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abstract: 'We measure the correlation between the arrival directions of the highest energy cosmic rays detected by the Pierre Auger Observatory with the position of the galaxies in the  Parkes All Sky Survey (HIPASS) catalogue, weighted for their  flux and Auger exposure. The use of this absorption–free catalogue, complete also along the galactic plane, allows us to use all the Auger events. The correlation is significant, being 86.2% for the entire sample of  galaxies, and becoming 99% when considering the richest galaxies in HI content, or 98% with those lying between 40–55 Mpc. We interpret this result as the evidence that spiral galaxies are the hosts of the producers of UHECR and we briefly discuss classical (i.e energetic and distant) long Gamma Ray Burst (GRBs), short GRBs, as well as newly born or late flaring magnetars as possible sources of the Auger events. With the caveat that these events are still very few, and that the theoretical uncertainties are conspicuous, we found that newly born magnetars are the best candidates. If so, they could also be associated with sub–energetic, spectrally soft, nearby, long GRBs. We finally discuss why there is a clustering of Auger events in the direction on the radio–galaxy Cen A and an absence of events in the direction of the radio–galaxy M87.'
author:
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    G. Ghisellini,$^1$[^1] G. Ghirlanda,$^1$ F. Tavecchio,$^{1}$, F. Fraternali$^2$ and G. Pareschi$^1$\
    $^1$INAF – Osservatorio Astronomico di Brera, Via Bianchi 46 Merate, Italy\
    $^2$Dept. of Astronomy, University of Bologna, via Ranzani 1, 40127 Bologna, Italy
title: 'Ultra–High Energy Cosmic Rays, Spiral Galaxies and Magnetars'
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cosmic rays – galaxies: gamma–rays: bursts – galaxies: statistics — radio lines: galaxies

Introduction
============

The origin of ultra–high energy cosmic rays (UHECR), exceeding 10 EeV (1 EeV=$10^{18}$ eV) has been a mystery for decades, but the recent findings of the large area detectors, such as AGASA (Ohoka et al. 1997), HIRes (Abu–Zayyad et al. 2000), and especially the Pierre Auger Southern Observatory (Abraham et al. 2004), began to disclose crucial clues about the association of the highest energy events with cosmic sources. The Auger collaboration (Abraham et al. 2007) found a positive correlation between the arrival directions of UHECR with energies grater than 57 EeV and nearby AGNs (in the optical catalogue of Veron–Cetty & Veron 2006). Although this result has not been confirmed by HIRes (Abbasi et al. 2008) and it has been criticised by Gorbunov et al. (2008), it received an important confirmation by George et al. (2008), who considered a complete sample of nearby hard X–ray emitting AGNs detected by the BAT instrument onboard [*Swift*]{}. This sample is much less affected by absorption than any optical sample although, to identify as such an AGN, one relies on optical identification. Moreover, George et al. (2008) found a correlation not simply with the AGN locations, but by weighting them for the X–ray flux and the Auger exposure.

This association, if real, is surprising, since the large majority of the correlating AGNs are radio–quiet, a class of objects not showing, in their electromagnetic spectrum, any sign of non–thermal high energy emission: no radio–quiet AGN was detected by the EGRET instrument onboard the [*Compton Gamma Ray Observatory*]{} (Hartman et al. 1999). Therefore they must accelerate particles (protons, nuclei, and presumably their accompanying electrons) to ultra–high energies without any noticeable radiative emission from these very same particles. Radio–loud AGNs, instead, together with Gamma Ray Bursts (of both the long and short category) do show high energy non–thermal emission, and have been considered for a long time better candidates as UHECR sources (Vietri 1995; Waxman 1995; Milgrom & Usov 1995; Wang, Razzaque & Mészáros 2008; Murase et al. 2008; Torres & Anchordoqui 2004 and Dermer 2007 for reviews, and Nagar & Matulich 2008 and Moskalenko et al. 2008 for the possible association of the AUGER events with radio–loud AGNs). Note also that some short GRBs could be due to the giant flares of highly magnetised neutron stars (“magnetars”, as the 27 Dec 2004 event from 1806–20; Borkowski et al. 2004; Hurley et al. 2005; Terasawa et al. 2005), and that, at birth, a fastly spinning magnetar can be much more energetic than when, later, it produces giant flares (Arons 2003).

