the statistical expectations with t1 > 1. Therefore, solving the problem was not based on particular feedback schemes which alter the luminosity function, but rather it must be due to physical interactions in the groups and clusters. We noted several physical interactions which would tend to produce the observed gaps and the additional experiments that we did help to pick the winner. In addition satellites moving through the gas in groups and clusters can be seen to be losing material by ram pressure stripping and this e\ufb00ect, which we cannot easily quantify, must also lead to an increase in the gap \u27e8M12\u27e9 and a lowering of t1. But one experiment that we performed in Section 3.4 showed us the dominant physical mechanisms. We looked at dark matter only simulations from EAGLE and IllustrisTNG and found the gap (expressed in magnitudes) to be \u27e8M12\u27e9= 3.43 \u00b1 1.44 and \u27e8M12\u27e9= 3.33 \u00b1 1.35 much larger than in randomized dark matter systems and the t1 statistic was t1 = 0.17 \u00b1 0.02 and t1 = 0.19 \u00b1 0.04, even lower than in the baryonic simulations or the real data. Since the sole physics acting in the dark matter experiments was based on gravity and dynamics, it is clear that none of the complicated \u201cbaryonic\u201d e\ufb00ects \u2013 including the \ufb01rst two mentioned in this section \u2013 can be dominant in causing the large gaps and low value of t1. Dynamical friction and the induced \u201ccannibalism\u201d can certainly produce the e\ufb00ects seen in the dark matter simulations so it is tempting to consider \u201cmergers\u201d to be the driving force in groups and clusters leading to the big gaps and small values of t1 seen in both the baryonic and dark matter only simulations. A primitive numerical test of this was performed by Ostriker & Hausman (1977) with promising results, but there is a strong argument on the other side. The total halo mass in solar type stars in our Milky Way (MW) is estimated by GAIA (and others) observations not to exceed 1-2 percent of the mass in the MW disk (Gaia Collaboration et al. 2018). Since a large fraction of the stars in any merging system would ultimately be found in the halo of a disk galaxy, that tells us that whatever systems merged with our galaxy must not have weighed, more than a few percent of MW system. Here of course we are only considering the stellar component. This is true for other edge-on similar observed galaxies such as NGC 4565 and for simulations as well. Using Illustris simulations Rodriguez-Gomez et al. (2016) estimate the fraction of ex-situ stars and they \ufb01nd roughly 10 percent for MW size systems in other published work with perhaps half that much in their own simulations. Thus both observations and simulations indicate that major mergers of stellar systems of MW scale are rare. Hence explaining the group properties of these systems in terms of merging stellar systems seems misguided. This argument applies to systems with total halo mass less than 1012.5 M\u2299. There are multiple lines of evidence, however in systems with total mass larger than 1013 M\u2299 that mergers can be signi\ufb01cant. The possibility remains, however, that mergers before signi\ufb01cant star formation has occurred could be important and could explain the well established gaps in the luminosity functions seen in normal groups and clusters \u2013 both in the real and simulated worlds. Further work must be done to test this possibility. But what is clear from the analysis presented in this paper is that \u201ctoo big to fail\u201d is not a problem in the CDM scenario (nor, in all probability in the variant competitors) because normal gravitational interactions within groups increase the mass of the most massive galaxy, decrease the mass of the second ranked system and tend to produce large gaps. We thank the anonymous referee for very helpful comments on the manuscript. We thank Gohar Dashyan, Daniel DeFelippis and Scott Tremaine for helpful discussions. Numerical simulations were run on the computer clusters of the Princeton Institute of Computational Science and engineering.",
                    "introduction": "1. There are two frequently discussed \u201cproblems\u201d found in galaxy statistics which are sometimes considered argu- ments against the standard \u039bCDM model of cosmology. Both are related to the apparent under-abundance of faint, low mass galaxies in local groups. One, \u201cthe miss- ing satellite problem\u201d (Kau\ufb00mann et al. 1993; Klypin et al. 1999; Moore et al. 1999) notes that the CDM sub- halo stellar mass function is steeper than the observed satellite mass function. The second, \u201cthe too big to fail problem (TBTF)\u201d (e.g. Boylan-Kolchin et al. 2011, 2012; Garrison-Kimmel et al. 2014) notes that given the ob- served stellar mass function, there should be many in- termediate mass systems in the local group and other nearby systems that are missing. The original paper, which introduced the TBTF issue, focused primarily on the gap between the third and forth brightest galaxies in the local group but most subsequent work has focussed on how much brighter the \ufb01rst brightest galaxy is than its companions. A recent paper entitled \u201cA Lonely Giant\u201d (Smercina et al. 2018) focusses on the under-abundance of moderate mass satellite galaxies in the nearby M94 system. Both the nature and the signi\ufb01cance of the two \u201cprob- lems\u201d are often confused. The \u201cmissing satellite prob- lem\u201d is an expression of our surprise that the mass func- tion for galaxies at the faint end is signi\ufb01cantly less steep than the mass function expected for dark matter halos \u2013 if the CDM model is correct. It also implies that ei- ther CDM produces too many low mass halos/subhalos or galaxies form in these halos with lower and lower e\ufb03ciency as the halo mass declines. Prevailing expert views at present seem to prefer the second explanation, and current high quality simulations based on the CDM paradigm do, in fact, produce the correct luminosity function (e.g. Schaye et al. 2015; Pillepich et al. 2018b; Dav\u00b4 e et al. 2019). However, using the observed luminosity function (or the one computed with appropriate baryonic physics) it is hard to understand the faintness of satellite systems in well observed groups and clusters in comparison to the \ufb01rst brightest system; that is the \u201ctoo big to fail problem\u201d: there are relatively bright galaxies that are expected to be present which are among the missing. What are missing here are moderate mass galaxies roughly one or two magnitudes fainter than the bright- est central galaxy. The problem shows up to observers as a large gap between the brightness of \ufb01rst and second brightest galaxies in groups and clusters. These anoma- lously large gaps were noticed as far back as Sandage & Hardy (1973) and Dressler (1978a). However, there is a brilliant paper by Tremaine & Rich- stone (1977) which sheds a blazing light on the issues and makes clear that there must be interactions amongst the group galaxies to be considered and that the gap be- tween \ufb01rst and second brightest galaxies is too big given the luminosity function. The problems are not with the luminosity function per se, or, in current nomenclative, they are not with the general, subhalo mass \u2013 stellar mass relation. We will attempt to show in this paper that this unexpectedly large gap is also found in current simula- tions of galaxy formation such as EAGLE (Schaye et al. 2015), Illustris (Genel et al. 2014), and our own work (Choi et al. 2017), that it is probably not due to feed- back and most likely arises from gravitationally induced merging processes in groups and clusters and to some ex- tent from tidal stripping of gas from satellite systems. A possible explanation of the physical basis for the e\ufb00ects was proposed in Ostriker & Hausman (1977): merging among bright galaxies makes the \ufb01rst brightest galaxy arXiv:1904.10471v2  [astro-ph.GA]  16 Jul 2019 2 Ostriker et al. brighter (and with less variance) and makes the (new) second brightest galaxy fainter. These gravitational pro- cesses increase the ratio de\ufb01ned by the Tremaine & Rich- stone (1977) parameter, t1 \u2261\u03c3(M1) \u27e8M12\u27e9, (1) which compares the variance in the brightness of the \ufb01rst brightest galaxy \u03c3(M1), to the mean gap between \ufb01rst and second brightest systems M12 helping to explain \u201ctoo big to fail\u201d and systems such as the \u201clonely giant\u201d, M94 group. A very careful recent study of the gap statistics by Trevisan & Mamon (2017) presents a review of recent statistical studies and their implications. We will show that modern data con\ufb01rm the observa- tional data presented in Tremaine & Richstone (1977) from Sandage & Hardy (1973), that \u039bCDM simulations show the same large M12 gap and that it is likely due to gravitational e\ufb00ects, since it also appears in dark mat- ter only sims and is not altered by changes in feedback physics (c.f. Garrison-Kimmel et al. 2013; Sawala et al. 2016). But there is one additional e\ufb00ect. The dimensionless quantity t1, statistically expected (c.f. Tremaine & Rich- stone 1977) to be greater than unity, is even smaller in dark matter only simulations than it is in those including baryonic physics. And the explanation for this is partly due to de\ufb01nitions, rather than physics, in hierarchical cosmologies. When subunits (e.g. subhalos) merge, the material stripped o\ufb00the satellite systems is summed up and included in our de\ufb01nition of the parent halo, thus in- creasing the gap between the parent and the largest sub- unit. This e\ufb00ect is less extreme for the stellar than the dark matter component, since tidal stripping is strongest for the latter subunits. In section 2 we remind readers of the conclusions of the two 1977 papers quoted earlier concerning appar- ently anomalous gaps found in galaxy group statistics, and present an update of the observational results. In section 3 we analyze current simulations both with and without baryonic physics and in Section 4 we present our conclusions. 2."
                },
                {
                    "url": "http://arxiv.org/abs/1004.2923v2",
                    "title": "Momentum Driving: which physical processes dominate AGN feedback?",
                    "abstract": "The deposition of mechanical feedback from a supermassive black hole (SMBH)\nin an active galactic nucleus (AGN) into the surrounding galaxy occurs via\nbroad-line winds which must carry mass and radial momentum as well as energy.\nThe effect can be summarized by the dimensionless parameter\n$\\eta=dot{M_outflow}/dot{M_accretion}= (2 \\epsilon_w c^2)/v_w^2$ where\n($\\epslion_w \\equiv dot{E}_w/(dot{M_accretion} c^2)$) is the efficiency by\nwhich accreted matter is turned into wind energy in the disc surrounding the\ncentral SMBH. The outflowing mass and omentum are proportional to $\\eta$, and\nmany prior treatments have essentially assumed that $\\eta=0$. We perform one-\nand two-dimensional simulations and find that the growth of the central SMBH is\nvery sensitive to the inclusion of the mass and momentum driving but is\ninsensitive to the assumed mechanical efficiency. For example in representative\ncalculations, the omission of momentum and mass feedback leads to an hundred\nfold increase in the mass of the SMBH to over $10^{10} \\Msun$. When allowance\nis made for momentum driving, the final SMBH mass is much lower and the wind\nefficiencies which lead to the most observationally acceptable results are\nrelatively low with $\\epsilon_w \\lesssim 10^{-4}$.",
                    "authors": "Jeremiah P. Ostriker, Ena Choi, Luca Ciotti, Gregory S. Novak, Daniel Proga",
                    "published": "2010-04-16",
                    "updated": "2010-07-13",
                    "primary_cat": "astro-ph.GA",
                    "cats": [
                        "astro-ph.GA"
                    ],
                    "main_content": "Paper I. Here we recall the most important aspects. The instantaneous bolometric accretion luminosity is LBH = \u01ebEM \u02d9 Maccc2, (6) and we adopt an advection-dominated accretion flow (ADAF)-like radiative efficiency as \u01ebEM = \u01eb0 A \u02d9 m 1 + A  m A \u02d9 m 1 + A \u02d9 m, \u02d9 m \u2261 \u02d9 Macc \u02d9 MEdd \u02d9 Macc \u02d9 MEdd , (7) where \u02d9 MEdd = LEdd/\u01eb0c2, and A is a free parameter so that \u01ebEM \u223c\u01eb0A \u02d9 m for \u02d9 m \u226aA\u22121. We fix A = 100 in our simulations (Narayan & Yi 1994), and we adopt for the peak EM efficiency \u01eb0 = 0.1 or 0.2 consistent with estimates based on the Soltan (1982) argument. In the treatment of radiation feedback, we consider the radiation pressure as well as heating/cooling feedback, including photoionization, Compton and line heating (Sazonov, Ostriker & Sunyaev 2004; Sazonov et al. 2005). In accordance with both observations and theoretical expectation, the transformation of accreted mass to electromagnetic energy output declines dramatically at low accretion rates. In the mechanical feedback treatment, the fiducial instantaneous mechanical luminosity of the disk wind is calculated as Ldw = \u01ebw \u02d9 Maccc2 + \u01ebIIc2(1 \u2212frem,h)Mdh\u2217 \u03c4\u2217h Mdh\u2217 \u03c4\u2217h (8) where \u01ebw is the mechanical efficiency of the wind, and the second term represents the energy associated with the Type II supernova (SNII) explosions of the high-mass stars in the circumnuclear disk (see Paper I, Equation (20) for details). Here, Mdh\u2217is the current mass in the disc in high mass (M > 8M\u2299) and \u03c4\u2217h is their typical lifetime. In this work, we restrict attention to the commonly assumed case of a constant value of \u01ebw (e.g. SDMH05), which corresponds to Type A models in Papers I and III. Physically, a fixed mechanical efficiency implies that the mass accreted by the central SMBH has a fixed relation to the mechanical energy flowing out of the central regions. We here neglect the jet effects, which are expected to be effective only in the low-luminosity, hot accretion phases at late-time evolution. The reference models (A0 and A1) from Paper III study the evolution of gas and the mechanical feedback from SMBHs, and solve Eulerian equations of hydrodynamics with mass, energy, and momentum sources (see Paper I). In order to study the effect of each physical process, i.e., mass, energy, and momentum feedback, we build several models which neglect one or two of physical terms. We discuss the details of each model and comparison of them in the following section. 3. EXPLORING ONE-DIMENSIONAL MODELS The model properties and results are given in Table 1. The mechanical efficiencies \u01ebw are given in Column 3 and the corresponding values of \u03b7 \u22612\u01ebwc2/v2 w are given in Column 4. We devote Column 5-9 to present (z = 0) model properties. First, for some models indicated with the symbol \u221ain Column 5, we distribute the mechanical feedback energy (momentum and mass) only at the lower boundary of the grids to Momentum Driving of AGN feedback 5 TABLE 1 Summary of One-dimensional Model Properties Bottom Feedback Model \u01ebw \u03b7(v\u22122 w,10)a Layerb Radiation Energy Momentum Mass log \u2206MBH log LX log le\ufb00 BH c log \u2206Ewd (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) 1 A0 e 5 \u00d7 10\u22123 9 \u00d7 \u221a \u221a \u221a \u221a 6.72 37.11 -7.98 58.67 2 MA0 e 5 \u00d7 10\u22123 9 \u00d7 \u00d7 \u221a \u221a \u221a 6.72 37.11 -7.98 58.67 3 EPM0-R 5 \u00d7 10\u22123 9 \u221a \u221a \u221a \u221a \u221a 7.07 39.75 -10.58 59.02 4 EPM0 5 \u00d7 10\u22123 9 \u221a \u00d7 \u221a \u221a \u221a 7.13 37.84 -10.58 59.08 5 PM0 5 \u00d7 10\u22123 9 \u221a \u00d7 \u00d7 \u221a \u221a 7.13 37.84 -10.58 59.08 6 E0 f 5 \u00d7 10\u22123 9 \u221a \u00d7 \u221a \u00d7 \u00d7 10.32 41.31 -3.61 62.27 7 A1 e 2.5 \u00d7 10\u22124 0.45 \u00d7 \u221a \u221a \u221a \u221a 7.38 36.36 -6.72 58.02 8 MA1 e 2.5 \u00d7 10\u22124 0.45 \u00d7 \u00d7 \u221a \u221a \u221a 7.52 38.09 -6.48 58.17 9 EPM1-R 2.5 \u00d7 10\u22124 0.45 \u221a \u221a \u221a \u221a \u221a 8.04 39.59 -8.23 58.69 10 EPM1 2.5 \u00d7 10\u22124 0.45 \u221a \u00d7 \u221a \u221a \u221a 7.76 38.82 -8.15 58.41 11 PM1 2.5 \u00d7 10\u22124 0.45 \u221a \u00d7 \u00d7 \u221a \u221a 7.76 38.82 -8.15 58.41 12 E1 f 2.5 \u00d7 10\u22124 0.45 \u221a \u00d7 \u221a \u00d7 \u00d7 10.33 41.29 -3.62 60.98 13 EPM2-R 1 \u00d7 10\u22123 1.8 \u221a \u221a \u221a \u221a \u221a 7.59 40.13 -9.25 58.85 14 EPM3-R 1 \u00d7 10\u22124 0.18 \u221a \u221a \u221a \u221a \u221a 8.24 40.39 -7.79 58.50 15 EPM4-R 5 \u00d7 10\u22125 0.09 \u221a \u221a \u221a \u221a \u221a 8.29 40.03 -7.51 58.25 16 EPM5-R 2.5 \u00d7 10\u22125 0.045 \u221a \u221a \u221a \u221a \u221a 8.78 40.33 -5.77 58.43 17 EPM6-R 1 \u00d7 10\u22125 0.018 \u221a \u221a \u221a \u221a \u221a 9.11 40.50 -5.30 58.37 18 EPM7-R 5 \u00d7 10\u22126 0.009 \u221a \u221a \u221a \u221a \u221a 9.29 39.97 -5.14 58.24 Note. Model names (except for Model 1, 2, 7 and 8) indicate the activated physics (symbol \u221a) in the simulations as detailed in Column 6-9. For example, in E0 and E1 models only mechanical energy feedback is allowed, while in PM0 and PM1 models momentum and mass are considered, but not mechanical energy. We adopt 0.2 for the peak EM e\ufb03ciency \u01eb0. a\u03b7 = 2\u01ebwc2/v2 w in v\u22122 w,10 unit where vw = 10, 000km/s bModels with mass, energy and momentum added to the bottom layer. cle\ufb00 BH \u2261Le\ufb00 BH,opt/LEdd where LBH is the SMBH luminosity in the optical band after absorption, i.e., as it will be seen from in\ufb01nity. d\u2206Ew \u2261\u01ebw\u2206MBHc2, in erg, where \u2206MBH is in M\u2299units. e These models correspond to the models A0, MA0, A1 and MA1 in Papers I and III, but calculated with some di\ufb00erence in the numerical grid spacing. f The model similar to one adopted in SDMH05. mimic the common treatment of mechanical feedback (e.g. SDMH05, Di Matteo, Springel & Hernquist 2005, JNB09). Instead, models indicated with the symbol \u00d7 in Column 5 have a distributed feedback as in Papers I and III where we attempt to estimate the gradual deposition of mass, energy and momentum taken from the out\ufb02owing wind and going into the ambient gas as a function of radius. We then build several models which neglect one or two of physical process, i.e., mass, energy, and momentum feedback in order to study their e\ufb00ects showing the inclusion of each term in Column 6-9. For example, Model 3 (EPM0-R, in bold face) distributes the mechanical feedback only into the bottom layer, and includes the radiation feedback and all physical terms, i.e., mass, energy, and momentum, in the mechanical feedback. On the other hand, Model 6 (E0) adopts a treatment similar to that in SDMH05 as it assumes the same mechanical feedback e\ufb03ciency, only includes the mechanical energy feedback and distributes it into the bottom layer of the grid, neglecting the mass and momentum added back into the \ufb02ow. Models 1-6 adopt the standard (high) e\ufb03ciency \u01ebw = 5 \u00d7 10\u22123, as SDMH05 and JNB09 and Models 7-12 assume a factor of 20 lower e\ufb03ciency, perhaps in better accord with observationally based estimates (Moe et al. 2009; Arav et al. 2010) and Models 13-18 adopt other e\ufb03ciencies to show how \ufb01nal properties depend on the assumed mechanical e\ufb03ciency. 3.1. High e\ufb03ciency models To mimic the common treatment (e.g., SDMH05, JNB09), we build the Model 6 (E0) that only includes the Mechanical energy feedback with the standard (high) e\ufb03ciency \u01ebw = 5 \u00d7 10\u22123. In this model, we estimate the mass in\ufb02owing to the SMBH, convert it to energy with the given e\ufb03ciency, and add this energy only into the bottom layers of the surrounding gases. For comparison, Model EPM0-R has identical e\ufb03ciency but adds also mass and momentum to the bottom layers using Equations (5a-d) with \u03b7 = 9, as appropriate for the chosen e\ufb03ciency and wind velocity of vw,10 = 1. These two models are shown as blue and green lines in Figure 1. We see that allowing for momentum and mass feedback reduces the black hole growth by a factor of 1000. The more consistent model has a much lower \ufb01nal X-ray luminosity and \ufb01nal SMBH Eddington ratio. The e\ufb00ect of including or not including radiative heating is relatively minor, as can be seen by comparing Models 3 and 4 or 1 and 2. Also the mechanical energy feedback is considerably less important (as expected) than the momentum input, as can be seen by comparing Models 4, 5, and 6. Finally it might be thought that some of the e\ufb00ects observed in these comparisons are due to the change from Paper I of adding the feedback to the bottom layers alone in the present simulations, rather than over a distributed range of radii to mimic the e\ufb00ects of due to a broad line wind. But comparison between Models 1 and 3, where 6 Ostriker et al. Fig. 1.\u2014 Models 1-6 with constant and high mechanical e\ufb03ciency \u01ebw = 5\u00d710\u22123 (\u03b7 = 9). From top to bottom, the SMBH luminosity, X-ray luminosity, mass accreted on the central SMBH, and star formation rate are shown with di\ufb00erent line types and colors as indicated in the third panel. Note how the model that excludes momentum feedback, \u201cE0\u201d, has by far the highest growth of the central SMBH. there are only small di\ufb00erences (and Model 1 is identical to A0 of Paper III), shows that the di\ufb00erences which may be attributed to distributed feedback are small. In summary, examination of Models 1-6 shows that including momentum drastically increases the e\ufb00ects of feedback. 3.2. Low e\ufb03ciency models Next, we turn our attention to Models 7-12 which have a much lower mechanical e\ufb03ciency than typically assumed and it is at a level better in accord with existing (and highly imperfect) observational indications. The value for the dimensionless parameter \u03b7 in these cases is only 0.45 (i.e. of order unity), so that we expect that inclusion or exclusion of the mass and momentum input will make relatively less di\ufb00erence. What do we \ufb01nd? In fact, the di\ufb00erences are reduced by about half an order of magnitude (0.5 dex), but it remains true that the Model 12 (like Model 6), without either momentum feedback or radiation, has an unacceptably large growth of the central SMBH and an unacceptably large \ufb01nal SMBH luminosity, as shown in Figure 2. Models 6 and 12 also show thermal X-ray emission greater than 1041 erg/s, which is on the upper side of what is typically observed in normal Fig. 2.\u2014 Models with constant and low (observation based) mechanical e\ufb03ciency, \u01ebw = 2.5 \u00d7 10\u22124 (\u03b7 = 0.45). From top to bottom, the SMBH luminosity, X-ray luminosity, mass accreted on the central SMBH, and star formation rate are shown, colors and line types as in Figure 1. Again momentum feedback is the most important physical process in protecting the central SMBH from excessive growth. elliptical galaxies. We summarize the properties of Models 1-12 in Figure 3 showing the present-day (14 Gyr) SMBH mass in solar mass versus X-ray gas and optical stellar luminosities. We show the high e\ufb03ciency models (Models 1-6) in blue and the low e\ufb03ciency models (Models 6-12) in red. The \ufb01ducial models, Models EPM0-R and EPM1-R with mass and momentum feedback, and Models E0 and E1 that only include energy feedback, are marked with their model numbers. As discussed above, including the momentum and mass feedback not only signi\ufb01cantly reduces the SMBH growth but also results in a much lower \ufb01nal X-ray luminosity and \ufb01nal SMBH Eddington ratio. 3.3. Wind e\ufb03ciency dependence of bottom-layer models We test eight di\ufb00erent values of \u01ebw for models ranging from 5 \u00d7 10\u22126 to 5 \u00d7 10\u22123 for models with the bottomlayer treatment and all feedback physics activated (i.e. Models EPM#-R). These models correspond to Models 3, 9, and 13-18 in Table 1. We summarize the results at the epoch of 14 Gyr in Figure 4, where the least square linear \ufb01ts of several global quantities of interest are also given. Note here that the growth of SMBH mass and Momentum Driving of AGN feedback 7 Fig. 3.\u2014 Distribution of all models in the mass-luminosity diagram measured at z=0, where di\ufb00erent colors show di\ufb00erent wind e\ufb03ciencies and \u03b7 values (\u01ebw = 5 \u00d7 10\u22123 and \u03b7 = 9 for blue, \u01ebw = 2.5 \u00d7 10\u22124 and \u03b7 = 0.45 for red). The distribution of models in the Eddington luminosity e\ufb00ective SMBH luminosity plane is shown in the bottom panel. Five diagonal lines (from top to bottom) show le\ufb00 BH = Le\ufb00 BH,opt/LEdd= 10\u22122, 10\u22124, 10\u22126, 10\u22128, 10\u221210 respectively. the BH luminosity Eddington ratio are decreasing functions of \u01ebw. If the feedback e\ufb03ciency is low, too much mass is accreted to the central SMBH, as expected. In the case of the gas mass and the predicted X-ray luminosity of the hot ISM, they are decreasing functions with increasing wind e\ufb03ciency but with large scatters. We also show the total mechanical feedback energy (i.e. \u2206Ew = \u01ebw\u2206MBHc2) in the last panel, which increases as the wind e\ufb03ciency increases. In this case as in several of the others, while the behavior is approximately monotonic in the direction expected, the approximate power law index is much less than unity, since larger e\ufb03ciency gives a larger value for our dimensionless parameter, \u03b7, and thus a smaller fraction of the in\ufb02owing gas is actually accreted onto the central SMBH. 3.4. The e\ufb00ect of mass removal from the circumnuclear disk on purely radiative models Fig. 4.\u2014 Dependencies of present-day, global quantities of EPM#-R models in Table 1, as a function of mechanical e\ufb03ciency \u01ebw. From top to bottom, the SMBH mass growth, BH Eddington ratio, galaxy gas mass inside 10 Re, X-raygas luminosity, and total wind feedback energy are shown. The linear \ufb01ts to the data are shown in dotted lines, and the \ufb01tting results are shown in each panel. As expected, the assumption of a higher wind energy e\ufb03ciency does correspond to greater feedback e\ufb00ects, but at a much less than linear rate. In line with the present exploratory discussion, it is of some interest also to check the e\ufb00ects of di\ufb00erent amounts of mass removal from the circumnuclear disk via disk wind, in the case of purely radiative models. In fact, we recall that in the purely radiative models presented in Paper I (such as model RB0 in Table 2 therein) we do not add mechanical feedback to the equations of hydrodynamics, but the mass, momentum and energy \ufb02uxes of the nuclear wind (and of the jet) are nonetheless computed, in order to satisfy Equations 1\u20135 for assigned mechanical e\ufb03ciency and \ufb01ducial nuclear wind velocity. Therefore, purely radiative models depend indirectly on the assumed mechanical e\ufb03ciency, with highe\ufb03ciency models ejecting a larger fraction of the gas from the circumnuclear wind, and therefore reducing the amount of gas available for accretion on the SMBH. Here we compare the evolution of the purely radiative model RB0 in Paper I (a model with radiative e\ufb03ciency 0.1 and with high constant mechanical e\ufb03ciency 5 \u00d7 10\u22123), with an identical purely radiative model, in which the mechanical e\ufb03ciency has been reduced to zero, therefore excluding mass loss from the circumnuclear disk. The situation is illustrated in Figure 5, where the left panels refer to model RB0, and the right panels to the model without mass ejection from the nuclear disk. In the top panels we show the time evolution of the total 8 Ostriker et al. Fig. 5.\u2014 Time evolution of relevant mass budgets (top panels) and corresponding mass rates (bottom panels) in two purely radiative models (without mechanical feedback), di\ufb00ereing in the treatment of the circumnuclear disk mass budget. The model on the left panels is Model RB0 (see Table 2 in Paper I), while the model in the right panels is identical in all its properties to RB0, except that no mass is lost by the circumnuclear disk. Top panels: total mass accreted by the central SMBH (black), of the total mass of ISM ejected at 10 Re (green), and of the total mass in new stars accumulated within 10 Re (red). Bottom panels: the corresponding mass rates are identi\ufb01ed by same colors as in top panels. The gas production of the passively evolving stellar population steadely declines from \u224810M\u2299/yr at the beginning down to less than 1M\u2299 at the end. mass accreted by the central SMBH (black line), of the total ISM mass ejected by the galaxy as a galactic wind (green line), and \ufb01nally of the accumulated mass in new stars (red line). In the bottom line, the corresponding rates are shown and identi\ufb01ed with the same colors. Unsurprisingly, the SMBH grows signi\ufb01cantly more (by a factor of \u223c2) in the model RB0 without nuclear wind mass loss (log \u2206MBH/M\u2299\u22439.78) than in the model with mass ejection (log \u2206MBH/M\u2299\u22439.45). The major di\ufb00erence in the accretion history of the two models is particularly evident in the \ufb01rst Gyr of evolution, when large amounts of gas \ufb02ow on the central region of the galaxy. Note how the SMBH mass of the model without nuclear mass ejection (right panels) reaches a value similar to the SMBH mass of model RB0 (left panels) at the end of the simulation. As a consequence, the gas near the SMBH is gravitationally more bound in the \ufb01rst model especially at early times when the mass losses are signi\ufb01cant. As can be seen, the star formation history in the two models is almost parallel to their SMBH accretion, and the larger radiative energy output in the model without nuclear mass ejection is accompanied by a larger starburst at early times, with a \ufb01nal mass of new stars of log \u2206M\u2217/M\u2299\u224310.5 (red lined), to be compared with log \u2206M\u2217/M\u2299\u224310.36 in RB0 model without disk mass ejection. Finally, consistently with the larger energy input of the model shown in the right panels, the galactic wind expelled a total ISM mass of log \u2206Mw/M\u2299\u224310.4 in the model without the disk wind, to be compared to log \u2206Mw/M\u2299\u224310.3 in RB0 model. 2.0 2.5 3.0 3.5 4.0 t (Gyr) 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 log LBH (erg/s) LEdd 3.18 3.19 3.20 3.21 3.22 3.23 3.24 3.25 t (Gyr) 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 log LBH (erg/s) LEdd Fig. 6.\u2014 Luminosity versus time for an axisymmetric A model with \u01ebM = 2.5 \u00d7 10\u22124. Above, the AGN luminosity for half a Gyr. Below, the AGN luminosity plotted for a shorter time showing the highly variable nature of the accretion events in two dimensions. The BH accretion is much more stochastic than the one-dimensional case, but the distribution of Eddington ratios is quite similar. Again, this very simple experiment shows how di\ufb00erent treatments in the mass balance equations used to describe SMBH can leads to signi\ufb01cantly di\ufb00erent evolutionary histories (cf. also Soker & Pizzolato 2005). 4. TWO-DIMENSIONAL MODEL COMPARISON One dimensional models continue to be very useful in establishing the basic physical processes that are relevant for AGN feedback in giant elliptical galaxies. However, one dimensional models are not able to capture important properties of the actual systems, including the convective, Rayleigh-Taylor, and Kelvin-Helmholtz instabilities. One dimensional models must also rely on a parameterization of the global deposition of mass, energy, and momentum via the disk wind, while higher dimensional models are able to simulate the evolution of the wind selfconsistently. We discuss below two-dimensional models where we have taken exactly the same galaxy model and feedback characteristics to allow comparisons that are easy to understand. There have been many numerical simulations of BH accretion and the subsequent e\ufb00ects on the galaxies containing resulting AGN. However, e\ufb00orts to date divide into three categories. Di Matteo, Springel & Hernquist (2005), DeBuhr et al. (2009), and Johansson, Naab & Burkert (2009) are Momentum Driving of AGN feedback 9 Fig. 7.\u2014 A snapshot from an axisymmetric simulation showing a cold blob falling to the center of the galaxy. On the left, log gas density in number of protons per cubic centimeter. In the center, log sound speed in kilometers per second. On the right, the radial velocity in kilometers per second. The x and y axes are logarithmic in the distance to the SMBH. The cold gas was produced by enhanced cooling in an overdense quasi-spherical shell with a covering fraction of about one third of the sphere. The gas quickly collapses to a ring with a small covering fraction and/or fragments as it freely falls to the center of the simulation. 2 3 4 5 6 7 t (Gyr) 2.0 2.5 3.0 3.5 4.0 4.5 5.0 MBH(M \u0000) 1e8 A No Mech P Mo Mech En No Rad Fig. 8.\u2014 Black hole mass as a function of time for A models with \u01ebw = 10\u22123. The blue line is the \ufb01ducial case with all physics included. The green line has mechanical momentum injection turned o\ufb00so that mechanical feedback is purely via energy; the SMBH grows prodigiously, indicating that mechanical momentum feedback is by far the dominant process in limiting the growth of the black hole. The red line has mechanical energy injection turned o\ufb00, leaving mass and momentum injection unchanged; the SMBH grows somewhat more than the \ufb01ducial case, indicating that energy feedback plays some role in limiting SMBH growth, albeit a subdominant one. The cyan line has \u01ebEM set to zero so that there is no energy or momentum feedback due to radiation from the central SMBH; this is indistinguishable from the \ufb01ducial case, indicating that radiative feedback plays essentially no role in limiting SMBH growth. examples where the simulations cover length scales from \u2243100 pc to tens of kpc and timescales from a fraction of a Myr to several Gyr. Galactic length and timescales are resolved, but the BH accretion and feedback processes are considered to be sub-resolution. Kurosawa & Proga (2009a,b) are examples of multi-dimensional simulations that cover the length scales from a few AU to \u22431 pc. Length and timescales relevant to BH accretion are resolved, but these simulations do not approach approach galactic length or timescales, and infall rates are taken as given. Finally, Hopkins et al. (2009) and Levine et al. (2008) are examples of a multi-resolution studies of BH accretion involving progressively higher spatial resolution simulations run for progressively shorted times. The highest spatial resolution simulations go down to a fraction of a pc, run for about one mega year of simulation time. These simulations spatially resolve the accretion process, but do not reach galactic timescales. Therefore they cannot self-consistently calculate the e\ufb00ect of AGN feedback on the gas in the galaxy as a whole and subsequent BH accretion. The present work is the only attempt of which we are aware to simultaneously resolve the inner length scales relevant to BH accretion (a few pc), outer length scales relevant to galaxies (tens of kpc), inner timescales relevant to BH accretion (a few years), and outer timescales relevant to galaxies and stellar evolution (10 Gyr). However, the region inside of 1 pc including the disk and BH itself are still treated as sub-resolution physics. A full description of the two-dimensional simulations and an analysis of the similarities and di\ufb00erences between the oneand two-dimensional models is forthcoming. Brie\ufb02y, we use the Zeus hydrodynamics code (Stone & Norman 1992) in spherical coordinates with log-spaced radial bins with \u2206r/r = 0.1. We have extended the code to include appropriate mass, energy, and momentum source terms corresponding to stellar evolution, star formation, type 1a and type II supernova feed10 Ostriker et al. back, radiative and mechanical feedback from AGN activity. See CO07, Papers I and III, Sazonov et al. (2005) for a full description of the input physics, which are carried over in all respects except that we have omitted the radiation pressure on dust. We require the cells to have an aspect ratio of one, giving 30 angular cells. Resolution studies have shown little di\ufb00erence in the SMBH accretion as a function of time as long as the opening angle of the disk wind is resolved. The major di\ufb00erences between the one-dimensional code and the two-dimensional code are in the way that the two codes handle angular momentum and the disk wind from the AGN. The one-dimensional simulations did not permit the simulated gas to have nonzero angular momentum. The 2D simulations assume axisymmetry, but compute the velocity in the \u03c6 direction. We must assume an angular momentum pro\ufb01le. In the present simulations, we avoid forming a rotationally supported gas disk by choosing the radius of centrifugal support to be inside the innermost grid cell. This allows us to avoid specifying an ad-hoc prescription for angular momentum transport. The net speci\ufb01c angular momentum of the stars providing gas in the simulation is assumed to be: 1 v\u03c6 = 1 f\u03c3 + R j + d \u03c3R (9) where R is the distance to the z axis. This parameterization gives solid body rotation at small radii and constant speci\ufb01c angular momentum at large radii. The \ufb01rst term prevents the rotational velocity from exceeding f\u03c3\u2014at intermediate radii, there may be a region with constant velocity. When gas is created in the simulation by stellar evolution, it is given this angular momentum pro\ufb01le. The subsequent evolution of the gas velocity on the computational grid is governed the standard \ufb02uid dynamics conservation laws. The one-dimensional code employs a phenomenological model to determine the radius at which energy, mass and momentum from the AGN-driven disk wind are deposited in the simulation grid. This model depends on an assumed instantaneous jet opening angle. The twodimensional code also requires an assumption about the angular dependence of the energy, mass, and momentum injected by the disk wind at the edge of the simulation grid. Once conserved quantities have entered the simulation grid, the two-dimensional code self-consistently calculates the time evolution of the material from the disk wind; a separate phenomenological model is not required. For the A models, the opening angle of the jet is chosen so that the disk wind covers \u03c0 steradians, giving a linear opening half-angle of cos\u22121 3 4 \u224341\u25e6. The opening angle does not depend on the BH luminosity in the A models. The 1D models simply require the jet opening angle as a parameter, but the 2D models require that the \ufb02ux of material be fully speci\ufb01ed as a function of angle from the z axis. We use dq d\u2126dt \u221dcos2(\u03b8) (10) where q is mass, energy, or radial momentum, \u2126is solid angle, and \u03b8 is the angle from the z axis. This parameterization gives half of input material within a half opening angle of \u224341\u25e6. For the present purpose, the primary result from the two-dimensional models is that the qualitative conclusions already drawn from one-dimensional models remain valid. The dominant physical mechanism regulating black hole growth is momentum injected by the broad-line wind. The energy provided by the mechanical wind has a noticeable but comparatively small e\ufb00ect. The e\ufb00ect of other feedback mechanisms is much smaller than either the mechanical momentum or mechanical energy. Figure 6 shows the AGN luminosity versus time for one of the two-dimensional models with a mechanical e\ufb03ciency of \u01ebw = 0.001 (corresponding to the onedimensional model EPM2-R). The primary di\ufb00erence in the SMBH growth between the oneand two-dimensional models is that the two-dimensional models have much more stochastic growth. There quiescent periods are not as quiescent, and the spacing between the major bursts is not as regular in time. Both of these are due to instabilities present in multiple dimensions: quasi-spherical shells of cold gas are able to fragment and fall into the center bit by bit rather than as a single large shell. In the one-dimensional simulations, bursts of accretion form a hot central bubble that is able to prevent further accretion until the hot bubble cools\u2014this often leads to very regular spacing of accretion events in time. In two-dimensional simulations, a similar hot bubble is formed, but cold gas is able to reach the center via Rayleigh-Taylor and convective instabilities. An example of this is shown in Figure 7. Hot gas simply moves out of the way leading to much more stochastic SMBH accretion with bursts much more closely spaced in time. Figure 8 shows the SMBH mass versus time for several two-dimensional simulations where each physical process is turned o\ufb00in turn, allowing us to identify which ones are negligible and which ones play a dominant role in regulating SMBH growth. Without mechanical momentum injection, the SMBH grows in a fashion only limited by LEdd. Without mechanical energy injection, the SMBH grows about a factor of two faster than the \ufb01ducial case. Mechanical energy plays a role, but it is much less important than mechanical momentum input. Turning o\ufb00all radiative feedback processes by setting \u01ebEM = 0 has little e\ufb00ect on the SMBH growth. Making this choice eliminates gas heating as computed by the expressions in Sazonov et al. (2005), momentum provided by the absorption of those same photons, as well as momentum provided by electron scattering that determines the Eddington limit. The code does not impose the Eddington limit\u2014it allows the accretion to be limited self-consistently by adding the Eddington force to the momentum equation. Therefore setting \u01ebEM = 0 means that the SMBH would not be limited by radiative momentum. In spite of this, the mechanical feedback is able to keep the accretion rate to physically plausible values. The actual optical depth in our simulation for electron scattering is typically small compared to unity. This is consistent with observations which show that only a minority of AGNs are \u201cCompton thick\u201d. 5. DISCUSSION The primary purpose of this paper is to quantitatively show, based on oneand two-dimensional computations, Momentum Driving of AGN feedback 11 exactly which processes are most important during AGN feedback episodes; which processes are most useful in protecting the central SMBH from excessive mass growth and which have most e\ufb00ect on the ambient galaxy. After a central outburst, the mechanical energy must be communicated to the ambient gaseous \ufb02uid by a wind and we, in fact, see these winds in luminous galaxies labeling them \u201cbroad-line regions\u201d with out\ufb02ow velocities observed to be \u223c10, 000 km/s covering conical regions subtending 20-25 % of the sky. These winds must carry mass and radial momentum to the ambient \ufb02uid, reducing thereby the mass deposited on the central SMBH and adding a driving component which cannot be reradiated away by thermal processes. Equations 5a-d summarize the physics, with the dimensionless parameter \u03b7, indicating the importance of mass and momentum out\ufb02ows. In the case of an assumed high mechanical e\ufb03ciency (\u01ebw = 0.005), we \ufb01nd that, if we suppress the mass and momentum input, then the SMBH grows by over a factor of 100 more than if momentum and mass \ufb02ux were properly included in the calculation, and reaches masses > 1010M\u2299in both oneand two-dimensional calculations. Turning on or o\ufb00the energy input has relatively much less e\ufb00ect, altering the SMBH growth by roughly a factor of 2. Ignoring the mass and momentum feedback inputs also leaves the galaxy with a central optical luminosity from the AGN which is orders of magnitude brighter than is seen in nearby elliptical systems. Compared to these dramatic e\ufb00ects, the uncertainty due to not knowing accurately the wind e\ufb03ciencies has a relatively minor e\ufb00ect. Reducing the e\ufb03ciency by a factor of 20 from 5\u00d710\u22123 to 2.5\u00d710\u22124 reduces the wind energy output by only a factor of 2 (to 1058.7 erg) and reducing the e\ufb03ciency by another factor of 10 reduces the wind energy output by only another factor of 2. We also found that redirecting much of the in\ufb02owing mass into a BAL wind has, by itself, an important e\ufb00ect on models with only radiative feedback. In those computations, which do not allow for the redirection, the central SMBH again grows far too much in both the oneand two-dimensional computations. In summary, it eventuates that enforcing the conservation of mass, momentum and energy provides extremely useful constraints in estimating the growth of central SMBHs and the feedback e\ufb00ects on the surrounding galaxies. We bene\ufb01ted from useful conversations with Lars Hernquist, Thorsten Naab, Eve Ostriker and Elliot Quataert. J.P.O. and E.C. acknowledge the support of NSF grant AST-0707505. G.S.N. acknowledges the support of the Princeton University Council on Science and Technology.",
                    "introduction": "1. Feedback from active galactic nuclei (AGNs) at the centers of galaxies is believed to have a signi\ufb01cant e\ufb00ect on the evolution of those galaxies. However, the precise physical mechanisms by which this feedback occurs are greatly uncertain\u2014perhaps more so than is commonly acknowledged. While much path-breaking and insight- ful work has been done, it is also true that some of the most basic requirements, such as the necessity that mass, energy, and momentum be conserved, have not been im- posed in several of the popular treatments of this subject. And the inclusion of the presently known and observed feedback processes is often treated selectively. The pur- pose of this paper is to attempt to lay out the physical framework for discussing the issues and to provide illus- trative examples of the results obtained primarily from one-dimensional computations that include or exclude speci\ufb01c processes. We also include a treatment of the two-dimensional, axisymmetric case, presented in less de- tail, to show how the qualitative features carry over to this more realistic case. De\ufb01nitive solutions are beyond present art in this \ufb01eld, so the focus will be on the qual- itative features of the physical solutions rather than the detailed comparison with observations. In outline, there are three phases to the overall phe- nomenon: 1) the provision of fuel for the central super- massive black hole (hereafter SMBH); 2) the generation of the out\ufb02owing stream of energy, mass and momentum from the vicinity of the SMBH; and 3) the absorption and transmission of this energy, mass and momentum by the ambient gas in the galaxy and the subsequent reactions of the ambient gas to that input. 1. The fueling is generally believed to be via in- falling gas, and typically, two origins for that gas have been proposed; at high redshift ambient gas in discs liberated by the non-axisymmetric forces released dur- ing mergers is certainly important (Barnes & Hernquist 1991), while at lower redshift mergers fail and proba- bly do not fuel AGNs (Li et al. 2001), but the processed gas released via normal stellar evolution provides an am- ple source (Mathews 1983; Shull 1983; Ciotti et al. 1991; Padovani & Matteucci 1993; Ciotti & Ostriker 2007, hereafter CO07). A primary clue as to which of these sources dominates in a speci\ufb01c case is provided by de- tails of the metallicity distribution, since the reprocessed gas probably has super-solar metal abundance and will also show signs of stellar evolution such as higher ni- trogen or S-process abundances. The clue to fueling by infalling globular clusters might be relatively low abun- dances of elements made in SN I such as Fe. In almost all treatments a central disc mediates between the in- \ufb02owing material and the SMBH. Other sources, such as small stellar systems dragged in by dynamical friction have been considered from time to time. These stars, or others added to the central regions via loss-cone pro- cesses (Begelman, Blandford & Rees 1980) can be shred- ded during tidal interactions with the central SMBH or by collisions with one another or with a central disc\u2014 the debris collecting in the disc and feeding the cen- tral SMBH via conventional mechanisms (Ostriker 1983; Dai, Fuerst & Blandford 2010). 2. The out\ufb02ows fall into three categories. The sig- nature of AGNs is, of course, the enormous electro- magnetic, luminous output, with major contributions from the IR bands to the gamma ray region. The bulk of the \ufb02ux is typically in the \u201cUV bump\u201d and the \ufb02ux from this region thus dominates for the \u201cmomen- tum driven winds\u201d (e.g., see Proga, Stone & Kallman 2000; King 2003; Proga & Kallman 2004; DeBuhr et al. 2009). The region where this driving occurs is fairly 2 Ostriker et al. close to the quasar (50RBH \u2272r \u2272500RBH, where RBH is the SMBH Schwarzschild radius). However, the moderately hard X-rays determine the average pho- ton energy: \u27e8h\u03bd\u27e9= h R L\u03bd\u03bdd\u03bd/ R L\u03bdd\u03bd when integrated over the spectrum. This region of the spectrum domi- nates the photon heating, causing the heated gas to ap- proach the mean photon energy: 1.5kTX = \u27e8h\u03bd\u27e9with TX \u223c2 \u00d7 107K (Sazonov, Ostriker & Sunyaev 2004). The resultant heating occurs over an extended range of radii: 100 pc< r <3 kpc (Ciotti, Ostriker & Proga 2009, 2010, hereafter Papers I and III), and it can be signi\ufb01cant for r \u22730.1 pc (Proga 2007). It can e\ufb03- ciently drive out\ufb02ows as shown in a series of papers by Ciotti, Ostriker and collaborators (cf.CO07 and refer- ences therein). For electromagnetic output there is, of course, no rest-mass component. The total energy emit- ted in this form has been established fairly accurately via the Soltan (1982) argument to be \u2206E = \u01ebrad\u2206Maccc2 with \u01ebrad \u223c0.1 \u22120.15 (Yu & Tremaine 2002). The mo- mentum output, of course, is \u2206p = \u2206E/c. In opti- cally thick cases (\u03c4 \u226b1), the total momentum absorbed by the \ufb02uid can approach \u2206p = \u03c4\u2206E/c (DeBuhr et al. 2009). Silk & Nusser (2010) also consider the impor- tance of radiative momentum driven winds on galactic and cluster scales but limit the input to L/c, which can be considerably less than allowed in the optically thick case by Ciotti & Ostriker (2007) or DeBuhr et al. (2009). Next, let us turn to mechanical output. Both broad- and narrow-line regions inject mass, energy and momen- tum into the surrounding gas, with the broad-line winds probably dominant. Since these are material \ufb02ows with velocity in the vicinity of the SMBH, vw, the mass out- \ufb02ow can be considerable. If we let the in\ufb02owing and out\ufb02owing mass rates be ( \u02d9 Minf, \u02d9 Moutf), then conserva- tion of mass, energy and momentum can be summed up with the following simple equations: \u02d9 Macc = \u02d9 Minf \u2212\u02d9 Moutf, (1) where \u02d9 Macc is the mass rate actually accreted by the SMBH, and \u02d9 Ew = 1 2 \u02d9 Moutfv2 w (2a) = \u01ebw \u02d9 Maccc2, (2b) \u02d9 pw = \u02d9 Moutfvw, (3) are the wind energy and momentum, respectively. We have oversimpli\ufb01ed matters by allowing only one wind velocity, when in fact Equation 2a requires \n v2 w \u000b and Equation 3 requires \u27e8vw\u27e9. Also, it is important to specify exactly where and when the quantities in equations 1\u20133 are to be measured. In the conventional treatment of this subject, the SMBH is surrounded by a disc or torus to which matter has fallen from larger radius. Then, plac- ing a sphere around this disc or torus (at r \u223c1 pc), the instantaneous spherically averaged infall through the sphere is \u02d9 Minf(t) and the spherically averaged out\ufb02ow is \u02d9 Moutf(t). The di\ufb00erence will be accreted onto the SMBH unless driven out in disc originating winds; the latter of course contributes to \u02d9 Moutf and so the remain- der \u02d9 Minf \u2212\u02d9 Moutf will be accreted. Two further compli- cations are allowed for in some detailed treatments: (i) the actual instantaneous value of \u02d9 Macc is a time-lagged convolution of the quantity in Equation 1 since a \ufb01nite time elapses as material is transported through the disc to the central SMBH and (ii) star formation may (in fact frequently will) occur in the disc, removing mass that would otherwise have accreted onto the SMBH. Both of these complications are allowed for in CO07 and other work, neither is of dominant importance. Now, de\ufb01ning the dimensionless ratio from Equation 2a and 2b to be, \u03b7 \u2261 \u02d9 Moutf \u02d9 Macc = 2\u01ebwc2 v2 w , (4) we can now rewrite Equations 1\u20133 as \u02d9 Macc = \u02d9 Minf 1 1 + \u03b7 , (5a) \u02d9 Moutf = \u02d9 Minf \u03b7 1 + \u03b7 , (5b) \u02d9 Ew = 1 2 \u02d9 Minfv2 w \u03b7 1 + \u03b7 = \u01ebw \u02d9 Minfc2 1 1 + \u03b7 , (5c) \u02d9 pw = \u02d9 Minfvw \u03b7 1 + \u03b7 . (5d) These Equations, 5a-d, are, in fact, the ones that most authors have adopted who treat AGN feedback as a uni- \ufb01ed process comprising both infall and out\ufb02ow. How- ever, they typically adopt \u03b7 = 0, implicitly assuming vw \u2192\u221e, so that \u02d9 Moutf and \u02d9 pw are neglected and the two terms that are included, \u02d9 Ew and \u02d9 Macc, may be overestimated. If it eventuated that \u03b7 really is a very small number, then not much error would be induced and one would be justi\ufb01ed in neglecting the out-\ufb02owing mass and momentum and in setting \u02d9 Ew \u223c\u01ebw \u02d9 Minfc2, as most authors assume. If we adopt for the e\ufb03ciency of generating mechanical energy the value \u01ebw = 5 \u00d7 10\u22123, as done by Springel, Di Matteo, & Hernquist (2005); Johansson, Naab & Burkert (2009), hereafter SDMH05 and JNB09 respectively, McCarthy et al. (2010) and other authors, and we take vw = 104 km/s (vw,10) (Moe et al. 2009), then we have from Equation 4, \u03b7 = 9v\u22122 w,10 and all of the neglected e\ufb00ects may in fact be dominant; the bulk of the in\ufb02owing mass may be ejected in a broad-line disc wind, and the mass and momen- tum input deposited in the ambient gas may dominate over the energy input, which may be largely radiated away. Papers I and Paper III do include these e\ufb00ects, but do not spell out their signi\ufb01cance. The principal purpose of the present paper is to do just that\u2014to show, in specially simple one- and two-dimensional calcula- tions the e\ufb00ects of including or excluding mass, energy and momentum conservation when \u03b7 > 0. In addition to the papers referred to above which attempt to com- pute both the infall to the central SMBH and the out- \ufb02ow from it in a uni\ufb01ed fashion, there are many others which postulate a central source and then, after esti- mating the mass, momentum and energy \ufb02owing at of that source (and some angular and temporal distribu- tion thereof) do e\ufb00ectively compute the e\ufb00ects of that injection of energy, mass and momentum onto the sur- rounding \ufb02uid. Space does not permit a comprehensive description of this related subject of research, but impor- Momentum Driving of AGN feedback 3 tant papers include the following: cf. Metzler & Evrard (1994); Sternberg & Soker (2008); Fabian et al. (2009); Reeves et al. (2009); Arieli, Rephaeli & Norman (2010); Gaspari et al. (2010). The wind e\ufb03ciency, \u01ebw, is not known very well\u2014 neither from observations nor from detailed physi- cal simulations. But the best estimates from ei- ther of these sources might be in the range 1 \u00d7 10\u22123 > \u01ebw > 3 \u00d7 10\u22124 (Proga, Stone & Kallman 2000; Proga & Kallman 2004; Krongold et al. 2007; Stoll et al. 2009; Kurosawa, Proga & Nagamine 2009), a factor of 5 to 17 smaller than the commonly adopted values and in a range where \u03b7 \u22721 if vw,10 \u22481. A speci\ufb01c example may be useful. Moe et al. (2009) study the quasar SDSS J0838+2955. They \ufb01nd a mechanical energy output of 4.5 \u00d7 1045 erg/s, a mass out\ufb02ow rate 10 times the accre- tion rate and a mechanical e\ufb03ciency of 1\u00d710\u22123, and they quote other observational studies which indicate similar numbers. From analyses of the ionization parameters in the broad-line winds, estimates of the radial extent of the winds can be made; the above paper, and those quoted within indicate radii measured in kpc\u2014consistent with the one-dimensional numerical work in Paper III. As shown in Papers I and III, an additional important question asks \u201cwhat fraction of the sky is covered with the broad-line winds?\u201d Again two approaches are possi- ble. Empirically, on the order of 20-25% of bright quasars show broad-line winds; this translates to \u223c\u03c0 steradians or \u03c0/2 steradians in each conical out\ufb02ow, if we assume that the wind is emitted symmetrically above and below the inner AGN disc. On the theory side, the radiation driven winds found by Proga & Kallman (2004), via de- tailed hydro radiation-transfer calculations, cover \u223c\u03c0 steradians, roughly consistent with the observational es- timates. Finally, let us turn to the narrow jets, the out\ufb02ow observed from AGN in \u201cradio mode\u201d, when the elec- tromagnetic luminosity is considerably below the Ed- dington limit. M87 is an excellent nearby example of such a system. These are standard FRI radio sources. Here the jets are quite narrow and appear to be com- prised primarily of a relativistic \ufb02uid. The same type of calculation as presented in the last section would indicate that the out-\ufb02owing mass is of negligible im- portance and the energy output greatly dominates over the momentum output. The total energy output from these phases is considerable, but the accretion rates are thought to be low in these phases so the e\ufb03ciencies of energy generation may be very high (cf. for a computa- tion McKinney & Gammie 2004). Since so little mass is accreted in radio mode, the Soltan argument cannot be used to empirically estimate e\ufb03ciencies, but, from the observational estimates of the energies available in the giant radio lobes, it may be that the AGN emits in ra- dio mode considerably more energy than it does in wind mode. However the deposition from the intense but ex- tremely narrow streams appears to be ine\ufb03cient, and the jet drills through the gas in the surrounding galaxy, dumping most the energy into the intergalactic medium. Thus, while it may act as the dominant feedback mecha- nism for the IGM (and we will return to this in a subse- quent paper), it is of lesser importance than the radiative or wind components in heating and driving out the am- bient gas from within a galaxy. 3. The interactions between the out-\ufb02owing energy, mass and momentum with the ambient \ufb02uids are com- plex and are just beginning to be studied with the needed detail. We focus here on the relatively gas poor ellip- tical systems, since it is in these that the bulk of the mass in SMBHs is found, The radiative interactions are perhaps easiest to describe. Since the mechanical mo- mentum is conserved and cannot be radiated away, it can be a dominant e\ufb00ect. The minimum level of inter- action is provided by electron scattering and, since the most luminous quasars are found to be clustered near the Eddington luminosity limit (at which level the momen- tum absorbed by electron scattering balances the gravi- tational force on the \ufb02uid from the central SMBH), we know that this e\ufb00ect is signi\ufb01cant in many cases. Ab- sorption of the out-\ufb02owing radiation will not, in gen- eral, reduce this e\ufb00ect, since typically the radiation is simply re-emitted in another band and electron scatter- ing opacity is wavelength independent until the Klein- Nishina limit is reached at very high energies. In fact, in the optically thick limit, the radiation is transformed by dust absorption into the infra-red, but the e\ufb00ects in this case are even greater than in the simple case, since the scattering opacity of the dust to infra-red is, per atom, larger (by roughly a factor of 5) than the electron scat- tering cross section. For the bright ULIRGs, which may contain both an active AGN and a brighter starburst, there will be a near balance between the inward grav- itational forces and the outward radiative momentum transfer on the dust (cf. Thompson, Quataert & Murray 2005, CO07). Under these circumstances, the inner sev- eral hundred parsecs of the galaxy are analogous in their equilibrium structure to a very massive star in so far as there is a nearly equilibrium balance between radiative and gravitational forces. The e\ufb00ects of heating from the AGN are, for quite dif- ferent reasons, also likely to be independent of absorp- tion (so long as it is not excessive, i.e. not Compton thick). Sazonov et al. (2005) present a simple analytical exploration of the e\ufb00ects and Paper I presents a more detailed one-dimensional treatment. The photons which dominate the heating process are in the moderately hard region (\u223c50keV), and we know from X-ray absorption studies that AGN are typically optically thin to such ra- diation. Metal line resonance absorptions dominate the absorption unless the spectrum is extremely hard, and in those cases Compton absorption would be dominant. If we consider the issue on a per atom basis, all that matters is the heating per atom, which scales as r\u22122 (as- suming that the \ufb02uid is optically thin to hard X-rays), and the cooling rate per atom which scales as the density. Since the latter can also scale as r\u22122 or even falls o\ufb00at a steeper rate in some circumstances, the heating can bal- ance or exceed cooling over an extended range of radii. If that happens, the gas temperature will rise towards the radiation temperature, TX \u223c2 \u00d7 107 K. Then, since this exceeds the virial temperature in almost all galaxies, the heated gas, having thermal energy higher than its gravi- tational energy, will be accelerated outwards and tend to drive a wind into the surrounding \ufb02uid. Of course, since this will shut o\ufb00the accretion \ufb02ow and the fuel to the central source, the result will be a burst of energy output followed by much slower cooling of the shocked gas and 4 Ostriker et al. a repeated burst at a much later time. Thus, episodic accretion is expected. The mechanical energy input is more localized to the vicinity of the SMBH and would be e\ufb03cient in \u201cprotect- ing\u201d the SMBH from very high rates of accretion, except for one important caveat. It necessarily happens that such episodes of high rates of energy deposition will oc- cur when the central gas densities are high, and under such circumstances the gas will tend to radiate away the input energy unless forbidden to do so as has occurred in some calculations (Booth & Schaye 2009). This, as we shall see, makes the energy input rather ine\ufb03cient in driving out\ufb02ows and in protecting the SMBH from ex- cessive accreation. But the momentum input cannot be radiated away, and, as we shall see in the remainder of the paper, it is very e\ufb03cient in limiting the infall and accretion onto the central SMBH. Mechanical input, via either thermal or momentum based mechanisms, will also tend to produces episodic accretion. The broad-line gas out\ufb02ow must drive a strong shock into the ambient gas, and that, in turn, given standard physics, should accelerate charged parti- cles e\ufb03ciently via a variant of the \ufb01rst order Fermi process (cf. Blandford & Ostriker 1978; Bell 1978; Blandford & Eichler 1987). Then this relativistic \ufb02uid will further drive the out\ufb02ow and, since thermal radia- tion is suppressed for this component, the conversion may somewhat enhance the e\ufb00ects of feedback. But, overall, this process simply transforms internal energy from one form to another and so, whereas it may be observation- ally quite signi\ufb01cant, it will have a relatively small global e\ufb00ect. Two recent papers that have explored these pro- cesses are Fujita et al. (2007) and Jiang et al. (2010); see also Sironi & Socrates (2010). 2."
                }
            ],
            "Tom Oosterloo": [
                {
                    "url": "http://arxiv.org/abs/1910.07865v1",
                    "title": "ALMA observations of PKS 1549-79: a case of feeding and feedback in a young radio quasar",
                    "abstract": "We present CO(1-0) and CO(3-2) ALMA observations of the molecular gas in PKS\n1549-79, as well as mm and VLBI 2.3-GHz continuum observations of its radio\njet. PKS 1549-79 is one of the closest young, radio-loud quasars caught in an\non-going merger in which the AGN is in the first phases of its evolution. We\ndetect three structures tracing the accretion and the outflow of molecular gas:\nkpc-scale tails of gas accreting onto PKS 1549-79, a circumnuclear disc (CND)\nin the inner few hundred parsec, and a very broad (>2300 \\kms) component\ndetected in CO(1-0) at the position of the AGN. Thus, in PKS 1549-79 we see the\nco-existence of accretion and the ejection of gas. The line ratio\nCO(1-0)/CO(3-2) suggests that the gas in the CND has both high densities and\nhigh kinetic temperatures. We estimate a mass outflow rate of at least 650\nmsun/yr. This massive outflow is confined to r < 120 pc, which suggests that\nthe AGN drives the outflow. Considering the amount of molecular gas available\nin CND and the observed outflow rate, we estimate a time scale of ~10^5 yr over\nwhich the AGN would be able to destroy the CND, although gas from the merger\nmay come in from larger radii, rebuilding this disc at the same time. The AGN\nappears to self-regulate gas accretion onto the super-massive black hole. From\na comparison with HST data, we find that the ionised gas outflow is more\nextended. Nevertheless, the warm outflow is about two orders of magnitude less\nmassive than the molecular outflow. PKS 1549-79 does not seem to follow the\nscaling relation between bolometric luminosity and the relative importance of\nwarm ionised and molecular outflows claimed to exist for other AGN. We argue\nthat, although PKS 1549-79 hosts a powerful quasar nucleus and an ultra-fast\noutflow, the radio jet plays a significant role in producing the outflow.",
                    "authors": "Tom Oosterloo, Raffaella Morganti, Clive Tadhunter, J. B. Raymond Oonk, Hayley E. Bignall, Tasso Tzioumis, Cormac Reynolds",
                    "published": "2019-10-17",
                    "updated": "2019-10-17",
                    "primary_cat": "astro-ph.GA",
                    "cats": [
                        "astro-ph.GA"
                    ],
                    "main_content": "2.1. Observations of CO(1-0) and 3-mm continuum The CO(1-0) data were obtained during Cycle 5 using Atacama Large Millimeter/submillimeter Array (ALMA) in configuration C43-10. The observations were pointed at the nucleus of PKS 1549\u221279, with a field of view (FoV) of \u223c60\". The observations were done in Band 3 making use of the correlator in Frequency Division Mode. The total bandwidth used was 1.875 GHz, corresponding to 5625 km s\u22121 using 1920 channels and giving a native velocity resolution of about 3.0 km s\u22121, but in the subsequent data reduction channels were combined to make image cubes with a velocity resolution better matching the obArticle number, page 2 of 14 Oosterloo et al.: Feeding and feedback in PKS 1549\u201379 Table 1. Parameters of the ALMA and VLBI data cubes and images. Frequency Beam & PA Velocity Res. Noise Description (GHz) (arcsec) (degree) ( km s\u22121) (mJy beam\u22121) CO(1-0) 0.167 \u00d7 0.126 9.5 18 0.29 low resolution CO(1-0) 0.090 \u00d7 0.055 \u20132.9 120 0.085 low velocity resolution CO(1-0) 0.31 \u00d7 0.16 \u201322.2 60 0.19 cube matching CO(3-2) CO(3-2) 0.31 \u00d7 0.16 \u201322.2 60 0.24 Continuum 100 0.047 \u00d7 0.026 \u201310.5 \u2013 0.085 Continuum 100 0.01 \u00d7 0.01 0 \u2013 super resolved Continuum 300 0.29 \u00d7 0.13 \u201322.5 \u2013 0.25 Continuum 300 0.05 \u00d7 0.05 0 \u2013 super resolved VLBI 2.3 0.0042 \u00d7 0.0012 0 \u2013 0.8 served line widths (see below). The observations were done with 45 antennas, giving a uv coverage with the shortest baseline being 35 k\u03bb and a maximum baseline of almost 5 M\u03bb, in three observing sessions of 0.63 hr on-source each (two on Oct 8, 2017 and one on Oct 15, 2017), resulting in a total on-source time of 6804 sec. In each observation session, we interleaved 1-minute scans on PKS 1549\u221279 with 20-second scans on the phase calibrator J1617\u20137717 . The initial calibration was done in CASA (v5.1.1; McMullin et al. 2007) using the reduction scripts provided by the ALMA observatory. The \ufb02ux calibration was done using scans on the source J1617\u20135848. These calibrated uv data were exported to MIRIAD (Sault et al. 1995) which was used to perform additional bandpassand self calibration which improved the quality of the images signi\ufb01cantly. The continuum \ufb02ux density of PKS 1549\u221279 at 100 GHz is about 370 mJy and most of this comes from the unresolved core of the source. The pipeline provided by the ALMA observatory, due to this relatively bright core, resulted in data cubes with insu\ufb03cient spectral dynamic range. To remedy this, we used the scans of the phase calibrator J1617\u20137717 (which has a \ufb02ux density of 2.9 Jy) that were interleaved with the scans on PKS 1549\u221279 to derive a timevariable bandpass calibration for all three CO(1-0) observations. This greatly improved the bandpass calibration, and all \ufb01nal data cubes we produced are not limited in spectral dynamic range. All further reduction steps (continuum subtraction in the image plane, imaging, cleaning) were also done in MIRIAD. As listed in Table 1, a number of cubes were made, adopting various weighting schemes and velocity resolutions in order to explore the optimum for imaging and for highlighting di\ufb00erent structures of the distribution and kinematics of the CO(1-0). Given the low surface brightness of the CO(1-0) emission, we produced a data cube using natural weighting to obtain the lowest noise level, albeit at somewhat lower resolution (0\u2032\u2032 .09 \u00d7 0\u2032\u2032 .05 = 240 \u00d7 147 pc). This cube was used to study the inner regions of PKS 1549\u221279. The velocity resolution of this cube is 120 km s\u22121 to match the large line widths of the CO(1-0) close to the centre. To better image the large-scale CO(1-0), we also made a cube with lower spatial resolution by tapering the data. The resolution of this cube is 0\u2032\u2032 .167 \u00d7 0\u2032\u2032 .126 (446 \u00d7 336 pc) and has a velocity resolution of 18 km s\u22121. All cubes were de-redshifted assuming a redshift of z = 0.1525. The 100-GHz continuum image was obtained by imaging the data, after self-calibration, at full spatial resolution using uniform weighting with a resulting beam of 0\u2032\u2032 .047 \u00d7 0\u2032\u2032 .026 (125 \u00d7 69 pc). The noise of the continuum image is 85 \u00b5Jy beam\u22121. The peak in the continuum image is 350 mJy at the location of the core, so the dynamic range is about 1:4000. The total extent of 100 pc Fig. 1. Continuum image obtained from the line-free channels of the 3mm observations (black contours and grey-scale). The white contours show the structure of the same emission as obtained from the superresolution image. Contour levels for standard image are 1.5, 3.0, 6.0, 12.0,... mJy beam\u22121, for the super-resolved image 0.15, 0.3, 0.6, 1.2,... mJy beam\u22121. Center at RA 15 56 58.8697047  DEC -79 14 04.281027 CONT: 1549-790  IPOL  2291.725 MHz  1549-790.ICL001.22 PLot file version 1  created 08-DEC-2017 16:34:31 Cont peak flux =  1.0932E+00 JY/BEAM Levs = 1.093E-02 * (-0.864, 0.864, 1.729, 3.458, 6.916, 13.83, 27.66, 55.33) MilliArc seconds MilliArc seconds 150 100 50 0 -50 60 40 20 0 -20 -40 -60 100 pc Fig. 2. VLBI continuum image at 2.3 GHz. The contour levels are 0.011 \u00d7 \u22120.864, 0.864, 1.729, 3.458, 6.916, 13.83, 27.66, 55.33 Jy beam\u22121. the radio source is about 0\u2032\u2032 .2 (about 500 pc) with an inner jet of 0\u2032\u2032 .06 (about 140 pc; see Fig. 1). Given the high quality of the data, the large number of antennas used, the resulting excellent uv coverage, and the strength of the central continuum point source, it turned out that the source Article number, page 3 of 14 A&A proofs: manuscript no. ALMA_PKS1549-aph model derived in the selfcalibration (using the clean method) contained information on smaller scales than the nominal resolution of the observations. In Fig. 1 we show both the nominal continuum image and this model image (where we have smoothed the model components for presentation purposes with a Gaussian with a resolution of 0\u2032\u2032 .01 corresponding to 27 pc). This very high resolution image compares very well with the 2.3-GHz VLBI image we discuss below (Fig. 2), lending support to its \ufb01delity. 2.2. Observations of CO(3-2) and 1-mm continuum The CO(3-2) data were also obtained during Cycle 5, in a single observing session on Sep 20, 2018 using ALMA in con\ufb01guration C43-5. The total on-source observing time was 0.75 hr. The observation made use of 45 antennas giving a uv coverage with the shortest baseline being 15 k\u03bb and a maximum baseline of 1 M\u03bb. The \ufb02ux calibration was done using observations of J1427\u2013 4206. The observations were done in Band 7, again making use of the correlator in Frequency Division Mode. The spectral setup used was the same at that for the CO(1-0) observations, giving a velocity resolution (due to the di\ufb00erent observing frequency) of about 1.0 km s\u22121 (de-redshifted), but also here in the later data reduction channels were combined to make image cubes with a velocity resolution better matching the observed line widths. The data reduction followed a very similar path as described for the CO(1-0), but given the lower continuum \ufb02ux density (\u223c60 mJy), additional bandpass calibration was not needed. The aim of the observations was to study to what extent the molecular gas is e\ufb00ected by the AGN by comparing the CO(1-0) and CO(32) emission and kinematics. Given the limited bandwidth of the CO(3-2) data in km s\u22121 (a third of that of the CO(1-0) observations), this is only possible for the for the larger, brighter CO structures with velocities within \u223c500 km s\u22121 from the systemic velocity, but not for the gas with the most extreme out\ufb02ow velocities detected in CO(1-0) (see below). As summarised in Table 1, we obtained a cube with spatial resolution of 0\u2032\u2032 .31 \u00d7 0\u2032\u2032 .16 (0.83 \u00d7 0.43 kpc). The noise of the cube used is 0.24 mJy beam\u22121(for a velocity resolution of 60 km s\u22121). A cube with matching spatial and velocity resolution was made from the CO(1-0) observations. The continuum was imaged at full resolution (0\u2032\u2032 .29 \u00d7 0\u2032\u2032 .13 = 780 \u00d7 347 pc). The noise in the continuum image is 0.25 mJy beam\u22121. Also for these observations we were able to make a super-resolved continuum image with in this case a resolution of 0\u2032\u2032 .05. Because of the lower resolution of these observations, the continuum images give information on the spectral index of the continuum emission, but does not add information on the structure of the continuum source. 3. VLBI observations PKS 1549\u221279 was observed at 2.3 GHz in June 2007 (project V235) using the Australian Long Baseline Array (LBA) with in addition the Hartebeesthoek 26-m antenna (South Africa). Stations involved were the ATCA tied array, Mopra, Parkes, Hobart 26-m, Ceduna, and Tidbinbilla 34-m in Australia, and the Hartebeesthoek 26-m antenna in South Africa. There is a large gap in (u, v) coverage between the baselines to Hartebeesthoek and the baselines between the Australian telescopes. The total observation covered 12 hours, with almost 11 hours integration on PKS 1549\u221279 at most stations; the source was visible at Hartebeesthoek only for the last 3.5 hours, and Tidbinbilla observed for just over three hours due to its limited availability for scheduling. The recorded bandwidth was 64 MHz in total, centred on a sky frequency of 2.3 GHz. Ceduna and Hobart recorded only the lower 32 MHz, limited by the recording capability at the time. All stations recorded dual polarisation data except for Tidbinbilla, which has only single polarisation (right-hand circular). The data were correlated using the DiFX software correlator at Swinburne University (Deller et al. 2007). Amplitude scaling based on nominal System Equivalant Flux Densities (SEFDs) for each antenna was applied at correlation, as was standard procedure for the LBA correlator at that time. Post-correlation, these a priori corrections were undone and scaling based on the measured system temperatures was applied where available, in this case only for Hobart, Ceduna and Tidbinbilla. This calibration, along with fringe-\ufb01tting, initial o\ufb00source and band-edge \ufb02agging, and bandpass calibration, was performed using standard tasks in AIPS. The data were then independently imaged in both AIPS and Difmap. The resulting synthesised beam for the full dataset has FWHM 4.2 \u00d7 1.2 mas (11.2 \u00d7 5.3 pc). Initially, several iterations of CLEAN and phase-only self-calibration were done, followed by an overall amplitude scaling using the latest CLEAN component model to scale the visibilities. This resulted in typical amplitude corrections in the range 5\u201320% for each antenna and 16MHz sub-band. Further iterations of CLEAN, phase-only selfcalibration, and phase and amplitude self-calibration with a 30minute solution interval, were used to re\ufb01ne the image. The resulting residual image has an RMS noise level of 0.8 mJy/beam, compared to the peak \ufb02ux density of 0.76 Jy/beam, giving a dynamic range of approximately 1000:1 in the full resolution image with uniform weighting. The resulting image is shown in Fig. 2. 4. Results: the molecular gas The ALMA observations clearly reveal the complex distribution and kinematics of the molecular gas in PKS 1549\u221279 on several scales. On the largest scale (i.e. few kpc), the emission appears to form extended tails in the north-south direction. In the inner few hundred parsec we see evidence for a circumnuclear disc. In addition, in CO(1-0) we detect a very broad (\u223c2300 km s\u22121) component at the position of the AGN. We do not detect this component in CO(3-2), but this is quite likely due to the limited bandwidth of the CO(3-2) data. We \ufb01rst describe the results for the two transitions separately, followed by a discussion of the line ratios. 4.1. Overall distribution and kinematics of the CO(1-0) The total intensity of the CO(1-0) is shown in Fig. 3 and the overall kinematics is illustrated in Fig. 4. We detect three main features in CO(1-0). On the largest scales of several kpc, we see that the CO(1-0) extends about 1\u2032\u2032 .7 (4.5 kpc) in the N-S direction in what appear to be two tails of gas. This orientation is perpendicular, in projection, to that of the radio jet, which emanates from the core more or less towards the east. The overall morphology of the CO is very similar to that seen for the ionised gas as observed with the Hubble Space Telescope (HST; Batcheldor et al. 2007) and for the stellar distribution with the VLT (Holt et al. 2006), which also show N-S tail-like structures. The ALMA observations show that these tails go all the way to the very central regions. The zoom-in of the central region (Fig. 3) shows that the CO(1-0) strongly peaks at the centre, at the location of the radio core. As is shown below, this is at least to some extent the e\ufb00ect of high excitation of the central CO gas and not only Article number, page 4 of 14 Oosterloo et al.: Feeding and feedback in PKS 1549\u201379 1 kpc 500 pc Fig. 3. Total intensity of the CO(1-0) obtained from the cube with a resolution of 0\u2032\u2032 .17 \u00d7 0\u2032\u2032 .13, corresponding to about 400 pc. This low-resolution allows to highlight the extent of the N-S tail of CO(1-0). In the right hand panel the continuum image is shown for reference (see details in Sec. 5). Contour levels are 0.04, 0.08, 0.12, ... mJy beam\u22121 km s\u22121. Tail Out\ufb02ow Tail Circumnuclear  disc Fig. 4. left: Position-velocity plot of the CO(1-0) taken along PA = \u20132\u25e6 .9, i.e. along the direction of the inner parts of tails and almost perpendicular to the radio jet. The data cube used has a resolution of 0\u2032\u2032 .09 \u00d7 0\u2032\u2032 .055 and a velocity resolution of 120 km s\u22121. Negative position o\ufb00sets are south of the core. Contour levels are 0.12 (1.5 \u03c3), 0.24, 0.36 and 0.48 mJy beam\u22121. right: Position-velocity plot of the CO(1-0) centred in the core in the direction of the radio jet (PA = 77\u25e6). negative o\ufb00sets are E of the core. Contour levels are 0.12 (1.5 \u03c3), 0.24, 0.36 and 0.48 mJy beam\u22121. of a very high central concentration of the gas. At the location of the jet east of the core, no anomalous feature is seen in CO(1-0). The position-velocity plot in the left panel of Fig. 4 shows the kinematics of the CO(1-0) in the N-S direction (PA \u20132\u25e6 .9, centred on the core and aligned with the inner parts of the largescale tails) as seen in the naturally weighted cube. The velocity resolution of the data cube used here is 120 km s\u22121 to highlight the broad component in the centre (see below). A few things can be noted from this \ufb01gure. In the \ufb01rst place that the velocity gradient over the large-scale tails is very small. This is somewhat surprising because the linear morphology of the tails suggests that we are seeing the large-scale gas distribution of PKS 1549\u221279 edge-on so that one should fully detect any rotation of the largescale gas. The small velocity gradient observed may suggest that the kinematics of the large-scale gas is dominated by radial motions (which will mostly be in the plane of the sky). If this is the case, the data suggest that there could be large-scale in\ufb02ow of gas towards the central regions. This would be consistent with Article number, page 5 of 14 A&A proofs: manuscript no. ALMA_PKS1549-aph 250 pc Fig. 5. Total blueand redshifted CO(1-0) emission of the circumnuclear disc superposed on the 100-GHz continuum image, illustrating the N-S velocity gradient (see text for details). Contour levels are 0.04, 0.08 and 0.12 mJy beam\u22121 km s\u22121. the idea that PKS 1549\u221279 is an ongoing merger with strong star formation fed by the accretion of gas. In contrast to what is seen on the largest scales, in the inner region (\u223c0\u2032\u2032 .5 = 1.3 kpc) there appears to be a distinct kinematical component with a total velocity width of \u223c500 km s\u22121. The kinematics suggests that on this scale, gas has settled, or is settling, in a rotating circumnuclear disc with a diameter of just over 1 kpc. This circumnuclear disc is even better visible in the CO(3-2) data (see below). The kinematics of the gas in the inner regions is further illustrated in Fig. 5 where we show the the blueand redshifted CO(1-0) emission of the circumnuclear disc. We have isolated these components by integrating the data over the intervals \u2013350 km s\u22121 to 0 km s\u22121 and 0 km s\u22121 to +350 km s\u22121 respectively. Figure 5 shows that the gas from the circumnuclear disc is extended N-S with the velocity gradient also in that direction. Most interestingly, in the very central region, at the location of the core, CO(1-0) is detected over a very large velocity range, with a total width of about 2300 km s\u22121. A spectrum taken at the position of the core is shown in Fig. 6. This very broad pro\ufb01le shows both a blue-shifted component (up to \u223c1800 km s\u22121 from the systemic velocity) and a narrower red-shifted wing (\u223c500 km s\u22121 from systemic). In the optical, the [O III] emission line shows a similarly broad, and similarly blue-shifted pro\ufb01le (Holt et al. 2006; Santoro et al. in prep.). Most likely, the broad emission near the core is evidence that the AGN is a\ufb00ecting the gas in its vicinity inducing large turbulent motions and driving a gas out\ufb02ow. This broad component is spatially unresolved in our data (r < 120 pc) and is only detected at the location of the core. No indications for large, anomalous velocities are seen at the location of the jet, about 0\u2032\u2032 .1 east from the core, even after spatial tapering of the data to enhance faint, extended emission. H i absorption is known to be present in PKS 1549\u221279 against the entire radio structure, including the few-hundred-pc sized jet (see Morganti et al. 2001; Holt et al. 2006). The H i absorption pro\ufb01le is much narrower (80 km s\u22121) than the broad CO pro\ufb01le, with velocities covering the blueshifted edge of the -3000 -2000 -1000 0 1000 2000 V (km/s) -0.5 0 0.5 1 1.5 S (mJy) CO(1-0)   core Fig. 6. Pro\ufb01le of the CO(1-0) emission at the location of the core of PKS 1549\u221279 velocity range of the circumnuclear disc and the large-scale tails. The small width of the H i pro\ufb01le suggests that the H i is likely located at larger radii and not a\ufb00ected by the interaction with the jet and is possibly associated with the larger-scale CO tails. 4.2. The CO(3-2) distribution and kinematics In Fig. 7 we show the integrated CO(3-2) emission with a resolution of 0\u2032\u2032 .31 \u00d7 0\u2032\u2032 .16 (820 \u00d7 427 pc). As expected, overall the CO(3-2) follows the distribution of the CO(1-0) quite well, although the contrast between the central regions and the outer tails is much larger, with the central regions being relatively much brighter in CO(3-2). This is very similar to what is seen, for example, in IC 5063 where the contrast between the inner regions a\ufb00ected by the radio jet and the outer, quiescent disc is larger in the higher CO transitions, evidencing the impact of the AGN on the gas conditions (Oosterloo et al. 2017). Figure 8 shows the kinematics of the CO(3-2) along the same direction as shown for the CO(1-0) in Fig. 4. The central circumnuclear disc shows up very clearly in this transition, while the \ufb01gure also shows the clear di\ufb00erence in brightness between the inner regions and the outer tails, underlining they are two distinct components. The broad component near the core seen in CO(1-0) is not visible in CO(3-2). This may be a real e\ufb00ect, but it might also be the consequence of the relatively narrow observing band used for the CO(3-2) (\u223c1800 km s\u22121) so that the broad component was subtracted away in the continuum subtraction, given that the broad component seen in CO(1-0) would extend to outside the observing band of the CO(3-2) observations. 4.3. Line ratios The very broad pro\ufb01le seen in the centre of PKS 1549\u221279, and the large contrast in CO(3-2) between the bright inner disc and the outer tails, suggest that the energy released by the AGN has an impact on the ISM surrounding it, both on the kinematics of the gas, and on the physical conditions. A way of illustrating this is to look at the line ratio CO(3-2)/CO(1-0) because this gives indications about the excitation conditions of the molecular gas. In order to be able to do this, data cubes were made with matching spatial and velocity resolutions for both transitions. Given the higher resolution of the CO(1-0) observations, a separate data cube for this transition was made by tapering the data Article number, page 6 of 14 Oosterloo et al.: Feeding and feedback in PKS 1549\u201379 2 kpc Fig. 7. Total intensity of the CO(3-2). The resolution is 0\u2032\u2032 .31 \u00d7 0\u2032\u2032 .16 (820 \u00d7 427 pc). Contour levels are 0.04, 0.08, 0.16,... mJy beam\u22121 km s\u22121. so that the spatial resolution matches that of the CO(3-2) cube discussed above. Following this, to improve the signal-to-noise of the data, N-S position-velocity slices centred on the core were computed from both data cubes by spatially averaging the data in the E-W direction over a length of 0\u2032\u2032 .375 (1 kpc). These slices are shown in Fig. 9. This \ufb01gure underlines that the contrast between the inner disc and the outer tails is very di\ufb00erent in the two transitions. One can also see that the pv diagram of the circumnuclear disc is somewhat di\ufb00erent in the two transitions, with the very inner region with the higher velocities being much brighter in CO(32). This suggests that there is a gradient over the circumnuclear disc in the excitation of the gas. This can be further seen in the bottom panel of Fig. 9 which shows the line ratio R31 = CO(3-2)/CO(1-0) (where the brightness used is in Kelvin) as computed from the pv-slices shown in Fig. 9. The line ratio was only computed for those pixels where S CO(1\u22120) > 0.4 K. In the outer tails, R31 is well below 0.5, which is typical for the ISM in large-scale gas discs in galaxies (Leroy et al. 2009; Oosterloo et al. 2017). In contrast, in the inner regions R31 is much larger. The average value in the core region of R31 is 1.25, with a maximum for R31 of 2.3. The zoom-in in Figure 10 shows that high values for R31 are mainly found in the inner parts of the circumnuclear disc, very close to the centre. In this \ufb01gure, the CO(1-0) intensity contours of the circumnuclear disc have been overplotted. This shows that the shape of the circumnuclear disc in CO(1-0) in the pv-plane is di\ufb00erent from that of the region of elevated line ratios. The intensity contours show the typical S shape of a pv diagram of a rotating disc, while the region with high ratios shows this to a much lesser extent, implying that the gas with the highest line ratios must be in the inner parts of the disc. Similarly, Fig. 10 also shows that the highest ratios occur at velocities away from the systemic velocity, meaning that the fastest moving gas has the highest excitation. The high values for R31 (> 1) observed in PKS 1549\u221279 suggest that the CO emission from the circumnuclear disc is optiFig. 8. Position-velocity plot along the same direction as in Fig. 4 but from the CO(3-2) data. The spatial resolution of this cube is 0\u2032\u2032 .31 \u00d7 0\u2032\u2032 .16 and the velocity resolution is 60 km s\u22121. Contour levels are 0.36 (1.5 \u03c3), 0.72, 1.44, 2.88,... mJy beam\u22121. cally thin. This is relevant for estimating the mass of the molecular gas in the inner regions (see below). In addition, they also indicate that the physical conditions of the molecular gas are characterised by much higher kinetic temperatures and densities than those found in a normal interstellar medium. This is likely caused by large amounts of energy being pumped into the ISM by star formations or by the AGN. Ultra Luminous Infrared Galaxies typically have R31 \u22641 (Greve et al. 2014), although this is based on integrated \ufb02uxes, so that locally higher values may occur. However, values for R31 well above 1 are observed in some AGN. An example is NGC 1068 (Viti et al. 2014) where very elevated values for R31 are seen in the circumnuclear disc, where the gas is likely excited by the AGN. The models of Viti et al. (2014) suggest densities up to 105 cm\u22123 and kinetic temperatures up to 150 K. A similar case is IC 5063 (Dasyra et al. 2016; Oosterloo et al. 2017), where the CO gas that is kinematically disturbed by the AGN has very high values for R31. Modelling the various line ratios in IC 5063 suggested that the disturbed gas has densities and kinetic temperatures similar to those observed in NGC 1068. Also in the case of IC 5063 this is very likely the result of the AGN dumping large amounts of energy in the ISM surrounding the AGN. 4.4. The molecular gas masses The masses of the di\ufb00erent components in the molecular gas were estimated from the CO(1-0) cube. We estimate the mass of the three structures separately: the tail, the central disc and the broad component seen in CO(1-0). The \ufb02ux integral of the broad component was derived by integrating the spectrum at the position of the core over the velocity range \u2212350 to \u22121800 km s\u22121, resulting in a \ufb02ux integral of 0.24 Jy km s\u22121. For the central disc, we integrated the signal in the data cube over a region of 0\u2032\u2032 .2 \u00d7 0\u2032\u2032 .2 and the velocity interval \u2212350 to +350 km s\u22121, obtaining a \ufb02ux integral of 1.0 Jy km s\u22121 Article number, page 7 of 14 A&A proofs: manuscript no. ALMA_PKS1549-aph Fig. 9. Average N-S position-velocity slices of the CO(1-0) (top) and CO(3-2) (middle) which were used to compute the line ratios, shown at the bottom. Contour levels are 0.4, 0.8, 0.12,... K (top) and 0.1, 0.4, 0.8, 0.12... K (middle). The direction of the slice is the same as in Figs 4 and 8. Fig. 10. Zoom-in of the position-velocity shown in Fig. 9 bottom, illustrating the line ratio in the central region of PKS 1549\u221279, clearly showing that the highest ratios are at the location of the core. Contour levels are 0.4, 0.8, 0.12,...K. for this component. For the fainter, extended tails we obtain a \ufb02ux integral of 1.85 Jy km s\u22121. It is likely that the emission of the central disc and of the broad component overlap in the data cube over a certain velocity range and it is di\ufb03cult to separate the two. A rough correction would be to assume that in the velocity range of the central disc, the broad component contains as much emission as it does in the blueshifted velocity interval not overlapping with the central disc. Making this assumption, the corrected \ufb02ux integral for the central disc is 0.76 Jy km s\u22121 and for the broad component 0.48 Jy km s\u22121. To convert these measurements into masses, one has to make assumptions about the conversion factor. For the extended tails we used a standard conversion of 4.6 K km s\u22121 pc2 because there are no indications that this gas has unusual excitation. This results in an estimate for the H2 mass of the tails of 9.7 \u00d7 109 M\u2299. Given that the observed line ratios are larger than 1, the gas in the central regions is likely optically thin and has di\ufb00erent excitation so a much lower conversion factor may have to be used. For a conversion factor of 0.3 K km s\u22121pc2 representative of such conditions (Bolatto et al. 2013), the mass in the broad component is 1.6 \u00d7 108 M\u2299and for the central disc 2.6 \u00d7 108 M\u2299. It is interesting to note that the total H2 mass derived from our observations is close to the 6.7 \u00d7 109 M\u2299estimated using the far-IR luminosity (LIR = 1.6 \u00d7 1012 L\u2299, Holt et al. 2006) and the conversion between FIR and CO luminosity from Oca\u00f1a Flaquer et al. (2010). These masses imply that the beam-average column density in the central region is about 9 \u00d7 1022 cm\u22122. Interestingly, this is consistent with the neutral column density NH = 5.2\u00b10.1\u00d71022 cm\u22122 found by Tombesi et al. (2014) from X-ray observations. In addition, by modelling the e\ufb00ect of extinction on the optical SED of PKS 1549\u221279, Holt et al. (2006) derived an H i colArticle number, page 8 of 14 Oosterloo et al.: Feeding and feedback in PKS 1549\u201379 umn density in the range 1.2 \u00d7 1022 < NHI < 2.4 \u00d7 1022 cm\u22122. Thus, although each of the column density tracers we use here has its uncertainties and they are not necessarily expected to give the same answer (e.g. due to di\ufb00erences in geometry), the column densities derived from them are comparable. From the 21cm H i absorption, Holt et al. (2006) derive a column density of NHI = 4.0 \u00b1 0.5 \u00d7 1018Tspin cm\u22122. The H i column densities derived from the optical data and from the HI absorption are consistent if the spin temperature of the absorbing gas would be in the range 3000\u20136000 K. This is not untypical for atomic gas in the immediate vicinity of an AGN due to the e\ufb00ects of the radiation \ufb01eld of the AGN on the excitation of the 21-cm line (Morganti & Oosterloo 2018). On the other hand, the small width of the H i pro\ufb01le suggests that the gas is not near the AGN but more likely associated with the large-scale gas at larger radii. 4.5. The molecular out\ufb02ow We use the time-average thin-shell approach \u02d9 M = MoutVout/Rout (Rupke et al. 2005) to estimate the mass out\ufb02ow rate of the molecular gas. It is not entirely clear what to use for Vout because the total width of the broad pro\ufb01le is the sum of the bulk out\ufb02ow velocity and the turbulence of the out\ufb02owing material and it is unknown what the relative contributions are. For the purpose of this paper, we assume an out\ufb02ow velocity of 600 km s\u22121. Using these numbers, we \ufb01nd the out\ufb02ow rate to be about 650 M\u2299 yr\u22121. This number is, however, quite uncertain. In the \ufb01rst place because it is di\ufb03cult to estimate the \ufb02ux of the molecular gas involved in the out\ufb02ow due to the overlap of the emission form the out\ufb02owing gas and from the circumnuclear disc in the 3-D data cube. Secondly, the conversion factor to use to convert \ufb02uxes to masses is quite uncertain and the value used here likely represents a lower limit. In addition, the out\ufb02ow velocity may well be larger than our conservative estimate, while we can also only set an upper limit to the projected size of the out\ufb02ow region. Projection e\ufb00ects could play a role and the true size of the out\ufb02ow region, if the out\ufb02ow is quite collimated and directed close to the line of sight, might be larger. Despite all these uncertainties, it is clear that the molecular out\ufb02ow is much more massive than the one seen in the ionised gas which has an out\ufb02ow rate of \u02d9 M < 10 M\u2299(Holt et al. 2006; Santoro et al. in prep.). The kinetic power associated with the molecular out\ufb02ow can be estimated using \u02d9 E = 6.34 \u00d7 1035( \u02d9 M/2)(v2 + 3\u03c32) (Rodr\u00edguez Zaur\u00edn et al. 2013; Mahony et al. 2016) where v is the velocity of the large-scale motion and \u03c3 the turbulent velocity. Our observations do not allow us to pin down accurate values for v and \u03c3 separately, however the kinetic power depends on the combination of the two and assuming a lower value for \u03c3 would have to be o\ufb00set by a larger assumed value for v. To obtain a rough estimate, we assume v = 600 km s\u22121 and \u03c3 = 510 km s\u22121 (FWHM = 1200 km s\u22121), giving an estimated kinetic power of the molecular out\ufb02ow of a few times 1044 erg s\u22121. Holt et al. (2006) estimated the bolometric luminosity of PKS 1549\u221279 to be between 9 \u00d7 1045 erg s\u22121 and 4 \u00d7 1047 erg s\u22121, while Santoro et al. (in prep.) estimate the bolometric luminosity to be 6 \u00d7 1045 erg s\u22121. Thus, the ratio between the kinetic energy carried away in the molecular out\ufb02ow and the bolometric luminosity is of the order of a few per cent. 5. Results: properties of the continuum emission 5.1. The structure of the radio continuum Figure 2 shows our 2.3-GHz radio continuum image as obtained from our VLBI observations while Fig. 11 shows the comparison of this image with our super-resolved 100-GHz image. The structure recovered in the new VLBI image is, to \ufb01rst order, similar to that in the VLBI image presented by Holt et al. (2006) based on observations performed between November 1988 and March 1992. It should be noted that this latter VLBI image was obtained using a smaller bandwidth (2 MHz) and single polarisation, therefore having much lower sensitivity. It is clear that the structure of the continuum source is strikingly similar at 2.3and 100 GHz, despite the factor 50 di\ufb00erence in frequency. This strong similarity shows that at mm wavelengths the radio continuum is dominated by non-thermal emission. The radio continuum emission of PKS 1549\u221279 consists of a strong central nuclear region with a strong core and a small jet with a position angle of about 45\u25e6. A small counterjet in the opposite direction is also detected near the core. In addition, a large jet-like structure is present, eastwards of the core, extending to about 120 mas (300 pc) and having a di\ufb00erent orientation than the inner jet, giving the overall appearance of a bent radio structure. The two features do not appear to be connected, with a gap of about 30 mas (80 pc) in between them. Interestingly, our new VLBI image shows that the nuclear region is relatively symmetric, showing a jet and a counter-jet. The counter-jet is also visible in the high-resolution 8.4 GHz image of Ojha et al. (2010) and in the super-resolution ALMA 100 GHz image. On the other hand, on larger scales, no emission is seen on the western side of the core and the radio structure is very asymmetric. This could be caused by the jet being more or less aligned with the line-of-sight so that relativistic beaming e\ufb00ects play a role as suggested in earlier studies (e.g. Holt et al. 2006), but it could also be caused by an asymmetric interaction between the jets and the ISM. To shed some light on this, we compared our VLBI image with the 2.3 GHz VLBI image presented in Holt et al. (2006) (see also Tzioumis et al. 2002 for more technical details) made from data taken between November 1988 and March 1992, about 17 years before our observations. Any change in the structure due to super-luminal motion over these 17 years would indicate that the jet is quite aligned with the line of sight. Although some details appear di\ufb00erent in the two images, no shift is seen in the position of the knots along the jet at the level of about 5 mas (i.e. 3 beam sizes in the E-W direction). Because of this, we conclude that, at least for the large-scale jet, we do not see evidence of superluminal motion to explain the strong asymmetry observed on the hundred-pc scale. In this respect, the detection of a counter-jet in the nuclear region is interesting because this makes the hypothesis of a the jet being along the line-of-sight less compelling than previously thought. This, together with the bending of the large scale jet, suggests that instead the morphology of the radio continuum is a\ufb00ected by a strong interaction of the jet with the surrounding rich ISM. 5.2. Spectral index The integrated spectral index (\u03b1, here de\ufb01ned by S \u223c\u03bd\u03b1) of PKS 1549\u221279 between 2.7 and 4.8 GHz was found to be relatively \ufb02at \u03b1 = \u22120.17 by Morganti et al. (1993). However, given that the observations were taken at di\ufb00erent epochs, the e\ufb00ect of radio variability cannot be excluded (as also noted by Holt et al. 2006). Indeed, looking at the data taken at di\ufb00erent times and Article number, page 9 of 14 A&A proofs: manuscript no. ALMA_PKS1549-aph Fig. 11. VLBI 2.3-GHz continuum (grey scale) superposed on the super-resolved 100-GHz image (black contours). Contour levels are 0.15, 0.3, 0.6, 1.2 and 2.4 mJy beam\u22121. frequencies as part of the monitoring campaign of ATCA calibrators2 (of which PKS 1549\u221279 is part), one can see that the spectral index between 2.1 and 5 GHz has become increasingly steeper in recent years. The \ufb02ux density of PKS 1549\u221279 at 5 GHz has decreased by about a factor 2 between the observations done in 1991\u20131992 as presented in Morganti et al. (1993) and monitoring measurements done in 2016. This suggests that the activity of the core, the component providing the dominant contribution to the \ufb02ux, is changing quite dramatically on relatively short time scales and, in addition, that other structures, such as the radio jets, provide a relatively larger contribution to the spectral index at later times. The change in the core activity could be taken as a signature of the intermittent fuelling of the SMBH, possibly as result of feedback. Furthermore, a clear curvature is present in the integrated spectrum, with the spectral index steepening at higher frequencies and a \ufb02attening observed at low frequency (below a few hundred MHz) when data from the GLEAM survey at 150 MHz (Hurley-Walker et al. 2017) are considered. Curvature of the spectrum at such low frequencies, if due to synchrotron selfabsorption, is usually associated with older sources with characteristic sizes of a few kpc (Snellen et al. 2000), much larger than PKS 1549\u221279. This could be an indication that the source is actually older than what the size would suggest, possibly due of the con\ufb01ning action of the rich gaseous medium. The steepening at high frequencies is further con\ufb01rmed by the \ufb02uxes derived from the ALMA data. Furthermore, using the VLBIand the super-resolved ALMA data, we can separate the emission of the core region (including the inner jet and the counter jet) from that of the more extended jet and derive their respective spectral indices (see Table 2). Table 2 shows that there is a clear di\ufb00erence between the spectral index of the nuclear region and that of the jet: between 2.3 and 100 GHz, the spectrum of the extended jet a few hundred pc from the core is steep (\u03b1 \u223c\u22121.15) while the core region has a \ufb02atter spectrum (\u03b1 \u223c\u22120.6). Steeper spectra are seen between 100 and 300 GHz for both components. A di\ufb00erence between the spectral indices of the core and of the large-scale jet was already noted by Holt et al. (2006), although we \ufb01nd a steeper spectral index for the core region than Holt et al. (2006). We reiterate that 2 See the ATCA calibrator database, https://www.narrabri. atnf.csiro.au/calibrators/calibrator_database_viewcal? source=1549-790 Table 2. Continuum \ufb02ux densities and spectral indices derived from the ALMA and VLBI observations. S 2.3 GHz S 100 GHz S 300 GHz \u03b12.3 100 \u03b1100 300 (Jy) (Jy) (Jy) Core 3.02 0.354 0.147 \u20130.57 \u20130.80 Jet 1.78 0.023 0.0038 \u20131.15 \u20131.64 the spectral index of the core region should be taken with care because it could be a\ufb00ected by variability. The steep spectral index of the jet found by Holt et al. (2006) is con\ufb01rmed by our data. A very steep spectrum (steeper than about \u20131.2) is often associated with dying structures where the energy injection by the active nucleus has stopped. However, for a limited number of sources that are still relatively young (and small), very steep spectrum structures have been detected. In particular, fader sources (e.g. 1542+323, Kunert-Bajraszewska et al. 2005; 0809+404, Kunert-Bajraszewska et al. 2006) are possible examples of young radio sources that are dying. A well studied case is PKS 1518+047 (Orienti et al. 2010), where the entire structure is characterised by a very steep spectrum and the core is lacking. An other possible example is PKS B0008\u2013421 (Callingham et al. 2017). In the case of PKS 1549\u221279, we may be seeing a dying remnant structure (the jet on hundred-pc scale) not being fed by the AGN anymore. This could be the result of a temporary disruption of the jet, or of intermittent fuelling of the AGN, both due to a strong interaction of the jet with the rich medium in which the AGN is embedded. 