The possibility that GRBs and magnetars are the sites of production of UHECR would directly imply the direct association of these events with (normal) galaxies. In this case the found association of UHECR with nearby AGNs might then be due to the fact that local AGNs just trace the distribution of galaxies. The aim of the present paper is to test this possibility directly correlating the locations of the ultra–high energy Auger events with a well defined, complete, and possibly absorption–free sample of galaxies. For this purpose we use the sample of  emitting galaxies, compiled using the Parkes 64–m radio telescope (Barnes et al. 2001; Staveley–Smith et al. 1996), which is conveniently located in the south hemisphere, as the Auger observatory. The entire sample covers the portion of the sky visible by Auger, making it possible to use, for the correlation analysis, all the 27 UHECR events with energies larger than 57 EeV detected by Auger, without excluding the galactic plane, as is instead necessary when dealing with AGNs or optically selected galaxies. Note that the presence of neutral hydrogen strongly favours spirals (or, more generally, gas–rich galaxies) with respect to elliptical galaxies.

We use a cosmology with $\rm{h}_0=\Omega_\Lambda=0.7$ and $\Omega_{\rm M}=0.3$.

Data
====

UHECR events
------------

The Auger Observatory (Abraham et al. 2004, 2008), operating in Argentina since 2004, is located at latitude $-35.2\degr$ and it has a maximum zenith angle acceptance of $60\degr$. The relative exposure is independent of the energy of the detected events and it is a nearly uniform in right ascension. The dependence on declination is given by Sommers (2001). The Observatory can detect Cosmic Rays from sources with declination $\delta<24.8^\circ$.

The available Auger list of UHECR events (Abraham et al. 2008) comprises 27 events with energies in excess of $5.7\times{}10^{19}\ev$ from an integrated exposure of $9000\crexp$. The event arrival directions are determined with an angular resolution of better than $1\degr$. However, magnetic fields of unknown strength will deflect charged particles on their trajectories through space. The advantage of studying the highest energy events is that this deflection is minimised, but it can still be up to $\sim{}10\degr$ in the Galactic field. The 27 UHECR detected by Auger are distributed in the range $\delta\in[-61,9.6]$ (or at galactic latitudes $b\in[-78.6,54.1]$ – open circles in Fig. \[HIn\] and Fig. \[HIflux\]).

HIPASS catalogue
----------------

We compare the arrival directions of Auger UHECRs with the locations of sources of the  Parkes All–Sky Survey (HIPASS – Meyer et al. 2004). This is a blind survey of sources in  covering the full southern sky at $\delta<25^\circ$ which is the same sky area accessed by the Auger Observatory. The full catalogue is composed by a list of 4315 sources at $\delta<2^\circ$ (HICAT – Meyer et al. 2004; Zwaan et al., 2004) and by its extension to the northern sky up to $\delta=25^\circ$ (NHICAT – Wong et al. 2006) which includes 1002 sources. All sources are shown in Fig. \[HIn\] with the 27 UHECR detected by Auger.

The HICAT and NHICAT have different level of completeness. To have a catalogue complete in flux at the 95% level, we cut the HICAT at $S_{\rm int}>7.4$ Jy km s$^{-1}$ and the NHICAT at $S_{\rm int}>15$ Jy km s$^{-1}$ as discussed in Zwaan et al. (2004) and Wong et al. (2006). $S_{\rm int}$ represents the total  line flux. For the purposes of this paper we also considered the sources within 100 Mpc which is the maximum distance at which UHECRs of $E>57$ EeV can survive the GZK suppression effect (see e.g. Harari et al. 2006). We call this sample 95HIPASS: it contains 2414 sources from the HICAT and 290 sources from the NHICAT for a total of 2704 sources and covers the entire sky at $\delta<25^\circ$. We will also consider the southern sky sample alone which is more complete and can be cut at 99% completeness for $S_{\rm int}>9.4$ Jy km s$^{-1}$ (also by considering sources at $<$100 Mpc). This sample contains 1946 sources and is called 99HICAT.

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Analysis
========

To quantify the possible correlation between UHECR Auger events and the distribution of  local galaxies we use the method adopted by George et al. (2008). In order to quantify the probability that two sets of sources are drawn from the same parent population of objects we perform the two-dimensional generalisation of the Kolmogorov–Smirnov (K–S) test (Peacock 1983) proposed by Fasano & Franceschini (1987).

In our case the test is used to compare two data samples, i.e. the UHECR and the  galaxies. This test can then measure either if UHECRs have a galaxy counterpart, and, viceversa, if a concentration of galaxies has an UHECR counterpart. The test relies on the statistic $D$, also used for the unidimensional K–S test, which represents the maximum difference between the cumulative distributions of the two data samples. For each UHECR data point $j$ we compute a set of four numbers $d_{j,i}$ ($i$=\[1,4\]) defined as the difference of the relative fraction of UHECR and  galaxies found in the four natural quadrants defined around point $j$. Hence, $D=\max(d_{j,i})$ for all the data points considered. Defining $Z_{\rm {n}}=D\sqrt{n}$, the strength of the correlation between two catalogues is the integral probability distribution $P(D\sqrt{n}>\rm{observed})$, where $n=N_1N_2/(N_1+N_2)$, and $N_1$ and $N_2$ are the number of data points in the two sets. This measurement can be used to determine the similarity of sets of positions on the sky.

The probability can be computed analytically for large data sets ($n>$80 – Fasano & Franceschini 1987). In our case, having only 27 UHECR, we have to rely on Monte Carlo simulations. We generate a large set of random UHECR events according to the relative Auger exposure. For each synthetic UHECR sample we compute $Z_{\rm {n}}$ by correlating it with the catalogue of  galaxies. The probability of the observed $Z_{\rm {n}}$ is given by the number of times we find a value of $Z_{\rm {n}}$ larger than the observed one. This is the probability that the correlation between the (real) UHECR sample and the  galaxies is not by chance. Large (low) values of the probability indicate a good (poor) correlation between the Auger UHECRs and the given  galaxy sample.

As noted by George et al. (2008), the two–dimensional K–S test can be performed with the number of data points or with the flux of the sources in the comparison sample. In our case $D$ represents the maximum difference between the number of UHECRs and that of the sum of the galaxies weighted for their flux and for the the relative Auger exposure. The advantage of using the weighted flux of the sources is that it accounts for their distance. George et al. (2008) found that the UHECRs are more correlated with the weighted flux of [*Swift*]{} AGN than with with their position. In Fig. \[HIflux\] we show the map of the flux of the HIPASS catalogue weighted for the Auger relative exposure.

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Results
=======

We found that with the 95HIPASS catalogue (2704  sources complete in flux at 95%) the probability that UHECRs are correlated with  galaxies is 71.6% by using the weighted flux of the  sources. Considering the more complete 99HICAT (1946  sources complete in flux at 99%) distributed within 100 Mpc and the 25 UHECRs distributed in the same sky region we find a larger flux–weighted probability of 87.8%. This probability is slightly smaller than found with local AGN by George et al. (2008).

However, having a large sample of  galaxies we can study if the correlation probability changes by considering different sub–samples of galaxies selected according to their distance or luminosity. We have considered 4 bins of distance with an equal number of sources ($\sim$500) per bin. The correlation probability shows a maximum of 95% (97.8% for the 99HICAT) for sources distributed between 37.8 and 55 Mpc. We show these results in Fig. \[bella\] (open circles and stars in the bottom panel).

Similarly we defined four equally populated luminosity bins, or, equivalently, four bins of HI mass content, since we can use $M/M_\odot = 2.36\times 10^5 D_{\rm Mpc}^2 S_{\rm int}$ to estimate the  mass (here $S_{\rm int}$ is measured in \[Jy km/s\]). We find that the probability (left panel in Fig. \[bella\]) is maximised by the most  luminous or massive (in ) sources (98% and 99% for the 95HIPASS and 99HICAT sample, respectively, for $M> 1.1\times 10^{10}\, M_{\odot}$).

Selecting those  galaxies located within two $20^\circ \times
20^\circ$ boxes centred on the radio–galaxies Cen A and M87 (green boxes in Fig. \[HIn\]), we can show where they lie in the luminosity–distance plane in Fig. \[bella\] (orange and green dots, respectively). While there is no clustering of points at the distances of Cen A and Virgo, we can see that  galaxies in the direction of Cen A do cluster at distances of 40–50 Mpc, where the Centaurus cluster is. This could explain why some UHECR events [*appear*]{} to be associated with the radio–galaxy Cen A, and none with M87: beyond Cen A there is the Centaurus cluster, richer of  emitting spirals than the Virgo cluster. The ratio of the integrated HI fluxes from the two $20^\circ\times20^\circ$ boxes (Virgo/Cen A) is 5.9. To this, we have to multiply by another factor 3 for the lower Auger exposure in the direction of Virgo.