6. Accreting and out\ufb02owing molecular gas 6.1. Overall properties of the molecular gas The high-resolution observations of the molecular gas that we present in this paper help to derive a picture of the crucial early phases of the evolution of PKS 1549\u221279, and of the role the AGN plays in this. Earlier observations had revealed several interesting features in PKS 1549\u221279 which we brie\ufb02y summarise here, following the results presented in Holt et al. (2006) and references therein. Optical observations had shown the presence of large-scale tail-like structures in the ionised gas and in the stellar distribution, indicating a recent merger has occurred and that this merger is still in progress. The high FIR luminosity of PKS 1549\u221279 indicates that this merger is gas rich and a that large amount of star formation is associated with this merger. In addition, the data showed that PKS 1549\u221279 contains a highly reddened AGN, associated with a small radio source, which must be obscured by a large amount of gas in the central regions. A newly born radio jet was detected which is \ufb01ghting its way out the dense, rich medium of the merger remnant and which appears to drive an out\ufb02ow of warm gas, as detected through blueshifted, very broad optical emission lines, although the energy carried by this warm out\ufb02ow is relatively small and is not capable of clearing the central regions. This picture is further con\ufb01rmed and expanded by our CO observations. Overall, our data show that the merger drives large amounts of molecular gas towards the central regions where this gas feeds strong star formation and where some of the gas is settling in a circumnuclear disc. Part of this central gas reservoir is able to feed the active super-massive black hole. On the other hand, a strong out\ufb02ow of gas occurs in the very centre. Given that this out\ufb02ow occurs only in the very inner regions suggests Article number, page 10 of 14 Oosterloo et al.: Feeding and feedback in PKS 1549\u201379 that the AGN drives the out\ufb02ow. Therefore feedback and fuelling co-exist and interact with each other. The variability and other properties of the radio continuum suggest that the fuelling of the AGN is intermittent, possibly as the result of a continuously changing balance between feedback and fuelling. On the larger, kpc scales, we detect a large amount (\u223c1010 M\u2299) of molecular gas. This is consistent with the ULIRG/FIR properties of PKS 1549\u221279 and its large amount of star formation. Our observations also show that, on these scales, the molecular gas forms two tails, which mirror those seen for the stars and for the ionised gas. The total extent of the northern tail is about 1\u2032\u2032 .5 arcsec (about 4 kpc), while the length of the southern tail is about 0\u2032\u2032 .5 arcsec (about 1 kpc). Interestingly, although the linear structure these tails form on the sky suggests that we see these tails fairly edge on, the velocity gradient we detect over them is very small, suggesting the kinematics on the largest scales is dominated by radial motions, in the plane of the sky. This could indicate a large-scale inward gas \ufb02ow which would lead to gas piling up in the central regions. In the inner regions, the brightness distribution and the kinematics of the CO gas is very di\ufb00erent and the gas forms a distinct component there, which is rotating about the centre. In particular, the CO(3-2) is bright in the inner few hundred parsec and the velocity width of the emission there is much larger than in the tidal tails. The kinematics in the central regions appears more settled, being quite symmetric with respect to the centre and with clear signs of rotation. All this suggests that in the inner regions, the molecular gas forms a circumnuclear disc with a radius of about 240 pc and which is seen at fairly high inclination. In projection, this disc runs north-south over the nucleus, perpendicular to the jet axis and covering the AGN. The observed column densities of the circumnuclear disc are consistent with those derived from optical and X-ray observations, suggesting that the strong extinction seen in the optical spectrum of the AGN is coming from this circumnuclear disc. The impact of the AGN on the gas of the circumnuclear disc in PKS 1549\u221279 becomes clear from studying the line ratio R31 of the molecular gas. Similar to what is seen for other AGN, the gas in the direct vicinity of the AGN shows high values for the line ratio (R31 > 1), very di\ufb00erent from the gas in the large-scale tails at larger radii which shows ratios typical for a normal ISM. The high values observed in the central regions imply that the molecular gas near the AGN is optically thin and has elevated excitation temperatures. Close inspection of the distribution of R31 in the data cube suggests that the inner parts of the circumnuclear disc have the highest values of R31. In this inner region, it is also the gas with the highest velocities with respect to the systemic velocity which has the highest line ratios, however this could be partly due to overlap in the data cube of AGN-a\ufb00ected emission from the circumnuclear gas and the quiescent largescale tails. Although the e\ufb00ect of the AGN on the cold ISM in PKS 1549\u221279 appears to be limited to the inner regions, the impact there is likely very signi\ufb01cant and with the observed mass out\ufb02ow rates, the circumnuclear disc could be destroyed on a relatively short time scale. The gas mass of the circumnuclear disc is a few times 108 M\u2299, while the mass out\ufb02ow rate is at least 650 M\u2299yr\u22121. This means that on a time scale of \u223c105 yr the AGN would be able to destroy the central disc. On the other hand, gas from large radius is \ufb02owing towards the centre, providing material for rebuilding the disc. 100 pc Fig. 12. Relative extent of the [O III] emission (HST data from Batcheldor et al. 2007; red contours) compared to the super-resolved 100-GHz radio continuum (green contours) and the region of the broad CO(1-0) pro\ufb01le (blue contours). The CO(1-0) distribution was obtained by integrating the CO(1-0) data cube over the velocity range \u2013300 km s\u22121 to \u20132000 km s\u22121. Contour levels for the HST data are 0.25, 35.4, 50, 70.7 and 100% of the peak emission while for the CO(1-0) they are 50 and 100% of the peak. 6.2. Possible scenarios for the out\ufb02ow The molecular out\ufb02ow we detect in the form of a very broad CO pro\ufb01le at the position of the AGN is likely the molecular counterpart of the ionised out\ufb02ow detected earlier by Holt et al. (2006). From our data we cannot unambiguously derive which mechanism (starburst, wind, radiation pressure or radio jet) is causing these phenomena. Indeed, all candidate processes are present in PKS 1549\u221279: a strong starburst is occurring in PKS 1549\u221279 and furthermore, of the objects studied so far where molecular out\ufb02ows have been detected, PKS 1549\u221279 is one of the strongest radio sources. At the same time, it harbours a powerful optical AGN (Holt et al. 2006). The existence of an Ultra Fast Out\ufb02ow (UFO) with a speed of about 0.28c is detected in the X-ray spectrum (Tombesi et al. 2014), which suggests that a wind from the accretion disc is also present. In Fig. 12 we compare the relative extent of the [O III] out\ufb02ow seen in the HST image of Batcheldor et al. (2007), the region of the CO out\ufb02ow and the radio jet3. We note that, based on the accurately measured o\ufb00set between the quasar nucleus that dominates the K-band image of Inskip et al. (2010) and a nearby star that is detected in both the K-band and the optical HST images, the AGN is not centred on the brightest part of the [O III] emission, but rather on a secondary peak \u223c0\u2032\u2032 .07 (190 pc) to the southwest. Thus, the brightest [O III] emission could represent the site of a past jet-cloud interaction that has de\ufb02ected the jet. However, the jet is unlikely to be currently interacting 3 The optical spectroscopy of Tadhunter et al. (2001); Holt et al. (2006) and Santoro et al. (in prep.) shows that the [O III] emission integrated over a large aperture centred on the AGN is dominated by the out\ufb02ow component, with the entire [O III] emission-line pro\ufb01le shifted by several 100 km s\u22121. Therefore we can be con\ufb01dent that the HST narrowband [O III] image maps the warm out\ufb02ow Article number, page 11 of 14 A&A proofs: manuscript no. ALMA_PKS1549-aph with the cloud, else we would expect to detect a bright radio knot close to the peak of the [O III] emission. Based on these HST data, Batcheldor et al. (2007) concluded that there is no evidence for bi-conical emission-line features which one would expect for an out\ufb02ow driven by strong star formation. Figure 12 indeed shows that the [O III] out\ufb02ow is one-sided. However, starformation driven out\ufb02ows can be asymmetric. In addition, extinction e\ufb00ects, which are known to play a role in PKS 1549\u221279 (Holt et al. 2006), could make the ionised out\ufb02ow appear much more asymmetric than it actually is. Hence, the one-sidedness observed for the ionised out\ufb02ow does not completely exclude it is driven by a star burst. The warm out\ufb02ow emerges from the nucleus with the same position angle as the inner radio jet which suggests a link between the jet and the out\ufb02ow, but the radiooptical agreement deteriorates as the jet curves around while the orientation of the [O III] out\ufb02ow does not seem to change there. Interestingly, Fig. 12 also shows that the spatial extent of the [O III] out\ufb02ow is larger than that of the CO out\ufb02ow. The [O III] out\ufb02ow extends to about a radius of 0\u2032\u2032 .07 whereas the CO out\ufb02ow is unresolved in our data (r < 0\u2032\u2032 .045). The fact that the molecular out\ufb02ow only occurs within r < 120 pc may argue for the AGN to be driving the out\ufb02ow, because the strong star formation is likely to happen over a larger region. The strati\ufb01cation we may be seeing between the molecularand ionised out\ufb02ow could \ufb01t with a scenario where a jet that is working its way through a clumpy ISM is responsible for the turbulence and the out\ufb02ow, as has been modelled recently using simulations of a jet moving through a clumpy ISM (e.g. Mukherjee et al. 2018a). In the initial stages of such an interaction, the progress of the jet is intermittently blocked by the denser clumps in the ISM, causing the jet to meander through the ISM, moving from dense cloud to dense cloud. This is suggested by the results on the morphology and spectral index of the radio continuum of PKS 1549\u221279 described in Sec. 5. The interaction process can be highly asymmetrical as it depends on the detailed local clumpy structure of the ISM. While the jet is temporarily blocked, large amounts of energy are dumped by it in the ISM. According to the simulations, in this way, the jet produces a cocoon of shocked gas of mixed density and temperatures, as well as a back\ufb02ow which expands in all directions through the ISM. This induces strong turbulence in the ISM in all directions, including in the molecular gas. After the jet has meandered through the ISM for a while, the over-pressured cocoon of warm/hot gas breaks out from the clumpy ISM and a strong out\ufb02ow of warm/hot gas is created into the halo of the galaxy, perpendicular to the ISM disc. The orientation of this second phase is more or less independent of the relative orientation of the jet and disc. In the models, the time scale of the e\ufb00ects depends on the relative orientation of the jet and the disc, being longer if the jet is oriented in the plane of the disc, but even if the jet is perpendicular to the denser disc, strong interactions and out\ufb02ows occur in the ISM. To some extent, in this kind of model, two kinds of feedback occur. One is the direct interaction of the jet with dense gas clumps, directly a\ufb00ecting the denser ISM near the AGN. The other is dumping energy, through the warm out\ufb02ow, in the larger-scale, less dense gaseous halo of the galaxy, increasing the time scale over which the gas in the halo can cool and form stars (maintenance mode feedback). At least qualitatively, this model may describe the out\ufb02ows we see in the molecularand in the ionised gas. The molecular out\ufb02ow would come from the region of direct feedback and would correspond to that part of the interaction where the jetin\ufb02ated cocoon is driving turbulence in the denser gas disc. The relatively small extent of the region showing elevated line ratios in the molecular gas suggests that the denser ISM is a\ufb00ected out to about 0.5 kpc radius. The turbulent/out\ufb02owing molecular gas could represent denser clumps in the jet-driven out\ufb02ow that have short cooling times, or clouds that have had more time to cool following an earlier interaction with the turbulent jet cocoon (earlier since closer to the nucleus). In contrast, the more extended emission-line out\ufb02ow detected in [O III] could represent gas that has broken out of the disc and is currently \ufb02owing into the lower density halo of the galaxy. This gas has perhaps been accelerated and ionised by a shock induced by the in\ufb02ating jet cocoon. The fact that this gas is still ionised and has not yet cooled to a molecular phase could be because it has a lower density and hence a longer cooling time. Alternatively, it has a higher density, but has been accelerated in a more recent interaction with the expanding jet cocoon and has not yet have time to cool. The latter would be consistent with the high densities observed in the [O III] out\ufb02ow in PKS 1549\u221279 from the X-shooter spectrum presented in Santoro et al. (in prep). The molecular gas in the large-scale tails at much larger radii (several kpc) appears to be una\ufb00ected by the AGN (so far) and it is unlikely that the evolution of the gas on these larger scales, and the star formation from this gas, will be changed by the AGN activity. If what we see in PKS 1549\u221279 represents a phase in galaxy evolution common to many galaxies, it is useful to compare the results presented here with what found for other objects available in literature. A number of cases are known now for which observations suggest the scenario of a jet interacting with dense clumps in the ISM is happening in many objects. Interestingly, these include AGN of both lowand high radio power. In Husemann et al. (2019a), a rich set of multi-wavelength observations are presented of the low-power AGN HE 1353 \u22121917. In this object, the jet is moving in the plane of the disc and is driving a multi-phase out\ufb02ow over a region of about 1 kpc. Using observations in several wavebands, Husemann et al. (2019a) were able to show that it is most likely that the plasma jet is responsible for this. Another recent case is the well-known quasar 3C 273 (Husemann et al. 2019b) where the data suggests the presence of an expanding over-pressured cocoon of hot gas created by the powerful radio jet which impacts on an inclined gas disc and which drives fast transverse and/or back\ufb02ow motions. Another case for which detailed information is available is IC 5063 (Morganti et al. 2015; Oosterloo et al. 2017), where the close morphological match between the radio jet and the region of molecular gas with elevated line ratios and extreme kinematics is a strong indication that the interaction between the radio plasma with the ISM is the main mechanism for disturbing the gas and for a\ufb00ecting its excitation. In HE 1353\u20131917 and IC 5063, the highest excitation and the most extreme kinematics do not occur at the core, but along the entire jet where it appears to be interacting strongly with the ISM. The spatial resolution of our CO(3-2) data on PKS 1549\u221279 is not su\ufb03cient to investigate in great detail whether similar processes occur in PKS 1549\u221279, but there are hints that in PKS 1549\u221279 the situation is di\ufb00erent and that instead the AGN-a\ufb00ected gas is found near the core and not along the jet. There are no features in the CO morphology and kinematics along the jet that would suggest that the conditions are peculiar there. Instead, both the CO(10) and CO(3-2) clearly peak at the core and the highest line ratios, as well as the kinematically disturbed gas, are observed there. One reason for these di\ufb00erences could be the large disparity in jet power between HE 1353\u20131917 and IC 5063 on the one hand and PKS 1549\u221279 on the other. The simulations of Mukherjee et al. (2018a,b) show that a low-power jet may afArticle number, page 12 of 14 Oosterloo et al.: Feeding and feedback in PKS 1549\u201379 fect a very large region of the dense ISM because the jet takes much more time to break through the ISM, while a more powerful jet pierces through the dense ISM relatively more quickly. In addition, the fact that in HE 1353\u20131917 and IC 5063 the orientation of the jet is such that the jet moves in the plane of the gas disc, while in PKS 1549\u221279 the jet is not aligned with the disc, may play a role in explaining the di\ufb00erences. Perhaps due to this, in PKS 1549\u221279 the out\ufb02ow, despite the more powerful AGN, is limited to the inner \u223c120 pc. Common among all examples mentioned here is that the radio jet seems to have an impact up to a few kpc from the AGN and less so on its overall ISM (see also Murthy et al. 2019). Despite the relatively small region a\ufb00ected in PKS 1549\u221279, the molecular out\ufb02ow rate is large, at least 650 M\u2299yr\u22121, and much larger than that seen for the ionised gas. This is similar to other cases of obscured quasars, or to galaxies observed to be in the process of quenching and where molecular out\ufb02ows have been found (e.g. Sun et al. 2014; Brusa et al. 2018; HerreraCamus et al. 2019; Veilleux et al. 2017). Fiore et al. (2017), albeit based on a heterogeneously selected sample, have claimed that the di\ufb00erence between ionisedand molecular out\ufb02ow rates decreases for the most luminous AGN (Lbol > 1046 erg s\u22121). An example is the powerful obscured quasar XID2028 for which Brusa et al. (2018) found similar mass out\ufb02ow rates for the ionised and the molecular gas. However, the reported trends do not take into account that in some objects the radio jets can be the dominant driver of the out\ufb02ow, instead of the AGN luminosity, so the situation may be more complicated. In the case of PKS 1549\u221279, despite being a powerful optical and radio AGN, we \ufb01nd a large di\ufb00erence in mass out\ufb02ow rate between the molecular and the ionised out\ufb02ow. This suggests that either the trends with AGN luminosity are more complicated, or a more prominent role for di\ufb00erent mechanisms, such as the radio jet (for which the connection between jet power and out\ufb02ow parameters is still not properly investigated). Statistical studies of representative samples are still scarce. The only survey of molecular gas in similar objects (local ULIRGs and QSO\u2019s) is the one of Cicone et al. (2014) where they con\ufb01rm the high incidence of molecular out\ufb02ows. The situation is less clear for dust-obscured galaxies (DOGs) with only a few (high redshift) objects studied so far with ALMA and where contradictory results were obtained, although not many out\ufb02ows were detected (see Toba et al. 2017; Fan et al. 2018). A common conclusion is that in all cases studied in detail, the gas depletion times of the inner region are relatively short (\u223c105 106 yr) and, therefore, these massive out\ufb02ows are representing a relatively short (but likely recurrent) phase in the evolution of these objects. These short depletion times may be connected to observations of AGN that seem to be dying or \ufb02ickering on very short time scales (e.g. Ichikawa et al. 2019; Schawinski et al. 2015). 7. Conclusions With our ALMA CO(1-0) and CO(3-2) observations of the obscured young radio quasar PKS 1549\u221279, we detect the presence of a large amount of molecular gas (\u223c1010 M\u2299) in this object. The data show that the distribution and the kinematics of the gas is complex. We detect three distinc components: extended gas tails related to an ongoing merger, a circumnuclear disc, and a fast molecular out\ufb02ow. The large-scale tails of molecular gas reach into the central regions, feeding the large starburst occurring there. In the inner few hundred pc, the large, regular velocity gradient suggests the presence of a disc-like structure with a molecular gas mass of a few \u00d7108 M\u2299. All this is likely connected with feeding the growth of the central SMBH, which is known to be accreting at a high Eddington ratio (Holt et al. 2006). Interestingly, the observations show that a nuclear disc manages to form, despite the presence of a powerful AGN disturbing the gas in the inner regions, suggesting that feeding and feedback can co-exist. The e\ufb00ect of the AGN is seen in the form of a fast and massive out\ufb02ow detected in CO(1-0). We estimate a mass out\ufb02ow rate of at least 650 M\u2299yr\u22121, possibly substantially higher. This is much larger than the mass out\ufb02ow rate detected for the ionised gas (Holt et al. 2006; Santoro et al. in prep.). The impact of the AGN on the gas is also con\ufb01rmed by the higher excitation of the molecular gas in the very central region as derived from the line ration R31. The molecular out\ufb02ow could destroy the circumnuclear disc on a time scale of only 105 yr, although gas from the merger is moving in radially, possibly (partly) rebuilding the disc at the same time. Despite the presence of a powerful radio source and a quasar nucleus, the massive out\ufb02ow is con\ufb01ned to the inner region (radius < 120 pc) of the galaxy. The region of the out\ufb02ow of ionised gas present in PKS 1549\u221279 appears to be more extended than that of the molecular gas. No AGN related e\ufb00ects are seen at radii larger than 0.5 kpc and most of the ISM in PKS 1549\u221279 is una\ufb00ected by the AGN. The data are consistent with recent numerical models of a young plasma jet interacting with a clumpy ISM. In such models, the progress of the jet is blocked intermittently by dense clumps, leading to large amounts of energy being dumped in the ISM. This results in an over-pressured cocoon of gas with a wide range of densities and temperatures, large amounts of turbulence in the ISM, and an out\ufb02ow of gas. The molecular gas a\ufb00ected by turbulence/out\ufb02ow may correspond to the denser clumps in this cocoon so they have a shorter cooling time. At some point in time, the hot/warm gas of the cocoon breaks out from the dense ISM, into the less dense halo of the host galaxy. The ionised out\ufb02ow may correspond to this phase. Alternatively (or additionally), the disturbed molecular gas may be gas closer to the AGN so that it was a\ufb00ected by the jet earlier and thus has had more time to cool while the ionised out\ufb02ow is gas at larger radius so that it is affected by the jet later and thus has had less time to cool. This warm out\ufb02ow will dump energy gaseous halo on larger scales and may help prevent cooling of the halo gas which may reduce future star formation (e.g. Costa et al. 2018). In summary, the data show the complexity of feeding and feedback in action at the same time in the inner regions. On the other hand, the AGN does not seem to have a large impact on the overall ISM on the largest scales and the feedback e\ufb00ects are limited to the central few hundred parsecs. A comparison of the properties of a, still small, group of AGN for which good data on both the warm, ionisedand the cold, molecular out\ufb02ows are available, shows similarities with PKS 1549\u221279, but also a number of di\ufb00erences. Like in IC 5063 and HE 1353 \u22121917, the AGN appears to a\ufb00ect not only the kinematics, but also the physical conditions of the surrounding gas. This is despite the more than two orders of magnitude difference in radio power between PKS 1549\u221279 and these two objects. Improved statistics on the e\ufb00ects of di\ufb00erences in radio power of the jet, as well as their inclination with respect to the distribution of the gas, is needed to properly quantify the impact of radio jets. Furthermore, the molecular out\ufb02ow, despite being limited to a small region, appears to carry most of the out\ufb02owing gas. This does not agree with the \ufb01ndings of Fiore et al. (2017) which suggest that the di\ufb00erence between warm Article number, page 13 of 14 A&A proofs: manuscript no. ALMA_PKS1549-aph ionised and molecular out\ufb02ow rates decreases for the most luminous AGN (Lbol > 1046 erg s\u22121). Considering the high bolometric luminosity of PKS 1549\u221279, the two order of magnitude di\ufb00erence between the warm ionised and the molecular out\ufb02ows suggests that understanding the relation between AGN luminosity and mass out\ufb02ow rate requires a better understanding of the driving mechanism (i.e. wind/radiation vs radio jet), something that has not been taken into account so far. PKS 1549\u221279 represents a rare, local example of an obscured quasar, but at higher redshift, such objects are now being detected in increasing numbers on the basis of their extreme Spitzer/Wise mid-IR colours (e.g. Dust-Obscured Galaxies or Hot DOGs, Wu et al. 2012), and at least some of them are radioloud (Lonsdale et al. 2015). Like PKS 1549\u221279, these sources are still enshrouded in their natal cocoon of gas. Our results demonstrate the potential of ALMA molecular line observations for understanding the evolution of such objects. Acknowledgements. We thank Katherine Inskip for providing the fully reduced VLT/ISAAC K-band image of PKS 1549\u221279 and the surrounding \ufb01eld that was used to improve the astrometric registration of the optical HST and and mm ALMA images. We also thank Joe Callingham for providing the GLEAM data. This paper makes use of the following ALMA data: ADS/JAO.ALMA#2017.1.01571.S. ALMA is a partnership of ESO (representing its member states), NSF (USA) and NINS (Japan), together with NRC (Canada), MOST and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO and NAOJ. The Australia Telescope Long Baseline Array is part of the Australia Telescope National Facility which is funded by the Australian Government for operation as a National Facility managed by CSIRO.",
                    "introduction": "Research in the past twenty years has told us that active super- massive black holes (SMBH) play an important role in galaxy evolution due to the enormous amount of energy they can re- lease. Interestingly, the attempts to understand the impact of such active galactic nuclei (AGN) feedback have brought new, unex- pected insights into the physical conditions in the central regions of their host galaxy. The presence of fast, massive out\ufb02ows of atomic (H i) and molecular gas represents an important manifes- tation of feedback. However, studies of AGN feedback have also shown how complex this process is. This partly re\ufb02ects the com- plexity of the AGN phenomenon itself, as well as the variety of the di\ufb00erent processes involved in the surrounding gas. Indeed, among the many open-ended questions is the relative role of dif- ferent types of AGN (Wylezalek & Morganti 2018, Harrison et al. 2018) and how the energy they release actually couples to the surrounding medium. Gas out\ufb02ows are believed to play an im- portant role in this. However, only in a few cases do the out\ufb02ows seem to go beyond a few kpc distance from the nucleus. This puts into question the impact they may have on regulating star formation on the scale of the entire galaxy. A better understand- ing of the properties of out\ufb02ows in relation to the properties of the AGN is still required. AGN-driven out\ufb02ows have been found to be multi-phase: gas in all phases \u2013 neutral atomic, molecular, and warm and hot ionised \u2013 can be present. Despite the large amount of en- ergy released by the active black hole, the cold component (i.e. atomic and molecular gas) of the out\ufb02ow often appears to be the most massive one, although observations are still limited to a relatively limited number of objects. Thus, these cold out\ufb02ows likely have the largest impact in terms of kinetic energy and mass out\ufb02ow rate (see e.g. Feruglio et al. 2010; Alatalo et al. 2011; Dasyra & Combes 2012; Cicone et al. 2014; Morganti et al. 2005; Morganti et al. 2013; Morganti et al. 2015; Herrera- Camus et al. 2019), with the possible exception of extremely powerful AGN (see Fiore et al. 2017; Brusa et al. 2018). Out\ufb02ows appear to be more common and more prominent in speci\ufb01c phases of the evolution of an AGN. The \ufb01rst phases of nuclear activity are particularly interesting in which the SMBH has just become active and is still embedded in the interstellar Article number, page 1 of 14 arXiv:1910.07865v1  [astro-ph.GA]  17 Oct 2019 A&A proofs: manuscript no. ALMA_PKS1549-aph medium (ISM) of the host galaxy. This phase has been explored in young radio galaxies (see e.g. Holt et al. 2008, 2009; Gupta & Saikia 2006; Ger\u00e9b et al. 2015), in highly obscured quasars (e.g. Brusa et al. 2018; Sun et al. 2014), and in dust-obscured galaxies (DOGs; Toba et al. 2017; Fan et al. 2018 and refs therein). In young radio galaxies, an out\ufb02ow of cold gas can already start very close (a few tens of pc) to the active SMBH (Schulz et al. 2018). This brings into question how cold gas can be involved in such energetic events so close to the AGN while also giving information on the relative lengths of the evolutionary time-scale of the AGN and the cooling time of the gas (e.g. Richings & Faucher-Gigu\u00e8re 2018). It also raises questions about possible interplay between these out\ufb02ows close to the AGN and the in- falling gas, which fuels the AGN. Several mechanisms have been suggested to drive gas out- \ufb02ows. This is important in the context of the relevance of di\ufb00er- ent types of AGN for feedback. Most commonly it is assumed that out\ufb02ows are driven by radiation pressure, or by a hot ther- mal wind launched from the accretion disc that interacts with the surrounding gaseous medium and extends to large scales (e.g. Faucher-Gigu\u00e8re & Quataert 2012; Zubovas & King 2012; Zubovas, & King 2014). Support for the latter mechanism comes from, for example, the correlation between the luminosity of the AGN and the properties of the out\ufb02ows as seen in samples of di\ufb00erent types of objects (e.g. Fiore et al. 2017; Fluetsch et al. 2018). However, out\ufb02ows can also be driven by radio plasma jets, and the number of known cases has been growing steadily, in- cluding low-power (e.g. Alatalo et al. 2011; Garc\u00eda-Burillo et al. 2014; Morganti et al. 2015; Rodr\u00edguez-Ardila et al. 2017; Runnoe et al. 2018; Husemann et al. 2019a) and high-power ra- dio AGN (e.g. Nesvadba et al. 2008; Holt et al. 2009; Morganti et al. 2005; Husemann et al. 2019b). Numerical simulations are \ufb01nding that radio plasma jets can actually couple strongly to the clumpy ISM of the host galaxy (Wagner et al. 2012; Mukherjee et al. 2016; Cielo et al. 2018; Mukherjee et al. 2018a,b). Ac- cording to these numerical simulations, a clumpy ISM, instead of a smooth one, can make the impact of the jet much larger than previously considered. Due to the clumpiness of the gaseous medium, the progress of the jet can be temporarily halted when it hits a dense gas cloud and the jet meanders through the ISM to \ufb01nd the path of minimum resistance and this creates a cocoon of shocked gas driving an out\ufb02ow in all directions (Wagner et al. 2012; Mukherjee et al. 2016, 2018a). The jet power, the distribu- tion of the surrounding medium and the orientation at which the jet enters the medium are important parameters that determine the \ufb01nal impact of such jet-ISM interactions (Mukherjee et al. 2018a). In this paper, we study the molecular gas in PKS 1549\u221279, an object where the AGN is in the crucial early phases of its evolu- tion, while still being embedded in a dense ISM. PKS 1549\u221279 is one of the closest (z = 0.1525) examples of a young, radio- loud quasar1 (P2.3GHz = 2.7 \u00d7 1025 W Hz\u22121), where the quasar nature is detected via broad emission lines in the near-IR, but is heavily obscured at optical wavelengths (Bellamy et al. 2003; Holt et al. 2006). In PKS 1549\u221279 a number of relevant processes are happen- ing. The AGN appears to be in the process of clearing its gas- rich surroundings in which it is enshrouded. A fast out\ufb02ow is observed in the warm ionised gas (Tadhunter et al. 2001; Holt 1 The cosmology adopted in this paper assumes a \ufb02at Universe and the following parameters: H\u25e6= 70 km s\u22121 Mpc\u22121, \u2126\u039b = 0.7, \u2126M = 0.3. For the assumed redshift, 1 arcsec corresponds to 2.67 kpc. et al. 2006; Batcheldor et al. 2007) and an Ultra-Fast Out\ufb02ow (UFO) has been revealed by X-ray observations (Tombesi et al. 2014). PKS 1549\u221279 is also a small radio source of only about 300 pc in size, with an asymmetric core-jet structure (Holt et al. 2006). This asymmetric structure suggests that relativistic ori- entation e\ufb00ects may play a role, or alternatively, that a strong, asymmetric interaction occurs between the radio plasma and the clumpy surrounding medium. Tadhunter et al. (2001) and Holt et al. (2006) presented a possible scenario where the newly born radio jet is \ufb01ghting its way out the dense, rich medium of the merger remnant, accelerating the out\ufb02ows and playing a key role in shedding its natal cocoon as expected in the early phases of strong feedback. At the same time, PKS 1549\u221279 has also undergone a recent major merger, as indicated by high-surface-brightness tidal tails (Holt et al. 2006; Batcheldor et al. 2007), bringing gas into the central regions of the host galaxy. Indeed, observations suggest that a large amount of gas is surrounding the nucleus and the radio source, for example as deduced from the high reddening along the line of sight to the quasar nucleus (Av > 4.9, Bellamy et al. 2003; Holt et al. 2006). The presence of a rich medium has been con\ufb01rmed by the detection of H i 21-cm absorption (Mor- ganti et al. 2001; Holt et al. 2006). A young stellar population (50\u2013250 Myr), likely resulting from gas accumulation from the recent merger, is also observed (Tadhunter et al. 2001; Holt et al. 2006). Further evidence for star formation is provided by its unusually strong far-infrared emission, which leads to its classi- \ufb01cation as an ultraluminous infrared galaxy with LIR = 1.6\u00d71012 L\u2299. Despite the high optical luminosity of the AGN and the pow- erful radio jet, the kinetic energy associated with the warm, ionised gas out\ufb02ow is only a tiny fraction of the Eddington lu- minosity of PKS 1549\u221279, and this out\ufb02ow is currently not ca- pable of removing the gas from the bulge of the host galaxy, as required by feedback models (Holt et al. 2006). Following what was found in other objects (e.g. Feruglio et al. 2010; Alatalo et al. 2011; Cicone et al. 2014; Morganti et al. 2015), much of the out\ufb02ow may be tied up in the cooler phases of the interstellar medium, in particular the molecular gas. Clearly, PKS 1549\u221279 represents an excellent object for studying how the energy released by the AGN couples to the rich surrounding medium in a stage of evolution of the AGN when feedback e\ufb00ects should be particularly prominent. Here we present new CO(1-0) and CO(3-2) observations, as well as 1- and 3-mm continuum observations obtained with the Ata- cama Large Millimeter/submillimeter Array (ALMA). We com- bine these data with new VLBI (LBA) 2.3-GHz images to shed light on the nature of the radio source and its role in the AGN- ISM interaction."
                },
                {
                    "url": "http://arxiv.org/abs/1710.01570v1",
                    "title": "Properties of the molecular gas in the fast outflow in the Seyfert galaxy IC 5063",
                    "abstract": "We present a detailed study of the molecular gas in the fast AGN-driven\noutflow in the nearby radio-loud Seyfert galaxy IC 5063. Using ALMA\nobservations of a number of tracers (12CO(1-0), 12CO(2-1), 12CO(3-2), 13CO(2-1)\nand HCO+(4-3)), we map the differences in excitation, density and temperature\nof the gas. The results show that in the immediate vicinity of the radio jet, a\nfast outflow, with velocities up to 800 km/s, is occurring of which the gas has\nhigh excitation temperatures in the range 30-55 K, demonstrating the direct\nimpact of the jet on the ISM. The relative brightness of the CO lines show that\nthe outflow is optically thin. We estimate the mass of the molecular outflow to\nbe 1.2 x 10^6 Msol and likely to be a factor 2-3 larger. This is similar to\nthat of the outflow of atomic gas, but much larger than that of the ionised\noutflow, showing that the outflow is dominated by cold gas. The total mass\noutflow rate we estimate to be ~12 Msol/yr. The mass of the outflow is much\nsmaller than the total gas mass of the ISM of IC 5063. Therefore, although the\ninfluence of the radio jet is very significant in the inner regions, globally\nspeaking the impact will be very modest. We use RADEX modelling to explore the\nphysical conditions of the molecular gas in the outflow. Models with the\noutflowing gas being quite clumpy give the most consistent results and our\npreferred solutions have kinetic temperatures in the range 20-100 K and\ndensities between 10^5 and 10^6 cm^-3. The resulting pressures are 10^6-10^7.5\nK cm^-3, about two orders of magnitude higher than in the outer quiescent disk.\nThe results strongly suggest that the outflow is driven by the radio jet\nexpanding into a clumpy medium, creating a cocoon of gas which is pushed away\nfrom the jet axis resulting in a lateral outflow, very similar to what is\npredicted by numerical simulations.",
                    "authors": "Tom Oosterloo, J. B. Raymond Oonk, Raffaella Morganti, Francoise Combes, Kalliopi Dasyra, Philippe Salome', Nektarios Vlahakis, Clive Tadhunter",
                    "published": "2017-10-04",
                    "updated": "2017-10-04",
                    "primary_cat": "astro-ph.GA",
                    "cats": [
                        "astro-ph.GA"
                    ],
                    "main_content": "Astronomy & Astrophysics manuscript no. I5063Alma c \u20ddESO 2017 Thursday 5th October, 2017 Properties of the molecular gas in the fast outflow in the Seyfert galaxy IC 5063 Tom Oosterloo1, 2, J. B. Raymond Oonk1, 3, Raffaella Morganti1, 2, Fran\u00e7oise Combes4, 5, Kalliopi Dasyra6, 7, Philippe Salom\u00e94, Nektarios Vlahakis6, and Clive Tadhunter8 1 ASTRON, the Netherlands Institute for Radio Astronomy, Postbus 2, 7990 AA Dwingeloo, The Netherlands 2 Kapteyn Astronomical Institute, University of Groningen, Postbus 800, 9700 AV Groningen, The Netherlands 3 Leiden Observatory, Leiden University, Postbus 9513, 2300 RA Leiden, The Netherlands 4 LERMA, Observatoire de Paris, CNRS, UPMC, PSL Univ., Sorbonne Univ., 75014 Paris, France 5 Coll\u00e8ge de France, 11 place Marcelin Berthelot, 75005, Paris, France 6 Department of Astrophysics, Astronomy & Mechanics, Faculty of Physics, National and Kapodistrian University of Athens, Panepistimiopolis Zografou, 15784, Greece 7 National Observatory of Athens, Institute for Astronomy, Astrophysics, Space Applications and Remote Sensing, Penteli, 15236, Athens, Greece 8 Department of Physics and Astronomy, University of Sheffield, Hounsfield Road, Sheffield S3 7RH, UK re-submitted: Thursday 5th October, 2017 ABSTRACT We present a detailed study of the properties of the molecular gas in the fast AGN-driven outflow in the nearby radio-loud Seyfert galaxy IC 5063. By using ALMA observations of a number of tracers of the molecular gas (12CO(1-0), 12CO(2-1), 12CO(3-2), 13CO(21) and HCO+(4-3)), we map the differences in excitation, density and temperature of the gas as function of position and kinematics. The results show that in the immediate vicinity of the radio jet, a fast outflow, with velocities up to 800 km s\u22121, is occurring of which the gas has high excitation with excitation temperatures in the range 30\u201355 K, demonstrating the direct impact of the jet on the ISM. The relative brightness of the 12CO lines, as well as that of 13CO(2-1) vs 12CO(2-1), show that the outflow is optically thin. We estimate the mass of the molecular outflow to be at least 1.2 \u00d7 106 M\u2299and likely to be a factor 2\u20133 larger than this value. This is similar to that of the outflow of atomic gas, but much larger than that of the ionised outflow, showing that the outflow in IC 5063 is dominated by cold gas. The total mass outflow rate we estimate to be \u223c12 M\u2299yr\u22121. The mass of the outflow is much smaller than the total gas mass of the ISM of IC 5063. Therefore, although the influence of the AGN and its radio jet is very significant in the inner regions of IC 5063, globally speaking the impact will be very modest. We use RADEX non-LTE modelling to explore the physical conditions of the molecular gas in the outflow. Models with the outflowing gas being quite clumpy give the most consistent results and our preferred solutions have kinetic temperatures in the range 20\u2013100 K and densities between 105 and 106 cm\u22123. The resulting pressures are 106\u2013107.5 K cm\u22123, about two orders of magnitude higher than in the outer quiescent disk. The highest densities and temperatures are found in the regions with the fastest outflow. The results strongly suggest that the outflow in IC 5063 is driven by the radio plasma jet expanding into a clumpy gaseous medium and creating a cocoon of (shocked) gas which is pushed away from the jet axis resulting in a lateral outflow, very similar to what is predicted by numerical simulations. Key words. galaxies: active galaxies: individual: IC 5063 ISM: jets and outflow radio lines: galaxies The ALMA data discussed in this paper come from a number of observing sessions, while we also re-use our earlier ALMA observations of the CO(2-1) emission of IC 5063 published in Morganti et al. (2015). Since only the 12-m array was used and observations at very different frequencies are involved, we have taken care to use the proper array configurations for the different observations. This was done to ensure that the various observations have very similar spatial resolution, while in addition the uv coverages are as similar as possible such that sensitivity to different spatial scales is the same at different frequencies. No signatures of missing large-scale flux (\u2019negative bowl\u2019) were present in any of the observations. 2 https://personal.sron.nl/\u223cvdtak/radex/index.shtml The CO(3-2) and HCO+(4-3) data were taken with Band 7 on March 22, 2016, using 37 antennas. The frequency setup of the telescope employed four observing bands. Two high-resolution spectral windows, each having a total bandwidth of 1.875 GHz split over 480 channels, were used to image the CO(3-2) (centred on 341.97 GHz) and the HCO+(4-3) emission (centred on 353.05 GHz) of IC 5063. In addition, two continuum spectral windows were used, each 2 GHz wide and having 128 channels, centred on 340.1 and 352.0 GHz. The total on-source observing time was about 0.5 hr. Standard calibration observations were done, involving Titan, J2056\u22124714 and J2141\u22126411 as flux, bandpass and phase calibrators respectively. To study the properties of the 13CO(2-1) emission in IC 5063, we used ALMA in Band 6 on May 19 and 23, 2016, employing 38 and 35 antennas on the respective days. The total on-source observing time is 2.5 hr. The calibration strategy is the same as for the Band 7 observations, except that Pallas was used as a flux calibrator. Two 2-GHz wide continuum spectral windows were used (at 230.0 and 232.5 GHz, each band covered with 128 channels) as well as a higher resolution spectral window centred on 217.8 GHz (1.875 GHz wide, using 960 channels). Finally, the CO(1-0) emission of IC 5063 was observed with ALMA in Band 3 on July 25 and 26, 2016 using 45 antennas. The total on-source time was 1.9 hr. High spectral resolution data were taken using a 1.875 GHz wide band (960 channels) centred on 114.0 GHz. Continuum spectral windows of 2 GHz wide centred on 100.1 and 101.9 GHz were used to image the continuum emission of IC 5063 in this band. Also for these observations, standard calibration was done, involving the same sources as for the 13CO(2-1) observations. For all observations, the initial calibration of the data was done in CASA3 (McMullin et al. 2007)) using the calibration scripts and calibration data provided by ESO. We found, however, that we were able to significantly improve the dynamic range of the images and cubes by additional self calibration (phase only) of the continuum images of IC 5063 and apply these calibrations also to the line data. This self calibration and all subsequent imaging and data reduction were done using the MIRIAD4 software (Sault et al. 1995) as well as self-made PYTHON scripts. Our main aim is to study the relative strength of the different line transitions in different regions of IC 5063. Hence, when making the images and data cubes, care has to be taken that they have the same spatial and velocity resolution. In addition, it is well known that self calibration can introduce small position offsets in images. Therefore, we used the continuum images to determine possible offsets between data sets after the self calibration. We indeed found that the self calibration had introduced offsets of the order of 0.1 arcsec. All images and data cubes we present are corrected for these offsets. The data cubes of the main CO transitions were made using the same spatial (0\u2032\u2032 .1 pixels) and velocity gridding (10 km s\u22121 channels, but Hanning smoothing was applied to the data cubes so that the velocity resolution is 20 km s\u22121). From all three observations, data cubes were made using natural weighting. Although the uv coverages of the different observations are very similar, they are not identical. This resulted in small differences (of about 0\u2032\u2032 .05) in the resolution of the data cubes of the different transitions. We corrected the data cubes for this by smoothing the data cubes to a common resolution. This resulted in data cubes 3 http://casa.nrao.edu 4 http://www.atnf.csiro.au/computing/software/miriad Article number, page 3 of 13 A&A proofs: manuscript no. I5063Alma CO(1-0) CO(3-2) CO(2-1) WL EL C Fig. 2. Top left: integrated brightness temperature of the CO(3-2) emission (grey scale) with superposed the contours of the 346 GHz continuum, to illustrate the close spatial correspondence between the radio continuum and the bright, inner molecular structure. The core (C) and the eastern and western lobe (EL and WL respectively) are indicated. Contour levels are 0.15, 0.45, 1.35 and 4.05 mJy beam\u22121. The other panels show the integrated brightness temperature for CO(1-0) (top right), CO(2-1) (bottom left) and CO(3-2) (bottom right). Contour levels are 5, 10, 20, 40,... K km s\u22121 for these three panels, while also the colour stretch is the same for these three images. having a resolution of 0\u2032\u2032 .62. This corresponds, for the distance to IC 5063 assumed, to a linear resolution of 143 pc. All cubes were cleaned using an iterative masking technique using a lower resolution version of a cube of a previous iteration to mask emission regions to be cleaned in the high-resolution cube in the next iteration. This ensures that the emission can be cleaned below the noise level while noise peaks are not included in the cleaning process. The noise level of the CO(1-0) data cube is 0.30 mJy beam\u22121 (corresponding to 73.0 mK), of the CO(2-1) data cube 0.23 mJy beam\u22121 (13.6 mK) and that of the CO(3-2) data cube 0.55 mJy beam\u22121(15.0 mK). The HCO+(4-3) and the 13CO(2-1) data were initially treated in the same way as those of the main CO transitions and data cubes were made with the same spatial and velocity resolution as described above. However, as expected, the HCO+(4-3) and 13CO(2-1) emission is much fainter than that of the main CO lines and in the full-resolution cubes the emission is detected only close to the noise level. Therefore, in order to improve the signal-to-noise of the emission, we tapered the data to much lower spatial and velocity resolution in order to better match the spatial and velocity structure of the emission. The HCO+(4-3) and 13CO(2-1) cubes we discuss have a spatial resolution of 1\u2032\u2032 .52 (corresponding to about 350 pc) and a velocity resolution of 100 km s\u22121. The noise level of the HCO+(4-3) cube is 0.90 mJy beam\u22121 (3.8 mK) and of the 13CO(2-1) cube 0.18 mJy beam\u22121 (2.0 mK). To enable comparison, data cubes with the same low spatial and velocity resolution were also made for the main CO transitions. To study the relation between the molecular gas and the radio continuum emission, a continuum image was made (Fig. 2) by combining the continuum spectral windows observed at 340.1 and 352.0 GHz using multi-frequency synthesis (giving an e\ufb00ective frequency of about 346 GHz). Also here, natural weighting was used for gridding the uv data. The noise level of this continuum image is 50 \u00b5Jy beam\u22121 and the spatial resolution is 0\u2032\u2032 .60. This continuum image shows the same triple structure seen at 8 GHz (Morganti et al. 1998, see also Fig. 1), 17.8 and 24.8 GHz (Morganti et al. 2007) and 230 GHz (Morganti et al. 2015). The central peak is the core of radio source which connects through jets to the eastern and western lobes. The great similarity between the continuum images over this wide range of frequencies Article number, page 4 of 13 Oosterloo et al.: Properties of the molecular gas in the fast out\ufb02ow in the Seyfert galaxy IC 5063 Fig. 3. Ratio R31 of the CO(3-2) and CO(1-0) integrated brightness temperatures I (in K km s\u22121) of Fig. 2, after primary beam correction. Only those pixels are shown for which the error in R31 is smaller than 0.3. Overplotted are the contours of the 346 GHz continuum emission of IC 5063 with contour levels 0.15 (3\u03c3), 0.6, 2.4 and 9.6 mJy beam\u22121. indicates that the bulk of the radio continuum at 346 GHz is nonthermal emission from the AGN and the radio lobes. In the following, we \ufb01rst compare the distribution and kinematics of the various lines observed to study the overall impact of the radio jet on the molecular gas in the centre of IC 5063. This is followed by a more detailed analysis of the physical conditions of the gas in various regions in IC 5063. 3. Comparison between the main CO lines 3.1. Spatial distribution One of the main aims of this paper is to further study the properties of the molecular gas participating in the fast out\ufb02ow in IC 5063. In Dasyra et al. (2016) we found marked di\ufb00erences in the line ratio R42 \u2261I4\u22123/I2\u22121 between the outer disk and the inner regions. At many locations in the inner regions, R42 takes values well above 1, indicating optically thin conditions as well as excitation temperatures in the range 30\u201350 K and in some locations even higher. On the other hand, the low values found for R42 in the outer disk indicates sub-thermal excitation of the molecular gas there. The large contrast between the two regions signi\ufb01es the impact of the radio jet on the gas in the central regions of IC 5063. Here, we will do a similar analysis of the conditions in the inner regions using our new observations. As a \ufb01rst approach, we compare the sky distributions of the integrated intensity of the main CO transitions which are shown in Fig. 2. These images were made in a standard way, i.e. by masking the full-resolution data cubes using a 2-\u03c3 clipped lower resolution version of the cubes, followed by integrating the masked, high-resolution cube over velocity. Our earlier data (Morganti et al. 2015; Dasyra et al. 2016) had already shown that the distribution of the molecular gas in IC 5063, as observed in the CO(2-1) and CO(4-3) lines, consists of a bright inner structure tightly surrounding the bright radio continuum emission of the core and radio lobes, and a more extended, lower surface brightness molecular counterpart of the large H i disk of IC 5063. Figure 2 shows that, as expected, this is also the case for the other CO transitions. Figure 2 also con\ufb01rms the large di\ufb00erence of the relative brightness of the bright inner and the fainter outer regions in the di\ufb00erent transitions with the inner region being relatively much brighter for the higher transitions. This is in line with the even larger contrast between the two components seen in the comparison of the CO(2-1) and CO(4-3) data presented in Dasyra et al. (2016). To quantify this di\ufb00erence in contrast, we have computed, using the images given in Fig. 2, the spatial distribution of the ratio R31\u2261I3\u22122/I1\u22120 (with I in K km s\u22121; see Fig. 3). The image of R31 clearly con\ufb01rms that there are two distinct regions in IC 5063: an inner region with values of R31 well above 1, and an outer region with values below 0.5. A similar pattern is seen in images (not shown here) for the ratio R32 \u2261I3\u22122/I2\u22121 where R32 is around 1.0 or somewhat larger in the inner region and has values in the range 0.3\u20130.6 in the outer disk. Figure 3 clearly shows that, either directly or indirectly, the radio jet in IC 5063 must be responsible for the very di\ufb00erent conditions of the gas in the inner regions. In Morganti et al. (2015) and Dasyra et al. (2016) we had already observed that the bright, inner CO structure is spatially closely connected to the radio continuum and interpreted this as that the inner CO is bright because the radio jet strongly a\ufb00ects the excitation of the gas in the inner regions. Our new image of R31 shows this in dramatic form: it is exactly the bright inner region where the high values for the line ratios are found and the region with high values of R31 very nicely encompasses the radio continuum. This is very similar to what seen in, e.g., NGC 1068 where the region with high CO line ratios is also closely connected to the region of the AGN (Garc\u00eda-Burillo et al. 2014). In addition, Fig. 3 shows that the locations with the highest line ratios (with values well above 2.0) exactly coincide with the two lobes. We also note that the transition between the region with the high values of R31 to the region with lower values at larger radii is very sharp. This underlines that the region with very di\ufb00erent conditions compared to the outer, quiescent disk, is limited to the direct environment of the radio jet. We will not further discuss the molecular gas in the outer quiescent disk, other than that we note that R31 in these regions has quite low values, in the range 0.3\u20130.6. We \ufb01nd similar values in our data for, e.g., R32 \u2261I3\u22122/I2\u22121. This is consistent with R42 being \u223c0.25 as we found in Dasyra et al. (2016) for the same region. The molecular gas in the star forming disks of spiral galaxies typically show values for R21 \u2261I2\u22121/I1\u22120 \u223c0.8 (e.g., Leroy et al. 2009) implying higher values for R31 and R32 than seen here in the outer disk of IC 5063. Beyond the central regions, the gas density of the ISM in the disk of IC 5063, as well as the amount of star formation, is lower than that typically seen in star forming spiral galaxies (Morganti et al. 1998) and the low values of R31, R32 and R42 in the disk of IC 5063 are likely due to, as suggested in Dasyra et al. (2016), the excitation of the molecular gas in the outer regions in IC 5063 being sub-thermal. 3.2. Kinematics of the main CO lines The results of the previous section clearly show the spatial relationship between the jet and the conditions of the molecular gas. However, because R31 as discussed above is derived after integrating the CO emission over velocity, no kinematical information can be obtained. To study how the gas conditions depend on the kinematics of the gas, we produced position-velocity (pv) diagrams of the CO(1-0), CO(2-1) and (3-2) emission by averaging the CO data cubes over a width of 1\u2032\u2032 .5 (corresponding to 350 pc) in the direction perpendicular to the jet axis (which we have taken to have position angle \u221265\u25e6). The resulting pv diagrams are shown in Fig. 4. The kinematics of the CO gas, in particular the fast out\ufb02ow in the inner regions, and the connection to the radio jet in IC 5063, we have discussed extensively in Morganti et al. Article number, page 5 of 13 A&A proofs: manuscript no. I5063Alma -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 Radius (arcsec) 2600 2800 3000 3200 3400 3600 3800 Velocity (km s\u22121) CO(1-0) 0.00 0.15 0.30 0.45 0.60 0.75 0.90 CO(1-0) (K) -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 Radius (arcsec) 2600 2800 3000 3200 3400 3600 3800 Velocity (km s\u22121) CO(2-1) 0.00 0.15 0.30 0.45 0.60 0.75 0.90 CO(2-1) (K) -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 Radius (arcsec) 2600 2800 3000 3200 3400 3600 3800 Velocity (km s\u22121) CO(3-2) 0.00 0.15 0.30 0.45 0.60 0.75 0.90 CO(3-2) (K) Fig. 4. Position-velocity plots along the jet axis for CO(1-0) (top), CO(2-1) (middle) and CO(3-2) (bottom) where the data have been averaged over 1.5 arcsec perpendicular to the jet axis. Contour levels are \u201371.25 (dashed), 71.25 (1.5 \u03c3), 142.5, 285.0, . . . for the CO(1-0) data and \u201315 (dashed), 15 (1.5 \u03c3), 30, 60, . . . mK for the other two panels. For all panels the colour stretch is the same. For display purposes, the data have not been corrected for the primary beam. The dashed vertical lines indicate the approximate extent of the radio continuum structure. Positive radii are west of the centre of IC 5063. The spatial resolution along the horizontal axis is 0\u2032\u2032 .63. The grey curve in the top panel indicates where one would expect in this pv diagram to detect gas which follows the normal kinematics of a regularly rotating gas disk (i.e. gas not participating in the out\ufb02ow; see text). (2015) and Dasyra et al. (2016) and we only brie\ufb02y comment on it here. To give a rough indication where one would expect in this pv diagram to detect gas which follows the normal kinematics of a regularly rotating gas disk (i.e. gas not participating in the out\ufb02ow), we have, as we did in Morganti et al. (2015), indicated a rotation curve based on the HST photometry of IC 5063 of Kulkarni et al. (1998). This photometry shows that the light distribution can be accurately described using a de Vaucouleurs\u2019 law. The rotation curve plotted is based on the assumption that light traces mass and that the mass distribution is spherical. These assumptions are most likely not entirely correct and therefore the rotation curve plotted is only approximate, but it su\ufb03ces Fig. 5. Ratio R32 of the CO(3-2) and CO(2-1) brightness temperatures along the jet axis of IC 5063 where the data, before taking the ratio, have been averaged over 1.5 arcsec perpendicular to the jet axis (i.e. using the data presented in Fig. 4 after applying the primary beam corrections). Only ratios with error smaller than 0.3 are shown. The black curve indicates where one would expect in this pv diagram to detect gas which follows the normal kinematics of a regularly rotating gas disk (i.e. gas not participating in the out\ufb02ow; see text). The black dashed vertical lines indicate the extent of the radio continuum. to illustrate the anomalous kinematics of the gas in the out\ufb02ow. The horizontal scale of the rotation curve is set by the observed e\ufb00ective radius of the light distribution (21\u2032\u2032 .5 corresponding to 5.0 kpc), while the amplitude of the rotation curve is chosen such to match the rotation velocities of the outer disk. Since IC 5063 is observed almost edge on, regularly rotating gas is expected to lie in the regions with velocities between the plotted rotation curve and the systemic velocity (Vhel = 3400 km s\u22121, Morganti et al. 1998). Gas found in other regions of the pv diagram has \"anomalous kinematics\", indicating non-circular motions which in this case mean that the gas is participating in the gas out\ufb02ow. The pv diagrams of the CO(2-1) and the CO(3-2) emission in Fig. 4 clearly show the fast molecular out\ufb02ow, i.e. the presence of gas, for radii smaller than 2 arcseconds and exactly coinciding with the extent of the radio source, of which the kinematics strongly deviates from that expected for a regularly rotating disk, with di\ufb00erences up to 700 km s\u22121. In many locations, the velocities of the gas even have the wrong sign compared to those of a regular disk, in particular near the western lobe where the fastest out\ufb02ow velocities are seen. We also note the dramatic di\ufb00erence and sharp transition between the kinematics of the molecular gas in the region coinciding with the radio continuum (r < 2\u2032\u2032) and the regular rotation of the large-scale quiescent disk beyond this radius. The diagrams presented in Fig. 4 show that, similarly to those of Fig. 2, the inner, bright CO structure, including the fast out\ufb02ow, is detected in an almost identical way in CO(2-1) and CO(3-2). The bright, inner ridge is also detected in CO(1-0), but the fast out\ufb02owing gas is much fainter (even considering the difference in sensitivity of the di\ufb00erent observations). Below, we study in detail the \ufb02ux ratios between the various lines we have detected in various locations, but to illustrate the main result, in Fig. 5 we show R32 as computed from the pv diagrams described above. The striking feature in Fig. 5 is that there is a strong correlation between R32 and whether the velocities of the gas are anomalous or not. In the inner region, at velocities consistent with those of a regularly rotating disk and not coinciding with the lobes, R32 has values in the range 0.7\u20130.8, while for gas with velocities well outside the expected range for a regular disk (i.e. Article number, page 6 of 13 Oosterloo et al.: Properties of the molecular gas in the fast out\ufb02ow in the Seyfert galaxy IC 5063 Fig. 6. Position-velocity diagram of the low-resolution HCO+(4-3) emission (contours) along the jet axis of IC 5063 where the data have been averaged over 1.5 arcsec perpendicular to the jet axis. The greyscale is the position-velocity slice of the full-resolution CO(3-2) data. Contour levels are 6.6 (2\u03c3) and 13.2 mK. The spatial resolution along the jet axis is 1\u2032\u2032 .52 and the velocity resolution of the HCO+(4-3) data is 100 km s\u22121. the gas participating in the fast out\ufb02ow), as well as the gas coinciding with the lobes, R32 is in the range 1.0\u20131.5. The regions with the highest out\ufb02ow velocities, e.g., for radii between 0 and 2 arcsec and velocities below the rotation curve or above the systemic velocity, R32 is highest. In Fig. 3 where we show R31 for the data integrated over velocity, it appears that the highest line ratios are found near the two radio lobes. However, Fig. 5 makes clear that this is, at least partially, due to mixing di\ufb00erent components having di\ufb00erent line ratios, leading to averaging of regular and jet-disturbed gas over velocity. Figure 5 shows that all along the radio jet, the emission with signi\ufb01cant anomalous velocities has similar values for the line ratio as the gas near the lobes. This suggests that the highest excitation not only occurs in the direct vicinity of the lobes, but also between the core and the lobes, and not only for gas with large out\ufb02ow velocities. The presence of gas with high excitation but relatively low apparent velocities indicates that the out\ufb02ow is also occurring in the plane of the sky, i.e. perpendicular to the large-scale disk of IC 5063, as was also observed by Dasyra et al. (2015). The kinematics of the inner region with small line ratios is consistent with being the inner continuation of the outer disk and we may well see a mix of out\ufb02owing gas with large line ratios and regular disk gas with small ratios. The kinematical superposition of two such components was already recognised in Dasyra et al. (2016). 4. HCO+ and 13CO(2-1) In an attempt to obtain more information about the physical conditions of the molecular gas in the inner regions of IC 5063 (see Sec. 5 for details), we also observed the galaxy in the J=4-3 transition of HCO+ as well as in the 13CO(2-1) line. As mentioned above, emission is detected in these two lines, but of course at a much lower level compared to the main CO transitions and we smoothed the data to lower spatial and velocity resolution in order to better match them to the spatial and velocity structure of the emission. The HCO+ and 13CO(2-1) cubes we discuss here have a spatial resolution of 1\u2032\u2032 .52 and a velocity resolution of 100 km s\u22121. Fig. 7. Position-velocity diagram of the ratio of the low-resolution HCO+(4-3) and CO(2-1) brightness temperatures along the jet axis of IC 5063 where the data, before taking the ratio, have been averaged over 1.5 arcsec perpendicular to the jet axis. Only pixels for which the error in the ratio is smaller than 0.07 are shown. The spatial resolution along the jet axis is 1\u2032\u2032 .52. Figure 6 shows the position-velocity diagram of the HCO+(4-3) emission obtained in the same way as described above for the main CO lines (i.e. the spatial axis is along the radio jet). The superposition on the CO(3-2) emission shows that the bulk of the HCO+(4-3) emission comes from the bright, inner ridge detected in the main CO lines (which is likely a mix of disturbed and regular gas), but that some faint emission is detected from the fast out\ufb02ow near the W lobe. Figure 7 shows the spatial distribution of the ratio of the low-resolution HCO+(43) and CO(2-1) brightness temperatures in the position-velocity diagrams where only those pixels are displayed that have an error in the line ratio smaller than 0.07. Although the HCO+(43) emission is detected at very faint levels and the errors in the ratios are relatively large, Fig. 7 nevertheless suggests that the line ratio of the gas of the out\ufb02ow is substantially higher than of the more quiescent gas. Given the high critical density of the HCO+(4-3) line (1.8\u00d7106 cm\u22123; Greve et al. 2009) this indicates that the gas is much denser in the fast out\ufb02ow. Relatively strong emission from HCO+ (and other high-density indicators such as HCN) has also been observed in other out\ufb02ows, such as NGC 1068 (Garc\u00eda-Burillo et al. 2014) and Mrk231 (Aalto et al. 2012; Cicone et al. 2012; Feruglio et al. 2015), and IC 5063 conforms to this rule. Figure 8 shows the position-velocity diagram of the 13CO(21) emission. Here, only emission is detected from the bright, inner region and from the undisturbed outer disk. Figure 9 shows the ratio of the 13CO(2-1) and 12CO(2-1) brightness temperatures for those locations where the error in this ratio is smaller than 0.07. Because no 13CO(2-1) emission is detected from the out\ufb02ow, for this gas we can only set an upper limit to the line ratio. The \ufb01gure shows that there is a clear relation between this line ratio and the kinematics of the gas and that the interaction of the radio jet with the ISM strongly impacts on the optical thickness of the clouds. High values (on average 0.13; see Sec. 5.3) are observed in the outer disk and much lower values in the out\ufb02ow (below 0.05). Fairly low values (around 0.05) are found in the bright inner structure and in the radio lobes for gas at normal velocities. This may indicate intermediate conditions there, or that two components, one with low and one with high line ratios, are superposed. The ratio 13CO(2-1)/12CO(2-1) depends on many factors, such as abundance, turbulence and optical depth e\ufb00ects. Article number, page 7 of 13 A&A proofs: manuscript no. I5063Alma Fig. 8. Position-velocity diagram of the low-resolution 13CO(2-1) emission along the jet axis of IC 5063 where the data have been averaged over 1.5 arcsec perpendicular to the jet axis. Contour levels are \u20133.6, 3.6 (2\u03c3), 7.2 and 14.4 mK. The spatial resolution along the jet axis is 1\u2032\u2032 .52. Fig. 9. Position-velocity diagram of the ratio of the low-resolution 13CO(2-1) and 12CO(2-1) brightness temperatures along the jet axis of IC 5063 where the data, before taking the ratio, have been averaged over 1.5 arcsec perpendicular to the jet axis. Only pixels for which the error in the ratio is smaller than 0.07 are shown. For the regions in the diagram where the fast out\ufb02ow is occurring, the values should be regarded as upper limits since no 13CO(2-1) emission is detected there. The spatial resolution along the jet axis is 1\u2032\u2032 .52. In relatively normal early-type galaxies, observed values for 13CO(2-1)/12CO(2-1) in general cover the range 0.05\u20130.3 (e.g. Crocker et al. 2012; Alatalo et al. 2015) where the lower values are found in galaxies where the gas is disturbed by interactions or other sources of turbulence such as star formation. Ratios in the upper part of this range are found in more quiescent conditions. Crocker et al. (2012) argue that these observed trends are mainly driven by optical depth e\ufb00ects. The di\ufb00erences in 13CO(2-1)/12CO(2-1) we see within IC 5063 mimic the same trend. The very low line ratios (below 0.015) occurring in the region of the fastest out\ufb02ow con\ufb01rm the optical thin conditions for this emission. For the gas in the bright, inner region, as well as for the gas near the radio lobes, somewhat higher line ratios are found, but the ratios are still low compared to many other earlytype galaxies. This may indicate that the gas is mildly optically thick there, or that we see a superposition of optically thin and thick gas. The much higher ratios in the outer disk or typical of regular gas disks and clearly show that optical thick conditions are present in the outer region. 5. Discussion 5.1. Excitation temperatures The results presented above give clear evidence that a significant fraction of the molecular gas is strongly a\ufb00ected by the interaction with the radio jet/cocoon, both in terms of the kinematics and in terms of the physical conditions of the gas. In an elongated structure around the radio continuum source, R32 has values larger than 1 and at many locations, in particular near the radio lobes, R31 is even larger than 2 (Figs. 4, 5 and 3). The gas that has these high line ratios is also the gas that participates in the out\ufb02ow. This is quite consistent with the results derived from comparing the CO(4-3) emission of IC 5063 with that of CO(21) by Dasyra et al. (2016). There we found that, in general, the jet a\ufb00ected gas has R42 > 1.0 and at some locations this ratio is even quite larger than this value. Such values suggest high excitation temperatures as well as that the CO emission is optically thin since such ratios are signi\ufb01cantly above the maximum value of 1 for optically thick emission. Given that in our data we also see line ratios (much) larger than 1.0, our data rea\ufb03rm the high excitations and that the emission from the jet a\ufb00ected gas is optically thin. The low values for 13CO(2-1)/12CO(2-1) we observe for the out\ufb02owing gas also indicate this. Below, we do a more detailed analysis of the conditions of the molecular gas using RADEX non-LTE modelling, but \ufb01rst we derive estimates of the excitation temperature of the out\ufb02owing CO gas by assuming local thermodynamicequilibrium (LTE) and that the gas is optically thin. For these assumptions, the average value of \u27e8R32\u27e9= 1.25 (for details, see below) for the gas with the most extreme out\ufb02ow velocities indicates an excitation temperature of Tex = 29 K, in good agreement with the value of Tex = 32 K found in Dasyra et al. (2016) as being characteristic for much of this gas. Another \ufb01nding of Dasyra et al. (2016) is that in some small regions, R42 has values higher than 1.25, implying that locally, Tex is well above 30 K. The images of R32 presented in Figs. 3 and 5 do not show such locations, but given that these images were computed from information integrated either spatially or in velocity, such small spots may have been averaged away in the process. To access the presence of regions with high line ratios, we have also computed pixel-by-pixel R32 ratios using the original three-dimensional data cubes, resulting in a three-dimensional dataset containing R32 for each 3-D pixel. We have not done this for line ratios involving CO(1-0) because the signal-to-noise of the emission of the out\ufb02owing gas is too low in the CO(1-0) cube. The highest values for R32 we \ufb01nd in this way are around 1.65. Such values correspond to Tex = 54 K assuming optically thin emission and LTE. This is in good agreement with Dasyra et al. (2016) where we \ufb01nd Tex = 56 K for the fastest out\ufb02owing gas. To illustrate the location of the gas with these highest line ratios, we selected only those pixels in the CO(2-1) data cube for which R32 > 1.55 and for which the error in R32 is smaller than 0.5. Using this selection of pixels in the data cube, we produced an image of the integrated CO(2-1) brightness of the emission for which R32 > 1.55 and this is shown in Fig. 10. This \ufb01gure shows that the gas with highest line ratios is located near the western lobe and between that lobe and the core, but, in fact, not coincident with the peak of the W lobe itself. In addition, inspection of the data cubes shows that the out\ufb02ow velocities of this gas are high, but not as high as the most extreme velocities seen near the W lobe. The locations of very high excitation gas we see here with those seen by Dasyra et al. (2016) roughly coincide. We note that only a small fraction (\u223c5%) of the total Article number, page 8 of 13 Oosterloo et al.: Properties of the molecular gas in the fast out\ufb02ow in the Seyfert galaxy IC 5063 Fig. 10. Integrated CO(2-1) intensity using only these pixels in the three-dimensional data cube for which R32 > 1.55 and the error in R32 is smaller than 0.5. Contours represents the 346 GHz continuum with levels 0.15, 0.6 and 2.4 mJy beam\u22121. CO(2-1) and CO(3-2) emission comes from gas with this very high excitation. 5.2. Mass estimates As we remarked in Dasyra et al. (2016), the fact that the molecular out\ufb02ow appears to be optically thin a\ufb00ects the estimate of the mass in the molecular out\ufb02ow compared to the one reported by Morganti et al. (2015) where it was assumed the emission is optically thick5. To estimate the amount of CO gas participating in the out\ufb02ow, we have estimated the \ufb02ux integral of the out\ufb02owing gas by adding the \ufb02ux from all 3-D pixels in the CO(2-1) cube, and similarly in the CO(3-2) cube, for which R32 > 1.0, taking this limit as a clear indication that the gas is a\ufb00ected by the radio jet. The \ufb02ux integrals we \ufb01nd are 9.5 Jy km s\u22121 for the CO(2-1) line and 25.3 Jy km s\u22121 for the CO(3-2) line. Given the uncertainties in separating the out\ufb02owing gas from the gas with regular kinematics, the \ufb02ux integral we \ufb01nd for the CO(21) lines compares well with the values of 10.0 Jy km s\u22121 and 12.3 Jy km s\u22121 given by Morganti et al. (2015) and Dasyra et al. (2016) respectively. These latter two values were derived using the kinematics to separate out\ufb02owingand regular gas, instead of line ratios. Both methods likely underestimate the \ufb02ux of the out\ufb02owing gas because, as Fig. 5 shows, at many pixels in the data cubes, regular and out\ufb02owing gas are superposed. Depending on the relative mix of regular and out\ufb02owing gas, the measured value for R31 can be lower than 1.0 even if a signi\ufb01cant component of out\ufb02owing gas is present. To illustrate the e\ufb00ect of this: lowering the value of R32 to separate the two components to 0.9 instead of 1.0, roughly doubles the \ufb02ux integrals. For the optically thin regime, the CO-luminosity-to-H2-mass conversion factor (\u03b1CO) depends somewhat on the excitation temperature. For Tex = 29 K the conversion factor \u03b1CO = 0.25 K km s\u22121 pc2 (Bolatto et al. 2013). Using this conversion factor, the above \ufb02ux integrals imply that the mass of the molecular gas participating in the out\ufb02ow is 1.3 \u00b7 106 M\u2299based on the CO(21) \ufb02ux integral and 1.1 \u00b7 106 M\u2299from the CO(3-2) data. This is about a factor 3 lower than would be derived assuming optically thick emission. Under the assumptions of optically thin 5 due to a numerical error, the mass estimate in that paper is about a factor 4 too high emission and LTE, the mass estimate depends on the excitation temperature Tex. If one uses the highest excitation temperatures we observe (\u223c55 K), the mass estimate roughly doubles. However, the main uncertainty in the mass estimate comes from the uncertainties in the separation of regular and anomalous gas. The results mentioned above from lowering the value of R32 to separate components suggest that the masses reported here are very likely lower limits and the true mass of molecular gas participating in the out\ufb02ow could be a factor of a few larger. This means that the cold molecular out\ufb02ow is about as massive as the atomic out\ufb02ow (3.6 \u00d7 106 M\u2299, Morganti et al. 2007), and much more massive that that of other gas phases (Morganti et al. 2007; Tadhunter et al. 2014). Our data clearly show that the impact of the jet on the inner regions of IC 5063 is very signi\ufb01cant. However, compared to the mass of the entire ISM of IC 5063 (\u223c5 \u00d7 109M\u2299, Morganti et al. 1998), the mass of the out\ufb02owing gas is insigni\ufb01cant and the e\ufb00ect of the out\ufb02ow on the galaxy as a whole is likely to be very limited. The mass out\ufb02ow rate can be estimated using \u02d9 M = 3vM/R (Maiolino et al. 2012) where M is the mass of the out\ufb02owing gas, R the size of the out\ufb02ow region and v a representative out\ufb02ow velocity. This assumes that the out\ufb02ow has a spherical geometry. Using R \u223c0.5 kpc and v = 300 km s\u22121 gives a gas mass out\ufb02ow rate of the about \u223c12 M\u2299yr\u22121 or somewhat higher. This is quite modest compared to many other molecular out\ufb02ows detected, but similar to the out\ufb02ow rate observed in AGN of comparable luminosity as the one in IC 5063 (Fiore et al. 2017). 5.3. Kinetic temperature, density and pressure Here, and in Dasyra et al. (2016), we \ufb01nd that the emission from the fastest out\ufb02ow is consistent with arising in optically thin gas. If this gas is in LTE, it must be warm and dense. However, in much of the jet-impacted area we \ufb01nd 13CO(2-1)/12CO(21)\u223c0.04. This indicates that the gas is mildly optically thick and therefore we will here perform a non-LTE analysis to investigate the temperature and density for di\ufb00erent regions in IC5063. In Fig. 6 we showed that the CO and HCO+ share the same dynamics and thus likely probe the same underlying gas distribution. We will therefore also include the HCO+(4-3) line in our analysis. We use the RADEX non-LTE radiative transfer code to estimate kinetic temperatures and densities for representative regions in the out\ufb02ow and in the disk of IC5063. Gas heating and excitation models will be presented in a forthcoming paper (Oonk et al. in prep.). To provide the necessary input for the modelling, we computed line ratios for four representative regions, indicated in Fig. 11, covering the various conditions of the molecular gas. The regions de\ufb01ned include the fast out\ufb02ow (FO) at the western lobe, the out\ufb02owing gas in the more central regions (O), the gas at the locations of the two lobes, but at velocities close to those expected for regular rotation (L), and the gas in the outer disk (D). We de\ufb01ned these regions using the position-velocity diagrams and their layout is shown. For each of the regions, line ratios were computed and results are given in Table 1. To incorporate uncertainties in the absolute \ufb02ux calibration of the di\ufb00erent observations, we have assigned a minimum error of 5% in the \ufb02ux estimates used (van Kempen et al. 2014). The very dissimilar line ratios for the various regions in Table 1 clearly underline the di\ufb00erent conditions for the gas in the different regions, in particular the large contrast between the outer disk and the regions a\ufb00ected by the radio jet. A \ufb01rst, main result that immediately emerges from Table 1 is that, while the ratios for the outer disk re\ufb02ect the normal, quiescent conditions in the Article number, page 9 of 13 A&A proofs: manuscript no. I5063Alma Region 12CO(2-1) CO(2-1)/ CO(3-2)/ CO(3-2)/ 13CO(2-1)/ HCO+/ (K km s\u22121) CO(1-0) CO(1-0) CO(2-1) 12CO(2-1) CO(3-2) fast out\ufb02ow 52.6 \u00b1 2.6 1.79 \u00b1 0.51 2.08 \u00b1 0.61 1.25 \u00b1 0.09 < 0.015 0.10 \u00b1 0.025 out\ufb02ow 425 \u00b1 21 1.39 \u00b1 0.15 1.37 \u00b1 0.15 1.06 \u00b1 0.07 0.030 \u00b1 0.007 0.024 \u00b1 0.011 lobes 270 \u00b1 14 1.08 \u00b1 0.09 0.99 \u00b1 0.09 0.97 \u00b1 0.07 0.047 \u00b1 0.003 0.045 \u00b1 0.005 disk 67.7 \u00b1 3.4 0.40 \u00b1 0.03 0.17 \u00b1 0.01 0.39 \u00b1 0.03 0.13 \u00b1 0.01 < 0.05 Table 1. Flux integrals and line ratios for the regions de\ufb01ned in Fig. 11 and that were use as input for the RADEX modelling. To incorporate uncertainties in the absolute \ufb02ux calibration of the di\ufb00erent observations, we have assigned a minimum error of 5% in the \ufb02ux estimates used (van Kempen et al. 2014). -10 -8 -6 -4 -2 0 2 4 6 8 Radius (arcsec) 2600 2800 3000 3200 3400 3600 3800 4000 Velocity (km s\u22121) FO FO D O O L L 0.00 0.08 0.16 0.24 0.32 0.40 0.48 0.56 0.64 Kelvin Fig. 11. Regions for which we computed line ratios as input for the RADEX modelling. The region labelled \u2019FO\u2019 correspond to the fast out\ufb02ow at the western lobe. Region labelled \u2019O\u2019 to the out\ufb02ow in the more central regions, while region \u2019L\u2019 to the eastern and western radio lobes at velocities close to those for regular rotation. The region labelled \u2019D\u2019 corresponds to the outer disk. The underlying gray scale is the position-velocity diagram of the CO(2-1) emission. Contour levels are 43.75, 87.5, 175.0 and 350 mK ISM in this region, the ratios in the jet-a\ufb00ected regions clearly indicate elevated temperatures and densities. Moreover, between the di\ufb00erent regions a\ufb00ected by the jet, conditions are more extreme for gas with more extreme kinematics. To attempt to obtain more information on this, we modelled the data using a single slab (1-D) model with constant kinetic temperature and density and use the collision rates from the LAMBDA database Sch\u00f6ier et al. (2005). For each line ratio, we predict values for a common grid in Tkin and nH2 (see Fig. 12). For Tkin, we sample the range from 10 to 200 K in logarithmic steps of 0.043 while for nH2 we sample the range 102 to 107 cm\u22123 in logarithmic steps of 0.167. We set the background temperature to 2.73 K and the line width to 100 km s\u22121. In general, the derived line ratios depend on the input 12CO column density. We computed models with column densities in the range from 5 \u00d7 1015 to 1 \u00d7 1020 cm\u22122 which we sampled in logarithmic steps of 0.5. For the ratio 12CO/13CO we have assumed 100. Given the sizeable errors in the line ratios involving 13CO, varying this ratio between 50 and 200 gives similar results, within the errors. In general, good measurements of the abundance of HCO+ relative to 12CO are scarce in the literature and the HCO+ abundance in IC 5063 is not known. The probably most relevant data are given by Viti et al. (2014) in their study of the circum-nuclear disk surrounding the AGN in NGC 1068. In this circum-nuclear disk they \ufb01nd a relatively high HCO+/12CO ratio of \u223c10\u22124 . We therefore opted to use a similarly high value of 1.3 \u00d7 10\u22124. Lowering the abundance has little e\ufb00ect because the HCO+(4-3)/CO(2-1) tracks shift to somewhat lower densities, but are still well within the error bars of the tracks of the nominal abundance. Increasing the abundance shifts the tracks to higher densities. This means that the results based on the nominal abundance give an indication of a lower bound to the gas density. The results are illustrated in Fig. 12 and are summarised Table 2. Figure 12 shows, for two di\ufb00erent assumed 12CO column densities, the combinations of nH2 and Tkin that reproduce the various line ratios for the various regions. The quality of models can be assessed by to what extent the di\ufb00erent lines in the panels of Fig. 12 intersect in a common region. The trends and di\ufb00erences visible in Fig. 12 are representative for the full range of column densities we considered (see below). The plots show that from the high signal-to-noise 12CO measurements alone, we can obtain tight constraints on the combination of nH2 and Tkin, but, as expected, there is a degeneracy between them in the models. Given the slope of the 12CO tracks, the pressure (nT) is, however, somewhat better constrained. In principle, since the dependence of the HCO+/12CO ratio on temperature and density is very di\ufb00erent than that of the pure CO line ratios, one can use it to break the degeneracy, but the uncertainty in the HCO+(4-3) data limits its use somewhat. For the outer disk it has no added value given the low densities of the ISM there. We \ufb01nd that the diagrams for 12CO column densities below 1018 cm\u22122 are all very similar to each other and those shown for N(12CO) = 1016 cm\u22122 are representative for this column density range. Here, the main CO line ratios do not quite occupy the same region of the diagrams, although for the fast out\ufb02ow region, the CO(1-0)/CO(2-1) ratio does not provide much constraints. For the out\ufb02ow and lobes regions, the mismatch between the di\ufb00erent tracks may be due to the fact that the observed line emission from these regions is a mix of gas with very di\ufb00erent conditions, as discussed above, and modelling the line ratio with a model with only one component is not entirely appropriate. For the fast out\ufb02ow region, gas mixing is not a problem. The two main CO lines, together with the HCO+(4-3)/CO(2-1) ratio, do not give a well de\ufb01ned solution. When focussing on the CO(3-2)/CO(2-1)(involving the strongest lines detected) and the HCO+(4-3)/CO(2-1) ratios, the low column density models indicate gas with high density (105 < n < 107 cm\u22123) and Tkin between 20 and 50 K for the jet a\ufb00ected gas, with the higher densities and temperatures in the fast out\ufb02ow region, but this may be related to the mixing of line emission for the out\ufb02ow and lobes regions discussed above. The resulting pressures are in the range 106\u2013107.5 K cm\u22123. When increasing the column density above 1018 cm\u22122, the character of the diagrams changes and this is illustrated in the right-hand column of Fig. 12. For the jet-a\ufb00ected regions, the tracks of the CO lines shift to higher temperatures and density, while the HCO+(4-3)/CO track shifts to lower density. Instead, Article number, page 10 of 13 Oosterloo et al.: Properties of the molecular gas in the fast out\ufb02ow in the Seyfert galaxy IC 5063 2 3 4 5 6 7 log (n/cm\u22123) 1 1.2 1.4 1.6 1.8 2 2.2 log (T/K) fastOutflow  N(CO) = 1 \u00d7 1016 CO(3-2)/CO(2-1) CO(1-0)/CO(2-1) 13CO(2-1)/12CO(2-1) HCO+(4-3)/CO(2-1) 2 3 4 5 6 7 log (n/cm\u22123) 1 1.2 1.4 1.6 1.8 2 2.2 log (T/K) fastOutflow  N(CO) = 5 \u00d7 1018 2 3 4 5 6 7 log (n/cm\u22123) 1 1.2 1.4 1.6 1.8 2 2.2 log (T/K) outflow  N(CO) = 1 \u00d7 1016 2 3 4 5 6 7 log (n/cm\u22123) 1 1.2 1.4 1.6 1.8 2 2.2 log (T/K) outflow  N(CO) = 5 \u00d7 1018 2 3 4 5 6 7 log (n/cm\u22123) 1 1.2 1.4 1.6 1.8 2 2.2 log (T/K) lobes  N(CO) = 1 \u00d7 1016 2 3 4 5 6 7 log (n/cm\u22123) 1 1.2 1.4 1.6 1.8 2 2.2 log (T/K) lobes  N(CO) = 5 \u00d7 1018 2 3 4 5 6 7 log (n/cm\u22123) 1 1.2 1.4 1.6 1.8 2 2.2 log (T/K) disk  N(CO) = 1 \u00d7 1016 2 3 4 5 6 7 log (n/cm\u22123) 1 1.2 1.4 1.6 1.8 2 2.2 log (T/K) disk  N(CO) = 5 \u00d7 1018 Fig. 12. RADEX models for the four regions (see Fig. 11). The constraints on nH2 and Tkin from the various line ratios are indicated (solid lines) and their 3-\u03c3 errors (dashed lines) for N(12CO) = 1 \u00d7 1016 cm\u22122 (left column) and for N(12CO) = 5 \u00d7 1018 cm\u22122 (right column). for the disk region the CO tracks move to lower density and temperature. This is likely an optical depth e\ufb00ect with the highexcitation gas being optically thin ( according to the RADEX models with optical depth in the range 10\u22124 \u2013 10\u22123) and the disk gas optically thick. In particular, the tracks of the main CO lines in the diagrams of the jet-a\ufb00ected regions become more consistent with each other and the models somewhat better de\ufb01ne a solution and therefore the models with high CO column densities in the jet a\ufb00ected regions, in the range 5\u00d71018 cm\u22122\u20135\u00d71019 cm\u22122, could be preferred. This may indicate that the true 12CO column densities in the out\ufb02owing gas are at least two orders of magnitude larger than the observed ones, assuming LTE, opArticle number, page 11 of 13 A&A proofs: manuscript no. I5063Alma region \u27e8N(12CO)\u27e9 log Tkin log nH2 log P (cm\u22122) (K) (cm\u22123) (K cm\u22123) fast out\ufb02ow 1.6 \u00d7 1016 1.5\u20132.0 4.5\u20136.0 6.5\u20137.5 out\ufb02ow 1.3 \u00d7 1017 1.3\u20132.0 4.0\u20135.9 6.0\u20137.2 lobes 8.2 \u00d7 1016 1.1\u20131.8 5.0\u20135.8 6.8\u20136.9 disk 3.7 \u00d7 1016 1.0\u20132.3 2.0\u20134.0 4.3\u20135.0 Table 2. RADEX analysis of the various regions in IC 5063 (see Fig. 11). Column 2 gives the observed area averaged 12CO column density. These area averaged measured column densities are derived assuming LTE and optically thin conditions and Tex = 40 K, n = 105 cm\u22123 and \u2206V = 100 km s\u22121. Columns 3, 4 and 5 provide the allowed range in physical conditions derived from single slab RADEX models with column densities of 5 \u00d7 1018 cm\u22122 or higher for the fast out\ufb02ow, out\ufb02ow and lobes region. For the disk region, the range given is for all models, also of lower column density. tically thin conditions, and that the emission \ufb01lls the beam and which are in the range 1016\u20131017 cm\u22122 (see Table 2). Since the observed column densities are an average over the ALMA beam, this would mean that gas is very clumpy and that the \ufb01lling factor of these clumps over the beam is low, at the level of 1% or lower. The peak 12CO brightness temperatures observed in our data are around 1 K which also indicate, for optically thick emission and the excitation temperatures observed, that the gas is clumpy. The densities resulting from these models are slightly lower than those for the low column density models, but the temperatures are higher and could be as high at 100 K. The pressures are similar as for the low column density models and are in the range 106.0\u2013107.5 K cm\u22123. Also for these models, the fast out\ufb02ow region has somewhat higher density and temperature (and hence pressure) than the out\ufb02ow and lobes regions de\ufb01ned in Table 2. For the disk region, since only ratios involving CO lines are available, the models mainly provide constraints to the combination of Tkin and n and not so much to these parameters separately. Nevertheless, it is clear that the densities in the disk are at least two orders of magnitude lower than in the jet a\ufb00ected regions. Given the slope of the tracks of the CO ratios, the pressure in the disk is better constrained and is in the range 104\u2013105 K cm\u22123 for the low column density models and about an order of magnitude lower for the high column density models. Although there are uncertainties in the modelling discussed above, nevertheless a fairly clear picture emerges about the physical conditions of the molecular gas in the out\ufb02ow in IC 5063 that we can summarise as follows: it is characterised by increased density and temperature, and the resulting pressure in the out\ufb02owing gas is at least two orders of magnitude higher than in the quiescent ISM of IC 5063. Moreover, the increase in all these physical parameters appears to be strongest for the gas participating in the fastest out\ufb02ow. The much higher densities and pressures of the gas of the out\ufb02ow would suggest that the gas is compressed and accelerated by fast shocks driven by the expanding radio source.. The alternative would be that the jets have hit unusually dens molecular material, but in that case the high (precursor) densities would have to be maintained across the 1kpc region encompassed by the radio components. 6. Conclusions The ALMA observations we present in this paper of a number of tracers of the molecular gas in IC 5063 give a very detailed, spatially resolved view of the impact of a radio jet expanding in the ISM of a galaxy, both in terms of the kinematics and in terms of the physical conditions of the ISM. As seen in our earlier ALMA CO(2-1) and CO(4-3) observations (Morganti et al. 2015; Dasyra et al. 2016) of this object, the new data of the main 12CO lines show the fast molecular out\ufb02ow as a bright inner molecular structure, of about 1 kpc in size and closely associated with the radio jet, embedded in a larger, quiescent regularly rotating gas disk. Particularly striking is the di\ufb00erence in relative brightness in the di\ufb00erent transitions of this inner molecular structure compared to that of the outer disk, with the inner structure being relatively brighter in the higher-J CO transitions (Fig. 2), showing that the gas in the inner molecular structure has very di\ufb00erent properties than the gas in the outer disk. Images and pv diagrams of the line ratios of the main CO lines (Figs 3 and 5) clearly show that the out\ufb02ow has high excitation over a region which is exactly coincident with the radio jet. These results con\ufb01rm the model presented in Morganti et al. (2015), inspired by the simulations of Wagner et al. (2012), where the radio jet is working its way through a clumpy ISM, in\ufb02ating a cocoon in the ISM which is driving the out\ufb02ow. At many locations along the entire jet, the line ratios R21, R31 and R32 are well above 1.0. This con\ufb01rms, as seen earlier in Dasyra et al. (2016) based on R42, that the out\ufb02owing gas is optically thin and that it has high excitation temperatures. The 13CO(2-1) data con\ufb01rm that the out\ufb02ow is optically thin. The observed line ratios indicate CO excitation temperatures around 30 K for much of the molecular out\ufb02ow, but at some locations excitation temperatures as high as 54 K are observed, consistent with the results found in Dasyra et al. (2016). The inner molecular structure is also detected in the HCO+(4-3) line and this emission is relatively bright in the fastest out\ufb02ow in particular. This implies that the densities in the out\ufb02owing gas are high. This is consistent with what is observed in other molecular out\ufb02ows, such as those in, e.g., NGC 1068 (Garc\u00eda-Burillo et al. 2014) and Mrk231 (Aalto et al. 2012; Cicone et al. 2012; Feruglio et al. 2015) Estimating the mass of the molecular out\ufb02ow is complicated by the fact that at many locations in the data cube out\ufb02owing and quiescent gas are superposed, making a clean separation between the two impossible. We estimate the mass of the molecular out\ufb02ow to be at least \u223c106 M\u2299and, due to the di\ufb03culty in separating out\ufb02owing and quiescent gas, it is likely a factor of a few larger than this value. This means that the molecular out\ufb02ow is similar in mass as the atomic out\ufb02ow (3.6 \u00d7 106 M\u2299, Morganti et al. 2007) and that the cold gas phases dominate the fast out\ufb02ow in IC 5063 (Morganti et al. 2007). The mass out\ufb02ow rate of the cold gas is \u223c12 M\u2299yr\u22121. This is lower than observed for many other molecular out\ufb02ows (Fiore et al. 2017) and is likely connected to the fact that IC 5063 is a relatively weak radio AGN. The mass of the fast out\ufb02ow in IC 5063 is only a small fraction of the mass of its total ISM (about 5 \u00d7 109 M\u2299, Morganti et al. 1998). The jet-ISM interaction clearly has a signi\ufb01cant impact on the ISM in the inner regions of the galaxy, but on the galaxy as a whole, the in\ufb02uence of the out\ufb02ow will be much less. Article number, page 12 of 13 Oosterloo et al.: Properties of the molecular gas in the fast out\ufb02ow in the Seyfert galaxy IC 5063 We have explored the physical conditions of the molecular gas using RADEX non-LTE modelling of the observed line ratios in a number of regions of IC 5063. Models with the out\ufb02owing gas being quite clumpy give the most consistent results and our preferred solutions have kinetic temperatures in the range 20\u2013100 K, densities ranging between 105 and 106 cm\u22123 and the resulting pressures being 106\u2013107.5 K cm\u22123, about two orders of magnitude higher than in the outer disk (Table 2). The higher densities and temperatures are found in the regions with the fastest out\ufb02ow. The high densities and pressures observed for the out\ufb02ow suggest that the gas is compressed and accelerated by fast shocks driven by the expanding radio structure. The results presented in this paper are providing a reference case illustrating the impact of a jet driven by a relatively lowluminosity AGN expanding in a gas-rich, clumpy medium. Spatially resolved observations of out\ufb02ows driven by higher power AGN are now also needed to build a more detailed picture of the complex processes involved and the impact of the AGN, both on the kinematics and on the physical conditions of the out\ufb02owing gas in order to provide realistic constraints for theoretical studies. Acknowledgements. This paper makes use of the following ALMA data: ADS/JAO.ALMA#2012.1.00435.S and ADS/JAO.ALMA#2015.1.00467.S. ALMA is a partnership of ESO (representing its member states), NSF (USA), and NINS (Japan), together with NRC (Canada) and NSC, and ASIAA (Taiwan), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO and NAOJ. The research leading to these results has received funding from the European Research Council under the European Union\u2019s Seventh Framework Programme (FP/2007-2013) / ERC Advanced Grant RADIOLIFE-320745.",
                    "introduction": "The study of fast, galactic scale gas out\ufb02ows (with velocities ex- ceeding 1000 km s\u22121 in some cases) driven by active galactic nuclei (AGN) has become very relevant for understanding the role of AGN in galaxy evolution because of the large amounts of energy such out\ufb02ows can dump into the ISM of the host galaxy or in the gaseous medium surrounding it, thereby a\ufb00ecting the progress of star formation and of the growth of the central super- massive black hole. Interestingly, such studies have brought a number of surprises about the physical properties of the gas im- pacted by the AGN. One of the unexpected results of recent work has been the \ufb01nding that these fast AGN-driven out\ufb02ows con- tain a large, in terms of mass often dominant, component of cold (atomic and molecular) gas (see Fiore et al. 2017, for a recent compilation). The presence of large amounts of cold gas in fast Send o\ufb00print requests to: oosterloo@astron.nl out\ufb02ows is interesting for at least two reasons: the origin \u2013 how can cold gas survive, or form, in fast out\ufb02ows \u2013 and whether fast out\ufb02ows not only quench star formation, but, instead, also can, under certain circumstances, induce star formation (e.g. Silk 2013; Maiolino et al. 2017). Despite the relevance of fast out\ufb02ows, detailed studies of cold, fast out\ufb02ows are still limited to a few objects, and, given the diversity of the characteristics of these objects, our understand- ing of the typical physical conditions of the cold gas is limited. Improving our knowledge of the properties of cold gas in such harsh environments is key for developing physical models for the out\ufb02ows and what drives them, as well as for assessing the overall impact of the AGN, and the out\ufb02ows it drives, on galaxy evolution. The limited number of objects where molecular out\ufb02ows not only have been detected, but in addition also have their physical properties investigated using multiple line transitions, Article number, page 1 of 13 A&A proofs: manuscript no. I5063Alma 1 kpc 10 kpc Fig. 1. Left: optical image of IC 5063. This image is taken, using EFOSC on the ESO 3.6-m telescope, through a narrow-band \ufb01lter centred on 5100 \u00c5, and shows the large-scale dust lanes and the overall structure of the galaxy (Tsvetanov et al. 1997). Right: HST image of IC 5063 of the central regions of IC 5063, taken from the public HST archive. This image is a single 500 s exposure obtained with WFPC2 through the F606W \ufb01lter, and it shows the structure of the inner dust lanes in the central region. Overplotted are the contours of the 8 GHz continuum emission of the central kpc-sized radio source showing the central core and the eastern and western radio lobes (data from Morganti et al. 1998). Contour levels are 2, 4, 8, 16, 32, 64 and 128 mJy beam\u22121. show large di\ufb00erences in physical conditions between the qui- escent, non-a\ufb00ected gas and the out\ufb02owing gas, underlin- ing the impact of the driving mechanism (e.g. NGC 1068, Viti et al. 2014; Garc\u00eda-Burillo et al. 2014; Mrk 231, Aalto et al. 2012; Cicone et al. 2012; Feruglio et al. 2015; NGC 1266, Alatalo et al. 2011; 4C12.50, Dasyra et al. 2014 and NGC 1433, Combes et al. 2013). The results indicate that the out\ufb02owing molecular gas is clumpy and has much higher temperatures and densities than the molecular gas in the normal ISM. The picture that emerges is that the gas is compressed and fragmented by the mechanism that drives the out\ufb02ow. One limiting factor is that not many objects are known for which one can do a detailed, spatially well resolved analysis of the properties and kinematics of the out\ufb02ow. One of the few ob- jects for which this is possible is the nearby Seyfert galaxy IC 5063. This was the \ufb01rst object where a fast AGN-driven out\ufb02ow of atomic hydrogen was discovered (Morganti et al. 1998). IC 5063 is an early-type galaxy (z = 0.11341) with a number of prominent dust lanes (see Fig. 1). The galaxy is gas rich, having a large-scale, regularly rotating gas disk containing 4.2\u00d7109 M\u2299 of atomic hydrogen (Morganti et al. 1998) , and at least 109 M\u2299 of molecular hydrogen (Morganti et al. 2015). IC 5063 is one of the most radio-loud Seyfert galaxies known (albeit, in a general sense, still a relatively weak radio AGN, 1 Assuming a Hubble constant H\u25e6= 70 km s\u22121 Mpc\u22121, \u2126\u039b = 0.7 and \u2126M = 0.3, the redshift of IC 5063 (Vhel = 3400 km s\u22121) implies an angular size distance of 47.9 Mpc and a scale of 1 arcsec = 232 pc. with power P1.4GHz = 3 \u00d7 1023 W Hz\u22121). The radio contin- uum emission comes from a linear triple structure, aligned with the inner dust lane, consisting of a central core and two lobes (Morganti et al. 1998), of about 4 arcseconds in size (corre- sponding to \u223c1 kpc; see Fig. 1). Observations of the atomic hydrogen in IC 5063 quite unexpectedly revealed the presence of a fast out\ufb02ow, with out\ufb02ow velocities up to 700 km s\u22121 (Morganti et al. 1998). Subsequent VLBI observations of the H i in IC 5063 (Oosterloo et al. 2000), as well as observations of the ionised gas (Morganti et al. 2007; Dasyra et al. 2015), suggested the likely dominant role of the radio jet, and the over-pressured cocoon surrounding it, in driving the out\ufb02ow. The presence of molecular gas associated with this out\ufb02ow was \ufb01rst found from APEX CO(2-1) observations (Morganti et al. 2013) and by the detection of warm molecular gas (H2 detected at 2.2 \u00b5m) using ISAAC on the VLT (Tadhunter et al. 2014). The latter study also showed that the warm H2 gas with the most extreme out\ufb02ow ve- locities is co-spatial with the bright radio hot-spot \u223c0.5 kpc west of the nucleus, underlining the importance of the jet in driving the out\ufb02ow. However, the high spatial resolution ALMA CO(2-1) obser- vations presented in Morganti et al. (2015) give the best view of the complex interplay between the radio plasma ejected by the AGN and the molecular gas in the central regions of IC 5063. These observations have shown the presence of a cen- tral, bright component of CO(2-1) emission (\u223c1 kpc in size) which has a close spatial correspondence with the radio jet (see Article number, page 2 of 13 Oosterloo et al.: Properties of the molecular gas in the fast out\ufb02ow in the Seyfert galaxy IC 5063 Fig. 1 in Morganti et al. 2015). In addition, this bright molec- ular gas has strongly disturbed kinematics, extending along the entire radio jet with out\ufb02ow velocities up to 800 km s\u22121 with the highest out\ufb02ow velocities occurring about 0.5 kpc from the nucleus, at the location of the bright hot-spot in the W lobe. The close spatial correspondence of this region of molecular gas hav- ing highly disturbed kinematics with the region of radio plasma, suggests a model \u2013 similar to, e.g., presented in the simulations of Wagner et al. (2012) \u2013 where the radio plasma jet is expand- ing into a clumpy gaseous medium and it creates a cocoon of (shocked) gas which is pushed away from the jet axis resulting in a lateral expansion. In the simulations of Wagner et al. (2012), di\ufb00erent zones in the gas a\ufb00ected by the AGN can be identi- \ufb01ed and, according to the model, di\ufb00erent conditions must oc- cur in these di\ufb00erent zones. Thus, given that the molecular out- \ufb02ow in IC 5063 is spatially well resolved, this object is an ideal candidate for studying the physical conditions of the molecular out\ufb02ows and to compare observations with models. A detailed comparison of our data with numerical models will be done in a following paper (Mukherjee et al. 2017). First results were presented in Dasyra et al. (2016) where new ALMA observations of the CO(4-3) transition were com- bined with the CO(2-1) data of Morganti et al. (2015). This com- bination showed that the physical conditions of the molecular gas in the jet-driven out\ufb02ow are very di\ufb00erent from those of the larger-scale quiescent molecular disk, with the former having much higher excitation temperatures. Importantly, the observed line ratios indicated that the out\ufb02owing gas is optically thin. This has important implications for how to convert the observed line intensity of the out\ufb02ow to its mass and results in a lower estimate of the mass of the out\ufb02ow compared to the optically thick case. Here, we further expand on these results by presenting new ALMA observations exploring other tracers of the molecular gas: 12CO(1-0), 12CO(3-2), 13CO(2-1) and HCO+(4-3). This larger range of molecular tracers allows more extensive charac- terisation of the physical conditions of the di\ufb00erent kinematical components of the molecular gas. The structure of the paper is as follows: in Sect. 2 we describe the ALMA observations and the data reduction. In Sect. 3 we compare the spatial distribution and kinematics of the 12CO lines, while in Sect. 4 we present the HCO+(4-3) and 13CO observational results. In Sect. 5 we discuss the excitation of the gas in the various regions of the out\ufb02ow and derive an estimate of the mass of the molecular out\ufb02ow. In this section we also present estimates of the kinetic temperatures and densities for representative regions in the out\ufb02ow and in the disk of IC5063 derived using the RADEX non-LTE radiative transfer code2 (van der Tak et al. 2007)."
                }
            ],
            "Michele Cappellari": [
                {
                    "url": "http://arxiv.org/abs/2208.14974v2",
                    "title": "Full spectrum fitting with photometry in pPXF: stellar population versus dynamical masses, non-parametric star formation history and metallicity for 3200 LEGA-C galaxies at redshift z~0.8",
                    "abstract": "I introduce some improvements to the pPXF method, which measures the stellar\nand gas kinematics, star formation history (SFH) and chemical composition of\ngalaxies. I describe the new optimization algorithm that pPXF uses and the\nchanges I made to fit both spectra and photometry simultaneously. I apply the\nupdated pPXF method to a sample of 3200 galaxies at redshift $0.6<z<1$ (median\n$z=0.76$, stellar mass $M_\\ast>3\\times10^{10}$ M$_\\odot$), using spectroscopy\nfrom the LEGA-C survey (DR3) and 28-bands photometry from two different\nsources. I compare the masses from new JAM dynamical models with the pPXF\nstellar population $M_\\ast$ and show the latter are more reliable than previous\nestimates. I use three different stellar population synthesis (SPS) models in\npPXF and both photometric sources. I confirm the main trend of the galaxies'\nglobal ages and metallicity $[M/H]$ with stellar velocity dispersion\n$\\sigma_\\ast$ (or central density), but I also find that $[M/H]$ depends on age\nat fixed $\\sigma_\\ast$. The SFHs reveal a sharp transition from star formation\nto quenching for galaxies with $\\lg(\\sigma_\\ast/\\mathrm{km\\, s^{-1}})>2.3$, or\naverage mass density within 1 kpc $\\lg(\\Sigma_1^{\\rm JAM}/\\mathrm{M_\\odot\nkpc^{-2}})>9.9$, or with $[M/H]>-0.1$, or with Sersic index $\\lg n_{\\rm\nSer}>0.5$. However, the transition is smoother as a function of $M_\\ast$. These\nresults are consistent for two SPS models and both photometric sources, but\nthey differ significantly from the third SPS model, which demonstrates the\nimportance of comparing model assumptions. The pPXF software is available from\nhttps://pypi.org/project/ppxf/.",
                    "authors": "Michele Cappellari",
                    "published": "2022-08-31",
                    "updated": "2023-09-07",
                    "primary_cat": "astro-ph.GA",
                    "cats": [
                        "astro-ph.GA"
                    ],
                    "main_content": "At significant redshift (e.g. \ud835\udc67> \u223c1) the cosmological surface brightness dimming (e.g. Hogg 1999) makes good-quality spectra more difficult to obtain as the contribution of the sky background starts to dominate. ppxf was used to measure the kinematic and stellar population of significant samples of galaxies at redshift \ud835\udc67\u22481 (e.g. Shetty & Cappellari 2015; Bezanson et al. 2018) but only of individual objects out to \ud835\udc67\u22482 (e.g. van de Sande et al. 2013; Belli et al. 2014, 2017) and \ud835\udc67\u22483 (e.g. Esdaile et al. 2021; Forrest et al. 2022). Most large studies of distant galaxies still had to rely on photometry alone. The most essential parameters one wants to extract from high-\ud835\udc67 galaxies are their redshift and stellar mass (e.g. Muzzin et al. 2013; Weaver et al. 2022). Various template-fitting codes were developed to measure masses and redshift from photometric observations in multiple bands (I ignore here methods based on machine learning; see Salvato et al. 2019 for a review). These include Hyperz (Bolzonella et al. 2000), bpz (Ben\u00b4 \u0131tez 2000), LePhare (Arnouts et al. 2002), zebra (Feldmann et al. 2006) and eazy (Brammer et al. 2008). These methods are conceptually similar to the template-based spectral fitting ones used for nearby galaxies, however, they all adopt a Bayesian approach, instead of a least-squares fitting one. This makes the codes simpler and allows for easy inclusion of priors on galaxy parameters or non-Gaussian uncertainties; e.g. one can assign a low probability to solutions where the galaxy has an unphysically large/small stellar mass. Building on the photometric-redshift and full-spectrum fitting approaches, new software was later developed to fit spectra together with the photometry, while still retaining the same Bayesian approach of photometric-redshift codes. Examples of these are fast (Kriek et al. 2009), beagle (Chevallard & Charlot 2016), bagpipes (Carnall et al. 2018), the code described by Mendel et al. (2020) and prospector (Johnson et al. 2021b). Contrary to what is sometimes stated, both least-squares, or maximum-likelihood, and Bayesian methods can return model posteriors, when needed. The former uses bootstrapping (e.g. Efron & Tibshirani 1994) or Monte Carlo approaches. In fact, bootstrapping can be seen as an efficient way to compute the Bayesian posterior, with non-informative priors (e.g. Rubin 1981; Efron 2011). Although bootstrapping is less flexible than general Bayesian methods, in many realistic situations, the uncertainties of model parameters are dominated by data systematic and model assumptions (as I also find later) rather than the details of the adopted statistical approach or by adopted priors. 1.3 This paper In this paper, I proceed differently than most existing methods. Instead of adopting the standard Bayesian approach to fit photometry and spectra, I present an extension of my ppxf least-squares full-spectrum fitting method to simultaneously fit photometry. A key difference in this approach is that it can be a few orders of magnitude faster than Bayesian methods. Apart from algorithmic differences, my ppxf approach to fitting photometry with spectra is analogue to the extension of the starlight least-squares full-spectrum fitting method (L\u00b4 opez Fern\u00b4 andez et al. 2016; Werle et al. 2019). Lest-squares methods appear complementary to existing ones as the extra speed allows for extra flexibility in the treatment of the stellar population, as shown later. I illustrate the characteristics of the approach by fitting the VIMOS spectra and COSMOS photometry (Muzzin et al. 2013; Weaver et al. 2022) to study the joint SFH metallicity distributions and the stellar population scaling relations of about 3200 galaxies from the LEGA-C survey (van der Wel et al. 2021) in the redshift range 0.6 < \ud835\udc67< 1. Readers interested in the ppxf techniques should keep reading how to measure velocities in Section 2 and the ppxf updates in Section 3. While those only interested in the scientific results should skip the next two sections and go directly to the description of the data in Section 4 and results in Section 7. In this work, I adopt a standard cosmology with \ud835\udc3b0 = 70 km \ud835\udc60\u22121Mpc\u22121, \u03a9\ud835\udc5a= 0.3 and \u03a9\u039b = 0.7. 2 MEASURING VELOCITY AND REDSHIFT In Cappellari (2017, sec. 2) I reviewed general and important facts that one should know before using any full spectral fitting method and ppxf in particular. Here I include only some updates, and I heavily refer the reader to my previous paper of this series to avoid duplicating material. 2.1 From measured velocity to observed redshift The physical meaning of the velocity \ud835\udc49returned by ppxf or any spectrum-fitting code is often a source of confusion. As discussed in Cappellari (2017, sec. 2.3), the reason for this is that \ud835\udc49has no physical meaning. Even the recession velocity itself, for a distant galaxy, is an ill-defined concept with a debated interpretation (e.g. Bunn & Hogg 2009). It should never be used for quantitative work. What is well-defined empirically is the redshift \ud835\udc67of a given spectrum: 1 + \ud835\udc67\u2261\ud835\udf06obsv \ud835\udf06emit \ud835\udf06obsv \ud835\udf06emit , (1) where \ud835\udf06obsv and \ud835\udf06emit are the observed and rest-frame wavelength of a given spectral feature. The key formula that is needed to convert the \ud835\udc49ppxf returned by ppxf into redshift is (Cappellari 2017, eq. 8) \ud835\udc49ppxf \u2261\ud835\udc50ln(1 + \ud835\udc67), (2) withthe speed of light. This formula is exact by construction and it \u2261( +) with \ud835\udc50the speed of light. This formula is exact by construction and it is the only one to use to attach a physical meaning to \ud835\udc49ppxf. 2.2 Separating peculiar velocities and cosmological redshift When observing spectra of distant galaxies from a single aperture, redshift is all one can measure. However, when obtaining spatiallyresolved observations of galaxies e.g. using integral-field spectroscopy (see review by Cappellari 2016) one needs to separate the cosmological redshift \ud835\udc67cosm, which only contains information on the galaxy distance, from the peculiar velocity \ud835\udc49pec. The latter is the one which satisfies e.g. Newton\u2019s law of gravitation in a reference system that moves MNRAS 000, 1\u201328 (2023) ppxf with spectra and photometry at \ud835\udc67\u22480.8 3 with the galaxy barycentre. It is the velocity that has to be used to construct dynamical models of the galaxy. In Cappellari (2017, sec. 2.4) I suggested using the standard way of separating peculiar and cosmological redshift. However, there is a simpler and formally even more accurate way. In fact, the conversion of \ud835\udc49ppxf into redshift is unnecessary (see Baldry 2018). One can directly obtain \ud835\udc49pec using the velocities returned by ppxf as follows \ud835\udc49pec(\ud835\udc65, \ud835\udc66) = \ud835\udc49ppxf(\ud835\udc65, \ud835\udc66) \u2212\ud835\udc49ppxf(bary). (3) Here \ud835\udc49ppxf(\ud835\udc65, \ud835\udc66) is the velocity returned by ppxf at the location (\ud835\udc65, \ud835\udc66) on the sky, \ud835\udc49ppxf(bary) is the velocity returned by ppxf for the galaxy (or cluster) barycentre and \ud835\udc49pec(\ud835\udc65, \ud835\udc66) is the peculiar velocity at location (\ud835\udc65, \ud835\udc66). The latter is the only one with a clear physical meaning: it is the one to use in a dynamical model (e.g. Cappellari 2008), or to estimate the level of rotation in a galaxy (e.g. Emsellem et al. 2011). Importantly, equation (3) is always valid, regardless of whether the spectrum was de-redshifted to the rest-frame or not, before measuring \ud835\udc49ppxf. Note that this formula only works because of the way ppxf defines the relation between velocity and redshift in equation (2) and cannot be used with alternative definitions (e.g. \ud835\udc49\u2261\ud835\udc50\ud835\udc67). As an example of a practical application of these formulas, let\u2019s assume I am fitting a single spectrum of a high-\ud835\udc67galaxy for which I have an estimate of the redshift \ud835\udc67\u2032 (e.g. from photometry). It is generally convenient to de-redshift the spectrum by dividing each observed wavelength \ud835\udf06obs to obtain an estimate of the rest-frame wavelength with \ud835\udf06\u2032 rest = \ud835\udf06obs (1 + \ud835\udc67\u2032) (4) I then fit the spectrum with ppxf to obtain \ud835\udc49ppxf. If the initial guess \ud835\udc67\u2032 was perfect, I would obtain \ud835\udc49ppxf = 0, but in general I will measure \ud835\udc49ppxf \u22600, with uncertainty \u0394\ud835\udc49ppxf. An improved estimate of the galaxy redshift \ud835\udc67and its uncertainty \u0394\ud835\udc67can be obtained using equation (2) and equation (3) as \ud835\udc49\u2032 = \ud835\udc50ln(1 + \ud835\udc67\u2032), (5a) \ud835\udc49tot = \ud835\udc49ppxf + \ud835\udc49\u2032 (5b) 1 + \ud835\udc67= exp \u0012\ud835\udc49tot \ud835\udc50 \u0013 = (1 + \ud835\udc67\u2032) exp \u0012\ud835\udc49ppxf \ud835\udc50 \u0013 (5c) \u0394\ud835\udc67 1 + \ud835\udc67\u2248\u0394 ln(1 + \ud835\udc67) \u2248\u0394\ud835\udc49ppxf \ud835\udc50 . (5d) Identical results are obtained without first bringing the spectrum to the restframe and setting \ud835\udc67\u2032 = 0 in equation (5). But one should remember to adjust the instrumental resolution as described in sec. 2.4 of Cappellari (2017). 3 UPDATES TO THE ppxf PACKAGE I gave a detailed overview of the ppxf method in Cappellari (2017, sec. 3). I will not repeat that summary here, but instead, I will refer the reader to specific sections of that paper, while trying to keep a consistent notation. However, I substantially evolved ppxf since then, driven by the needs of my research and requests from colleagues. I only describe here the ppxf features that have changed. The description corresponds to the current version 8.2 of the public ppxf Python package1. 1 Available from https://pypi.org/project/ppxf/ 3.1 Well-sampled variable-\ud835\udf0econvolution As discussed in Cappellari (2017, sec. 2.2), when fitting stellar templates to galaxy spectra, one generally needs to first match their resolution to that of the galaxy observations by convolving the templates with a Gaussian with dispersion \ud835\udf0ethat varies with wavelength \ud835\udf06. In a previous version of ppxf, I implemented this step as a direct summation of the spectrum, weighted by the Gaussian centred on every pixel (function ppxf util.gaussian filter1d in ppxf). Given that the Gaussian is typically nonzero only over \ud835\udc5bgau \u223c10 pixels, while the templates have \ud835\udc5bpix > \u223c1000 spectral pixels, I limited the summation only to the nonzero pixels of the Gaussian kernel. In this way, the computation time of this summation scales as \ud835\udc61\u221d\ud835\udc5bpix \u00d7\ud835\udc5bgau, which is comparable to that \ud835\udc61\u221d\ud835\udc5bpix \u00d7 ln(\ud835\udc5bpix) achievable using Fourier convolution using the Fast Fourier Transform (FFT, Cooley & Tukey 1965). A limitation of performing a convolution as a summation is that, when the \ud835\udf0eof the Gaussian becomes comparable to the size of the sampled pixels, the convolution suffers from the same undersampling problems that motivated the use of an analytic Fourier Transform (FT) for the convolution in ppxf discussed in Cappellari (2017). For this reason, I now implemented an alternative procedure ppxf util.varsmooth which performs the variable-\ud835\udf0econvolution using the FFT and uses the same approach of ppxf of using an analytic Fourier Transform of the kernel, to avoid undersampling issues. A natural idea to use the FFT for the convolution of a vector of values with a kernel with variable scale is to stretch the coordinate with the inverse of the scale, via interpolation, in such a way that the kernel has the same scale in the new coordinates. This idea was discussed e.g. in 2014 on StackOverflow2 and implemented in 2016 by Janez Kos on GitHub3 in the procedure varconvolve. It was also discussed in Johnson et al. (2021b). The interpolation approach is also central for algorithms for the Non-Uniform FFT (NUFFT, e.g. Greengard & Lee 2004). Here I combine the interpolation approach with the use of an analytic Fourier Transform as in Cappellari (2017) to produce Algorithm 1. The algorithm can also be used with a non-Gaussian kernel (e.g. Cappellari 2017, eq. 38) as long as only its scale changes with wavelength. Algorithm 1 varsmooth: well-sampled variable-\ud835\udf0econvolution Given x, y, \ud835\udf48\ud835\udc65, xout \u22b2len(x) = len(y) = len(\ud835\udf48\ud835\udc65) = \ud835\udc5d \ud835\udf48= \ud835\udf48\ud835\udc65/\u2207x \u22b2Convert \ud835\udf48\ud835\udc65into pixels4 \ud835\udf0emax = max(\ud835\udf48) \u00d7 \ud835\udc5a \u22b2Optional oversampling \ud835\udc5a\u22651 s = cumsum(\ud835\udf0emax/\ud835\udf48) \u22b2Cumulative sum \ud835\udc5b= ceil(\ud835\udc60\ud835\udc5d\u2212\ud835\udc601) \u22b2Ensure oversampling xnew = subdivide(\ud835\udc601, \ud835\udc60\ud835\udc5d, \ud835\udc5b) \u22b2\ud835\udc5bequispaced values ynew = interpolate(s, y)(xnew) F (gauss) = exp(\u2212\ud835\udf0e2 max\ud835\udf4e2/2)/ \u221a 2\ud835\udf0b \u22b2Gaussian Analytic FT yconv = F \u22121[F (ynew)F (gauss)] \u22b2Convolution theorem & FFT if xout is given then s = interpolate(x, s)(xout) yconv = interpolate(xnew, yconv)(s) This algorithm works well in practice, but one should be aware of its theoretical limitations. In fact, most interpolation methods can 2 https://stackoverflow.com/a/24186800 3 https://github.com/sheliak/varconvolve 4 I use a centred finite-difference approximation of the gradient \u2207\ud835\udc65instead of the spectral pixels size \u0394\ud835\udc65, which is generally not provided. The two quantities coincide in uniformly-sampled regions of the spectrum. MNRAS 000, 1\u201328 (2023) 4 M. Cappellari be described as a convolution with a specific kernel (e.g. Getreuer 2011) and one may think it would be better to remove the effect of this extra convolution as done e.g. in the NUFFT methods. However, this situation is different as the spectra have noise and one would have to perform the interpolation in a Bayesian framework (e.g. MacKay 1992, 2003). One should also consider that the spectra to fit generally already include additional interpolation and resampling, which would have to be modelled for rigorous results. But all this is unlikely to affect scientific results, and for this reason, is beyond the scope of this paper. 3.2 CapFit nonlinear least-squares with linear constraints 3.2.1 The problem When fitting the kinematics of multiple kinematics components with ppxf, both for the stellar and gas emission components, it is often useful to be able to set constraints on some parameters as a function of other parameters. For example, when looking for spectra containing both narrow and broad gas emission lines to study Active Galactic Nuclei (AGN, e.g. Oh et al. 2015; Fu et al. 2023), to avoid the degeneracy of fitting two similar lines, one may want to constrain the dispersion of the broad emission component, if present, to be significantly larger than that of the narrow one \ud835\udf0ebroad > \ud835\udf0enarrow + \u0394\ud835\udf0e, or as a fractional difference \ud835\udf0ebroad > \ud835\udc53\u00d7 \ud835\udf0enarrow. Or one may want to constrain the velocity of a possible broad emission component to differ less than a certain value from that of the narrow one |\ud835\udc49broad \u2212\ud835\udc49narrow| < \u0394\ud835\udc49. Efficiently setting this kind of constraint requires solving a constrained non-linear optimization problem. For maximum computational efficiency and accuracy, one should exploit the special problem that ppxf has to solve (Cappellari 2017, sec. 3.4). In particular, the function to minimize \ud835\udc53(x) is a sum of squares and the typical constraints are linear. The problem to solve can be expressed as minimize \ud835\udc53(x) = 1 2 \u2225r(x)\u22252 subject to Aeq \u00b7 x = beq (6) Aineq \u00b7 x \u2264bineq, where r(x) are the residual from the fit, and x are the nonlinear parameters, like the kinematics of different components. I have searched extensively for specialized software or an algorithm that I could easily use in ppxf to efficiently solve this specific problem but did not find any. For this reason, I developed my own. One of the most effective ways of solving nonlinear problems with general constraints is the sequential quadratic programming (SQP) method, where at every iteration the algorithm solves a constrained quadratic problem that approximates the function at the current location (e.g. Nocedal & Wright 2006, chap. 18). In least-squares problems, one can approximate the function near the current point x\ud835\udc58as a second-order Taylor series, with p = x \u2212x\ud835\udc58, as follows (e.g. Nocedal & Wright 2006, sec. 10.2) \ud835\udc53(x) \u22481 2 \u2225J\ud835\udc58\u00b7 p + r\ud835\udc58\u22252 (7a) = 1 2 \u2225r\ud835\udc58\u22252 + p \u00b7 (J\ud835\udc47 \ud835\udc58\u00b7 r\ud835\udc58) + 1 2p \u00b7 (J\ud835\udc47 \ud835\udc58\u00b7 J\ud835\udc58) \u00b7 p (7b) \u2248\ud835\udc53(x\ud835\udc58) + p \u00b7 \u2207\ud835\udc53(x\ud835\udc58) + 1 2p \u00b7 \u22072 \ud835\udc53(x\ud835\udc58) \u00b7 p, (7c) where J\ud835\udc58is the Jacobian, which can be computed by finite differences, \u2207\ud835\udc53(x\ud835\udc58) = J\ud835\udc47 \ud835\udc58\u00b7 r\ud835\udc58is the gradient and \u22072 \ud835\udc53(x\ud835\udc58) = J\ud835\udc47 \ud835\udc58\u00b7 J\ud835\udc58is the quasi-Newton approximation of the Hessian matrix, whose full form is the following, but I ignored the second term (e.g. Nocedal & Wright 2006, eq. 10.5) \u22072 \ud835\udc53(x) = J\ud835\udc47\u00b7 J + \ud835\udc5a \u2211\ufe01 \ud835\udc57=1 \ud835\udc5f\ud835\udc57\u22072\ud835\udc5f\ud835\udc57. (8) It is a characteristic of least-squares problems that one can approximate the Hessian \u201cfor free\u201d using J and the reason it is important to adopt specialized methods for their solution. In the case of ppxf, the Hessian approximation is always especially good, even far from the solution, because the algorithm separates the linear and nonlinear optimizations (Cappellari 2017, sec. 3.3\u20133.4) and ensures that \u00cd \ud835\udc57\ud835\udc5f\ud835\udc57= 0 at every step. This tends to cancel out the second term in the Hessian of equation (8). In essence, a specialized SQP algorithm to solve equation (6) would consist of solving a sequence of quadratic sub-problems as follows minimize \ud835\udc54(p) = \u2225J\ud835\udc58\u00b7 p + r\ud835\udc58\u22252 subject to Aeq \u00b7 x = beq (9) Aineq \u00b7 x \u2264bineq. Algorithms for this type of problem are discussed e.g. by Fletcher (1987, sec. 11.2) or Gill et al. (1981, chapter 5). I implemented those ideas into a trust-region algorithm (Nocedal & Wright 2006, chap. 4) but I discovered that the approach is not sufficiently robust for my rather special situation. The difficulty of the optimization problem I have to solve consists of the fact that the Jacobian can sometimes be completely degenerate. A common situation where this happens is when ppxf is fitting for the kinematics of emission lines or multiple stellar kinematic components. In this situation, the weights associated with a given emission line or stellar component may become exactly zero, because the line or component is simply not present in a certain galaxy spectrum. In other cases, the signal-to-noise ratio \ud835\udc46/\ud835\udc41may be too low to give any constraints to some parameters. In these cases, the gradient (column of J) with respect to the parameters describing the kinematics of the missing component will be zero. I tried using the Singular Value Decomposition (SVD, e.g. Press et al. 2007, sec. 15.4.2) during the iterations required to solve the quadratic sub-problem. But after extensive testing, e.g. during the development of the MaNGA Data Analysis Pipeline (Westfall et al. 2019), I was unable to find a robust criterion to decide which singular values must be edited and find the effective rank of my Jacobian. 3.2.2 The solution To solve unconstrained least-squares optimization problems one of the most widely used techniques is the Levenberg-Marquardt (LM) method (Levenberg 1944; Marquardt 1963) and its state-of-the-art implementation in minpack (Mor\u00b4 e 1978; Mor\u00b4 e et al. 1980). The success of the LM method comes from the fact that the method penalizes the J matrix adaptively defining the quadratic sub-problem, in such a way that it always prevents degeneracy. This also makes the LM method a robust trust-region algorithm, as discussed in Fletcher (1987, sec. 5.2) or Nocedal & Wright (2006, sec. 10.3). Press et al. (2007, sec. 15.5.2) provides a less technical description. In a previous version (<6.5) of ppxf, I used the LM algorithm, as modified in the mpfit implementation (Markwardt 2009), which included a very useful but non-optimal treatment of box constraints (i.e. upper/lower limits on the parameters). Comparable box-constrained least-squares methods exist in Scipy (Virtanen et al. 2020) as implemented in the trust-region reflective algorithm (method=\u2018trf\u2018; Branch et al. 1999) and the dogleg algorithm (method=\u2018dogbox\u2018, Voglis & Lagaris 2004, Nocedal MNRAS 000, 1\u201328 (2023) ppxf with spectra and photometry at \ud835\udc67\u22480.8 5 & Wright 2006, chapter 4) in scipy.optimize.least squares. These methods are also available in ppxf but cannot support linear constraints. After extensive experimentation with real-world cases, I implemented a novel hybrid between the SQP and LM methods, specialized for the nonlinear least-squares with linear constraints (both equality and inequality). The algorithm consists of a trust-region quasi-Newton SQP method, with linear constraints, in which the matrix defining the quadratic sub-problem is penalized to avoid the risk of degeneracy, as in the LM method. I achieve this by replacing the quadratic subproblem of equation (9) with the following (see Nocedal & Wright 2006, eq. 10.41) minimize \ud835\udc54(p) = \r \r \r \r \u0012 J\ud835\udc58 \u221a\ud835\udf06\ud835\udc58D\ud835\udc58 \u0013 \u00b7 p + \u0012 r\ud835\udc58 0 \u0013\r \r \r \r 2 subject to Aeq \u00b7 x = beq (10) Aineq \u00b7 x \u2264bineq, where Dk is a diagonal matrix, which makes the problem scale invariant. By default, the diagonal elements of Dk are initialized with the norm \u2225\u00b7\u2225of the columns of J and are updated during the iterations as suggested in Mor\u00b4 e (1978, eq. 6.3). Close to the solution, when the quadratic model provides a good approximation of \ud835\udc53(x), then \ud835\udf06\ud835\udc58becomes small and equation (10) approximates equation (9). In this limit, the method behaves as an SQP method. When the quadratic approximation is inaccurate, \ud835\udf06\ud835\udc58becomes large and the method behaves as a trust-region LM method. My resulting algorithm is rather simple because I did not worry about the efficiency of the solution of the quadratic programming sub-problem. The latter generally dominates the complexity of other state-of-the-art algorithms, which devise approximated matrix updates to save computation time (e.g. see the description of LM in Mor\u00b4 e 1978). I also did not try to deal with large-scale problems and sparse matrices which also increase complexity and require specialized methods (e.g Gill et al. 2005). Instead, I focused on the fitting of rather small nonlinear problems (\ud835\udc5b< \u223c50 variables) in which computing the function \ud835\udc53(x) involves creating a complex model, as in ppxf. In this rather common situation, the time to solve the small quadratic programming sub-problem becomes negligible compared to that of evaluating \ud835\udc53(x). The solution is given in Algorithm 2, which I implemented in the capfit procedure in the ppxf package. Except for the fact that the quadratic sub-problem is penalized and linearly-constrained, the algorithm uses the standard trust-region framework (e.g. Nocedal & Wright 2006, algorithm 4.1, or Fletcher 1987, algorithm 5.2.7). For the convergence criteria, I follow the description in Mor\u00b4 e et al. (1980, sec. 2.3). 3.2.3 Solving the quadratic sub-problem I implemented two procedures to solve the quadratic programming subproblem of equation (10). In both cases, I avoid explicitly constructing the Hessian J\ud835\udc47 \ud835\udc58\u00b7J\ud835\udc58as this would degrade the conditioning of the system. The first procedure (lsq box) is specialized for the common situation where only box constraints are present. It solves min \u2225A \u00b7 x \u2212b\u22252 with lb < x < ub. For this, I use the active-set method adopted in the non-negative least-squares (nnsl) method (Lawson & Hanson 1995, algorithm 23.10), which was generalized for box constraints with the Bounded-Variables Least-Squares (bvls) procedure in the same book and in Stark & Parker (1995). My implementation closely follows Lawson & Hanson (1995) except for the important fact that (i) I allow for a starting guess and (ii) I include an initialization step (Algorithm 3) which generalizes to the box-constrained case Algorithm 2 CapFit: linearly-constrained nonlinear least-squares Given x1, \ud835\udc53, \ud835\udf06> 0, \ud835\udf02\u2208[0, 1/4) r1 = \ud835\udc53(x1) J = J(x1) Compute the scaling matrix D \u22b2See text loop Obtain p as solution of equation (10) with J, D, r1, \ud835\udf06 x2 = x1 + p r2 = \ud835\udc53(x2) \ud835\udc5fact = \ud835\udf122(r1) \u2212\ud835\udf122(r2) \u22b2Using \ud835\udf122(x) \u2261x \u00b7 x \ud835\udc5fpre = \ud835\udf122(r1) \u2212\ud835\udf122(J \u00b7 p + r1) \ud835\udf0c= \ud835\udc5fact/\ud835\udc5fpre \u22b2Actual vs predicted reduction if convergence test is satisfied then stop with solution x2 if \ud835\udf0c< 1/4 then \ud835\udf06= 4\ud835\udf06 else if \ud835\udf0c> 3/4 then \ud835\udf06= \ud835\udf06/2 if \ud835\udf0c> \ud835\udf02then \u22b2Successful step: move on J = J(x2) Adjust the scaling matrix D \u22b2See text x1, r1 = x2, r2 the initialization loop in the fastnnls code5 by Andersson & Bro (2000). In realistic ppxf problems, using my new lsq box with hundreds of spectral templates produced a typical speedup of a factor four compared to using the scipy.optimize.nnls, which is a wrapper to the Lawson & Hanson (1995) Fortran code. The procedure scipy.optimize.lsq linear currently also does not support passing a starting guess. Algorithm 3 Initializiation lsq box box-constrained least-squares Given x, A, b, lower lb and upper ub bounds, B \u2260\u2205 while B \u2260\u2205do B = {x | (x < lb) \u2228(ub < x)} Set all x \u2208B to the nearest bound F = {x | lb < x < ub} x\u2032 = min \u2225A \u00b7 x \u2212b\u22252 for x \u2208F Set x = x\u2032 for x \u2208F The second procedure (lsq lin) solves general linearlyconstrained quadratic programming problems like in equation (9) using a modified version of the standard active-set technique described by Nocedal & Wright (2006, algorithm 16.3). The approach consists of solving a sequence of equality-constrained linear least-squares problems, for which I follow Golub & Van Loan (2013, algorithm 6.2.2), allowing for degenerate matrices using SVD. If the initial guess is unfeasible, I find a feasible point using the linear programming procedure scipy.optimize.linprog and the method=\u2019highs\u2019 by Huangfu & Hall (2017). Alternatively, the quadratic sub-problem can be solved within ppxf by minimizing the quadratic function in the form of equation (7b) using a general quadratic programming solver. In the current implementation, I use the interior-point solver solvers.coneqp from the cvxopt package6 by Andersen et al. (2011), which is much faster for large-scale problems. I have extensively tested the lsq box and lsq lin procedure described in this 5 Available from https://ucphchemometrics.com/ 6 Available from https://cvxopt.org/ MNRAS 000, 1\u201328 (2023) 6 M. Cappellari section by constructing batteries of tests using both exact analytic solutions and comparisons against cvxopt. The capfit procedure has been the default nonlinear optimization algorithm in ppxf for about three years and has been used as a general optimizer independently of ppxf too. During this time ppxf was used to fit millions of spectra from a variety of surveys (e.g. MaNGA Bundy et al. 2015 and SAMI Bryant et al. 2015). This allowed me to fix its handling of rare failures in degenerate situations, which are difficult to encounter in idealized examples. When applied to unconstrained nonlinear least-squares problems capfit produces essentially the same iterates as the state-of-the-art LM implementations in minpack or mpfit, as expected. When used for box-constrained nonlinear least-squares problems capfit is generally at least as efficient as the best algorithms in scipy.optimize.least squares. However, capfit allows for the extra flexibility of using linear constraints, as well as for keeping variables tied to others or fixed. 3.3 Setting linear constraints on the template weights In the previous section, I discussed the use of linear constraints on the kinematic parameters during the ppxf fit. Here I note that linear constraints can be used also during the linear-fitting procedure in Cappellari (2017, sec. 3.3). These were used for example to constrain the sum of weights (e.g. the luminosity) of different template groups to constitute a certain fraction of the total light, e.g. to perform kinematic bulge/disks decompositions (e.g. Tabor et al. 2017, 2019; Oh et al. 2020) or to study stellar population of different kinematic components (e.g. Shetty et al. 2020b). 3.4 Multi-dimensional regularization Considering without loss of generality that stellar population depends only on age, the fundamental equation used to model the spectrum of a composite stellar population is (e.g. Cid Fernandes et al. 2005; Ocvirk et al. 2006; Conroy 2013, sec. 2.3) \ud835\udc3amod(\ud835\udf06) = \u222b\ud835\udc61=\ud835\udc47 \ud835\udc61=0 SSP\ud835\udf06(\ud835\udc61, \ud835\udc4d) \u00b7 SFR(\ud835\udc47\u2212\ud835\udc61) d\ud835\udc61, (11) where SFR is the star formation rate, SSP\ud835\udf06is a Single Stellar Population spectrum per unit mass, with age \ud835\udc61and metallicity \ud835\udc4d, while \ud835\udc47is the age of the Universe at the redshift of the galaxy. This expression is generalized in ppxf to study the distribution of more parameters, like e.g. metallicity, \ud835\udefcenhancement or IMF, in addition to the SFR. I pointed out in Cappellari (2017, sec. 3.5) that equation (11) is an inhomogeneous Fredholm equation of the first kind, with kernel SSP\ud835\udf06. And the recovery of the SFR(\ud835\udc61) from the observed \ud835\udc3amod is a textbook example of ill-conditioned inverse problem (e.g. Hansen 1998; Kabanikhin 2011; Press et al. 2007, sec. 19.0). This means that one cannot find a unique solution from real data without further assumptions. In Cappellari (2017, sec. 3.5) I discussed the implementation of linear regularization (e.g. Press et al. 2007, sec. 19.5) in ppxf to address this issue and study the stellar population in galaxies. I gave a formula for the second-order one-dimensional regularization. Given that there are alternative ways of generalizing a measure of smoothness of a function in dimension larger than one (e.g. Brady & Horn 1983), I clarify here that the second-order regularization (reg ord=2) in ppxf minimizes the total squared Laplacian (\u0394\ud835\udc64)2 of the weights \ud835\udc64distribution, while the first-order one (reg ord=1) minimizes the total squared gradient (\u2207\ud835\udc64)2. Both operators are implemented by standard finite differences. 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 rest ( m) 0.25 0.50 0.75 1.00 1.25 Relative Flux (f ) Synthetic composite-population spectrum with S/N = 50 lg Age (yr) 1.5 1.0 0.5 0.0 [M/H] True Input pPXF Light Fractions lg Age (yr) 1.5 1.0 0.5 0.0 [M/H] Single non-regularized pPXF fit lg Age (yr) 1.5 1.0 0.5 0.0 [M/H] Average of 100 pPXF fits to Montecarlo realizations 8.0 8.5 9.0 9.5 10.0 lg Age (yr) 1.5 1.0 0.5 0.0 [M/H] Single regularized pPXF fit 0.00 0.02 0.04 0.06 0.08 0.00 0.02 0.04 0.06 0.08 0.00 0.02 0.04 0.06 0.08 0.00 0.02 0.04 0.06 0.08 Figure 1. Top panel: synthetic input spectrum with Gaussian noise at \ud835\udc46/\ud835\udc41= 50. Second panel: input distribution of the \ud835\udc49-band templates luminosity. Third panel: recovered weights from a single non-regularized ppxf fit to one Monte Carlo realization of the noise. Fourth panel: average of the weights recovered with ppxf by fitting 100 Monte Carlo realizations of the synthetic spectrum. Bottom panel: weights recovered with a single ppxf fit with regularization regul=30. This approximates the average distribution as expected. Press et al. (2007, 19.4.1) point out that, under some sensible conditions, the regularized solution has a simple Bayesian interpretation: it represents the most likely solution for the weights, given an adjustable prior on the amplitude of the fluctuations. However, the meaning of the fundamental degeneracy of the stellar population inversion, as well as of regularization, is best illustrated with an example. I used a grid of 25 logarithmically-spaced ages \ud835\udc61and 6 metallicities [\ud835\udc40/\ud835\udc3b] from the SPS models by Vazdekis et al. (2015) to construct a synthetic spectrum in which the distribution of light contributed by each spectrum in the \ud835\udc49band follows a bivariate Gaussian distribution N (\ud835\udc61, [\ud835\udc40/\ud835\udc3b]) with mean age \ud835\udc610 = 1 Gyr, mean [\ud835\udc40/\ud835\udc3b]0 = \u22120.3 and dispersion of 0.25 dex in both age and metallicity. I logarithmically sampled the spectrum at a velocity scale \u0394\ud835\udc49= \ud835\udc50\u0394 ln \ud835\udf06= 50 km \ud835\udc60\u22121 per spectral pixel. I show the resulting spectrum in the top panel of Fig. 1 and the MNRAS 000, 1\u201328 (2023) ppxf with spectra and photometry at \ud835\udc67\u22480.8 7 input light-weights distribution in the second panel. The third panel shows a single ppxf fit, which is characterized by discrete sharp peaks as expected due to the ill-conditioning of the inversion problem. The fourth panel shows the result of averaging the weights obtained by fitting with ppxf 100 Monte Carlo realizations obtained by adding Gaussian noise on the same noiseless synthetic spectrum. Here, the average converges towards the true input distribution. Finally, in the bottom panel, I show the result of performing a single regularized ppxf fit (with reg order=2 and a typical regul=30). Here the distribution looks comparable to that of the average of multiple realizations. Regularization has its limitations, in fact, it is by construction a trade-off between agreement with the data and smoothness (e.g. Press et al. 2007, fig. 19.4.1), which may introduce biases. In general, when one is one is obtaining results by averaging many spectra, it may be better not to use regularization, or only use a minimal amount, to reduce possible biases, while allowing the differences in the noise between spectra to act as Monte Carlo realizations. But regularization is very useful when interpreting individual spectral fits and even to reduce noise in the SPS models themselves, which may introduce spurious features in the solutions (as I found later). One can use bootstrapping of the residuals, while repeating the ppxf fits multiple times, to obtain averages as well as uncertainties in the distribution of the weights as done e.g. by Kacharov et al. (2018, figs. 8\u201313). In this case, it is important to perform the initial ppxf fit, from which the residuals are extracted, using some regularization, to obtain a less noisy and more representative best-fitting spectrum. I achieved good results perturbing the residuals using the easy-to-use wild bootstrap method (Davidson & Flachaire 2008). 3.5 Global nonlinear fitting In the most common situations, e.g. when fitting a single stellar kinematic component with emission lines, the spectral fitting problem has a single global minimum and the local optimization method of Section 3.2 is guaranteed to efficiently converge to it. However, in more complex situations, like when fitting multiple stellar or gas kinematic components, the fitting problem may present multiple minima and a local optimizer is not guaranteed to converge to the global minimum. The standard way of dealing with multiple minima in ppxf is to perform the optimization of the variables in which the \ud835\udf122 function is multi-modal outside of ppxf, while calling ppxf with those variables fixed, from inside a wrapper function. For example, when studying multiple kinematic components one may sample a grid of velocities and call ppxf with fixed velocities at every location (e.g. Mitzkus et al. 2017; Tabor et al. 2017; Bevacqua et al. 2022). If one is interested in the full posterior of certain parameters, and computation time is not an issue, one may call ppxf with those parameters fixed from within a Bayesian method like MultiNest (Feroz et al. 2009), emcee (Foreman-Mackey et al. 2013), AdaMet (Cappellari et al. 2013a) or dynesty (Speagle 2020), assuming the contribution of the non-fixed parameters to the posterior can be neglected. In the current version of ppxf one can also perform the global optimization within ppxf. This is currently implemented using the function scipy.optimize.differential evolution, which uses the Differential Evolution algorithm by Storn & Price (1997). The Scipy function allows for linear constraints using the method by Lampinen (2002). To save computation time, by default, I do not run the global optimization step until convergence, but I use it as starting point for the usual CapFit procedure. An example of a situation where using both the global optimization and the linear constraints options can be useful, and the corresponding 0.652 0.654 0.656 0.658 0.660 0.662 rest ( m) 0 2 4 6 8 10 12 Relative Flux (f ) [NII] [NII] H NGC1386: three gas kinematics components 0.494 0.496 0.498 0.500 0.502 rest ( m) 0 5 10 15 Relative Flux (f ) [OIII] [OIII] Figure 2. Fit of a MUSE spectrum of the active galaxy NGC 1386 (thin black line, mostly hidden by the fit), using the global-optimization option (global search=True) and linear constraints (constr kinem) in ppxf. Each of the five emission lines is modelled with three kinematic components (see text). The orange line is the ppxf total best fit, the red line is the best fitting stellar spectrum alone, while the magenta is for the gas emissions alone, with individual components shown in blue. The fit residuals, arbitrarily offset, are shown with green diamonds. I only plot the region with the key emissions, but I fitted the full optical spectrum, which is needed to constrain the underlying stellar contribution. ppxf fit is shown in Fig. 2. The plots show the central spectrum of the active galaxy NGC 1386, extracted from the MUSE (Bacon et al. 2010) integral-field spectroscopic observations presented in Venturi et al. (2021). The emission line spectrum clearly requires at least three distinct kinematic components (see also Lena et al. 2015). The definition of the three kinematics components may appear ill-defined, due to the extensive blending of the lines. However, a meaningful decomposition can be obtained with some simple assumptions. Here I required the kinematics (\ud835\udc49, \ud835\udf0e) of all five emission lines to be the same within each of the three kinematic components. I additionally required the \ud835\udf0ebroad of the broad component to be at least 200 km \ud835\udc60\u22121 broader than either of the two narrow components as follows \ud835\udf0ebroad > \ud835\udf0enarrow,1 and \ud835\udf0ebroad > \ud835\udf0enarrow,2. These are linear constraints that I enforced using the constr kinem keyword in ppxf. I also fix the ratios of the [OIII] and [NII] doublets to 1/3. Linear constraints in ppxf were used extensively to produce the recent catalogue of broad and multiple gas emission line components for the full MaNGA galaxy survey (Fu et al. 2023). 3.6 Fitting spectra and photometry Adding photometry to a full-spectrum fitting method is similar to adding a few extra pixels to the fit, which represent the fluxes measured MNRAS 000, 1\u201328 (2023) 8 M. Cappellari in some observed photometric bands. The main differences are (i) that the photometric fluxes are independent of the line-of-sight velocitydistribution (LOSVD) L\ud835\udc5b(\ud835\udc63), unlike the spectroscopic ones and (ii) the photometry of a single galaxy is usually not enough to determine both the calibration errors and the template weights. This means that one cannot use polynomials as done for the spectroscopy. I define a function that describes an individual template spectrum \ud835\udc47\ud835\udc5b(\ud835\udf06) (either stars or gas), convolved \u2217with the LOSVD, which is allowed to be different for each of the \ud835\udc41templates \ud835\udc54\ud835\udc5b(\ud835\udf06) = \ud835\udc47\ud835\udc5b(\ud835\udf06) \u2217L\ud835\udc5b(\ud835\udc63). (12) With this notation, the model for the galaxy spectrum becomes \ud835\udc3aspec mod(\ud835\udf06) = \ud835\udc41 \u2211\ufe01 \ud835\udc5b=1 \ud835\udc64\ud835\udc5b \" \ud835\udc54\ud835\udc5b(\ud835\udf06) \ud835\udc34\ud835\udc5b(\ud835\udf06) \ud835\udc3e \u2211\ufe01 \ud835\udc58=1 \ud835\udc4e\ud835\udc58P\ud835\udc58(\ud835\udf06) # + \ud835\udc3f \u2211\ufe01 \ud835\udc59=0 \ud835\udc4f\ud835\udc59P\ud835\udc59(\ud835\udf06) + \ud835\udc3d \u2211\ufe01 \ud835\udc57=1 \ud835\udc50\ud835\udc57\ud835\udc46\ud835\udc57(\ud835\udf06), (13) where the P\ud835\udc58and P\ud835\udc59are multiplicative and additive polynomials respectively (of Legendre or trigonometric type) and the \ud835\udc46\ud835\udc57are optional spectra of the sky. This model is similar to the one in Cappellari (2017, eq. 11), except that here each template spectrum can have a different attenuation function \ud835\udc34\ud835\udc5b. Moreover, both the attenuation and multiplicative polynomials can be used simultaneously, rather than being alternatives. This is especially useful when including photometry in the fit. The reason for this modification is that, when we have photometric bands that span a large wavelength range, we can infer the attenuation from the photometry itself, which is not modelled with polynomials. At the same time, we can use multiplicative polynomials to correct small errors in the spectral flux calibration. However, if we do not have photometry, we cannot tell apart reddening and multiplicative polynomials, because reddening is a special case of polynomials. The model for the photometric measurements, in linear units which allow for negative fluxes, not magnitudes, is given by the following expression \ud835\udc3aphot mod(\ud835\udf06\ud835\udc5e) = \ud835\udc41 \u2211\ufe01 \ud835\udc5b=1 \ud835\udc64\ud835\udc5b\u27e8\ud835\udc54\ud835\udc5b(\ud835\udf06) \ud835\udc34\ud835\udc5b(\ud835\udf06)\u27e9\ud835\udc5e, (14) where \u27e8\u00b7\u27e9\ud835\udc5erepresents the attenuated mean flux of the \ud835\udc5b-th template in the \ud835\udc5e-th photometric band with effective wavelength \ud835\udf06\ud835\udc5e. Unlike the spectroscopic model of equation (13), the photometric model of equation (14) does not include polynomials or the sky spectrum. In the common case of a photon-counting or energy-integrating detectors, and assuming fluxes as \ud835\udc53\ud835\udf06(e.g. in units of erg cm\u22122 s\u22121 \u02da A\u22121) the mean flux is given by (e.g. Bessell & Murphy 2012, eq. A11) \u27e8\ud835\udc53\ud835\udf06\u27e9\ud835\udc5e= \u222b \ud835\udc53\ud835\udf06(\ud835\udf06)\ud835\udc46\ud835\udc5e(\ud835\udf06)\ud835\udf06\ud835\udc51\ud835\udf06 \u222b \ud835\udc46\ud835\udc5e(\ud835\udf06)\ud835\udf06\ud835\udc51\ud835\udf06 , (15) where \ud835\udc46\ud835\udc5e(\ud835\udf06) is the system photon response function and the integral extends over the region where \ud835\udc46\ud835\udc5eis nonzero. The definition of mean flux in equation (15) is the one used in the standard definition of magnitudes in the ultraviolet (e.g for the GALEX spacecraft Martin et al. 2005), in the optical (e.g. for the SDSS optical survey York et al. 2000), or in the near-infrared (e.g. for the 2MASS survey Skrutskie et al. 2006). We can exactly convert mean fluxes in units of \ud835\udc53\ud835\udf08(for example, erg cm\u22122 s\u22121 Hz\u22121) using this formula \u27e8\ud835\udc53\ud835\udf06\u27e9\ud835\udc5e= \u27e8\ud835\udc53\ud835\udf08\u27e9\ud835\udc5e \ud835\udc50 \ud835\udf062 \ud835\udc5d , (16) where \ud835\udc50is the speed of light and \ud835\udf06\ud835\udc5dthe source-independent pivot wavelength defined as (e.g. Koornneef et al. 1986; Bessell & Murphy 2012, eq. A16) \ud835\udf062 \ud835\udc5d= \u222b \ud835\udc46(\ud835\udf06)\ud835\udf06\ud835\udc51\ud835\udf06 \u222b [\ud835\udc46(\ud835\udf06)/\ud835\udf06] \ud835\udc51\ud835\udf06 . (17) One could use different definitions of the observed mean fluxes by simply replacing equation (15). In the common situation in which the covariance between the spectroscopic \ud835\udc3aspec or photometric \ud835\udc3aphot measurements are not known, or ignored, the residuals r from the fit are as in Cappellari (2017, eq. 22) \ud835\udc5f\ud835\udc5d= \ud835\udc3aspec mod(\ud835\udf06\ud835\udc5d) \u2212\ud835\udc3aspec(\ud835\udf06\ud835\udc5d) \u0394\ud835\udc3aspec(\ud835\udf06\ud835\udc5d) , \ud835\udc5d= 1, . . . , \ud835\udc43 (18a) \ud835\udc5f\ud835\udc5e= \ud835\udc3aphot mod(\ud835\udf06\ud835\udc5e) \u2212\ud835\udc3aphot(\ud835\udf06\ud835\udc5e) \u0394\ud835\udc3aphot(\ud835\udf06\ud835\udc5e) , \ud835\udc5e= \ud835\udc43+ 1, . . . , \ud835\udc43+ \ud835\udc44, (18b) with the difference that the vector of residuals now includes both the \ud835\udc43spectroscopic and the \ud835\udc44photometric values. In other words, the total log-likelihood ln Ltotal of a fit now becomes the sum of the spectroscopic and photometric ones ln Ltotal = ln Lspec + ln Lphot = \u2212 \ud835\udf122 spec + \ud835\udf122 phot 2 + const. (19) Both the linear and nonlinear fit, the regularization and the possible treatment of covariances, proceed unchanged as already described in Cappellari (2017, sec. 3.3\u20133.5). The only difference is one extra row in the matrix A, defined in Cappellari (2017, sec. 3.3), for every photometric measurement. According to the mean value theorem for integration, for every \ud835\udc5e-th band and \ud835\udc5b-th template, there exists a wavelength \ud835\udf06\ud835\udc5e,\ud835\udc5bwhich satisfies exactly \ud835\udc34\ud835\udc5b(\ud835\udf06\ud835\udc5e,\ud835\udc5b) \u27e8\ud835\udc54\ud835\udc5b(\ud835\udf06)\u27e9\ud835\udc5e= \u27e8\ud835\udc54\ud835\udc5b(\ud835\udf06) \ud835\udc34\ud835\udc5b(\ud835\udf06)\u27e9\ud835\udc5e. (20) When one has a good estimate of the galaxy redshift (e.g. from previous photometric redshift), or when performing a grid search for the best-fitting redshift with ppxf, the redshift of the spectrum does not change much during each ppxf fit. This makes the quantities \u27e8\ud835\udc54\ud835\udc5b(\ud835\udf06)\u27e9\ud835\udc5eessentially independent of L\ud835\udc5b(\ud835\udc63). If I rewrite equation (14) as \ud835\udc3aphot mod(\ud835\udf06\ud835\udc5e) = \ud835\udc41 \u2211\ufe01 \ud835\udc5b=1 \ud835\udc64\ud835\udc5b\ud835\udc34\ud835\udc5b(\ud835\udf06\ud835\udc5e,\ud835\udc5b) \u27e8\ud835\udc54\ud835\udc5b(\ud835\udf06)\u27e9\ud835\udc5e, (21) I can precompute the \u27e8\ud835\udc54\ud835\udc5b(\ud835\udf06)\u27e9\ud835\udc5eand \ud835\udf06\ud835\udc5e,\ud835\udc5bfor all templates before the fit, using the initial redshift estimate. With this approach, adding photometry to a fit takes almost no extra time compared to fitting only the spectrum. I found that the flux-weighted effective wavelength (e.g. Bessell & Murphy 2012, eq. A21) \ud835\udf06eff \ud835\udc5e,\ud835\udc5b= \u222b \ud835\udc54\ud835\udc5b(\ud835\udf06)\ud835\udc46\ud835\udc5e(\ud835\udf06)\ud835\udf062 \ud835\udc51\ud835\udf06 \u222b \ud835\udc54\ud835\udc5b(\ud835\udf06)\ud835\udc46\ud835\udc5e(\ud835\udf06)\ud835\udf06\ud835\udc51\ud835\udf06 , (22) well approximates the wavelength \ud835\udf06\ud835\udc5e,\ud835\udc5bdefined by equation (20), for a range of attenuation parameters. In Fig. 3 I illustrate how accurately equation (20) is verified when approximating \ud835\udf06\ud835\udc5e,\ud835\udc5b\u2248\ud835\udf06eff \ud835\udc5e,\ud835\udc5b. I used all the 28 photometric bands described in Section 4.2 and all 387 fsps SPS templates introduced in Section 4.3, which span extreme ranges of age and metallicity. I adopt the attenuation function of equation (23), with realistic parameters (\ud835\udc34\ud835\udc49, \ud835\udeff, \ud835\udc38\ud835\udc4f, \ud835\udc53nodust) = (1, 0, 0.25, 0) and MNRAS 000, 1\u201328 (2023) ppxf with spectra and photometry at \ud835\udc67\u22480.8 9 0.1 1 0.2 0.3 0.4 0.6 2 3 eff q, n ( m) 0 1 2 3 4 5 Attenuation (mag) GALEX 1500 GALEX 2500 Testing the accuracy of A( eff) g( ) g( ) A( ) 2.5 lg A( eff q, n) 2.5 lg gn( ) An( ) q gn( ) q Figure 3. Comparison between the variation in the mean flux due to dust attenuation \u27e8\ud835\udc54\ud835\udc5b(\ud835\udf06) \ud835\udc34\ud835\udc5b(\ud835\udf06)\u27e9\ud835\udc5e/\u27e8\ud835\udc54\ud835\udc5b(\ud835\udf06)\u27e9\ud835\udc5e(red circles) and the value of the attenuation curve at the rest-frame effective wavelength \ud835\udc34\ud835\udc5b(\ud835\udf06eff \ud835\udc5e,\ud835\udc5b) (blue solid line), plotted versus the rest-frame effective wavelength \ud835\udf06eff \ud835\udc5e,\ud835\udc5bof each \ud835\udc5e-th filter and \ud835\udc5b-th template combination. This is computed for 28 filters at redshift \ud835\udc67= 0.8 and a set of templates spanning extreme ages and metallicities as described in the text. The \ud835\udf06eff \ud835\udc5e,\ud835\udc5brelative variation and the corresponding variation of the attenuation at that wavelength for a given filter are only significant in the far ultraviolet GALEX filters (indicated by the blue arrows). Even in that case, \ud835\udc34\ud835\udc5b(\ud835\udf06eff \ud835\udc5e,\ud835\udc5b) accurately predicts the true integrated attenuation. the median redshift \ud835\udc67= 0.8 of the LEGA-C sample. For every template-band combination, I compare the rigorous variation in mean flux due to the attenuation of each \ud835\udc5b-th template in the \ud835\udc5e-th band \u27e8\ud835\udc54\ud835\udc5b(\ud835\udf06) \ud835\udc34\ud835\udc5b(\ud835\udf06)\u27e9\ud835\udc5e/\u27e8\ud835\udc54\ud835\udc5b(\ud835\udf06)\u27e9\ud835\udc5ewith the value of the attenuation curve at the effective wavelength \ud835\udc34\ud835\udc5b(\ud835\udf06eff \ud835\udc5e,\ud835\udc5b). The two quantities must agree when the photometric band is narrow or the attenuation is approximately constant within the band, as is generally the case at optical or near-infrared wavelengths. However, in the far ultraviolet, in the GALEX bands, \ud835\udf06eff \ud835\udc5e,\ud835\udc5band the corresponding \ud835\udc34\ud835\udc5b(\ud835\udf06eff \ud835\udc5e,\ud835\udc5b) vary significantly for different templates in the same band. Even so, as shown in Fig. 3 the approximation is still much better than our uncertainty of the attenuation curve itself. Moreover, for these large attenuations, generally little flux is detected in the far ultraviolet, making the observed uncertainties very large. For these reasons, in the analysis presented here, I use equation (21) to model the attenuation on the photometry. When higher accuracy is required the full expression of equation (15) can be used. 3.7 Dust attenuation As shown in equation (13) and equation (14), the new ppxf method allows each template to have a different attenuation curve. This feature can be used to vary the attenuation curve for specific groups of templates, based on the current understanding of dust attenuation in galaxies (see review by Salim & Narayanan 2020). Three groups of attenuation curves are expected to be useful: (i) for very young stars (with ages \ud835\udc61< \u223c107 yr), which are still embedded in their birth clouds (Charlot & Fall 2000; Granato et al. 2000); (ii) for the entire stellar population (both young and old), due to diffuse dust; and (iii) for the gas emission lines from star-forming regions. In ppxf one can adopt a generic function, which can be different for different templates and can have an arbitrary number of parameters. The parameters can have bounds or can be kept fixed. By default I currently implemented a four-parameters attenuation function in linear units \ud835\udc34(\ud835\udf06) = \ud835\udc53(\ud835\udc34\ud835\udc49, \ud835\udeff, \ud835\udc38\ud835\udc4f, \ud835\udc53nodust) defined by \ud835\udc37(\ud835\udf06) = \ud835\udc38\ud835\udc4f(\ud835\udf06\u0394\ud835\udf06)2 (\ud835\udf062 \u2212\ud835\udf062 0)2 + (\ud835\udf06\u0394\ud835\udf06)2 (23a) \ud835\udc58(\ud835\udf06) = \ud835\udc34\ud835\udc49 \ud835\udc45\ud835\udc49 \u0002 \ud835\udc58\u2032(\ud835\udf06) + \ud835\udc37(\ud835\udf06) \u0003 \u0012 \ud835\udf06 \ud835\udf06\ud835\udc49 \u0013 \ud835\udeff (23b) \ud835\udc34(\ud835\udf06) = \ud835\udc53nodust + (1 \u2212\ud835\udc53nodust) 10\u22120.4 \ud835\udc58(\ud835\udf06). (23c) Here equation (23a) is the Lorentzian-like Drude function adopted by Noll et al. (2009) to describe the UV bump around \ud835\udf060 = 0.2175 \ud835\udf07m, with width \u0394\ud835\udf06= 0.035 \ud835\udf07m. The equation (23b) is the expression adopted by Kriek & Conroy (2013), which includes the attenuation \ud835\udc58\u2032(\ud835\udf06) and \ud835\udc45\ud835\udc49= 4.05 from Calzetti et al. (2000, eq. 4 and 5), and allows for a variable UV slope \ud835\udeffaround the pivot \ud835\udc49-band wavelength \ud835\udf06\ud835\udc49= 0.55 \ud835\udf07m. Optionally, one can make \ud835\udc38\ud835\udc4fa function of \ud835\udeff(Kriek & Conroy 2013, eq. 3) \ud835\udc38\ud835\udc4f= 0.85 \u22121.9 \u00d7 \ud835\udeff. (24) Finally equation (23c) allows one to specify the fraction \ud835\udc53nodust of the stellar population (for the given template) that is unattenuated, as suggested by Lower et al. (2022). The resulting \ud835\udc34(\ud835\udf06) is the factor to multiply the template at the given wavelength to model the attenuation effect. 4 DATA AND SPS MODELS In the rest of this paper, I present an analysis of the combined photometric and spectroscopic data, for a sample of about 3200 galaxies at 0.6 < \ud835\udc67< 1, making use of various of the new features of ppxf introduced in the first part of the paper. 4.1 Spectroscopy I study a subset of the galaxy sample of the LEGA-C survey (van der Wel et al. 2016). It is an ESO ESO/Very Large Telescope (VLT) public spectroscopic survey targeting galaxies in the redshift range 0.6 < \ud835\udc67< 1, selected based on their observed \ud835\udc3e\ud835\udc60-band luminosity in the UltraVISTA/COSMOS catalogue by Muzzin et al. (2013), with a small variation of the \ud835\udc3e\ud835\udc60limit with \ud835\udc67. In this work, I use the data from the LEGA-C third data release (DR3) presented in van der Wel et al. (2021). This redshift selection results in a mass-complete sample of 3445 galaxies in DR3 (90% completeness above lg(\ud835\udc40\u2217/M\u2299) > \u223c10.3). The selection, the completeness level, the characteristics of the sample and the data reduction are discussed extensively in van der Wel et al. (2016) and Straatman et al. (2018). For my study, I focused only on the subsample of 3197 galaxies (including duplicates) in the DR3 catalogue with spectroscopic redshift 0.6 < \ud835\udc67< 1 and with measured stellar velocity dispersion \ud835\udf0e\u2217. This a sample has redshift \ud835\udc67= [0.67, 0.76, 0.93] and average \ud835\udc46/\ud835\udc41= [7, 14, 26] per \u02da A at the 16th (\u22121\ud835\udf0e), 50th (median) and 84th (+1\ud835\udf0e) percentiles. However, I verified that all my results are unchanged if I restrict the sample to the redshift range to 0.7 < \ud835\udc67< 0.9. The survey data consist of spectra observed with the VLT/VIMOS multi-object spectrograph (Le F` evre et al. 2003) covering the wavelength range 0.63-0.88 \ud835\udf07m with a spectral resolution \ud835\udc45\u22483500, equivalent to an instrumental dispersion \ud835\udf0einst \u224836 km \ud835\udc60\u22121 (van der Wel et al. 2021). For the ppxf fits I logarithmically rebinned the spectra to a velocity scale \u0394\ud835\udc49= \ud835\udc50\u0394 ln \ud835\udf06= \ud835\udf0einst (Cappellari 2017, eq. 8) to make sure the spectrum is Nyquist sampled. MNRAS 000, 1\u201328 (2023) 10 M. Cappellari 4.2 Photometry I use two large collections of photometric measurements for the LEGA-C galaxies. The first is the UltraVISTA/COSMOS catalogue by Muzzin et al. (2013). It includes PSF-matched photometry in 30 bands from 0.15 to 24 \ud835\udf07m. The catalogue is based on the \ud835\udc4c\ud835\udc3d\ud835\udc3b\ud835\udc3e\ud835\udc60NIR imaging data from UltraVISTA (McCracken et al. 2012). The optical data consist of broad-band Subaru/SuprimeCam data (\ud835\udc54+\ud835\udc5f+\ud835\udc56+\ud835\udc67+\ud835\udc35\ud835\udc57\ud835\udc49\ud835\udc57), as well as \ud835\udc62\u2217data from the CFHT/MegaCam (Taniguchi et al. 2007; Capak et al. 2007). It also includes the 12 optical medium bands (IA427\u2013IA827) from Subaru/SuprimeCam (Capak et al. 2007). Also included are the GALEX FUV and NUV channels (Martin et al. 2005), and the 3.6 \ud835\udf07m 4.5 \ud835\udf07m 5.8 \ud835\udf07m 8.0 \ud835\udf07m and 24 \ud835\udf07m channels from Spitzer\u2019s IRAC+MIPS cameras (Sanders et al. 2007). The model predictions within the FUV GALEX band at \ud835\udc67\u223c0.8 are quite uncertain and few photons are generally expected to escape at those wavelengths. However, I still include this band in the fit to verify that this is indeed the case in the data. Moreover, significant detections are observed for the most star-forming galaxies. The second photometric catalogue is the COSMOS2020 by Weaver et al. (2022). Highlights of this catalogue, compared to the one by Muzzin et al. (2013), are much deeper Subaru Hyper Suprime-Cam \ud835\udc54\ud835\udc5f\ud835\udc56\ud835\udc67\ud835\udc66broadband photometric measurements (Aihara et al. 2019) and deeper UltraVISTA DR4 observations \ud835\udc4c\ud835\udc3d\ud835\udc3b\ud835\udc3e\ud835\udc60. The extra depth is not an important feature for my study, as the LEGA-C galaxies were all well-detected in Muzzin et al. (2013) by design. However, I use the COSMOS2020 to assess the sensitivity of my results to the use of independent datasets. For this work, I adopt the catalogue produced with the farmer profile-fitting photometric extraction tool. For both photometric catalogues, I only included the typically 28 bands which have a transmission FWHM fully contained in the wavelength range of the adopted stellar population templates (see later) at the redshift of each galaxy. The current COSMOS2020 farmer catalogue does not have the two GALEX bands, so I added them to compare it more closely with the UltraVISTA/COSMOS catalogue. I used the following steps for each galaxy: (i) I selected the bands that were common between the COSMOS2020 and the UltraVISTA/COSMOS catalogues. (ii) I used equation (34) to perform a linear least-squares fit and find a normalization factor \ud835\udf05that matches the two photometries for that galaxy. (iii) I applied the same factor \ud835\udf05to scale the two GALEX bands and included them in the COSMOS2020 bands. 4.3 Stellar population synthesis models I used three independent SPS models to assess the sensitivity of the results to some of the adopted model assumptions. I selected the models based on two criteria (i) the ability to generate model spectra from the far UV at 0.1 \ud835\udf07m to about 2 \ud835\udf07m, to be able to constrain the decrease of \ud835\udc53\ud835\udf06towards the NIR region of the galaxy spectra and (ii) to include model spectra down to a young age of 1 Myr, to reproduce the many actively star-forming galaxies that are present in the sample. The age criterion forces me to exclude from this study the models by Vazdekis and Maraston, which I have extensively used in the past. The three SPS models that satisfy my requirement and that I adopted are (i) the fsps7 (Conroy et al. 2009; Conroy & Gunn 2010), (ii) the galaxev8 (Bruzual & Charlot 2003) and (iii) the Bpass9 SPS models (Stanway & Eldridge 2018; Byrne et al. 2022). 7 Available from https://github.com/cconroy20/fsps 8 Available from http://www.bruzual.org/bc03/ 9 Available from https://bpass.auckland.ac.nz/ For all three models, I tried to select a consistent set of templates. In all cases, I adopted the same set of 43 ages logarithmically spaced by 0.1 dex from 1 Myr to 15.85 Gyr, defined as lg(Age/yr) = 6, 6.1, 6.2, . . . , 10.2. (25) The oldest age is 2\u20133\u00d7 older than the age of the Universe at the redshift of the sample, which varies in my standard cosmology from 5.75 \u2013 7.75 Gyr between \ud835\udc67= 1 \u2013 0.6, but I did not truncate the models to physical ages, to check how well the data themselves can constrain the galaxy ages. For comparison, I additionally ran models where I constrained the maximum age in the fit to each galaxy to the age of the Universe at its redshift. I also excluded from all models the most extreme low metallicities [\ud835\udc4d/\ud835\udc3b] < \u22122. Here is my other setup for the three SPS: (i) The fsps models allow one to compute SPS models for a specified set of parameters. I used the Python bindings10 (Johnson et al. 2021a) and the latest public v3.2 to compute a set of spectra with the above ages and 9 equally-spaced metallicities [\ud835\udc4d/\ud835\udc3b] = [\u22121.75, \u22121.5, \u22121.25, \u22121., \u22120.75, \u22120.5, \u22120.25, 0, 0.25], for a total of 387 SPS templates. I adopted a Salpeter (1955) IMF with a lower/upper mass cut of 0.08 and 100 M\u2299respectively, for consistency with bpass, and used the MIST isochrones (Choi et al. 2016). But I note that my results are virtually insensitive to the slope of the IMF at lower masses. I computed the SPS without including the effect of gas or dust and adopted default parameters for the other parameters. This returns SPS spectra computed using the MILES stellar library (S\u00b4 anchez-Bl\u00b4 azquez et al. 2006; Falc\u00b4 on-Barroso et al. 2011) for the optical region, which is the one I fit in the LEGA-C spectra. (ii) The galaxev models provide a Fortran code (version 2020) which I used to produce a set of SPS spectra with the same ages as above and computed at the provided 5 metallicities [\ud835\udc40/\ud835\udc3b] = [\u22121.74, \u22120.73, \u22120.42, 0, 0.47], for a total of 215 SPS templates. This SPS model also uses the MILES library to generate spectra of the optical region. Also here I adopted a Salpeter IMF. The models use the Padova isochrones (Bertelli et al. 1994; Girardi et al. 2000; Marigo et al. 2008). (iii) The bpass models v2.3 are provided as a set of files precomputed at a given set of metallicity. I adopted the 10 metallicities11 [\ud835\udc4d/\ud835\udc3b] = [\u22121.3, \u22121, \u22120.8, \u22120.7, \u22120.5, \u22120.4, \u22120.3, 0, 0.2, 0.3], for a total of 430 SPS templates. The models are provided for a single IMF having a power slope -2.35 (Salpeter slope) above \ud835\udc40> 0.5 M\u2299and a slope -1.3 at lower masses. I used the version of the SPS for single stars, ignoring binaries, with [\ud835\udefc/\ud835\udc39\ud835\udc52] = 0, for consistency with the other two SPS models. These SPS models are fully synthetic. They use isochrones produced by a derivative of the Cambridge stars code (Eggleton 1971) as described by Eldridge et al. (2008). 5 DYNAMICAL MASSES FROM SERSIC PHOTOMETRY We don\u2019t know the true masses of galaxies, so we can\u2019t tell how good the mass estimates from different stellar population codes are. One way to test the accuracy is to use good dynamical models. I show how I do this in this section. I use mass-follow-light axisymmetric JAM dynamical models which are as quick and simple to use as the usual virial estimator (e.g. Cappellari et al. 2006), and require the same data, but do not have its problems. 10 Available from https://github.com/dfm/python-fsps 11 The models are specified in metal mass fraction \ud835\udc4d, and I converted it to [\ud835\udc4d/\ud835\udc3b] with \u223c10 % accuracy. MNRAS 000, 1\u201328 (2023) ppxf with spectra and photometry at \ud835\udc67\u22480.8 11 This Paper C&B99 0.5 1 5 10 0 2 4 6 8 10 Sersic n [bn/btrue 1] (%) Sersic bn approximation for 0.2 \u2264 n \u2264 16 0.5 1 5 10 -0.10 -0.05 0.00 0.05 0.10 Figure 4. Fractional difference between the true coefficient \ud835\udc4f(\ud835\udc5bSer) in equation (26) and the minimax approximation (red line) for the interval 0.2 < \ud835\udc5bSer < 16 of equation (28). I also show for comparison the approximation (blue line) by Ciotti & Bertin (1999), which is very accurate for \ud835\udc5bSer > 0.5, but starts deviating rapidly at smaller \ud835\udc5bSer. The inset shows the same thing using a different scale for the \ud835\udc66-axis. 5.1 Updated coefficient for the Sersic profile I assume a galaxy with surface brightness described by a Sersic profile with elliptical isophotes of constant axial ratio \ud835\udc5eSer obs \ud835\udc3c(\ud835\udc5a) = \ud835\udc3c(0) exp \uf8ee \uf8ef \uf8ef \uf8ef \uf8ef \uf8f0 \u2212\ud835\udc4f(\ud835\udc5bSer)   \ud835\udc5a \ud835\udc45Ser e !1/\ud835\udc5bSer\uf8f9 \uf8fa \uf8fa \uf8fa \uf8fa \uf8fb , (26) where the elliptical radius is \ud835\udc5a2 = \ud835\udc652 +   \ud835\udc66 \ud835\udc5eSer obs !2 , (27) with \ud835\udc65aligned along the galaxy photometric projected major axis. The parameter \ud835\udc4f(\ud835\udc5bSer) is defined by the requirement that \ud835\udc45Ser e represents the semi-major axis of the isophote containing half of the total luminosity of the Sersic model. This implies that \ud835\udc4f(\ud835\udc5bSer) is the solution of \u0393(2 \ud835\udc5bSer) = 2 \u0393(2 \ud835\udc5bSer, \ud835\udc4f(\ud835\udc5bSer)) (Ciotti 1991), where \u0393(\ud835\udc4e, \ud835\udc67) is the incomplete gamma function (Olver et al. 2010, equation 8.2.2) and \u0393(\ud835\udc4e) = \u0393(\ud835\udc4e, 0) is the complete one (Olver et al. 2010, equation 5.2.1). A useful approximation for \ud835\udc4f(\ud835\udc5bSer) was presented by Ciotti & Bertin (1999). This is very accurate for values of \ud835\udc5bSer > \u223c0.5 but starts becoming rapidly inaccurate for smaller \ud835\udc5bSer values. The LEGA-C catalogue contains values of the Sersic index down to \ud835\udc5bSer = 0.2 where I found that the Ciotti & Bertin (1999) approximation for \ud835\udc4f(\ud835\udc5bSer) reaches an error of 11% (Fig. 4). To overcome this limitation I computed an alternative approximation for \ud835\udc4f(\ud835\udc5bSer). I adopted the same number of terms and the same mathematical form, but I adjusted the coefficients to obtain the minimax solution, minimizing the maximum absolute relative error of \ud835\udc4f(\ud835\udc5bSer) using nonlinear optimization over an interval including the most extreme Sersic indices existing in the literature. I found the following expression \ud835\udc4f(\ud835\udc5bSer) = 0.000207 \ud835\udc5b2 Ser + 0.015987 \ud835\udc5bSer \u22120.34025 + 2.0015 \u00d7 \ud835\udc5bSer, (28) which has a maximum absolute relative error of 5.6 \u00d7 10\u22124 in the whole interval 0.2 \u2264\ud835\udc5bSer \u226416. The fact that the relative error reaches its maximum value, with alternating sign, at five values of \ud835\udc5bSer (Fig. 4) confirms that this is indeed the minimax solution for the adopted function and interval (e.g. Press et al. 2007, sec. 5.15). 5.2 Jeans Anisotropic Models from Sersic photometry I performed dynamical modelling of the full LEGA-C sample of 3197 galaxies with measured \ud835\udf0e\u2217and 0.6 < \ud835\udc67< 1 using the Jeans Anisotropic Modelling (JAM) method12 (Cappellari 2008, 2020). Dynamical modelling of LEGA-C galaxies with JAM was previously done for a subset of 797 galaxies by van Houdt et al. (2021) using a Bayesian approach, but I extended it to all galaxies with measured \ud835\udf0e\u2217. A simpler alternative to dynamical models would be to use a virial estimation of the galaxy masses (e.g. Cappellari et al. 2006) based on the fitted parameters of the (Sersic 1968) profiles provided in the LEGA-C DR3 catalogue (van der Wel et al. 2021). The virial estimates are also included in the DR3 catalogue. The main advantage of virial estimators is that they are fast and easy. However, a common limitation is that they do not account for differences in the spectroscopic aperture and the instrumental pointspread function, which can be significant, especially in high-redshift observations like LEGA-C. Moreover, virial estimators do not allow one to explicitly assume an intrinsic shape or anisotropy for the galaxies under study. Although virial estimators are still useful to study scaling relations (e.g. Cappellari et al. 2013a; Li et al. 2018; Zhu et al. 2023a), nowadays there is no reason to use them to compute galaxy masses. In fact, using e.g. the public JAM package, one can compute a more reliable dynamical mass for a galaxy approximated by a Sersic model with a similar time and effort as using the virial estimator, while allowing for intrinsic shape, anisotropy, aperture and PSF effects, without introducing unnecessary approximations. To simplify this task of computing accurate dynamical masses of galaxies with available fitted Sersic parameters and \ud835\udf0e\u2217, I developed a simple procedure jam axi sersic mass and I have made it publicly available in the updated version 7.2 of the JAM package. The procedure requires the following inputs from the users: (i) The parameters of the Sersic model for a galaxy: (a) The semi-major axis of the half-light isophote \ud835\udc45Ser e , (b) The Sersic index \ud835\udc5bSer, and (c) The observed axial ratio of the isophotes \ud835\udc5eSer obs. (ii) The assumptions about the intrinsic properties of the galaxy: (a) The intrinsic axial ratio \ud835\udc5eSer intr and (b) The typical orbital anisotropy \ud835\udefd. (iii) The parameters of the spectroscopic observations: (a) The size and shape of the spectroscopic aperture, and (b) The parameters of the PSF. (iv) The observed second moment \ud835\udf0e\u2217(which includes both rotation and random motions) and uncertainty of the stellar line-of-sight velocity distribution, preferably measured at a similar wavelength as the imaging used to fit the Sersic model. Given an angular diameter distance \ud835\udc37\ud835\udc34, the procedure then returns the dynamical mass \ud835\udc40JAM of the Sersic model and its formal uncertainty in a fraction of a second. The procedure uses the method and mge fit 1d routine within 12 I used v7.2 of the JamPy Python package https://pypi.org/project/jampy/ MNRAS 000, 1\u201328 (2023) 12 M. Cappellari the MgeFit package13 (Cappellari 2002) to accurately fit the onedimensional Sersic profile of equation (26) with a one-dimensional Multi-Gaussian Expansion (MGE). Then assumes a fixed axial ratio \ud835\udc5eSer obs for all MGE Gaussians and an arbitrary reference total mass \ud835\udc400 for the model. It uses the jam axi proj procedure in the JAmPy package (Cappellari 2008, 2020) to calculate a PSF-convolved prediction for the \ud835\udc49rms, \ud835\udc57at a large set of discrete sky locations (\ud835\udc65\ud835\udc57, \ud835\udc66\ud835\udc57) finely sampling the adopted spectroscopic aperture. The luminosityweighted second moment inside the whole aperture is computed as \ud835\udc492 rms = \u00cd \ud835\udc57\ud835\udc3c\ud835\udc57\ud835\udc492 rms, \ud835\udc57 \u00cd \ud835\udc57\ud835\udc3c\ud835\udc57 , (29) where the summation extends to the pixels of flux \ud835\udc3c\ud835\udc57inside the aperture. Given the general scaling \ud835\udc40\u221d\ud835\udc492 between the total mass and velocities in a dynamical model, the dynamical mass of the Sersic model is then given by \ud835\udc40JAM = \ud835\udc400 \ud835\udf0e2 \u2217 \ud835\udc492 rms . (30) The physical meaning of the dynamical mass \ud835\udc40JAM, as derived from mass-follow-light dynamical models or virial estimators, is often a source of confusion. This is because \ud835\udc40JAM is neither a total stellar mass, nor a total mass of a galaxy which includes its dark halo. Moreover, the value of \ud835\udc40JAM is highly dependent on the extrapolated outer profile. For example, a Sersic model with \ud835\udc5bSer = 6 contains 21% of its total light outside 4\ud835\udc45e, which is about the maximum radius one can observe in typical photometry. This strong dependence on extrapolation prevents comparison of masses when accuracies better than a few 20% are desired. The quantity that both dynamical and stellar population models are robustly measuring is the mass-to-light radius within the region covered by the spectroscopic (for the dynamics) or photometric (for the population) observations. Specifically, if one divides the Sersic dynamical mass \ud835\udc40JAM returned by the procedure by the analytic total luminosity of the same Sersic model (Ciotti 1991) \ud835\udc3fSer = \ud835\udf0b\ud835\udc3c(0) \u0393(2\ud835\udc5bSer + 1)   \ud835\udc45Ser e \ud835\udc4f\ud835\udc5bSer !2 \ud835\udc5eSer obs, (31) the mass-to-light ratio (\ud835\udc40/\ud835\udc3f)JAM = \ud835\udc40JAM/\ud835\udc3fSer (32) provides a very accurate approximation of the average \ud835\udc40/\ud835\udc3fwithin a sphere of radius comparable to the size of the spectroscopic aperture. I used jam axi sersic mass to compute \ud835\udc40JAM and (\ud835\udc40/\ud835\udc3f)JAM for all the LEGA-C galaxies in my subsample. I assumed a spectroscopic aperture of 1\u2032\u2032\u00d71\u2032\u2032 and a characteristic PSF of 0. \u2032\u203275 FWHM from van Houdt et al. (2021). I adopted as the intrinsic axial ratio for all galaxies the mean value \ud835\udc5eSer intr = 0.41 of the Gaussian distribution inferred by van Houdt et al. (2021) by inverting the observed shape distribution of the LEGA-C sample. For the anisotropy, I used a typical value \ud835\udefd= 0.2 expected for the assumed mean intrinsic shape (Cappellari 2016, fig. 9). I assumed a cylindrically-oriented (align=\u2019cyl\u2019) velocity ellipsoid for JAM (Cappellari 2008). The parameters of the Sersic profiles \ud835\udc45Ser e , \ud835\udc5bSer, \ud835\udc5eSer obs and \ud835\udc3fSer come from the LEGA-C DR3 catalogue (van der Wel et al. 2021). I also used the dynamical models to calculate the average projected density \u03a3JAM 1 within a circle of radius \ud835\udc45= 1 kpc at the angular 13 V5.0 of Python MgeFit from https://pypi.org/project/mgefit diameter distance of the galaxy. This quantity was shown to closely relate to galaxy quenching (Cheung et al. 2012; Fang et al. 2013), like \ud835\udf0e\u2217. However, here instead of using the stellar mass as in previous studies, I used the dynamical mass from JAM. I obtained this value by circularising and analytically integrating the best fitting MGE as described in equation (11) of Cappellari et al. (2013a). 6 SETUP FOR ppxf AND TESTS In this study, fitting (twice) the VIMOS spectrum (\u22482800 spectral pixels) and typically 28 photometric bands for a single galaxy with ppxf takes about 1 min. This compares with the \u201croughly 100 CPU hours\u201d reported by Tacchella et al. (2022) in a similar state-of-the-art study using DEIMOS spectroscopy and the prospector Bayesian code (Johnson et al. 2021b). This is a computation time difference of nearly four orders of magnitude! Of course, the two methods perform quite different tasks and the large computational cost is a standard feature of Bayesian methods and not a weakness by itself. However, the execution time of a method affects the kind of tasks one can address and the variety of modelling choices one can explore as I outline in this section. 6.1 Non-parametric population model A key feature made possible by least-squares methods is the ability to explore non-parametrically the joint distribution of SFH and chemical composition with high resolution. My setup uses 43 non-parametric age bins, and each age bin is allowed to have a different non-parametric metallicity (5 \u2013 10 bins depending on the SPS code) for a total of up to 430 bins. This contrasts with the 10 non-parametric age bins and the single metallicity for the entire galaxy adopted by Tacchella et al. (2022). Crucially, even when using a non-parametric grid of a few hundred templates the least-squares method guarantees global convergence to the most likely weights distribution. This is because the constrained quadratic-programming problem being solved (Cappellari 2017, eq. 27) is known to possess a unique global minimum (e.g. Nocedal & Wright 2006). This contrast with Bayesian methods, where Tacchella et al. (2022, sec. 3.2) reported that \u201cthe fits do not converge within a reasonable amount of time\u201d with 14 non-parametric bins. The use of non-parametric models is important for a proper recovery of the stellar population in galaxies (Lower et al. 2020). 6.2 Polynomials A least-squares method like ppxf allows for a quick exploration of different modelling assumptions. In the course of this study, I was able to easily test different options, each with all three SPS models, for all 3200 galaxies, to test how they affected the final results. To fit the spectrum, we can choose between additive or multiplicative polynomials (the photometry does not use any polynomials). Additive polynomials are specified by the ppxf keyword degree and can help with template mismatch, AGN modeling or sky subtraction errors. Multiplicative polynomials are specified by the ppxf keyword mdegree and can account for spectral flux calibration issues or reddening effects. For my tests, I run models with both multiplicative and additive polynomials degree from mdegree=degree=-1 (i.e. using only attenuation and no polynomials) to degree 4 and found that the solution changes slightly without polynomials but quickly stabilizes as soon as one allows for a nonzero degree. Results were similar when only using MNRAS 000, 1\u201328 (2023) ppxf with spectra and photometry at \ud835\udc67\u22480.8 13 additive or only multiplicative polynomials to adjust the spectral stellar continuum. This was a non-obvious result in the present analysis, given that the LEGA-C spectra were calibrated using SPS models (van der Wel et al. 2021) and this non-standard calibration may leave an influence on the results. The polynomials should effectively remove any memory of possible inaccuracies in spectral calibration. I adopted the ppxf keywords mdegree=2, degree=-1 for my standard setup. 6.3 Dust attenuation model I truncated all three the SPS templates to 0.01 \ud835\udf07m < \ud835\udf06< 5 \ud835\udf07m (except for the bpass SPS which only extend to \ud835\udf06< 2 \ud835\udf07m) to remove the influence of dust on the spectral shape (e.g. Conroy 2013, fig. 1). This is because the modelling of dust from the energy balance of UV light reradiated to the IR requires several further assumptions and is not implemented in all modelling codes. Moreover, the currently available bands are included in the fitted range anyway. This situation is changing rapidly with the James Webb Space Telescope (JWST) and will soon be revisited. For the full set of 3200 galaxies, I experimented with three different assumptions for the attenuation: (i) I adopted a single four-parameter attenuation for all stellar templates as in equation (23); (ii) I reduced the attenuation curve to two parameters (\ud835\udc34\ud835\udc49, \ud835\udeff) by assuming \ud835\udc53nodust = 0 and adopting the \ud835\udc38\ud835\udc4f\u2212\ud835\udeffrelation by Kriek & Conroy (2013, eq. 3); I still applied this attenuation for all stellar templates; (iii) I adopted the two-components attenuation model by Charlot & Fall (2000). For this, I used a birth-cloud attenuation of the form \ud835\udc58(\ud835\udf06) = \ud835\udc34\u2032 \ud835\udc49 \u0012 \ud835\udf06 0.55 \ud835\udf07m \u0013\u22121 . (33) I apply this only to the stellar templates younger than 10 Myr, while I used the same attenuation as in (ii) for the diffuse dust component affecting all stellar templates. In all three cases, I fit a different Calzetti et al. (2000) attenuation curve (equation (23) with \ud835\udc38\ud835\udc4f= \ud835\udeff= \ud835\udc53nogas = 0) for the gas emission lines templates. I found that options (i) and (ii) produce an insignificant difference in the final results, but in the first case there is more degeneracy in the attenuation parameters, which makes any trend between dust parameters less obvious. Option (iii) generates a similar result for the older and intermediate populations, as expected. However, when allowing the youngest population to have its own attenuation, this becomes completely degenerate with the amount of star formation in that same young component. As a result, one can obtain good fits with an unlikely large attenuation associated with an equally large star formation, but with complete degeneracy between the two parameters. This is the well-known SFR-dust degeneracy mentioned in Section 1. It can be broken by introducing extra assumptions on the dust geometry and reradiated UV fraction, combined with rest-frame IR data, which I do not have. In conclusion, I adopted as my standard choice the two-parameters attenuation function of option (ii), which applies to the whole population, as done e.g. by Kriek & Conroy (2013). I enforced bounds on the parameters as \u22121 < \ud835\udeff< 0.4 and 0 < \ud835\udc34\ud835\udc49< 4. As illustrated by Kriek & Conroy (2013, fig. 1), their two-parameters parametrization differs from both the Milky Way (Cardelli et al. 1989) and Calzetti et al. (2000) attenuation laws, but appear to better describe high-\ud835\udc67 galaxies. However, using the full four-parameter attenuation curve, which covers the Calzetti et al. (2000) curve and other curves from the Milky Way to the Large Magellanic Cloud (Gordon et al. 2003), does not alter my scientific conclusions. 6.4 Matching photometry and spectra I have a spectroscopic redshift for every galaxy from the LEGA-C catalogue. I only included photometric bands in the fit if their FWHM is fully enclosed by the template\u2019s wavelength coverage at that redshift. Before the ppxf fits, I pre-computed the \u27e8\ud835\udc54\ud835\udc5b(\ud835\udf06)\u27e9\ud835\udc5eand \ud835\udf06\ud835\udc5e,\ud835\udc5bin equation (21). I used the same photonic throughput file for all filters, produced for the eazy code (Brammer et al. 2008) and available online14. Spectroscopy was observed within 1\u2032\u2032 slits, while photometric observations were either measured within a 2. \u2032\u20321 aperture (Muzzin et al. 2013) or are total magnitudes (Weaver et al. 2022). This means that calibration is needed to match the flux levels of photometry and spectroscopy. It\u2019s important to note that in some cases, the photometric fluxes may correspond to a different stellar population than that sampled by the spectra. With this in mind, I assumed that spectroscopy and photometry originate from a single spectral energy distribution and applied a constant scaling factor \ud835\udf05to the spectrum \ud835\udc3aspec(\ud835\udf06\ud835\udc5d). This factor ensures that the synthetic photometry derived from the spectrum using filter transmission curves matches the observed LEGA-C photometry in bands covered by the spectroscopy. This step calibrates the overall normalization of the spectrum flux using photometry before starting the ppxf fit. To match the VIMOS spectra to the photometry, before calling ppxf, for every galaxy I first computed synthetic photometric fluxes \u27e8\ud835\udc53\ud835\udf06\u27e9\ud835\udc5efrom its VIMOS spectrum using equation (15), for the subset of photometric bands (typically 7) contained within the VIMOS wavelength range. I then multiplied the spectrum by a factor \ud835\udf05to minimise the \ud835\udf122 between the synthetic and observed photometry, only for the few bands in common. It can be computed with the general analytic linear-fitting relation (e.g. Cappellari 2008, eq. 51) \ud835\udf05= d \u00b7 m m \u00b7 m, (34) where the \u201cdata\u201d vector d has elements \ud835\udc51\ud835\udc5e= \ud835\udc5d\ud835\udc5e/\u0394\ud835\udc5d\ud835\udc5e, the observed photometric fluxes \ud835\udc5d\ud835\udc5e, divided by their uncertainties \u0394\ud835\udc5d\ud835\udc5eand the \u201cmodel\u201d vector m has elements \ud835\udc5a\ud835\udc5e= \u27e8\ud835\udc53\ud835\udf06\u27e9\ud835\udc5e/\u0394\ud835\udc5d\ud835\udc5e, the synthetic fluxes also divided by the data uncertainties. Like Kriek & Conroy (2013), I didn\u2019t use the catalogues\u2019 formal photometric uncertainties in any of my fits, including when calculating \ud835\udf05and during ppxf fits. This is because the small error bars at longer wavelengths would have dominated the fits. Additionally, after many fits, it became apparent that systematic imperfections in the SPS model assumptions or data were the main source of uncertainty, rather than random noise. Instead, I use fixed linear uncertainties for all photometric bands of a given galaxy as explained in the next section. 6.5 Outliers removal To remove outliers from the spectral fits, I follow a common practice (e.g. Westfall et al. 2019) that involves multiple ppxf fits and adjusting the uncertainties based on the fit residuals. My approach is designed for robustness as follows: (i) I perform an initial ppxf fit assuming a reasonable fixed uncertainty \u0394\ud835\udc3aphot(\ud835\udf06\ud835\udc5e) for all bands of 3% of the maximum photometric flux \ud835\udc3aphot(\ud835\udf06\ud835\udc5e) for that galaxy. Similarly, for the spectrum uncertainty \u0394\ud835\udc3aspec(\ud835\udf06\ud835\udc5d), I adopt a constant value of 10% of the median galaxy spectrum \ud835\udc3aspec(\ud835\udf06\ud835\udc5d). A constant uncertainty is a good approximation for the VIMOS spectra and reduces the noise in the fit, with respect to 14 Available from https://github.com/gbrammer/eazy-photoz MNRAS 000, 1\u201328 (2023) 14 M. Cappellari adopting a more accurate but noisy error spectrum (e.g. as given by the reduction pipeline). The best fit is not sensitive to the scaling of uncertainties, which only affects the relative weight of the spectrum and photometry. (ii) After the fit, I estimate the rms noise spectrum \ud835\udf0espec noise per pixel from the fit residuals, in a statistically robust way, by computing for every spectral pixel the interval containing 68% of the residuals, within a moving window of 100 pixels. (iii) I mask the pixels deviating more than 3\ud835\udf0espec noise from the best fit. I repeat the masking in a loop, while iteratively adjusting the normalization of the best-fitting spectrum using the non-masked pixels from equation (34), until the mask does not change anymore. (iv) I multiply \u0394\ud835\udc3aspec(\ud835\udf06\ud835\udc5d) by \u221a\ufe03 \ud835\udf122 spec/\ud835\udc43, where \ud835\udc43is the number of non-masked spectral pixels, and I compute \ud835\udf122 spec from the spectrum alone, in such a way that, after rescaling of the uncertainties, the resulting \ud835\udf122 spec = \ud835\udc43. (v) I do the same constant rescaling for the photometric uncertainties to enforce \ud835\udf122 phot = \ud835\udc44. Here \ud835\udc44is the number of fitted photometric bands, and I compute \ud835\udf122 phot from the photometry alone. (vi) After the spectral masking and the rescaling of the photometric \u0394\ud835\udc3aphot(\ud835\udf06\ud835\udc5e) and spectral \u0394\ud835\udc3aspec(\ud835\udf06\ud835\udc5d) uncertainties, I perform a second ppxf fit, from which I extract the final results. The rescaled uncertainties are generally of the same order of magnitude as the formal ones provided by the pipelines. However, there can be significant relative differences between different photometric bands. I tested the full LEGA-C sample and found that none of the results in this paper depended on whether I used the formal or rescaled uncertainties. However, the approach I adopted significantly reduced the number of cases where, after visual inspection, the formal best fit did not match the data well because of unrealistically small formal uncertainties that overemphasized certain photometric bands. 6.6 Gas model and kinematic constraints For galaxies without Active Galactic Nuclei, gas emission could be approximately predicted based on the galaxy SFH and could be included in the models, with some extra assumptions, based on photoionization models like cloudy (Ferland et al. 1998, 2013). This feature is implemented in fsps and can be useful when fitting photometry alone where the gas emission are poorly constrained by the data. However, in my case, I have many good-quality spectra in addition to photometry and I want to be able to fit the gas more accurately than a model could predict. For this reason, I fit the gas emission lines in a model-independent way with ppxf. With ppxf one can fit many gas emission lines simultaneously to the stellar continuum. This is especially important when studying the stellar population of star-forming galaxies or AGNs, where key absorption lines like the Balmer series are filled by emission. However, when fitting gas lines in relatively low S/N spectra, it is essential to set constraints on the parameters of the gas lines, to prevent possible degenerate situations. An example of a situation to avoid is when the spectrum does not have gas emission and the Gaussian describing an emission line becomes so wide as to become degenerate with the shape of the stellar continuum. This is one of the types of situations for which I designed the linearly constrained algorithm of Section 3.2. For my fits to the LEGA-C spectra, after some experimentation focusing on the few problematic fits, I found it sufficient to require the dispersion of the gas emission lines to be smaller than the stellar one \ud835\udf0egas < \ud835\udf0e\u2217and in addition I required the gas and mean stellar velocities to satisfy |\ud835\udc49gas \u2212\ud835\udc49\u2217| < 500 km \ud835\udc60\u22121. I enforced these requirements as linear constraints in ppxf (keyword constr kinem). My strict constraints on the gas dispersion is not always verified in galaxies and I would not recommend it when one is interested in the gas kinematics. However, it appears to work well in eliminating spurious solutions for the stellar population alone from the present type of spectra. The emission lines that I included in the ppxf fits are all the lines listed in Belfiore et al. (2019, table 1). In particular, those falling within the LEGA-C wavelength range for 0.6 < \ud835\udc67< 1 are the Balmer series bluer than H\ud835\udefd, the [OII]\ud835\udf06\ud835\udf063726,29, [NeIII]\ud835\udf06\ud835\udf063868,69 and [OIII]\ud835\udf06\ud835\udf064959,5007 doublets, and the HeII\ud835\udf064687. I force the kinematics of all the gas lines to be the same and I additionally fix the [OIII] doublet to the 1/3 ratio. I fit the Balmer series as a single gas template with decrement for Case B recombination, for temperature \ud835\udc47= 104 K and electron density \ud835\udc5b\ud835\udc52= 100 cm\u22123 from Storey & Hummer (1995). I allow the gas templates to have their own Calzetti et al. (2000) attenuation curve. Fixing the intrinsic ratios of the Balmer series allows me to provide a better extrapolation of the gas filling the weakest (higher-order) absorption lines of the series, even when the S/N of the spectrum is not high enough to constrain them. Note that, although I do not include theoretical gas emission predictions in the SPS models, I do include the contribution of the emission lines that are spectroscopically constrained in the photometry. In particular, when Balmer lines are present in the spectrum, the line fluxes of the Balmer series, and in particular of H\ud835\udefc, which is outside the LEGA-C wavelength range, are included in the photometric fit. However, I checked that this inclusion has a minimal effect on the final results. 6.7 Velocity dispersion matching The LEGA-C data have an instrumental dispersion of \ud835\udf0einst \u224836 km \ud835\udc60\u22121 (Section 4.1), ignoring possible variations within the rather small wavelength range. The MILES stellar templates used in both the fsps and galaxev models were observed with an instrumental resolution of \u0394\ud835\udf06\u22482.50 \u02da A FWHM (Falc\u00b4 on-Barroso et al. 2011), equivalent to \ud835\udc45= \ud835\udf06/\u0394\ud835\udf06\u22481600 at the typical wavelength \ud835\udf06\u22480.4 \ud835\udf07m covered by LEGA-C. This corresponds to an instrumental dispersion \ud835\udf0einst = \ud835\udc50 \ud835\udc45 \u221a 4 ln 4 \u224880 km \ud835\udc60\u22121. (35) Ideally, I would like to use SPS models based on stars with higher resolution than the galaxy spectra. However, assuming that the instrumental line spread functions are approximately Gaussian, one can still use a template with higher instrumental dispersion \ud835\udf0einst,tem than that \ud835\udf0einst,gal of the observed galaxy spectrum as long as (\ud835\udf0e2 inst,gal + \ud835\udf0e2 \u2217) > \ud835\udf0e2 inst,tem, where \ud835\udf0e\u2217is the real \u201castrophysical\u201d dispersion of the galaxy stars. After the ppxf fit one can compute the corrected stellar dispersion with the standard expressions (Cappellari 2017, sec. 2.2) \ud835\udf0e2 diff = \ud835\udf0e2 inst,gal \u2212\ud835\udf0e2 inst,tem (36a) \ud835\udf0e2 \u2217= \ud835\udf0e2 ppxf \u2212\ud835\udf0e2 diff. (36b) As \ud835\udf0e2 diff is in this case a negative quantity, I can model the dispersion of galaxies down to \ud835\udf0e\u2217> \u223c|\ud835\udf0e2 diff|1/2 = 71 km \ud835\udc60\u22121. I compared my fitted dispersions \ud835\udf0e\u2217with the values in the LEGA-C DR3 catalogue, which were measured with ppxf using higher resolution synthetic templates as described in Bezanson et al. (2018). I found a good agreement assuming |\ud835\udf0e2 diff|1/2 \u224848 km \ud835\udc60\u22121, which suggests possible inaccuracies in the quoted relative instrumental dispersion of the galaxies MNRAS 000, 1\u201328 (2023) ppxf with spectra and photometry at \ud835\udc67\u22480.8 15 0.1 1 0.2 0.3 0.4 0.6 2 3 rest ( m) 0.00 0.25 0.50 0.75 1.00 Relative Flux (f ) ID: 215825; fsps; z=0.7542; lg M * =10.4; =186 km s 1; S/N=49 0.40 0.42 0.44 0.46 0.48 0.50 0.52 rest ( m) 0.25 0.50 0.75 1.00 1.25 Relative Flux (f ) 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 1.5 1.0 0.5 0.0 [M/H] regul = 0 0.0 0.1 0.2 0.3 0.4 light fraction 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 1.5 1.0 0.5 0.0 [M/H] regul = 10 0.00 0.02 0.04 0.06 0.08 0.10 light fraction 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 lg Age (yr) 1.5 1.0 0.5 0.0 [M/H] regul = 100 0.00 0.02 0.04 0.06 light fraction 0.1 1 0.2 0.3 0.4 0.6 2 3 4 rest ( m) 0.0 0.5 1.0 Relative Flux (f ) ID: 250391; fsps; z=0.8893; lg M * =11.0; =173 km s 1; S/N=29 0.34 0.36 0.38 0.40 0.42 0.44 0.46 rest ( m) 0.0 0.5 1.0 1.5 Relative Flux (f ) 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 1.5 1.0 0.5 0.0 [M/H] regul = 0 0.0 0.1 0.2 0.3 0.4 light fraction 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 1.5 1.0 0.5 0.0 [M/H] regul = 10 0.00 0.02 0.04 0.06 0.08 light fraction 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 lg Age (yr) 1.5 1.0 0.5 0.0 [M/H] regul = 100 0.00 0.01 0.02 0.03 0.04 0.05 light fraction 0.1 1 0.2 0.3 0.4 0.6 2 3 rest ( m) 0.00 0.25 0.50 0.75 1.00 1.25 Relative Flux (f ) ID: 56670; fsps; z=0.6686; lg M * =11.5; =230 km s 1; S/N=38 0.38 0.40 0.42 0.44 0.46 0.48 0.50 0.52 rest ( m) 0.00 0.25 0.50 0.75 1.00 1.25 Relative Flux (f ) 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 1.5 1.0 0.5 0.0 [M/H] regul = 0 0.0 0.1 0.2 0.3 0.4 light fraction 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 1.5 1.0 0.5 0.0 [M/H] regul = 10 0.000 0.025 0.050 0.075 0.100 0.125 light fraction 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 lg Age (yr) 1.5 1.0 0.5 0.0 [M/H] regul = 100 0.00 0.01 0.02 0.03 0.04 0.05 light fraction 0.1 1 0.2 0.3 0.4 0.6 2 3 rest ( m) 0.0 0.5 1.0 1.5 2.0 2.5 Relative Flux (f ) ID: 213036; fsps; z=0.6112; lg M * =10.8; =94 km s 1; S/N=41 0.38 0.40 0.42 0.44 0.46 0.48 0.50 0.52 rest ( m) 0.4 0.6 0.8 1.0 1.2 Relative Flux (f ) 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 1.5 1.0 0.5 0.0 [M/H] regul = 0 0.00 0.05 0.10 0.15 0.20 0.25 light fraction 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 1.5 1.0 0.5 0.0 [M/H] regul = 10 0.00 0.01 0.02 0.03 light fraction 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 lg Age (yr) 1.5 1.0 0.5 0.0 [M/H] regul = 100 0.000 0.005 0.010 0.015 light fraction 0.1 1 0.2 0.3 0.4 0.6 2 3 rest ( m) 0.0 0.2 0.4 0.6 0.8 1.0 Relative Flux (f ) ID: 65508; fsps; z=0.6606; lg M * =11.4; =180 km s 1; S/N=33 0.38 0.40 0.42 0.44 0.46 0.48 0.50 rest ( m) 0.2 0.4 0.6 0.8 1.0 1.2 Relative Flux (f ) 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 1.5 1.0 0.5 0.0 [M/H] regul = 0 0.00 0.05 0.10 0.15 0.20 light fraction 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 1.5 1.0 0.5 0.0 [M/H] regul = 10 0.00 0.01 0.02 0.03 0.04 0.05 light fraction 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 lg Age (yr) 1.5 1.0 0.5 0.0 [M/H] regul = 100 0.000 0.005 0.010 0.015 0.020 light fraction 0.1 1 0.2 0.3 0.4 0.6 2 3 rest ( m) 0.00 0.25 0.50 0.75 1.00 1.25 Relative Flux (f ) ID: 121995; fsps; z=0.7237; lg M * =11.6; =206 km s 1; S/N=36 0.36 0.38 0.40 0.42 0.44 0.46 0.48 rest ( m) 0.25 0.50 0.75 1.00 1.25 Relative Flux (f ) 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 1.5 1.0 0.5 0.0 [M/H] regul = 0 0.00 0.05 0.10 0.15 0.20 0.25 light fraction 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 1.5 1.0 0.5 0.0 [M/H] regul = 10 0.00 0.02 0.04 0.06 light fraction 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 lg Age (yr) 1.5 1.0 0.5 0.0 [M/H] regul = 100 0.000 0.005 0.010 0.015 0.020 light fraction Figure 5. Examples of ppxf fits to the LEGA-C galaxy spectra and 28-bands photometry using the fsps models. The top three galaxies require a model with a single short star formation event, while the bottom three galaxies require multiple discrete star formation events. For each galaxy, the top panel shows the photometric measurements (blue error bars) and the best fit (green diamonds), while the golden line shows the underlying best-fitting template with included emission lines. The grey vertical band indicates the range where spectroscopy was also fitted. The second panel shows the observed spectrum (black line) and the best-fitting total spectrum (orange line). The best-fitting stellar spectrum alone is shown in red and the gas emission one is in magenta. The residuals (arbitrarily offset) are indicated with green diamonds and the masked pixels with blue lines (and corresponding grey vertical bands). The last three panels show the distribution of the ppxf weights, indicating the bolometric luminosity \ud835\udc3fbol of each stellar population of given age and metallicity. The weights are shown for (i) no regularization, (ii) regularization regul=10 and (iii) regul=100 as written in the plots. MNRAS 000, 1\u201328 (2023) 16 M. Cappellari Table 1. JAM dynamical masses and ppxf stellar population results using SPS templates from fsps. ID LEGA-C RA DEC lg \ud835\udc40JAM lg \u03a3JAM 1 lg \ud835\udc40ppxf \u2217 \u27e8lg Age\u27e9 \u27e8[\ud835\udc40/\ud835\udc3b]\u27e9 \ud835\udc34\ud835\udc49 \ud835\udeff (\u25e6) (\u25e6) (M\u2299) (M\u2299kpc\u22122) (M\u2299) (yr) (mag) (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) 1 150.415222 1.758146 11.560 10.028 11.348 8.982 -0.271 1.122 0.111 4 150.412292 1.777617 11.405 9.548 11.350 9.107 -1.040 1.356 0.377 5 150.381104 1.780024 10.847 9.436 10.947 8.719 -0.475 0.304 -0.075 6 150.449783 1.783690 11.119 9.981 11.189 9.538 -0.140 0.000 0.400 8 150.378815 1.792945 11.653 9.919 11.445 9.088 -0.279 1.711 0.400 10 150.407440 1.803214 11.695 10.587 11.698 9.737 -0.094 0.097 0.239 11 150.423050 1.807328 11.601 9.649 11.579 9.032 -0.102 0.075 -1.000 12 150.405838 1.813150 10.817 9.137 11.082 8.554 -0.572 0.579 -0.165 13 150.385376 1.816353 11.113 10.036 11.190 9.285 -0.036 0.000 0.400 14 150.430817 1.820639 11.217 9.246 11.217 8.159 -0.740 0.770 -0.038 Note. \u2013 Columns (1), (2) and (3): ID, right ascension and declination J2000 in degrees from the LEGA-C catalogue of van der Wel et al. (2021). Column (4): JAM dynamical masses from Section 5.2 in solar masses. For accurate quantitative use, one should divide these masses by the luminosities of the Sersic models in the LEGA-C catalogues to obtain the total (\ud835\udc40/\ud835\udc3f)JAM as described in Section 7.3; Column (5): dynamically-determined average mass density within a cylinder of radius \ud835\udc45= 1 kpc along the line-of-sight. I computed this from the best-fitting JAM model; Column (6): Stellar masses from ppxf using SPS templates from fsps. These masses include living stars and stellar remnants, but exclude gas lost during stellar evolution. I assume a Salpeter IMF with a lower/upper mass cutoff of 0.08 and 100 M\u2299respectively; Columns (7) and (8): lg Age and [\ud835\udc40/\ud835\udc3b] weighted by the bolometric luminosity (Section 7.4). Columns (9) and (10): \ud835\udc49-band attenuation in mag and slope \ud835\udefffrom equation (23), for the two-parameters attenuation described in Section 6.3. I show only the first ten rows of this table, while the full electronic table for 3197 galaxies (including duplicates) is available as Supporting Information from the MNRAS website. and the templates. Regardless of the reason for this discrepancy, only 40 of the 3197 galaxies in the catalogue with measured dispersion have \ud835\udf0e\u2217< 48 km \ud835\udc60\u22121, likely due to measurement uncertainties. This implies that I can safely use the SPS based on MILES models to study the stellar population of LEGA-C galaxies. 7 RESULTS In this section, I describe the results of my stellar population modelling with ppxf. I also compare masses from stellar population and galaxy dynamics. The key quantities used in this paper are given in Table 1. 7.1 Spectral fit examples In this paper, I focus on galaxy observable trends rather than on comparisons with models of galaxy formation. For this reason, instead of converting the SFH recovered by ppxf into stellar masses formed in a given time interval, I will always show the fraction of bolometric luminosity contributed by each template, as a function of their age and metallicity [\ud835\udc40/\ud835\udc3b]. More precisely, I integrate the luminosity from the template spectra only within the region 0.1 < \ud835\udf06< 3 \ud835\udf07m covered by the data. This is to avoid the possibility of interpreting very young stars, which emit most of their luminosity for \ud835\udf06< 0.1 \ud835\udf07m, as contributing significantly to my observables, even when their flux is not detected in the data, but simply extrapolated. I still indicate my luminosity as \ud835\udc3fbol because, except for extremely young stars, it still represents a very good approximation for it. The advantage of using \ud835\udc3fbol rather than SFH, is that one can get a direct sense of what the data actually show, without strongly nonlinear conversions into masses, due to the large \ud835\udc40/\ud835\udc3fdifferences of different stellar populations. In fact, I would argue that comparisons with models of galaxy formations are generally more meaningful when the models, for which all quantities are known accurately, are converted into luminous observables, rather than trying to do the reverse by extracting SFH in masses from the data. In the course of this study, I fitted the 3197 galaxies of my subsample (Section 4.1) with ppxf multiple times with different levels of regularization, or no regularization at all, to test the sensitivity of the results. In Fig. 5 I illustrate the effect of regularization on some high\ud835\udc46/\ud835\udc41spectra. These figures, like Fig. 1, illustrate the ill-conditioning of the stellar population inversion, which prevents one from obtaining a unique solution, even from very good data. Nonetheless, the figure also illustrates the ability of the method to distinguish the striking difference between (i) galaxies that can only be described, even at high regularization15 (regul=100) by a single star formation event at a very localized lg Age (top three panels in Fig. 5) and (ii) galaxies that require multiple and separated star formation events to be described (bottom three panels in Fig. 5). The galaxies in the top panels are essentially described by a single SPS model, from 0.1 \ud835\udf07m to 3 \ud835\udf07m, for both spectra and photometry. This highlights the success of the SPS models in accurately predicting real galaxy spectra. In Fig. 6 I show additional examples of ppxf fits to good quality spectra to give a sense of the variety of spectral morphologies and the corresponding variations in the \ud835\udc3fbol weights distributions. I used in all these cases a high regularization (regul=100). Also here one can clearly see the striking difference between (i) the three galaxies in the top row, which can only be described as a single burst of star formation, which happened at different times and (ii) galaxies requiring multiple discrete star formation events. Star formation events appear to have a similar extent in ln Age, which seems to imply that events in the past lasted longer than recent ones. This is likely an artefact of our general ability to more accurately detect age differences in recent events. 7.2 Comparing ppxf stellar masses with other methods The weights for different ages and metallicities produced by a fit with ppxf can be converted into stellar masses. In this section I compare 15 A given value of the ppxf keyword regul roughly implies that neighbouring weights \ud835\udc64\ud835\udc56\ud835\udc57can differ by \u0394\ud835\udc64\ud835\udc56\ud835\udc57\u223c1/regul. As I normalize all galaxy spectra to the same average flux (e.g. average=1), setting a given regul value roughly corresponds to requiring a similar level of smoothness in the distribution of the weight. MNRAS 000, 1\u201328 (2023) ppxf with spectra and photometry at \ud835\udc67\u22480.8 17 0.1 1 0.2 0.3 0.4 0.6 2 3 rest ( m) 0.00 0.25 0.50 0.75 1.00 1.25 Relative Flux (f ) ID: 86349; fsps; z=0.6713; lg M * =10.9; =156 km s 1; S/N=35; regul=100 0.36 0.38 0.40 0.42 0.44 0.46 0.48 rest ( m) 0.00 0.25 0.50 0.75 1.00 1.25 Relative Flux (f ) 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 lg Age (yr) 1.5 1.0 0.5 0.0 [M/H] 0.00 0.02 0.04 0.06 light fraction 0.1 1 0.2 0.3 0.4 0.6 2 3 rest ( m) 0.00 0.25 0.50 0.75 1.00 1.25 Relative Flux (f ) ID: 38648; fsps; z=0.6744; lg M * =11.7; =310 km s 1; S/N=45; regul=100 0.40 0.42 0.44 0.46 0.48 0.50 0.52 rest ( m) 0.25 0.50 0.75 1.00 1.25 Relative Flux (f ) 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 lg Age (yr) 1.5 1.0 0.5 0.0 [M/H] 0.00 0.01 0.02 0.03 0.04 light fraction 0.1 1 0.2 0.3 0.4 0.6 2 3 rest ( m) 0.00 0.25 0.50 0.75 1.00 1.25 Relative Flux (f ) ID: 57389; fsps; z=0.6619; lg M * =11.6; =214 km s 1; S/N=39; regul=100 0.38 0.40 0.42 0.44 0.46 0.48 0.50 0.52 rest ( m) 0.00 0.25 0.50 0.75 1.00 1.25 Relative Flux (f ) 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 lg Age (yr) 1.5 1.0 0.5 0.0 [M/H] 0.00 0.01 0.02 0.03 0.04 0.05 light fraction 0.1 1 0.2 0.3 0.4 0.6 2 3 rest ( m) 0.0 0.5 1.0 1.5 Relative Flux (f ) ID: 217632; fsps; z=0.8252; lg M * =10.7; =65 km s 1; S/N=19; regul=100 0.34 0.36 0.38 0.40 0.42 0.44 0.46 rest ( m) 0.0 0.5 1.0 Relative Flux (f ) 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 lg Age (yr) 1.5 1.0 0.5 0.0 [M/H] 0.000 0.005 0.010 0.015 0.020 light fraction 0.1 1 0.2 0.3 0.4 0.6 2 3 4 rest ( m) 0 1 2 3 Relative Flux (f ) ID: 75921; fsps; z=0.9897; lg M * =10.6; =134 km s 1; S/N=17; regul=100 0.30 0.32 0.34 0.36 0.38 0.40 rest ( m) 0.5 1.0 1.5 Relative Flux (f ) 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 lg Age (yr) 1.5 1.0 0.5 0.0 [M/H] 0.000 0.005 0.010 0.015 0.020 0.025 light fraction 0.1 1 0.2 0.3 0.4 0.6 2 3 rest ( m) 0.0 0.5 1.0 1.5 2.0 Relative Flux (f ) ID: 229359; fsps; z=0.8504; lg M * =10.9; =80 km s 1; S/N=25; regul=100 0.38 0.40 0.42 0.44 0.46 0.48 rest ( m) 0.25 0.50 0.75 1.00 1.25 Relative Flux (f ) 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 lg Age (yr) 1.5 1.0 0.5 0.0 [M/H] 0.0000 0.0025 0.0050 0.0075 0.0100 0.0125 light fraction 0.1 1 0.2 0.3 0.4 0.6 2 3 rest ( m) 0.00 0.25 0.50 0.75 1.00 Relative Flux (f ) ID: 234337; fsps; z=0.6763; lg M * =11.8; =210 km s 1; S/N=32; regul=100 0.38 0.40 0.42 0.44 0.46 0.48 0.50 0.52 rest ( m) 0.25 0.50 0.75 1.00 1.25 Relative Flux (f ) 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 lg Age (yr) 1.5 1.0 0.5 0.0 [M/H] 0.000 0.005 0.010 0.015 0.020 0.025 light fraction 0.1 1 0.2 0.3 0.4 0.6 2 3 rest ( m) 0.00 0.25 0.50 0.75 1.00 Relative Flux (f ) ID: 216176; fsps; z=0.8599; lg M * =11.4; =154 km s 1; S/N=35; regul=100 0.38 0.40 0.42 0.44 0.46 0.48 rest ( m) 0.25 0.50 0.75 1.00 1.25 Relative Flux (f ) 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 lg Age (yr) 1.5 1.0 0.5 0.0 [M/H] 0.000 0.005 0.010 0.015 light fraction 0.1 1 0.2 0.3 0.4 0.6 2 3 rest ( m) 0.0 0.2 0.4 0.6 0.8 1.0 Relative Flux (f ) ID: 65508; fsps; z=0.6606; lg M * =11.4; =180 km s 1; S/N=33; regul=100 0.38 0.40 0.42 0.44 0.46 0.48 0.50 rest ( m) 0.2 0.4 0.6 0.8 1.0 1.2 Relative Flux (f ) 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 lg Age (yr) 1.5 1.0 0.5 0.0 [M/H] 0.000 0.005 0.010 0.015 0.020 light fraction Figure 6. More examples of ppxf fits to spectra and photometry. The meaning of the symbols is the same as in Fig. 5, but I show a single regularization (regul=100). The top three galaxies require a single star formation event, while the rest can only be modelled with multiple discrete star formation events. the masses derived with ppxf against the stellar masses produced by other codes. For my comparisons I used the published stellar masses \ud835\udc40\u2217for the LEGA-C galaxies from the three stellar population codes: (i) LePhare (Arnouts et al. 2002), (ii) EAZY (Brammer et al. 2008) and (iii) Prospector (Johnson et al. 2021b). I extracted the values of stellar masses for the first two codes from the Farmer version of the COSMOS2020 catalogue (Weaver et al. 2022), while for the last code, I used the values described in the LEGA-C DR3 paper (van der Wel et al. 2021, appendix B) as kindly provided by Arjen van der Wel. I tried to isolate the effect of the fitting methods from differences in the extrapolation of the galaxy\u2019s total luminosities. For this, with the \ud835\udc40\u2217from the COSMOS2020 catalogues, I rescaled the masses by the difference in the total \ud835\udc3e\ud835\udc60band luminosity between the Weaver et al. (2022) and Muzzin et al. (2013) catalogues. No correction is needed to compare ppxf and Prospector, given that for both I used the values based on the Muzzin et al. (2013) catalogue. I show the comparison between the stellar masses derived with ppxf and the other three codes in Fig. 7. I coloured the values with the stellar age derived by ppxf. I loess smoothed the measured age values using the algorithm by Cleveland & Devlin (1988) as implemented MNRAS 000, 1\u201328 (2023) 18 M. Cappellari 9.0 9.5 10.0 10.5 11.0 11.5 12.0 lg M (M ) (ppxf + fsps) 9.0 9.5 10.0 10.5 11.0 11.5 12.0 lg M (M ) (Prospector + fsps) S/N > 0 lg Age > 6.0 Ngal = 3191 = 0.163 dex M * / 2 = 30% Comparing M *  determinations Clipped lg Age  (yr) 9.6 8.0 9.0 9.5 10.0 10.5 11.0 11.5 12.0 lg M (M ) (ppxf + fsps) 9.0 9.5 10.0 10.5 11.0 11.5 12.0 lg M (M ) (EAZY + GALAXEV) S/N > 0 lg Age > 6.0 Ngal = 2327 = 0.147 dex M * / 2 = 27% Comparing M *  determinations Clipped lg Age  (yr) 9.6 8.0 9.0 9.5 10.0 10.5 11.0 11.5 12.0 lg M (M ) (ppxf + fsps) 9.0 9.5 10.0 10.5 11.0 11.5 12.0 lg M (M ) (LePhare + GALAXEV) S/N > 0 lg Age > 6.0 Ngal = 2319 = 0.168 dex M * / 2 = 31% Comparing M *  determinations Clipped lg Age  (yr) 9.6 8.0 Figure 7. Comparison of ppxf stellar population mass \ud835\udc40\u2217estimates against different methods. I use the \ud835\udc40\u2217values from Prospector in van der Wel et al. (2021) or from EAZY and LePhare in Weaver et al. (2022), for the galaxies that are common in both catalogues. The three panels show the comparison for each method. The red line is the one-to-one relation, and the black line is the best fit using LtsFit (Cappellari et al. 2013a). The x-symbols are the outliers identified by LtsFit, and the dotted lines are the selection limits. The colours show the luminosity-weighted mean stellar age \u27e8lg Age\u27e9, smoothed by loess. The grey contours show the kernel density estimation of the galaxy distribution. I indicate the \ud835\udc46/\ud835\udc41and \u27e8lg Age\u27e9selection criteria, the number of selected galaxies, the rms scatter \u0394, and an approximate relative 1\ud835\udf0eerror \ud835\udf0e\ud835\udc40\u2217in \ud835\udc40\u2217for each panel. I estimated the latter as \ud835\udf0e\ud835\udc40\u2217\u2261\u0394/ \u221a 2 by assuming both \ud835\udc40\u2217have the same uncertainty. 10.5 11.0 11.5 12.0 lg M (M ) (ppxf + fsps) 10.50 10.75 11.00 11.25 11.50 11.75 12.00 lg M (M ) (Prospector + fsps) S/N > 10 lg Age > 9.5 Ngal = 703 = 0.090 dex M * / 2 = 16% Comparing M *  determinations Clipped lg *  (km s 1) 2.4 2.2 Figure 8. Same as in Fig. 7 for a subsample with high spectral \ud835\udc46/\ud835\udc41> 10 and old ages \u27e8lg Age\u27e9> 9.5. As the age range is limited, the colours show here the loess smoothed stellar velocity dispersion. in the loess package16 by Cappellari et al. (2013b) and using the keyword rescale=True to equalize the axes of maximum/minimum variance before smoothing. I used a small smoothing parameter frac=0.1 in all plots of this paper. The loess-smoothed values are the two-dimensional equivalent of the average trend that is often shown in one-dimensional plots. The key difference is that the scatter cannot be easily shown in two dimensions together with the average trend. The scatter is better visualized using a different projection. To estimate the scatter between two pair of measurements, while removing outliers, I used the LtsFit package17 described in Cappellari et al. (2013a, sec. 3.2), which combines the Least Trimmed Squares robust technique of Rousseeuw & Van Driessen (2006) into a leastsquares fitting algorithm which allows for errors in all variables and intrinsic scatter. Instead of using a fixed \ud835\udf0e-clipping criterion with the \u2019clip\u2019 keyword in the ltsfit procedure, I used an adaptive clipping that depends on the sample size. This is the value that would produce on average one outlier in a Gaussian distribution of the given sample size. It can be computed using the Scipy class scipy.stats.norm as clip=abs(norm.ppf(p/2)), with \ud835\udc5d= 1/\ud835\udc5band \ud835\udc5bthe sample size. For reference, with \ud835\udc5b= 100 this gives clip=2.58 (default for ltsfit), for \ud835\udc5b= 500, clip=3.09 and for \ud835\udc5b= 3000, clip=3.59. The ltsfit procedure returns a robust estimate of the rms scatter \u0394 from the best-fitting relation. When the uncertainty of the two quantities I am comparing is the same, one can estimate it as \ud835\udf0e\ud835\udc40\u2217= \u0394/ \u221a 2. In all my plots I rescaled the masses provided by all other methods to have the same median as the ppxf values, which I did not modify. This is the reason why all plots follow the one-to-one relation without any overall offset. This is to remove the effect of differences in the assumed stellar IMF, gas loss or stellar remnants, whose investigation is outside the scope of this paper. I find that the observed scatter in all galaxies, when selected irrespective of their age or \ud835\udc46/\ud835\udc41, is in agreement with a 1\ud835\udf0euncertainty in the stellar mass of about 30% for every method. This result is consistent across all six pairwise comparisons of the methods, with differences within the measurement uncertainties. However, the behaviour of the differences is markedly different as a function of mean ages. The comparison of ppxf against Prospector (Fig. 7), 16 I used loess v2.1 available from https://pypi.org/project/loess/ 17 I used LtsFit v6.0 available from https://pypi.org/project/ltsfit/ MNRAS 000, 1\u201328 (2023) ppxf with spectra and photometry at \ud835\udc67\u22480.8 19 show that the scatter is smaller for older galaxies at given mass, but the younger ones generally scatter symmetrically around the one-to-one relation. The exception are the outliers, which have generally lower masses in Prospector than in ppxf. The comparison of ppxf and LePhare is similar to Prospector, but with less low-mass outliers. However there is no evidence for a tightening of the correlation for older models. The comparison of ppxf and EAZY, unlike the other two models, shows a strong asymmetry as a function of age: older models tend to be less massive in EAZY than ppxf, while younger models are more massive in EAZY. This asymmetry is reminiscent of the difference between Prospector and EAZY reported in Leja et al. (2019). In fact, the same age asymmetry is seen when comparing EAZY with either Prospector or LePhare. As suggested by Fig. 7, the scatter dramatically decreases (Fig. 8) if I compare ppxf and Prospector only for the galaxies with the oldest ages and largest spectral \ud835\udc46/\ud835\udc41(which also implies brightest photometry). Given the small age range, I coloured galaxies by their \ud835\udf0e\u2217. For this subset of galaxies, the inferred scatter of about 16% is half of that for the general population, without significant trends, except again for some outliers where Prospector gives lower masses than ppxf. When comparing stellar mass estimates of real galaxies, it is often difficult to assess the real accuracy between different methods, because the true masses are unknown. In the next section, I will address this issue, for a subsample of the LEGA-C sample, using mass determinations from stellar dynamics. 7.3 Comparing JAM dynamical with stellar population \ud835\udc40/\ud835\udc3f One of the sources of confusion in comparing galaxy masses from stellar populations and dynamical modelling is the ambiguity of the so-called \u2018dynamical mass\u2019 of a galaxy. This term does not refer to a well-defined physical quantity, because in the standard cosmological model, the galaxy\u2019s total mass is largely composed of dark matter, which is difficult to constrain with the available kinematic data of limited radial coverage. The quantity that the dynamical models reliably measure is the total density profile within the spatial extent of the kinematic tracer. However, this density profile cannot be easily converted into a mass, because it depends on the choice of the integration volume and on the assumptions about the galaxy shape and orientation (Cappellari et al. 2013a, sec. 3.3.1). A more robust and convenient quantity for comparing population and dynamics is the total mass-to-light ratio (\ud835\udc40/\ud835\udc3f)JAM, within the inner regions of a galaxy. This quantity has a weak dependence on the integration volume and galaxy inclination. It should be always preferred for accurate comparisons. In Section 5, I presented unbiased dynamical models of the stellar kinematics, based on the Sersic photometric models in the F814W/ACS band, for all the galaxies in the LEGA-C sample with available velocity dispersion. Previous studies of nearby galaxies using high-resolution integral-field stellar kinematics have demonstrated that this kind of models can reliably estimate the total dynamical mass-to-light ratios (\ud835\udc40/\ud835\udc3f)JAM in the central regions of galaxies with uncertainties of about 5% (Cappellari et al. 2006, 2013a; Shetty et al. 2020b; Zhu et al. 2023a). Importantly, these studies have also shown that precise and unbiased (\ud835\udc40/\ud835\udc3f)JAM can be obtained using models where the total mass distribution follows the luminous one. In fact, these mass-follow-light models are more robust and precise than those that explicitly separate the luminous and dark matter, when the main goal is to measure the total (\ud835\udc40/\ud835\udc3f)JAM (Cappellari et al. 2013a; Zhu et al. 2023b). An additional complication is that the dynamics is sensitive to all 0.25 0.00 0.25 0.50 0.75 1.00 1.25 lg(M/L)JAM (M /L g) 0.4 0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 lg(M * /L)pop (M /L g) (ppxf + fsps) S/N > 10 lg Age > 9.5 Ngal = 655 = 0.090 dex M * / 2 = 16% Photometry + Spectrum ppxf Chab Salp Dynamics vs Population M/L Clipped lg *  (km s 1) 2.4 2.2 0.25 0.00 0.25 0.50 0.75 1.00 1.25 lg(M/L)JAM (M /L g) 0.4 0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 lg(M * /L)pop (M /L g) (Prospector + fsps) S/N > 10 lg Age > 9.5 Ngal = 655 = 0.117 dex M * / 2 = 21% Photometry Only Prospector Chab Salp Dynamics vs Population M/L Clipped lg *  (km s 1) 2.4 2.2 Figure 9. Comparison of dynamical and stellar population mass-to-light ratios. The dynamical mass-to-light ratio (\ud835\udc40/\ud835\udc3f)JAM is derived from the JAM modelling, while the stellar population mass-to-light ratio (\ud835\udc40/\ud835\udc3f)pop is derived from either ppxf(top panel) or Prospector (bottom panel). The red line shows the one-to-one relation, while the red dashed line indicates the shift that would be produced by changing the IMF from Chabrier to Salpeter. The black line shows the best linear fit using LtsFit, which strongly deviates from the one-to-one relation. The x-symbols mark the outliers identified by LtsFit, and the dotted lines mark the selection limits. The colours indicate the stellar velocity dispersion \ud835\udf0e\u2217, smoothed by loess. The grey contours indicate a kernel density estimate of galaxies. For each panel, I show the signal-to-noise ratio \ud835\udc46/\ud835\udc41and the mean logarithmic age \u27e8lg Age\u27e9selection criteria, the number of selected galaxies \ud835\udc41, the root mean square scatter \u0394, and an approximate relative error \ud835\udf0e\ud835\udc40\u2217in stellar mass \ud835\udc40\u2217for both methods. I estimate \ud835\udf0e\ud835\udc40\u2217as \ud835\udf0e\ud835\udc40\u2217\u2261\u0394/ \u221a 2 by assuming both methods have the same uncertainty. mass components: stellar, gas, and dark matter, while the population only measures the stellar one. However, detailed nearby studies have shown that for the passive galaxy population, dark matter contributes only about \u224810% of the total mass within 1\ud835\udc45e (Cappellari et al. 2013a; Zhu et al. 2023b), while gas mass has an even smaller contribution (e.g. Young et al. 2011). This allows us to assume that the dynamical (\ud835\udc40/\ud835\udc3f)JAM accurately approximates the stellar one. To compare the dynamical (\ud835\udc40/\ud835\udc3f)JAM I need the same quantity from stellar population (\ud835\udc40/\ud835\udc3f)pop. Having the full spectra from the stellar population models, one can compute the (\ud835\udc40/\ud835\udc3f)pop in any band. However, since I only have total stellar masses \ud835\udc40\u2217from Prospector LEGA-C catalogue, I divide \ud835\udc40\u2217by the total luminosity MNRAS 000, 1\u201328 (2023) 20 M. Cappellari 1.0 0.5 0.0 0.5 1.0 lg(M/L)JAM (M /L g) 1.0 0.5 0.0 0.5 1.0 lg(M * /L)pop (M /L g) (ppxf + fsps) S/N > 10 lg Age > 6.0 Ngal = 2006 Photometry + Spectrum ppxf Chab Salp Dynamics vs Population M/L lg Age  (yr) 9.67 7.92 Figure 10. Same as in Fig. 9 but for all ages. The colours here indicate loess-smoothed mean luminosity-weighted ages \u27e8lg Age\u27e9. The contours of constant age are almost horizontal, meaning that the stellar population massto-light ratio (\ud835\udc40/\ud835\udc3f)pop depends on age as expected, but the dynamical (\ud835\udc40/\ud835\udc3f)JAM does not. Variations in the initial mass function (IMF) can explain the (\ud835\udc40/\ud835\udc3f)JAM differences for the old ages, while the mass fraction of dark matter and gas must drive the (\ud835\udc40/\ud835\udc3f)JAM variations for the young ages. \ud835\udc3f\ud835\udc56in SUBARU \ud835\udc56-filter from Muzzin et al. (2013) catalogues. This assumes that (\ud835\udc40/\ud835\udc3f)pop is constant over the full galaxy, which is likely a decent approximation for passive galaxies. Using photometry consistent with mass derivation ensures no spurious differences in mass and luminosity extrapolation. However, differences between \ud835\udc56-band and F814W filters may introduce some small systematic offset in the \ud835\udc40/\ud835\udc3fcomparison. However, I am interested in relative uncertainties more than absolute offsets. The \ud835\udc40/\ud835\udc3fis usually reported in solar units. For this, I assume a solar luminosity \ud835\udc3f\ud835\udc54= 5.11 mag in AB system from Willmer (2018) and report \ud835\udc40/\ud835\udc3fin units of M\u2299/L\u2299, given that F814W approximately corresponds to rest-frame SDSS \ud835\udc54-band filter at median redshift \ud835\udc67\u22480.8 of my sample. This normalization is a constant and does not affect the comparison. The rest-frame wavelength of the filter varies by up to \u224810% within the redshift range, however, this shift is the same for both dynamical and population \ud835\udc40/\ud835\udc3fand does not affect the scatter. I compare the (\ud835\udc40/\ud835\udc3f)JAM from dynamical modelling and the (\ud835\udc40/\ud835\udc3f)pop from stellar population synthesis using a sample of old galaxies with high-quality spectra in Fig. 9. I only use the passive population for this comparison. I adjust the Prospector (\ud835\udc40/\ud835\udc3f)pop by adding 0.19 dex to match the JAM median. I also convert the ppxf (\ud835\udc40/\ud835\udc3f)pop from the Salpeter (1955) IMF to the Chabrier (2003) IMF by subtracting 0.215 dex (Madau & Dickinson 2014, fig. 4). I do not change the ppxf value after this conversion. The main findings from Fig. 9 are: (i) The ppxf (\ud835\udc40/\ud835\udc3f)pop values are more consistent with the (\ud835\udc40/\ud835\udc3f)JAM values than the Prospector ones. The scatter is 0.090 dex for ppxf and 0.117 dex for Prospector. This suggests that adding spectra to ppxf improves the mass estimates. (ii) The ppxf (\ud835\udc40/\ud835\udc3f)pop comparison does not have the low-\ud835\udc40/\ud835\udc3f outliers that appear in the Prospector comparison, indicating more reliable (\ud835\udc40/\ud835\udc3f)pop or \ud835\udc40\u2217estimates in ppxf with spectra than in Prospector with photometry only. (iii) Both ppxf and Prospector show a similar trend in the (\ud835\udc40/\ud835\udc3f)pop \u2212(\ud835\udc40/\ud835\udc3f)JAM relation, which clearly deviates from a oneto-one relation. The trend implies that the galaxies with higher \ud835\udf0e\u2217 have more mass from dynamics than from population models at a fixed IMF. The variation is comparable to the mass difference between Chabrier and Salpeter IMF. This trend is consistent with previous studies that suggested a non-universal IMF based on dynamics and population of nearby (Cappellari et al. 2012; Li et al. 2017; Shetty et al. 2020a) and distant galaxies (Shetty & Cappellari 2014). Whatever the origin of this trend, this comparison shows that it is robust across different samples, redshift and methods. From the cross-comparisons between the scatter observed when comparing different estimates of the stellar masses, one can infer the accuracy of each individual technique, assuming as an approximation that it is constant. In fact, if we define \ud835\udf0emethod the uncertainty of \u2018method\u2019, then the squared uncertainties between each pair of methods add linearly as follows \uf8f1 \uf8f4 \uf8f4 \uf8f2 \uf8f4 \uf8f4 \uf8f3 \ud835\udf0e2 ppxf + \ud835\udf0e2 Pros = \u03942(ppxf/Pros) \ud835\udf0e2 ppxf + \ud835\udf0e2 JAM = \u03942(ppxf/JAM) \ud835\udf0e2 Pros + \ud835\udf0e2 JAM = \u03942(Pros/JAM) (37) where the scatter \u0394 was measured in Fig. 8 (\u0394(ppxf/Pros) = 0.090 dex) and Fig. 9 (\u0394(ppxf/JAM) = 0.090 and \u0394(Pros/JAM) = 0.117 dex). The positive solution of equation (37) gives the 1\ud835\udf0erelative uncertainty of the three different methods on this dataset: \uf8f1 \uf8f4 \uf8f4 \uf8f2 \uf8f4 \uf8f4 \uf8f3 \ud835\udf0eppxf = 0.035 dex = 9 % \ud835\udf0eJAM = 0.083 dex = 21 % \ud835\udf0ePros = 0.083 dex = 21 % (38) This result shows that, at least for the limited case of the old population, where we can assume we know the \u2018true\u2019 stellar mass from galaxy dynamics, the inclusion of spectra in ppxf gives masses significantly more accurate than those using Prospector with photometry alone. This is encouraging, but of course, it should not be interpreted as ppxf being more accurate than Prospector, given that the latter could fit spectra as well and this would likely lead to comparable accuracy as ppxf. However, these extra comparisons are beyond the scope of this paper. In Fig. 10 I also show the comparison between stellar dynamics and stellar population \ud835\udc40/\ud835\udc3ffor the full set of galaxies with high-\ud835\udc46/\ud835\udc41 regardless of their age. This plot cannot be used to infer the accuracy of the mass estimates. In fact, detailed modelling of the MaNGA survey has shown that younger galaxies contain significant fractions of gas and dark matter (Zhu et al. 2023a), making the mass estimate from the stellar population significantly lower than the dynamical one, as observed. 7.4 Stellar population scaling relations As I am focusing on observable trends, I define luminosity-weighted population quantities, summed over the template weights, as \u27e8lg Age\u27e9= \u00cd \ud835\udc57\ud835\udc3fbol, \ud835\udc57\u00d7 lg Age\ud835\udc57 \u00cd \ud835\udc57\ud835\udc3fbol, \ud835\udc57 (39a) \u27e8[\ud835\udc40/\ud835\udc3b]\u27e9= \u00cd \ud835\udc57\ud835\udc3fbol, \ud835\udc57\u00d7 [\ud835\udc40/\ud835\udc3b] \ud835\udc57 \u00cd \ud835\udc57\ud835\udc3fbol, \ud835\udc57 . (39b) In Fig. 11 I show the distribution of ages, metallicities and the Sersic (1968) index \ud835\udc5bSer on the (\ud835\udc40JAM, \ud835\udc45maj e ) plane, where the dynamical mass \ud835\udc40JAM closely approximates the total stellar masses \ud835\udc40\u2217, and the half-light radius \ud835\udc45maj e is the semi-major axis of the isophote containing half of the total light of the Sersic (1968) fitted to the galaxy photometry. Both \ud835\udc45maj e and \ud835\udc5bSer are tabulated in the LEGA-C MNRAS 000, 1\u201328 (2023) ppxf with spectra and photometry at \ud835\udc67\u22480.8 21 9 10 11 12 lg MJAM (M ) 0.5 0.0 0.5 1.0 1.5 lg Rmaj e  (kpc) M Re = const. Only Quenched lg Age 9 10 11 12 lg MJAM (M ) 0.5 0.0 0.5 1.0 1.5 M Re = const. Only Quenched [M/H] 9 10 11 12 lg MJAM (M ) 0.5 0.0 0.5 1.0 1.5 M Re = const. Only Quenched lg nSer 9.65 8.00 0.05 -0.60 0.6 0.0 Figure 11. Galaxy properties on the dynamical mass vs size (\ud835\udc40JAM, \ud835\udc45maj e ) plane at \ud835\udc67\u22480.8. To good approximation \ud835\udc40JAM \u2248\ud835\udc40\u2217, see text. Galaxies are coloured by their luminosity-weighted ages \u27e8lg Age\u27e9(left panel), luminosity-weighted metallicities \u27e8[\ud835\udc40/\ud835\udc3b]\u27e9(middle panel) and by the Sersic index \ud835\udc5bSer of a fit to their photometry. I used the values from the fsps models, but those from galaxev are very similar. All values are loess-smoothed to show average trends and I used regul=10 in ppxf. The grey contours are a kernel density estimate of the galaxy distribution (using scipy.stats.gaussian kde). Galaxy properties mainly follow lines of constant stellar velocity dispersion, which is indicated by the dashed grey lines for \ud835\udf0e\u2217= 50, 100, 200, 300, 400, 500 km \ud835\udc60\u22121 from left to right, while mass is not a good predictor of their stellar population. However, above a stellar mass lg(\ud835\udc40\u2217/M\u2299) > \u223c11.5 (blue vertical line), all galaxies are old (quenched), have a high metallicity and large Sersic index. The thick red line is the \u201czone of avoidance\u201d for nearby galaxies from Cappellari et al. (2013b), scaled down by a factor 1.6\u00d7 to account for redshift evolution.  (km/s) 7 8 9 10 lg Age  (yr) SPS method: fsps 1.6 1.8 2.0 2.2 2.4 2.6 lg  (km/s) 1.5 1.0 0.5 0.0 0.5 [M/H] [M/H] 0.04 -0.59 lg Age  (yr) 9.63 8.14  (km/s) 7 8 9 10 lg Age  (yr) SPS method: galaxev 1.6 1.8 2.0 2.2 2.4 2.6 lg  (km/s) 1.5 1.0 0.5 0.0 0.5 [M/H] [M/H] 0.20 -0.51 lg Age  (yr) 9.42 7.90  (km/s) 7 8 9 10 lg Age  (yr) SPS method: bpass 1.6 1.8 2.0 2.2 2.4 2.6 lg  (km/s) 1.5 1.0 0.5 0.0 0.5 [M/H] [M/H] -0.27 -0.77 lg Age  (yr) 9.51 7.87 Figure 12. Luminosity-weighted ages \u27e8lg Age\u27e9and metallicities \u27e8[\ud835\udc40/\ud835\udc3b]\u27e9vs stellar velocity dispersion \ud835\udf0e\u2217for the LEGA-C galaxies. The top panels show the age distribution, coloured by loess-smoothed metallicity. The grey horizontal band is the Universe age range between 0.6 < \ud835\udc67< 1 and the red dashed line is the present age. The bottom panels show the metallicity distribution coloured by loess-smoothed age. In all panels, the grey contours are the kernel density estimator of the galaxies\u2019 distribution. From left to right I show results using the fsps, galaxev and bpass SPS models, all with regul=10 in ppxf. There is a clear bend of the (Age, \ud835\udf0e\u2217) trend around lg(\ud835\udf0e\u2217/km \ud835\udc60\u22121) \u22482.3. At fixed \ud835\udf0e\u2217metallicity depends on age with younger galaxies having lower \u27e8[\ud835\udc40/\ud835\udc3b]\u27e9. catalogue (van der Wel et al. 2021). See Cappellari et al. (2013a) for a discussion of why dynamical mass approximates the total stellar mass. I loess smoothed the measured values in all coloured plots of this paper. The resulting loess-smoothed values represent the twodimensional equivalent of the average values that are routinely shown in one-dimensional plots. However, in two-dimension one cannot show the scatter together with the average values. To visualize the scatter, which is significant and not random, I use a projection along the \ud835\udf0e\u2217axes later. This figure shows the well-known fact, in the nearby Universe, that both ages and metallicities approximately follow lines of constant stellar velocity dispersion \ud835\udf0e\u2217, or equivalently lines where \ud835\udc40\u2217\u221d\ud835\udc45maj e (compare this figure with MaNGA results in fig. 4 of Li et al. 2018 MNRAS 000, 1\u201328 (2023) 22 M. Cappellari 0.75 0.50 0.25 0.00 0.25 0.0 0.5 1.0 1.5 2.0 2.5 AV SPS method: fsps lg Age  (yr) 9.25 8.09 0.75 0.50 0.25 0.00 0.25 0.0 0.5 1.0 1.5 2.0 2.5 AV SPS method: galaxev lg Age  (yr) 9.15 8.02 0.75 0.50 0.25 0.00 0.25 0.0 0.5 1.0 1.5 2.0 2.5 AV SPS method: bpass lg Age  (yr) 9.05 7.74 Figure 13. Dust properties vs galaxy age. The \ud835\udc49band attenuation \ud835\udc34\ud835\udc49in mag is plotted against the UV slope \ud835\udeffand coloured by loess-smoothed luminosityweighted ages. The grey contours are the kernel density estimator of the galaxies\u2019 distribution. At every \ud835\udeffthe youngest galaxies have larger attenuation, while the largest \ud835\udc34\ud835\udc49are only observed around the Calzetti et al. (2000) attenuation curve, which has \ud835\udeff= 0. From left to right I show results using the fsps, galaxev and bpass SPS models. The first two are highly consistent, but the latter, while still qualitatively similar is quantitatively very different. or Lu et al. 2023). I also show to guide the eye the local \u201czone of avoidance\u201d at high densities (Cappellari et al. 2013b, eq. 4), which I scaled down by a factor 1.6\u00d7 in \ud835\udc45maj e , roughly consistent with the general trends of decreasing galaxy sizes with redshift (e.g. van der Wel et al. 2014). The Sersic index \ud835\udc5bSer also approximately follows the distribution of ages and metallicity, in the sense that passive galaxies tend to have ln \ud835\udc5bSer > \u223c0.4 or \ud835\udc5bSer > \u223c2.5 (red colour in the right panel of Fig. 11). This \ud835\udc5bSer value is the one sometimes adopted to separate early-type from late-type galaxies (e.g. Bell et al. 2003; Shen et al. 2003). In the local Universe, below the stellar mass lg(\ud835\udc40\u2217/M\u2299) < \u223c11.5 the trend of \ud835\udc5bSer is due to a sequence of increasing bulge fraction, while above lg(\ud835\udc40\u2217/M\u2299) > \u223c11.5 is the region of slow rotators with cores (see review by Cappellari 2016, fig. 23). This result has a rather long history, both locally and at \ud835\udc67\u223c1 (Chauke et al. 2018, 2019; Beverage et al. 2021; Barone et al. 2022; Hamadouche et al. 2022; Tacchella et al. 2022) but had not been seen so cleanly at this redshift before LEGA-C. For nearby galaxies, Kauffmann et al. (2003) clearly noted that galaxy population correlates better with mass surface density \u03a3 than with \ud835\udc40\u2217. It was later observed that \u03a3, or even better the virial predictor \ud835\udf0evir \u221d\ud835\udc40\u2217/\ud835\udc45e of the stellar velocity dispersion, inferred from photometry alone, remains a better predictor of galaxy colours out to \ud835\udc67\u22483 (Franx et al. 2008; Bell et al. 2012). However, it was still unclear at that time how accurately the photometric estimates were able to predict the actual stellar masses and the velocity dispersion of the stars. To address this issue I used masses from dynamical models, and \ud835\udf0e\u2217from good quality integral-field stellar kinematics, rather than photometric estimates. In Cappellari (2011) I clearly concluded that \u201c\ud835\udf0e\u2217(not \u03a3e or \ud835\udc40\u2217) is the best predictor of galaxy properties\u201d (see also Cappellari et al. 2013b). These early results were confirmed by several papers using larger samples and stellar kinematics of ever-increasing quality (e.g. Wake et al. 2012; McDermid et al. 2015; Scott et al. 2017; Li et al. 2018; Barone et al. 2018, 2020). In parallel, Cheung et al. (2012) and Fang et al. (2013) introduced the use of central surface density \u03a31 from photometry, within a fixed radius of 1 kpc, to predict quenching. A review is given in Cappellari (2016, see fig. 22). Given that in Fig. 11 the main stellar population trends follow \ud835\udf0e\u2217, in Fig. 12 I show how the luminosity-weighted ages and metallicity depend on \ud835\udf0e\u2217in the LEGA-C sample. The trends resemble quite closely the local results from the best integral-field spectroscopy from both SAMI (Scott et al. 2017) and MaNGA (Li et al. 2018). However, the top panels of Fig. 12 additionally illustrate the clear dependency between age and [\ud835\udc40/\ud835\udc3b] at fixed \ud835\udf0e\u2217: the population of old galaxies at large \ud835\udf0e\u2217is characterized by a larger metallicity than their younger counterpart at the same \ud835\udf0e\u2217. Very clear is the bend in the (\ud835\udf0e\u2217, Age) distribution around lg(\ud835\udf0e\u2217/km \ud835\udc60\u22121) \u22482.3 (also see Chauke et al. 2018). The results are very consistent between both the fsps and galaxev SPS models. It is reassuring to see that the ridge of the age distribution in the top panels converges towards the age of the Universe at that redshift (grey horizontal band), while being slightly younger for galaxev vs fsps. I also run models where I restricted the age of each galaxy to the Universe\u2019s age at its redshift, as generally done for local studies. All results were qualitatively similar, except for the obvious truncation and corresponding clustering of the Ages values at the maximum Universe Age \u22486.6 Gyr at \ud835\udc67\u22480.8, which is indicated by a grey band in Fig. 12. The bpass results are qualitatively in agreement but show substantial quantitative differences, especially in the \ud835\udf0e\u2217\u2212[\ud835\udc40/\ud835\udc3b] trend. Overall, this figure confirms the quality and consistency of these global results compared to local surveys. Fig. 13 shows the distribution of the two dust attenuation parameters \ud835\udc34\ud835\udc49and \ud835\udeff(Section 6.3) coloured by mean stellar age. One can see that at every UV slope \ud835\udeffthe youngest galaxies have the strongest attenuation, except for the largest \ud835\udeff. Moreover, the largest attenuations in galaxies are only observed at large \ud835\udeff, close to the Calzetti et al. (2000) slope \ud835\udeff= 0. Note, however, that there is a degeneracy between attenuation and continuum normalization near the upper limit of \ud835\udeff. Results are extremely consistent for the fsps and galaxev SPS models, but again the bpass results look quite different, although they all qualitatively agree. 7.5 Non-parametric star formation histories Fig. 14 shows the non-parametric star formation history of the galaxies in the LEGA-C sample as a function of key galaxy parameters. For this plot I sorted the quantity of interest (e.g. \ud835\udf0e\u2217) and constructed 30 bins in that quantity, each containing the same number of about 100 galaxies, in such a way that different bins have the same level of shot noise. I show the dependency of the SFH, parametrized as discussed by the light \ud835\udc3fbol contributed in the spectrum by stellar populations of different ages, as a function of the following parameters: (i) Stellar velocity dispersion: the plots show a clear trend of SFH with \ud835\udf0e\u2217as expected from the trends between \ud835\udf0e\u2217and age. What MNRAS 000, 1\u201328 (2023) ppxf with spectra and photometry at \ud835\udc67\u22480.8 23 1.75 2.00 2.25 lg  (km s 1) 6 7 8 9 10 lg Age (yr) Quenching Boundary 9 10 lg JAM 1  (M kpc 2) 10 11 lg MJAM (M ) 1.0 0.5 0.0 [M/H] 0.5 0.0 0.5 lg nSer Main Star Formation 0.00 0.02 0.04 0.06 0.08 0.10 Light Fraction (Lbol) Star Formation History vs Galaxy Properties (SPS: fsps) 1.75 2.00 2.25 lg  (km s 1) 6 7 8 9 10 lg Age (yr) Quenching Boundary 9 10 lg JAM 1  (M kpc 2) 10 11 lg MJAM (M ) 0.5 0.0 [M/H] 0.5 0.0 0.5 lg nSer Main Star Formation 0.00 0.02 0.04 0.06 0.08 0.10 Light Fraction (Lbol) Star Formation History vs Galaxy Properties (SPS: galaxev) 1.75 2.00 2.25 lg  (km s 1) 6 7 8 9 10 lg Age (yr) 9 10 lg JAM 1  (M kpc 2) 10 11 lg MJAM (M ) 0.75 0.50 0.25 [M/H] 0.5 0.0 0.5 lg nSer 0.00 0.02 0.04 0.06 0.08 0.10 Light Fraction (Lbol) Star Formation History vs Galaxy Properties (SPS: bpass) Figure 14. Star formation history (SFH) vs galaxy properties. In all panels, the colours represent the SFH recovered with ppxf (with regul=100) parametrized by the bolometric light \ud835\udc3fbol fraction contributed by populations of different ages. The SFHs are shown as a function of key galaxy parameters: (1) the stellar velocity dispersion \ud835\udf0e\u2217; (2) the dynamical mass \ud835\udc40JAM, which well approximates \ud835\udc40\u2217; (3) the dynamically-determined average density \u03a3JAM 1 inside a circle of radius 1 kpc centred on the galaxy; (4) the luminosity weighted metallicity \u27e8[\ud835\udc40/\ud835\udc3b]\u27e9and (5) the exponent \ud835\udc5bSer of a Sersic profile fitted to the galaxy photometry (see text for definitions). Average values are computed for equal bins in \ud835\udf0e\u2217(or the other parameters) of 100 galaxies each. Galaxies with largest \ud835\udf0e\u2217, \ud835\udc40\u2217, \u27e8[\ud835\udc40/\ud835\udc3b]\u27e9or \ud835\udc5bSer on average experienced their main star formation event long ago, but the typical age for the bulk of their star formation increases with \ud835\udf0e\u2217(or the other parameters) as indicated by the slanted black dashed wavy lines in the left and right panels. For lower \ud835\udf0e\u2217galaxies can form the stars at any time until the present. The plots show a beautifully clear and sharp quenching boundary at lg(\ud835\udf0e\u2217/km \ud835\udc60\u22121) \u22482.3, or lg(\u03a3JAM 1 /M\u2299kpc\u22122) \u22489.9, or \u27e8[\ud835\udc40/\ud835\udc3b]\u27e9\u2248\u22120.2 for fsps and \u27e8[\ud835\udc40/\ud835\udc3b]\u27e9\u22480.0 for galaxev, or lg \ud835\udc5bSer \u22480.5, as indicated by the vertical yellow dashed wavy lines. There is no sharp boundary as a function of galaxy mass, but the transition is gradual and roughly happens around lg(\ud835\udc40\u2217/M\u2299) \u224811.5. Note the generally good agreement between the results from the fsps and galaxev SPS. The results using the bpass models look problematic, with spurious structures at specific ages, which are most likely artefacts of the models. is new is the striking sharpness of the boundary between a regime lg(\ud835\udf0e\u2217/km \ud835\udc60\u22121) > \u223c2.3 (or \ud835\udf0e\u2217> \u223c200 km \ud835\udc60\u22121), above which the spectra are dominated by a population nearly as old as the Universe at that redshift, without evidence for subsequent star formation events, and below which suddenly galaxies have star formation at any time until the present time. Both the fsps and galaxev SPS models indicate that galaxies still form the bulk of their stars at old times, but this age increases with \ud835\udf0e\u2217by roughly a factor between 6\u201310 for a variation in \ud835\udf0e\u2217by a factor of 10. In the case of the galaxev models, the SFH indicate ongoing star formation at the lowest \ud835\udf0e\u2217bins, while this is less so for the fsps models. (ii) Density within 1 kpc: this panel shows the same trend as the previous one, but with different units. This is because \u03a3JAM 1 is closely related to \ud835\udf0e\u2217(see Fang et al. 2013), especially when using JAM dynamical masses instead of stellar population masses. (iii) Galaxy mass: contrary to the dependency of SFH with \ud835\udf0e\u2217, there is no sharp transition as a function of stellar mass, but rather a gradual trend. Only galaxies more massive than lg(\ud835\udc40\u2217/M\u2299) > \u223c11.5 are characterized by a single event of star formation at old times. (iv) Galaxy metallicity: this panel shows that [\ud835\udc40/\ud835\udc3b] is as good as \ud835\udf0e\u2217at predicting the boundary between the region of fully quenched galaxies and those that can have multiple star formation events. Here MNRAS 000, 1\u201328 (2023) 24 M. Cappellari 6 7 8 9 10 lg Age (yr) 1.5 1.0 0.5 0.0 [M/H] 20 < < 122 km s 1 6 7 8 9 10 lg Age (yr) 122 < < 161 km s 1 6 7 8 9 10 lg Age (yr) 161 < < 203 km s 1 6 7 8 9 10 lg Age (yr) SPS method fsps 203 < < 486 km s 1 0.2 0.4 0.6 0.8 1.0 Lbol/max(Lbol) 6 7 8 9 10 lg Age (yr) 1.5 1.0 0.5 0.0 [M/H] 20 < < 122 km s 1 6 7 8 9 10 lg Age (yr) 122 < < 161 km s 1 6 7 8 9 10 lg Age (yr) 161 < < 203 km s 1 6 7 8 9 10 lg Age (yr) SPS method fsps COSMOS 2020 photometry 203 < < 486 km s 1 0.2 0.4 0.6 0.8 1.0 Lbol/max(Lbol) 6 7 8 9 10 lg Age (yr) 2 1 0 [M/H] 20 < < 122 km s 1 6 7 8 9 10 lg Age (yr) 122 < < 161 km s 1 6 7 8 9 10 lg Age (yr) 161 < < 203 km s 1 6 7 8 9 10 lg Age (yr) SPS method galaxev 203 < < 486 km s 1 0.2 0.4 0.6 0.8 1.0 Lbol/max(Lbol) 6 7 8 9 10 lg Age (yr) 1.0 0.5 0.0 [M/H] 20 < < 122 km s 1 6 7 8 9 10 lg Age (yr) 122 < < 161 km s 1 6 7 8 9 10 lg Age (yr) 161 < < 203 km s 1 6 7 8 9 10 lg Age (yr) SPS method bpass 203 < < 486 km s 1 0.2 0.4 0.6 0.8 1.0 Lbol/max(Lbol) Figure 15. Joint star-formation history (SFH) and metallicity distributions. Each panel shows the average distribution of weights recovered with ppxf (with regul=10) for 4 bins containing 800 LEGA-C galaxies sorted by their stellar velocity dispersion \ud835\udf0e\u2217(as indicated in the plot titles). The weights represent the bolometric luminosity \ud835\udc3fbol contributed by populations of different ages and metallicities. The top row shows the results obtained with the fsps SPS models. The second row still uses fsps but adopts the COSMOS2020 (Weaver et al. 2022) instead of my default UltraVISTA photometric catalogue (Muzzin et al. 2013). The third row is derived using the galaxev SPS models and the bottom one with the bpass models. One can see that the fsps and galaxev SPS provide qualitatively consistent results even for some of the main \u201cblobs\u201d in the distributions. Using an alternative photometric catalogue has virtually no effect on the results. At large \ud835\udf0e\u2217galaxies on average quenched long ago and their stars have high metallicity. At progressively lower \ud835\udf0e\u2217the age of the bulk of the star formation decreases, while still being dominated by high metallicity stars. However, the population is polluted by fresh accretion events of lower metallicity and a range of accretion times. As previously noted, the results using bpass SPS models are significantly different and should not be trusted, without further analysis. it happens at [\ud835\udc40/\ud835\udc3b] \u2248\u22120.2 for the fsps and [\ud835\udc40/\ud835\udc3b] \u22480.0 for the galaxev, which are systematically shifted to larger values of metallicity. (v) Sersic index: This panel show the SFH as a function of the Sersic (1968) exponent \ud835\udc5bSer. The boundary between fully quenched galaxies and galaxies that can have multiple star formation events happens here at lg \ud835\udc5bSer \u22480.5 or \ud835\udc5bSer \u22483.2. Remarkably this boundary is here nearly as clean as that with \ud835\udf0e\u2217. In all panels, the results using the bpass SPS models are again quite different from the other two. They show significant structure at specific ages and a less clear quenching boundary. The structure seen using the bpass models is likely an artefact of the SPS rather than a real conspiracy in the star formation events. The trends for different galaxy parameters, and the overall consistency between the four panels, for both the fsps and galaxev SPS models, can be understood by looking at Fig. 11 and noting that there is a region lg(\ud835\udc40\u2217/M\u2299) > \u223c11.5 above which all galaxies are quenched, high metallicity and have large Sersic index. Below that mass galaxies follow a trend of increasing bulge fraction, which increases \ud835\udf0e\u2217, metallicity and makes galaxies more likely to quench. These results parallel those which have been extensively reported for local galaxies (see review by Cappellari 2016). What is new here is the clarity and sharpness of the empirical evidence of the boundary to quenching and the fact that this can be detected so well at a time when the Universe was half of its current age. A rapid cessation of star formation for galaxies above a given critical value of \ud835\udf0e\u2217, or of some other estimate of the central stellar density, varying with \ud835\udc67, has often been invoked to explain the evolution of galaxy parameters over time (e.g. van Dokkum et al. 2015). An excellent review of the empirical evidence and models of a quenching boundary in galaxies is given in Chen et al. (2020, sec. 1). The physical mechanism for quenching is still under debate. Very briefly, one can group the main proposed theories into three broad classes: (i) \u201chalo quenching\u201d, where the gas gets shock-heated when falling into the gravitational potential of massive dark halos (e.g. Dekel & Birnboim 2006); (ii) \u201cactive galactic nucleus (AGN) feedback\u201d, where a jet from the supermassive black hole either ejects the gas from its host galaxy (e.g. Silk & Rees 1998) or prevent it from infalling (e.g. Bower et al. 2006; Croton et al. 2006). See review by Somerville & Dav\u00b4 e (2015). The panels in Fig. 14 provide a beautiful empirical confirmation of the theoretical assumptions that are made in many of those models. MNRAS 000, 1\u201328 (2023) ppxf with spectra and photometry at \ud835\udc67\u22480.8 25 7.6 Non-parametric joint SFH and metallicity distributions Fig. 15 presents the non-parametric joint luminosity distribution of the age and metallicities of the stellar populations of galaxies in four different bins of \ud835\udf0e\u2217. As in Fig. 14, also for this figure I sorted galaxies as a function of their \ud835\udf0e\u2217and constructed four groups, of about 800 galaxies each, to ensure all panels have the same level of shot noise. Like before, I compare all three SPS models (fsps, galaxev and bpass). In addition, In the second row of Fig. 15 I show the result when using the fsps model but adopting the photometric measurements from COSMOS2020 (Weaver et al. 2022) instead of the UltraVISTA catalogue (Muzzin et al. 2013). The first and second rows are barely distinguishable and this shows that any possible difference in the photometric calibration has a completely insignificant effect on the results. The distribution from both fsps and galaxev is highly consistent, almost at the level of the individual \u201cblobs\u201d, except for slightly older younger ages and higher metallicities for the galaxev vs the fsps models. The plots indicate that even galaxies with low \ud835\udf0e\u2217are still dominated by stars with high metallicity, but this is diluted by extra lowermetallicity populations acquired at different times. I should stress that the relatively smooth distribution in the maps are averages of many galaxies and should not be interpreted as the evolution of one individual galaxy, which is generally characterized by discrete star formation events. Moreover, not every feature of the maps is robust against variations in the data and SPS models. The overall observed distribution could be interpreted in the context of the two-phases of galaxy formation (e.g. Oser et al. 2010). According to this scenario, the formation of galaxies has a \u201ctwo-phase\u201d nature: a fast initial phase at \ud835\udc67> \u223c2 where \u201cin situ\u201d stars are created inside the galaxy from cold gas that falls in, and a longer phase since \ud835\udc67< \u223c3 where \u201cex-situ\u201d already-formed stars are mainly acquired. In this phase, large systems increase their mass and radius by absorbing smaller stellar systems that were formed very early (\ud835\udc67> \u223c3) outside of the central galaxy\u2019s virial radius, or by smooth gas accretion from cosmological filaments (see Naab & Ostriker 2017, for a review). Specifically, the old, high-metallicity component observed in Fig. 15 could be interpreted as the relic of the in-situ formation, which was quickly metal enriched, while the lower metallicity would correspond to either acquired stars, previously formed in smaller stellar components, or to star formation due to accretion from low-metallicity cosmological filaments. The accreted component is only present below the critical \u201cquenching boundary\u201d of \ud835\udf0e\u2217< \u223c200 km \ud835\udc60\u22121. Below that boundary, accretion can continue throughout the galaxies evolution. The high-metallicity old peak is visible for all four subsets of \ud835\udf0e\u2217, but its age decreases with \ud835\udf0e\u2217. This age trend in the old-age peak is the same already pointed out in Fig. 14. The LEGA-C spectra I analysed are not spatially resolved, but a similar analysis of spatially-resolved integral-field spectroscopic data for the MaNGA survey shows that, in low \ud835\udf0e\u2217galaxies in the nearby Universe, the oldest higher-metallicity component is associated to the galaxy bulge, while low-metallicity gas accretion happens in the disk (e.g. Lu et al. 2023). As expected, the bpass models show again quite different results, with a markedly different metallicity distribution. As commented earlier, the results from this model should be treated with caution as they are likely dominated by spurious unknown effects in the models. A caveat on these results on the metallicity distribution, which also affects other similar results on metallicity determinations from galaxy stellar spectra, is that the signature of metallicity variations becomes weaker at younger ages, where the \ud835\udc46/\ud835\udc41of the data also generally decreases. This can introduce possible systematic effects on metallicity trends. To exclude the effect of \ud835\udc46/\ud835\udc41, I verified that all results remain unchanged if I restrict the analysis to the 873 galaxies with \ud835\udc46/\ud835\udc41> 20 and even, at coarser resolution, for the subset of 126 galaxies with \ud835\udc46/\ud835\udc41> 40. It would still be valuable to compare the reported metallicity trends e.g. with those inferred from gas tracers from similar data. 8 SUMMARY In the first half of this paper, I described some modifications to the ppxf method (Cappellari 2017), which is used to extract the stellar and gas kinematics, as well as the stellar population of galaxies. First, I described a novel constrained least-squares optimization algorithm that ppxf has been using for the past few years. Then I outlined the changes I made to ppxf to be able to fit photometric data together with the usual full-spectrum fitting. I also described some other minor changes. In the second half of the paper, I presented an application of ppxf to the extraction of non-parametric star formation histories and metallicity distributions for a sample of 3200 galaxies at redshift 0.6 < \ud835\udc67< 1 with spectroscopy from the LEGA-C survey DR3 (van der Wel et al. 2021), and with 28-bands photometric measurements covering from the far ultraviolet (0.1 \ud835\udf07m) to the near-infrared (3 \ud835\udf07m) from either the UltraVISTA (Muzzin et al. 2013) or the COSMOS2020 catalogues (Weaver et al. 2022). I also constructed JAM dynamical models (Cappellari 2008, 2020) for all galaxies with measured stellar dispersion \ud835\udf0e\u2217and available Sersic profile fits to the photometry. For this study, I used and compared three spectral population synthesis (SPS) methods satisfying some criteria of age and wavelength coverage. This led to my selection of the fsps (Conroy et al. 2009; Conroy & Gunn 2010), galaxev (Bruzual & Charlot 2003) and bpass (Stanway & Eldridge 2018; Byrne et al. 2022) SPS methods. I compared the dynamical masses from JAM against the stellar masses from the different stellar-population fitting methods. I found that ppxf with photometry and spectra provides more accurate masses than the other methods with photometry alone, as one would have expected. I found that ppxf on these data reveals a striking difference between galaxies that are only consistent with a single star formation event from those that require multiple bursts of star formation. I constructed scaling relations for the global stellar population parameters and found a remarkable similarity, but even clearer trends, between these results at \ud835\udc67\u22480.8 and those from the latest spectroscopic surveys in the nearby Universe. This gives some confidence in the meaningfulness of the results and highlights the quality of the spectrophotometric data. Finally, I explored the non-parametric star formation histories (SFH) and the joint SFH and metallicity [\ud835\udc40/\ud835\udc3b] distributions. I found that the data indicate, on average over many galaxies, a remarkably sharp quenching boundary for the cessation of star formation, at a stellar velocity dispersion lg(\ud835\udf0e\u2217/km \ud835\udc60\u22121) \u22482.3 (\ud835\udf0e\u2217\u2248200 km \ud835\udc60\u22121), or equivalently with average mass density within 1 kpc lg(\u03a3JAM 1 /M\u2299kpc\u22122) > \u223c9.9 (\u03a3JAM 1 > \u223c7.9\u00d7109 M\u2299kpc\u22122), or at metallicity [\ud835\udc40/\ud835\udc3b] \u2248\u22120.1 (with some variation dependent on the adopted SPS model) or at Sersic (1968) index lg \ud835\udc5bSer \u22480.5 (\ud835\udc5bSer \u22483.2). As expected, the transition is more gradual as a function of stellar mass. This abrupt quenching boundary has been invoked by several models of galaxy formation. These data provide one of the cleanest empirical evidence to date. The joint age-metallicity distribution appears to support the twophase scenario of galaxy evolution by revealing the relic of an old MNRAS 000, 1\u201328 (2023) 26 M. Cappellari quickly-formed high-metallicity component and, below the quenching boundary \ud835\udf0e\u2217< \u223c200, multiple events of lower-metallicity accretion. This paper only scratches the surface of what can be done with this dataset and with similar ones that are being acquired at comparable and higher redshift. I have not explored e.g. obvious dependencies between SFH and stellar kinematics or environment (e.g. Cole et al. 2020; Sobral et al. 2022). Comparisons with galaxy formation models should be performed in the space of observable rather than using stellar masses which are empirically more uncertain. A similar analysis at higher redshift can reveal the onset and variation of the quenching boundary, which is a key but still quite uncertain parameter in galaxy formation models. James Webb Space Telescope (JWST) data are ideal to extend this kind of study to higher redshift. ACKNOWLEDGEMENTS I am grateful to the referee for an expert and very useful report. Based on observations made with ESO Telescopes at the La Silla Paranal Observatory under program IDs 194-A.2005 and 1100.A-0949 (The LEGA-C Public Spectroscopy Survey). DATA AVAILABILITY The LEGA-C DR3 spectra and catalogue are available HERE, the UltraVISTA photometric catalogue HERE, the COSMOS2020 catalogue from https://cosmos2020.calet.org/, the ppxf software from https://pypi.org/project/ppxf/, the JAM software from https://pypi.org/ project/jampy/, the MgeFit software from https://pypi.org/project/ mgefit/ and the LtsFit software from https://pypi.org/project/ltsfit/.",
                    "introduction": "The study of the stellar population of galaxies is an essential tool when trying to uncover how they have assembled. For this reason, a vast number of papers have tried to infer the galaxies\u2019 star formation history (SFH) and chemical composition from observations. The earliest results were based on simple galaxy colours as these were easier to obtain (see e.g. the lectures by Baade 1963). However, galaxy colours alone cannot strongly constrain both the galaxies\u2019 chemical composition and SFHs. Inferences from galaxy photometry alone are strongly affected for example by the age-metallicity (e.g. Worthey 1994) as well as by the SFH-dust degeneracies (e.g. Silva et al. 1998; Devriendt et al. 1999; Pozzetti & Mannucci 2000). For this reason, most of our knowledge on both the star formation and chemical composition of galaxies has been obtained from the numerous absorption features in their spectra. 1.1 Full spectrum fitting of nearby galaxies Over the past two decades, libraries of high-resolution (\ud835\udc45> \u223c2000) empirical stellar spectra were observed, which try to optimally sample all stages of stellar evolution. Prominent examples in the optical region \u2605E-mail: michele.cappellari@physics.ox.ac.uk include the STELIB (Le Borgne et al. 2003), ELODIE (Prugniel & Soubiran 2001), MILES (S\u00b4 anchez-Bl\u00b4 azquez et al. 2006; Falc\u00b4 on- Barroso et al. 2011) and recently the MaStar (Yan et al. 2019) stellar libraries. An exception is the X-Shooter spectral library (XSL), which reaches \ud835\udc45\u224810000 and extends up to 2.5 \ud835\udf07m (Chen et al. 2014; Verro et al. 2022a). Stellar population synthesis (SPS) models based on empirical stellar spectra have been developed that can produce synthetic galaxy spectra at high resolution. Examples of these kind of models are the galaxev (Bruzual & Charlot 2003), the Vazdekis (Vazdekis et al. 2010, 2015), the fsps (Conroy et al. 2009; Conroy & Gunn 2010), the Maraston (Maraston 2005; Maraston & Str\u00a8 omb\u00a8 ack 2011; Maraston et al. 2020) and most recently the XSL models (Verro et al. 2022b). Most current SPS models complement empirical stellar spectra with fully synthetic ones like BaSeL (Westera et al. 2002) or MARCS (Gustafsson et al. 2008). This allows one to cover stages of stellar evolution not well sampled by observations and also can extend the wavelength coverage, especially to the ultraviolet and infrared regions which are poorly covered by observations. Fully synthetic SPS were also developed like bpass (Stanway & Eldridge 2018; Byrne et al. 2022) or the MARCS version of the Maraston models. Initially, large spectroscopic studies of the stellar population in nearby galaxies were based on line indices of specific absorption features, generally using the LICK system (e.g. Worthey et al. 1994), \u00a9 2023 The Authors arXiv:2208.14974v2  [astro-ph.GA]  7 Sep 2023 2 M. Cappellari but the availability of good-quality high-resolution SPS models (see review by Conroy 2013) motivated a shift to using full-spectrum fitting (see review by Walcher et al. 2011). Various templates-fitting methods were developed for this task, like ppxf (Cappellari & Emsellem 2004; Cappellari 2017), starlight (Cid Fernandes et al. 2005), stecmap (Ocvirk et al. 2006), vespa (Tojeiro et al. 2007), fit3D (S\u00b4 anchez et al. 2016; Lacerda et al. 2022) and firefly (Wilkinson et al. 2017). These methods and software were extensively used e.g. to analyse the millions of spectra produced by integral-field spectroscopic surveys in the local Universe like ATLAS3D (Cappellari et al. 2011), CALIFA (S\u00b4 anchez et al. 2012), SAMI (Bryant et al. 2015) and MaNGA (Bundy et al. 2015). 1.2 Spectral fitting of high-\ud835\udc67"
                },
                {
                    "url": "http://arxiv.org/abs/1907.09894v2",
                    "title": "Efficient solution of the anisotropic spherically-aligned axisymmetric Jeans equations of stellar hydrodynamics for galactic dynamics",
                    "abstract": "I present a flexible solution for the axisymmetric Jeans equations of stellar\nhydrodynamics under the assumption of an anisotropic (three-integral) velocity\nellipsoid aligned with the spherical polar coordinate system. I describe and\ntest a robust and efficient algorithm for its numerical computation. I outline\nthe evaluation of the intrinsic velocity moments and the projection of all\nfirst and second velocity moments, including both the line-of-sight velocities\nand the proper motions. This spherically-aligned Jeans Anisotropic Modelling\n(JAM_sph) method can describe in detail the photometry and kinematics of real\ngalaxies. It allows for a spatially-varying anisotropy, or stellar\nmass-to-light ratios gradients, as well as for the inclusion of general dark\nmatter distributions and supermassive black holes. The JAM_sph method\ncomplements my previously derived cylindrically-aligned JAM_cyl and spherical\nJeans solutions, which I also summarize in this paper. Comparisons between\nresults obtained with either JAM_sph or JAM_cyl can be used to asses the\nrobustness of inferred dynamical quantities. As an illustration, I modelled the\nAtlas3D sample of 260 early-type galaxies with high-quality integral-field\nspectroscopy, using both methods. I found that they provide statistically\nindistinguishable total-density logarithmic slopes. This may explain the\npreviously-reported success of the JAM method in recovering density profiles of\nreal or simulated galaxies. A reference software implementation of JAM_sph is\nincluded in the publicly-available JAM software package.",
                    "authors": "Michele Cappellari",
                    "published": "2019-07-23",
                    "updated": "2020-04-23",
                    "primary_cat": "astro-ph.GA",
                    "cats": [
                        "astro-ph.GA"
                    ],
                    "main_content": "2.1 The collisionless Boltzmann equation The positions x and velocities v of a large system of stars can be described by the distribution function (DF) f(x, v). When the system has reached near equilibrium and is in a steady state under the gravitational influence of a smooth potential \u03a6, the DF must satisfy the fundamental equation of stellar dynamics, the steady-state collisionless Boltzmann equation (BT equation 4-13b) 3 \ufffd i=1 \ufffd i=1 \ufffd vi \u2202f \u2202xi \u2202f \u2202xi \u2212\u2202\u03a6 \u2202xi \u2202xi \u2202f \u2202vi \ufffd = 0. (1) Given that f is a function of six variables, equation (1) is satisfied by an infinite family of solutions. One needs additional assumptions and simplifications for a practical application of the equation. One classic way of constraining the problem consists of drastically reducing it, from that of recovering the DF to that of studying only the velocity moments of the DF. This approach leads to the Jeans equations, which are discussed in the next section. MNRAS 000, 1\u201319 (2020) Spherically-aligned Jeans equations 3 z r R x y \u0001\u0002 \u0003 Figure 1. De\ufb01nition of the spherical polar (r, \u03b8, \u03c6), cylindrical polar (R, \u03c6, z) and Cartesian (x, y, z) coordinate systems adopted in this paper. 2.2 The Jeans equations in spherical coordinates By rewriting equation (1) in standard spherical polar coordinates (r, \u03b8, \u03c6) (Fig. 1) and making the important assumption of axial symmetry (\u2202\u03a6/\u2202\u03c6 = \u2202f/\u2202\u03c6 = 0), with \u03b8 = 0 on the axis of symmetry, one obtains (e.g. BT problem 4-3) 0 = vr \u2202f \u2202r + v\u03b8 r \u2202f \u2202\u03b8 + \uf8eb \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ed v2 \u03b8 + v2 \u03c6 r \u2212\u2202\u03a6 \u2202r \uf8f6 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f8 \u2202f \u2202vr + 1 r \uf8eb \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ed v2 \u03c6 tan \u03b8 \u2212vrv\u03b8 \u2212\u2202\u03a6 \u2202\u03b8 \uf8f6 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f8 \u2202f \u2202v\u03b8 \u2212v\u03c6 r \u0012 vr + v\u03b8 tan \u03b8 \u0013 \u2202f \u2202v\u03c6 (2) Multiplication of equation (2) respectively by vr and by v\u03b8, and integration over all velocities, gives the two1 Jeans (1922) equations in spherical coordinates (e.g. de Zeeuw et al. 1996, equation 2.4) \u2202(\u03bdv2 r) \u2202r + 1 r \"\u2202(\u03bdvrv\u03b8) \u2202\u03b8 + 2\u03bdv2 r \u2212\u03bdv2 \u03b8 \u2212\u03bdv2 \u03c6 + \u03bdvrv\u03b8 tan \u03b8 # = \u2212\u03bd\u2202\u03a6 \u2202r (3a) r \u2202(\u03bdvrv\u03b8) \u2202r + \u2202(\u03bdv2 \u03b8) \u2202\u03b8 + 3\u03bdvrv\u03b8 + \u03bdv2 \u03b8 \u2212\u03bdv2 \u03c6 tan \u03b8 = \u2212\u03bd\u2202\u03a6 \u2202\u03b8 (3b) where I use the notation \u03bdvkv j \u2261 Z vkvj f d3v. (4) Wegg et al. (2019) used equation (3) to infer the gravitational force \ufb01eld of the Milky Way using Gaia DR2 data and concluded that the gravitational potential of the dark matter is nearly spherical. These equations are still quite general, as they derive from the steady-state Boltzmann equation (1) with the only assumption of axisymmetry. They do not require self-consistency (a potential \u03a6 generated by the luminosity density \u03bd) and they make no assumptions on the DF. However, even if one assumes \u03a6 to be known (it may be derived from the observed \u03bd via the Poisson equation), the two equation (3) are still a function of the four unknown v2 r, v2 \u03b8, v2 \u03c6 and vrv\u03b8 and do not uniquely specify a solution. 1 The third Jeans equation, involving a multiplication by v\u03c6, is not useful. 2.3 On the alignment of the velocity ellipsoid To obtain a unique solution for the axisymmetric Jeans equations one needs to assume a shape and orientation for the velocity ellipsoid. In Cappellari (2008) I reviewed the possible natural choices for the alignment of the velocity ellipsoid, namely (i) prolate spheroidal coordinates, (ii) spherical coordinates and (iii) cylindrical ones. I pointed out that real galaxies cannot be described globally neither by spherically-aligned nor by cylindrical-aligned solutions. Instead, the velocity ellipsoid must be aligned in a coordinate system qualitatively similar to the prolate-spheroidal one (\ufb01g. 1 of Cappellari 2008). The alignment of the velocity ellipsoid, unlike its axial ratios, is a characteristic of the gravitational potential alone. It contains no information on the dynamical status of the galaxy or its past evolution. In fact, for an assumed axisymmetric gravitational potential, a description of the alignment of the velocity ellipsoid can be determined numerically without a dynamical model by simply integrating orbits in that potential. The velocity ellipsoid must be aligned with the envelopes of the orbits in the (R, z) meridional plane (e.g. \ufb01g. 6 of Cappellari et al. 2006) because along the principal axes of the velocity ellipsoid it must be possible, for the regular orbits, to approximate the orbital motions as a linear combination of two independent oscillations (plus a rotation around \u03c6) (Eddington 1915). The orbital envelopes are radially oriented only when the potential is spherical, as in that case, the orbits are planar. The envelopes are cylindrically oriented only when the potential is plane-parallel, as in that case, the amplitude of the \u2018vertical\u2019 z oscillation is independent of cylindrical radius R. This implies that a spherical alignment of the velocity ellipsoid is only possible for spherical potentials and a cylindrical alignment for plane-parallel ones. These expectations were proven analytically by Evans et al. (2016), who also showed that alignment in strictly prolate-spheroidal coordinates only holds for separable or St\u00e4ckel potentials. Given that no real galaxy is either a sphere, a plane parallel distribution, or has a separable potential, does this imply any of those assumptions is unphysical and not useful for the dynamical modelling of real galaxies? The answer to this question must rely on actual measurements rather than purely theoretical arguments. After all, science invariably relies on sensible approximations of reality. No real galaxy is in a steady-state, nor has a simple spherical, axisymmetric or triaxial shape as the dynamical models invariably assume. Nonetheless, approximated dynamical modelling proved very useful: They allowed us to learn e.g. about supermassive black holes (see review by Kormendy & Ho 2013), dark matter (see review by Courteau et al. 2014) and orbital distributions (see review by Cappellari 2016) in galaxies. The usefulness of a dynamical modelling approach must be quanti\ufb01ed by its ability to measure the physical quantities one is interested in studying as discussed in Section 1. 2.4 Spherically-aligned Jeans solution To \ufb01nd a solution for the Jeans equations I start from equation (3) and assume that the velocity ellipsoid is aligned with the spherical coordinate system. The cross-terms of the second velocity moment tensor vanish and the Jeans equations become \u2202(\u03bdv2 r) \u2202r + 2\u03bdv2 r \u2212\u03bdv2 \u03b8 \u2212\u03bdv2 \u03c6 r = \u2212\u03bd\u2202\u03a6 \u2202r (5a) \u2202(\u03bdv2 \u03b8) \u2202\u03b8 + \u03bdv2 \u03b8 \u2212\u03bdv2 \u03c6 tan \u03b8 = \u2212\u03bd\u2202\u03a6 \u2202\u03b8 . (5b) MNRAS 000, 1\u201319 (2020) 4 M. Cappellari Bowden et al. (2016) pointed out that equation (5b) \u201cdoes not involve the radial velocity dispersion at all\u201d and solved it by itself to study the \ufb02attening of the gravitational potential. Their solution involves expanding in a Fourier series the angular variation of the v2 \u03c6/v2 \u03b8 ratio. A feature of this approach is that one needs to specify a boundary condition in v2 \u03b8 (they obtain this from the data) at the adopted radius rather than specifying the usual boundary condition at in\ufb01nity. Here I follow the more common approach and look for a global solution. For this, I de\ufb01ne the anisotropy as \u03b2 = 1 \u2212v2 \u03b8/v2 r = 1 \u2212\u03c32 \u03b8/\u03c32 r (6) the Jeans equation (5) become (e.g. Bacon et al. 1983, eq. 1, 2) \u2202(\u03bdv2 r) \u2202r + (1 + \u03b2) \u03bdv2 r \u2212\u03bdv2 \u03c6 r = \u2212\u03bd\u2202\u03a6 \u2202r (7a) (1 \u2212\u03b2)\u2202(\u03bdv2 r) \u2202\u03b8 + (1 \u2212\u03b2) \u03bdv2 r \u2212\u03bdv2 \u03c6 tan \u03b8 = \u2212\u03bd\u2202\u03a6 \u2202\u03b8 . (7b) I eliminate \u03bdv2 \u03c6 between the two equations, obtaining (1 \u2212\u03b2) tan \u03b8 r \u2202(\u03bdv2 r) \u2202\u03b8 \u22122\u03b2 \u03bdv2 r r \u2212\u2202(\u03bdv2 r) \u2202r = \u03a8(r, \u03b8) (8) where I de\ufb01ned \u03a8(r, \u03b8) = \u03bd(r, \u03b8) \u00d7  \u2202\u03a6 \u2202r \u2212tan \u03b8 r \u2202\u03a6 \u2202\u03b8 ! . (9) Now equation (8) is a linear \ufb01rst-order partial di\ufb00erential equation for \u03bdv2 r(r, \u03b8) in two independent variables for which well-established procedures of solution exist. It can be solved with the method of characteristics (e.g. section 9.2 of Arfken et al. 2013) and a detailed solution was given by Bacon et al. (1983) and Bacon (1985). I now make the key assumption that the anisotropy \u03b2 is spatially constant2. Moreover I assume the natural boundary condition that \u03bdv2 r = 0 as r \u2192\u221e. Note that this condition is much less restrictive than requiring v2 r = 0 as r \u2192\u221ebecause the tracer density \u03bd decreases much faster than the velocity dispersion in real galaxies. Written explicitly, the solution reads \u03bdv2 r(r, \u03b8) = Z \u221e r  r\u2032 r !2\u03b2 \u03a8(r\u2032, \u03b8\u2032) dr\u2032 (10a) \u03b8\u2032 = arcsin \uf8ee \uf8ef \uf8ef \uf8ef \uf8ef \uf8f0  r\u2032 r !\u03b2\u22121 sin \u03b8 \uf8f9 \uf8fa \uf8fa \uf8fa \uf8fa \uf8fb. (10b) After obtaining \u03bdv2 r, the second moment in the tangential direction is derived e.g. from equation (7b) as \u03bdv2 \u03c6(r, \u03b8) = (1 \u2212\u03b2) \uf8ee \uf8ef \uf8ef \uf8ef \uf8ef \uf8ef \uf8f0\u03bdv2 r + \u2202(\u03bdv2 r) \u2202\u03b8 tan \u03b8 \uf8f9 \uf8fa \uf8fa \uf8fa \uf8fa \uf8fa \uf8fb+ \u03bd \u2202\u03a6 \u2202\u03b8 tan \u03b8 (11) By de\ufb01nition the other components of the second velocity moment tensor, and the mean velocity, are given by v2 \u03b8 = (1 \u2212\u03b2) v2 r (12a) \u03c32 \u03c6 = (1 \u2212\u03b3) v2 r (12b) v\u03c6 2 = v2 \u03c6 \u2212\u03c32 \u03c6 (12c) 2 As will become clear later, the constant anisotropy assumption only applies to an individual component of my expansion, not to the whole galaxy. The \ufb01nal solution will allow for general spatial variations of the anisotropy. \u03b2 = 1 \u03b2 = 1/2 \u03b2 = 0 \u03b2 = -1 \u03b2 = -\u221e 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 R z Integration Paths Figure 2. Integration paths for the Jeans solution, for points at di\ufb00erent radii R along a galaxy equatorial plane z = 0. The value of the solution at a given R is uniquely determined by the values of the tracer density and the gravitational potential along that curve. Di\ufb00erent colours refer to di\ufb00erent anisotropies, as given in the \ufb01gure legend. In the spherical limit \u2202\u03a6/\u2202\u03b8 = 0 and equation (10) reduces, as expected, to the spherical solution of equation (B2) \u03bdv2 r(r) = Z \u221e r  r\u2032 r !2\u03b2 \u03bd(r\u2032) d\u03a6(r\u2032) dr\u2032 dr\u2032 (13) while in the general axisymmetric case, on the symmetry z-axis, tan \u03b8 = 0 and the solution becomes \u03bdv2 r(r, 0) = Z \u221e r  r\u2032 r !2\u03b2 \u03bd(r\u2032, 0)\u2202\u03a6(r\u2032, 0) \u2202r\u2032 dr\u2032, (14) which is the same solution as for a spherical anisotropic model that has the same \u03a6(r\u2032) = \u03a6(r\u2032, 0) and \u03bd(r\u2032) = \u03bd(r\u2032, 0) radial pro\ufb01le as the axisymmetric model along the symmetry axis. This is useful for testing and to get a qualitative sense of the solutions. In the semiisotropic limit \u03b2 = 0 the solution reduces to the cylindrically-aligned one of equation (A3) \u03bdv2 r(R, z) = Z \u221e z \u03bd(R, z)\u2202\u03a6(R, z) \u2202z dz, (15) To interpret a dynamical model it is instructive to consider the integration path of equation (10), in the galaxy meridional plane. To compute the solution at a given position, the galaxy density and gravitational potential are only sampled along this curve and no information on the density and potential can be inferred outside of this path. The integration curves for points along the galaxy equatorial plane, for di\ufb00erent anisotropies, are shown in Fig. 2. As one may have expected, the path is radially oriented in the limit of purely radial orbits \u03b2 = 1, it is parallel to the symmetry z-axis, for semi-isotropy \u03b2 = 0 as in the cylindrically-aligned solution, and is along circles for purely tangential orbits \u03b2 = \u2212\u221e(and continues to in\ufb01nity along the symmetry axis to satisfy the boundary condition). MNRAS 000, 1\u201319 (2020) Spherically-aligned Jeans equations 5 3 GENERAL LINE-OF-SIGHT PROJECTION When the Jeans equations are used to study the intrinsic kinematics of galaxies (e.g. from Gaia data), or when they are used to compute the starting conditions for the particles of N-body models (e.g. Emsellem 2013), a solution of the equations in Section 2.4 is all that is needed. However for most of the galaxies in the Universe, currently, only projected quantities can be observed. In this situation, one has to project the kinematic along the line-of-sight (LOS) to compute a prediction of the model observables to compare with the observations. A list of formulas for the projection of an axisymmetric model in cylindrical coordinates was given e.g. in Appendix A of Evans & de Zeeuw (1994). However, I have not found a similar treatment for the spherically-aligned case. The only expression I found is equation (8) of Bacon (1985) for the second moment of the lineof-sight velocity. However, that expression misses one term and is only correct in the semi-isotropic case. For these reasons, instead of merely listing the \ufb01nal formulas, I give a concise tutorial about the general procedure for the derivation of the line-of-sight projections here. I additionally provide a compact description, in matrix notation, for the corresponding transformation from cylindrical to sky coordinates. 3.1 From spherical to sky coordinates I adopt the standard convention of measuring the angle \u03b8 from the z-axis and the angle \u03c6 from the x-axis, in the x\u2013y plane (see Fig. 1). The components of a vector (vr, v\u03b8, v\u03c6) in the spherical-polar basis can be transformed into the components of a vector (vx, vy, vz) in the Cartesian basis as follows (e.g. section 3.10 of Arfken et al. 2013) \uf8eb \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ed vx vy vz \uf8f6 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f8= R \u00b7 \uf8eb \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ed vr v\u03b8 v\u03c6 \uf8f6 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f8 with R = \uf8eb \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ed sin \u03b8 cos \u03c6 cos \u03b8 cos \u03c6 \u2212sin \u03c6 sin \u03b8 sin \u03c6 cos \u03b8 sin \u03c6 cos \u03c6 cos \u03b8 \u2212sin \u03b8 0 \uf8f6 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f8 (16) I assume the Cartesian system (x, y, z) has the z-axis aligned with the galaxy symmetry axis and the x-axis aligned with the projected major axis, parallel to the plane of the sky. I de\ufb01ne an additional inclined (x\u2032, y\u2032, z\u2032) Cartesian system of coordinates with the x\u2032-axis coincident with the x-axis and the z\u2032-axis parallel to the LOS. I de\ufb01ne the inclination i as the angle between z and z\u2032, which implies i = 90\u25e6when the galaxy is edge-on, as in the most common convention. A vector in the galaxy Cartesian system (x, y, z) transforms into the observer\u2019s system (x\u2032, y\u2032, z\u2032) as follows \uf8eb \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ed vx\u2032 vy\u2032 vz\u2032 \uf8f6 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f8= S \u00b7 \uf8eb \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ed vx vy vz \uf8f6 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f8 with S = \uf8eb \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ed 1 0 0 0 cos i \u2212sin i 0 sin i cos i \uf8f6 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f8 (17) Note that both matrices are orthogonal, namely R \u00b7 RT = S \u00b7 ST = I, with I the identity matrix. The general rules of transformation of tensors (e.g. section 4.1 of Arfken et al. 2013) now imply that the second order tensor in spherical basis, represented by a 3 \u00d7 3 matrix, with zero non-diagonal terms due to the assumed spherical alignment3, transforms into a symmetric tensor in the observer\u2019s 3 Of course the expression is generally valid, even when the velocity ellipsoid is not radially oriented, in which case the initial tensor would not be diagonal. Cartesian basis as T = \uf8eb \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ed v2 x\u2032 vx\u2032vy\u2032 vx\u2032vz\u2032 vy\u2032vx\u2032 v2 y\u2032 vy\u2032vz\u2032 vz\u2032vx\u2032 vz\u2032vy\u2032 v2 z\u2032 \uf8f6 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f8 = Q \u00b7 \uf8eb \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ed v2 r 0 0 0 v2 \u03b8 0 0 0 v2 \u03c6 \uf8f6 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f8 \u00b7 QT (18) with the orthogonal matrix Q = S \u00b7 R Q = \uf8eb \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ed sin \u03b8 cos \u03c6 cos \u03b8 cos \u03c6 \u2212sin \u03c6 sin \u03b8 sin \u03c6 cos i \u2212cos \u03b8 sin i cos \u03b8 sin \u03c6 cos i + sin \u03b8 sin i cos \u03c6 cos i sin \u03b8 sin \u03c6 sin i + cos \u03b8 cos i cos \u03b8 sin \u03c6 sin i \u2212sin \u03b8 cos i cos \u03c6 sin i \uf8f6 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f8 (19) The \ufb01rst moment of the velocities transform from the spherical (or cylindrical) basis to the observer\u2019s basis like all vectors. Considering that in a steady-state axisymmetric system vr = v\u03b8 = 0, the relation is \uf8eb \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ed vx\u2032 vy\u2032 vz\u2032 \uf8f6 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f8= Q \u00b7 \uf8eb \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ed 0 0 v\u03c6 \uf8f6 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f8. (20) All components of the \ufb01rst velocity moment and the second velocity moment tensor, including the non-diagonal terms, can be obtained straightforwardly from equation (18) and equation (20) and I will not list all the resulting expressions. I give, however, for illustration, the projected velocities and the diagonal elements of the second moment tensor in the observer\u2019s coordinates, where x\u2032 is parallel to the galaxy projected major axis, y\u2032 is parallel to the projected minor axis and z\u2032 is along the LOS. This implies that vlos \u2261vz\u2032 and v2 los \u2261v2 z\u2032: vx\u2032 = v\u03c6 Q13 = \u2212v\u03c6 sin \u03c6 (21a) vy\u2032 = v\u03c6 Q23 = v\u03c6 cos \u03c6 cos i (21b) vz\u2032 = v\u03c6 Q33 = v\u03c6 cos \u03c6 sin i. (21c) The elements of the symmetric tensor T in equation (18) can be written as T jk = v2 r Q j1Qk1 + v2 \u03b8 Q j2Qk2 + v2 \u03c6 Q j3Qk3. (22) When the full second velocity moment tensor is needed, this formula is simpler and more e\ufb03cient for the numerical computation than the following explicit ones. However, as an example, the expressions for the diagonal elements of the second moment tensor are v2 x\u2032 = T11 = \u0012 v2 r sin2\u03b8 + v2 \u03b8 cos2\u03b8 \u0013 cos2\u03c6 + v2 \u03c6 sin2\u03c6 (23a) v2 y\u2032 = T22 = v2 r (sin \u03b8 sin \u03c6 cos i \u2212cos \u03b8 sin i)2 + v2 \u03b8 (cos \u03b8 sin \u03c6 cos i + sin \u03b8 sin i)2 + v2 \u03c6 cos2\u03c6 cos2i (23b) v2 z\u2032 = T33 = v2 r (sin \u03b8 sin \u03c6 sin i + cos \u03b8 cos i)2 + v2 \u03b8 (cos \u03b8 sin \u03c6 sin i \u2212sin \u03b8 cos i)2 + v2 \u03c6 cos2\u03c6 sin2i. (23c) 3.2 From cylindrical to sky coordinates The transformation of vectors and tensors from the cylindrical coordinate system to a coordinates system aligned with the plane of the sky and observer\u2019s line of sight is completely analogue to what I described in Section 3.1. Only the matrix R is di\ufb00erent. I adopt the standard convention of measuring the angle \u03c6 from the x-axis, in the x\u2013y plane (see Fig. 1). The components of a vector (vR, v\u03c6, vz) in the cylindrical basis can be transformed into the MNRAS 000, 1\u201319 (2020) 6 M. Cappellari components of a vector (vx, vy, vz) in the Cartesian basis as follows \uf8eb \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ed vx vy vz \uf8f6 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f8= Rcyl \u00b7 \uf8eb \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ed vR v\u03c6 vz \uf8f6 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f8 with Rcyl = \uf8eb \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ed cos \u03c6 \u2212sin \u03c6 0 sin \u03c6 cos \u03c6 0 0 0 1 \uf8f6 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f8 (24) I assume the same Cartesian systems (x, y, z) and (x\u2032, y\u2032, z\u2032) as in Section 3.1. In the case of cylindrical alignment, the transformation of tensors, with zero non-diagonal terms due to the assumed alignment, into a symmetric tensor in the observer\u2019s Cartesian basis is \uf8eb \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ed v2 x\u2032 vx\u2032vy\u2032 vx\u2032vz\u2032 vy\u2032vx\u2032 v2 y\u2032 vy\u2032vz\u2032 vz\u2032vx\u2032 vz\u2032vy\u2032 v2 z\u2032 \uf8f6 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f8 = Qcyl \u00b7 \uf8eb \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ed v2 R 0 0 0 v2 \u03c6 0 0 0 v2 z \uf8f6 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f8 \u00b7 QT cyl (25) with the orthogonal matrix Qcyl = S \u00b7 Rcyl, where S is still given by equation (17), resulting into Qcyl = \uf8eb \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ed cos \u03c6 \u2212sin \u03c6 0 sin \u03c6 cos i cos \u03c6 cos i \u2212sin i sin \u03c6 sin i cos \u03c6 sin i cos i \uf8f6 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f8 (26) The projection of the \ufb01rst moment of the velocity is the same as for the spherically-aligned case and is still given by equation (21). While for the second velocity moment tensor, as an illustration, the resulting expressions for the diagonal elements are v2 x\u2032 = v2 R cos2\u03c6 + v2 \u03c6 sin2\u03c6 (27a) v2 y\u2032 = \u0012 v2 R sin2\u03c6 + v2 \u03c6 cos2\u03c6 \u0013 cos2i + v2 z sin2i (27b) v2 z\u2032 = \u0012 v2 R sin2\u03c6 + v2 \u03c6 cos2\u03c6 \u0013 sin2i + v2 z cos2i (27c) The expression for v2 z\u2032 has been given many times, starting with Satoh (1980), while the other components were included in the list by Evans & de Zeeuw (1994) (in both cases with a di\ufb00erent de\ufb01nitions for the coordinate systems than adopted here). 3.3 Line-of-sight integration The observed \ufb01rst or second velocity moments are computed by luminosity-weighting the expressions for the components of the projected \ufb01rst or second velocity moment tensor, given in Section 3.1 and Section 3.2, along the LOS as follows \u03a3(x\u2032, y\u2032) = Z \u221e \u2212\u221e \u03bd dz\u2032, (28a) \u03a3 v\u03b1(x\u2032, y\u2032) = Z \u221e \u2212\u221e \u03bdv\u03b1 dz\u2032 (28b) \u03a3 v\u03b1v\u03b2(x\u2032, y\u2032) = Z \u221e \u2212\u221e \u03bdv\u03b1v\u03b2 dz\u2032 (28c) where \u03b1 and \u03b2 represent one of the three di\ufb00erent components (x\u2032, y\u2032, z\u2032) of the velocity (e.g. \u03b1 = z\u2032 for the mean LOS velocity vlos) or the tensor (e.g. \u03b1 = \u03b2 = z\u2032 for the projected LOS second moment v2 los). In the case of an MGE surface brightness, the integral of equation (28a) is analytic and \u03a3(x\u2032, y\u2032) is given by equation (33). To perform the LOS integration, a given set of sky coordinates (x\u2032, y\u2032, z\u2032) along the LOS is transformed into the galaxy (x, y, z) Cartesian coordinate systems with S\u22121 = ST \uf8eb \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ed x y z \uf8f6 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f8= ST \u00b7 \uf8eb \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ed x\u2032 y\u2032 z\u2032 \uf8f6 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f8 (29) the trigonometric functions in equation (19) or equation (26) can then be evaluated as (see Fig. 1) R2 = x2 + y2 r2 = R2 + z2 (30a) sin \u03c6 = y/R cos \u03c6 = x/R (30b) sin \u03b8 = R/r cos \u03b8 = z/r. (30c) When the object under study is at a small distance and covers a large \ufb01eld of view, one needs to include perspective e\ufb00ects in the LOS integration. The matrix projection of equation (17) should be replaced with a perspective transformation (van der Marel et al. 2002). 3.4 PSF convolution For the LOS components, the kinematics is generally a\ufb00ected by the instrumental PSF and the atmospheric seeing. To account for this e\ufb00ect I proceed as in Appendix A of Cappellari (2008). The observed mean LOS velocity [vlos]obs and the second moment [v2 los]obs are related to the intrinsic ones by the following relations, where PSF represents a normalized MGE PSF \u03a3obs = \u03a3 \u2297PSF (31a) [vlos]obs = (\u03a3vlos) \u2297PSF \u03a3obs (31b) [v2 los]obs = (\u03a3v2 los) \u2297PSF \u03a3obs . (31c) 4 MULTI-GAUSSIAN EXPANSION FORMALISM To derive solutions for the Jeans equations I make an explicit choice for the parametrization of the number density of the tracer population and the total density (which can include dark matter and a central black hole). I adopt for both the MGE parametrization (Emsellem et al. 1994; Cappellari 2002). Strengths of this approach are its \ufb02exibility in reproducing with great detail the surface-brightness of real galaxies, its analytic projection, and the availability of a robust method and a corresponding software implementation4 to \ufb01t the galaxy photometry in a fully-automated manner (Cappellari 2002). The expressions in this section are written in spherical polar coordinates. They can be converted to cylindrical coordinates using the transformation below, which considers that the angles \u03b8 are measured from the symmetry z-axis (R, z) = (r sin \u03b8, r cos \u03b8) (32) 4.1 Tracer surface density or surface brightness If the x\u2032-axis is aligned with the photometric major axis, the surface brightness \u03a3 at the location (x\u2032, y\u2032) on the plane of the sky can be written as \u03a3(x\u2032, y\u2032) = N X k=1 \u03a30k exp \" \u22121 2\u03c32 k   x\u20322 + y\u20322 q\u20322 k !# , (33) where N is the number of the adopted Gaussian components, having peak surface brightness \u03a30k, observed axial ratio q\u2032 k and dispersion \u03c3k along the major axis. 4 Available from https://pypi.org/project/mge\ufb01t/ MNRAS 000, 1\u201319 (2020) Spherically-aligned Jeans equations 7 4.2 Deprojection The deprojection of the surface brightness to obtain the intrinsic luminosity density is not unique unless the axisymmetric galaxy is seen edge-on (i = 90\u25e6) (Rybicki 1987; Kochanek & Rybicki 1996), and the degeneracy becomes quite dramatic when the galaxy is seen at low inclinations (Gerhard & Binney 1996; Romanowsky & Kochanek 1997; van den Bosch 1997; Magorrian 1999). The MGE method provides a simple possible choice for the deprojection by assuming that each projected 2-dim Gaussian is deprojected into an intrinsic 3-dim Gaussian (Monnet et al. 1992). One of the advantages of the MGE method is that one can easily enforce the roundness of the model (Cappellari 2002), thus producing realistic densities, which look like real galaxies when projected at any angle. However, one should keep in mind that the MGE method, like any other alternative technique, cannot eliminate the mathematical degeneracy of the deprojection. In fact this degeneracy represent one of the major uncertainties in the dynamical modelling (Lablanche et al. 2012). Regardless of the adopted technique, I cannot overemphasise the relevance of the deprojection degeneracy on the dynamical models. This crucial fact is sometimes ignored when one constructs overly-detailed dynamical models of galaxies that are far from edge-on, without considering that, at low inclination, the recovered stellar density can only crudely represent the true one, and any inferred dynamical quantity will be signi\ufb01cantly in error. With this caveat in mind, the deprojected MGE axisymmetric luminous density \u03bd can be written as \u03bd(r, \u03b8) = N X k=1 \u03bd0k exp \" \u2212r2 2\u03c32 k   sin2 \u03b8 + cos2 \u03b8 q2 k !# , (34) where the individual components have the same dispersion \u03c3k as in the projected case of equation (33), and the intrinsic axial ratio of each Gaussian becomes, in the most common axisymmetric oblate case (qk < 1) q2 k = q\u20322 k \u2212cos2 i sin2 i , (35) where i is the galaxy inclination (i = 90\u25e6being edge-on). The expression for the rarely-used axisymmetric prolate case (qk > 1) is q2 k = sin2 i 1/q\u20322 k \u2212cos2 i. (36) The total luminosity Lk of each Gaussian must remain unchanged during deprojection and is obtained by integrating the Gaussians, using respectively either the projected equation (33) or the intrinsic equation (34) Lk = 2\u03c0 \u03a30k\u03c32 kq\u2032 k = \u03bd0k \u0010 \u03c3k \u221a 2\u03c0 \u00113 qk. (37) This gives the following relation between the projected peak surface number density of the tracer \u03a30k of each Gaussian (often approximated with the observed surface brightness in L\u2299pc\u22122), and the corresponding peak intrinsic number density \u03bd0k (often quoted in L\u2299 pc\u22123) \u03bd0k = \u03a30kq\u2032 k qk\u03c3k \u221a 2\u03c0 . (38) 4.3 Mass density The total mass density \u03c1 can be generally described by a di\ufb00erent set of M Gaussian components \u03c1(r, \u03b8) = M X j=1 \u03c10j exp \uf8ee \uf8ef \uf8ef \uf8ef \uf8ef \uf8ef \uf8f0\u2212r2 2\u03c32 j \uf8eb \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8edsin2 \u03b8 + cos2 \u03b8 q2 j \uf8f6 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f8 \uf8f9 \uf8fa \uf8fa \uf8fa \uf8fa \uf8fa \uf8fb. (39) Throughout this paper I use the j-index to indicate the parameters of the MGE Gaussians related to the gravitational potential and the k-index to refer to the parameters of the Gaussians describing the luminosity density or the tracer population. In the self-consistent case the Gaussians in equation (39) are the same as those in equation (34) and one has M = N, \u03c3 j = \u03c3k, q j = qk and \u03c10 j = \u03a5\u03bd0k, where \u03a5 is the mass-to-light ratio, which can account for the stellar population and the possible dark matter contribution. In the non-self-consistent case the density does not follow the luminosity. For example it can be described with the sum of two sets of Gaussians: the \ufb01rst derived by deprojecting the surface brightness with equation (34), and the second e.g. obtained by \ufb01tting a (one-dimensional) MGE model to some adopted analytic parametrization for the dark matter (e.g. NFW, Navarro, Frenk & White 1996), or by \ufb01tting an estimate of the stellar mass which allows for M/L variations inferred from stellar population models (Mitzkus et al. 2017; Li et al. 2017). 4.4 Gravitational potential An expression for the gravitational potential generated by the density of equation (39) was given by Emsellem et al. (1994) as a single integral over a \ufb01nite interval. I used that form in the solution of the cylindrically-aligned Jeans equations in Cappellari (2008). Here I proceed di\ufb00erently and use instead the original form of the gravitational potential derived with the general formula for densities strati\ufb01ed on similar ellipsoids (Sec. 20 of Chandrasekhar 1969; Sec. 2.3 of of Binney & Tremaine 1987) \u03a6(R, z) = \u03c0Gq Z \u221e 0 du \u2206(u) Z \u221e Q(u) \u03c1(m2) dm2, (40) where m2 = R2 + z2/q2 (41) \u2206(u) = (1 + u) p q2 + u (42) Q(u) = R2 1 + u + z2 q2 + u. (43) This is valid for both oblate (q < 1) and prolate (q > 1) density distributions. Substituting equation (39) into equation (40) and performing the analytic inner integral separately for every j-th Gaussian gives \u03a6(r, \u03b8) = \u22122\u03c0G Z \u221e 0 M X j=1 \u03c10jq j\u03c32 j exp \" \u2212r2 2\u03c32 j   sin2 \u03b8 1+u + cos2 \u03b8 q2 j+u !# (1 + u) q q2 j + u du. (44) Rather than transforming this integral into a \ufb01nite interval, I deal with the way of performing this semi-in\ufb01nite integral as an implementation detail, which I discuss in Section 6. This allows for testing of alternative approaches and produces a more robust and e\ufb03cient implementation of the numerical solution. The circular velocity is often a useful quantity to extract from MNRAS 000, 1\u201319 (2020) 8 M. Cappellari the models e.g. to describe the motion of the gas in a galaxy equatorial plane (z = 0). Using the MGE potential above, this is computed at the galactocentric radius R as v2 c(R) = \u2212R\u2202\u03a6 \u2202R = 2\u03c0GR2 Z \u221e 0 M X j=1 \u03c10 jq j exp \" \u2212 R2 2\u03c32 j(1+u) # (1 + u)2 q q2 j + u du. (45) This numerical quadrature can be done with the same DE transformation for the u variable used for the gravitational potential in Section 6.2. A supermassive black hole can be modelled by adding the analytic Keplerian potential to equation (44) and deriving a specialized simpler Jeans solution. However, I proceed as in Cappellari (2008) by modelling it as as a small Gaussian having mass M j = M\u2022, q j = 1 and 3\u03c3 j \u2272rmin, where rmin is the smallest distance from the black hole that one needs to accurately model (e.g. one could choose rmin \u2248\u03c3psf). 5 JEANS SOLUTION FOR AN MGE MODEL In this section, I specialize the general spherically-aligned Jeans solution to the case in which both the tracer population and the total mass density distribution are parametrized with an MGE model. 5.1 Solution for each luminous Gaussian Replacing the tracer density \u03bd of equation (34) and the gravitational potential \u03a6 of equation (44) into equation (9) and equation (10), I obtain the radial dispersion for each luminous Gaussian of the MGE as [\u03bdv2 r]k = 2\u03c0G Z \u221e r dr\u2032 \" \u03bd0k exp(Ak + Bk) r\u2032(r\u2032/r)2\u03b2k \u00d7 Z \u221e 0 du M X j=1 \u03c10jq j exp(C j + D jk) (1 + u) (q2 j + u)3/2 # (46) with Ak = \u2212 r\u20322 2q2 k\u03c32 k Bk = (1 \u2212q2 k) Ek 2q2 k\u03c32 k (47) C j = \u2212 r\u20322 2(q2 j + u) \u03c32 j Djk = (1 \u2212q2 j) Ek 2 (1 + u) (q2 j + u) \u03c32 j (48) Ek = (r\u2032/r)2\u03b2k(r sin \u03b8)2 (49) Now replacing equation (46) into equation (11) and considering that the only angular dependency in the expression for [\u03bdv2 r]k is inside Ek, I obtain an expression for the tangential second velocity moment as [\u03bdv2 \u03c6]k = 2\u03c0G (1 \u2212\u03b2k) Z \u221e r dr\u2032 ( \u03bd0k exp(Ak + Bk) r\u2032(r\u2032/r)2\u03b2k \u00d7 Z \u221e 0 du M X j=1 \u03c10 jq j h 1 + 2(Bk + D jk) i exp(C j + Djk) (1 + u) (q2 j + u)3/2 ) + \u03bdk(r, \u03b8) M X j=1 \u2202\u03a6j(r, \u03b8) \u2202\u03b8 tan \u03b8 (50) where \u03bdk(r, \u03b8) is one term of the sum in equation (34) and \u2202\u03a6j(r, \u03b8) \u2202\u03b8 tan \u03b8 = 2\u03c0G Z \u221e 0 (\u03c10jq j(q2 j \u22121)(r sin \u03b8)2 (1 + u) (q2 j + u)3/2 \u00d7 exp \uf8ee \uf8ef \uf8ef \uf8ef \uf8ef \uf8ef \uf8f0\u2212r2 2\u03c32 j \uf8eb \uf8ec \uf8ec \uf8ec \uf8ec \uf8ec \uf8ed sin2 \u03b8 1 + u + cos2 \u03b8 q2 j + u \uf8f6 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f7 \uf8f8 \uf8f9 \uf8fa \uf8fa \uf8fa \uf8fa \uf8fa \uf8fb ) du. (51) In a more compact form equation (46) and equation (50) can be rewritten as [\u03bdv2 r]k = 2 \u03c0G Z \u221e r Z \u221e 0 M X j=1 Fjk du dr\u2032 (52a) [\u03bdv2 \u03c6]k = 2 \u03c0G (1 \u2212\u03b2k) Z \u221e r Z \u221e 0 M X j=1 h 1 + 2(Bk + D jk) i Fjk du dr\u2032 + \u03bdk M X j=1 \u2202\u03a6j \u2202\u03b8 tan \u03b8 (52b) with Fjk = \u03bd0k \u03c10 j q j exp(Ak + Bk + C j + D jk) r\u2032(r\u2032/r)2\u03b2k (1 + u) (q2 j + u)3/2 . (53) The outer r\u2032 integral in equation (52) can be written analytically when 2\u03b2k is integer. The outer integral can also be written in terms of special functions along the symmetry axis \u03b8 = 0. But these special cases are of little usefulness in practice, so I won\u2019t write down the relevant expressions. In the semi-isotropic limit \u03b2k = 0 the spherically-aligned MGE Jeans solution coincides with the cylindrically-aligned one, given as a single quadrature in equation (A7) and equation (A6). And in the spherical limit, the solution coincides with the spherical one given as single quadrature in equation (B2). Moreover, when \u03b2k = \u03b2 is constant for the di\ufb00erent MGE Gaussians, the inner u integral in equation (46) does not depend on k, allowing for a potential speedup of the calculation. 5.2 Solution for the whole MGE model After computing the [\u03bdv2 r]k and [\u03bdv2 \u03c6]k solutions, the intrinsic velocity dispersion components and the mean streaming motion of the whole MGE are then computed as \u03bd\u03c32 r = \u03bdv2 r = N X k=1 [\u03bdv2 r]k (54a) \u03bd\u03c32 \u03b8 = \u03bdv2 \u03b8 = N X k=1 (1 \u2212\u03b2k) [\u03bdv2 r]k (54b) \u03bd\u03c32 \u03c6 = N X k=1 (1 \u2212\u03b3k) [\u03bdv2 r]k (54c) \u03bdv2 \u03c6 = N X k=1 [\u03bdv2 \u03c6]k (54d) \u03bdv\u03c6 2 = \u03bdv2 \u03c6 \u2212\u03bd\u03c32 \u03c6 (54e) The Jeans equations do not constrain the splitting of v2 \u03c6 into ordered v\u03c6 and random \u03c3\u03c6 motions. This can be understood physically from the fact that, for a given equilibrium model, one can always revert the sense of rotation of an arbitrary set of orbits, without affecting neither the v2 \u03b8/v2 r ratio, nor the gravitational potential, nor the distribution of the tracer population. This statement is the anisotropic analogue of the result that, in two-integral, semi-isotropic models, MNRAS 000, 1\u201319 (2020) Spherically-aligned Jeans equations 9 the density distribution determines only the part of the DF that is even in the axial angular momentum (Lynden-Bell 1962). For this reason, the splitting of v2 \u03c6 can be performed in an arbitrary way of which equation (54c) only represents a possible choice5. Another simple alternative is to use the approach \ufb01rst proposed by Satoh (1980) in the isotropic case and also adopted e.g. by Binney et al. (1990) and van der Marel et al. (1990). In that case, it consists of assuming the velocity \ufb01eld v\u03c6 is a scaled version of that of the isotropic model, for which \u03c3R = \u03c3\u03c6 = \u03c3z. The analogue assumption, for the cylindrically-aligned anisotropic case, was used in Cappellari (2008) as it appears to describe well real observations (see review by Cappellari 2016). It assumes the velocity \ufb01eld is a scaled version of that of a model with oblate velocity ellipsoid, for which \u03c3R = \u03c3\u03c6 , \u03c3z. When using the analogue of Satoh (1980) approach, given the spherical symmetry of the alignment adopted here, there are two natural possibilities for the reference model used to de\ufb01ne the shape of the v\u03c6: (i) either to assume a model with velocity ellipsoid axially symmetric around the radial r-axis, namely \u03c3r , \u03c3\u03b8 = \u03c3\u03c6. This choice satis\ufb01es the symmetry requirement along the symmetry zaxis and naturally converges to a non-rotating spherically-symmetric model in the spherical limit. (ii) Alternatively, one can assume a model with symmetry around the \u03b8 direction, namely \u03c3r = \u03c3\u03c6 , \u03c3\u03b8. This model has an oblate velocity ellipsoid in the equatorial plane, but looks unrealistic near the symmetry axis, or in the spherical limit. These two choices imply respectively [v\u03c6]k = \u03bak \u0014 [v2 \u03c6]k \u2212(1 \u2212\u03b2k)[v2 r]k \u00151/2 (55) [v\u03c6]k = \u03bak \u0012 [v2 \u03c6]k \u2212[v2 r]k \u00131/2 . (56) Note that these Satoh-like assumptions do not imply that the velocity ellipsoid is itself actually axisymmetric! In all cases, this is only true if \u03bak = 1. Instead, in general, once [v\u03c6]k is obtained, the corresponding \u03c3\u03c6 is given implicitly by equation (54e). Unlike the assumption of equation (54c), these Satoh-like assumptions generally correspond to a \u03b3k anisotropy that varies spatially even for each single Gaussian component. 6 NUMERICAL IMPLEMENTATION The numerical evaluation of the intrinsic \ufb01rst and second velocity moments of Section 5 requires two nested quadratures, while an additional nested quadrature is needed for the LOS integration of equation (28). The relevant integrals are improper with semi-in\ufb01nite intervals and can present sharp peaks for certain sets of parameters. For these reasons, a brute-force approach to this triple quadrature, e.g. as an iterated one-dimensional quadrature, would lead to either an unreliable or a very time-consuming and impractical algorithm. The e\ufb03ciency of the numerical computation I describe in this section depends on three implementation choices: (i) the use of a speci\ufb01c two-dimensional adaptive quadrature to limit the increase of the function evaluations with the number of dimensions, (ii) the use of e\ufb03cient transformations fo the improper semi-in\ufb01nite integrals and (iii) the exploitation of the axisymmetry of the problem in the LOS integration. I discuss each of these in turn in this section. 5 The equation (54e) speci\ufb01es the magnitude of v\u03c6 but not its direction. To model counter-rotating stellar components one can adopt a di\ufb00erent velocity sign for the di\ufb00erent MGE Gaussians (e.g. \ufb01g. 12 of Cappellari 2016). 12.5 10.0 7.5 5.0 2.5 0.0 y 2 1 0 1 2 x 12.5 10.0 7.5 5.0 2.5 0.0 y Figure 3. The top panel shows with crosses of di\ufb00erent colours the function evaluations at di\ufb00erent stages of the re\ufb01nement process of the adaptive twodimensional quadrature, where denser crosses imply later stages. The twodimensional integrand is only evaluated densely where the corresponding sub-integral is not su\ufb03ciently accurate. The bottom panel shows the contours of the integrand of equation (52b) with over-plotted all locations where it was evaluated. Here the x-axis is the u coordinate mapped onto the x \u2208[\u22123, 3] interval with a DE transformation, and the y-axis is r\u2032 coordinate mapped to the interval y \u2208ln([10\u22126, rmax]) with a TANH transformation (see Section 6.2 for an explanation). 6.1 Two-dimensional adaptive quadrature After exploring various alternatives, my approach to evaluating the two integrals of equation (52) is to treat it as a single twodimensional integral, which I compute with the speci\ufb01c adaptive two-dimensional quadrature method by Shampine (2008a), which I implemented in my function quad2d in the Python language (Van Rossum & Drake Jr 1995). Apart from its high e\ufb03ciency, the method is designed to be used with vectorized functions, making optimal use of the Numpy package (Oliphant 2007) characteristics, or for parallel evaluation by multiple CPU cores. The integrator is based on a pair of quadrature rules by Kronrod (1965) which consists of a 3 point Gaussian formula of a degree of precision 5 embedded in a 7 point formula of a degree of precision 11. A graphical illustration of how the adaptive quadrature can reduce the number of function evaluations for the Jeans solution is given in Fig. 3. The \ufb01gures show that one achieves a large saving in function evaluations by restricting the re\ufb01nement of the evaluation coordinates to a small region in the domain. This e\ufb03ciency would not be possible with the more straightforward approach of using two nested one-dimensional quadratures. The \ufb01gure also shows how the function rapidly drops to zero before reaching the edges MNRAS 000, 1\u201319 (2020) 10 M. Cappellari of the integration domain, thanks to the integration transformation discussed in the next section. 6.2 Choice of transformation for improper integrals The integrals of equation (52) are improper as they have semi-in\ufb01nite intervals and the standard approach to deal with this situation is by using a variable transformation (e.g. Sec. 4.4 of Press et al. 2007). This changes the improper integral, assumed convergent, into a proper one over a \ufb01nite interval as follows I = Z \u221e 0 f(x) dx = Z b a f \u0002\u03c6(t)\u0003 \u03c6\u2032(t) dt (57) with x = \u03c6(t) \u03c6(a) = 0 \u03c6(b) = \u221e. I experimented with di\ufb00erent semi-in\ufb01nite transformations like x = \u2212log t, x = t/(1 \u2212t) (e.g. Chapter 3 of Davis & Rabinowitz 1984), x = [t/(1 \u2212t)]2 (Shampine 2008b), the transformation x = (1 \u2212t2)/t2 originally used for the MGE potential by Emsellem et al. (1994), the semi-in\ufb01nite TAHN transformation x = exp(t) (Schwartz 1969), the popular double-exponential DE transformations x = exp(\u03c0/2 sinh t) and the corresponding version for exponentially-declining integrands x = exp[t \u2212exp(\u2212t)] (Takahasi & Mori 1974). The di\ufb00erent approaches all provided consistent results within the requested accuracy, albeit with signi\ufb01cant variations in the smoothness of the transformed integral and correspondingly di\ufb00erent execution times. Ultimately I found the best results experimentally, guided by some theoretical insights, namely by measuring the smallest number of function evaluations for di\ufb00erent transformations at a \ufb01xed prescribed accuracy, and by studying the behaviour of the transformed integrand at di\ufb00erent spatial positions using plots like Fig. 3, for a variety of realistic test cases evaluating equation (52). The inner Chandrasekar\u2019s integrand in u decreases relatively slowly at large radii like I \u221du\u22125/2 as u \u2192\u221e. This explains the fact that I measured the best performance using the full DE transformation u = exp(\u03c0/2 sinh t) with t \u2208[\u22123, 3]. Instead, the outer integrand in r\u2032 from the Jeans solution decreases exponentially as I \u221dexp(\u2212r\u20322) as r\u2032 \u2192\u221e, and is not singular at the lower r\u2032 bound. A single exponential is su\ufb03cient to e\ufb00ectively achieve DE decrease of the integrand at in\ufb01nity. This explains why I measured best performance with the TANH transformation r\u2032 = r+exp(t) with t \u2208ln([10\u22126, rmax]), where rmax = 3 max(\u03c31, \u00b7 \u00b7 \u00b7 \u03c3N) is the radius beyond which the MGE surface brightness, and the integrand, become negligible. Importantly, to make the e\ufb03ciency of my algorithm insensitive to the scaling of the input, I scale the spatial coordinates and the MGE parameters by requiring mean(\u03c31, \u00b7 \u00b7 \u00b7 , \u03c3N) = 1, before calling the integrator. I computed the single integral of equation (51) with the onedimensional adaptive algorithm of Shampine (2008b), which I also ported to Python and is the same I used in the cylindrically-oriented Jeans solution (Cappellari 2008). Also for this improper integral over a semi-in\ufb01nite interval I used the same x = exp(\u03c0/2 sinh t) DE transformation as for the Chandrasekhar\u2019s integrand in the twodimensional ones, as they both have the same asymptotic behaviour. 6.3 Exploiting axisymmetry in the LOS integration For the LOS integration of equation (28) I used a di\ufb00erent approach. Instead of performing a brute-force quadrature in the additional z\u2032 dimension, I exploit the axisymmetry of the problem and in particular the fact that the Jeans solution is independent of \u03c6. I evaluate the model\u2019s predictions of equation (52) only in the meridional (R, z) plane, on a grid which is linear in the logarithm of the elliptical radius m2 = R2 + (z/q)2 and in the eccentric anomaly E. This is achieved by de\ufb01ning a logarithmically-spaced radial grid Rj and then computing the moments at the cylindrical coordinate positions (R, z) = (Rj cos Ek, q Rj sin Ek), for linearly spaced Ek values in the [0, \u03c0/2] interval, with q a characteristic (e.g. the median) observed axial ratio of the MGE model. During the computation of the integrals of equation (28), the Jeans solution is simply linearly interpolated from the grid. This makes the computation time of the extra LOS quadrature essentially negligible compared to the double integral. Also for the improper LOS in\ufb01nite integral in z\u2032 it is e\ufb03cient to use a variable transformation. Also in this case, the integrand decreases exponentially as I \u221dexp(\u2212z\u20322) as z\u2032 \u2192\u221e. To achieve a DE decrease of the integrand, a single exponential transformation is needed. For this reason I use the TAHN transformation x = sinh t for the (\u2212\u221e, \u221e) interval (Schwartz 1969). After some experimentation, here I scale the variable t in such a way that the break t = \u00b11 between the linear and exponential regimes of the sinh t function happens for x = \u00b1rmax/8. I also limit the LOS integral to the interval (\u2212rmax, rmax) outside which the model surface brightness is negligible. 6.4 Availability A reference implementation for the spherically-aligned JAMsph method is included in the JAM (Cappellari 2008) Python software package6 jampy starting from version 6.0. JAMsph complements the cylindrically-aligned JAMcyl and spherical solutions, which were already included in earlier versions of jampy. For all assumed orientations of the velocity ellipsoid, jampy can compute either the intrinsic \ufb01rst or second velocity moments (e.g. to model Milky Way surveys like Gaia or to generate N-body realizations of galaxies) or any component of the line-of-sight velocity \ufb01rst moments or of the second moments tensor (e.g. to model external galaxies). 7 JEANS SOLUTIONS FOR SATOH\u2019S MODEL In this section I provide two relatively simple test cases for both the spherically-aligned and cylindrically-aligned anisotropic Jeans solutions, using the potential-density pair by Satoh (1980). In both cases the derived anisotropic Jeans solutions require one quadrature less than my general MGE solution, allowing for a reliability test of the latter. Moreover, the radically di\ufb00erent formalism compared to the MGE one provides thorough testing of the relatively-cumbersome equations and implementation as well. 7.1 Spherically-aligned solution To test the algorithm it is crucial to compare its result against alternative formulas that provide the solution with fewer numerical quadratures. For this one can use potential-density pairs, namely expressions for which both the density and the corresponding selfconsistent gravitational potential can be computed analytically. A convenient and su\ufb03ciently realistic expression is provided by the 6 Available from https://pypi.org/project/jampy/ MNRAS 000, 1\u201319 (2020) Spherically-aligned Jeans equations 11 Satoh (1980) potential-density pair, which is given in polar coordinates, with \u03b8 measured from the symmetry axis, by \u03a6(r, \u03b8) = \u2212GM S (58) \u03bd(r, \u03b8) = b2M h aS 2 + 3 \u0010 S 2 \u2212r2\u0011 p b2 + (r cos \u03b8)2i 4\u03c0S 5 \u0002b2 + (r cos \u03b8)2\u00033/2 (59) S 2 = a2 + 2a p b2 + (r cos \u03b8)2 + r2, (60) where M is the total mass of the model and (a, b) are scale parameters. Plugging these density and potential into equation (10) gives the radial dispersion for the Jeans equations with spherically-aligned velocity ellipsoid as a single integral \u03bdv2 r = ab2GM2 4\u03c0 Z \u221e r (a + Q) h (a + 2Q)(a + 3Q) + r\u20322i r\u2032(r\u2032/r)2\u03b2 \u0002Q \u0000a2 + 2aQ + r\u20322\u0001\u00034 dr\u2032 (61) Q2 = b2 + r\u20322 \u2212(r\u2032/r)2\u03b2(r sin \u03b8)2. (62) The second moment \u03bdv2 \u03c6 of the tangential velocity is then obtained using equation (11) with \u03bd from equation (59), \u03bdv2 r from equation (61) and \u2202(\u03bdv2 r) \u2202\u03b8 tan \u03b8 =ab2GM2 4\u03c0 Z \u221e r dr\u2032 ( (r sin \u03b8)2r\u2032(r\u2032/r)4\u03b2 \u0002Q \u0000a2 + 2aQ + r\u20322\u0001\u00035 \u00d7 \u0014 2aQ \u0010 53a2 + 69aQ + 30Q2\u0011 + 6Q(6a + Q)r\u20322 + \u0010 a2 + r\u20322\u0011 \u0010 34a2 + 3r\u20322\u0011 + 4a \u0010 a2 + r\u20322\u00112/Q \u0015) (63) \u2202\u03a6 \u2202\u03b8 tan \u03b8 = \u2212 aGM(r sin \u03b8)2 S 3 p b2 + (r cos \u03b8)2 . (64) The numerical quadratures for the semi-in\ufb01nite improper integrals in this section can be performed with the same TANH transformation for the r\u2032 variable discussed in Section 6.2. 7.2 Cylindrically-aligned solution The density distribution of the Satoh model can be written in cylindrical coordinates as \u03bd(R, z) = ab2M h 3Q(a + 2Q) + S 2i 4\u03c0Q3S 5 (65) S 2 = a2 + 2aQ + R2 + z2 (66) Q2 = b2 + z2, (67) with the corresponding self-consistent gravitational potential still given by the same expression of equation (58). In the isotropic limit the Jeans solutions for both v2 z and v2 \u03c6 can be written analytically and the resulting expressions where given by Satoh (1980). The same analytic solution applies to the v2 z component in the cylindrically-aligned case when \u03b2z , 0. The general Jeans solution in this case is given by equation (A3), which for the Satoh model, replacing the corresponding density and potential, becomes simply v2 z(R, z) = GMQ(a + 2Q) 2S \u00023Q(a + 2Q) + S 2\u0003 (68) The general anisotropic \u03b2z , 0 Jeans solution for the tangential velocity second moment v2 \u03c6 is given by equation (A4), which for Table 1. Parameters for the MGE \ufb01t to the intrinsic density of the Satoh model of Fig. 4 with total mass M = 1 and scale a = b = 1 lg \u03bd0k lg \u03c3k qk (a\u22123) (a) -1.834 -0.238 0.581 -1.686 -0.093 0.695 -1.934 0.053 0.374 -2.208 0.076 0.739 -3.019 0.228 0.808 -2.339 0.236 0.397 -2.977 0.378 0.162 -3.850 0.406 0.792 -3.171 0.417 0.424 -4.960 0.485 0.970 -3.305 0.558 0.174 -4.964 0.643 0.653 -4.305 0.644 0.386 -5.610 0.694 0.863 -4.124 0.754 0.170 -4.057 0.781 0.074 -6.695 0.809 1.000 -5.611 0.972 0.271 -6.350 0.998 0.493 -5.160 1.068 0.118 -4.596 1.072 0.058 -7.518 1.085 1.000 20 15 10 5 0 5 10 15 20 R/a 15 10 5 0 5 10 15 z/a Figure 4. MGE \ufb01t to the intrinsic density of a Satoh (1980) model with scale parameters a = b = 1. The black contours represent the analytic model and the red ones the MGE \ufb01t. Contours are spaced by 1 mag. the self-consistent Satoh model I found can be written in the very simple form v2 \u03c6(R, z) = v2 z(R, z) 1 \u2212\u03b2z   1 \u22126R2 S 2 ! + GMR2 S 3 . (69) 8 RESULTS 8.1 Numerical accuracy Careful testing is needed to validate the implementation of the equations of Section 5. I start by comparing the results for v2 r and v2 \u03c6 of the MNRAS 000, 1\u201319 (2020) 12 M. Cappellari 0 5 10 0 2 4 6 z/a 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0 5 10 0.15 0.18 0.21 0.24 0.27 0.30 0.33 0.36 0.0 0.1 0.2 0.3 0.1 0.2 0.3 0.4 0 5 10 R/a 0 2 4 6 z/a 0 5 10 R/a 0.2 0.1 0.0 0.1 0.2 % error (v2 r )1/2 / r = 1 = 0 (v2) 1/2 Figure 5. Comparison between the cylindrically-oriented JAMcyl and the new spherically-oriented JAMsph Jeans solutions for the Satoh\u2019s model of Fig. 4, in the isotropic limit, where both solutions must be identical. Top Panels: The colours and the grey contours with labels are the JAMsph solutions while the magenta dashed contours are the solutions of Section 7.1. The unit of velocity is \u221aGM/a. The white contours are the model isodensity, spaced by factors of 10 starting from the maximum value. Bottom Panels: Fractional residuals between JAMsph and JAMcyl. In this example, I set an error of 1% in the adaptive two-dimensional quadrature of JAMsph and a signi\ufb01cantly smaller one for the one-dimensional quadrature of JAMcyl. The resulting error in JAMsph is always well within the requested accuracy, with small discontinuities dependent on the levels of adaptive re\ufb01nements employed by the quadrature at a given position. spherically-aligned Jeans solution against the cylindrically-aligned solution7 of Cappellari (2008) as reproduced in equation (A6) and equation (A7). In the semi-isotropic limit, the velocity ellipsoid is a circle in the meridional plane, which implies that the velocity dispersion is the same along any axis and in particular v2 r = v2 z and the spherically-aligned and cylindrically-aligned solutions must be identical. For the tests I use as input an MGE \ufb01t to the parametrization of the density by Satoh (1980) in equation (59), with total mass M = 1 and scale parameters a = b = 1. The two-dimensional MGE \ufb01t (Fig. 4) was obtained in a fully-automated manner with the method and mgefit Python package8 of Cappellari (2002). It consists of 24 Gaussians (Table 1) and contains 96% of the total mass of the analytic model. Given that both Jeans solutions use the very same MGE model, but the cylindrically-aligned solution relies on a single quadrature, this test allows me to verify in detail the numerical accuracy of the two-dimensional quadrature. In the computation, I set an accuracy of 1% on the two-dimensional quadrature (epsrel = 0.01 in the procedure quad2d). The resulting comparison is displayed in Fig. 5. The maps of residuals show that the accuracy is always well within the requested tolerance, with errors never exceeding 0.2%. For comparison, the di\ufb00erence between JAMsph and the analytic solution of Section 7.2, in the semi-isotropic limit, is on the order of 7 I used v6.0 of the jampy package from https://pypi.org/project/jampy/ 8 I used v5.0 of the mgefit package from https://pypi.org/project/mge\ufb01t/ 0 5 10 0 2 4 6 z/a 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26 0 5 10 0.12 0.15 0.18 0.21 0.24 0.27 0.30 0.33 0 5 10 R/a 0 2 4 6 z/a 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0 5 10 R/a 0.18 0.21 0.24 0.27 0.30 0.33 0.36 0.39 0.0 0.1 0.2 0.3 0.1 0.2 0.3 0.4 (v2 r )1/2 / r = 3/4 = 0.44 (v2) 1/2 (v2 r )1/2 / r = 4/3 = -0.78 (v2) 1/2 Figure 6. Intrinsic moments of JAMsph for two di\ufb00erent anisotropies. The Satoh\u2019s model, the meaning of the contour lines and the colour levels are like in the top panels of Fig. 5. The anisotropy is di\ufb00erent and is written in the plot titles. a couple of percents, due to the slight di\ufb00erences between the MGE \ufb01tted density and the analytic one. A test of the numerical accuracy for the anisotropic case can be performed in the spherical limit, where the axisymmetric cylindrically-aligned solution converges to the spherical solution of Section B2. 8.2 Intrinsic moments at di\ufb00erent anisotropy To test the algorithm in the general anisotropic case, I compare the MGE spherically-aligned Jeans solution presented in Section 5 against the corresponding solution for the Satoh model presented in Section 7. For the tests I used a relatively large anisotropy with axial ratios of the velocity ellipsoid of \u03c3\u03b8/\u03c3r = (3/4, 1, 4/3) respectively, corresponding to \u03b2 = (0.44, 0, \u22120.78). The results are shown in Fig. 6. The tests show that the Jeans solution based on the MGE and the one based on the Satoh model agree extremely well. The small di\ufb00erences are because the MGE model does not perfectly reproduce the Satoh density distribution. This is clear from the fact that some di\ufb00erences are also present in the isotropic case, where I know the solution is accurate to the 0.2% level. The MGE \ufb01t could be improved with more Gaussians, but I decided to keep a comparable number of Gaussians as one could use on state-of-the-art photometric observations of real galaxies. Fig. 6 qualitatively illustrates the general trends in the Jeans solution that one should expect to \ufb01nd for real galaxies. Radial anisotropy (\u03c3r > \u03c3\u03b8 \u21d2\u03b2 > 0) produces an increase in both v2 r and v2 \u03c6 towards the centre and a decrease of the tangential component v2 \u03c6 at larger radii. The opposite happens with tangential anisotropy (\u03c3r < \u03c3\u03b8 \u21d2\u03b2 < 0): a central depression develops in both v2 r and v2 \u03c6, while the peak of v2 \u03c6 at larger radii increases. Overall, the mean v2 r decreases while v2 \u03b8 correspondingly increases. MNRAS 000, 1\u201319 (2020) Spherically-aligned Jeans equations 13 5 0 5 y'/a / r = 3/4 5 0 5 y'/a 5 0 5 y'/a 5 0 5 y'/a 5 0 5 y'/a 5 0 5 y'/a 5 0 5 y'/a 5 0 5 y'/a 10 0 10 x'/a 5 0 5 y'/a / r = 1/1 10 0 10 x'/a / r = 4/3 10 0 10 x'/a 0.10 0.15 0.20 0.25 0.30 (v2 x\u2032)1/2 0.10 0.15 0.20 (v2 y\u2032) 1/2 0.10 0.15 0.20 0.25 0.30 (v2 z\u2032)1/2 0.02 0.00 0.02 vx\u2032vy\u2032 0.02 0.00 0.02 vx\u2032vz\u2032 0.00 0.02 0.04 vy\u2032vz\u2032 0.2 0.1 0.0 0.1 0.2 vx\u2032 0.1 0.0 0.1 vy\u2032 0.2 0.1 0.0 0.1 0.2 vz\u2032 Figure 7. Projected moments for the Satoh\u2019s model of Fig. 4 seen at an inclination of i = 60\u25e6, for three di\ufb00erent anisotropies as written in the titles. The di\ufb00erent rows show the six components of the symmetric second velocity moment tensor and the three components of the projected mean velocity, as written in the colour bars. The unit of velocity is \u221aGM/a. The black surface brightness contours are spaced by 1 mag. 8.3 Projected moments at di\ufb00erent anisotropy In Fig. 7 I illustrate the qualitative variation of the projected moments as a function of anisotropy, for the same Satoh model as in Section 8.2, seen at an inclination of i = 60\u25e6, and the same set of anisotropies as for the intrinsic moments in Fig. 6. The adopted inclination is the average value for random orientations on a sphere. I show all \ufb01rst and second velocity moments, namely the three projected components of the \ufb01rst velocity moment, and all six components of the symmetric second velocity moment tensor. The most easily observable projected moment is the line-of-sight component, namely the mean line-of-sight velocity vlos \u2261vz\u2032 and the second line-of-sight velocity moment v2 los \u2261v2 z\u2032. When the kinematics is extracted from observed spectra using a Gaussian approximation for the line-of-sight velocity distribution (e.g. Cappellari 2017), the \ufb01rst moment is empirically approximated by the location of the Gaussian peak V and the second moment by the V2 rms \u2261V2 + \u03c32, where \u03c3 is the Gaussian dispersion. As discussed in sec. 3.1.5 of Cappellari (2008), when one is interested in studying mass distributions, one should only \ufb01t the second moments and ignore the \ufb01rst ones. This is because the \ufb01rst moments do not contain extra information on the gravitational potential that is not already contained in the second ones. Moreover, the second moments only require an assumption on the \u03c3\u03b8/\u03c3r ratio and not the \u03c3\u03c6/\u03c3r one. The \ufb01rst moment also have the issue that one has to split the v2 \u03c6 into order and random motion using equation (12c) and this can lead to unphysical results when v2 \u03c6 < \u03c32 \u03c6, for the assumed \u03b3 anisotropy or Satoh-like \u03ba parameter. The same considerations summarized for JAMcyl apply unchanged to this JAMsph solution. In practice, to compute the \ufb01rst moments in Fig. 7 I assumed, just for reference, a radially symmetric shape for the velocity ellipsoid, namely \u03c3\u03b8 = \u03c3\u03c6 \u21d2\u03b2 = \u03b3. From Fig. 7 one can generally see the same features already described for the intrinsic moments in Fig. 6. Again, radial anisotropy produces a central peak in the diagonal second moments (v2 x\u2032, v2 y\u2032, v2 z\u2032) and reduces the amplitude of the peak in both the \ufb01rst and second moments at larger radii. A central depression in the second moments appears with tangential anisotropy. In the models shown here, I did not include a supermassive black hole, and I did not model seeing e\ufb00ects, to limit the number of arbitrary parameters to explore. It is well known that the presence of a supermassive black hole, which is expected to be present in all stellar spheroids, qualitatively changes the behaviour of the second velocity moments in the centre, generally producing nuclear peaks for a range of surface brightness pro\ufb01les (Tremaine et al. 1994) and anisotropies. As a test for the projection of all the \ufb01rst and second velocity moments I used the formulas for the cylindrically-aligned Jeans solution (JAMcyl) summarized in Section A3. For both approaches, I adopted the isotropic model for which the two solutions must coincide. The JAMcyl provides all the projected second moments with a single quadrature (Cappellari 2008, 2012), and the \ufb01rst moments with a two-dimensional quadrature, as opposed to the three quadratures required for JAMsph. I found a close agreement, within the uncertainties of the numerical implementation, between the projected model predictions provided by the two radically-di\ufb00erent formalisms and implementations. 8.4 Spherically versus cylindrically aligned solutions In Fig. 8 I compare the vlos and v2 los computed from both JAMcyl of Cappellari (2008) and JAMsph presented in this paper. For the comparison, I selected the set of galaxies for which the JAMcyl selfconsistent models provides an excellent \ufb01t to the real data presented in \ufb01g. 10 of Cappellari (2016). From this set, I extracted the subset with signi\ufb01cantly non-zero anisotropy \u03b2z \u22650.1. The MGE models for these galaxies are taken from Scott et al. (2013), while the best \ufb01tting model parameters9 are taken from Cappellari et al. (2013). For both models, I adopt the same MGE, the same inclination and M/L. I additionally adopt \u03c3\u03b8/\u03c3r = \u03c3z/\u03c3R, and \u03c3\u03c6/\u03c3r = \u03c3\u03c6/\u03c3R. In this way, the two sets of models have the same oblate shape of the velocity ellipsoid in the galaxies equatorial planes, where, by symmetry \u03c3\u03b8 = \u03c3z and \u03c3r = \u03c3R, while the shape of the two velocity ellipsoids gradually di\ufb00ers away from the equatorial plane. The result of the qualitative comparison of Fig. 8 is that the two solutions look relatively similar, with di\ufb00erences roughly at the level one can expect from measurement errors in the stellar kinematics. The similarity is perhaps not surprising, given that the anisotropy of real fast rotator galaxies tends to be quite small, with typical values 9 The model parameters and the tables with the MGEs are available from the ATLAS3D website http://purl.org/atlas3d MNRAS 000, 1\u201319 (2020) 14 M. Cappellari 5 0 5 arcsec 10 0 10 5 0 5 arcsec 10 0 10 200 100 0 100 200 V 150 180 210 240 270 Vrms JAMsph        NGC4111:  = 0.17; = 0        JAMcyl 5 0 5 arcsec 10 0 10 5 0 5 arcsec 10 0 10 200 100 0 100 200 V 150 175 200 225 Vrms JAMsph        NGC4342:  = 0.23; = 0        JAMcyl 5 0 5 arcsec 10 0 10 5 0 5 arcsec 10 0 10 80 40 0 40 80 V 60 70 80 90 100 Vrms JAMsph        NGC4452:  = 0.16; = 0        JAMcyl 5 0 5 arcsec 10 0 10 5 0 5 arcsec 10 0 10 120 60 0 60 120 V 105 120 135 150 Vrms JAMsph        NGC4638:  = 0.22; = 0        JAMcyl 5 0 5 arcsec 10 0 10 5 0 5 arcsec 10 0 10 120 60 0 60 120 V 135 150 165 180 Vrms JAMsph        NGC4660:  = 0.14; = 0        JAMcyl 5 0 5 arcsec 10 0 10 5 0 5 arcsec 10 0 10 120 60 0 60 120 V 120 140 160 180 200 Vrms JAMsph        NGC5845:  = 0.10; = 0        JAMcyl Figure 8. Comparison between the JAMsph (left) and JAMcyl (right) Jeans solutions using the MGEs describing the surface brightness of a set of real galaxies and the corresponding best \ufb01tting parameters \ufb01tted with JAMcyl to their integral-\ufb01eld kinematics. For each galaxy, the two rows show the mean LOS stellar velocity V and the LOS second velocity moment Vrms. The V is computed assuming for both models the same shape of the velocity ellipsoid in the equatorial plane (see text for details). The black surface brightness contours are spaced by 1 mag. The kinematics of these galaxies and JAMcyl \ufb01ts were shown in \ufb01g. 10 of Cappellari (2016). 5 0 5 arcsec 10 0 10 5 0 5 arcsec 10 0 10 100 50 0 50 100 V 120 140 160 180 200 Vrms JAMsph        NGC4660:  = 0.44; = 0        JAMcyl Figure 9. This \ufb01gure is the same as Fig. 8, for the galaxy NGC 4660. Except for the fact that here I adopted an anisotropy \u03c3\u03c6/\u03c3r = \u03c3z/\u03c3R = 3/4. Note the strong vertical elongation in the Vrms of the JAMcyl solution. as measured from Schwarzschild models around \u03b2 \u223c0.2 (Cappellari et al. 2007; Thomas et al. 2009), and of course, JAMcyl and JAMsph must coincide in the isotropic limit. The comparison using the rather small measured anisotropy of real galaxies should not give the misleading impression that JAMcyl and JAMsph remain close for any anisotropy. This is not the case. JAMsph is characterized by a relative insensitivity of the model predictions to anisotropy. Instead, JAMcyl quickly develops a vertical elongation in v2 los, along the symmetry axis, for large positive \u03b2z. This dramatic di\ufb00erence in the model behaviour is illustrated in Fig. 9, where I construct models for one of the galaxies in Fig. 8 while adopting for both models an anisotropy that is signi\ufb01cantly larger than that inferred using JAMcyl. While JAMsph remains qualitatively similar to the solution in Fig. 8, JAMcyl becomes radically di\ufb00erent and would be strongly inconsistent with the original \ufb01t (and the kinematic data in \ufb01g. 10 of Cappellari 2016). Fig. 10 shows the intrinsic moments10 of JAMcyl for the same Satoh\u2019s model and the same anisotropies as shown in Fig. 6 for JAMsph. The cylindrical solution for v2 z in equation (A3) is obviously independent of \u03b2z. Instead, the solution for v2 \u03c6 shows a strong vertical elongation for \u03b2z = 0.44, which is the cause of the similar elongation in the v2 los for the projected moments in Fig. 9. This radi10 Note that the left panel now shows v2 z instead of v2 r. The two quantities are only comparable on the symmetry z-axis. MNRAS 000, 1\u201319 (2020) Spherically-aligned Jeans equations 15 0 5 10 0 2 4 6 z/a 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0 5 10 0.09 0.12 0.15 0.18 0.21 0.24 0.27 0.27 0.30 0.30 0 5 10 R/a 0 2 4 6 z/a 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0 5 10 R/a 0.12 0.15 0.18 0.21 0.24 0.27 0.30 0.33 0.36 0.39 0.0 0.1 0.2 0.3 0.1 0.2 0.3 0.4 (v2 z )1/2 z/ R = 3/4 z = 0.44 (v2) 1/2 (v2 z )1/2 z/ R = 4/3 z = -0.78 (v2) 1/2 Figure 10. Intrinsic moments of JAMcyl for two di\ufb00erent anisotropies, for the Satoh\u2019s model of Fig. 4. The colours and the grey contours with labels are the JAMcyl solutions while the magenta dashed contours are the solutions of Section 7.2. The unit of velocity is \u221aGM/a. The white contours are the model isodensity, spaced by factors of 10 starting from the maximum value. The anisotropy is written in the titles. This \ufb01gure can be directly compared to the JAMsph solution shown in Fig. 6. ally anisotropic v2 \u03c6 solution also shows a diagonal depression (black colour in Fig. 10), which, in this example, I found starts developing unphysical negative v2 \u03c6 values for \u03b2z > 0.51. 8.5 Which JAM method should one use? The availability of two di\ufb00erent axisymmetric JAMsph and JAMcyl model implementations with either spherical or cylindrical alignment raise the question about which method one should use when studying real galaxies. In some cases, like for the outer stellar halo of the Milky Way, the answer is clear, given that we can measure the alignment of the velocity ellipsoid directly. However, for external galaxies, I have found that in general the two solutions can give quite comparable \ufb01ts to the observed kinematics and it may not be clear which one provides the most reliable results for a certain quantity of interest. My practical recommendation is not to prefer one over the other one, but instead to use both extreme assumptions on the alignment of the velocity ellipsoid made by the JAMcyl and JAMsph methods to asses the sensitivity of the model results to the model assumptions. When the two methods provide consistent results, one can be con\ufb01dent of derived physical quantities, while where the two methods di\ufb00er, one should treat the results with caution. The di\ufb00erence between the results inferred using either JAMsph or JAMcyl, especially when applied to large statistical samples, can be used as an estimate of the expected modelling errors. The \ufb01rst application of this approach of comparing JAMsph or JAMcyl was presented in Nitschai et al. (2020), which uses JAM to model the Gaia DR2 stellar kinematics and infer the mass distribution of the Milky Way. In that work we found that the two JAM methods give nearly-indistinguishable total density pro\ufb01les, providing strong con\ufb01dence in the derived result. An application to the statistically signi\ufb01cant ATLAS3D sample (Cappellari et al. 2011) of early-type galaxies is presented in the next section. 0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 lg( 2/DOF) using JAMcyl 0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 lg( 2/DOF) using JAMsph a = 0.5001 \u00b1 0.0014 b = 0.9922 \u00b1 0.0041 = 0.022 (x0 = 0.5) Fit accuracy of JAMsph vs JAMcyl Fitted Clipped Figure 11. Comparison between the goodness-of-\ufb01t \u03c72 per degrees-offreedom (DOF) obtained when \ufb01tting the Vrms kinematics of the ATLAS3D galaxies using either the JAMsph or the JAMcyl methods. The parameters of the best-\ufb01tting linear relation y = a+b(x\u2212x0), the resulting 1\u03c3 uncertainties and the observed scatter \u2206are printed in the top-left corner. The green line is the best-\ufb01tting relation while the dotted lines indicate the 1\u03c3 (68% of values) and 2.6\u03c3 (99% of values) scatter around the relation. The \ufb01t was performed with the robust lts_linefit procedure by Cappellari et al. (2013) and the values clipped by the program are shown as green diamonds. 8.6 Applying JAMsph and JAMcyl to the ATLAS3D sample As an illustration of how to use in practice the recommendation given in the previous section, here I applied both the JAMsph and JAMcyl methods to asses the robustness of the measurement of the total density slope for the whole ATLAS3D sample of early-type galaxies (Cappellari et al. 2011), which were presented in Poci et al. (2017). Even in this epoch, with the availability of the much larger MaNGA (Bundy et al. 2015) and SAMI (Bryant et al. 2015) integral\ufb01eld spectroscopic (IFS) surveys, the ATLAS3D sample represents a useful and very well-studied benchmark due to its consistently high IFS data quality and higher spatial resolution. The modelling approach I used is the same as the model (D) in Cappellari et al. (2013) and I \ufb01tted the same Vrms kinematics from Cappellari et al. (2011). In brief, the models adopt a stellar component embedded in a spherical halo. The stellar components is parametrized by the MGE models11 from Scott et al. (2013), with constant stellar mass-to-light ratio, while the halo density is described by a generalized NFW pro\ufb01le with free inner logarithmic slope (gNFW, Wyithe et al. 2001). The \ufb01ts of the JAM models to the kinematic data were performed with the CapFit constrained least-squares optimization program, which combines the Sequential Quadratic Programming and the Levenberg-Marquardt methods and is included in the ppxf Python package12 of Cappellari (2017). Datamodel comparisons were already shown, for very similar models and 11 Both kinematics and MGEs are available from http://purl.org/atlas3d 12 I used v7.0 of the ppxf package from https://pypi.org/project/ppxf/ MNRAS 000, 1\u201319 (2020) 16 M. Cappellari 3.0 2.5 2.0 1.5 1.0 tot using JAMcyl 3.0 2.5 2.0 1.5 1.0 tot using JAMsph a = 2.1517 \u00b1 0.0070 b = 1.022 \u00b1 0.027 = 0.094 (x0 = 2.2) Density slope with JAMsph vs JAMcyl Fitted Clipped Figure 12. Same as in Fig. 11, for the best-\ufb01tting total slopes \u03b3tot inferred using either the JAMsph or the JAMcyl methods to \ufb01t the ATLAS3D integral\ufb01eld stellar kinematics. the same data, in \ufb01g. 1 of Cappellari et al. (2013), and the present \ufb01ts are nearly indistinguishable from those. Fig. 11 compares the goodness of \ufb01t \u03c72/DOF per degrees-offreedom for both JAMsph and JAMcyl. I perform a linear \ufb01t to the two quantities with the robust lts_linefit procedure13 by Cappellari et al. (2013), which combines the Least Trimmed Squares robust technique of Rousseeuw & Van Driessen (2006) into a least-squares \ufb01tting algorithm which allows for errors in both variables and intrinsic scatter. I \ufb01nd that the quality of the \ufb01ts with the two methods is, on average, statistically indistinguishable, except for some outliers. After obtaining the best \ufb01ts, I computed the resulting totaldensity average logarithmic slope \u03b3tot = \u2206log \u03c1tot(r)/\u2206log r. I computed the spherically-averaged density \u03c1tot(r) from the dark+luminous MGEs using the procedure mge_radial_density included in the JAM package, which implements the footnote 11 of Cappellari et al. (2015). I considered a radial interval from 2 arcsec, which is a bit larger than the typical resolution of the kinematics, to the largest radius included in each IFS kinematics. The resulting average density slope \u03b3tot inferred from the best\ufb01tting models is shown in Fig. 12. This too shows no systematic di\ufb00erences between the two JAM methods, except for some outliers. In the \ufb01gure I only included galaxies with kinematic quality \ufb02ag qual > 0 in table 1 of Cappellari et al. (2013). The \u03b3tot derived with the two methods has an observed scatter \u2206= 0.094. Assuming the uncertainties are the same for the two methods, this scatter implies a 1\u03c3 uncertainty of \u03f5\u03b3 = \u2206/ \u221a 2 \u22480.07 in each slope determination. This value is close to the estimate \u03f5\u03b3 \u22480.09 obtained by Poci et al. (2017), con\ufb01rming the validity of the approach. The observed near insensitivity of the total slope inferred using either JAMsph and JAMcyl on real galaxies, namely its insensitivity to the assumed orientation of the velocity ellipsoid, appear to ex13 I used v5.0 of the LtsFit package from https://pypi.org/project/lts\ufb01t/ plain the accuracy of the total slopes previously reported for JAMcyl (Section 1.2). 9 CONCLUSIONS I presented a general anisotropic solution for the axisymmetric Jeans equations of stellar hydrodynamics under the assumption of a velocity ellipsoid that is aligned with the spherical polar coordinate system. The solution requires a triple numerical quadrature with improper integrals for general gravitational potentials. I described an e\ufb03cient and robust numerical method for its computation. The resulting algorithm is just one order of magnitude slower than my previously derived cylindrically-aligned solution, which only required a single quadrature. For reference, the computation of all components of the second velocity moment tensor and the mean velocities in Fig. 7, with my current Python implementation of the algorithm, took 7 s on a 2 GHz CPU. I derived analytic equations for testing both the sphericallyaligned and cylindrically-aligned anisotropic Jeans solutions and used them to verify the accuracy of both the formalism and the numerical implementations of the algorithms. I described the general procedure and a method for the e\ufb03cient numerical computation of the sky projection of all six components of the symmetric second velocity moment tensor and the three mean velocity components. I gave examples illustrating the qualitative trends in galaxy observables as a function of anisotropy. I compared the spherically-aligned JAMsph and cylindricallyaligned JAMsph Jeans solutions using parameters describing the kinematics of real galaxies and found that for these cases the two methods produce rather similar observables, for the range of observed anisotropies, but can di\ufb00er dramatically at larger anisotropy. This JAM method has already been applied to model the Gaia DR2 data, where we found it describes the observations remarkably well with minimal freedom and good accuracy (Nitschai et al. 2020). Here, I also used both JAMsph and JAMcyl to model the ATLAS3D sample of early-type galaxies with high-quality integral-\ufb01eld stellar kinematics. I found that the inferred total-density slopes are nearly insensitive to the adopted orientation of the velocity ellipsoid and this appears to explain the previously-reported accuracy of JAMcyl in recovering density pro\ufb01les of real and simulated galaxies.",
                    "introduction": "1.1 Dynamical modelling methods We live in a very interesting Universe. According to our current understanding, some of its key constituents do not directly emit electromagnetic radiation. For this reason, their masses or distri- bution can only be quanti\ufb01ed through gravitational interactions or equivalently, by their curvature of space-time. One dark component is the mysterious dark matter, which, despite being a key piece of our model of the Universe (e.g. Blumenthal et al. 1984), has been recently experiencing an existential \u2018crisis\u2019 due to the lack of viable candidate particles, despite enormous e\ufb00orts to look for them (see review by Bertone & Tait 2018). The other dark com- ponents are supermassive black holes in galaxy nuclei. For them, strong evidence does exist, and in the past few decades, they have been promoted from mere physical curiosity to a key element in galaxy evolution (see review by Kormendy & Ho 2013). Additional nearly-dark components are stellar remnants (stellar black holes and neutron stars) and low mass stars, whose fractional contributions depends on the stellar Initial Mass Function, (IMF) which seems \u22c6E-mail: michele.cappellari@physics.ox.ac.uk to be varying among di\ufb00erent galaxies (e.g. van Dokkum & Con- roy 2010; Cappellari et al. 2012) and a\ufb00ects our understanding of galaxy evolution. The dark components are best studied using either galaxy dynamics (e.g. Binney & Tremaine 1987, hereafter BT) or gravitational lensing (see review by Treu 2010). This paper deals with the former technique. Earlier dynamical models (e.g. Satoh 1980; Binney et al. 1990; van der Marel et al. 1990; Emsellem et al. 1994) assumed axisym- metry and were based, due to their simplicity and computational e\ufb03ciency, on the equations that Jeans (1922) described as \u201chydro- dynamical equations of motion for the stars\u201d. These initial models additionally relied on the assumption of a semi-isotropic velocity ellipsoid (\u03c3R = \u03c3z and vRvz = 0), which is a characteristic of mod- els where the distribution function (DF) only depends on the two classic isolating integral of motion. The knowledge that the DF of galaxies depends on three integrals (Ollongren 1962; Contopoulos 1963), combined with the empirical \ufb01nding that indeed \u03c3R , \u03c3z in a large sample of real galaxies (van der Marel 1991), motivated the development of the more general Schwarzschild (1979) orbit- superposition dynamical models (e.g. Richstone & Tremaine 1988; van der Marel et al. 1998; Gebhardt et al. 2000; Cappellari et al. 2006; van den Bosch et al. 2008), including the related \u201ctorus map- per\u201d technique (Binney & McMillan 2016) and the Syer & Tremaine c \u20dd2020 The Authors arXiv:1907.09894v2  [astro-ph.GA]  23 Apr 2020 2 M. Cappellari (1996) \u201cmade-to-measure\u201d particle-based models (e.g. de Lorenzi et al. 2007; Dehnen 2009; Long & Mao 2010). The \ufb01rst and major fundamental problem when modelling external galaxies is the non-uniqueness of the surface brightness de- projection, which a\ufb00ects any technique (Rybicki 1987). It is already severe in the axisymmetric limit at a low inclination (e.g. Lablanche et al. 2012 and Section 4.2) and becomes even more important from any viewing direction in triaxiality (Gerhard 1996). A second problem is the fact that the observations can provide at best a three- dimensional data-cube, when using state-of-the-art integral-\ufb01eld stellar kinematics (see review by Cappellari 2016), and, for dimen- sional arguments alone, this cannot be expected to tightly constrain both the three-dimensional DF and the gravitational potential or galaxy shapes (e.g. sec. 3 of Valluri et al. 2004). A third issue, which is often ignored, is that dynamical modelling methods only represent an approximate and, in the case of orbit or particle-based methods, a severely-discretized solution of the original mathematical problem. Even in an ideal situation, with noiseless integral-\ufb01eld data, where one arti\ufb01cially removes the mass deprojection non-uniqueness and assumes the intrinsic mass is perfectly known, numerical exper- iments have revealed that one still cannot robustly recover a basic parameter like the galaxy inclination (Krajnovi\u00b4 c et al. 2005; van den Bosch & van de Ven 2009). Similar results were found when modelling real galaxies (Cappellari et al. 2006; de Lorenzi et al. 2009). The severity of these degeneracies, supported by additional extensive experiments with Schwarzschild\u2019s modelling at that time, motivated my search for simpler, less-general, but hopefully more robust models, based on the Jeans equations, but this time allow- ing for an anisotropic (three-integral DF) \u03c3R , \u03c3\u03c6 , \u03c3z velocity ellipsoid. In Cappellari (2008) I presented a very e\ufb03cient Jeans solution based on the assumption of an alignment of the velocity ellipsoid in cylindrical polar coordinates. The latter approximate assumption aimed at capturing the main global characteristics of the velocity ellipsoid inferred from Schwarzschild\u2019s modelling of integral-\ufb01eld stellar kinematics (Cappellari et al. 2007). I dubbed the resulting method the cylindrically-aligned Jeans Anisotropic Modelling method (JAMcyl). 1.2 Motivation for this work On purely theoretical grounds, because of its generality, one may have expected Schwarzschild\u2019s method to be able to recover mass densities more accurately than JAMcyl. However, recent studies suggest that the reverse is true in practice, using both real galaxies and N-body simulations. The \ufb01rst study used 54 real early-type and spiral galaxies for which the true circular velocity vc was assumed to be traced by the gas rotation velocity measured from the CO emission lines by the EDGE-CALIFA survey (Bolatto et al. 2017). These vc were compared against those independently obtained by \ufb01tting either Schwarzschild\u2019s or the JAMcyl dynamical models to the same CAL- IFA (S\u00e1nchez et al. 2012) stellar kinematics. The study found that the vc inferred using the JAMcyl method agree more closely with the true vc, than those inferred using Schwarzschild\u2019s method, especially at large radii where the gas velocities are better-determined (\ufb01g. 8 of Leung et al. 2018). The second work used N-body simulations. A direct compari- son between JAMcyl and Schwarzschild\u2019s methods was performed by Jin et al. (2019) using the currently state-of-the-art Illustris cos- mological N-body simulation (Vogelsberger et al. 2014). In this case, the true density pro\ufb01les are known, as they can be inferred directly from the N-body particles. Consistently with the study on real galaxies, also this work found that the total enclosed masses Mtot(R) recovered by JAMcyl agree more accurately with the true Mtot(R), than those inferred using Schwarzschild\u2019s method, on the same set of simulated galaxies and for the same set of adopted viewing directions (\ufb01g. 6 of Jin et al. 2019). Of course, masses and density pro\ufb01les are not the only useful metric to test and compare dynamical modelling methods. As an example, Schwarzschild\u2019s method non-parametric description of the DF can become crucial, with very high-quality data and espe- cially for nearly edge-on galaxies, when one is trying to explicitly decompose galaxies into stellar orbital families according to their integrals of motions (e.g. Zhu et al. 2018) or stellar population (e.g. Long & Mao 2018; Poci et al. 2019). I do not intend to review all characteristics of the di\ufb00erent modelling methods here. The above reliability tests demonstrate the usefulness of the JAM technique and its complementarity to Schwarzschild\u2019s ap- proach, even where more general methods are available and compu- tationally feasible. These results motivate further developments in Jeans\u2019s approach which are the focus of this paper. Moreover, the availability of di\ufb00erent Jeans methods allows for crucial tests of the sensitivity of the results to the modelling assumptions. More speci\ufb01cally, the impetus for the present work comes from the existence of the Gaia DR2 data (Gaia Collaboration et al. 2018), which provide three-dimensional positions and velocities for mil- lions of stars in our Milky Way galaxy. At a signi\ufb01cant height above the Galaxy equatorial plane, one expects the cylindrical-alignment assumption to become inaccurate as discussed in Section 2.3. This theoretical expectation was con\ufb01rmed by recent Gaia studies which found that the velocity ellipsoid is well approximated by an align- ment with the spherical polar coordinate system, both in the outer stellar halo (Wegg et al. 2019) and in the disk region (Hagen et al. 2019; Everall et al. 2019). These data motivates the development of a practically-usable spherically-aligned solution for the Jeans equations, which we already successfully applied to the Gaia data (Nitschai, Cappellari & Neumayer 2020)."
                }
            ],
            "Davor Krajnovic": [
                {
                    "url": "http://arxiv.org/abs/1802.02591v2",
                    "title": "Climbing to the top of the galactic mass ladder: evidence for frequent prolate-like rotation among the most massive galaxies",
                    "abstract": "We present the stellar velocity maps of 25 massive early type galaxies\nlocated in dense environments observed with MUSE. Galaxies are selected to be\nbrighter than M_K=-25.7 magnitude, reside in the core of the Shapley Super\nCluster or be the brightest galaxy in clusters richer than the Virgo Cluster.\nWe thus targeted galaxies more massive than 10^12 Msun and larger than 10 kpc\n(half-light radius). The velocity maps show a large variety of kinematic\nfeatures: oblate-like regular rotation, kinematically distinct cores and\nvarious types of non-regular rotation. The kinematic misalignment angles show\nthat massive galaxies can be divided into two categories: those with small or\nnegligible misalignment, and those with misalignment consistent with being 90\ndegrees. Galaxies in this latter group, comprising just under half of our\ngalaxies, have prolate-like rotation (rotation around the major axis). Among\nthe brightest cluster galaxies the incidence of prolate-like rotation is 50 per\ncent, while for a magnitude limited sub-sample of objects within the Shapley\nSuper Cluster (mostly satellites), 35 per cent of galaxies show prolate-like\nrotation. Placing our galaxies on the mass - size diagram, we show that they\nall fall on a branch extending almost an order of magnitude in mass and a\nfactor of 5 in size from the massive end early-type galaxies, previously\nrecognised as associated with major dissipation-less mergers. The presence of\ngalaxies with complex kinematics and, particularly, prolate-like rotators\nsuggests, according to current numerical simulations, that the most massive\ngalaxies grow predominantly through dissipation-less equal-mass mergers.",
                    "authors": "Davor Krajnovic, Eric Emsellem, Mark den Brok, Raffaella Anna Marino, Kasper Borello Schmidt, Matthias Steinmetz, Peter M. Weilbacher",
                    "published": "2018-02-07",
                    "updated": "2018-04-20",
                    "primary_cat": "astro-ph.GA",
                    "cats": [
                        "astro-ph.GA"
                    ],
                    "main_content": "In this section we briefly describe the M3G sample of galaxies, the observations and the extraction of the kinematic information. Further details on these aspects will be presented in a following M3G paper (Krajnovi\u00b4 c et al. in prep.). 2.1 The M3G sample and MUSE observations The M3G sample comprises 25 early-type galaxies selected to be brighter than -25.7 magnitude in the 2MASS Ks\u2212band and found in the densest environments. We created two sub-samples of galaxies: one consisting of the brightest galaxies in the densest known structure, the core of the Shapley Super Cluster (SSC) (Shapley 1930; Merluzzi et al. 2010, 2015), and the other targeting BCGs in rich clusters. We selected galaxies in the SSC using the 2MASS All Sky Extended Source Catalog (XSC, Jarrett et al. 2000; Skrutskie et al. 2006) centred on the three main clusters near the core of the SSC: Abell 3562, 3558 and 3556 (Abell et al. 1989). This selection yielded 14 galaxies, with 3 being BCGs. The complementary sub-sample of BCGs was defined using a parent sample of clusters richer than the Virgo Cluster and observed with the HST (Laine et al. 2003). We included 11 BCGs residing in clusters with richness larger than 40, where the richness is defined as the number of galaxies with magnitudes between m3 and m3 + 2 within an Abell radius of the cluster centre (m3 is the magnitude of the third brightest cluster galaxy). Here we also used the information given in Laine et al. (2003). The full M3G sample therefore consists of 14 galaxies in the SSC, and 14 BCG (three being in the SSC). In this paper we use 2MASS photometry as a reference, but as part of the M3G project, we have collected photometry from other imaging campaigns, which will be described in detail in future papers. In addition to the visibility requirement that the galaxies are observable from Paranal, we imposed a selection criterion based on the distance and size of the galaxies: these had to be such that the MUSE field-of-view covers up to two effective radii of each target. The effective radii were collected from the XSC catalog, using the k r eff keyword. The most massive galaxies in the SSC have the right combination of parameters to satisfy this criterion, while the additional 11 BCGs were selected to be at similar redshifts. The galaxies span the redshift range 0.037 < z < 0.054, with a mean of z=0.046. The redshift of the SSC is assumed to be 0.048 (Metcalfe et al. 1987). Adopting cosmology H0 = 70 km s\u22121 Mpc\u22121, \u2126M = 0.3, \u2126\u039b = 0.7, 1\u2032\u2032 is 904 pc at the mean redshift of the sample, while this scales changes from 735 to 1050 pc between galaxies (Wright 2006). The observations of the sample were performed within the MUSE Guaranteed Time Observations (GTO) during ESO Periods of discs, while non-regular rotation is used for twisted and complex velocity maps. 94 99 (starting in the fall of 2014 and finishing in the spring of 2017). The observing strategy consisted of combining a short Observing Block (OB) of exposures during better-than-average seeing conditions (< 0.8\u2032\u2032) to map the central structures, and a set of OBs with longer exposure times to reach a sufficient signal-to-noise ratio (S/N) at two effective radii. The high spatial (short exposure time) resolution MUSE data will be presented in a forthcoming paper. The total exposure time for each galaxy varied from about 2 to 6 hours. The brightest galaxy in the sample (see Table 1 for details) was mosaiced with 2 \u00d7 2 MUSE fields, each observed up to 6h. All individual OBs consisted of four on-target observations and two separate sky fields sandwiched between the on-target exposures. On-target observations were each time rotated by 90\u25e6and dithered in order to reduce the systematics introduced by the 24 MUSE spectrographs. 2.2 Data reduction and kinematics extraction Data reduction was performed as the observations were completed. This means that several versions (from v1.2 to the latest v1.6) of the MUSE data reduction pipeline (Weilbacher et al. 2014) were used. Despite continued improvement of the reduction pipeline, given the brightness of the M3G sample, and the nature of the current study, the differences in the reductions do not affect the results and conclusions presented here. All reductions followed the standard MUSE steps, producing the master calibration files of the bias and flat fields, as well as providing the trace tables, wavelength calibration files and line-spread function for each slice. When available we also used twilight flats. Instrument geometry and astrometry files were provided by the GTO team for each observing run. These calibrations files, as well as the closest in time illumination flats obtained during the night, were applied to the on-target exposures. From separate sky fields we constructed the sky spectra which were associated with the closest in time on-target exposure, and from the observation of a standard star (for each night) we extracted the response function as well as an estimate of the telluric correction. These, together with the line-spread function (LSF) and the astrometric solution, were used during the science post-processing. The final data cubes were obtained by merging all individual exposures. As these were dithered and rotated, a precise alignment scheme was required. This was achieved using stars or unresolved sources, and for a few cases in which the MUSE field-of-view was devoid of such sources, using the surface brightness contours in the central regions. The final cubes have the standard MUSE spatial spaxel of 0.2\u2032\u2032\u00d70.2\u2032\u2032 and a spectral sampling of 1.25 \u00c5 per pixel. As a first step before extraction of the kinematics, we proceeded to spatially bin each data cube to homogenise the signalto-noise ratio throughout the field-of-view via the Voronoi binning method (Cappellari & Copin 2003)2. We first estimated the S/N of individual spectra from the reduction pipeline propagated noise, masking all stars or satellite galaxies within the field-of-view. Spatial binning is ultimately an iterative process, in which our goal was to achieve relatively small bins beyond one effective radius, but which provide a sufficient signal for extraction of robust kinematics. The quality of the extraction was measured using the signal-toresidual noise ratio (S/rN), where the residual noise is the standard deviation of the difference between the data and the model (as explained below). S/rN was required to be similar to the target S/N in bins at large radii. As the data quality varies between galaxies, 2 Available at http://purl.org/cappellari/software MNRAS 000, 1\u201311 (2017) 4 Davor Krajnovi\u00b4 c et al. 4500 5000 5500 6000 6500  rest frame [\u00c5] 0.4 0.6 0.8 1.0 1.2 1.4 1.6 Noramlized Flux galaxy pPXF fit residuals mask Figure 1. An example of the pPXF \ufb01t to a spectrum extracted within an e\ufb00ective radius from PGC047177, which also shows ionised gas emission. The observed spectrum is shown in black and the best \ufb01t in red. Green dots are residuals. Light green shaded areas were masked and not \ufb01tted. These include the strongest emission-lines expected between 4500 \u00c5 and 7000 \u00c5, as well as potential strong sky lines or telluric residuals. it is possible for some galaxies to have su\ufb03ciently small bins in the central regions with S/rN \u223c100, while for some galaxies S/rN \u223c50 is the most that can be achieved for a reasonable bin size. For this work, we set the target S/N required by the Voronoi binning method to 50 for all galaxies. Additionally, before binning we removed all spectra (individual spaxels) with S/N less than 2.5 in the continuum (based on the pipeline estimated noise)3. In this way we excluded the spectra at the edge of the MUSE FoV, which essentially do not contain any useful signal and limited the sizes of the outermost bins. Stellar kinematics were extracted using the pPXF method4 (Cappellari & Emsellem 2004). Our pPXF set up included an additive polynomial of the 4th order, and we \ufb01tted a line-of-sight velocity distribution parametrised by Gauss-Hermit polynomials (van der Marel & Franx 1993; Gerhard 1993) with the mean velocity V, the velocity dispersion \u03c3 and the higher order moments h3 and h4. We masked all potential emission-lines and a few narrow spectral windows with possible sky-line residuals. Finally, we limited the \ufb01t to blue-wards of 7000 \u00c5, to exclude potentially strong telluric and sky residuals. For each galaxy, a pPXF \ufb01t was \ufb01rst performed on the spectrum obtained by summing all MUSE spectra within one e\ufb00ective radius (covering an elliptical area equivalent to \u03c0\u00d7R2 e) and using the full MILES stellar library (S\u00b4 anchez-Bl\u00b4 azquez et al. 2006; Falc\u00b4 on-Barroso et al. 2011) as templates. The MUSE LSF signi\ufb01cantly varies with wavelength with a full-width half maximum from 2.85 \u00c5 at 5000\u00c5 to 2.5 \u00c5 at 7000 \u00c5 (Gu\u00b4 erou et al. 2017). We used the parametrisation of the LSF from Gu\u00b4 erou et al. (2017) and convolved the MILES templates to the MUSE LSF (varying with wavelength). Possible emission-lines were masked. As an example, we show the \ufb01t to the spectrum extracted within the half-light redius of one of our galaxies in Fig. 1. This \ufb01rst global pPXF \ufb01t provides an optimal set of stellar templates, which we propagate for each individual Voronoi-binned spectrum, using the same pPXF set-up. The quality of the \ufb01t was checked via the S/rN of each bin, where the residual Noise was the standard deviation of the di\ufb00erence between the data and the best\ufb01t pPXF model. As outlined above, this S/rN was required to be at least 50 over most of the \ufb01eld-of-view. We extracted up to the 3 The value of S/N \u223c2.5 was selected as a compromise between removing too many pixels in the outer regions and reducing the size of the outermost bins. 4 See footnote 2 for software availability. 4th Gauss-Hermit coe\ufb03cient, but in this work we will primarily focus on the mean velocity maps of our 25 galaxies. The velocity dispersion and higher order velocity moments maps, as well as the analysis of the angular momentum will be presented in a future paper. The global velocity dispersion values are given in Table 1. 3 PREVALENCE OF LONG-AXIS ROTATION IN MASSIVE GALAXIES The velocity maps for the full M3G sample are shown in Fig. 2. The sample is split into BCGs (\ufb01rst 14 maps) and non-BCGs from the SSC. In each subgroup galaxies are plotted in order of decreasing 2MASS K-band absolute luminosity. There are several noteworthy features in these maps, which we interpret within the kinematic classi\ufb01cation system of the ATLAS3D survey (Krajnovi\u00b4 c et al. 2011). To start with, we note that almost all galaxies show some level of rotation. While the maximum velocity amplitudes reached within the two e\ufb00ective radii covered by our MUSE observations are often low (\u224830 \u221250 km/s), only one galaxy, e) PGC 043900, does not show a clear indication for net streaming motion within the \ufb01eld of view. This is somewhat di\ufb00erent from the trend expected from the ATLAS3D data (Emsellem et al. 2011; Krajnovi\u00b4 c et al. 2011), where a few of the most massive systems (about 15 per cent for galaxies more massive than 2 \u00d7 1011 M\u2299), can be characterised as having no net rotation. Other studies of massive galaxies (e.g. Veale et al. 2017b) also \ufb01nd a large number of galaxies with negligible net rotation. It is likely that, as in the case of NGC 4486 (Emsellem et al. 2014), our MUSE data are of such quality and extent that the rotation is revealed even in systems such as r) PGC 047590, where the amplitude of the rotation is only 30 km/s5. The coverage beyond one e\ufb00ective radius helps to determine the net rotation trend, but also reveals changes in the kinematics. This is especially noticeable among BCGs, where the velocity maps change orientation (e.g. b) PGC 048896), or there is a loss of coherent motions (e.g. h) PGC 065588). Non-BCGs, which we will call satellites in this context, do not show such changes. It might be the case that the changes are found at larger radii (as for some lower5 A similar change of kinematic classi\ufb01cation based on higher quality kinematics could happen to NGC 5846, another ATLAS3D \u201dnon-rotator\u201d with a hint for prolate-like rotation in the SAURON data. MNRAS 000, 1\u201311 (2017) Prolate-like rotation in massive galaxies 5 20 10 0 10 20 arcsec -150/150 OBL BCG a) PGC047202 -50/50 PRO BCG b) PGC048896 -70/70 PRO BCG c) PGC073000 -50/50 TRI BCG d) PGC046832 -80/80 TRI BCG e) PGC043900 20 10 0 10 20 arcsec -50/50 PRO BCG f) PGC003342 -50/50 TRI BCG g) PGC015524 -90/90 TRI BCG h) PGC065588 -50/50 OBL BCG i) PGC019085 -50/50 OBL BCG j) PGC018236 20 10 0 10 20 arcsec -50/50 PRO BCG k) PGC047752 -50/50 OBL BCG l) PGC004500 -70/70 OBL BCG m) PGC049940 -40/40 PRO BCG n) PGC007748 -100/100 OBL SAT o) PGC046785 20 10 0 10 20 arcsec -70/70 TRI SAT p) PGC047154 -60/60 OBL SAT q) PGC099522 -30/30 PRO SAT r) PGC047590 -80/80 PRO SAT s) PGC099188 -30/30 PRO SAT t) PGC047197 20 0 20 20 10 0 10 20 arcsec -200/200 OBL SAT u) PGC047177 20 0 20 -150/150 OBL SAT v) PGC046860 20 0 20 -200/200 OBL SAT w) PGC097958 20 0 20 -250/250 OBL SAT x) PGC047355 20 0 20 -200/200 OBL SAT y) PGC047273 0 1 Figure 2. The mean stellar velocity maps of the M3G sample galaxies. Galaxies are divided in two groups, the BCGs and satellites (non-BCGs in the SSC). BCGs are plotted in the \ufb01rst 14 panels starting from the top left, followed by satellites (as indicated with \u201cSAT\u201d). The two groups of galaxies are ordered by decreasing K-band absolute magnitude. The values in the lower right corner of each panel indicate the range of the velocities, where the negative are shown with blue and positive with red colours, as indicated by the colourbar. Black dashed contours are isophotes plotted in steps of one magnitude. All velocity maps are approximately 1\u2032 \u00d7 1\u2032 in size. Full red ellipses indicate the size and the orientation of the half-light region, speci\ufb01ed by the ellipticity of the galaxy and the semi-major axis length equal to the 2MASS Ks-band e\ufb00ective radius. Green and brown lines indicate the orientation of the kinematic and the photometric major axes, respectively. Letters in upper right corner of each panel (\u201cPRO\u201d, \u201cTRI\u201d and \u201cOBL\u201d) indicate broad shape-related categories of the galaxy based on the kinematic misalignment (see Fig. 3 for details). Note that PGC 043900 is characterised as \u201dTRI\u201d due to its non-rotation. The letters in front of the galaxy names will be used in text for easier location of the object. MNRAS 000, 1\u201311 (2017) 6 Davor Krajnovi\u00b4 c et al. mass fast rotators, Arnold et al. 2014), but there is no clear evidence for this within 2 Re. Another striking feature is that there are galaxies which show regular rotation, with peak velocity in excess of 200 km/s. These galaxies are in fact among the lower luminosity bin of our set of massive galaxies, and found within the group of satellites. Galaxies that belong to this class are v) PGC046860, u) PGC047177, y) PGC047273, x) PGC047355 and w) PGC097958. Their dynamical masses (see Section 4) are around 1012 M\u2299, and they are all among the most massive galaxies with regular rotation. Their existence is expected (e.g. Brough et al. 2007; Loubser et al. 2008; Veale et al. 2017b; Lagos et al. 2017), although their number likely decreases with increasing mass (e.g. Krajnovi\u00b4 c et al. 2011; Jimmy et al. 2013; Houghton et al. 2013; Veale et al. 2017b; Brough et al. 2017). The fact that these galaxies are not found among BGCs is indicative of their less violent evolution maintaining the regular rotation. However, there is also the case of a) PGC 047202, the largest and the most luminous galaxy in the SSC, and a BCG, which shows high level of rotation, albeit non-regular. Non-regular rotation is the most common characteristics of the M3G velocity maps. It is especially among BCGs, but it also occurs in non-BCGs. The existence of kinematically distinct cores (KDC), counter-rotation, the radial variation of the kinematic position angle, as well as the analysis of the velocity features beyond the e\ufb00ective radius will be discussed in a future paper. Here we quantify the kinematic misalignment angle \u03a8 as the di\ufb00erence between the position angle de\ufb01ned by the photometric major axis (PAphot) and the global kinematic position angle (PAkin) approximately within 1 effective radius. We measure PAkin using the method presented in Appendix C of Krajnovi\u00b4 c et al. (2006)6, which provides a global orientation of the velocity map. PAphot was measured by calculating the moments of inertia7 of the surface brightness distribution from the MUSE white-light images (obtained by summing the MUSE cubes along the wavelength dimension). At the same time, the method provides the global ellipticity \u03f5. As we used MUSE cubes for both PAkin and PAphot, they were estimated approximately within the same region. In Table 1 we report the measured photometric and kinematic position angles as well as other relevant properties used in this paper. Kinematic and photometric position angles are shown in Fig. 2 as green and brown lines, respectively. Systems with regular rotation have almost overlapping lines, while systems with non-regular rotation often show that the kinematic misalignment angle \u03a8 is close to 90\u25e6. To quantify this, we also present the distribution of \u03a8 as a function of the galaxy projected ellipticity \u03f5 for the M3G sample in Fig. 3. We split galaxies into BGCs and satellites and draw two horizontal lines at 15\u25e6and 75\u25e6to separate oblate, triaxial and prolate geometries. The most noteworthy characteristic of Fig. 3 is that galaxies seem to group in two regions, one with low and one with high \u03a8. Galaxies with \u03a8 < 15\u25e6are generally consistent with having oblate symmetries. Their velocity maps look regular, and all galaxies with high rotation amplitudes are found in this group. In order of rising ellipticity these BCGs are: l) PGC 004500, m) PGC 049940, a) PGC 047202, j) PGC 018236 and i) PGC 019085. Their intrinsic shapes are likely not axisymmetric, as their velocity maps show 6 See footnote 2 for software availability. 7 The routine can be found within the MGE Package (Cappellari 2002) at http:/www.purl.org/cappellari/ 0.1 0.2 0.3 0.4 0.5 0 20 40 60 80  [degrees] OBL TRI PRO BCG SAT 0 5 N(gal) Figure 3. Distribution of the kinematic misalignment angle as a function of ellipticity, both measured within the e\ufb00ective radius of M3G sample galaxies. Red circles show BCGs, while blue squares are non-BCGs in the SSC (we call them satellites or SAT for simplicity). The symbol with an upper limit error bar is PGC 043900, the system with no net rotation and, therefore, no reliable PAkin measurement. Horizontal lines at \u03a8 = 15\u25e6and 75\u25e6are used to guide the eye for an approximate separation of shapes of galaxies, between mostly oblate (indicated with \u201cOBL\u201d), triaxial (\u201cTRI\u201d) and prolate (\u201cPRO\u201d). These divisions are not meant to be rigorous but indicative. Colours on the right-hand side histogram follow the same convention as shown on the main plot and the legend. kinematic twists and are not regular, but the velocity maps are close to aligned with their photometric axes. Galaxies with \u03a8 signi\ufb01cantly larger than 0 (and lower than 90) cannot be axisymmetric as their net angular momentum is not aligned with one of the principle axes. Very indicative is also that 8 galaxies have \u03a8 > 75\u25e6, while for one galaxy (e PGC 04390) it was not possible to determine \u03a8 as it does not show rotation. Among those 8 galaxies a closer examination shows rotation around the major axis within a large fraction of the half-light radius. These galaxies exhibit prolate-like rotation, as it is de\ufb01ned in Section 1, within a signi\ufb01cant part of the MUSE \ufb01eld-of-view. The rotation amplitude is, as in the case of other non-regular rotators, typically small, mostly around 50 km/s or lower, and the observed (luminosity-weighted) rotation has to be supported by the existence of long-axis tube orbits. There are 4 galaxies with 15o < \u03a8 < 75o: h) PGC 065588, p) PGC 047154, g) PGC 015524 and d) PGC 046832 (in order of decreasing \u03a8). The \ufb01rst three have similar rotation pattern as other galaxies with prolate-like rotation. Strictly speaking the \u03a8 values are inconsistent with 90\u25e6, but their velocity maps resemble those of galaxies with prolate-like rotation. We will, therefore, also refer to them as having prolate-like rotation. On the other hand, d) PGC 046832 exhibits a very complex velocity map with multiple changes between approaching and receding velocities, but its velocity map does not resemble prolate-like rotation, and its \u03a8 is signi\ufb01cantly smaller than for other galaxies in this group. Therefore, we will not consider it to have prolate-like rotation. As mentioned before, another special case is e) PGC 043900, which does not have any rotation and its \u03a8 is not well de\ufb01ned. Therefore, it is plotted as an upper limit. The prolate-like rotation comes in two \ufb02avours. It can be present across the full observed \ufb01eld-of-view (approximately 2 effective radii), for example in n) PGC007748, h) PGC065588 and r) PGC047590, but most galaxies have it within a speci\ufb01c area, MNRAS 000, 1\u201311 (2017) Prolate-like rotation in massive galaxies 7 Table 1. General properties of the galaxies. Name MK PAkin PAphot \u03a8 \u03f5 \u03c3e Re log (M\u2217) BCG Fig. 2 2MASS mag [degree] [degree] [degree] [km/s] [kpc] [log(M\u2299)] (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) PGC003342 -26.34 139.2 \u00b1 29.7 36.7 \u00b1 0.3 77.5 \u00b1 29.7 0.25 270.0 \u00b1 1.6 24.5 12.283 1 f) PGC004500 -25.85 157.3 \u00b1 29.7 153.5 \u00b1 1.4 3.8 \u00b1 29.7 0.11 256.5 \u00b1 1.6 13.2 12.026 1 l) PGC007748 -25.76 143.7 \u00b1 8.8 66.0 \u00b1 0.8 77.7 \u00b1 8.8 0.28 265.6 \u00b1 1.2 15.9 12.072 1 n) PGC015524 -26.10 116.5 \u00b1 12.6 172.9 \u00b1 7.5 56.4 \u00b1 14.6 0.19 272.9 \u00b1 1.4 20.7 12.233 1 g) PGC018236 -25.93 52.9 \u00b1 4.5 65.7 \u00b1 0.5 12.8 \u00b1 4.5 0.31 274.5 \u00b1 1.5 18.3 12.142 1 j) PGC019085 -26.04 119.5 \u00b1 11.8 125.3 \u00b1 0.3 5.8 \u00b1 11.8 0.52 261.2 \u00b1 1.4 28.4 12.358 1 i) PGC043900 -26.46 146.7 \u00b1 89.1 177.5 \u00b1 1.7 < 90 0.24 376.7 \u00b1 2.2 25.8 12.539 1 e) PGC046785 -26.39 63.5 \u00b1 4.0 75.4 \u00b1 14.7 11.9 \u00b1 15.2 0.07 333.9 \u00b1 1.8 18.2 12.464 3 o) PGC046832 -26.59 167.9 \u00b1 11.8 145.7 \u00b1 9.6 22.2 \u00b1 15.2 0.32 311.9 \u00b1 1.4 21.4 12.359 2 d) PGC046860 -25.89 56.0 \u00b1 1.8 57.6 \u00b1 1.0 1.6 \u00b1 2.0 0.33 282.8 \u00b1 1.2 13.0 12.038 3 v) PGC047154 -26.29 71.1 \u00b1 12.9 134.2 \u00b1 0.2 63.1 \u00b1 12.9 0.16 319.5 \u00b1 2.2 16.0 12.254 3 p) PGC047177 -25.89 95.3 \u00b1 2.0 98.4 \u00b1 1.3 3.1 \u00b1 2.4 0.37 287.3 \u00b1 1.5 15.3 12.104 3 u) PGC047197 -25.99 24.2 \u00b1 29.7 118.4 \u00b1 2.1 85.8 \u00b1 29.8 0.23 301.7 \u00b1 1.8 14.3 12.136 3 t) PGC047202 -27.19 166.4 \u00b1 2.8 172.2 \u00b1 2.5 5.8 \u00b1 3.8 0.26 318.9 \u00b1 2.2 39.3 12.668 2 a) PGC047273 -25.69 96.8 \u00b1 2.3 93.6 \u00b1 2.2 3.2 \u00b1 3.2 0.24 261.3 \u00b1 1.4 18.4 12.064 3 y) PGC047355 -25.79 86.2 \u00b1 1.0 81.9 \u00b1 1.2 4.3 \u00b1 1.6 0.24 252.9 \u00b1 1.3 14.8 12.026 3 x) PGC047590 -26.09 46.9 \u00b1 29.7 132.4 \u00b1 3.8 85.5 \u00b1 29.9 0.21 288.8 \u00b1 2.1 16.8 12.254 3 r) PGC047752 -25.89 3.0 \u00b1 29.7 89.9 \u00b1 3.3 86.9 \u00b1 29.9 0.22 261.0 \u00b1 1.7 21.2 12.073 2 k) PGC048896 -26.70 87.7 \u00b1 13.1 3.0 \u00b1 0.5 84.7 \u00b1 13.1 0.50 322.0 \u00b1 1.9 34.9 12.611 1 b) PGC049940 -25.83 51.4 \u00b1 9.1 51.7 \u00b1 1.9 0.3 \u00b1 9.3 0.14 298.6 \u00b1 1.7 12.6 12.078 1 m) PGC065588 -26.05 136.1 \u00b1 2.3 62.1 \u00b1 1.1 74.0 \u00b1 2.5 0.09 274.0 \u00b1 2.1 22.3 12.309 1 h) PGC073000 -26.65 66.6 \u00b1 5.0 160.8 \u00b1 0.3 85.8 \u00b1 5.0 0.30 283.6 \u00b1 1.8 30.4 12.450 1 c) PGC097958 -25.79 45.4 \u00b1 1.5 47.3 \u00b1 0.3 1.9 \u00b1 1.5 0.29 285.9 \u00b1 1.3 9.70 11.972 3 w) PGC099188 -25.99 149.7 \u00b1 29.7 62.1 \u00b1 1.4 87.6 \u00b1 29.7 0.13 224.2 \u00b1 1.2 26.2 12.198 3 s) PGC099522 -26.09 102.9 \u00b1 11.1 89.4 \u00b1 9.8 13.5 \u00b1 14.8 0.25 234.6 \u00b1 0.9 19.0 12.036 3 q) Notes: Column 1: names of galaxies; Column 2: Absolute magnitudes; Column 3: kinematic position angle; Column 4: photometric position angle: Column 5: kinematic misalignment error; Column 6: ellipticity; Column 7: velocity dispersion within the e\ufb00ective radius; Column 8: e\ufb00ective radius based on the j r eff 2MASS XSC keyword; Column 9: stellar mass; Column 10: galaxy is a BCG 1, galaxy is a BCG in the SSC 2, galaxy is a \u201csatellite\u201d in the SSC 3; Column 11: the letter referring to the position of the object in Fig. 2. Absolute K-band magnitudes are based on the 2MASS K-band total magnitudes and the distance moduli obtained from NED (http://ned.ipac.caltech.edu). The same distance moduli were used to convert sizes to kiloparsecs. Note that while we report actual measurements for the kinematic and photometric position angles, the kinematic misalignment \u03a8 for PGC043900 is an upper limit, as there is no net streaming in this galaxy. The stellar mass reported in the last column was estimated using columns 7 and 8, and the virial mass estimator from Cappellari et al. (2006). either outside the central region (but within one e\ufb00ective radius, s) PGC099188), or more typically covering the full half-light radius (e.g. k) PGC047752, f) PGC003342, c) PGC007300 or b) PGC048896). In these cases, the rotation at larger radii either disappears (e.g. t) PGC047197) or there is a change in the kinematic position angle and the rotation is consistent with being around the minor axis (f) PGC003342, c) PGC073000, b) PGC048896). The change in the kinematic position angle is relatively abrupt and occurs over a small radial range. Therefore, such galaxies could even be characterised as having large-scale KDCs, with the central component exhibiting prolate-like rotation. More typical and standard size KDCs are found in a few M3G targets (i) PGC019085 and d) PGC046832), but these will be discussed in more detail in a future paper devoted to the analysis of the high spatial resolution MUSE data cubes. Finally, for a few galaxies there is evidence for a signi\ufb01cant change beyond one e\ufb00ective radius in the properties of the velocity maps: regardless of regular or non-regular rotation within the effective radius, the outer parts show no rotation. They are, however, characterised by a spatially symmetric shift of velocities to larger values compared to the systemic velocity of the galaxy. Examples are the BCGs: m) PGC049940, i) PGC019085 and g) PGC015524. Except for stressing that such velocities at larger radii are only found in the BCGs, we will postpone the discussion of these features to a future paper when it will be put in the full context of the kinematics of M3G galaxies. 4 DISCUSSION In Fig. 4 we place the M3G sample on the mass size diagram. We indicate the type of observed kinematics with di\ufb00erent symbols and colours and also add the galaxies from the ATLAS3D magnitude-limited sample for comparison. Galaxy masses and sizes for ATLAS3D galaxies were obtained from Cappellari et al. (2013b). For M3G objects we used their 2MASS sizes (XSC keyword j r eff), de\ufb01ning the size as Re = 1.61\u00d7j r eff as in Cappellari (2013). Masses of the sample galaxies were approximated using the virial mass estimator M\u2217= 5\u00d7(Re\u03c32 e)/G (Cappellari et al. 2006), where \u03c3e is the e\ufb00ective velocity dispersion extracted from the MUSE data within an ellipse of area equal to \u03c0 \u00d7 R2 e. Using the full M3G sample, up to 44 per cent of galaxies have prolate-like rotation (here we include h) PGC 065588, p) PGC 047154 and g) PGC 015524 with \u03a8 > 60\u25e6, but do not consider e) PGC 043900). The M3G objects located in the SSC form a magnitude-limited subsample within a well de\ufb01ned environment. MNRAS 000, 1\u201311 (2017) 8 Davor Krajnovi\u00b4 c et al. This subsample contains 5/14 (35 per cent) galaxies with prolatelike rotation. Of these 5 galaxies one is a BCG, while the other two BCGs in the SSC, including the most luminous and the largest galaxy in the sample, do not show prolate rotation. The fraction of prolate-like rotation is somewhat higher among BCGs. In our sample there are 7/14 BCGs with prolate-like rotation (excluding e) PGC 043900 with an uncertain \u03a8), or 50 per cent. A comparison with the ATLAS3D sample indicates that galaxies with prolatelike rotation are mostly found in massive galaxies and that they are typical for dense environments. This can be quanti\ufb01ed using the literature data. Within the ATLAS3D sample there are six known galaxies with prolate-like rotation (NGC 4261, NGC 4365, NGC 4406, NGC 5485, NGC 5557 and NGC 4486), while Tsatsi et al. (2017) found 8 new systems in the CALIFA sample (LSBCF56004, NGC0810, NGC2484, NGC4874, NGC5216, NGC6173, NGC6338, and UGC10695; Falc\u00b4 on-Barroso et al. 2017)8. Together with the previously known cases such as NGC1052 (Schechter & Gunn 1979), NGC4589, NGC5982 and NGC7052 (Wagner et al. 1988), this means a total of 17 galaxies with apparent prolate-like rotation were previously known in the nearby universe. The MASSIVE survey (Ma et al. 2014) found 11 galaxies with kinematic misalignment larger than 60\u25e6, whereas 7 of those have \u03a8 > 75\u25e6 and can therefore be considered to have prolate-like rotation (Ene et al. 2018). These galaxies are: NGC 708, NGC 1060, NGC 2783, NGC 2832, NGC 7265, NGC 7274, and UGC 2783, where all of them except NGC7274 are classi\ufb01ed as BCGs or brightest group galaxy (BGG). A recent study of the kinematic misalignment angle of more than 2000 MANGA galaxies (Graham et al. 2018) \ufb01nds also a secondary peak at \u03a8 \u223c90\u25e6among galaxies more massive than 2 \u00d7 1011 M\u2299. Combining the M3G sample of galaxies with prolate-like rotation with those from the literature, we see that such rotation typically does not occur for M\u2217\u22721011 M\u2299, and that for M\u2217\u22731012 M\u2299velocity maps with prolate-like rotation correspond to the most populated kinematic category. Within the M3G sample, the prolate-like rotation is mostly found in BCGs, but is also present in non-BCGs. However, all galaxies in the M3G sample are members of groups or clusters of galaxies. Even when including the literature data, most galaxies with prolate-like rotation have been observed in galaxy clusters or groups. A similar \ufb01nding is reported by the MASSIVE survey (Ene et al. 2018), where galaxies with prolate-like rotation are almost exclusively found in BCGs/BGGs, and generally misaligned galaxies (\u03a8 > 15\u25e6) are rare in the low density environments, but common among the BCGs/BGGs or satellites. As the creation of non-regularly rotating, massive galaxies with low angular momentum (typical hosts for prolate-like rotation) can a priori occur in any environment (e.g. Cappellari et al. 2011b; Veale et al. 2017a), we expect that galaxies with prolate-like rotation, if rare, still exist outside of dense environments. The evidence that this might be so could be seen in recent merger galaxies, such as NGC 1222 (Young et al. 2018) or NGC 7252 (Weaver et al. 2018). These galaxies are in late merging phases, and have not yet fully settled, but show prolate-like rotation of the stellar component. What makes them signi\ufb01cantly di\ufb00erent from other prolate-like systems, is their richness in atomic and emission-line gas, as well as ongoing star formation, implying that there are multiple ways of creating prolate-like kinematics. Such galaxies seem however rare, as 8 We excluded NGC 5485 as it is already in ATLAS3D sample. UGC10695 is only a candidate for prolate-like rotation. Barrera-Ballesteros et al. (2015) does not report a signi\ufb01cant incidence of large kinematic misalignment in mergers. A survey of massive galaxies across various environments could constrain the dependence of prolate-like rotation on the environment, as well as o\ufb00er new possible scenarios for their formation. Numerical simulations suggest that prolate-like rotation may be the outcome of binary mergers for speci\ufb01c orbital con\ufb01gurations (e.g \u0141okas et al. 2014). For example, major (1:1) dissipationless mergers in the study by Naab & Burkert (2003) exhibit rotation around the minor axis. Furthermore, the orbital structure and the shapes of remnants of major collisionless mergers indicate signi\ufb01cant triaxiality and dominance of orbits that support triaxial or prolate shapes (Jesseit et al. 2005, 2009; R\u00a8 ottgers et al. 2014). Numerical simulations of binary (disk) mergers often end up with mildly elongated and low angular momentum remnants, with triaxial shapes and prolate-like rotation (Hernquist 1992; Naab & Burkert 2003; Cox et al. 2006; Ho\ufb00man et al. 2010; Bois et al. 2011; Moody et al. 2014). More speci\ufb01cally, Tsatsi et al. (2017) emphasised that a polar merger of gas-free disc galaxies can lead to a prolate-like remnant. Ebrov\u00b4 a & \u0141okas (2015), looking at a broader set of merging con\ufb01gurations, found that radial orbits are more likely to produce prolate-like rotation, other orbital con\ufb01gurations (speci\ufb01c combinations of orbital and disk angular momentum) not being excluded. Similar results are recovered in numerical simulations set within a cosmological context. Cosmological zoom-in simulations produce galaxies with prolate-like rotation (Naab et al. 2014). The Illustris (Vogelsberger et al. 2014), EAGLE (Schaye et al. 2015) and cosmo-OWLS (Le Brun et al. 2014) numerical simulations \ufb01nd that there is an increasing fraction of (close to) prolate shapes among the most massive galaxies (Velliscig et al. 2015; Li et al. 2016, for EAGLE+cosmo-OWLs and Illustris, respectively). Major mergers seem to be ubiquitous among galaxies with prolate-like rotation (Ebrov\u00b4 a & \u0141okas 2017). Speci\ufb01cally, a late (almost dry) major merger seems to be crucial to decrease the overall angular momentum and imprints the prolate-like rotation. A recent study by Li et al. (2018) on the origin of prolate galaxies in the Illustris simulation, shows that they are formed by late (z < 1) major dissipation-less mergers: galaxies might have a number of minor or intermediate mass mergers, but the last and late major merger is the main trigger for the prolate shape. Similarly to the \ufb01ndings from idealised binary mergers, most mergers leading to prolate-like systems have radially biased orbital con\ufb01gurations. Lower-mass remnants may allow a broader set of possible orbital parameters, mass ratios as well as gas content among the (higher angular momentum) progenitors leading to prolate-like rotation (Ebrov\u00b4 a & \u0141okas 2017). Prolate-like rotation does not strictly imply that the galaxy has a prolate mass distribution (or potential). This is nicely illustrated with idealised St\u00a8 ackel potentials, where prolate systems allow only inner and outer long-axis tube orbits (de Zeeuw 1985). Hence prolate galaxies can have velocity maps that either show prolate-like rotation or no-rotation. This is indeed found for the Illustris prolatelike galaxies; about 51% of actually prolate galaxies (using a tridimensional account of the mass distribution) show prolate-like rotation while the others have no net rotation (Li et al. 2018), presumably as they contain both prograde and retrograde long-axis tube orbits. Nevertheless, galaxies with prolate-like rotation cannot be oblate spheroids. Velocity maps of the M3G sample objects with prolate-like rotation show spatial variations, sometimes changing at larger radii to rotation around the major axis. This suggests more complex shapes, supporting various types of orbital families (de Zeeuw & Franx MNRAS 000, 1\u201311 (2017) Prolate-like rotation in massive galaxies 9 1010 1011 1012 1013 M  [M ] 1 10 Re [kpc] 50 70 100 150 200 250300 350 M3G NRR M3G PRO M3G RR A3D NRR A3D RR A3D PRO Figure 4. The distribution of the M3G sample on the mass size plane. The M3G sample is shown with symbols that have black edges and dominate the high-mass end. For reference we also show galaxies from the ATLAS3D sample with coloured symbols. The shape and the colour of the symbol is related to the kinematic type as indicated in the legend. The classi\ufb01cation is taken from Krajnovi\u00b4 c et al. (2011) with the following meanings: RR regular rotation, NRR non-regular rotation, and PRO prolate-like rotation (nominally the latter are part of the NRR group, but we highlight them here). Diagonal dashed lines are lines of constant velocity dispersion calculated using the virial mass estimator. The green shaded region shows the expected region where galaxies growing through dissipation-less mergers should lie, assuming major 1:1 mergers (dot-dashed red line) and multiple minor mergers (dotted blue line). The orange hatched region encompasses the mass size evolution of major merger remnants depending on the merger orbital parameters, as explained in Section 4. 1991). A classical example of such galaxies is NGC 4365 (Bender 1988), which has a large KDC and outer prolate-like rotation. Its orbital distribution is complex with both shortand long-axis tubes responsible for the formation of the observed (luminosity-weighted) kinematics (van den Bosch et al. 2008). This is also a characteristic of high-mass merger remnants, which often contain a large fraction of box orbits, shortand long-axis tubes, varying relatively to each other with radius (e.g. R\u00a8 ottgers et al. 2014). With such caveats in mind, it is worth assuming for a moment that M3G galaxies with prolate-like rotation are actually signi\ufb01cantly triaxial and close to being prolate. Prolate galaxies in the Illustris simulation are found only at masses larger than 3 \u00d7 1011 M\u2299, and above 1012 M\u229962 per cent of galaxies are prolate or triaxial, 43 per cent being prolate (Li et al. 2018). This is coincidentally close to our observed fraction of prolate-like systems (44%) within the M3G sample. The similarity between these fractions should be taken with caution, as we stress the M3G sample is neither complete nor a representative sample, and the number of actually prolate galaxies is certainly lower then the number of galaxies with prolate-like rotation. Notwithstanding the actual frequency and shape of galaxies with prolate-like rotation, they cluster in a special region of the mass size diagram, as Fig. 4 shows. The M3G sample lies on an extension of the arm-like protuberance arising from the cloud of galaxies at high masses and large sizes. The M3G data extend this arm by almost an order of magnitude in mass and a factor of 5 in size. At masses below 6 \u00d7 1011 M\u2299covered by previous surveys, galaxies that were found on this extension were typically old and metal-rich slow rotators characterised by a de\ufb01cit of light (cores) in their nuclear surface brightness pro\ufb01les (Emsellem et al. 2011; Cappellari et al. 2013a; Krajnovi\u00b4 c et al. 2013; McDermid et al. 2015). Speci\ufb01cally, their kinematic properties and the corelike light pro\ufb01les were used as an indication that the formation of these galaxies was di\ufb00erent from other galaxies populating the mass size plane, which are characterised as star-forming disks, or bulge dominated, oblate and fast rotating early-type galaxies (Cappellari et al. 2013a; Cappellari 2016). The most likely formation process of galaxies populating that extension is through dissipationless mergers of already massive galaxies: these may provide a way to explain their kinematics, low angular momentum content, cores in light pro\ufb01les (through binary black hole mergers, e.g. Ebisuzaki et al. 1991; Milosavljevi\u00b4 c & Merritt 2001) and old stellar populations. The M3G extension of the arm supports this picture in two additional ways. Firstly, it shows that while these galaxies span a large range in both mass and size, their e\ufb00ective velocity dispersions are not very di\ufb00erent, as expected in major dissipation-less mergers (e.g. Hopkins et al. 2009; Bezanson et al. 2009; Naab et al. 2009). Following the argument outlined in Naab et al. (2009), if a massive galaxy grows via equal-mass mergers (of progenitors with similar sizes and/or velocity dispersions), both the mass and the size of the remnant will increase by a factor of 2, while it will follow a line of constant velocity dispersion in Fig. 4. We illustrate this path with a red dot-dashed line, where products of consecutive equal-mass mergers would fall, for example starting with systems of M= 6 \u00d7 1011 M\u2299and Re = 7 kpc, representative of the most massive galaxies in the local Universe. The same increase in mass achieved through multiple minor mergers (with smaller mass, size and velocity dispersion progenitors) would lead to a size increase by a factor of 4, while the velocity dispersions would typically be reduced by a factor of 2. This corresponds to the blue dotted line in Fig. 4, starting from the same main galaxy progenitor (see also \ufb01g. 2 in Bezanson et al. 2009). Equal mass merger simulations show that the relation between the mass and the size of galaxies also depends on the merger parameters, such as the pericentric distance, type of the orbit and its angular momentum (Boylan-Kolchin et al. 2006). This study showed that depending on the merger orbit, the mass size relations follows Re \u223cM\u03b1 \u2217, where \u03b1 = 0.7\u22121.3. We add this range of possibilities on Fig. 4 as a hatched region, indicating the possible location for massive galaxies after major mergers, and fully encompassing M3G sample galaxies. A caveat in this simple argument is that some of the massive galaxies today will start merging as more compact objects in the early Universe, as is evident from the evolution of the mass size relation with redshift (van der Wel et al. 2014) and implied by compact size of high redshift quiescent galaxies and their subsequent evolution (e.g. van Dokkum et al. 2008, 2010). Inevitably the merger history of massive galaxies will be a combination of multiple minor mergers and a small number of major (or even equal) mass mergers (e.g De Lucia & Blaizot 2007; Johansson et al. 2012; Naab et al. 2014). The evidence for such a combination is visible in the di\ufb00erences between the central region (about 1 Re) and the outskirts, as they often do not share the same kinematics or stellar populations, which will be the topic of future papers. The tightness of the region on the mass size diaMNRAS 000, 1\u201311 (2017) 10 Davor Krajnovi\u00b4 c et al. gram within which the M3G galaxies lie suggests that the growth of the most massive galaxies (> 1012 M\u2299) and, in particular, BCGs is dominated by major mergers. This would be consistent with the \ufb01ndings by Li et al. (2018) that also links such massive mergers with prolate-like rotation. Given that more than half of the BCGs in our sample exhibits prolate-like rotation, we speculate that indeed most of these experienced a late major (dry) merger, between two massive (possibly both central) galaxies. A radial bias in the orbital con\ufb01gurations for such mergers leading to an increase fraction of prolate-like rotators may naturally emerge from the preset of phasespace distribution of massive galaxies, also relative to the largescale structures (West et al. 1995; Niederste-Ostholt et al. 2010; West et al. 2017). 5 CONCLUSIONS In this work, we report that a large fraction of galaxies more massive than 1012 M\u2299show prolate-like rotation. This is shown by the analysis of MUSE data of the magnitude-limited sample of massive galaxies in the Shapley Super Cluster and a matching (in luminosity) sample of BCGs. This M3G sample consists of 25 galaxies, of which 14 are BCGs, 11 are satellites in the SSC and 3 are BCGs in the SSC. We present their stellar velocity maps, and measure their kinematic misalignment angles, showing that 44 per cent of galaxies in the M3G sample have their main rotation around their major axes. Selecting only BCGs the fraction increases to 50 per cent, while in a magnitude limited subsample of satellites, prolate-like rotation is detected in 35 per cent of galaxies. The prolate-like rotation is suggestive of a triaxial or close to prolate intrinsic shape. For most of our galaxies rotation amplitudes are low, but velocity maps typically shows net streaming. These kinematics indicate a violent assembly history, with at least one major dissipation-less merger. The M3G data support a scenario where the \ufb01nal growth of the most massive galaxies is dominated by late dissipation-less merging of similar mass systems. This could be associated with the prevalence of prolate-like rotation in the most massive BCGs and is consistent with the location of these systems within a mass size diagram, which we extend by almost an order of magnitude in mass and a factor of 5 in size. The current sample suggests that there is a rather narrow path for climbing the last rung of the galaxy mass ladder, which would be characteristic of dense cluster environments. Answering whether or not such very massive systems require the merging of already central systems would require a more extended studies and a closer look at relevant simulations. The fact that BCGs seem to show an alignment trend with respect to the larger-scale structures may be a interesting avenue to consider, as it would naturally explain a bias in the orbital con\ufb01guration for equal-mass massive and late mergers. Interestingly enough, prolate-like rotation is also found in lower-mass galaxies (e.g. as seen by the ATLAS3D and the CALIFA surveys, as well in some dwarf galaxies). This further suggests that galaxies with prolate-like rotation should be present in low galactic density regions, while the progenitors may be quite di\ufb00erent (i.e. gas-rich). ACKNOWLEDGEMENTS We wish to thank Joop Schaye, Michael Maseda and Marijn Franx for useful discussions and the full MUSE GTO team for support during observations and preliminary work on this paper. We thank Chung-Pei Ma and the MASSIVE team for sharing their results on the kinematic misalignment. This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. This research made use of Astropy, a communitydeveloped core Python package for Astronomy (Astropy Collaboration, 2013).",
                    "introduction": "The orbital structure is a powerful tracer of the formation pro- cesses shaping galaxies. As galaxies acquire gas, accrete satellites or merge with similar size objects, new populations of stars are cre- ated and the mass and luminosity distributions evolve. The changes in the gravitational potential have a direct in\ufb02uence on the allowed and realised trajectories, providing for a variety of observed stellar kinematics. As observers, we thus hope to constrain the ingredi- ents (and chronology) which shaped galaxies by probing the spatial variations of the line-of-sight velocity distribution (LOSVD). Theoretical insights, based on analytical and numerical work, are crucial for the interpretation of the observed stellar kinemat- ics of galaxies (see e.g., de Zeeuw & Franx 1991). In an idealised \u22c6E-mail:dkrajnovic@aip.de system with triaxial symmetry, assuming a gravitational potential expressed in a separable form (e.g. St\u00a8 ackel potentials as introduced by Eddington 1915), there exist a few families of dissipation-less orbits which stars can adopt: box orbits, short-axis tubes, inner and outer long-axis tubes (de Zeeuw 1985). In such systems, symme- try changes, for example between spherical, oblate or prolate axial symmetries, limit the stability of orbital families. de Zeeuw (1985) showed that a purely oblate spheroid should consist of only short- axis tubes, and therefore show a typical streaming around its mi- nor axis, unless there is an equal amount of stars on both prograde and retrograde orbits canceling out the net streaming. A prolate spheroid allows only inner and outer long-axis tubes, and stream- ing around the major axis of the galaxy. The argument can also be reversed to state that galaxies with only long axis tubes cannot be oblate and axisymmetric, or even triaxial, and that a galaxy with short axis tubes does not have prolate symmetry. c \u20dd2017 The Authors arXiv:1802.02591v2  [astro-ph.GA]  20 Apr 2018 2 Davor Krajnovi\u00b4 c et al. The velocity maps of triaxial spheroids, viewed at random angles, can exhibit a rich variety of kinematic features. This is a direct consequence, as pointed out by de Zeeuw & Franx (1991), of the freedom in the direction of the total angular momentum re- sulting from the orbital mixture, and the momentum vector which can lie anywhere in the plane containing the major and minor axis of the galaxy. This was illustrated by Statler (1991) with models viewed along various orientation angles, and associated with ac- tually observed galaxies with complex kinematics (e.g. NGC 4356 and NGC 5813; van den Bosch et al. 2008; Krajnovi\u00b4 c et al. 2015, respectively) Observational studies using long-slits were able to investigate velocity features along selected angles (often along the minor and major photometric axes), and revealed that a majority of galaxies exhibit negligible rotation along their minor photometric axis (e.g. Davies et al. 1983; Davies & Illingworth 1983; Bender et al. 1994), while a few massive elliptical galaxies show more complex rotation indicating the presence of long-axis tubes and signi\ufb01cant rotation around their major axis (e.g. Illingworth 1977; Schechter & Gunn 1979; Wagner et al. 1988). A major change in this \ufb01eld came from the proliferation of the integral-\ufb01eld spectrographs (IFS) and their ability to map the distribution of velocities over a signi\ufb01cant frac- tion of the galaxy. The last decade of IFS observations has revealed that the vast majority of galaxies actually has very regular velocity maps within their half light radii (e.g. Emsellem et al. 2004; Kra- jnovi\u00b4 c et al. 2011; Houghton et al. 2013; Scott et al. 2014; Fogarty et al. 2015; Falc\u00b4 on-Barroso et al. 2017; Graham et al. 2018). The ATLAS3D project (Cappellari et al. 2011a) addressed this more speci\ufb01cally via a volume limited survey of nearby early-type galaxies, demonstrating that galaxies with complex velocity maps comprise only about 15% of the local population of early-type galaxies (Krajnovi\u00b4 c et al. 2011), and that the majority is consis- tent with oblate rotators (notwithstanding the presence of a bar, see Krajnovi\u00b4 c et al. 2011; Weijmans et al. 2014). The regular and non- regular rotator classes seem to re\ufb02ect a signi\ufb01cant di\ufb00erence in their speci\ufb01c stellar angular momentum content, allowing an em- pirical division of early-type galaxies into fast and slow rotators (Emsellem et al. 2007, 2011). Krajnovi\u00b4 c et al. (2008) also empha- sised the fact that axisymmetric fast rotators have regular velocity \ufb01elds which qualitatively resemble those of disks. The internal or- bital structure of these galaxies can, however, be complex, as ev- idenced by the range of photometric properties (e.g. disk-to-bulge ratio) and the common presence of tumbling bars. There are several caveats which need to be emphasised. Firstly, the intrinsic shape of a galactic system is seldom well de- \ufb01ned by a single number, e.g., the apparent ellipticity varies with radius. Along the same lines, the terms \u201dtriaxial\u201d or \u201doblate\u201d sys- tems may not even be appropriate when the intrinsic ratios and/or the position angle of the symmetry axes change with distance from the centre: the gravitational potential of a galaxy could smoothly vary from oblate in the centre to strongly triaxial or prolate in the outer part, with the main symmetry axes not even keeping the same orientation. Secondly, ellipsoids are certainly a very rough approx- imation when it comes to describing the intrinsic shapes of galax- ies, as they have overlapping components with di\ufb00erent \ufb02attenings, varying bulge-to-disk ratios, and often host (tumbling) bars. While the observed kinematics of fast rotators (including also higher mo- ments of the LOSVD, Krajnovi\u00b4 c et al. 2008, 2011; van de Sande et al. 2017) seem to indicate that their internal orbital structure is dominated by short-axis tube orbits (and streaming around the minor axis), numerical simulations of idealised mergers and those performed within a cosmological context naturally predict the co- existence of multiple orbital families, the central and outer regions often being dominated by box and short-axis tube orbits, respec- tively (e.g. Jesseit et al. 2005; Ho\ufb00man et al. 2010; R\u00a8 ottgers et al. 2014). The division of galaxies into fast and slow rotators connects also with two dominant channels of galaxy formation (as reviewed in Cappellari 2016). Present spirals and fast rotators are mostly de- scendants of star forming disks and their evolution is dominated by gas accretion, star formation, bulge growth and eventual quench- ing. The slow rotators may also start as turbulent star-bursting disks at high redshift (e.g. Dekel et al. 2009; Kere\u02c7 s et al. 2009), or be hosted by haloes with small spin parameters (Lagos et al. 2017), but the late evolution of most slow rotators is dominated by merg- ers with gas poor galaxies (De Lucia & Blaizot 2007; Dekel et al. 2009; Williams et al. 2011; Kaviraj et al. 2015). The \ufb01rst channel therefore favours regular kinematics and internal orbital structure dominated by short-axis tubes, while the second channel implies dynamically violent redistribution of orbits and the creation of tri- axial or prolate-like systems, which include a signi\ufb01cant fraction of long-axis tubes. A strong mass dependence has been emphasised, with more massive galaxies being more likely to follow the second channel (Rodriguez-Gomez et al. 2016; Qu et al. 2017). A clear manifestation of the triaxial nature of galaxies is a non-zero value of the kinematic misalignment angle, \u03a8, the an- gle between the photometric minor axis and the orientation of the apparent angular momentum vector (Franx et al. 1991). In an ax- isymmetric galaxy, the apparent angular moment coincides with the intrinsic angular momentum and is along the minor axis, hence \u03a8 = 0. Triaxial galaxies can exhibit any value of \u03a8, while pro- late galaxies with signi\ufb01cant rotation would have \u03a8 closer to 90\u25e6. Galaxies with large \u03a8 exist (Franx et al. 1991; Cappellari et al. 2007; Krajnovi\u00b4 c et al. 2011; Fogarty et al. 2015; Tsatsi et al. 2017) and are typically more massive than 1011 M\u2299(but for dwarf galax- ies see e.g. Ho et al. 2012; Ry\u00b4 s et al. 2013). It is, however, not clear if prolate-like systems feature prominently at high mass and if this links preferentially to a speci\ufb01c channel of galaxy evolution. Galaxies at the top of the mass distribution are intrinsically rare. They are mostly found in dense environments, often as the brightest members of groups or clusters. Brightest cluster galaxies (BCGs) are usual suspects, and are known to have low amplitude or zero rotation (Loubser et al. 2008; Jimmy et al. 2013; Oliva- Altamirano et al. 2017). Still, current surveys of massive galaxies have so far o\ufb00ered little evidence for large \u03a8 values or clear-cut signatures for strong triaxiality (e.g. Veale et al. 2017b). In this work, we present the \ufb01rst results from an observation-based survey, the M3G (MUSE Most Massive Galaxies; PI: Emsellem) project, aimed at mapping the most massive galaxies in the densest galaxy environments at z \u22480.045 with the MUSE/VLT spectrograph (Ba- con et al. 2010). We focus on presenting the stellar velocity maps, emphasising the relatively large number of prolate-like systems, i.e., galaxies with rotation around the major axis. The orbital dis- tribution of galaxies exhibiting large values of \u03a8 (and having net rotation around the major axis) are thought to be dominated by long-axis tubes: we will thus refer to such cases as prolate-like ro- tation1. However, as mentioned above, and discussed in Section 4, 1 An alternative name used in the literature is minor-axis rotation, as the gradient of the velocities is along the major axis, and it should be di\ufb00eren- tiated from rotation around the minor axis present in oblate axisymmetric systems. To avoid any ambiguity, next to the de\ufb01ned prolate-like rotation, we will use the nomenclature from Krajnovi\u00b4 c et al. (2011), where regular rotation is used for oblate rotators with velocity maps consistent with those MNRAS 000, 1\u201311 (2017) Prolate-like rotation in massive galaxies 3 we caution the reader that this does not imply that these are prolate systems. Presenting the complete survey, its data products and sub- sequent results is beyond the scope of the current publication and will be presented in forthcoming papers. In Section 2 we brie\ufb02y report on the observations and the data analysis. We present the main results on the rotational characteris- tics of the M3G sample in Section 3, which is followed by a discus- sion in Section 4 and a brief summary of conclusions in Section 5."
                },
                {
                    "url": "http://arxiv.org/abs/1305.4973v2",
                    "title": "The ATLAS3D Project -- XXIII. Angular momentum and nuclear surface brightness profiles",
                    "abstract": "[Abridged and Edited] We investigate nuclear light profiles in 135 ATLAS3D\ngalaxies for which the Hubble Space Telescope (HST) imaging is available and\ncompare them to the large scale kinematics obtained with the SAURON\nintegral-field spectrograph. Specific angular momentum, lambda_R, correlates\nwith the shape of nuclear light profiles, where cores are typically found in\nslow rotators and core-less galaxies are fast rotators. Cores are found only in\nmassive galaxies and only in systems with the stellar mass M>8x10^10 Msun.\nBased on our sample, we, however, see no evidence for a bimodal distribution of\nnuclear slopes. The best predictor for finding a core is based on the stellar\nvelocity dispersion within an effective radius, sigma_e, and specific angular\nmomentum, where cores are found for lambda_R<0.25 and sigma_e>160 km/s. We\nestimate that only about 10% of nearby early-type galaxies contain cores.\nFurthermore, we show that there is a genuine population of fast rotators with\ncores. We also show that core fast rotators are morphologically, kinematically\nand dynamically different from core slow rotators. The cores of fast rotators\ncould harbour black holes of similar masses to those in core slow rotators, but\ntypically more massive than those found in core-less fast rotators. Core-less\ngalaxies, and especially core-less fast rotators, are under-luminous in the\ndiffuse X-ray emission, but the presence of a core does not imply high X-ray\nluminosities. We postulate a possible population of core-less galaxies among\nslow rotators, which can not be explained as face-on discs, but comprise a\ngenuine sub-population of slow rotators. These galaxies are typically less\nmassive and flatter than core slow rotators, and show evidence for dynamical\ncold structures and exponential photometric components. We discuss possible\nprocesses for formation of cores and their subsequent preservation.",
                    "authors": "Davor Krajnovic, A. M. Karick, Roger L. Davies, Thorsten Naab, Marc Sarzi, Eric Emsellem, Michele Cappellari, Paolo Serra, P. T. de Zeeuw, Nicholas Scott, Richard M. McDermid, Anne-Marie Weijmans, Timothy A. Davis, Katherine Alatalo, Leo Blitz, Maxime Bois, Martin Bureau, Frederic Bournaud, Alison Crocker, Pierre-Alain Duc, Sadegh Khochfar, Harald Kuntschner, Raffaella Morganti, Tom Oosterloo, Lisa M. Young",
                    "published": "2013-05-21",
                    "updated": "2013-06-13",
                    "primary_cat": "astro-ph.CO",
                    "cats": [
                        "astro-ph.CO"
                    ],
                    "main_content": "The ATLAS3D sample is defined in Paper I and consists of 260 early-type galaxies, visually selected from a magnitude (brighter than -21.5 mag in the K-band) and volume limited (within 42 Mpc) parent sample. The full sample was observed with the integral-field spectrograph (IFS) SAURON (Bacon et al. 2001) mounted on William Herschel Telescope. The extraction of kinematics from the SAURON data is described in Paper I and Emsellem et al. (2004, for the subsample of 48 galaxies previously presented in the SAURON survey). We searched the HST archive for observations of ATLAS3D galaxies with three imaging instruments: Widefield Planetary Camera 2 (WFPC2, Holtzman et al. 1995), Advanced Camera for Surveys (ACS, Ford et al. 1998) and Wide-field Camera 3 (WFC3). We imposed the requirements that the nucleus is positioned on the central chip (PC1) of the WFPC2, and that it is close to its centre. The first requirement ensures the data are of high spatial resolution and sampling, and the second that one can derive large enough radial light profiles. While our choice of using only the PC1 chip ensures that the three instruments have similar and highest available spatial resolution (0.045\u2032\u2032/pixel for WFPC2, 0.049\u2032\u2032/pixel for ACS and 0.05\u2032\u2032/pixel for WFC3), the radial extent of the data is different. ACS and WFC3 have a larger field-of-view of \u223c100\u2032\u2032compared to 34\u2032\u2032 for WFPC2 PC1. This distinction between the data sets will be used later as an argument for the analysis method (see Section 3). The search yielded 135 galaxies which satisfied these basic criteria, originating in a variety of observing programmes. A number of galaxies were observed with multiple instruments and we always favoured ACS data, unless the ACS imaging contained nuclear artefacts which could not be accounted for. While WFPC2 provides somewhat higher spatial resolution and a better behaved point-spread function (PSF), ACS images have a larger extent. As there were no galaxies observed only with WFC3, we again decided to favour ACS data to keep the analysis as uniform and similar as possible. Some of the observing programmes were initiated with the analysis of the nuclear profiles in mind and there are 86 ATLAS3D objects with already published light profiles. However, the characterisation of their light profiles was heterogeneous, and we decided to (re)analyse a total of 104 galaxies, often to exploit the more recent ACS imaging, while we used the published values for 31 profiles. In the following two subsections we outline our approach to previously published and unpublished analysis of the nuclear properties of ATLAS3D galaxies. A table with results of our analysis can be found in Appendix C. 2.1 Published ACS and WFPC2 surface brightness profiles Forty-four ATLAS3D galaxies are in the ACS Virgo Cluster Survey (ACSVCS, C\u02c6 ot\u00b4 e et al. 2004) and their deconvolved surface brightness profiles were already published in Ferrarese et al. (2006). The data were kindly provided to us by the ACSVCS team (L. Ferrarese, private communication). A full description of their data reduction, PSF deconvolution and isophote fitting are described in Ferrarese et al. (2006). In Section 3 we describe our choice of profile parameter fitting, which is different to the analysis presented in Ferrarese et al. (2006). Finally, we used ACS imaging for 43 galaxies, excluding one object due to a nuclear artefact on the image. A comprehensive collection of WFPC2 data was presented in Lauer et al. (2007b) and of their 219 objects collected from the literature there are 61 in common with the ATLAS3D sample (used by Lauer 2012), excluding two galaxies with only Wide Field/Planetary Camera 1 imaging. Of these, we used the information for 18 objects presented in Lauer et al. (2005), which include some data previously published by the same team in Lauer et al. (1995) and Faber et al. (1997). Furthermore, we used 10 objects c \u20dd2012 RAS, MNRAS 000, 2\u201332 Angular momentum and nuclear light pro\ufb01les 5 Table 1. Summary of observations analysed in this work from the HST Legacy Archive. Observations no. of objects instrument \ufb01lter GO-9353 1 ACS/WFC1 F555W GO-9293 1 ACS/WFC2 F814W GO-9399 1 ACS/WFC F606W GO-9788 4 ACS/WFC1 F814W GO-10003 1 ACS/WFC F475W GO-10554 3 ACS/WFC F475W GO-11679 2 ACS/WFCENTER F475W GO-10594 3 ACS/WFCENTER F475W GO-10705 1 ACS/WFC F555W GO-6554 2 WFPC2/PC1 F555W GO-5741 1 WFPC2/PC1 F555W GO-6357 8 WFPC2/PC1-FIX F702W GO-6633 2 WFPC2/PC1-FIX F555W GO-8212 1 WFPC2/PC1 F814W SNAP-5479 4 WFPC2/PC1 F606W GO-7403 1 WFPC2/PC1 F702W SNAP-5446 1 WFPC2/PC1 F555W SNAP-5446 7 WFPC2/PC1 F606W SNAP-8597 2 WFPC2/PC1 F606W SNAP-9042 1 WFPC2/WFALL F606W GO-6785 1 WFPC2/PC1 F702W SNAP-5999 3 WFPC2/PC1 F555W GO-6107 1 WFPC2/PC1-FIX F555W GO-5454 1 WFPC2/PC1 F555W GO-7450 3 WFPC2/PC1 F814W GO-5920 1 WFPC2/PC1 F555W GO-8686 1 WFPC2/PC1 F814W from Rest et al. (2001), 4 from Ravindranath et al. (2001) and 1 from Quillen et al. (2000). The latter \ufb01ve objects were actually observed with NICMOS, but a further search through the archive did not return galaxies only observed with NICMOS. The remaining objects have ACS imaging, either already published or in the archive. For NGC4660 we used the published WFPC2 pro\ufb01le of Lauer et al. (1995, 2005) instead of the ACS image which had an artefact in the nuclear region. For further 14 galaxies we used archival WFPC2 images to extract pro\ufb01les (see Section 2.2) and performed our own \ufb01ts. This was done based on disagreement between Lauer et al. (2007b) and subsequent studies (see Appendix A) or to test for the in\ufb02uence of dust (see Appendix B). 2.2 Archival HST/ACS and WFC2 data A search through the Hubble Legacy Archive (HLA) revealed additional 58 galaxies in common with the ATLAS3D sample. In Table 1 we list the observing programs, instruments and \ufb01lters used. Of these 42 galaxies have WFPC2/PC1 imaging and the remaining 16 have ACS images. In Sections 3.1 and 3.2 we outline the extraction of surface brightness pro\ufb01les and the analysis. 3 ANALYSIS 3.1 Surface-brightness pro\ufb01les Surface-brightness pro\ufb01les were constructed using the iraf.stsdas task ellipse. A full description of the task is given in Jedrzejewski (1987). Briey, the intensity I(\u03a6) is azimuthally sampled along each ellipse, described by the semimajor axis length from the ellipse centre, position angle \u03a6 and ellipticity \u01eb. As the \ufb01tting proceeds the semi-major axis is increased logarithmically such that the proceeding ellipse has a semi-major axis which is 10 per cent larger. The best\ufb01tting parameters for each ellipse (ellipse centre, \u03a6 and \u01eb) are determined by minimising the sum of squares of the residuals between the data and the \ufb01rst two moments in the Fourier expansion. Since these parameters may be signi\ufb01cantly in\ufb02uenced by dust and foreground stars, bad object masks were created prior to \ufb01tting. This method is similar to that used in Ferrarese et al. (2006). Deconvolved pro\ufb01les were approximated in the following way. For each instrument and \ufb01lter combination a single PSF image was created (at the aperture centre of the ACS/WFC and WFC2/PC1 \ufb01elds), using TinyTIM (Krist et al. 2011), representative of a galaxy with a blackbody spectrum with temperature of 6500K. The original source HST image was convolved with the PSF image, using the iraf.stsdas task fconvolve, to create a smoothed image. We applied the same best-\ufb01tting ellipse parameters (ellipse centre, \u03a6 and \u01eb) from the source image to the convolved image to extract smoothed surface brightness pro\ufb01les. Using convolution theory a good approximation to the deconvolved pro\ufb01le is described as: SBdeco \u223c2 \u00d7 SBorig \u2212SBconv, where SBdeco, SBorig and SBconv are the deconvolved, original and convolved (smoothed) surface brightness pro\ufb01les, respectively. The errors on the SBdeco are estimated as a quadrature sum of the errors on SBorig and SBconv pro\ufb01les. To make comparisons with previous work (Rest et al. 2001; Lauer et al. 2005, 2007b), the HST/ACS g\u2212(F475W) band surface brightness pro\ufb01les (both ACSVCS pro\ufb01les and archival observations) were converted to F555W (broadband V) photometry, following the photometric transformations in Sirianni et al. (2005) and using g\u2212band and r\u2212band colours (Petrosian magnitudes) from SDSS DR5. 3.2 Nuker Pro\ufb01le A number of analytic \ufb01tting functions can be used to probe the internal structure of galaxies. To explore the core region of galaxies we \ufb01t the \u201cNuker law\u201d (Lauer et al. 1995), to our surface brightness pro\ufb01les: I(r) = 2(\u03b2\u2212\u03b3)/\u03b1Ib \u0010rb r \u0011\u03b3 \u0014 1 + \u0012 r rb \u0013\u03b1\u0015(\u03b3\u2212\u03b2)/\u03b1 (1) where \u03b3 is the inner cusp slope as r \u21920 and is distinguished from \u03b3\u2032, which is the purely local (logarithmic) gradient of the luminosity pro\ufb01le evaluated at the HST angular resolution limit, r\u2032 (by default we adopt r\u2032 = 0. \u2032\u20321, except for objects taken from the literature where we keep the published values), where (Rest et al. 2001; Trujillo et al. 2004): \u03b3\u2032 \u2261\u2212d log I d log r \f \f \f \f \f r=r\u2032 = \u2212\u03b3 + \u03b2(r\u2032/rb)\u03b1 1 + (r\u2032/rb)\u03b1 (2) c \u20dd2012 RAS, MNRAS 000, 2\u201332 6 Davor Krajnovi\u00b4 c et al. In this description, core galaxies exhibit a \u201cbreak\u201d radius, rb which marks a rapid transition (moderated by \u03b1) to a shallower cusp in surface brightness. We also follow Carollo et al. (1997) and Lauer et al. (2007a) in de\ufb01ning a \u201ccusp radius\u201d: r\u03b3 \u2261rb \u0012 0.5 \u2212\u03b3 \u03b2 \u22120.5 \u00131/\u03b1 (3) With this de\ufb01nition r\u03b3 is a radius at which the negative logarithmic slope of the galaxy surface brightness pro\ufb01le, \u03b3\u2032, as de\ufb01ned by the parameters of the \u201cNuker\u201d \ufb01t, equals 0.5. For galaxies with cores, r\u03b3 can be used as a core scale parameter, as advocated by Carollo et al. (1997) and demonstrated by Lauer et al. (2007a) on a large sample. As recently shown by Dullo & Graham (2012), r\u03b3 can be used as an approximate break radius of the core-S\u00b4 ersic model, or a transition radius between the inner core and the outer S\u00b4 ersic pro\ufb01le3. For galaxies with \u03b3 \u2a7e0.5 at r = 0.5\u2032\u2032we adopt R\u03b3 < 0.1\u2032\u2032, or the size that was used in the original publication, re\ufb02ecting the spatial resolution of our study. When necessary, light pro\ufb01les were previously prepared as described in Section 2.2. The \ufb01ts were done using our own least squares minimization routine which is based on the IDL routine mpfit.pro4 (Markwardt 2009), an idl implementation of the minpack algorithm (Mor\u00b4 e et al. 1980). To minimise the e\ufb00ect of the PSF and when working with deconvolved pro\ufb01les, we \ufb01t for radii beyond 2 \u22123\u03c3 of the ACS/WFPC2 point-spread function (0.1\u20130.2\u2032\u2032). We apply the same weighting to each data point in order to limit any bias from the outermost isophotes which may depend signi\ufb01cantly on the sky determination. A similarly robust technique was adopted by Stott et al. (2011) in their study of the pro\ufb01les of bright cluster galaxies. Table C1 contains the Nuker best-\ufb01tting parameters and additional parameters used in the study. In order to classify the pro\ufb01les depending on their local slope \u03b3\u2032, we begin by adopting the same nomenclature from Lauer et al. (2005): core galaxies are de\ufb01ned to have \u03b3\u2032 \u2a7d0.3 and power-law (\u201ccuspy\u201d) galaxies are de\ufb01ned to have a steeper inner slope with \u03b3\u2032 \u2a7e0.5. Galaxies with 0.3 < \u03b3\u2032 < 0.5, \ufb01rst introduced by Rest et al. (2001), we also call intermediate galaxies, but we stress that this does not represent a physical transition between power-law and core galaxies. Likewise, we consider power-law and intermediate galaxies to be galaxies that have no resolved cores. This does not exclude the possibility of nuclear cores on smaller spatial scales than probed by our data. Galaxies which are not \ufb01tted well with this functional form we call uncertain and we discuss them in more details below and show their images in Section B. The largest number of galaxies can be classi\ufb01ed as power-law (78/135 or 58 per cent), second most numerous are cores (24/135 or 18 per cent), followed by the number of intermediate galaxies (20/135 or 15 per cent). There were also 13 (9 per cent) uncertain galaxies, namely: NGC2824, NGC3032, NGC3073, NGC3607, NGC4111, NGC4233, NGC4435, NGC4526, NGC4694, 3 We note that for calculation of r\u03b3 we use the parameters of the \u201cNuker\u201d model, while Dullo & Graham (2012) use a nonparametric estimate. 4 http://purl.com/net/mp\ufb01t NGC4710, NGC5866, NGC7465 and UGC05408. All these galaxies have strong dust features in the nuclei, which we show in Fig B1 and discuss in Appendix B. For these galaxies we simply do not o\ufb00er a classi\ufb01cation and we exclude them from analysis, although a reasonable assumption would be that they do not harbour cores. 3.3 The choice of parametrisation While the \u201cNuker law\u201d might not be the best choice to describe the global light pro\ufb01les of galaxies (Graham et al. 2003; Trujillo et al. 2004), a consensus as to what method one should use when describing the galaxy nuclei does not seem to be reached in the recent literature (e.g. Lauer et al. 2005; Ferrarese et al. 2006; Lauer et al. 2007b; C\u02c6 ot\u00b4 e et al. 2007; Kormendy et al. 2009; Dullo & Graham 2012; Lauer 2012). As an alternative to the \u201cNuker law\u201d, Graham et al. (2003) proposed a hybrid function, combing a power-law with the S\u00b4 ersic (1968) function into a so-called \u201ccore-S\u00b4 ersic\u201d model5. The main bene\ufb01t of this model is that it can \ufb01t well a large radial range of the light pro\ufb01les (using the S\u00b4 ersic pro\ufb01le), as well as the depleted cores of elliptical galaxies (using a power-law function). With this parametrisation, powerlaw and intermediate galaxies are typically \ufb01tted with a pure S\u00b4 ersic model, while core galaxies require the core-S\u00b4 ersic model. The underlying problem is that none of the proposed \ufb01tting formulas have a physical foundation, and it is natural to expect that di\ufb00erent methods will give di\ufb00erent parameters, even if these parameters characterise the same property, such as the break radius. The classi\ufb01cation into core or core-S\u00b4 ersic pro\ufb01les, as well as into power-law (and intermediate) and S\u00b4 ersic, could di\ufb00er by up to 20 per cent (Dullo & Graham 2012, who \ufb01tted Sersic models only to the inner \u223c10\u2032\u2032 of light pro\ufb01les), but this is argued against by Lauer (2012), who suggest some 10 per cent discrepancies when outer regions of the light pro\ufb01les are included in the \ufb01t, as advocated by Graham et al. (2003) and Kormendy et al. (2009). We \ufb01nd a discrepancy between the two approaches in a few special cases. For these galaxies, it is not clear if this is actually driven by the way the \ufb01tting is done (i.e. radial extent used), by the data quality (e.g. PSF e\ufb00ects), or they can be similarly well described by both approaches. Furthermore, one should keep in mind that depleted cores from the S\u00b4 ersic formalism and the \u201cNuker\u201d cores are not exactly the same structures. In Appendix A we compare our classi\ufb01cation with results in recent literature and show that, if one is only interested to separate cores from the rest of the pro\ufb01les within the data collected in this work, there are no signi\ufb01cant di\ufb00erence between the two approaches. It is obvious that the \u201cNuker law\u201d can not \ufb01t the full radial range of a galaxy light pro\ufb01le, and it was intended to describe only its central regions. Rest et al. (2001) show that its double power law form is not adequate to \ufb01t those pro\ufb01les that change smoothly (from steep to \ufb02at). Ultimately, the full light pro\ufb01les of galaxies can not be parameterised in such a way (e.g. de Vaucouleurs 1953; S\u00b4 ersic 1968; Caon et al. 1993). To obtain robust physical parameters, such as the 5 See also Gualandris & Merritt (2012) for a discussion on di\ufb00erences between core-S\u00b4 ersic and King (1962) models. c \u20dd2012 RAS, MNRAS 000, 2\u201332 Angular momentum and nuclear light pro\ufb01les 7 Figure 1. Surface brightness pro\ufb01les as a function of semi-major radius of all HST ACS (top) and WFPC2 (bottom) galaxies analysed in this work. On each panel are shown (from left to right): \u201dcore\u201d \u03b3\u2032 \u2a7d0.3, \u201dintermediate\u201d 0.3 < \u03b3\u2032 < 0.5, \u201dpower-law\u201d \u03b3\u2032 \u2a7e0.5 galaxies. The region over which the Nuker \ufb01t is applied is shown in red, and corresponds to typically 0.1\u2032\u2032\u2013 50\u2032\u2032 for ACS imaging and 0.1\u2032\u2032\u2013 10\u2032\u2032 for WFPC2 PC1 imaging. In both top and bottom panels galaxies are ordered by their total K-band luminosity starting with the brightest at the top and o\ufb00set downwards for 0.25 mag/\u2032\u20322 (left panels) and 0.1 mag/\u2032\u20322 (middle and right panels). Galaxy names follow the sequence of pro\ufb01les. The information on the \ufb01lters used is given in Table C1. The pro\ufb01le with the steep rise in the top left panel is NGC4486, where the inner pro\ufb01le is dominated by the contribution of the active nucleus. This component is ignored in the \ufb01t as well in the ordering of this galaxy in the \ufb01gure. c \u20dd2012 RAS, MNRAS 000, 2\u201332 8 Davor Krajnovi\u00b4 c et al. break radius, or the amount of light that is depleted, or in excess, one needs to parameterise robustly the full radial range. Therefore, S\u00b4 ersic and core-S\u00b4 ersic \ufb01tting functions are more suitable as they can reproduce most of the pro\ufb01le, although it is often necessary to add multiple components to (e.g. de Jong et al. 2004; Weinzirl et al. 2009; Richings et al. 2011; Fabricius et al. 2012; Turner et al. 2012,; Paper XVII). When using the S\u00b4 ersic function, however, it is imperative to have large radial extent of the light pro\ufb01les as the overall results will depend on the actual radial range used during the \ufb01t (e.g. Graham et al. 2003; Trujillo et al. 2004; Kormendy et al. 2009). Additionally, as shown by Ferrarese et al. (2006) and Kormendy et al. (2009), the local nature of \u201cNuker\u201d pro\ufb01les can result in missing compact nuclear structures, such as large cores with extra light or extralight pro\ufb01les with small cores (see \ufb01g. 111 in Ferrarese et al. 2006, for an informative illustration of possible pro\ufb01les). The light pro\ufb01les we wish to analyse extend to di\ufb00erent radii, due to observations with di\ufb00erent HST cameras (e.g. limited extent of WFPC2/PC1 data), \ufb01lters and exposure times. In Paper XVII, we showed that our sample consists of a large number of galaxies whose outer light pro\ufb01les require multiple components (e.g. S\u00b4 ersic and exponential pro\ufb01les and/or components describing bars, rings and ovals). As we are primarily interested in determining whether a galaxy has a core or not, in order to ensure a uniform and relatively simple analysis across the sample, we prefer to use the \u201cNuker law\u201d and \ufb01t only the nuclear regions. An alternative would be to assemble deep ground-based data (in various \ufb01lters) and combine it with HST pro\ufb01les, but this is beyond the scope of this paper. 3.4 Core and core-less nuclei In Fig. 1 we show light pro\ufb01les of the 91 galaxies analysed in this work (13 \u201duncertain\u201d galaxies are not shown here). They are grouped in those obtained with the ACS (top) and those with WFPC2 (bottom). Furthermore, we separate them according to standard classi\ufb01cations into core, intermediate and power-law pro\ufb01les. As shown by other studies (Graham & Guzm\u00b4 an 2003; Trujillo et al. 2004; Ferrarese et al. 2006; C\u02c6 ot\u00b4 e et al. 2006, 2007), this separation is not necessary related to a strong physical di\ufb00erence between these pro\ufb01les, and by putting them all together emerges a continuous sequence of pro\ufb01les. In the top panel of Fig. 2 we plot the \u03b3\u2032 slope of the Nuker pro\ufb01les against the total absolute luminosity in the r-band from Table 1 of Cappellari et al. (2012b, hereafter Paper XV), which was derived from the MGE models (Emsellem et al. 1994) of the ATLAS3D sample by (Scott et al. 2012, hereafter Paper XXI). As previously noted (van den Bosch et al. 1994; Faber et al. 1997; Rest et al. 2001; Ravindranath et al. 2001; Lauer et al. 2005), there is an overlap in luminosity between of galaxies with di\ufb00erent nuclear slopes, but there is also a clear trend that brighter galaxies have lower \u03b3\u2032 slopes, with no galaxies fainter than \u221220.6 and \u03b3\u2032 < 0.3 and there are no galaxies brighter than \u221221.5 and \u03b3\u2032 > 0.5, using our r-band parametrisation. There are a few galaxies with \u221222 < Mr < 21.5 and intermediate values of \u03b3\u2032. In the bottom panel, we use mass estimates from Paper XV to investigate the \u03b3\u2032 dependence further. The mass Figure 2. Distribution of total r-band magnitude (top) and dynamical mass (bottom) with respect to the \u03b3\u2032 slope of the \u201cNuker\u201d pro\ufb01les at the angular resolution of 0.1\u2032\u2032. is obtained from Jeans anisotropic models (Cappellari 2008) and comprises both the stellar and dark matter, although the dark matter typically does not contribute with more than 12 per cent (see Paper XV for details). The mass6 is de\ufb01ned as M = L\u00d7(M/L)e \u22482\u00d7M1/2, where M1/2 is the mass within a sphere enclosing half of the galaxy light and (M/L)e is the mass to light ratio within the same region. As is the case in the magnitude plot, there is an overlap zone in mass between \u223c10.8 and \u223c11.2 (in logM\u2299), with no core galaxies below and no power-law or intermediate (except one) galaxies above this zone, respectively. While there seems to be a continuous sequence in mass and magnitude, similar to what was found before (C\u02c6 ot\u00b4 e et al. 2007; Glass et al. 2011), the continuity of \u03b3\u2032 parameters seems to be interrupted at just above \u03b3\u2032 = 0.3. To investigate this further we plot in Fig. 3 two histograms of \u03b3\u2032, highlighting the dependence on mass and angular momentum in the top and bottom panels, respectively. Signi\ufb01cantly more than reported in previous studies (Rest et al. 2001; Ravindranath et al. 2001; Lauer et al. 2007b), we \ufb01nd in our sample a number of galaxies populating the intermediate range of 0.3 < \u03b3\u2032 < 0.5, but we also see a mild excess of galaxies with \u03b3\u2032 \u223c0.15 \u22120.2. This excess is, however, statistically not signi\ufb01cant, but it is strongly dependant on the de\ufb01nition of \u03b3\u2032. \u03b3\u2032 is not a physically well de\ufb01ned parameter as it is a measure of the pro\ufb01le curvature at a radius \ufb01xed by the resolution of the HST. Studies applying the \u201cNuker law\u201d used a range of radii to calculate \u03b3\u2032. Lauer et al. (2005) and Lauer et al. (2007b) used 0. \u2032\u203202 or 0. \u2032\u203204 depending on the quality of the imaging, attempting to use the smallest angular radius at which a pro\ufb01le\u2019s slope could be estimated. 6 The mass we use is the one called MJAM in Paper XV. c \u20dd2012 RAS, MNRAS 000, 2\u201332 Angular momentum and nuclear light pro\ufb01les 9 Figure 3. Histograms of the \u03b3\u2032 distribution. The top histogram divides galaxies into those with mass greater (red hashed to the left) or smaller (blue hashed to the right) than 2 \u00d7 1011 M\u2299. The distribution for the galaxies belonging to the Virgo cluster are shown with a green line. The bottom histogram divides galaxies into slow (red hashed to the left) or fast (blue hashed to the right) rotators. Vertical bars on both histograms show an estimate of the systematic uncertainty when di\ufb00erent radii are used for estimating \u03b3\u2032. Laine et al. (2003) used 0. \u2032\u203205, while Rest et al. (2001) used 0. \u2032\u20321. As noted above, we also use 0. \u2032\u20321 for our galaxies, unless their \u201cNuker\u201d parameters were taken directly from other studies. Crucially, however, the radius is not chosen with respect to the galaxy distance or size (see C\u02c6 ot\u00b4 e et al. 2007). We investigated the dependence of our \u03b3\u2032 determinations on the distance, but we did not \ufb01nd a signi\ufb01cant correlation, in spite the fact that about half of ATLAS3D galaxies with the HST imaging are found at distance less or similar to the Virgo Cluster, while the other half between 20 and 40 Mpc (for distance determinations of the ATLAS3D sample see Paper I). However, we selected ATLAS3D galaxies which belong to the Virgo cluster (and are all at comparable distances) and over-plot their distribution of \u03b3\u2032, which is mostly continuous rising towards the higher values of \u03b3\u2032. We also investigated the robustness of the \u03b3\u2032 with respect to the radius at which it is measured, as a simple test for the in\ufb02uence of the galaxy size. This was done by estimating \u03b3\u2032 at r = 0.05, 0.1, 0.15 and two \ufb01xed physical scales of r = Re/100, when Re > 10\u2032\u2032and r = Re/200, when Re > 20\u2032\u20327 (so that the minimum radius is comparable to the resolution of our data 0.1\u2032\u2032). A standard deviation of these estimates is a measure for the systematic variation of \u03b3\u2032, and it is shown with vertical bars in histograms of Fig. 3. These systematic uncertainties con\ufb01rm the non-signi\ufb01cance of the 7 Note that the formal median half-light radius of ATLAS3D galaxies with HST imaging is 23.6\u2032\u2032, using the size estimates of Paper I. double peaked structure in the distribution of \u03b3\u2032. As it is not clear at what physical size one should actually measure \u03b3\u2032, we keep the practice as in previous studies, but would like the highlight the importance of this particular choice. We found, however, that dividing galaxies by mass or by angular momentum is not in\ufb02uenced by the details of \u03b3\u2032 estimation, and two clear trends can be seen. We use a characteristic mass of 2\u00d7 1011 M\u2299, which was highlighted in Paper XX as separating early-type galaxies between typically disc-dominated fast rotators from more round and massive slow rotators. Considering only lower mass galaxies, there is a tail monotonically falling o\ufb00from the peak in \u03b3\u2032 \u223c0.65 all the way to \u03b3\u2032 = 0. The most massive galaxies, however, have only \u03b3\u2032 values associated with cores. This indicates that the sample selection is crucial when considering the distribution of the nuclear slopes, as stressed by C\u02c6 ot\u00b4 e et al. (e.g. 2007) and Glass et al. (2011). As expected, the division of galaxies into fast and slow rotators re\ufb02ects, to the \ufb01rst order, the division by mass (Paper III). There are, however, two notable di\ufb00erences: some slow rotators have large \u03b3\u2032 values and are therefore core-less galaxies, while also a number of fast rotators have cores. The latter issue was pointed out by Lauer (2012), who argued that this warrants a change in the de\ufb01nition of line that separates slow and fast rotators, such that the line could be raised to include also core fast rotators present above the line de\ufb01ned in Paper III. In the next section we investigate this further and o\ufb00er an alternative view. As \u03b3\u2032 is not a physically well de\ufb01ned parameter, and as we are primarily interested in the presence of cores, we proceed by separating our sample into core (\u03b3\u2032 \u2a7d0.3) and core-less (\u03b3\u2032 > 0.3), but we keep the power-law and intermediate classi\ufb01cations in Table C1 for clarity and comparison with previous studies based on the \u201cNuker\u201d law. 4 NUCLEAR LIGHT PROFILES OF ATLAS3D GALAXIES In order to put the following discussion in context, we note that \u03bbR tries to capture in a single parameter the large amount of information provided in the kinematic maps. Also, the distinction between fast and slow rotators in the \u03bbR \u2212\u01eb diagram is an empirical one (Paper III). It is based on the fact that within one e\ufb00ective radius the velocity maps of early-type galaxies can be divided on the basis of their similarity with those of inclined discs (Krajnovi\u00b4 c et al. 2008). In this respect the slow\u2013fast separation was done by analysing the ATLAS3D velocity maps (Paper II) with kinemetry8 (Krajnovi\u00b4 c et al. 2006), which is based on a Fourier expansion of the velocity pro\ufb01les along the best \ufb01tting ellipses. Those maps that have larger Fourier coe\ufb03cients, also show disturbed velocity maps or non-regular rotation, and typically have lower speci\ufb01c angular momentum. Galaxies with small Fourier terms (typically 4 per cent of the \ufb01rst Fourier term describing the rotational velocity) are, on the other hand, characterised by regular (disc-like) rotation, while their angular momentum is also dependent on the inclination. The separatrix line between fast and slow rotators, 8 http://www.davor.krajnovic.org/idl c \u20dd2012 RAS, MNRAS 000, 2\u201332 10 Davor Krajnovi\u00b4 c et al. drawn in Paper III, minimises the overlap between galaxies with regular and non-regular rotation. Hence, slow rotators have low speci\ufb01c angular momentum, but their velocity maps are also irregular, whether being disturbed, containing kinematically distinct cores, counter-rotating structures or showing little or no rotation (for velocity maps see Emsellem et al. 2004, and Paper II) This is important for the consideration of inclination e\ufb00ects in the \u03bbR \u2212\u01eb diagram. These we address in Section 5.1 (for previous discussions see Emsellem et al. 2007; Cappellari et al. 2007; Jesseit et al. 2009). The volume limited ATLAS3D sample allowed us to de\ufb01ne the curve between the slow and fast rotators taking into account the apparent shape of objects (Paper III). The point to keep in mind is that, while it is still possible that a few face-on fast rotators are misclassi\ufb01ed as slow rotators (likely one or two galaxies in ATLAS3D sample), the vast majority of slow rotators are objects with intrinsically di\ufb00erent shape, kinematics and dynamics (hence, also likely di\ufb00erent formation scenarios) with respect to fast rotators, which make up the majority of early-type galaxies. Other separations of early-type galaxies are possible, for example one involving the galaxies masses or the steepness of the nuclear light pro\ufb01les, but they are complex. Our approach here is to keep the classi\ufb01cation as simple as possible (as in Paper III), expecting that a comparison with the nuclear structure can highlight possible formation paths for ETGs. Therefore, in this section we investigate a range of properties of early-type galaxies and look for correlations with observed nuclear light pro\ufb01les. 4.1 \u03bbR \u2212\u01eb diagram In Fig. 4 we show two \u03bbR \u2212\u01eb diagrams separating core (red) and core-less (blue) galaxies according to their measured \u03b3\u2032 values, as de\ufb01ned in Section 3.4. As anticipated by Fig. 3, there are nine core galaxies above the green line which separates fast (above) from slow (below) rotators. As also pointed out by (Lauer 2012), they are preferentially found at both low \u03bbR and \u01eb values. More speci\ufb01cally, core fast rotators are clustered around \u01eb \u223c0.15 and \u03bbR \u223c0.15 (six of nine currently known fast rotators with cores). Outside of this group, there are two \ufb02at objects and one galaxy with high angular momentum. Among slow rotators core galaxies are the dominant population, but there are also core-less galaxies. They notably occur for \u01eb > 0.35, but a few are found around \u01eb \u223c0.15. They seem to be present at all, but the very lowest, values of \u03bbR. The distribution of galaxies with HST imaging is mostly uniform in the \u03bbR \u2212\u01eb diagram, except in the region approximately centred on \u03bbR \u223c0.15 and \u01eb \u223c0.28. Most of the galaxies lacking HST imaging in this regions are slow rotators, close to the slow-fast separatrix. We do not know their nuclear pro\ufb01les, but just the distribution of core and core-less galaxies around them suggest a possible mixed population, and an additional number of core-less slow rotators. We highlight these galaxies here as they will feature prominently in the rest of the paper. In the right panel we add the information about the types of velocity maps of galaxies with HST imaging. These are divided in \ufb01ve groups (Paper II): group a \u2013 non-rotating galaxies, group b \u2013 featureless non-regularly rotating galaxies, group c \u2013 kinematically distinct cores, group d \u2013 2\u03c3 galaxies made of two counter-rotating discs, and group e regularly rotating galaxies. This shows that cores can be present also in galaxies which have regularly rotating, disclike velocity maps. Similarly, core-less galaxies are also possible in KDCs, but this is not the case for non-rotating galaxies, which are always cores, and found at the lowest values of \u03bbR. Cappellari et al. (2007) used Schwarzschild (1979) orbit-superposition axisymmetric dynamical models of a subsample of 24 galaxies with SAURON data, to study the (V/\u03c3, \u03b5) diagram of the full SAURON sample. They found fast rotators to be consistent with systems characterised by an approximately oblate (\u03c3\u03c6 \u2248\u03c3R \u2273\u03c3z) average velocity ellipsoid, satisfying an upper limit in anisotropy approximated by \u03b2z \u22611 \u2212\u03c32 z/\u03c32 R \u22480.7 \u00d7 \u03b5intr. This trend was also independently found using similar models by Thomas et al. (2009). Constructing simple axisymmetric models based on the Jeans (1922) equations, Cappellari (2008) and Scott et al. (2009) explicitly showed that the SAURON kinematics (both V and \u03c3) of fast rotators can indeed be predicted in quite some detail under the oblate velocity ellipsoid assumption. A much more extensive comparison between the predictions of these dynamical models and the ATLAS3D kinematics for the full sample was presented in Paper XV. It con\ufb01rms that the kinematics, within about 1Re, of real fast rotators is well captured by the simple models with oblate velocity ellipsoid. The projection for di\ufb00erent inclinations of these galaxy models with oblate velocity ellipsoid and following the \u03b2z = 0.7\u00d7\u03b5intr relation is shown using an analytic formalism in the left panel of Fig. 4 (grid of dotted and dashed lines) and using Monte Carlo simulations (from \ufb01g. 15 of Paper III) in the right panel (contours). These plots show that fast rotators need to have very low inclination to have su\ufb03ciently low \u03bbR to be classi\ufb01ed as slow rotators. Similar tests on the robustness of the fast \u2013 slow rotator classi\ufb01cation were performed using realistic galaxy N-body simulations by Jesseit et al. (2009), con\ufb01rming that only a handful of fast rotators may be misclassi\ufb01ed in a sample of the size of the present one. As already shown in Paper III, the grid on the left panel of Fig. 4 encloses the majority of fast rotators (note that for clarity we did not plot the cases with intrinsic ellipticities of less than 0.25). Notably the lines avoid (are above) the boundary between fast and slow rotators, although the green fast-slow separatrix was constructed only with regard to how regular (or irregular) the velocity maps are (see beginning of Section 4 and Papers II and III). Cores are typically found only in galaxies which lie below the dotted line for the intrinsic \u01eb = 0.3 (given the anisotropy trend found by Cappellari et al. 2007). In the left panel of Fig 4 we show the contours of MonteCarlo simulation from \ufb01g.15 of Paper III, made by assumption that all fast rotators have a similar intrinsic shape, \u01eb = 0.7\u00b10.2 (Gaussian distribution), and are randomly projected into \u03bbR \u2212\u01eb diagram. The contours, which do not overlap (signi\ufb01cantly) with the region of slow rotators, enclose majority of fast rotators. However, in the region where core fast rotators are found, we see a change in the shape of the contours, indicating that objects of that particular intrinsic shape are not often found there. Galaxies in this region could have di\ufb00erent formation scenarios from the majority of fast c \u20dd2012 RAS, MNRAS 000, 2\u201332 Angular momentum and nuclear light pro\ufb01les 11 Figure 4. \u03bbR versus the ellipticity \u01eb for 260 ATLAS3D galaxies. On both panels, open small symbols are galaxies with no available HST observations, and \ufb01lled small symbols are galaxies for which the classi\ufb01cation was not possible (uncertain). Also on both panels, colours of symbols indicate the class of the nuclear pro\ufb01les: red \u2013 core (\u03b3\u2032 \u2a7d0.3), blue \u2013 core-less (\u03b3\u2032 > 0.3). The green solid line separates fast from slow rotators (Paper III). Left: Core galaxies are shown with squares and core-less galaxies with circles. The dashed magenta line shows the edge-on view for ellipsoidal galaxies integrated up to in\ufb01nity with \u03b2 = 0.7 \u00d7 \u03b5intr, as in Cappellari et al. (2007). Other dashed lines show the same relation at inclinations of 80\u25e6, 70\u25e6, 60\u25e6, 50\u25e6, 40\u25e6, 30\u25e6, 20\u25e6and 10\u25e6(from right to left). The dotted curves show the change of location for galaxies of intrinsic \u01eb = 0.85, 0.75, 0.65, 0.55, 0.45, 0.35, 0.25 (from top to bottom). Right: Shapes of symbols indicate the kinematic group (Paper II): group a \u2013 non-rotating galaxies, group b \u2013 featureless non-regularly rotating galaxies, group c \u2013 kinematically distinct cores, group d \u2013 2\u03c3 galaxies made of two counter-rotating discs, and group e regularly rotating (disc-like) galaxies. Kinematic classi\ufb01cation is not provided for galaxies with no HST data. The contours show the distribution of a family of oblate objects with an intrinsic shape of \u01ebintr = 0.7 \u00b1 0.2 (as in \ufb01g. 15 of Paper III). rotators (Bois et al. 2011, hereafter Paper VI), and we will return to this point in Section 5.2. 4.2 Kinematic and morphological properties of core-less slow rotators and fast rotators with cores There are nine fast rotators with cores and there are nine core-less slow rotators among ATLAS3D galaxies with HST imaging. In the next three sub-sections we analyse their respective global morphologies and kinematics. 4.2.1 Core-less slow rotators Core-less slow rotators are (in order of increasing ellipticity): NGC6703, NGC4458, NGC5831, NGC3414, NGC5576, NGC4476, NGC3796, NGC4528 and NGC4550. These galaxies could be separated in two main groups comprising \ufb02at and relatively round objects. We start from the group of \ufb02at slow rotators (\u01eb \u22730.35), characterised by very special kinematic structure. A number of these galaxies are counter-rotating discs and classi\ufb01ed as 2\u03c3 galaxies (Paper II). The most obvious example is NGC4550 (Rubin et al. 1992; Rix et al. 1992; Cappellari et al. 2007). The fact that they do not have cores is consistent with their generally disclike appearance while the low angular momentum is the consequence of the opposite spins of two rotating components. The only non 2\u03c3 galaxy in this group is NGC4476, actually classi\ufb01ed as a regularly-rotating object. At \u01eb = 0.3, and just outside the group of \ufb02at slow rotators, is NGC5576, one of the galaxies for which our classi\ufb01cation disagrees with that of Lauer et al. (2005, see Appendix A for a discussion of our \ufb01t), who detect a core. This is a galaxy with non-regular kinematics, but with global rotation, as well as a signi\ufb01cant kinematic misalignment (Paper II). Its outer (beyond 2.5\u2032\u2032) light pro\ufb01le is best \ufb01tted with a single S\u00b4 ersic component of high S\u00b4 ersic index (e.g. Paper XVII and Lauer 2012), while Dullo & Graham (2013) show that the pro\ufb01le can be \ufb01tted with two S\u00b4 ersic functions. The second group of core-less slow rotators is found at low ellipticities (0.1 < \u01eb < 0.2). In this group there is also one galaxy (NGC4458) for which our classi\ufb01cation disagrees with that of Lauer et al. (2005, who classify it as core) and we discuss our \ufb01t in Appendix A. All galaxies harbour KDCs, while NGC3414 and NGC4528 have also signi\ufb01cant exponential components (about 65 and 28 per cent of light, respectively, Paper XVII), and NGC3414 shows signatures of a recent interaction. Finally, the galaxy with the lowest ellipticity in the ATLAS3D sample, NGC6703, is also core-less, but this one could be a rare case of a face-on disc. This is consistent with the dynamical models of Paper XV, which can only \ufb01t the c \u20dd2012 RAS, MNRAS 000, 2\u201332 12 Davor Krajnovi\u00b4 c et al. kinematics if this galaxy is nearly face-on (i \u224818). However the disc-bulge decomposition in Paper XVII does not recover an exponential component (see also Paper III for a speci\ufb01c discussion on this galaxy). Therefore among the investigated galaxies, core-less slow rotators are those that are \ufb02at (not taking into account the misclassi\ufb01ed face-on disc) or possibly a few special cases. However, a signi\ufb01cant number of slow rotators was not observed with the HST and remains unclassi\ufb01ed into core and core-less galaxies. We will address them in Section 5.3. 4.2.2 Cored fast rotators There are nine fast rotators with cores (in order of increasing ellipticity): NGC0524, NGC4278, NGC3379, NGC3193, NGC4649, NGC5485, NGC4382, NGC4473 and NGC3613 (please see discussion on light pro\ufb01les of NGC3193 and NGC4473 in Appendix A). The velocity maps for all but two are classi\ufb01ed as regular (Fig. 4 and Paper II); they typically have outer exponential components (Paper XVII), but do now show (obvious) signatures of bars (Paper II). This is signi\ufb01cant as at least 30 per cent of ATLAS3D galaxies are barred, and all except two are found among the fast rotators9. A few galaxies deserve a special mention. NGC0524 has the highest \u03bbR and a signi\ufb01cant amount of gas and dust distributed in a spiral con\ufb01guration. NGC4473 does not warrant a core-S\u00b4 ersic \ufb01t (Ferrarese et al. 2006; Dullo & Graham 2012). Kormendy et al. (2009) detect an excess above a S\u00b4 ersic \ufb01t to speci\ufb01c and disconnected regions of the pro\ufb01le, while Dullo & Graham (2013) \ufb01tted it with an inner exponential and outer S\u00b4 ersic models. Therefore, this galaxy is one the few galaxies for which our classi\ufb01cation, as well as the previous classi\ufb01cation by Lauer et al. (2005), do not agree with those based on the (core-)S\u00b4 ersic \ufb01ts. NGC4382 shows signs of a recent major merger, while NGC4649 is a massive galaxy, but with ordered rotation within the observed e\ufb00ective radius (with an indication that this might not be the case outside the SAURON FoV), and it sits close to the fast \u2013 slow separatrix. Its classi\ufb01cation is, therefore, uncertain. Finally, NGC5485 is a prolate rotator with an inner dust disc in a \u201dpolar ring\u201d con\ufb01guration. Typically low angular momentum and low ellipticity, together with cores and some peculiarities outlined above, suggest that these galaxies are very similar to slow rotators. Their dynamics is obviously somewhat di\ufb00erent as it follows the di\ufb00erence in velocity maps on which the fast slow separation is made. However, the crucial distinction between slow and fast rotators is in the signature of embedded discs. In the next section we try to answer if discs could be present in core fast rotators. 4.2.3 V/\u03c3 \u2212h3 diagram The kinematic information on the embedded high angular momentum components can be extracted from the line-ofsight velocity distribution (LOSVD). Speci\ufb01cally, they are found in the steep leading wings of the LOSVD. When the LOSVD is parametrized with a Gauss-Hermite series 9 NGC4528, a barred, 2\u03c3 slow rotator has notably a core-less nuclear pro\ufb01le. (Gerhard 1993; van der Marel & Franx 1993), the third coe\ufb03cient, h3, measures the anti-symmetric deviations of the LOSVD from a Gaussian. Bender et al. (1994) showed that galaxies with (embedded) discs and showing ordered rotation typically show an anti-correlation between V/\u03c3 and h3, where V , \u03c3 and h3 are used to describe the local LOSVDs measured at di\ufb00erent locations in galaxies. Therefore the so-called \u201clocal\u201d V/\u03c3 \u2212h3 diagram, constructed from spatially resolved spectra, can be used to indicate those galaxies that are likely to have embedded discs. In Paper II, we showed that ATLAS3D galaxies with regular rotation show a strong anti-correlation pattern10, while galaxies with irregular kinematics, KDCs, or with no net rotation, do not show it. Furthermore, in Paper XVII we showed that V/\u03c3 \u2212h3 is strongly anti-correlated for those galaxies with structural components that can be \ufb01tted with an exponential pro\ufb01le (as opposed to a general S\u00b4 ersic pro\ufb01le of a large index n). In the upper left panel of Fig. 5 we present the V/\u03c3\u2212h3 diagram for all galaxies with \u03bbR < 0.3 without bars, dividing them into slow and fast rotators to illustrate the general di\ufb00erence in the kinematics between the objects in these two classes. Fast and slow rotators, in spite of having similar extent of |h3|, have di\ufb00erent distributions of combined V/\u03c3 \u2212h3: slow rotators do not show the anti-correlation. Note that |V/\u03c3| is di\ufb00erent between fast and slow rotators almost by de\ufb01nition as it enters the equations for calculating the speci\ufb01c angular momentum, \u03bbR, (Emsellem et al. 2007). Therefore, we are primarily interested in the shape of the contours on Fig. 5 and not their extent along the x\u2212axes. In particular, we want to see to what extent fast rotators with cores follow the two trends observed in the \ufb01rst panel, as this would imply to which class they are dynamically similar. In other panels of Fig. 5 we show V/\u03c3 \u2212h3 diagrams for individual core fast rotators. Most objects show an anticorrelation indicative of disc components. The exceptions are NGC3613, NGC4649 and NGC5485. The last one is a prolate rotator, NGC4649 is one of the most massive ATLAS3D galaxies and on the border with slow rotators, while NCG3613 is also unusual as it is the \ufb02attest core galaxy. These three galaxies are indeed kinematically and structurally (no embedded disks) more similar to slow rotators. Among other core fast rotators, the anti-correlation trend is the strongest in NGC0524, which also has the largest \u03bbR (actually \u03bbR \u223c0.33, hence more than any fast rotator used in making of the upper left panel). In summary, fast rotators with cores typically have regular kinematics, while a few have some peculiar features. Most show a signi\ufb01cant V/\u03c3 \u2212h3 anti-correlation and exhibit regular velocity maps. This indicates they contain embedded disc-like structures, which makes them morphologically, kinematically and dynamically di\ufb00erent from (core) slow rotators, typically harbouring KDCs (or are not rotating at all) and showing no V/\u03c3 \u2212h3 anti-correlation. The existence of cores in rapidly rotating galaxies was reported before (Faber et al. 1997), and discs were seen in core galaxies (Lauer et al. 2005). Recently it was also emphasised by 10 Barred galaxies show a less pronounced anti-correlation, as bars are often characterised by correlation between V/\u03c3 and h3 within the bar (e.g. Chung & Bureau 2004) c \u20dd2012 RAS, MNRAS 000, 2\u201332 Angular momentum and nuclear light pro\ufb01les 13 Figure 5. Local V/\u03c3 \u2212h3 relation for non-barred ATLAS3D galaxies with \u03bbR < 0.3 (upper left panel) and for individual core fast rotators. Only spatial bins with \u03c3 > 120 km/s and an error on h3 < 0.05 are used in all panels (number of bins used is indicated by numbers in parentheses). On the upper left panel fast rotators are shown with solid black contours while slow rotators with dot-dashed red contours. The contours show distribution of values in bins of 0.1 in V/\u03c3 and 0.01 in h3, smoothed with a boxcar \ufb01lter of a window of 2 pixels in both dimensions. The lowest level is 0.25 and the step is 0.25 in logarithmic units. Note that NGC0524 has \u03bbR > 0.3. Dullo & Graham (2013) that there are S0 galaxies (also most likely fast rotators) with cores. This suggests that a core and a disc can be found in the same object although their formation scenarios (e.g. non-dissipative and dissipative processes, respectively) di\ufb00er dramatically, if not mutually exclude each other, and as such present a puzzle. 4.3 Mass dependence We investigate further the properties of ATLAS3D galaxies with HST imaging by plotting them in the mass \u2013 size diagram in Fig. 6. Both dynamical masses and sizes were previously reported in Paper XV (and we already used masses for Fig. 2), while the ATLAS3D mass\u2013size plot was presented previously in Paper XX as a non edge-on projection of the Mass plane (Paper XV), which is, in essence, the fundamental plane where luminosity is substituted with mass. For a general discussion on the mass \u2013 size relation and its demographics with respect to Hubble types we refer the reader to Paper XX and its \ufb01gs. 9 and 14. Slow and fast rotators, coloured by the type of nuclear pro\ufb01les, are separated into the top and bottom panels, respectively. As expected (Faber et al. 1997), core galaxies are found in massive and large galaxies, populating the narrow tail in the mass \u2013 size diagram, to which early-types extend from the general population of galaxies. This dependence on high mass for the existence of cores is, particularly, the property of slow rotators, while there is, at present, some room for uncertainty for fast rotators. Namely, out of eight fast rotators more massive than 2\u00d71011 M\u2299, three do not have HST data, one has strong dust features which prevent its classi\ufb01cation (NGC3607), and one is classi\ufb01ed as an intermediate case (NGC2768). The most massive fast rotator (cored) is NGC4649 which sits very close to the fast\u2013slow separatrix in the \u03bbR\u2212\u01eb diagram. The other two core fast rotators are (in order of decreasing mass): NGC4382 and NGC0524. The three galaxies with no HST data have \u03bbR > 0.4, and are also \ufb02atter compared to all other galaxies in this mass range, which would imply, according to the trends in diagrams of Fig. 4, they are most likely core-less galaxies. This suggests that the occurrence of cores in massive galaxies is strictly true only for slow rotators. Massive core-less fast rotators can exist. Continuing down in mass, in the regime between 8\u00d71010 and 2 \u00d7 1011 M\u2299we \ufb01nd a mixture of nuclear pro\ufb01les, both for slow and fast rotators. For fast rotators this could just be the continuation of the trend seen at the high mass, but for slow rotators this is the region where both core and core-less pro\ufb01les occur. For masses lower than 8\u00d7 1010 M\u2299only coreless galaxies seem to exist. The lack of HST data for slow rotators in the same region prohibits a strong statement; the four observed slow rotators, mostly of the lower masses, do not have cores, but they also mostly belong to the category of the \ufb02attest slow rotators and counter-rotating discs. A property which is found in both slow and fast rotators with cores (above M = 8 \u00d7 1010 M\u2299) is the alignment of the host galaxies on the lines of constant velocity dispersion. As Paper XX demonstrated (see also Wake et al. 2012), various properties of early-type galaxies remain constant along lines of constant \u03c3. This was shown to be due to the fact that \u03c3 traces the bugle fraction, as a large bulge is needed to quench star formation. Therefore, a contrast in the appearance between the narrow tail at high masses (and large sizes) and the region with the bulk of the galaxy population, is related to the di\ufb00erence in the evolutionary processes. Paper XX suggested that the distribution of galaxies on this diagram is due to two main processes: (i) bulge growth, which increases the galaxy concentrations and \u03c3 while decreasing Re and inc \u20dd2012 RAS, MNRAS 000, 2\u201332 14 Davor Krajnovi\u00b4 c et al. Figure 6. Mass \u2013 size relation for ATLAS3D galaxies (Paper XX). The top and bottom panels show slow and fast rotators, respectively. Small open symbols are galaxies for which HST imaging is not available. Colour of symbols indicate the class of the HST nuclear pro\ufb01les: red \u2013 core, blue \u2013 core-less, black \u2013 uncertain (only on bottom panel). Vertical lines are drawn at characteristic masses of 0.8 and 2 \u00d7 1011 M\u2299, and dashed-dotted lines are for constant \u03c3e = 130, 170 and 240 km/s. creasing the likelihood for the star formation to be quenched and for the galaxy to appear as an early-type galaxy; (ii) dissipationless mergers, which move galaxies along lines of nearly constant \u03c3, while increasing Re and mass. The dominance of core early-type galaxies above M = 2 \u00d7 1011 M\u2299and the lack of low-mass core slow rotators, seems consistent with this picture in which fast rotators need a su\ufb03cient number of dissipationless mergers to scour their cores and also transform into slow rotators. It indicates that not all slow rotators are the same and it emphasises the physical importance of the characteristic mass M= 2 \u00d7 1011 M\u2299(as in \ufb01g.14 of Paper XX). Furthermore, there is a notable alignment of core fast rotators with lines of constant \u03c3, similar to that seen for massive (and core) slow rotators. Semi-analytic models (Khochfar et al. 2011, hereafter Paper VIII) suggest that there are two types of fast rotators, with the main di\ufb00erence in the availability of the gas for star formation. It is tempting to interpret the existence of cores in fast rotators above cerFigure 7. A correlation of \u03bbR with the velocity dispersion measured within the e\ufb00ective radius, \u03c3e. Galaxies with cores are shown with red squares, core-less galaxies with blue circles, galaxies with an uncertain nuclear pro\ufb01les with small black circles, while galaxies with no HST data with small open circles. The lines delineate the region where mostly cores occur. The core galaxy outside the box and the core-less galaxy within the box are NGC0524 and NGC3414, respectively. The uncertain galaxy within the box is NGC3607. tain mass, as well as their alignment with constant \u03c3 lines as an indication of this separation between the two sub-classes, where the core galaxies represent clear cases for no additional star formation which would re\ufb01ll the cores. This is also interesting if one takes into account that the distribution of fast rotators in the mass \u2013 size plot forms a smooth parallel sequence and lower boundary to the distribution of spirals (Paper XX). As it can be seen from the mass \u2013 size diagram there are no core galaxies for M < 8 \u00d7 1010 M\u2299, but there also seems to be a well de\ufb01ned lower limit in the global velocity dispersion. In Fig. 7 we correlate \u03bbR with the observed velocity dispersion within an e\ufb00ective radius, \u03c3e (from Paper XV). Indeed, core galaxies are clustered in the lower right corner, of high velocity dispersion and low angular momentum values. Speci\ufb01cally, cores dominate for \u03bbR \u22720.25 and \u03c3e \u2273160 km/s. Fast rotators with cores are found in the upper part of the boxed region with \u03bbR > 0.15 (and \u03c3e < 220 km/s). Taking into account that top three core galaxies in the boxed region are (in order of decreasing \u03bbR): NGC4473, NGC3613 and NGC3193, of which both NGC4473 and NGC3913 are marginal cases in terms of their core classi\ufb01cation (see Appendix A), a conservative upper limit for separating cores from core-less galaxies is around \u03bbR \u22720.2. The relatively clean separation of core and core-less galaxies in Fig. 7 re\ufb02ects the main \ufb01nding of this paper: cores are typically found in galaxies with low speci\ufb01c angular momentum and high mass (high \u03c3). Most of the information in Fig. 7 is already visible from Fig. 6, but we highlight it c \u20dd2012 RAS, MNRAS 000, 2\u201332 Angular momentum and nuclear light pro\ufb01les 15 here as particularly interesting as it has a predictive power to separate core from core-less galaxies based on two direct observables of any survey with integral-\ufb01eld spectrographs: \u03bbR and \u03c3e. 4.4 Correlation with other parameters We now investigate potential correlations between the presence of cores in fast and slow rotators with other properties such as stellar populations, presence of the atomic and molecular gas, X-rays and the in\ufb02uence of the environment. 4.4.1 Stellar populations We investigated the residuals from the best-\ufb01tting linear relations between age, metallicity and abundances and the velocity dispersion (McDermid et al. in prep) with respect to the presence of cores, and found no signi\ufb01cant trends. Cored and core-less galaxies in the same \u03c3e (or mass) range have consistent distributions in age, metallicity and abundances. The same is true if one only selects core fast and core slow rotators, or core-less fast and slow rotators. We looked for the di\ufb00erences in single stellar population parameters measured within apertures of one e\ufb00ective radius and one eight of the e\ufb00ective radius. This test gave consistent results. Stellar populations indicate that the cores and core-less nuclei in massive galaxies, both in fast and slow rotators, are typically made of old stars. This indicates that cores were either created early (z > 1.5, with a few exceptions) and survived until present, or they were scoured in dissipationless mergers which did not involve creation of new stars. 4.4.2 Molecular and atomic gas A comparison with Young et al. (2011, hereafter Paper IV) shows that carbon monoxide (CO) is detected in only one core galaxy (NGC0524). This galaxy has spiral dust structure and it also has the highest \u03bbR among core objects. The lack of molecular gas in core galaxies is not surprising, as this gas is typically associated with star-formation, which would \ufb01ll in the cores. In the ATLAS3D sample it is only detected in fast rotators, although not all of them experienced a strong star forming period recently (McDermid et al. in prep). Notably, all galaxies for which we were not able to extract reliable pro\ufb01les and classify their nuclear structures (uncertain), as they were very dusty, are also strong CO detections. Of particular interest here is NGC3607, which is one of the most massive fast rotators and it is found close to the region in \u03bbR \u2212\u01eb diagram populated by other core fast rotators. It is also found in the regions where mostly core galaxies occur in both Fig. 6 and Fig. 7. There are a number of similarities between NGC0524 and NGC3607, such as the existence of prominent dust spiral structure, CO detection (Welch & Sage 2003), the galaxy mass and similar position in the above mentioned diagrams. NGC3607 has some what higher inferred mass of H2 (Paper IV, Welch & Sage 2003), and this might have made a di\ufb00erence for the shape of their nuclear pro\ufb01le. While NGC0524 has a core, the dust content of NGC3607, unfortunately, impedes this analysis at present, but we note that Lauer et al. (2005) detected a core in this galaxy. HI is found in similar quantities in both slow and fast rotators (Morganti et al. 2006; Oosterloo et al. 2010; Serra et al. 2012, hereafter Paper XIII), but it is not often found among core galaxies. A comparison with Table B1 of Paper XIII shows there are three core slow rotator with HI detections (NGC4406, NGC5198 and NGC5557) all of which are in unsettled con\ufb01gurations. Additionally, NGC3608 has some HI clouds in the vicinity. Noteworthy is also that a coreless slow rotator and three further slow rotators with no HST imaging (see Section 5.3) have ordered HI structures (discs or rings). Core fast rotators show a similar fraction of HI detections: two galaxies, NGC3193 and NGC4278, as unsettled clouds and a large scale settled HI disc, respectively. 4.4.3 X \u2013 rays Within the earlier context of a division of early-type galaxies into massive boxy galaxies with nuclear cores and less massive discy objects with nuclear cusps (core-less), a number of papers have also looked into the hot-gas content of early-type galaxies (e.g. Bender et al. 1989; Pellegrini 2005; Kormendy et al. 2009) with Pellegrini (2005), in particular, being the \ufb01rst to recognise how galaxies with central cores tend to display higher X-ray luminosity values, LX, than core-less galaxies. In Sarzi et al. (2013, hereafter Paper XIX) we have looked into the hot-gas content of early-type galaxies in the ATLAS3D sample by using LX measurements from Xray observations of both low and high angular resolution, as measured with ROSAT or Einstein (O\u2019Sullivan et al. 2001) and Chandra (Boroson et al. 2011), respectively. Based on these X-ray data and our integral-\ufb01eld measurements we found that slow-rotators display LX values that are consistent with hot-gas emission that is sustained by the thermalisation of the kinetic energy carried by stellar mass-loss material, whereas fast rotators generally fall short from such a simple prediction. Considering that fast rotators are intrinsically \ufb02atter than slow-rotators (see \ufb01g. 2 of Paper VII and Weijmans & et al. 2013, hereafter Paper XXIV), in Paper XIX we concluded that the intrinsic shape of an earlytype galaxy is the most likely driver for the X-ray luminosity of its hot-gas halo, consistent with the suggestion of Ciotti & Pellegrini (1996), whereby \ufb02atter systems are less capable of holding on to their hot gas. Following the work of Paper XIX and the earlier suggestions of a connection between nuclear properties and X-ray luminosity, here we have also looked into the hot-gas content of the core and core-less galaxies in the ATLAS3D sample. The overlap with the HST subset of our sample with the subsets with either low or high X-ray angular resolution from Paper XIX is small, but it enables us to recognise some general trends. Including the information regarding the presence of cores into plots similar to those presented in Paper XIX (Fig. 8) shows that core-less galaxies are indeed X-ray de\ufb01cient, and that cores are found in the most X-ray luminous galaxies. Yet, the presence of a core does not imply high X-ray luminosities, as in the case of the relatively \ufb02at slowrotators NGC4365 and NGC5322 and in fast-rotators such as NGC3379 or NGC4278 which may all be X-ray de\ufb01cient by virtue of their intrinsic \ufb02at shape. c \u20dd2012 RAS, MNRAS 000, 2\u201332 16 Davor Krajnovi\u00b4 c et al. Figure 8. Top: LK\u03c32 e vs. LX diagrams for low (top panel) and high (bottom panel) X-ray resolution ATLAS3D sub-samples galaxies with HST imaging (based on \ufb01gs. 3 and 6 in Paper XIX, respectively). On both panels, core and core-less galaxies are represented by red and blue colours, respectively, while symbols corresponds to fast and slow rotators. On both panels the dashed line shows the contribution to the X-ray luminosity from hot-gas emission sustained by the thermalisation of the kinetic energy that stellar-mass loss material inherit from their parent stars, which follow a simple LX,diff = 3/2 \u02d9 M\u03c32 law. On the top panel, the solid line shows also the contribution of unresolved X-ray binaries (LX,discr, as in Boroson et al. 2011, dotted lines shows uncertainties of such a model), while the grey solid line traces the sum of the both di\ufb00use and discrete components that ought to be compared with the low-resolution X-ray measurements. The grey labels indicate low-mass galaxies or objects with the X-ray measurements signi\ufb01cantly contaminated by an AGN or the X-ray emission from the cluster medium. The presence of a core in the X-ray luminous galaxies of the ATLAS3D sample is consistent with the point made by Kormendy et al. (2009), where the presence of halo of hot gas, or even more the fact of being deeply embedded in the hot medium of a galaxy cluster, would prevent the accretion of cold gas and the reforming of a central stellar cusp. In fact, as noticed in Paper XIX, the presence of a hot medium would also prevent the cooling of stellar-mass loss material and its recycling into new stars. Conversely, the \ufb01nding of cores in X-ray de\ufb01cient galaxies does not necessarily pose a problem since the accretion of fresh gas would depend also on environmental e\ufb00ects and would thus not be guaranteed. In contrast, the processes leading to the formation of a core do not have to signi\ufb01cantly alter the overall shape of a galaxy, for instance making it rounder and more capable to retain a halo of hot gas. 4.4.4 Environment dependence We also investigated the in\ufb02uence of galaxy environment on the type of nuclear pro\ufb01les. Using the density estimators of Paper VII, which probe cluster and group environments, we did not see clear correlations, which are not related to the fact that slow rotators are found in large numbers only in the densest environments. A possible exception are less massive slow rotators, for which HST imaging is not available and we do not know their nuclear light pro\ufb01les. These galaxies are typically found in low density environments. In Section 5.3 we discuss if these objects contain cores or are a core-less subpopulation of slow rotators. 4.5 A caveat: are there more cores? As the de\ufb01nition of core/core-less galaxies depends on the choice of radius at which \u03b3\u2032 is evaluated it is likely that we do not recognise smaller cores in more distant galaxies. The sizes of our cores, using the \u201ccusp radius\u201d r\u03b3 as a measure, range from tens to hundreds of parsecs, and for some galaxies we probe the light pro\ufb01les down to a few parsec. Still, as mentioned earlier, a galaxy with a \u201cNuker\u201d power-law at the HST resolution could still harbour a core at smaller scales. Therefore we wish to compare how our conservative radius limit for estimating \u03b3\u2032 biases our ability to detect cores. In Fig. 9 we show the ratio of r\u03b3 and the adopted radius for \u03b3\u203211, r\u2032 = 0.1\u2032\u2032 as a function of the global angular momentum, \u03bbR, for all galaxies that have pro\ufb01les less steep than 0.5 at 0.5\u2032\u2032. When this ratio is below 1, our probe of the nuclear region is larger than a possible core, given the \u201cNuker\u201d \ufb01t, hence, we cannot detect a core. As the \ufb01gure shows, this is indeed the case (no cores for r\u03b3/r\u2032 < 1). In Appendix A we discuss galaxies for which our classi\ufb01cation di\ufb00ers from the literature and in Fig. 9 we highlight these galaxies as open squares (di\ufb00erence with \u201cNuker\u201d \ufb01ts) and open circles (di\ufb00erence with core-S\u00b4 ersic \ufb01ts). It is evident that at least some galaxies which were previously classi\ufb01ed as core using the \u201cNuker\u201d \ufb01t have the ratio close to 1, and, therefore, the scale at which they are characterised is important. We postpone the further discussion about these objects to Appendix A. The cores we detect typically occur for \u03bbR \u22720.25 (except NGC0524). It is noteworthy that below this value for \u03bbR there is only one galaxy with r\u03b3/r\u2032 < 1: formally a slow rotator and face-on candidate NGC6703, which we classify as core-less. Other galaxies with r\u03b3/r\u2032 < 1 occur for \u03bbR > 0.25, the \ufb01rst three being NGC0821, NGC4434 and NGC4621. 11 Note that for galaxies for which we use Lauer et al. (2005) values, r\u2032 is not the radius at which \u03b3\u2032 was estimated, but 0. \u2032\u203202 or 0. \u2032\u203204 were used instead. See that paper for details. c \u20dd2012 RAS, MNRAS 000, 2\u201332 Angular momentum and nuclear light pro\ufb01les 17 Figure 9. Ratio of the \u201ccusp radius\u201d, r\u03b3, and r\u2032 = 0.1\u2032\u2032, the radius at which \u03b3\u2032 was evaluated (see eq. 2) as a function of the global angular momentum, \u03bbR. The dashed horizontal line highlights the ratio of 1, and the vertical line is an indication of the angular momentum below which cores occur in our sample (with the exception of NGC0524). Large open squares and open circles show galaxies for which our classi\ufb01cation di\ufb00ers from those of the \u201cNuker\u201d \ufb01ts and core-S\u00b4 ersic/S\u00b4 ersic parametrisation, respectively, as found in the literature (see Appendix A for details). According to their respective \u03c3, \u03bbR and their position in Figs. 6 and 7, NGC4434 is unlikely to have a core (too small \u03c3), while NGC0821 and NGC4621 are close to the space occupied by cores in these \ufb01gures. For NGC0821 we use the data from Lauer et al. (2005) and their derivation of \u03b3\u2032 at radius 0. \u2032\u203204, and this galaxy remains core-less. For NGC4434 we used an ACS image (and 0. \u2032\u20321 radius for \u03b3\u2032), but analysis in Byun et al. (1996) and Lauer et al. (2007b) suggests that our conservative resolution does not change the classi\ufb01cation of this galaxy. Furthermore, as galaxies with higher \u03bbR values are typically fainter and less massive, they are also less likely to have cores (e.g. Faber et al. 1997, and results in previous sections). Therefore, we conclude that our estimates of core/core-less nuclear pro\ufb01les does not su\ufb00er greatly due to our conservative approach in estimating \u03b3\u2032, and that this is not the prime reason why there are no cores for \u03bbR > 0.25. 5 DISCUSSION 5.1 The in\ufb02uence of projection e\ufb00ects A simple question di\ufb03cult to answer is: are projections effects responsible for the observed mismatch between structural and kinematic properties? Lauer (2012) suggested that core-less (power-law) galaxies that fall among galaxies with cores in the \u03bbR \u2212\u01eb diagram (basically all power-laws with \u03bbR < 0.25) are indeed there due to projection e\ufb00ects. Emsellem et al. (2007) and Cappellari et al. (2007) argued that fast and slow rotators are two separate galaxy populations and that inclination e\ufb00ects can not move galaxies from one to the other group, except in a not very common case of perfectly face-on discs, where no radial velocity gradients could be detected. This is supported by the over-plotted lines in the right panel of Fig 4 (see also Section 4.1), which encompass fast rotors and suggest that the majority of these objects can be explained as a single population of objects, with speci\ufb01c dynamics, seen at di\ufb00erent inclinations. Moreover, the contours in the right panel of Fig 4, indicate the distribution of a family of objects with an intrinsic shape, \u01eb = 0.7 \u00b1 0.2 (Gaussian distribution). These contours avoid the region of slow rotators and suggest that these two classes of galaxies have di\ufb00erent intrinsic shapes (as explicitly shown in Paper XXIV), structural and dynamical properties. Jesseit et al. (2009) showed that the intrinsic shape of galaxies has a limited in\ufb02uence on the actual classi\ufb01cation of galaxies as fast or slow rotators. Investigating the \u03bbR parameter of simulated galaxies they showed that intrinsically oblate objects are almost always classi\ufb01ed as fast rotators independently of projection, which is in agreement with the results of Cappellari et al. (2007). Similarly, intrinsically triaxial objects are always classi\ufb01ed as slow rotators. Only prolate objects can change from fast to slow rotators, depending on the viewing angles. Jesseit et al. (2009) argue that this is a consequence of their speci\ufb01c orbital structure. Based on the investigation of kinematic misalignment angle (Paper II) ,there are only two prolate galaxies in the ATLAS3D sample of 260 galaxies. Indeed, one is classi\ufb01ed as a fast and the other as a slow rotator, and both of them harbour cores. The two plots in Fig. 4 and the \ufb01ndings of Jesseit et al. (2009) suggest that projection e\ufb00ects can not explain the existence of slow rotators with core-less pro\ufb01les or fast rotators with cores. The evidence for embedded discs (Fig. 5, Section 4.2.3) in cored fast rotators also challenges the grouping of all cored galaxies under the same class (both morphologically and dynamically). Raising the fast-slow separatrix at low ellipticities to a value of \u03bbR \u223c0.2 (or similar) as suggested by Lauer (2012), and similarly by Kormendy & Bender (2012), in order to include all core galaxies among slow rotators, is, however, not advisable as in that case one would include a large number of fast rotators which are indeed at low inclinations12. Misclassi\ufb01cation due to projection is expected only in a few rare objects: face on discs and prolate rotators. The expected frequency of these objects (one to two cases of both types in the ATLAS3D sample, Papers II and III) does not explain the observed number of, speci\ufb01cally, core fast rotators. The answer to the question at the beginning of this section is: inclination effects do not (typically) change a fast into a slow rotator. The mismatch between global angular momentum and nuclear pro\ufb01les, more likely, indicates variations in assembly history within the class. 5.2 Two types of fast and slow rotators Evidence presented in papers of the SAURON survey and of the ATLAS3D project show that fast and slow rotators are two separate populations of galaxies. Emsellem et al. (2007) and Cappellari et al. (2007) showed that the distinction between fast and slow rotators is not sensitive to the projection e\ufb00ects. Paper III put the separation of fast and slow rotators on a more statistical basis in the nearby Universe. In Paper II we showed that all fast rotators are nearly axisymmetric 12 This was noted by Lauer (2012). c \u20dd2012 RAS, MNRAS 000, 2\u201332 18 Davor Krajnovi\u00b4 c et al. (modulo bars), while slow rotators are not. Krajnovi\u00b4 c et al. (2008) suggested that fast rotators contain discs, while in Paper XVII we showed that fast rotators contain exponential components in their large-scale light pro\ufb01les (or are best \ufb01tted with a S\u00b4 ersic model of low n). Additionally, the different intrinsic shapes of fast and slow rotators were shown in Paper XX (via dynamical models) and Paper XXIV (via statistical deprojection). Fast and slow rotators also di\ufb00er in the presence of molecular gas (Paper IV, Alatalo et al. 2012), while this is not the case in terms of ionised (Sarzi et al. 2006) and atomic gas at large scales (Morganti et al. 2006; Oosterloo et al. 2010, Paper XIII). Fast and slow rotators, however, di\ufb00er in their X-ray emission originating in the hot gas component (Paper XIX). Nevertheless, these pieces of evidence do not exclude that there could be sub-populations among fast and slow rotators as result of somewhat di\ufb00erent formation paths, with a continuous range of parameters. The existence or the lack of cores can be used as an indication for the di\ufb00erences between the sub-populations among fast and slow rotators, respectively. In particular, one should consider the evolution of galaxies within the two phase formation scenario (Oser et al. 2010), where the early phase is dominated by gas in\ufb02ows and formation of stars within galaxies (e.g Kere\u02c7 s et al. 2005; Dekel et al. 2009), and the further evolution is seen in the second phase of assembly of starts created in other galaxies dominated by frequent, and often non-dissipative, merging (e.g. Johansson et al. 2012; Lackner et al. 2012; Oser et al. 2012). The large range of angular momentum values, coupled with the full range of ellipticities, indicates that properties of fast rotators could be explained as a combination of projection e\ufb00ects and di\ufb00erent formation processes. This is supported by the contours in the right panel of Fig. 4. The relatively regular and elsewhere ellipsoidal shape of the second contour is twisted such that it does not include values around (0.2, 0.15) in (\u03bbR, \u01eb). Galaxies in that region could come from a population with a di\ufb00erent intrinsic shape or have di\ufb00erent formation histories from the majority of fast rotators. The latter can be the case as this is exactly the location of a number of fast rotators exhibiting cores. For example, remergers of major disc mergers of Paper VI (see their \ufb01g. 11) fall in this region, suggesting that indeed galaxies which suffered more signi\ufb01cant major merging (either dry and wet) could populate it. Additionally, the semi-analytic models of Paper VIII predict that the class of fast rotators comprises two sub-populations with di\ufb00erent histories in terms of availability of cold gas. These two di\ufb00erent classes are not easy to recognise, neither using morphology (e.g. disc-bulge decomposition of Paper XVII) due to inclination e\ufb00ects, nor by considering kinematics (Paper II), which might not be sensitive enough to the subtle di\ufb00erences in the star formations histories. The existence of cores in fast rotators, however, could point to, at least, a subset of formation scenarios still consistent with producing a fast rotator. As outlined in Papers III and VII, there is a clear case for di\ufb00erent types among slow rotators. Slow rotators with \u01eb \u22730.35 are often made of counter-rotating discs and classi\ufb01ed as S0s, while rounder galaxies are characterised by no net rotation or harbour large KDCs (Paper II), which are not necessarily separate components (van den Bosch et al. 2008), but could originate in complex orbital structure, and Figure 10. Local V/\u03c3 \u2212h3 diagram for all slow rotators with no HST imaging. The same selection criteria as in Fig. 5 were used to select the spatial bins suitable for plotting, but typically low \u03c3 (<120 km/s) values remove a signi\ufb01cant number of bins. projections of triaxial bodies (Statler 1991). Here we also show that \ufb02at slow rotators typically have core-less nuclear pro\ufb01les. This supports the notion that their assembly histories are di\ufb00erent from those of more round slow rotators with cores, with implication to their ability to retain hot gas and inhibit further star formation. The lack of cores in some slow rotators points to those extreme formation scenarios consistent with producing a slow rotator, but incapable of producing or maintaing the core. 5.3 Are there more core-less slow rotators? Open symbols plotted in Figs. 4, 6 and 7 represent galaxies for which HST data suitable for this analysis is unavailable. They are present over the full extent of the \u03bbR \u2212\u01eb diagram, but as highlighted in Section 4.1, there is a speci\ufb01c region where they seem to dominate: for 0.1 \u2272\u03bbR \u22720.2 and 0.2 \u2272\u01eb \u22720.35. This region is of particular interest as it is a transitional region between slow and fast rotators. It also comprises a population of \ufb02atter slow rotators of similar angular momentum as the majority of core fast rotators. They are particularly interesting as they are less massive than other slow rotators (1010.5 \u22121011 M\u2299), typically have \u03c3e < 160 km/s, and a number of them are morphologically classi\ufb01ed as S0. They are bounded by core fast rotators on the left and core slow rotators below. Following trends on Fig. 4, one could expect these galaxies to have \ufb02at nuclear pro\ufb01les. According to Fig. 10 their V/\u03c3 and h3 are weakly anti-correlated; not as much as for a typical fast rotator, but signi\ufb01cantly more than for other slow rotators. Their global structures suggest they contain exponential components or are well \ufb01tted with a single S\u00b4 ersic function of low n (Paper XVII). These trends present them as di\ufb00erent from typical slow rotators, but more similar to c \u20dd2012 RAS, MNRAS 000, 2\u201332 Angular momentum and nuclear light pro\ufb01les 19 fast rotators, and perhaps even to core fast rotators (at least in the sense that having a core and an embedded disc seems to be possible). However, according to the trends in the mass \u2013 size diagram (Fig. 6 and discussion in Section 4.3, low mass, low sigma), and the fact they are found in low density environments, these galaxies are most likely core-less, and hence very special cases for understanding the formation of slow rotators. If they are indeed core-less galaxies, then the conjecture of Lauer (2012) that below \u03bbR < 0.25 only slow rotators and face-on fast rotators exist cannot be true; these galaxies are too \ufb02at to be considered face on discs. There is no doubt that these galaxies are di\ufb00erent from other fast rotators, including those with similar \u03bbR values. Their velocity maps are disturbed, although not as irregular as of other slow rotators. Obtaining high resolution imaging of these galaxies would settle the issue, and robustly calibrate the separation between core and core-less galaxies in the \u03bbR \u2212\u03c3 diagram. 5.4 Are cores in fast and slow rotators di\ufb00erent? We showed above that core fast rotators cover a similar range in masses as core slow rotators. On the other hand, the signi\ufb01cant kinematic di\ufb00erence between fast and slow rotators suggests that properties of cores could also be di\ufb00erent in these two classes of galaxies. Lauer (2012) compared the sizes of cores in fast and slow rotators using the \u201ccusp radius\u201d, r\u03b3, and found that there is no di\ufb00erence between core sizes in fast and slow rotators. Here we look at the relation between the mass of the central black hole, MBH, and a global property of the host galaxy, namely, its global velocity dispersion: the MBH \u2212\u03c3 relation (Ferrarese & Merritt 2000; Gebhardt et al. 2000). We use the recent compilation of black hole masses by Graham & Scott (2013). The sample consists of 72 measurements, but the overlap with the ATLAS3D sample is rather small: only 32 galaxies. As before, we divide galaxies according to their angular momentum and nuclear structure. We do not attempt to assign other galaxies with measured MBH into fast and slow rotator classes as they do not have the necessary integral-\ufb01eld data. Recent compilations of data show a possible trend that at the high \u03c3 end of the relations, mostly populated by core galaxies, MBH increases faster than \u03c3 (e.g. McConnell et al. 2011), as well as a possible di\ufb00erent best \ufb01tting relation for core and core-less galaxies (especially when plotted against spheroid mass or luminosity, McConnell & Ma 2013; Graham & Scott 2013; Scott et al. 2013). This could be a consequence of selection e\ufb00ects (Bernardi et al. 2007) or an indication of a di\ufb00erent growth process for both black holes and host galaxies (e.g. Paper XX; Lauer et al. 2007a; Graham & Scott 2013; Scott et al. 2013). In Fig. 11 we show residuals obtained by subtracting the best \ufb01t relation of Graham & Scott (2013) from the measured values. We focus here on the regime within the range 170 < \u03c3 < 260 km/s, where the core fast rotators occur. There are MBH estimates for three13 such galaxies (in or13 The only other core fast rotator of the ATLAS3D sample with a MBH is NGC4649 harbouring one of the most massive known Figure 11. Residuals from the best \ufb01tting MBH \u2212\u03c3 scaling relation of Graham & Scott (2013) for all galaxies in their sample. Horizontal dashed lines show the scatter of the MBH \u2212\u03c3. Core fast rotators are found only (see footnote 13) in the limited \u03c3 range bounded by the vertical dotted lines and used for statistical analysis (see the text). Open triangles represent galaxies not in the ATLAS3D sample. Solid symbols represent galaxies in the ATLAS3D sample. Core-less galaxies are plotted with blue symbols and core galaxies with red symbols, while fast and slow rotators are shown with circles and squares, respectively. Therefore, core fast rotators are shown as red circles, core-less fast rotators as blue circles, while blue squares represent core-less slow rotators and red squares represent core slow rotators. Of four open triangles above the best \ufb01tting relation, two objects have cores (their names are shown), while two do not. der of increasing \u03c3): NGC4473, NGC337914, and NGC524. All have MBH more massive than the best-\ufb01tting relations. This is irrespective of which relation is used (we investigated also those from Ferrarese & Ford 2005 and McConnell & Ma 2013). Noteworthy is also that there are estimates for two core-less slow rotator (NGC3414 and NGC5576), and their MBH fall below and above15 the best \ufb01tting relations, respectively. Within the selected \u03c3 range, the mean value of residuals for core fast rotators is 0.23 \u00b1 0.07, while for core slow rotators is 0.22 \u00b1 0.02. In contrast the mean value of residuals for core-less fast rotators is \u22120.19 \u00b1 0.02. This suggests that MBH of core fast rotators are similar to MBH of slow rotators in this limited \u03c3 range, at which both types of galaxies occur. Core-less galaxies seem to typically have lower MBH. This black holes and with \u03c3 \u223c340 km/s. We discussed this galaxy in Section 4.2.2. 14 Even when using the lower (axisymmetric) MBH estimate for NGC3379 of Shapiro et al. (2006) instead of the more massive triaxial estimate of van den Bosch & de Zeeuw (2010), this galaxy remains above the mean relations. 15 We remind the reader that NGC5576 is classi\ufb01ed as core in Lauer et al. (2005). c \u20dd2012 RAS, MNRAS 000, 2\u201332 20 Davor Krajnovi\u00b4 c et al. suggests that black holes in all core galaxies (of the same velocity dispersion or mass) are similar, regardless whether they live in a fast or a slow rotator, implying that core formation proceeded in a similar process. There are signi\ufb01cant systematics associated with determination of MBH, such as using triaxial instead of axisymmetric models (van den Bosch & de Zeeuw 2010), or inclusion of a dark matter halo (e.g. Gebhardt & Thomas 2009; Schulze & Gebhardt 2011). The systematics in\ufb02uence the determination of MBH by at least a factor of 2. Additionally our statistic is based on a limited number of galaxies. Finally, in the investigated \u03c3 range there are eight galaxies which we cannot classify as fast or slow rotators, four above and four below the best \ufb01tting relations. Only two of these galaxies have cores, NGC5077 (Rest et al. 2001) and NGC7768 (McConnell et al. 2012, but see Laine et al. 2003) and these are found above the best \ufb01tting relations. The other two galaxies above the best \ufb01tting relation, NGC3115 and NGC3585, are core-less (Lauer et al. 2005), but including those to the core-less fast rotators would not change signi\ufb01cantly the statistics (the mean of the core-less fast rotator residuals moves to \u22120.17\u00b10.02). Therefore we conclude that there is a tentative result that black holes in core fast rotators are similar in mass to those in core slow rotators, but di\ufb00erent from those in core-less fast rotators (of the same galaxy mass or \u03c3). 5.5 Multiple scenarios for formation of cores The currently favoured scenario for formation of cores is based on evidence from numerical models of binary black hole interactions (Ebisuzaki et al. 1991; Makino & Ebisuzaki 1996; Quinlan 1996; Quinlan & Hernquist 1997; Milosavljevi\u00b4 c & Merritt 2001; Milosavljevi\u00b4 c et al. 2002; Merritt et al. 2007; Kulkarni & Loeb 2012; Gualandris & Merritt 2012). The idea (Begelman et al. 1980) is that as black holes spiral down, the binary loses its angular momentum by ejecting stars found in the vicinity. The binary black hole might not fully merge, but the stars are quickly depleted form the nucleus (e.g. Yu 2002; Milosavljevi\u00b4 c & Merritt 2003; Makino & Funato 2004; Merritt & Milosavljevi\u00b4 c 2005; Merritt 2006b). The de\ufb01cit of the stellar mass can be estimated by counting the number of mergers and assuming a certain e\ufb03ciency for depletion, f, (e.g. Faber et al. 1997), which will depend on the initial nuclear density, types of stellar orbits and the peculiarities of the binary interaction (e.g. Gualandris & Merritt 2012; Khan et al. 2012). For a review of dynamics and evolution of black hole binaries see Merritt (2006a). According to this scenario, the major ingredient for removing stars in galactic nuclei is a secondary black hole, which will interact gravitationally with the one that is already present (but see Kulkarni & Loeb 2012). This black hole has to be relatively massive (comparable with the host black hole) in order to sink rapidly to the nucleus. This implies that core formation happens in comparablemass merger events. Finally, if the merger involves significant quantities of gas, it is likely that the core will be \ufb01lled in by new stars created in a nuclear starburst associated with the gas-rich merger (e.g. Mihos & Hernquist 1994; Barnes & Hernquist 1996; Rothberg & Joseph 2004; Hopkins et al. 2008, 2009a). Therefore, the equal mass mergers should also be mostly non-dissipative (but see Hopkins et al. 2009b, who show that it is possible to have some star-formation resulting in a younger component of the galaxy, but not su\ufb03ciently large to prevent the formation of a core.) On the other hand, the existence of massive black holes in core-less galaxies, as evident in the MBH \u2212\u03c3 relation, suggests that the actual time-scales of the coalescence of black holes (and core formation) could be shorter than that of nuclear star-bursts (Faber et al. 1997; Kormendy et al. 2009). Additionally, the presence of gas could contribute in taking away the energy of the shrinking binary (instead of sling shot stars) and prevent the creation of a core (Milosavljevi\u00b4 c & Merritt 2001). Furthermore, a core created early (e.g. Kulkarni & Loeb 2012) could be erased by a later (even minor) gas rich accretion or merger events. There are other scenarios for the re-growth of steep core-less pro\ufb01les. For example, through adiabatic growth of black holes (van der Marel 1999) or via an energy exchange between stars moving in the gravitational \ufb01eld of the single black hole (Merritt & Szell 2006). The hardening binary scenario for core formation is interesting also as it takes place on the right spatial scales of 1-100 pc, which closely corresponds to the observed sizes of cores (Faber et al. 1997; Ferrarese et al. 2006; C\u02c6 ot\u00b4 e et al. 2007). It is, however, not the only possible scenario for formation of cores (e.g. see also Gualandris & Merritt 2008). An alternative scenario is based on a rapid mass-loss in the nucleus of a stellar system (e.g. globular cluster) which in\ufb02uences its dynamical evolution and, in particular, increase of size (Hills 1980). A side e\ufb00ect of such an adiabatic expansion is that as the stars are redistributed, the light pro\ufb01le changes and becomes \ufb02atter in the centre (e.g. Hopkins et al. 2010). Supernova feedback and AGNs are invoked as possible initiators of the mass-loss (Navarro et al. 1996; Gnedin & Zhao 2002; Read & Gilmore 2005; Governato et al. 2010; Teyssier et al. 2012), speci\ufb01cally in the context of creation of cores in dark matter pro\ufb01les (Pontzen & Governato 2012). As stars and dark matter share collision-less dynamics, these processes could be responsible for production of both extended sizes of galaxies at low redshift, as well as stellar cores that are of interest here (e.g. Martizzi et al. 2012a). The simulations of Martizzi et al. (2012a,b), which investigate the in\ufb02uence of repeatedly occurring AGN in a galaxy equivalent to a brightest cluster galaxy, show that resulting gravitational \ufb02uctuations can be very e\ufb00ective in creating a stellar core, in addition to a core in the dark matter density. These simulations, however, can not resolve the nuclei of galaxies (their stellar cores are \u223c10 kpc in size). An additional signi\ufb01cant complication is that, unlike in the case of dark mater, each of the cooling episodes, which follow the cessation of nuclear activity, could result in formation of new stars. Those would not have the memory of the previous perturbations, and thus prohibit the formation of stellar cores. More simulations of higher resolution are, however, needed to give weight to this process of stellar core formation. c \u20dd2012 RAS, MNRAS 000, 2\u201332 Angular momentum and nuclear light pro\ufb01les 21 5.6 Using nuclear pro\ufb01les to di\ufb00erentiate between formation histories Generally, cores are found in slow rotators and core-less galaxies are in fast rotators, adding to the separation of early-type galaxies based on their physical properties as outlined in Kormendy & Bender (1996), Paper VII and Kormendy & Bender (2012). The most dominant processes that shape early-type galaxies are those that create (or maintain) core-less fast rotators and core slow-rotators. As a \ufb01rst approximation, they can be divided into dissipational and dissipationless, respectively, where the general properties of early-type galaxies can be explained by a sequence of the relative mass fractions and the quantity of gas involved. In addition to this global division, the existence of core fast rotators and core-less slow rotators, even if they are rare, points to possible additional scenarios, or speci\ufb01c combinations thereof. As seen in simulations of binary mergers (Paper VI; Ho\ufb00man et al. 2010), even dry mergers can spin up the remnant, and, depending on the orbital con\ufb01guration of the merger, produce fast rotators. Furthermore, slow rotators can be produced in mergers with gas, where the gas fraction plays a less important role compared with the orbital arrangement of the progenitors (e.g. Paper VI, Ho\ufb00man et al. 2009). Following the core scouring scenario, all those galaxies su\ufb00ering from major mergers, that end up either as fast or as slow rotators, should have cores. A crucial distinction is that dissipationless major mergers do not result in an anticorrelated V/\u03c3 \u2212h3, contrary to dissipative major mergers (e.g. Naab et al. 2007; Ho\ufb00man et al. 2009). Given that fast rotators, including those with cores, show an anti-correlated V/\u03c3 \u2212h3, explaining the cores in fast rotators requires an additional constraint on the formation process. Cores in fast rotators point to either a gasrich merger with a nuclear starburst that is shorter than the time needed for the hardening of the black hole binary (Faber et al. 1997; Kormendy et al. 2009), or to scenarios in which the core was either created afterwards (e.g. AGN induced as outlined above), or the galaxy was spun up later in a process that did not destroy the core. The main point here is that there has to be a process that regulates the star formation in the nucleus, such that the core is not (completely) \ufb01lled, as the spinning up of the main body, such that V/\u03c3 and h3 get anti-correlated, is likely possible only with acquisition of gas (but for the e\ufb00ect of multiple minor dissipationless mergers on the V/\u03c3 only see Bournaud et al. 2005). The current literature suggests two such processes: feedback from the black hole (e.g. Di Matteo et al. 2005) or morphological quenching (Martig et al. 2009). NGC0524 is a possible example of the latter case. The core of this galaxy is relatively small, but the galaxy contains a dusty disc as well as a signi\ufb01cant amount of molecular gas in the nucleus (Paper IV, Alatalo et al. 2012). It is, however, not forming stars signi\ufb01cantly (Crocker et al. 2011), while Martig et al. (2012) argue that this is due to the large bulge mass of this galaxy, which quenches star formation by stabilising the local turbulences. A small core in one of the most massive fast rotators with a mid-range \u03bbR, could be a relic of a larger core which was only partially re\ufb01lled by a quenched starburst. Generally, it is most likely that formation scenarios di\ufb00er from object to object, which Figure 12. Velocity dispersion radial pro\ufb01les for galaxies with \u03bbR < 0.3 obtained with kinemetry from SAURON maps. Each panel shows pro\ufb01les for a di\ufb00erent population of objects: (top left) slow-rotators with no HST imaging together with core-less slow rotators separated in \ufb02at (\u01eb > 0.2, blue dashed lines) and round (\u01eb < 0.2, red, dashed-dotted lines), (top right) fast rotators with core-less pro\ufb01les, (bottom left) slow rotators with cores and (bottom right) fast rotators with cores. All pro\ufb01les are normalised to a third of the e\ufb00ective radius for presentation purpose. could explain (the second order) peculiarities in the observed kinematics of core fast rotators (see Section 4.2). In Section 5.3 we suggested there is a sub-class of slow rotators with likely core-less light pro\ufb01les (although no HST imaging is available). As these galaxies show evidence for anti-correlation in V/\u03c3 \u2212h3, their evolution has to be linked to those dissipative (gas-rich) mergers (e.g. Naab et al. 2006, 2007; Jesseit et al. 2007), which are, however, also able to decrease the overall angular momentum. The mechanism of making slow rotators in major mergers with gas is related to orbital con\ufb01guration of galaxies (Paper VI, Naab et al. in prep.), but it is not trivial to detect it in simulations as it strongly depends on resolution (Bois et al. 2010). If these galaxies contained cores before the last major merger, cores could be re-\ufb01lled with a central starburst fuelled by the gas, provided the above outlined quenching processes are not e\ufb00ective (indeed \u03c3e of these galaxies are smaller), and there exist a \ufb01ne-tuning between the duration of the nuclear starburst and the evolution of the binary black hole, such as that the coalescence of the binary is shorter than the starburst (a contrary case to one mentioned above for the creation of cores). The existence of gas could indeed speed up the hardening of the black hole binary (Armitage & Natarajan 2002), although feedback effects need to be better understood Simulations show that galaxies, which experienced a major dissipative merger that decreased the global angular momentum, should show evidence for drops in the central velocity dispersion associated with embedded disc-like structures c \u20dd2012 RAS, MNRAS 000, 2\u201332 22 Davor Krajnovi\u00b4 c et al. created in the starburst (Naab et al. in prep). We investigate this by plotting in Fig. 12 radial velocity dispersion pro\ufb01les for core fast and slow rotators, core-less fast and slow rotators (with \u03bbR < 0.3) and slow rotators with no HST data (which we assume are also core-less). The pro\ufb01les were obtained by running kinemetry (in even mode) on \ufb01xed ellipses corresponding to the measured global ellipticity and position angle (Paper II). As expected, the majority of velocity dispersion pro\ufb01les are rising in the centre. This is in particular the case for core galaxies (with a few exceptions). Core-less fast rotators often have signi\ufb01cant \u03c3 drops. Assumed core-less slow rotators (those with no HST data) are perhaps best described as having \ufb02at central velocity dispersion pro\ufb01les, making them marginally consistent with expectations. Similar \u03c3 pro\ufb01les are found in all \ufb02at (\u01eb > 0.2) core-less slow rotators, but not in those that are more round. This suggests that all \ufb02at slow rotators in the ATLAS3D sample experienced a gas rich merger event, which did not create a bona \ufb01de fast rotator, but it left cuspy nuclear light pro\ufb01les (including in those galaxies with no available HST data), and created a sub-population of slow rotators. From the stellar populations point of view, cores follow the trends of host galaxies: as they are found in massive galaxies, cores are made of old and metal rich stars. This implies that at least some cores were made early, during the more violent, \ufb01rst phase of mass assembly, as outlined by Oser et al. (2010). They are subsequently kept frozen, while the main body of the galaxy grew during the second phase of galaxy evolution. If this evolution induces regular rotation, then it could be a possible path for formation of core fast rotators. On the other hand, some cores were carved out in non-dissipative processes via black hole binaries with no new star formation, providing an applicable path for formation of cores at later times. In Fig. 13 we summarise processes that dominate in the creation of core and core-less early-type galaxies. The majority of galaxies are found in the upper right box (core-less fast rotators). Their mass assembly is dominated by dissipative processes with varying gas fractions, while the nuclear cusps are created in a nuclear starburst or, perhaps, in interaction between the single black hole and surrounding stars (as mentioned in Section 5.5). Similar processes act to produce core-less slow rotators (lower right box), comprising perhaps up to a quarter of the total population of slow rotators. Likely, there is a continuity of properties in the formation scenarios which create core-less fast and slow rotators, with a notable di\ufb00erence in the merging con\ufb01guration, such that those processes forming slow rotators can signi\ufb01cantly lower the angular momentum of the remnant. The second most numerous group in the ATLAS3D sample is represented by the lower left box. These are the most massive, weakly triaxial galaxies living mostly in centres of clusters harbouring classical cores. As previous studies evoked (e.g. De Lucia & Blaizot 2007; Naab et al. 2007; Kere\u02c7 s et al. 2009; Khochfar & Silk 2009; Dekel et al. 2009; Feldmann et al. 2010), their formation is dominated by nondissipative major and multiple minor mergers. Duc et al. (2011) showed, however, that major dissipative mergers are also possible among at least some of these objects. The cores are grown by scouring via black hole binaries, but they could also be induced by AGNs that remove signi\ufb01cant amounts of mass in a short time-scale and hence change the Figure 13. A summary of the dominant processes that shape the angular momentum of a host galaxy and its nuclear pro\ufb01le. potential. This process could adiabatically grow both cores and the host galaxies (e.g. Hills 1980; Hopkins et al. 2010; Ragone-Figueroa & Granato 2011). If the cores have been created early, the ability to maintain them is likely linked to the existence of hot halo gas (Kormendy et al. 2009, Paper XIX), especially for those galaxies with an excess of di\ufb00use X-ray emission, such as those living in cluster cores (Fig. 8). Finally, the kinematic structure of the rare core fast rotators (i.e. velocity maps, V/\u03c3\u2212h3 anti-correlation) indicates that they are also formed in gas rich assembly processes, but their cores could be explained as results of a \ufb01ne tuning between the duration of the binary black hole coalescence and duration of the starburst. Alternatively, existing cores could be maintained through mechanisms that regulate (perhaps fully stop) star formation in the nucleus, but allow rebuilding of disc-like structures at large radii, such as the AGN feedback, or morphological quenching. Cored fast rotators seem to have similar di\ufb00use X-ray emission like core-less galaxies. A simple possibility might be that their gas reservoirs are depleted (e.g. in dense environments), or are kept at large radii where the densities are not su\ufb03cient for star formation (Paper XIII). Dullo & Graham (2013) link these systems with compact galaxies at z \u223c1.5, which were able to grow a disk. Indeed, multiple non-dissipative minor mergers (e.g. mass ratios larger than 1:4, Bournaud et al. 2005) could provide the required large-scale kinematics and photometric structure (e.g Scannapieco & Tissera 2003; Eliche-Moral et al. 2012), but it is not clear to what extent they would preserve the existing core. 6 SUMMARY In this paper we connect data from the HST archive with ATLAS3D results to investigate the links between the nuclear structure and global kinematic properties of early-type galaxies. The observations show: (i) There is a general correspondence between the classi\ufb01cations into fast \u2013 slow rotators and core \u2013 core-less pro\ufb01les, c \u20dd2012 RAS, MNRAS 000, 2\u201332 Angular momentum and nuclear light pro\ufb01les 23 as one would expect if both slow rotators and cores were related to dry merging. However, there are exceptions, which indicate that the detailed process that form a core galaxy do not always produce a slow rotator and vice versa. (ii) Galaxies without cores dominate the population of early-type galaxies: of 135 ATLAS3D galaxies with HST imaging there are 98 core-less galaxies (78 power-law, 20 intermediate cases), 24 cores and 13 galaxies for which we were unable to characterise the nuclear pro\ufb01les. We do not \ufb01nd evidence for a dichotomy between core and core-less galaxies. (iii) The 135 galaxies we analysed are divided in 112 fast rotators and 23 slow rotators. We were able to investigate 50 per cent of the fast rotators and about 68 per cent of the slow rotators in the ATLAS3D sample. A consequence is that the observed 72 per cent (98 of 135) of core-less galaxies is almost certainly a lower limit. Based on trends in Figs. 4, 6, 7 and 9, it is likely that only a few more slow and fast rotators contain cores. We estimate that they occur in about 10 per cent of nearby early-type galaxies. (iv) Cores are found in the most massive and most luminous bodies. Fast rotators with cores are on average less massive than slow rotators with cores, but the lower mass limit for existence of cores is the same in both types: there seem to be no cores in galaxies less massive than 8 \u00d7 1010 M\u2299. All slow rotators above 2 \u00d7 1011 M\u2299have cores. The same might not be true for fast rotators. (v) A a good predictor for determining if a galaxy has a core is \u03bbR \u2212\u03c3e diagram, readily obtained with integral\ufb01led spectrographs. More speci\ufb01cally, based on our data any galaxy with observed \u03bbR \u22720.25 and \u03c3e \u2273160 km/s will, most likely, have a core. As a more conservative estimate we suggest using \u03bbR \u22720.2. Future IFS surveys might be able to both distinguish between core and core-less pro\ufb01les and di\ufb00erentiate fast and slow rotators, creating a more complete picture of possible processes forming early-type galaxies. (vi) Slow and fast rotators with cores share similar projected shape (\u01eb < 0.2)16, if NGC4473 and NGC3613 are excluded. The majority of slow rotators and some fast rotators with cores populate the region in mass \u2013 size diagram that is expected to be dominated by evolutionary processes, which do not change \u03c3 of the galaxy, but change its mass and size. Lower mass (below 2 \u00d7 1011 M\u2299) core galaxies (both slow and fast rotators) are in the regime where dissipative (gas rich) processes also in\ufb02uence the evolution. (vii) Compared to core slow rotators, X-ray luminosities of core fast rotators are typically smaller, and similar to those found in core-less galaxies. While the presence of a hot medium prevents cooling of external and internal gas, and, therefore inhibits star formation, the lack of this medium does not imply a core-less structure. Similarly, the creation of a core does not require a formation of a rounder galaxy, which would be more capable of retaining the hot gas halo. (viii) Slow and fast rotators with cores share some additional characteristics: similar stellar populations, and a general lack of atomic and molecular gas. Additionally, we conjecture, based on only a few cases, that masses of central black holes in core fast rotators are similar to those found in core slow rotators. The implication of this results may be 16 Note that among these there could be galaxies that are likely intrinsically \ufb02at that cores in both fast and slow rotators were made through the same process (i.e. black hole binary interaction), but the subsequent evolution of the host galaxies was di\ufb00erent. (ix) Slow and fast rotators with cores do not have the same dynamics. The majority of core fast rotators shows evidence of embedded disc components seen in regularly rotating velocity maps, exponential S\u00b4 ersic components and anticorrelation in V/\u03c3 \u2212h3 distribution. (x) Based on the present data, core-less slow rotators are rare and often found in slow rotators with large ellipticities (\u01eb > 0.35). There is, however, another potential subpopulation of slow rotators which could also contain coreless nuclei, even though they share similar ellipticity range as core slow rotators (0.2 < \u01eb < 0.35) and similar angular momentum as core fast rotators (0.1 < \u03bbR < 0.2). These systems are dynamically di\ufb00erent from fast rotators because their velocity maps are irregular and they are too \ufb02at to be considered discs at low inclinations, but they show a minor anti-correlation in V/\u03c3\u2212h3 distribution and have central drops in the velocity dispersion maps. Furthermore, they are less massive (< 8 \u00d7 1010 M\u2299) and have low \u03c3 (<160 km/s). (xi) The lack of cores in some slow rotators suggest the existence of a sub-population of slow rotators. Similarly, fast rotators with cores could be part of a sub-populations of fast rotators with di\ufb00erent formation scenario from the majority of objects in this class, as predicted by semi-analytic models. (xii) Cores do not occur only in non-rotating or triaxial objects with KDCs, but can also be found in quite regularly rotating galaxies, with embedded disc-like structures, provided they are massive. Therefore, core formation should not be linked only to dissipationless dry mergers and binary black holes. Additional possible processes include: dissipative major mergers where the evolution of the black hole binary is longer than the duration of the nuclear starburst and an AGN induced growth of cores linked with the size evolution of the host. Furthermore, cores could be maintained by regulation of the nuclear star formation via AGN feedback or morphological quenching. The existence of core-less slow rotators also suggest di\ufb00erent formation scenarios from those creating the majority of (round and cored) slow rotators. ACKNOWLEDGEMENTS We thank Laura Ferrarese, Patrick C\u02c6 ot\u00b4 e and the ACSVCS team for providing the 44 light pro\ufb01les of Virgo Cluster galaxies. MC acknowledges support a Royal Society University Research Fellowship. MS acknowledges support from an STFC Advanced Fellowship ST/F009186/1. RMcD is supported by the Gemini Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc., on behalf of the international Gemini partnership of Argentina, Australia, Brazil, Canada, Chile, the United Kingdom, and the United States of America. SK acknowledges support from the Royal Society Joint Projects Grant JP0869822. TN and MBois acknowledge support from the DFG Cluster of Excellence \u2018Origin and Structure of the Universe\u2019. PS is an NWO/Veni fellow. LY acknowledges support from NSF AST-1109803. The research leading to these results has received funding from the European Community\u2019s Seventh Framework Programme (/FP7/2007-2013/) under grant agreement No 229517. This work was supported by the c \u20dd2012 RAS, MNRAS 000, 2\u201332 24 Davor Krajnovi\u00b4 c et al. rolling grants \u2018Astrophysics at Oxford\u2019 PP/E001114/1 and ST/H002456/1 and visitors grants PPA/V/S/2002/00553, PP/E001564/1 and ST/H504862/1 from the UK Research Councils. Based on observations made with the NASA/ESA Hubble Space Telescope, and obtained from the Hubble Legacy Archive, which is a collaboration between the Space Telescope Science Institute (STScI/NASA), the Space Telescope European Coordinating Facility (ST-ECF/ESA) and the Canadian Astronomy Data Centre (CADC/NRC/CSA).",
                    "introduction": "Dichotomies of physical parameters o\ufb00er safe anchor points to which one can tie theoretical scenarios of galaxy evolution. It is, therefore, no wonder that a lot of e\ufb00ort was devoted to establish the existence of separate classes of early-type galaxies, in particular, ellipticals. Based purely on imaging, early-type galaxies can be divided into those that have and do not have discs, and this gave rise to the classical dis- tinction between elliptical and S0 galaxies (Reynolds 1920; Hubble 1922, 1926; Jeans 1928) and the Hubble sequence of galaxies (Hubble 1936; Sandage 2005, for a review). As the appearance of a galaxy is strongly dependant on its chance orientation in space, separating ellipticals and S0s as two separate classes is, however, not entirely founded on their physical properties (e.g Michard 1994; Jorgensen & Franx 1994). A promising path was established by using the disci- ness parameter (e.g Lauer 1985a; Bender et al. 1988), which showed there are discs in galaxies classi\ufb01ed as ellipticals. However, when the inclination is below \u223c60\u25e6, the discy deformation of the isophotes ceases to be seen even in high signal-to-nose data (or models) of elliptical galaxies \u22c6E-mail: dkrajnovic@aip.de \u2020 Dunlop Fellow (Rix & White 1990; Gerhard & Binney 1996). While disci- ness enables one to connect these systems to disc dominated galaxies, S0s and spirals (Kormendy & Bender 1996, 2012), its degeneracy with inclination does not provide a robust picture. A more promising path is to consider kinematics and, hence, the dynamical state of galaxies. Indeed, as soon as samples of early-type galaxies with resolved kinematics were available (e.g. Illingworth 1977; Kormendy & Illingworth 1982; Davies et al. 1983), galaxies were plotted in theo- retically motivated V/\u03c3 diagrams (Binney 1978), where V is the maximum rotational speed, a measure of or- dered motion, and \u03c3 the central velocity dispersion, a measure of random motion. The combination of isopho- tal parameters and kinematic properties accumulated dur- ing the 1980s and 1990s clearly showed that there are two types of elliptical galaxies: luminous ellipticals with round or boxy isophotes that rotate slowly, and faint ellipticals with discy isophotes that rotate fast (e.g. Bender et al. 1989; Nieto & Bender 1989; Kormendy & Djorgovski 1989; Nieto et al. 1991; Kormendy & Bender 1996). Next to the issue of a strong degeneracy with in- clination for isophotal shapes1, the kinematic results of 1 The degeneracy applies really to the disciness parame- c \u20dd2012 RAS, MNRAS 000, 2\u201332 Angular momentum and nuclear light pro\ufb01les 3 the 1980s and 1990s were based on information along long-slits, often only one (along the major axis) or, at best, two (along minor and major axes), but rarely more (but see Davies & Birkinshaw 1988). While the main kinematic properties of galaxies can be inferred in this way (e.g. the existence of kinematically distinct cores, hereafter KDCs; Efstathiou et al. 1982; Bender 1988; Jedrzejewski & Schechter 1988; Franx & Illingworth 1988), the characterisation of the kinematic properties, such as angular momentum, is di\ufb03cult and not robust (e.g. Cappellari & McDermid 2005). This was improved with the advent of integral- \ufb01eld spectrographs which can cover a signi\ufb01cant part of the galaxy body. One of these instruments is SAURON (Bacon et al. 2001), initially used to survey a representa- tive sample of nearby-early types galaxies (SAURON Sur- vey, de Zeeuw et al. 2002). The SAURON survey showed it is possible to derive a measure of the speci\ufb01c angular mo- mentum, \u03bbR (Emsellem et al. 2007), and use it to divide early-type galaxies in two classes, slow and fast rotators, in a way that is robust to inclination e\ufb00ects (Cappellari et al. 2007). The ATLAS3D Project (Cappellari et al. 2011a, here- after Paper I) surveyed a complete and volume limited sam- ple of nearby early-type galaxies, providing a statistical view of the relative numbers of ETGs belonging to the fast and slow rotator categories. In the nearby Universe the vast ma- jority of early-type galaxies, including as much as 66 per cent of the galaxies classi\ufb01ed as ellipticals, are fast rotators (Emsellem et al. 2011, hereafter Paper III), close to axisym- metric galaxies (modulo bars) with regular disc-like rotation (Krajnovi\u00b4 c et al. 2011, hereafter Paper II). The project showed that the fast rotator class is domi- nated by discs (Krajnovi\u00b4 c et al. 2012, hereafter Paper XVII). Furthermore, fast rotators form a smooth parallel sequence to spiral galaxies on the luminosity/mass\u2013size plane (e.g. \ufb01g. 4 of Paper I). This was found to be due to a trend in the bulge fraction which appears the key driver for galaxy prop- erties (Cappellari et al. 2012a, hereafter Paper XX). This motivated a re-visitation of van den Bergh\u2019s proposed revi- sion to Hubble\u2019s tuning fork, which emphasised a parallelism between S0 and spiral galaxies. We showed that the true parallelism is the one between fast rotator ETGs and spi- rals instead (Cappellari et al. 2011b, hereafter Paper VII). Similar conclusions were also reached using photometry by Laurikainen et al. (2011) and Kormendy & Bender (2012). The improved imaging capabilities of the 1980s and 1990s also brought to light another distinction between early-type galaxies: those that contain steep and \ufb02at sur- face brightness pro\ufb01les in the nuclei (e.g. Lauer 1985b; Kormendy 1985; Nieto et al. 1991). This \ufb01eld of research was revolutionised by Hubble Space Telescope (HST) imaging ters. Its counter-part, the boxiness parameter (Lauer 1985a; Nieto & Bender 1989), is less susceptible, but su\ufb00ers from two setbacks. As galaxies showing boxy isophotes are often triaxial, there are projections at which the isophotes will look more round (Franx et al. 1991). Furthermore, bars viewed edge-on often have a shape of a peanut, and hence show strong boxy distortion to the isophotal shape. Galaxies harbouring such bars should, naturally, not be confused with triaxial ellipticals as they are dynamically di\ufb00erent. which con\ufb01rmed the distinction between galaxies with cores, where a core is the region in which the surface brightness pro\ufb01les \ufb02atten out, and those, often referred to as power- laws, that exhibit a rise in the surface brightness pro\ufb01le up to the resolution limit of 0.1\u2032\u2032 (or less), corresponding to \u223c8 pc at the distance of Virgo (e.g. Ferrarese et al. 1994; Lauer et al. 1995; Faber et al. 1997; Rest et al. 2001; Ravindranath et al. 2001). An alternative way of looking at the distinction in the surface brightness pro\ufb01les is to emphasise the di\ufb00er- ence between those galaxies that exhibit excess (related to power-laws) to those that show a de\ufb01cit (related to cores) of light compared to a S\u00b4 ersic \ufb01t to large radial range (e.g. Graham et al. 2003; Trujillo et al. 2004; Ferrarese et al. 2006; Kormendy et al. 2009). An obvious next step was to compare the three physical properties which suggest two populations of ellipticals: large- scale structure (i.e. isophotal shapes - disciness and boxi- ness), kinematics (dominance of ordered or random motions) and nuclear pro\ufb01les (cores and power-laws). An initial com- parison (not including kinematics) of Ferrarese et al. (1994), based on a small sample, indicated a link between power-law (Type II in their study) and discy ellipticals, as well as core galaxies (Type I in their study) and \u201cclassical disk-free el- lipticals\u201d. As a step further, Faber et al. (1997) compared the nuclear light pro\ufb01les of a larger sample with both global structural and kinematic properties (see also for a contem- porary study of KDC galaxies Carollo et al. 1997). Their conclusion was that cores were found in luminous, boxy2 and slowly rotating galaxies, while power-law galaxies were associated with less luminous discy and rapidly rotating el- lipticals and S0s. A con\ufb01rmation of this trend was given in Rest et al. (2001) who found only one of nine core galaxies with discy isophotes. The aim of this work is to connect the angular mo- mentum based separation of early-type galaxies from the ATLAS3D survey with properties of their nuclear surface brightness pro\ufb01les. Paper III showed there is a clear trend that cores (or de\ufb01cits of light) are found in slow rotators, while power-laws (or excesses of light) in fast rotators. Re- cently, this was expanded by Lauer (2012), who, based on a larger sample, concluded that the division in slow and fast rotators essentially follows the division in core and power- law galaxies, and therefore re\ufb02ects the Kormendy & Bender (1996) division of ellipticals based on isophote shape, rota- tion and central structure. We agree with the motivating statement of Lauer (2012) that the division of galaxies in power-laws and cores is signi\ufb01cant and o\ufb00ers important clues about galaxy evolution, but we prefer to retain a pure kine- matic classi\ufb01cation of early-type galaxies and not to move the boundary between fast and slow rotators such as to in- clude all core galaxies. Here we look in more detail into those cases which seem to spoil the clean separation of early-type galaxies in two classes. Our work di\ufb00ers from that of Lauer (2012) in two ma- jor points. First, in this work we extend the data base of ATLAS3D galaxies with core/power-law classi\ufb01cation by al- most a factor of 2. This allows us to show the existence of 2 Note that in Faber et al. (1997) boxy are those galaxies with boxy, round and strongly varying isophotes. c \u20dd2012 RAS, MNRAS 000, 2\u201332 4 Davor Krajnovi\u00b4 c et al. signi\ufb01cant populations of power-law slow rotators and core fast rotators. Secondly, the separation of fast and slow rota- tors from Paper III is robust and core fast rotators are not kinematically misclassi\ufb01ed galaxies. Additionally, we show that inclination e\ufb00ects can not be used to explain the exis- tence of power-law galaxies among slow rotators. Based on our larger sample, and using additional ATLAS3D data, we reach some conclusions that di\ufb00er from Lauer (2012). The main \ufb01nding could be summed up in the following way: di\ufb00erences between early-type galax- ies are unquestionable, and they lie along the lines sum- marised by Kormendy & Bender (1996), Paper VII and Kormendy & Bender (2012). Nevertheless, the actuality of both core fast rotators and (likely a signi\ufb01cant sub- population of) core-less slow-rotators has serious implica- tions for the range of core formation mechanisms as well as the whole assembly history of early-type galaxies, which might be more varied than heretofore appreciated. A particular strength of our work is in relying on a clearly selected volume limited sample of nearby early-type galaxies using the largest available sample of HST obser- vations. Regarding the later point, our results are only as robust as the match between ATLAS3D and HST observed samples. Only about half of ATLAS3D galaxies are actually observed with the HST, but the half that is in the archive clearly points out that with observations of an additional two dozen galaxies all remaining questions could be removed (as we argue in Section 5.3). Our study is divided into six sections. In Section 2 we brie\ufb02y describe the ATLAS3D sample and our search through the HST archive. In Section 3 we discuss in detail our pre- ferred choice of analysis of nuclear pro\ufb01les and de\ufb01ne the two classes of core and core-less galaxies. In Section 4 we present the main results of this study, namely the relations between nuclear pro\ufb01les and other global properties of galaxies, such as angular momentum, kinematics, mass, stellar populations, X-ray content and environment. This is followed by a dis- cussion in Section 5 where we look into implications of our results with respect to the galaxy evolution scenarios. In Sec- tion 6 we summarise our results. An interested reader can \ufb01nd a comparison of our classi\ufb01cation with the literature and other possible parameterisations in Appendix A, images of galaxies for which we were not able to extract robust light pro\ufb01les in Appendix B and a table with the results in Ap- pendix C."
                },
                {
                    "url": "http://arxiv.org/abs/1210.8167v2",
                    "title": "The ATLAS3D project - XVII. Linking photometric and kinematic signatures of stellar discs in early-type galaxies",
                    "abstract": "[Abridged] We analyse the morphological structures in galaxies of the ATLAS3D\nsample by fitting a single Sersic profile and decomposing all non-barred\nobjects (180 of 260 objects) in two components parameterised by an exponential\nand a general Sersic function. The aim of this analysis is to look for\nsignatures of discs in light distributions of nearby early-type galaxies and\ncompare them to kinematic properties. Using Sersic index from single component\nfits for a distinction between slow and fast rotators, or even late- and\nearly-type galaxies, is not recommended. Assuming that objects with n>3 are\nslow rotators (or ellipticals), there is only a 22 per cent probability to\ncorrectly classify objects as slow rotators (or 37 per cent of previously\nclassified as ellipticals). We show that exponential sub-components, as well as\nlight profiles fitted with only a single component of a low Sersic index, can\nbe linked with the kinematic evidence for discs in early-type galaxies. The\nmedian disk-to-total light ratio for fast and slow rotators is 0.41 and 0.0,\nrespectively. Similarly, the median Sersic indices of the bulge (general Sersic\ncomponent) are 1.7 and 4.8 for fast and slow rotators, respectively. Overall,\ndiscs or disc-like structures, are present in 83 per cent of early-type\ngalaxies which do not have bars, and they show a full range of disk-to-total\nlight ratios. Discs in early-type galaxies contribute with about 40 per cent to\nthe total mass of the analysed (non-barred) objects. The decomposition into\ndiscs and bulges can be used as a rough approximation for the separation\nbetween fast and slow rotators, but it is not a substitute, as there is only a\n59 per cent probability to correctly recognise slow rotators. Kinematics (i.e.\nprojected angular momentum) remains the best approach to mitigate the influence\nof the inclination effects.",
                    "authors": "Davor Krajnovic, Katherine Alatalo, Leo Blitz, Maxime Bois, Frederic Bournaud, Martin Bureau, Michele Cappellari, Roger L. Davies, Timothy A. Davis, P. T. de Zeeuw, Pierre-Alain Duc, Eric Emsellem, Sadegh Khochfar, Harald Kuntschner, Richard M. McDermid, Raffaella Morganti, Thorsten Naab, Tom Oosterloo, Marc Sarzi, Nicholas Scott, Paolo Serra, Anne-Marie Weijmans, Lisa M. Young",
                    "published": "2012-10-30",
                    "updated": "2012-11-13",
                    "primary_cat": "astro-ph.CO",
                    "cats": [
                        "astro-ph.CO"
                    ],
                    "main_content": "The ATLAS3D sample and its selection are described in detail in Paper I. Briefly, ETGs were visually selected from a parent sample of objects in the Northern hemisphere (|\u03b4 \u221229\u25e6| < 35\u25e6, where \u03b4 is the sky declination), brighter than MK < \u221221.5 mag and within a local volume of radius of D = 42 Mpc. The final sample contains 260 nearby early-type galaxies, which were observed with the SAURON IFS (Bacon et al. 2001) mounted on the William Herschel Telescope (WHT). The SAURON kinematics was introduced in Paper I, and we refer to that paper for details on the extraction, while the stellar velocities maps used here were presented in Paper II. Photometric data of 258 galaxies were assembled from the Sloan Digital Sky Survey (SDSS) DR7 (Abazajian et al. 2009) and from our own imaging with the Wide-Field Camera (WFC) mounted on the 2.5m Isaac Newton Telescope (INT). These data, their reduction and photometric calibrations are presented in Scott et al. (2012). In this study we use the r-band imaging. We exclude two galaxies without SDSS or INT imaging from further analysis. We used the same zero points and the photometric calibration as Scott et al. (2012). In Paper II we showed that at least 30% of galaxies in ATLAS3D sample contain bars and/or rings. These systems obviously have more than two components, comprising at least: a bulge, c \u20dd2011 RAS, MNRAS 000, 1\u201329 4 Davor Krajnovi\u00b4 c et al. a bar, a ring (alone or in addition to the bar), and a disc. A two component \ufb01t will not describe these systems well. Crucially, bars (and rings) are disc phenomena; they happen only if there is a disc in the \ufb01rst place. Therefore, we removed from the sample all galaxies showing clear bars (and/or large scale rings), according to classi\ufb01cation in Paper II. This reduced the number of galaxies for the decomposition analysis to 180. Included are 34 of 36 slow rotators (two slow rotators are actually barred galaxies), and 146 of 224 fast rotators, as classi\ufb01ed in Paper III. It is, however, still possible that among the remaining galaxies there are barred systems or galaxies with more than two components. The global one component \ufb01ts, however, we do on all ATLAS3D galaxies (258 galaxies with the SDSS or INT imaging). We caution the reader that in all statistical consideration throughout the paper we use the limited sample of 180 galaxies (no barred galaxies), unless stated otherwise. Specifically, in Section 5.1, which deals with the one components S\u00b4 ersic \ufb01ts, we use the 258 galaxies of the ATLAS3D sample. 3 DECOMPOSITION OF ONE DIMENSIONAL PROFILES 3.1 One or two dimensional decomposition? Parametric decomposition of light into various structural components is often done in two dimensions (e.g MacArthur et al. 2003; de Jong et al. 2004; Allen et al. 2006; Benson et al. 2007; Gadotti 2009; Simard et al. 2009; Weinzirl et al. 2009; Laurikainen et al. 2010; Simard et al. 2011), as more information is available to constrain the parameters of the components. The extra information held in the original images (e.g. on ellipticy and position angle) may be diluted when deriving a one-dimensional pro\ufb01le, and the analysis of one-dimensional pro\ufb01les may not use changes in the other properties to constrain the model parameters. This is important because, for example, while position angle can remain unchanged between the components, the ellipticity will generally differ; if a systems is composed of a spheroidal bulge and a thin disc, there will be a marked change in the ellipticity as one of the components starts dominating over the other (e.g. Binney & Merri\ufb01eld 1998, p 217). Based on simulations, Byun & Freeman (1995), de Jong (1996) and Simard et al. (2002) argued that two dimensional decompositions are superior to those done in one dimension, and several algorithms, of which some are publicly available, have been developed with that purpose, such as GIM2D (Simard et al. 2002), GALFIT (Peng et al. 2002), BUDDA (de Souza et al. 2004; Gadotti 2008), GASPHOT (Pignatelli et al. 2006, using a hybrid 1D/2D approach), GASP2D (M\u00b4 endez-Abreu et al. 2008) and GALPHAT (Yoon et al. 2011). A number of authors, however, continue to work in one dimension (e.g. Graham 2001; Aguerri & Trujillo 2002; Balcells et al. 2003; Blanton et al. 2003; Naab & Trujillo 2006; Fisher & Drory 2008; Kormendy & Bender 2012; Fabricius et al. 2012), while Courteau et al. (1996) and MacArthur et al. (2003) argued that one dimensional decompositions should not be disfavoured as they give similar results as two dimensional \ufb01ts, provided the data have high signal-to-noise ratios. Our purpose here is to attempt to decompose and look for discs in a robust and homogenous way in both fast and slow rotators. To do this, we limit ourselves to considering only simple oneor twocomponent models. We therefore consider that the additional information gained in \ufb01tting two-dimensional images is offering a negligible improvement while introducing signi\ufb01cant additional complexity and computational effort. The high signal-to-noise images and the large size of the ATLAS3D galaxies ensures that extraction of the pro\ufb01les can be done robustly. In the next section we present our method in detail, and in Appendix A we present additional considerations regarding the choice of our methods. 3.2 Method One dimensional light pro\ufb01les were extracted by azimuthally averaging the light along the best \ufb01tting ellipses obtained by means of an isophotal analysis (for an overview of other possibilities see Appendix A). The best \ufb01tting ellipses were found using the method of kinemetry1 (Krajnovi\u00b4 c et al. 2006), run in the even mode optimised for images. It this case, kinemetry reduces to the analysis of even moments of the line-of-sight velocity distribution (e.g. light distributions) and the methodology is similar to Jedrzejewski (1987) and the iraf task ELLIPSE. For a given ring of radius r (semi-major axis length) and thickness \u2206r (which is a geometric function of r such that rings at larger radii are wider), the intensity I(r) is sampled at equal intervals in the eccentric anomaly \u03b8 along a trial ellipse de\ufb01ned by the position angle PA, \ufb02attening Q = b/a, where a and b are the lengths of the semi-major and semi-minor axis, respectively, and the centre (X0,Y0). The intensity I(r,\u03b8) is expanded into a Fourier series and the amplitudes of the Fourier coef\ufb01cients are minimised until a \ufb01t as close as possible to I(r, \u03b8) = const. is achieved. In practice, the centre of a galaxy was pre-determined as the centroid of the light distributions, obtained in the same way as the global photometric position angle and ellipticity in Paper II, and kept \ufb01xed during the analysis. Bright stars and companion galaxies were masked prior to the \ufb01t. Dust is not often seen in our galaxies, and we masked or excluded from \ufb01tting the most contaminated regions. Sky levels were estimated and subtracted from the images using a routine sky.pro available from the IDL Astronomy Library (Landsman 1993). In addition to extracting along the best \ufb01tting ellipses where PA and Q were allowed to vary freely, we also extracted a second set of pro\ufb01les for which PA and Q were \ufb01xed to the global values from Paper II. These two sets of light pro\ufb01les are used for different purposes: the set from the \ufb01xed ellipses for a global single component \ufb01t (see Section 4) and the set from free ellipses for the decompositions as outlined below. We use two different forms of the S\u00b4 ersic (1968) \ufb01tting function to describe the components in the light pro\ufb01les. The \ufb01rst one is a general r1/n model, often used to describe the surface brightness pro\ufb01les (and images) of bulges or whole galaxies (e.g Caon et al. 1993; Graham 2001; de Jong et al. 2004; Weinzirl et al. 2009; Hoyos et al. 2011): I(r) = Ie exp ( \u2212bn \"\u0012 r Re \u00131/n \u22121 #) (1) where Ie is the intensity at the effective radius Re that encloses half of the light of the component, n is the parameter which describes the shape of the function, while bn is dependent on n, and not an additional free parameter. It can be obtained by solving the equation \u0393(2n) = 2\u03b3(2n, bn), where \u0393 is the gamma function and \u03b3(2n, bn) is the incomplete gamma function (Ciotti 1991). We use an accurate numerical approximation of bn = 2n \u22121/3 + 1 An IDL implementation of kinemetry is available at this address: http://www.eso.org/\u223cdkrajnov/idl c \u20dd2011 RAS, MNRAS 000, 1\u201329 Stellar discs in early-type galaxies 5 4/(405n)+46/(25515n2) given in Ciotti & Bertin (1999). A number of useful mathematical expressions related to the S\u00b4 ersic model are given in Graham & Driver (2005). The other function is a special case of the S\u00b4 ersic model when n = 1. In this case the model simpli\ufb01es to an exponential function: Id(r) = I0 exp \u0012 \u2212r Rd \u0013 (2) where I0 = Ieebn is the central surface brightness, Rd = Re/bn is the scale length and bn = 1.678 for n = 1. This exponential form is usually used to de\ufb01ne a disc component, as it reproduces well the outer light pro\ufb01les of disc galaxies (Freeman 1970). In this work we use two sets of parameters linked with eq. (1), one for a single component \ufb01t to the light pro\ufb01le, where the S\u00b4 ersic function describes the total light, and a two components \ufb01t to the light pro\ufb01le, where the general S\u00b4 ersic function describes the bulge light (more precisely, light not belonging to the exponential component). In the former case, the parameters of the eq. (1) are: Ie,tot, Re,tot and ntot, and in the latter case: Ie,b, Re,b and nb . As will be seen later, after the decomposition of some galaxies it is evident that a suf\ufb01ciently good \ufb01t is obtained using the general S\u00b4 ersic component only (i.e the decomposition and the exponential component are not necessary). In these cases, we will still refer to the parameters of the \ufb01t as the bulge parameters (e.g nb), even though they describe the full galaxy, to differentiate if from the direct single component \ufb01t. In spite of both being results of single component \ufb01ts, they are not necessary equal, as will become apparent in Section 4. We decompose the light pro\ufb01les I(r) of ATLAS3D galaxies by assuming that I(r) = Ie,b(r) + Id(r), with Ie,b, Re,b, nb, I0 and Rd as free parameters. The \ufb01t is performed using mpfit (Markwardt 2009), an IDL implementation of the MINPACK algorithm (Mor\u00b4 e et al. 1980) of the Levenberg-Marquardt method. As more parameters will always provide a better \ufb01t to the data, to decide on whether a one component model is suf\ufb01cient to describe the galaxy, we used the following method. The same light pro\ufb01les were \ufb01tted also using only the general r1/n S\u00b4 ersic model eq. (1), within the same radial range. The root-mean-square (rms) of the residuals (within the \ufb01tting range) of these single component \ufb01ts (rms1) were then compared with the rms of the residuals of the two component \ufb01ts (rms2). If rms1 > 1.5\u00d7rms2 then the two components \ufb01t was deemed better than the one component \ufb01t, and its parameters were adopted. It is important to note that we visually inspected all residuals (both one and two components) as it is not only the rms what should be considered, but also the systematic changes in the correlated residuals visible as wiggles. In this respect, adopting a higher threshold value (e.g. rms1 > 2\u00d7rms2) does not change the results signi\ufb01cantly, as long as one considers that the disappearance of the correlated wiggles is the prime evidence for the existence of multiple components (see Section 3.3 and Fig. 1 for more details and examples). The total luminosity of the individual sub-components can be estimated by integrating: B(r) = Z \u221e 0 Ie,b(r)2\u03c0qbrdr = 2\u03c0Ie,bR2 e,bebnnbqb b2nb n \u0393(2nb) (3) and for the case of an exponential disc: D(r) = Z \u221e 0 Id(r)2\u03c0qdrdr = 2\u03c0I0R2 dqd (4) where we assumed that the \ufb02attening of the sub-component qb and qd does not change with radius. The \ufb02attening of a sub-component was determined as the \ufb02attening at the representative radius of the sub-component. For the sub-component described with an R1/n model this means qb = q(Re,b) and for the exponential qd = q(Rd). Finally, we want to know what is the relative fraction of light contained in the exponential sub-component and we calculate \u201ddisc-to-total\u201d (D/T) ratio2, with this expression: D/T= D/(B+D), where D and B are the expressions from eqs. (3) and (4). We also estimated the total luminosity within the radius, Rmax which corresponds to the largest coverage of our IFU observations (matching the coverage of our kinematics). This was done by integrating the integrals in eqs. (3) and (4) from r = 0 to r = Rmax to estimate the bulge and disc light within this regions, respectively. In practice, for the bulge component we use eq. (2) from Graham & Driver (2005) and apply the tabulated form of the integral in eq (4) (e.g. Gradshteyn et al. 2000, page 357) for the exponential component. Depending on the coverage of the individual objects there are some modi\ufb01cations to D/T ratios, but non of the conclusions of this work change if we consider this limited luminosity instead of the (standard) total luminosity. The main reason why this is the case comes from the fact that our IFU coverage is on average twice as large as Rb and Rd estimated in this study. In the rest of the paper we only consider the total luminosities de\ufb01ned by eqs. (3) and (4). A number of studies discuss the robustness of the decomposition parameters (Schombert & Bothun 1987; de Jong 1996; MacArthur et al. 2003; Kormendy et al. 2009). We found that the crucial step of our \ufb01tting procedure is an adoption of the radial range within which the \ufb01t is done, and partially the initial conditions for the \ufb01t. We use one continuous range excluding the central parts in\ufb02uenced by the effects of seeing and running until the sky level. Scott et al. (2012) estimate that the average point spread function (PSF) of our data has full-width-half-maximum of 1.25\u2032\u2032and we as a rule exclude a region twice as big (the \ufb01tted region starts at \u223c2.5\u2032\u2032, or \u223c300 pc assuming the average distance to ATLAS3D galaxies). If necessary, and in a limited number of cases, both inner and outer radii for the \ufb01ts were adapted for each galaxy individually (see Section 3.3). 3.3 Decomposition examples In Fig. 1 we show six example \ufb01ts to light pro\ufb01les extracted along the best \ufb01tting ellipses. These include three pro\ufb01les which can be reproduced with a single component of a low S\u00b4 ersic index, and three light pro\ufb01les which are reproduced with two components of various relative fractions. We also show residuals of both one and two component \ufb01ts for comparison. These examples are representative of the \ufb01ts to other galaxies in the sense of their quality, types of residuals, \ufb01tting ranges and types of models that reproduce the observed light pro\ufb01les. The residuals within the \ufb01tted range are generally small indicating good model \ufb01ts; a median of the rms deviation is 0.05 mag/\u2032\u20322 and its standard deviation is 0.03 mag/\u2032\u20322. On the top left panel (NGC 3156), we show an example of a galaxy for which residuals of the two component \ufb01t are not signi\ufb01cantly smaller than the one component \ufb01t residuals. Hence, the one component \ufb01t was deemed suf\ufb01cient, and the decomposition results were discarded. Contrary 2 At this moment we call the exponential components a disc component without proof that this is applicable for all early-type galaxies. This is done by convention, but in Section 5.4 we address this issue in detail justifying our choice. c \u20dd2011 RAS, MNRAS 000, 1\u201329 6 Davor Krajnovi\u00b4 c et al. Figure 1. Decomposition examples. Each galaxy is represented by three panels, where top panel shows the extracted light pro\ufb01le, the middle panel show the residuals (data best \ufb01t model) in mag/\u2032\u20322, and the bottom panel shows the \ufb02attening (q=1 \u2212\u01eb) pro\ufb01le extracted at the same time as the light pro\ufb01le. On the top panel the data are shown with solid symbols. Results of the two component \ufb01t (the effective radius Re,b and the bulge S\u00b4 ersic index nb, disc scale height Rd, the total light for both components, \u00b5e,b and \u00b5d, and the disc-to-total light ratio) are given in the upper right corner. The results of the one component \ufb01t (total light \u00b5, S\u00b4 ersic index n and effective radius R) are shown in the lower left corner. Vertical dashed lines indicate the region used in the \ufb01t. The actual values in seconds of arc are given in the upper left corner. These lines are also shown in the middle and bottom panels. The horizontal dashed line is our estimate of the sigma of the sky level. Light pro\ufb01les of the different components are shown with lines: red dashed for the bulge model, blue tripple-dot-dashed for the exponential model and solid cyan for the combined \ufb01t. We do not show the one component \ufb01t. On the middle panel solid symbols show residuals for the two component \ufb01t and open squares for the one component \ufb01t. The root-mean-square values for the \ufb01tted (RMS) and the full (RMSa) data range are shown in the upper and lower right corners for two and one component \ufb01ts, respectively. On the bottom panel vertical red (dashed) and blue (triple-dot-dashed) lines correspond to the sizes of the bulge (Re,b) and the exponential (Rd) components, respectively, and green (dot-dashed) line to the one \ufb01t component effective radius (Re). The horizontal red and blue lines give the values of q used in eqs. (3) and (4), respectively. c \u20dd2011 RAS, MNRAS 000, 1\u201329 Stellar discs in early-type galaxies 7 examples, when a two component \ufb01t was considered necessary, are shown for NGC 4434, NGC 4623 and NGC 5198. After carrying out similar comparisons for all galaxies and choosing if the decomposition is necessary, we examined all galaxies with rms > 0.1 mag (29 objects) to understand the reasons for the deviations. In only one case (NGC 4753), residuals could be connected with dust features, with a characteristically jagged distribution of values. In all other cases, the distribution of residuals was monotonically varying. These kind of features suggest there are possible additional components in the light pro\ufb01le, which can not be described by the assumed decomposition in two components only. Among the galaxies with high residuals, we found both those \ufb01tted with one (16 objects), and with two components (13 objects). The majority (9/13) of galaxies \ufb01tted with two components have \u01eb > 0.6, and are often seen in disc dominated systems close to edge on. NGC 4623 from Fig. 1 is an example. We tested these cases by decomposing their light pro\ufb01les obtained as major axis cuts, but there were no signi\ufb01cant improvements to the two components \ufb01ts, nor large difference in the parameters of the best \ufb01tting components. The cause for the poor \ufb01ts can be fully attributed to the existence of additional components, which could be interpreted as manifestations of instabilities (e.g. bars, rings) induced by secular evolution and hard to recognise due to the inclination angle. On the other hand, systematic variations of residuals in galaxies with only one component might suggest that these galaxies are actually better \ufb01t with two components and that our threshold criterion should not apply here. However, for 9 (of 16) objects the \ufb01tting algorithm actually automatically excluded the two components solutions and this result was robust to changes in both the initial conditions and \ufb01tting ranges. Additionally, only 1 (of 16) objects has n > 3, while for the majority (12/16) objects S\u00b4 ersic index ranges from 0.8 to 1.2. These single components, near exponential galaxies have additional structures, often seen in the shape of correlated wiggles in the residuals, but a two component \ufb01t is not suf\ufb01cient to describe them. Inwards of the inner \ufb01tting range point (2.5\u2032\u2032), one can often detect departures from the \ufb01tted and the observed light pro\ufb01les. This trend is particularly visible in NGC 3156 and NGC 5322 of Fig. 1. The models either overor under-predict the light in the centres of the galaxies. In some cases, these can be directly associated with the excess/de\ufb01cit observed within ETGs with the HST (Ferrarese et al. 1994; Faber et al. 1997; Graham et al. 2003; Ferrarese et al. 2006; Kormendy et al. 2009), or small nuclear components, but we do not attempt to quantify the effects as one generally needs higher spatial resolution for this analysis (e.g. the Hubble Space Telescope data) to allow \ufb01ts that extend to smaller radii. Finally, we note that our decomposition was performed on relatively shallow SDSS images focusing on morphological structures within a few effective radii. Deeper images are likely to show more varied structures at larger radii introducing a need for more than just two components to describe the light distributions of galaxies (e.g. Duc et al. 2011). 3.4 Uncertainties As mentioned above, we obtain the best \ufb01t parameters by doing a linear least-squares \ufb01t with the mpfit routine. In doing so we assume constant relative errors, which ensures equal weighting to all points on our light pro\ufb01les. To estimate the uncertainties to S\u00b4 ersic parameters we perform Monte Carlo simulations based on the rms scatter of the residuals to the \ufb01t. We perturb original light pro\ufb01les, \ufb01t them again 100 times and estimate the uncertainties as the standard deviation of the simulations. These are only statistical estimates of the uncertainties, and they do not properly represent the systematic ones coming from the choice of the method, initial condition, sky levels and, in particular, the choice of the \ufb01tting range. In Appendix A we discuss the systematic effects when using different methods outlined above. We caution the reader that these sources of the systematic uncertainties are what could drive the difference between our and literature results. In Appendix B we present a comparison of our results (focusing on the S\u00b4 ersic index and the D/T ratio) with the results of other studies. We compare our results both directly and in a statistical sense: \ufb01rstly, with studies that analyse samples which overlap with our own (i.e comparison of individual galaxies), and, secondly, with studies that analyse large numbers of galaxies. The reason for this approach is in the presence of large systematics (e.g. de\ufb01nition of the sample and \ufb01tting technicalities such as the \ufb01tting range or choice of one over two component \ufb01ts) and absence of a similar to our own data set for which calculations were done in a comparable way (e.g. decomposition into free S\u00b4 ersic and exponential components for a signi\ufb01cant number of galaxies in common with this study). Our conclusion is, based on comparing individual cases, that there is a suf\ufb01ciently good agreement with previous work, but that different types of above mentioned systematics are the dominant factor for uncertainties. 4 S \u00b4 ERSIC FITS TO ONE DIMENSIONAL PROFILES We also \ufb01tted a single component S\u00b4 ersic function to the light pro\ufb01les of all ATLAS3D galaxies with SDSS and INT imaging, in order to derive their global structural parameters, as it is often done with early-type galaxies (e.g. Caon et al. 1993; Graham et al. 1996; Trujillo et al. 2004; Ferrarese et al. 2006). After some testing, and contrary to our choice for the decomposition, we decided to \ufb01t azimuthally averaged light pro\ufb01les obtained along \ufb01xed ellipses. Note that in Section 3.2, when we outlined the method for choosing whether a pro\ufb01le needs to be decomposed or not, we stated that we \ufb01tted both one and two components to the same light pro\ufb01le extracted along the best-\ufb01tting ellipses. We, however, do not think these pro\ufb01les are best suited for determination of the global parameters, and, hence, use pro\ufb01les extracted along the \ufb01xed ellipse. Our choice for \ufb01xed ellipse pro\ufb01les is motivated by our wish to parameterise the whole galaxy with a single component. As shown by Erwin et al. (2008), multicomponent systems will have different light pro\ufb01les depending whether they are extracted along \ufb01xed or free ellipses. Our choice of \ufb01xing PA and Q is justi\ufb01able as we are \ufb01tting a single function to objects which are predominantly two or more component systems (see Section 5). For some objects, such as massive, triaxial slow rotators, the change in ellipticity or position angle is most likely not an indication of multiple components but of triaxiality or smoothly varying orbital structure. For these objects an approach with free ellipses could also be preferred. As there are, however, only a handful of such objects, we choose to \ufb01t a constant in PA and Q model, as for all other galaxies. As these galaxies typically do not warrant a decomposition (see Section 5.2), an interested reader can \ufb01nd in Appendix C values for single component \ufb01ts obtained on light pro\ufb01les extracted from free ellipses. Our choice is similar to what a typical 2D \ufb01tting algorithm does: the component used to \ufb01t the galaxy image has a \ufb01xed shape and orientation. We support our decision with a discussion in Appendix A. The parameters of the ellipses (PA, Q) were taken from Paper c \u20dd2011 RAS, MNRAS 000, 1\u201329 8 Davor Krajnovi\u00b4 c et al. Figure 2. Distribution of the effective radius Re,tot (left column) and the global S\u00b4 ersic index ntot (right column) of single S\u00b4 ersic \ufb01ts to light pro\ufb01les obtained averaging along \ufb01xed ellipses, for 258 ATLAS3D galaxies. In the top row galaxies are divided in fast (blue histogram hatched to the left), slow (red histogram hatched to the right) rotators, and barred objects (orange histogram with vertical lines), while the open histogram is for all galaxies. In the bottom row, galaxies are divided by mass into less (open histogram) and more massive (green hatched histogram) than 4 \u00d7 1010 M\u2299, which splits the sample in two roughly equal halves. . II, which are global and measured at large radii (typically around 23 effective radii). As another difference from the approach outlined in Section 3, we performed the \ufb01ts on all galaxies, including objects with bars and/or rings. Note that the PA and Q used are not related to bars, because in Paper II we took care to obtain them at radii beyond these structures and, hence, in barred systems they describe the shape and orientation of host discs. We \ufb01tted the light pro\ufb01les in the same radial range as for the two component \ufb01ts with the general r1/n pro\ufb01le of eq. (1). The results of the \ufb01ts are the global S\u00b4 ersic index ntot, effective radius Re,tiot and the intensity Itot at the effective radius. As can be expected, one component \ufb01ts have somewhat larger residuals than two component \ufb01ts. The median rms is 0.08 mag/\u2032\u20322, while the standard deviation is 0.05 mag/\u2032\u20322. If we exclude barred galaxies and compare the rms for only those objects for which we also performed the disc/bulge decompositions, the median rms drops to 0.06 and its standard deviation to 0.04 mag/\u2032\u20322. 5 RESULTS 5.1 Global structural parameters of ETGs Results of the single S\u00b4 ersic \ufb01ts to all galaxies are presented in Fig. 2 and given in Table C1. In addition to division into slow and fast rotators (top panels), we split the sample by mass in two subsets similar in number using Mdyn = 4 \u00d7 1010 M\u2299as the divider (bottom panels), a value similar to the characteristic mass derived by Shen et al. (2003). The mass is constrained by the ATLAS3D integral-\ufb01eld kinematics, images used in this paper and the Jeans Anisotropic Models (Cappellari 2008). It is de\ufb01ned as Mdyn = L \u00d7 (M/L)dyn, where L is the galaxy total luminosity and the mass to light-ratio was obtained via dynamical models. This mass represents Mdyn \u2248 2 \u00d7 M1/2 where M1/2 is the total dynamical mass within a sphere containing half of the galaxy light. Given that the stellar mass dominates the mass inside Mdyn(r = r1/2), Mdyn provides a very good approximation (in median within 10%) to the galaxy stellar mass (Cappellari et al. 2012b, hereafter Paper XIX). When mass is used as a proxy, there are clear trends in size (global effective radius of the S\u00b4 ersic pro\ufb01les) and the S\u00b4 ersic index: high mass galaxies are typically larger and have larger ntot. c \u20dd2011 RAS, MNRAS 000, 1\u201329 Stellar discs in early-type galaxies 9 However, when using this particular mass pivot point, the overlap between the values of the two samples is large. When dividing galaxies into slow and fast rotators, there is a signi\ufb01cant difference between the two classes based on these two parameters. A Kolmogorov-Smirnov (K-S) test gives a probability of 10\u22125 and 10\u22124 that sizes and S\u00b4 ersic n of fast and slow rotators are drawn from the same distribution, respectively. On the other hand, barred galaxies (Paper II) show a very similar distribution of sizes and S\u00b4 ersic indices as other fast rotators. A K-S test gives a 98 per cent probability that bars are drawn from the distribution of fast rotators, implying that a typical non-barred fast rotator will have the same size or S\u00b4 ersic index as a barred galaxy. Detailed comparisons with literature data are dif\ufb01cult due to various ways samples of early-type galaxies are selected (e.g. morphology, magnitude cuts or colour properties). However, in terms of the distribution of the S\u00b4 ersic index, our results are in a reasonable agreement with previous studies of early-type galaxies, (e.g. Caon et al. 1993), who found a large fraction of galaxies with ntot < 4. A more detailed comparison can be found in Appenidix B. The main differences between slow and fast rotators is that distributions of both Rtot and ntot are \ufb02atter for slow than for fast rotators. The latter show a peak in size at about Re,tot = 1.5 kpc and a peak for S\u00b4 ersic index at about ntot = 2. Slow rotators do not display any speci\ufb01c peak, but their distributions are somewhat limited in the sense that there are no small galaxies (e.g. less than 1 kpc in effective radius) and the smallest ntot is about 2. Furthermore, slow rotators are also found at the upper extremes of the size and S\u00b4 ersic index distributions. Noteworthy is to mention that the low values in Rtot and ntot among slow rotators occur for special kinematics, such as for galaxies with counter-rotating components. The distribution of the S\u00b4 ersic index ntot in this sample of ETGs is of special importance. Various authors use the S\u00b4 ersic index to separate galaxies into discs and spheroids, or lateand early-type galaxies (e.g. Shen et al. 2003; McIntosh et al. 2005; Barden et al. 2005). The typical divide is taken to be ntot = 2 or ntot = 2.5, but some authors separate galaxies into an exponential (ntot < 1.5) and a concentrated (ntot > 3) group3 (e.g. Blanton et al. 2003), or use S\u00b4 ersic indices as part of their classi\ufb01cations (e.g. Scarlata et al. 2007). If these values are adopted, about 21 per cent (using ntot < 2), 34 per cent (using ntot < 2.5), or 48 per cent (using ntot < 3) of the ATLAS3D galaxies, would not be considered early-type galaxies. As shown in Paper I, none of the ATLAS3D galaxies have spiral arms or large dust lanes (across the full body when seen edge on). However, as we argued in Papers II, III and VII, and show below, it is a fact that the majority of earlytype galaxies are discs or strongly related to discs. Furthermore, parameterising with a single S\u00b4 ersic function, and using any values of S\u00b4 ersic index, is not suf\ufb01cient to separate slow from fast rotators. It is true that only a few slow rotators have low ntot values (and none of them has ntot < 2), and these might be special cases. However, there is a large number of fast rotators with S\u00b4 ersic index value as high as that of more typical slow-rotators. There are 6 slow rotators with ntot < 3 (out of 124 objects) and 104 fast rotators with ntot > 3 (out of 134 objects). These fractions give a probability to classify an object as a slow rotator if its ntot > 3 is only 0.22. If we use the Hubble classi\ufb01cation (data 3 In the rest of the paper we will similarly use ntot = 3 (or nb = 3) to distinguish between galaxies with concentrated and non-concentrated S\u00b4 ersic pro\ufb01les. Figure 3. Distribution of disc-to-total light (D/T) ratios (top panel) and S\u00b4 ersic n indices (middle and bottom panels) for non-barred ATLAS3D galaxies. In all panels blue (right slanted) hatched histograms are for fast rotators and red (left slanted) hatched histograms are for slow rotators. The bottom histogram is made of galaxies in the \ufb01rst bin of the top panel (galaxies with D/T< 0.05) from HyperLeda, (Paturel et al. 2003), see Section 5.5), one gets that a probability for classifying an elliptical if its ntot > 3 is 37 per cent (there are 50 of 134 galaxies with ntot > 3 classi\ufb01ed as ellipticals). S\u00b4 ersic index alone can not distinguish between slow and fast rotators (beyond saying that objects with ntot < 3 are most likely fast rotators), and hence does not suf\ufb01ciently distinguish between two dynamically different classes of objects with likely different formation histories. This is an important caveat which should be kept in mind in all studies of large number of galaxies, or samples at large redshifts. 5.2 The decomposition results In Fig. 3 we plot the results of our decompositions for non-barred ATLAS3D galaxies following the procedure outlined in Section 3.2. The values are tabulated in Table C1. The top panel shows D/T light ratios. Using Monte-Carlo simulations we estimate the errors to D/T light ratios and \ufb01nd that a median uncertainty is 0.08 for cases where D/T> 0. Three main features are obvious: (i) 43 per cent of the analysed galaxies are in the \ufb01rst bin with D/T < 0.05, (ii) early-type galaxies show a full range of D/T ratios, and (iii) there is an increase of galaxies around D/T \u223c0.8. We consider that the \ufb01rst bin (D/T < 0.05) contains galaxies with no exponential sub-components, hence, it is remarkable that more than half of c \u20dd2011 RAS, MNRAS 000, 1\u201329 10 Davor Krajnovi\u00b4 c et al. all non-barred ETGs contain at least some evidence, and typically a signi\ufb01cant amount, of light parameterised with an exponential component. This is perhaps not so surprising when considering the \ufb01nding of Simard et al. (2009) that visually selected early-type galaxies can have low B/T ratios (or high D/T ratios in our notation). Separating galaxies according to their angular momentum into fast and slow rotators reveals that the majority of slow rotators (71 per cent, or 24 of 34) actually have no exponential component, but six slow rotators (18 per cent, or 6 of 34 objects) have D/T > 0.3, and ten (29 per cent) have D/T > 0.1. The latter value con\ufb01rms the choice in Paper VIII to separate fast and slow rotators. In conclusion, the majority of slow rotators are early-type galaxies with no exponential components, while those that have an exponential component typically also have speci\ufb01c signatures of rotation. We will return to this issue in Section 5.5. The middle panel of Fig. 3 shows the distribution of S\u00b4 ersic indices of the bulge. There is a strong peak at low S\u00b4 ersic indices and a long tail at larger values, and a bump between nb \u223c4 \u2212 6. This protuberance is obviously caused by slow rotators, which predominantly lie between 4-6, and 76 per cent (26 of 34 objects) of slow rotators have nb > 3. While the distribution of S\u00b4 ersic indices for slow rotators is as expected (nb is typically large), the distribution of nb for fast rotators is more surprising. There are galaxies with large indices (about a quarter of fast rotators have nb > 3), and a fast rotator can have as large a S\u00b4 ersic index as a slow rotator. The majority of fast rotators (61 per cent, or 89 of 146 objects), however, have small indices (nb < 2) and the large indices are distributed in a long tail of the distribution. This comparison is only partially proper, as more than two thirds of slow rotators are single components systems, while this is true only for a third of fast rotators. In the bottom panel of Fig. 3 we show the distribution of the S\u00b4 ersic indices for all galaxies in the \ufb01rst bin (D/T < 0.05) of the top panel. We consider these galaxies to be made of a single component; the decomposition did not improve on the one component \ufb01t signi\ufb01cantly. There are 53 and 24 such fast and slow rotators, respectively. The distribution of nb is again asymmetric with a peak at low values of the S\u00b4 ersic index (nb = 1 \u22123) and two peaks at larger values (nb = 4\u22126). As on the plot above, fast rotators make up the \ufb01rst peak and slow rotators the secondary bumps, with an overlap of a few galaxies in both directions, suggesting a clear difference in the structure of these two classes of early-type galaxies. A most likely S\u00b4 ersic index for a single component fast rotator is between 1 and 2. This is remarkable, as not only more than half of fast rotators have a signi\ufb01cant amount of light in an exponential component (e.g. 59 per cent, or 86 of 146, of fast rotators have D/T > 0.2), but the majority of fast rotators which can be described as single component systems have nb < 3 (79 per cent, or 42 of 53, of single component fast rotators) and a pro\ufb01le similar to that of the exponential. There are 11 single component fast rotators with nb > 3, of which 4 show prominent shells and tidal tails, and one is actually a prolate rotator. We will discuss these galaxies in more detail below. 5.3 Correlation between single S\u00b4 ersic \ufb01ts, the decomposition parameters and angular momentum In Fig. 4 we show four diagrams with S\u00b4 ersic index of the single component \ufb01ts, S\u00b4 ersic index of the bulge sub-components, D/T ratio, and angular momentum, \u03bbR, plotted against each other. The general conclusion is that there are no strong trends, except a general relation between D/T and \u03bbR. As it was reported previously Figure 4. From left to right, top to bottom: correlations between D/T ratio and S\u00b4 ersic index of the single component \ufb01ts, \u03bbR and S\u00b4 ersic index of the single component \ufb01ts, \u03bbR and D/T ratio, and \u03bbR and S\u00b4 ersic index of the bulge sub-component. In panels with D/T ratios, we show only those galaxies that required two components \ufb01ts (e.g. D/T> 0.) (e.g. Gadotti 2009; Lackner & Gunn 2012), D/T (or rather bulgeto-total ratio4) ratio correlates poorly with the S\u00b4 ersic index, of both global and of the bulge sub-component. We will discuss further the relations between D/T and nb with \u03bbR in the next section. There is a weak correlation between D/T and \u03bbR, which is tighter for larger values of \u03bbR and high D/T ratios. On a contrary, there is no signi\ufb01cant correlation between \u03bbR and the S\u00b4 ersic index of single component \ufb01ts, which con\ufb01rms the \ufb01nding of Section 5.1. 5.4 Exponential pro\ufb01les in ETGs are discs 5.4.1 Morphological properties and angular momentum of early-type galaxies As pointed out by de Jong et al. (2004) and Naab & Trujillo (2006), \ufb01nding exponential components in the light pro\ufb01les of ETGs does not imply they correspond to discs. Combining the bulge/disc decomposition results with the stellar kinematics analysis, however, can elucidate the true nature of structural components of ETGs. Judging from Fig. 3 there is a clear separation between slow and fast rotators in their structural properties. To investigate in greater detail the relationship between kinematics and photometric structures we present in Fig. 5 two \u03bbR vs \u01eb diagrams. In the left hand panel we compare the amount of light in the exponential component, as quanti\ufb01ed by the D/T ratio, and the S\u00b4 ersic index nb of the 4 Note that B/T = 1D/T only if the decomposition was done into two components like here and, hence, a comparison with other studies that decompose galaxies into, for example, bulge, bar and discs might not be straightforward. We prefer to use D/T ratio, where D is associated with the exponential component, while bulges are an in-homogenous set of objects with a range of S\u00b4 ersic indices (for de\ufb01nitions of various types of bulges see Athanassoula 2005). c \u20dd2011 RAS, MNRAS 000, 1\u201329 Stellar discs in early-type galaxies 11 Figure 5. \u03bbR versus \u01eb for ATLAS3D galaxies. Barred galaxies not used for the decomposition are shown as small dots for completeness. Left: Symbols represent S\u00b4 ersic indices as shown on the legend, while colour coding quanti\ufb01es the D/T ratio, as shown on the colour bar under the diagram. Right: Symbols show different types of kinematics from Paper II and are described in the legend: a non rotating galaxies, b featureless non-regular rotators, c KDC, d 2\u03c3 and e regular rotators. Colours again quantify D/T ratios, as shown on the colour bar, but now we also highlight those galaxies which do not have an exponential component, but have nb < 3 (purple). The green line separates slow (below the line) from fast (above the line) rotators (Paper III). The dashed magenta line shows the edge-on view for ellipsoidal galaxies with anisotropy \u03b2 = 0.7 \u00d7 \u01eb, from Cappellari et al. (2007). bulge component. In the right hand panel we correlate the types of rotation found in our galaxies with the amount of light in the exponential component. Looking at the left hand panel of Fig. 5, and as seen in Fig. 4, galaxies with low S\u00b4 ersic indices are typically found at high \u03bbR, while the fraction of galaxies with low D/T ratios is higher at low \u03bbR. There are some outliers, especially that galaxies with D/T < 0.05 can be found also at larger \u03bbR. These objects, however, typically have a low S\u00b4 ersic index, typically nb < 3 (shown as ellipses). On the contrary, objects with D/T < 0.05 at low \u03bbR (e.g. slow rotators), have typically higher S\u00b4 ersic indices (> 3). This division sets two extremes of early-type galaxies: those with low angular momentum and that are best described with a single S\u00b4 ersic component of a high index, and those with high angular momentum, best described with two S\u00b4 ersic components of a similar index or with a single S\u00b4 ersic component of a low index. Until this point we did not consider the detailed kinematic properties of our galaxies, except their global angular momentum. In Paper II we analysed our integral-\ufb01eld data by means of kinemetry, optimised for the mean velocity maps, and divided the galaxies in \ufb01ve groups depending on their complexity. We plot these on the right hand panel of Fig. 5, colour coding with the D/T ratios. Here we also separate galaxies best parameterised with single components of low S\u00b4 ersic indices. This allows us to recognise that galaxies classi\ufb01ed as non-rotators (Group a) are single component systems with high S\u00b4 ersic indices. Galaxies showing featureless but non-regular rotatation (group b) and kinematically distinct cores (KDCs; Group c), are typically made of a single component with a high index, but in some cases low fractions of the exponential components can be attributed to their light pro\ufb01les. Finally, galaxies made of two-counter rotating discs (2\u03c3 galaxies or Group d) are mostly single component systems of low S\u00b4 ersic index, or have large D/T (> 0.25) and low nb (< 3). In that respect they are structurally similar to Group e, or galaxies with regular and most disc-like rotation, which are also characterised with low S\u00b4 ersic indices and a range of D/T values. These include both single component systems (of low S\u00b4 ersic index) and systems with the highest contributions of the exponential light pro\ufb01les. 5.4.2 V/\u03c3 \u2212h3 correlation Next to kinematic information presented in Fig. 5 based on the angular momentum content and kinemetric analysis of the disclike rotation in ATLAS3D galaxies, we now use the information found in h3, analogous to the skewness, the higher order moment of the line-of-sight velocity distribution (van der Marel & Franx 1993; Gerhard 1993). In Fig. 6 we show h3 values against V/\u03c3 for all ATLAS3D galaxies which we decomposed and for which we were able to measure this moment on individual spectra. We divided galaxies in those that are characterised by a single component of a large S\u00b4 ersic index, those that have a low contribution of exponential components, those with a high contribution of the exponential c \u20dd2011 RAS, MNRAS 000, 1\u201329 12 Davor Krajnovi\u00b4 c et al. components and galaxies of single components with small S\u00b4 ersic indices. The \ufb01rst two classes are shown on the top panel (solid and dashed contours, respectively) and the second two on the bottom panel (solid contours) of Fig. 6. There is an evident difference between the distributions on the two panels. Galaxies with high contribution of the exponential components show strong anti-correlation between h3 and V/\u03c3, which is often used as a kinematic manifestation of stellar disc kinematics, or at least evidence for stars at high rotational speeds (e.g. Bender et al. 1994). There is also a small difference between the two distributions on the top panel, as galaxies with single components (and large S\u00b4 ersic indices) are dominated by V/\u03c3 \u223c0 values. On the bottom panel of this \ufb01gure one can see that the tightest anticorrelation of h3 \u2212V/\u03c3 is seen in single component galaxies of small S\u00b4 ersic indices. The combination of various kinematic information and the decomposition results allows us to conclude that the rotation in earlytype galaxies is typically associated with the presence of the exponential components in the light pro\ufb01les. More speci\ufb01cally, the exponential pro\ufb01les are only present when there is at least some indication of rotation, and galaxies in which the light is dominated by the exponential pro\ufb01les are all galaxies with high stellar angular momentum. Furthermore, in cases where \ufb01ts did not warrant the existence of exponential sub-components, but regular disc-like rotations is present and h3 is anti-correlated with V/\u03c3, the pro\ufb01les are described by a single component of a small (< 3) S\u00b4 ersic index. This leads to a conclusion that any component with a S\u00b4 ersic index less than about three can be associated with a disc, or is at least closely related to discs. The inverse is also true as galaxies with no detected rotation are typically single component systems of high S\u00b4 ersic indices. 5.4.3 Similarities of fast rotators galaxies and spirals The existence of bulges of low nb, a large range of D/T ratios, and a substantial fraction of objects with large D/T ratios in fast rotators con\ufb01rms their similarity with spirals (e.g. Graham 2001; MacArthur et al. 2003; Weinzirl et al. 2009; Laurikainen et al. 2010), and strongly suggest an evolutionary link. Our results support the revision of the Hubble diagram put forward initially by van den Bergh (1976), which we revised to include fast and slow rotators in Paper VII (for photometric investigations see Laurikainen et al. (2011) and Kormendy & Bender (2012)). Additionally, the low values of S\u00b4 ersic indices for the bulges of fast rotators are characteristic of central light concentrations built from discs (e.g. discy-bulges, Kormendy 1993; Athanassoula 2005)5. We remind the reader that we did not analyse barred galaxies and that our sample is devoid of spirals (and late-type galaxies in general). Also we have excluded from the \ufb01tting the central regions, while including higher resolution images could have an effect of decreasing the S\u00b4 ersic index (e.g. Balcells et al. 2003). Nevertheless, it is clear from Figs. 3 and 5 that bulges of low S\u00b4 ersic index are typical among fast rotators and that their kinematics are disclike, linking further the properties of earlyand late-type galaxies. 5 These are sometimes referred to as pseudo-bulges (e.g. Laurikainen et al. 2007; Fisher & Drory 2008), in order to highlight their structural and presumably evolutionary differences from the classical bulges (Kormendy & Kennicutt 2004). We, however \ufb01nd this terminology unnecessarily confusing as it encompasses structures with various morphologies, scales and potential origins. Figure 6. Local h3 \u2212V/\u03c3 relation for every spectrum in galaxies with \u03c3 > 120 kms\u22121 and an error on h3 < 0.05. The contours show distribution of values in bins of 0.1 in V/\u03c3 and 0.01 in h3, smoothed with a boxcar \ufb01lter of a window of 2 pixels in both dimensions. The contour levels decrease in step of 0.5 in log from 2 for the smallest contours. Top: solid contours show the distribution of values for galaxies described by a single component of a high S\u00b4 ersic index and dashed (red) contours show galaxies with low D/T fraction. Bottom: solid contours show the distribution for galaxies with substantial disc fractions, while dashed (blue) contours show values for galaxies described by single components of a low S\u00b4 ersic index. Similar results were reported recently by Fabricius et al. (2012) for S0s and late-type galaxies. It is, however, also evident on Fig. 5 that there are fast rotators with disc-like kinematics and with bulges of high S\u00b4 ersic index, as well as fast rotators which are suf\ufb01ciently well described with single components of low S\u00b4 ersic indices. 5.4.4 Masses of discs Using dynamical masses from Paper XIX, we can estimate what mass fraction is in the exponential components. In calculating we assume that there is no difference in stellar populations between the bulge and the exponential components and that galaxies are well \ufb01tted by a single mass-to-light ratio in the dynamical models. With this caveat in mind and selecting galaxies with D/T > 0.05, we \ufb01nd that the total mass in the exponential components is \u223c4.12 \u00d7 1012 M\u2299, or 27 per cent of the total mass of investigated galaxies. Selecting galaxies with D/T < 0.05 and nb < 3, gives the total mass of 2.10 \u00d7 1012 M\u2299or 14 per cent of the total mass of investigated galaxies. Combining these two \ufb01gures we \ufb01nd that \u223c41 per cent of stellar mass in early-type galaxies is in discs or disc-like components. The rest is shared mostly between single c \u20dd2011 RAS, MNRAS 000, 1\u201329 Stellar discs in early-type galaxies 13 component slow rotators and bulges of fast rotators. Note that we did not include here the contribution of the barred galaxies. 5.5 Decomposition and classi\ufb01cations of early-type galaxies 5.5.1 Hubble types and angular momentum On Fig. 7 we repeat the \u03bbR \u2212\u01eb plot, with symbols differentiating between galaxies classi\ufb01ed as ellipticals and S0s using morphological types from the HyperLeda catalog Paturel et al. (2003). In Paper III we commented on the discrepancy between E/S0 and fast/slow rotator classi\ufb01cations. Here we want to compare our decomposition results with both of these approaches, and with solid symbols we plot those galaxies, which are suf\ufb01ciently well described with a single S\u00b4 ersic pro\ufb01les of a large index (nb > 3). There are 31 galaxies with that property, of which 20 are slow and 11 fast rotators. As fractions of the analysed slow and fast rotators, these galaxies make up 59 and 7 per cent, respectively. Based on their morphological classi\ufb01cation, ellipticals best \ufb01t with a single component pro\ufb01les of a large index are typically found under the green line de\ufb01ning the slow rotator class. As a contrary, among the fast rotators, objects with the same structural properties are typically classi\ufb01ed as S0s. Concentrating on the \u03bbR > 0.25 region, there are such 7 galaxies, 2 classi\ufb01ed as ellipticals (NGC 0680 and NGC 4486A) and 5 as S0s (NGC 2695, NGC 4753, NGC 4459, NGC 5869 and NGC 3182, in order of decreasing \u03bbR). NGC 0680 is characterised by having evidence for a major merger, with a series of shells, arcs and two plumes rich in HI (Duc et al. 2011, hereafter Paper IX). A similar shell like structure is also visible in NGC 5869 and in NGC 4753. Although these galaxies have significant and ordered rotation in their inner regions, the outer regions seem not to be fully relaxed, possibly having multiple structural components which are not any better described with two than with one components. The light pro\ufb01le of NGC 4486A is unfortunately contaminated by a bright star, nearly co-spatial with the nucleus of the galaxy, and we moved the inner \ufb01tting limit out to 5\u2032\u2032, which is comparable to the effective radius of this galaxy, and the \ufb01t is likely not robust. Other S0 galaxies either have dust (NGC 4459 and NGC 4753) or show signi\ufb01cant wiggles in their pro\ufb01les (NGC 2695, NGC 3182), which are not removed with a two component \ufb01ts. Light pro\ufb01les of fast rotators with \u03bbR < 0.25 are different from the above mentioned galaxies. The four galaxies characterised by single components of high S\u00b4 ersic indices in this region are: NGC 3607 (S0), NGC 3193 (elliptical), NGC 5485 (S0) and NGC 3073 (S0). All galaxies except NGC 5485 do not show strong evidence for an exponential pro\ufb01les. A blind decomposition assigns between 0.03 and 0.08 of the light fraction to an exponential pro\ufb01le, but the \ufb01ts are barely improved with respect to one component \ufb01ts. All four galaxies are somewhat special, but NGC 5485 is the most intriguing as this is the one of the two galaxies in the entire ATLAS3D sample which shows a prolate rotation (around its major axis), coinciding with a dust disc in a polar con\ufb01guration. Even though this galaxy has a signi\ufb01cant exponential component, it is not possible to associate it to the observed rotation, and call this component a disc. Below the green line, most interesting are the galaxies that can be decomposed or have one component with a low S\u00b4 ersic index. There are 14 such objects (NGC 4168, NGC 3608, NGC 5198, NGC 4458, NGC 5813, NGC 3414, NGC 7454, NGC 4191, NGC 4559, UGC03960, PGC050395, NGC 1222, PGC28887 and NGC 4690, in order of increasing \u03bbR), 7 classi\ufb01ed as S0 and 7 as Es. The pro\ufb01les for these galaxies, except NGC 4191 Figure 7. Distribution of elliptical (morphological type T < \u22123.5) and S0 (morphological type T > \u22123.5) galaxies in \u03bbR versus \u01eb diagram, as in Fig. 8 of Paper III. Solid symbols show ellipticals and S0s which are best \ufb01t with a single component S\u00b4 ersic function of a large index (n > 3), and a decomposition of their pro\ufb01les was not deemed necessary. As in Fig. 5, the green line separates slow (below the line) from fast (above the line) rotators (Paper III), the dashed magenta line shows the edge-on view for ellipsoidal galaxies with anisotropy \u03b2 = 0.7\u00d7\u01eb from Cappellari et al. (2007), and dots are not-analysed barred ATLAS3D galaxies. The dotted lines correspond to the location of galaxies with intrinsic ellipticities between 0.25 and 0.85 in steps of 0.1. The dashed lines show the location of galaxies originally on the magenta line as the inclination is varied in steps of 10\u25e6, decreasing from the magenta line (90\u25e6) to the left. As a guide line, the line that was plotted solid corresponds for the inclination of 50\u25e6. The formulas to plot these lines can be found in Cappellari et al. (2007). and NGC 7454, require a signi\ufb01cant fraction (> 0.2) of the exponential components in their lights. NGC 4191 and NGC 4550 are 2\u03c3 galaxies, and their low S\u00b4 ersic indices are consistent with these galaxies being made of counter-rotating discs (Rubin et al. 1992; Rix et al. 1992; Cappellari et al. 2007; Coccato et al. 2011). NGC 7454 and NGC 5198 are galaxies with non-regular but featureless kinematics. Atypically for slow rotators, NGC 5198 and UGC03960 have HI gas, in both cases in peculiar con\ufb01gurations (Serra et al. 2012, hereafter Paper XIII). The last \ufb01ve galaxies in this list are found close to the green line, and they are likely to be transitional objects in terms of \u03bbR. The other \ufb01ve galaxies have KDCs and possibly the exponential pro\ufb01les could be associated with the stellar distributions forming the KDCs 5.5.2 A transitional region in \u03bbR There seems to exist a transitional region between fast and slow rotators, and it can be broadly put to be between 0.1 < \u03bbR < 0.25. Almost all galaxies above this region can be considered disc dominated galaxies or at least galaxies with signi\ufb01cant disk fractions. Below this region galaxies are typically, with a few exceptions, single component systems of high S\u00b4 ersic index. Within the region, however, there is a mix of objects, fast rotators with no and slow rotators with a signi\ufb01cant fraction of light in exponential components. This region was also highlighted in the study of binary mergers by Bois et al. (2011, hereafter Paper VI). There we found that slow rotator remnants of binary mergers (of 1:1 and 1:2 mass ratios) are typically found below this region. Above the region, however, is the area populated by fast rotators remnants of binary mergers, c \u20dd2011 RAS, MNRAS 000, 1\u201329 14 Davor Krajnovi\u00b4 c et al. Table 1. Median values and standard deviation of S\u00b4 ersic indices and D/T ratios for galaxies as classi\ufb01ed by apparent shape or angular momentum. Classi\ufb01cation D/T \u03c3D/T nb \u03c3nb (1) (2) (3) (4) (5) E 0.19 0.29 3.8 2.2 S0 0.37 0.39 1.4 1.0 SR 0.00 0.16 4.8 1.9 FR 0.41 0.36 1.7 1.3 E FR 0.32 0.28 2.7 2.1 S0 FR 0.58 0.43 1.4 0.8 E SR 0.00 0.14 5.1 1.7 S0 SR 0.00 0.19 4.1 2.4 Note that a number of galaxies are single components systems with D/T=0. In these cases nb was the S\u00b4 ersic index of the single component. whose progenitors were on prograde orbits (prograde or retrograde motion of the main progenitor has a strong in\ufb02uence on the dynamical structure of the remnant). The transitional region itself is also populated by merger remnants, but this time remnants of re-mergers of galaxies that lie above or below this region (see Fig. 11 in Paper VI). Although these were non-cosmological mergers, their results highlight that this region will likely contain galaxies with special dynamical structures. Furthermore, part of this region is populated by galaxies seen at low inclination, while their edge on projections are on the dashed magenta line on Fig. 5 (see Fig. 1 of Paper III for the illustration of the projections in \u03bbR \u2212\u01eb diagram). This means that galaxies in this region could be a mix of two populations, oblate galaxies with discs projected at low inclinations and remnants of major mergers. In this respect the varied properties of light pro\ufb01les of galaxies are no more surprising than their varied kinematic properties, and one could expect more surprises from galaxies in this region. 5.5.3 Hubble types, angular momentum and decomposition results In Table 1 we list the median values and the standard deviations of S\u00b4 ersic indices and D/T ratios, splitting the analysed galaxies into ellipticals and S0s, fast and slow rotators, as well as the combination of the two classi\ufb01cation: fast rotating ellipticals (E FR), fast rotating S0 (S0 FR), slow rotating ellipticals (E SR) and slow rotating S0s (S0 SR). In terms of the decomposition parameters, both classi\ufb01cations give similar results, but fast \u2013 slow division highlights more the differences between the objects with higher and lower D/T ratios and S\u00b4 ersic indices, than the standard Hubble classi\ufb01cation. This is enhanced if we sort ellipticals and S0s depending on their angular momentum content. We can see that slow rotating ellipticals and S0s are structurally very similar, while fast rotating ellipticals and S0 show a certain range of properties, but they are rather very different from their slow rotating counterparts. As general conclusion of this section, based on Fig. 7 and Table 1 we stress that results of the decomposition are more closely related to the fast \u2013 slow classi\ufb01cation. They could be used to improve on the standard Hubble classi\ufb01cation, but they cannot be used as a substitute for the kinematic classi\ufb01cation. As a guideline, when stellar kinematics is not available, we recommend to use the following combination of criteria to select tentative fast and slow rotators: a D/T > 0.05 (a D/T > 0.1 is also acceptable, depending on the con\ufb01dence of the decomposition) for galaxies which need to be decomposed in (at least) two components, and n < 3 for galaxies not requiring a decompositions. We stress that with this selection one can misclassify up to 40 per cent of slow rotators. The large spread of possible values for D/T ratios when elliptical/S0 classi\ufb01cation is used, as well as for fast rotators is likely a manifestation of the inclination effects. In addition, the semianalytic models of Paper VIII suggest that there are differences between fast rotators. In particular, there is a range of D/T ratios (as we con\ufb01rm in Section 5.2), where those with small ratios are likely to grow discs via cold accretion \ufb02ows or grow bulges via minor mergers, while fast rotators with large D/T have exhausted their gas reservoirs (and can not replenish it) and live in dense environments resembling passively evolved spirals. In the following two sections we address these two issues, by investigating the in\ufb02uence of the inclination on our results and looking for differences among fast rotators. 5.6 Inclination effects The change of D/T ratios or values of nb from the top right (mostly blue) corners of the panels in Fig. 5 to the bottom left (orange and red) corners could be caused by inclination effects. This is expected as ellipsoidal galaxies viewed edge-on, and having an anisotropy as found in Cappellari et al. (2007), lie on the dashed magenta line. Their projections due to varying inclinations are found to the left of this line (see Fig 7), within the region inhabited by the majority of fast rotators, where the changes in D/T and nb are the most obvious. Given the known effects of the inclination on the ability to \ufb01nd discs in model galaxies (e.g. Rix & White 1990; Gerhard & Binney 1996), we can also expect that \ufb01nding discs using the decomposition method will be affected as well. In order to gain a qualitative understanding of the effects of the inclination on the decomposition parameters we performed the following test. We selected two galaxies (NGC 4621 and NGC 5308), a galaxy with a weak and a strong disc (and small and large D/T ratios), respectively, which can be reasonably assumed to be close to edge on. We used the Multi-Gaussian Expansion (MGE) method (Monnet et al. 1992; Emsellem et al. 1994) as implemented by Cappellari (2002) to parameterise their light distributions as a series of two-dimensional gaussians. Assuming the galaxies are seen edge-on, the MGE models specify the intrinsic shapes of these galaxies. The models were projected at a series of inclinations. Each of these models was then analysed in the same way as the original images: we extracted an azimuthally averaged light pro\ufb01le (letting the ellipse parameters free during the \ufb01t) and \ufb01tted the light pro\ufb01le as described in Section 3.2 with a general S\u00b4 ersic and an exponential component. In Table 2 we list the parameters of the decompositions of our MGE models. The results of this idealised analysis is that although there are some changes in the recovered parameters, they are systematic, but not large. The D/T fraction decreases as the viewing inclination approaches the face-on orientation, but the amplitude of the change is relatively small. In addition, the change of nb and the sizes of the two components are also increasing, where the increase is more pronounced for the models with the smaller disc. The changes of the model D/T and nb with inclination can account for a change of at most 20-25% in D/T and 1-1.5 in nb in Fig. 5. The reason for this is likely in the systematics associated with the decomposition of the pro\ufb01les. We illustrate this with Fig. 8, where we show the radial pro\ufb01les of the surface brightness, c \u20dd2011 RAS, MNRAS 000, 1\u201329 Stellar discs in early-type galaxies 15 Table 2. Inclination effect on the parameters of the decomposition name Incliantion D/T nb Re Rs (1) (2) (3) (4) (5) (6) 10 0.72 1.56 3.1 19.8 20 0.73 1.49 4.6 19.9 30 0.74 1.45 4.7 19.7 NGC 5308 40 0.77 1.39 4.6 19.3 50 0.79 1.33 4.4 19.0 60 0.82 1.24 4.2 18.5 70 0.85 1.10 3.9 18.0 90 0.88 0.87 3.5 17.3 10 0.17 6.0 58.5 30.8 20 0.20 5.6 49.4 31.8 30 0.17 5.9 56.7 29.9 NGC 4621 40 0.17 5.7 54.7 29.4 50 0.18 5.6 52.3 28.8 60 0.25 5.0 39.0 30.4 70 0.27 4.8 35.3 30.7 90 0.33 4.4 29.3 31.2 ellipticity and the disciness parameter (e.g. Bender et al. 1989, we plot the Fourier term, a4/a0, associated with the cos(4\u03b8) harmonics, normalised by the intensity), for our two model galaxies seen at different inclinations (we show every other inclination for clarity). Looking at the edge-on case (90\u25e6) of the NGC 5308 model, the disc component is clearly visible as a bump in the surface brightness pro\ufb01le at about log(R) = 1.3. The same bump is clearly associated with the rise in ellipticity and high a4/a0 which measures the disciness. At this inclination we can be sure that the recovered parameters indeed describe a disc. As the inclination decreases, the pro\ufb01les also change. Ellipticity and disciness show a dramatic change, while the surface brightness changes less prominently, but the bump in the pro\ufb01le steadily decreases. These same changes are also visible for the models of NGC 4621, but the differences at various inclinations are much smaller. As demonstrated by Rix & White (1990), the disciness parameter looses its usefulness below an inclination of 50-60\u25e6. The differences in ellipticity between a bulge and a disc, if they existed in the \ufb01rst place, are erased below an inclination of 30-40\u25e6. The only signature of a disc, or, to be more precise, a necessity for another component, is visible in the light pro\ufb01le of the model such as NGC 5308. The light pro\ufb01les of the NGC 4621 model, which had a relatively small disc, become less curved as the inclination is decreasing, and offer less hints for a need of a disc. In this model, below an inclination of 70\u25e6there is basically no clear photometric evidence for a disc. Our results are in agreement with Gerhard & Binney (1996), who also note that only strong discs are visible at low inclinations. These examples show the dramatic effect of the inclination on the photometry and the observed shape of galaxies. Unless the disc is the dominant component, it will not be possible to recognise it below a certain inclination (\u223c50\u25e6). A decomposition method might recover a certain amount of the disc at a low inclination in a galaxy such as represented by our model of NGC 4621, but the con\ufb01dence that this model could really be distinguished from a single component model, or that the exponential is really needed, is generally low. This should be taken into account when judging the decomposition results, including those presented here. Below an inclination of 50\u25e6, the photometric evidence for discs disappear and this might explain the large fraction of galaxies classi\ufb01ed as ellipticals among Figure 8. Top to bottom: Surface brightness, \ufb02attening and disciness radial pro\ufb01les for model galaxies with different fractions of light in the exponential components. Left to right: MGE models and their projections at 70\u25e6, 50\u25e6, 30\u25e6and 10\u25e6are based on NGC 5308 (D/T\u223c0.8) and NGC 4621 (D/T\u223c0.35). These galaxies were chosen as they are seen close to edge on and the intrinsic MGE model is considered to be seen at 90\u25e6. Colours on all panels correspond to models projected at different inclinations, as shown in the legend. Note that as the inclination decreases, the pro\ufb01les of the corresponding model also decrease in the maximum amplitude. fast rotators left of the line corresponding to this inclination (and above the magenta line) in Fig. 7. It can also be used to explain why fast rotators with single component of high S\u00b4 ersic index are also found left of that line. Kinematic signatures of discs are more robust with respect to the changes in inclinations. The disc-like kinematics, found in nearly oblate axisymmetric objects (as well as bars) is visible at inclinations of 20\u25e6or even less (Krajnovi\u00b4 c et al. 2008). Complex kinematics, on the other hand is a clear signature that the mass distribution is not favourable for the existence of discs. 5.7 Two types of ETGs with discs The incidence of discs among slow rotators, large ranges of D/T ratios and S\u00b4 ersic indices (both n and nb) among fast rotators suggest there are sub-populations present among these galaxies. Additionally, different types of fast rotators are predicted by the semianalytic models (Paper VIII). In this section we explore this by dividing galaxies in three bins, using both kinematic and photometric information on the disc components. The galaxies in the three bins can be described as having: no discs, intermediate discs or dominant discs. Following the results of Sections 5.2 and 5.4, the selection of bins is made by requiring that galaxies are: i) No discs: those slow rotators with D/T < 0.05, nb > 3 and not 2\u03c3 galaxies. This selection yields 20 objects (only slow rotators). c \u20dd2011 RAS, MNRAS 000, 1\u201329 16 Davor Krajnovi\u00b4 c et al. ii) Intermediate discs: those slow rotators which have 0.05 < D/T < 0.5 or those that have D/T < 0.05, but nb < 3, or those fast rotators which have D/T < 0.5 and nb > 3. No 2\u03c3 galaxies are taken in this bin. This selection yields 36 objects, including 9 slow rotators. iii) Dominant discs: those slow and fast rotators with D/T > 0.5, or those fast rotators with D/T < 0.5 but nb < 3, and all (both fast and slow rotator) 2\u03c3. This selection yields 124 objects, including 5 slow rotators. The no disc bin comprises slow rotators which do not have any signature (neither in the kinematics nor in the photometry) of disc-like components, and it is the most conservative estimate for non-existence of discs in early-type galaxies. We required nb > 3 (actually, for these galaxies nb is the global S\u00b4 ersic index, as they are all best \ufb01t with a single component) to remove the few galaxies with low S\u00b4 ersic index. As 2\u03c3 galaxies are made of two counter-rotating discs, or at least of two \ufb02attened families of counter-rotating orbits of high angular momentum (for detailed dynamical models of 2\u03c3 galaxies see Cappellari et al. 2007), these galaxies should be considered to have large disc contributions, even though their kinematics are not disc like. Therefore, we also removed all slow rotator 2\u03c3 galaxies. The Intermediate discs contain all galaxies which have some indications of discs, but these discs do not dominate the total light. This bin collects most of the slow rotators of typically higher \u03bbR (for the range of \u03bbR found among slow rotators; see open symbols on Fig 7), and those fast rotators that have relatively small exponential discs and bulge components of high S\u00b4 ersic indices. The reason for this requirement is that a systems with a bulge component \ufb01t by a low S\u00b4 ersic index next to an exponential disc could be approximated as a double discs system or at least as being made of two disc-like components and should be excluded from this class. Again, no 2\u03c3 galaxies are taken in this bin. Finally, the Dominant discs bin gathers all remaining galaxies, including all remaining slow rotators with strong photometric disc contribution, all 2\u03c3 galaxies, and all fast rotators which either have a D/T > 0.5 or D/T > 0.5 and nb > 0.3, for the same reason as explained in the previous paragraph. Given the previous results, it is not a surprise that most of our galaxies indeed fall in this group. We did not include barred galaxies as they were not analysed in this paper. However, if we were to include barred and ringed systems, it is likely that they would be split between Dominant discs and Intermediate discs, stronger barred systems probably contributing to the latter. In Fig. 9, which summarises the results of this section, we include barred galaxies in a separate bin for comparison with other three bins de\ufb01ned above. In Fig. 9, we present the mass and environment dependence for ATLAS3D galaxies. We used mass estimates from Paper IX, and the density estimator from Paper VII (see Section 5.4.4). As a measure of the environment, we use the volume density in Mpc\u22123 of galaxies inside a sphere of a radius which includes ten nearest neighbours. Here we used the best distance estimates to get the three-dimensional distribution of galaxies (for more details see Paper VII). This density estimator is good to differentiate between cluster and \ufb01eld regions, or Virgo and non-Virgo densities in the ATLAS3D sample. In both histograms shown on Fig. 9 there is a substantial overlap between the bins, but a clear trend in mass can be seen on the left hand panel. The Dominant discs are typically found in lower mass systems (centred around 1010.3 M\u2299), the Intermediate discs in intermediate and more massive systems (centred around 1010.9 M\u2299), while the population of No discs dominates the most massive end of the distribution of ATLAS3D galaxies (beyond 1011.5 M\u2299). Bars are distributed similarly like Dominant discs, and the K-S test gives a probability of 0.98 that these two distributions are drawn from the same parent sample. A contrary result is obtained if one compares the distribution of bars and Intermediate discs (K-S test probability is 0.003). This result is consistent with the observed distribution of galaxy properties on the mass \u2013 size diagram and our interpretation of ETGs scaling relations Cappellari et al. (2012a, hereafter Paper XX)). A more complex picture is evident in the right hand plot of the same \ufb01gure which considered the environmental dependence. There is no major difference between fractions of different types of galaxies between Virgo (log(volume density) >0) and non-Virgo environments. Outside of Virgo, Dominant discs and Intermediate discs have similar distributions, while bars favour a bit more dense environments. Within Virgo, densest regions are favoured by No disc populations (as shown already in Paper VII), while Intermediate discs are found more towards the outskirts. Bars and Dominant Discs are found also in denser environments within the cluster, but bars tend to be more similarly distributed like No disc galaxies. 6 CONCLUSIONS In this work we performed a disc-bulge decomposition of ATLAS3D galaxies with the aim to investigate the photometric evidence for discs in early-type galaxies, and to link them with our kinematic data. For this purpose we selected all (obviously) nonbarred galaxies from our sample (180 galaxies out of 260, with 34 slow and 146 fast rotators), and performed a two component decomposition onto an exponential disc and a bulge described by the S\u00b4 ersic function of a free index. We did not try to reproduce other components (i.e. bars and rings). The removal of the barred objects is justi\ufb01able as these galaxies are known to contain discs and they are found in fast rotators, therefore, the link between photometry and kinematics for these systems is clear, and we can not \ufb01t them accurately with our two component approach. We also performed a single component \ufb01ts with a S\u00b4 ersic function and several tests with 1D and 2D decompositions methods (presented in the Appendix A). The results of the \ufb01ts are presented in Table C1. Before listing our main conclusion, we would like to highlight that global S\u00b4 ersic index is a poor estimate of galaxy morphology. It is widely used to differentiate between earlyand late-type galaxies, but even when applied on a sample of only early-type galaxies it does not recover either the traditional Hubble classi\ufb01cation based on the apparent shapes or the modern kinematic classi\ufb01cation based on the speci\ufb01c angular momentum. Using the decomposition into a bulge and a disc does improve the agreement between morphological and kinematic classi\ufb01cations, but it is still not suf\ufb01ciently good. While it can be used to highlight those objects which are likely consistent with being fast rotators and disc related (by assuming low S\u00b4 ersic index for light pro\ufb01les requiring only a single component and D/T > 0.05 for two component \ufb01ts), it still fails in recognising slow rotators (or even galaxies commonly classi\ufb01ed as ellipticals). This is of particular importance for higher redshift studies and studies of large samples of galaxies. Our main conclusions are: \u2022 Using the S\u00b4 ersic index alone (obtained by \ufb01tting a single S\u00b4 ersic function to the light pro\ufb01le) is not suf\ufb01cient to distinguish between fast and slow rotators. The distribution of S\u00b4 ersic indices for slow c \u20dd2011 RAS, MNRAS 000, 1\u201329 Stellar discs in early-type galaxies 17 Figure 9. Distribution of ATLAS3D galaxies of different disc content with respect to the total galaxy mass (left) and environment (right). In both panels galaxies are divided in three classes as speci\ufb01ed in the legend (left panel) and in text (Section 5.7) and we added all barred galaxies for which we did not attempt a decomposition. Open histogram shows no discs, red (left slanted) histogram shows intermediate discs, blue (right slanted) histogram dominant discs distributions and orange \ufb01lled histogram shows barred galaxies. and fast rotators are not drawn from the same sample, and typically fast rotators have low n (< 3). There is, however, a signi\ufb01cant overlap of slow and fast rotators for n > 3. Based on the ATLAS3D sample of nearby early-type galaxies there is a 5 per cent chance that an object with n < 3 is a slow rotator. For an object with n > 3 there is, however, only a 22 per cent chance that it is a slow rotator. \u2022 Single-component Sersic \ufb01ts were adequate for 43 per cent of the analysed early-type galaxies (77 of 180 galaxies). The light pro\ufb01les of other galaxies were better \ufb01t with two sub-components. The single-component galaxies do not contain a formal exponential component (with n=1), but 46 (of 77 or 59 per cent) of them have a low S\u00b4 ersic index (n < 3), frequently around a value of 1. \u2022 The exponential sub-components, or single-components with low S\u00b4 ersic indices (n < 3), are found in the majority of earlytype galaxies. We show that these components are present in galaxies with regular rotation, intermediate to high angular momentum and objects with h3 \u2212V/\u03c3 anti-correlation typical for discs. Therefore, we associate exponential sub-components with discs. Similarly, single-components of low S\u00b4 ersic indices can be associated with discs (if n \u223c1) and disc-like structures (for other n that are < 3). \u2022 About 17 per cent of ATLAS3D (early-type) galaxies (31 of 180 galaxies, or 12 per cent of 258 ATLAS3D galaxies with good imaging, assuming here not analysed bars are disc related structures) do not have any evidence for discs or disc-like structures. \u2022 About 41 per cent of the stellar mass of early-type galaxies is in discs or disc-like components. \u2022 Disc or disc-like components are typically found in fast rotators, while in some slow rotators the presence of exponential subcomponents or single-components with low S\u00b4 ersic indices (n < 3) could be related to structures made of more complex orbital families (with high angular momentum) allowed in non-axisymmetric potentials. These components are often related to kinematically distinct cores (KDCs). We note that one galaxy, NGC 5485, has an exponential sub-component, but its orientation is perpendicular to the sense of rotation, and, hence, it can not be taken as an evidence for a disc. \u2022 24 of 34 (70 per cent) slow rotators are best \ufb01tted with singlecomponents. Of these 4 have a low S\u00b4 ersic index (< 3). Other slow rotators (10) have a substantial fraction of light in the exponential components. \u2022 93 of analysed 146 fast rotators (64 per cent) have exponential sub-components (discs). 42 of the remaining 53 fast rotators have single-components of low S\u00b4 ersic index (< 3). There are only 11 fast rotators that do not show clear evidence for discs or disc like structures in their photometry. For some of these galaxies inclination effects could be the reason for not detecting the disc-like structures in photometry, some are recent merger remnants while rest are complex systems. \u2022 S\u00b4 ersic index of the bulge sub-component is smaller than 3 for 73 of 103 early-type galaxies, for which a two component \ufb01t was deemed necessary. The same is true for 70 objects if n = 2.5 is used. It is not obvious that only secular evolution is responsible for build up of these sub-components. \u2022 There are trends between D/T and nb with \u03bbR, such that for c \u20dd2011 RAS, MNRAS 000, 1\u201329 18 Davor Krajnovi\u00b4 c et al. high \u03bbR, D/T is high and nb is low, but there is no clear correlation. The S\u00b4 ersic index ntot from a single \ufb01t to galaxies does not correlate strongly with D/T ratio, as shown by other studies, or with \u03bbR. \u2022 Decomposing those galaxies that require two components into discs and bulges improves the differentiation between fast and slow rotators compared to using a single component S\u00b4 ersic index. To a \ufb01rst approximation, it is possible to describe fast rotators as earlytype galaxies with exponential discs (D/T > 0.05) or, for single component S\u00b4 ersic \ufb01ts, low n (n < 3). Similarly, slow rotators can be described as galaxies without exponential components and high n. We recommend this criteria when stellar kinematics is not available, but the correspondence is not 1:1, with a 7 per cent probability (11 of 146 analysed fast rotators) to miss a fast rotator and a 59 per cent probability (20 of 34 analysed slow rotators do not have disclike components) to correctly recognise a slow rotator, implying that the decomposition can be used only as a guidance for classi\ufb01cation. In general, kinematic analysis and classi\ufb01cation based on the angular momentum content remains the best attempt to mitigate the in\ufb02uence of inclination effects. \u2022 As noted previously by other authors, there is a signi\ufb01cant dependance of photometric parameters on the inclination effects. Strong (exponential) disc signatures, however, can be seen in the light pro\ufb01les even at low inclinations, while weak discs disappear sooner and are hard to detect below an inclination of \u223c50\u25e6. \u2022 Disc dominated galaxies are typically the least massive, while galaxies with no tracers of discs are the most massive systems in the nearby Universe. Barred galaxies have a consistent distribution of mass as systems dominated by discs. \u2022 There is no strong relation between the environment and the amount of disc light and discs are found in all environments. At high densities there is a weak evidence that disc dominated systems are found in more denser regions than galaxies with smaller disc contributions. Barred galaxies are found at all densities, but typically in denser regions than dominant discs, and have a similar distribution like galaxies with no discs. Acknowledgements MC acknowledges support a Royal Society University Research Fellowship. MS acknowledges support from an STFC Advanced Fellowship ST/F009186/1. RMcD is supported by the Gemini Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc., on behalf of the international Gemini partnership of Argentina, Australia, Brazil, Canada, Chile, the United Kingdom, and the United States of America. SK acknowledges support from the Royal Society Joint Projects Grant JP0869822. TN and MBois acknowledge support from the DFG Cluster of Excellence \u2018Origin and Structure of the Universe\u2019. PS is an NWO/Veni fellow. The research leading to these results has received funding from the European Community\u2019s Seventh Framework Programme (/FP7/2007-2013/) under grant agreement No 229517. This work was supported by the rolling grants \u2018Astrophysics at Oxford\u2019 PP/E001114/1 and ST/H002456/1 and visitors grants PPA/V/S/2002/00553, PP/E001564/1 and ST/H504862/1 from the UK Research Councils. RLD acknowledges travel and computer grants from Christ Church, Oxford and support from the Royal Society in the form of a Wolfson Merit Award 502011.K502/jd. We acknowledge the usage of the HyperLeda database (http://leda.univ-lyon1.fr).This paper is based on observations obtained at the William Herschel Telescope, operated by the Isaac Newton Group in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrof\u00b4 \u0131sica de Canarias. Funding for the SDSS and SDSS-II was provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, the U.S. Department of Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society, and the Higher Education Funding Council for England. The SDSS was managed by the Astrophysical Research Consortium for the Participating Institutions.",
                    "introduction": "Excluding those unsettled systems undergoing mergers, bright galaxies come in two \ufb02avours: with and without discs. This was recognised in the early part of the twentieth century (Reynolds 1920; Hubble 1922, 1926; Jeans 1929; Hubble 1936) and today is characterised as the Hubble sequence of galaxies (Sandage 2005, for a review). Recognising where discs disappear on the sequence, however, is a much more dif\ufb01cult task as projection effects play a key role in our (in)ability to quantify their incidence. This is evi- dent in the fact that the idea of S0 galaxies actually being similar to spirals, while present in the works of Spitzer & Baade (1951) and Sandage et al. (1970), waited some forty years after the ap- pearance of the Hubble tuning fork to be qualitatively presented (van den Bergh 1976). The importance of the parallelism between the two sequences of late- and early-type galaxies for the under- standing of galaxy structure was nearly ignored for decades. The parallelism between the two classes of galaxies was recently re- vived by our project, thanks to the use of integral-\ufb01eld stellar kine- matics (Cappellari et al. 2011b, hereafter Paper VII), which allowed us to recognise discs even at low inclinations. This was followed a few months later by two independent photometric studies reaching the same conclusion (Laurikainen et al. 2011; Kormendy & Bender 2012). \u22c6E-mail: dkrajnov@eso.org \u2020 Dunlop Fellow In practice, there are three ways to look for discs in galaxies: by means of photometric or kinematic analysis, or by construct- ing dynamical models using both types of information. Dynamical models are often complex and typically rely on certain assumptions. One of these is an assumption on the shape, which could be a limita- tion if we are interested in quantifying structural components such as discs. The photometric analysis is based on recognising structural components of galaxies in their light distributions, while the kine- matic analysis is based on recognising features in the higher mo- ments of the line-of-sight velocity distribution (i.e. the mean veloc- ity, velocity dispersion). Stellar discs, which are the main topic of this study, are \ufb02attened structures in which stars move on orbits of high angular momentum, hence they should leave both photometric and kinematic traces. Next to their \ufb02attened shape, which is clearly recognisable only when viewed directly from a side, or edge-on, discs could be expected to have a speci\ufb01c distribution of light. In- deed, discs of late-type spirals were found to have exponential light pro\ufb01les (Freeman 1970). By contrast, ellipticals and bulges of spi- rals were \ufb01rst \ufb01tted with an R1/4 pro\ufb01le (de Vaucouleurs 1959; Kormendy 1977), but since the early 1990s the paradigm shifted to- wards describing these structures with a more general S\u00b4 ersic (1968) R1/n law which provided a continuous parameter applicable across the Hubble sequence (e.g. Caon et al. 1993; Andredakis et al. 1995; Graham et al. 1996; de Jong 1996). Early-type galaxies, traditionally divided into ellipticals and S0s, are particularly interesting as among them the separation into c \u20dd2011 RAS, MNRAS 000, 1\u201329 Stellar discs in early-type galaxies 3 objects with and without discs is ambiguous. Photometric analy- sis of their isophotes revealed that some do contain non-obvious discs (Bender et al. 1989), that these might be very common (Rix & White 1990), and that inclination effects misclassify S0s as ellipticals (Jorgensen & Franx 1994). A new way of searching for discs in early-type galaxies was found in the so-called bulge-disc decompositions (e.g. Kent 1985; Saglia et al. 1997; Scorza et al. 1998; D\u2019Onofrio 2001). The essence of these techniques is that they attempt to separate the light contribution from a bulge (having an R1/4 or an R1/n light pro\ufb01le) and a disc (having an exponential light pro\ufb01le). As disc dominated galaxies are frequently made of more than just a bulge and a disc, and contain also bars, rings, ovals, nuclear discs and nuclear clusters, as well as of bulges which are not necessary similar to elliptical galaxies (e.g Kormendy & Kennicutt 2004), recent decomposition techniques allow for a more gen- eral description of sub-components (e.g. MacArthur et al. 2003; de Jong et al. 2004; Laurikainen et al. 2009; Weinzirl et al. 2009; Laurikainen et al. 2010; Kormendy & Bender 2012), as well as ap- plying it on two-dimensional spectra (Johnston et al. 2012). The other way of looking for discs is by observing the kine- matics of galaxies. As stars in discs rotate at large velocities, and as their motion is typically ordered, observing regular rotation sim- ilar to those expected from ideal thin discs, implies those systems are discs, contain discs, or are related to discs by evolution. Ellip- tical galaxies, or bulges that are similar to them, should not exhibit such ordered and simple rotations (e.g. Statler 1991; Arnold et al. 1994). Early studies of kinematics of early-type galaxies indeed pointed out there are differences between them (Davies et al. 1983; Bender et al. 1994), but to bring kinematic and photometric analy- sis to a comparable level it was necessary to wait for integral-\ufb01eld spectrographs (IFS) and two-dimensional maps of stellar kinemat- ics. The bene\ufb01ts of such observations were clearly pointed out by the SAURON Survey (de Zeeuw et al. 2002) and ATLAS3D project (Cappellari et al. 2011a, hereafter Paper I). Using velocity and ve- locity dispersion maps (e.g. Emsellem et al. 2004), it is possible to robustly classify early-type galaxies according to their global angular momentum, even though it is still a projected quantity (Emsellem et al. 2007; Cappellari et al. 2007). This study proposed a separation of early-type galaxies into fast and slow rotators based on a physical property more robust to the effects of the inclination, instead of the traditional elliptical/S0 separation which is based on the apparent shape. This point was taken further with the ATLAS3D data, which comprise observations of a sample of nearby ETGs, volume limited and complete down to a magnitude of -21.5 in the K-band. Using this statistical sample, Emsellem et al. (2011, here- after Paper III) showed that 86 \u00b1 2 per cent of ETGs are fast and 14 \u00b1 2 per cent are slow rotators. This separation agrees closely with a quantitative separation of the morphology of the kinemat- ics maps Krajnovi\u00b4 c et al. (2011, hereafter Paper II), supporting the robustness of the distinction between the two classes. Furthermore, utilising kinemetry (Krajnovi\u00b4 c et al. 2006), it is possible to quantify how well the velocity maps of early-type galax- ies agree with those of ideal discs. Krajnovi\u00b4 c et al. (2008) and Paper II found that differences of only 2-4 per cent, between observed stel- lar velocity maps of early-type galaxies and maps of inclined discs, are typical for fast rotators, while velocity maps of slow rotators simply can not be represented by those of ideal discs. This suggest that fast rotators as a class are indeed discs or at least disc-like ob- jects, and this is the essence of the fast-slow rotators separation used in Cappellari et al. (2011b, hereafter Paper VII) to set apart objects with and without discs and update the Hubble sequence accord- ingly. The fact that the presence, or lack of, discs differentiates fast from slow rotators is also con\ufb01rmed though semi-analytical mod- elling. In Khochfar et al. (2011, hereafter Paper VIII), we show that selecting galaxies by disc fraction, where fast rotators are selected to have more than 10 per cent of mass in discs, semi-analytic model is able to reproduce the observed abundance of fast and slow rota- tors as a function of mass or luminosity. Armed with these results on galaxies\u2019 internal kinematics, we now turn our attention to the photometric analysis of ATLAS3D galaxies. We \ufb01t single S\u00b4 ersic pro\ufb01les to all ATLAS3D galaxies and attempt to separate the light contributions into a general S\u00b4 ersic and an exponential pro\ufb01les. It is generally assumed that exponential pro\ufb01les can be associated with discs. This is applicable to spiral and edge-on S0s galaxies, where discs are obvious, but for a general early-type galaxy, seen at a random orientation, where a disc might be masked due to the projection, it is not obvious that the exponen- tial pro\ufb01le is really related to a (hidden) disc. Put in another way, the existence of an exponential pro\ufb01le does not necessary prove that the galaxy contains a disc. This was pointed out by de Jong et al. (2004) and Naab & Trujillo (2006), who suggest that the kinematic information is crucial for determining the disc nature of early-type galaxies. The purpose of this work is to quantify the incidence of exponential light pro\ufb01les, make a link with the observed kinematics and investigate the difference between fast and slow rotators from the point of view of their light distributions. In Section 2 we brie\ufb02y outline the ATLAS3D sample, relevant observations and de\ufb01ne samples of galaxies used in this work. In Section 3 we present the method used for the parametrisation of the light distributions and for the disc/bulge decomposition. In Sec- tion 4 we outline our global \ufb01ts with a single S\u00b4 ersic function. In Section 5 we show and discus the results, while in Section 6 we summarise the main conclusions of this work. A further discussion on the merits of the chosen method is presented in Appenidx A, a comparison of our results with literature is in Appendix B and Table with the results is in Appendix C."
                }
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