The sample has too few galaxies beyond 100 Mpc to test the GZK effect (that would be revealed by finding no correlation for these galaxies).

Discussion
==========

The 27 Auger events above 57 EeV, with a total exposure of $9000\crexp$ correspond to an integrated flux, in CGS units: $$F_{\rm A}(E>57\, {\rm EeV})\, \sim \, 1.1 \times 10^{-11} \,\,\, 
{\rm erg\,\, cm^{-2}\, s^{-1}}
\label{fa}$$ This flux is smaller than the electromagnetic flux that we receive from nearby radio–quiet AGNs in hard X–rays (see e.g. Tueller et al. 2008). We now compare this flux with the expected flux of other candidate sources. We will consider flaring or bursting sources, that is impulsive events, but the spreading of the arrival times of UHECRs from a source located at a distance $D$, $\Delta t \sim D \theta^2/2 c$, due to even tiny magnetic deflections, ensure that we can treat all candidate sources as continuous. We will estimate the predicted flux in two different ways.

First, assume that a class of sources is characterised by a pulse of emission of UHECRs, of average total energy $<E>$. Assume also that these events occur at a rate $R$ per galaxy, per year, and consider those events occurring within the GZK radius $D_c$. We have: $$F \, = \, <E> {R \over 3.15 \times 10^7} 
\, { N_{\rm g}(D<D_c) \over 4\pi (a D_c)^2}$$ where $3.15\times 10^7$ is the number of seconds in one year and $N_{\rm g}(D<D_c)$ is the number of galaxies within $D_c$ of $L_*$ luminosity. The average distance of the sources is $a D_c$ ($a=3/4$ for sources homogeneously distributed). Setting the mean local galaxy density $n_{\rm g}= N_{\rm g}/(4\pi D_c^3/3)= 10^{-2} n_{\rm g, -2}$ Mpc$^{-3}$ we have: $$F  \sim 1.2 \times 10^{-57}  <E> R\, n_{\rm g, -2} {D_{c, 100} \over a^2}
 \,\,\, {\rm erg\, cm^{-2}\, s^{-1}}
\label{rate}$$ where $D_c =100 D_{c,100}$ Mpc.

The second estimate on the predicted UHECR flux uses the electromagnetic flux as a proxy. Assume that we detect, for a typical member of a class of sources, an average fluence $<{\cal F}>$, and that there are $N$ events per year. If a fraction $\eta$ of these events comes from sources within $D_c$, we have $$F\, = \, {\eta <{\cal F}> N  \over 3.15 \times 10^7} 
\label{m2}$$ This estimate is more appropriate when dealing with sources, such as long and short GRBs, whose fluences and occurrences are known, while Eq. \[rate\] is more appropriate when dealing with possible sources of unknown electromagnetic output, but predicted energetics and rates, such as newborn magnetars (Arons 2003) or giant flares from old magnetars.

Let us consider the above classes of sources in turn, starting from short GRBs. In the BATSE catalog (cossc.gsfc.nasa.gov/docs/cgro/batse/BATSE\_Ctlg/flux.html) we have 490 short GRBs of total fluence $5.5\times 10^{-4}$ erg cm$^{-2}$ in 9 years of operation. Tanvir et al. (2005) correlated these short GRBs with local optically selected galaxies finding that a fraction between 5 and 25% of BATSE short GRBs might be nearby, i.e. at $z < 0.025$, corresponding to 109 Mpc. Considering that BATSE saw half of the sky and setting $\eta=0.1$ we have an average flux of $3.9\times 10^{-13}$ erg cm$^{-2}$ s$^{-1}$. Then, if the UHECR flux is similar to the electromagnetic one, short GRBs do not match the required flux. Classical long GRBs (namely, energetic GRBs at $z\gsim 1$) in the BATSE sample have a total fluence of 0.024 erg cm$^{-2}$ (for the listed 1490 long GRBs in the BATSE catalog), corresponding to an average (all sky) flux of $1.7\times 10^{-10}$ erg cm$^{-2}$ s$^{-1}$, larger than the one given by Eq. \[fa\]. However, for long BATSE GRBs, $\eta$ must be much smaller than 0.1, as directly suggested by the paucity of nearby events, and by the lack of correlation with nearby galaxies and clusters (Ghirlanda et al. 2006). While we cannot dismiss them as sources of UHECRs, it seems likely that classical BATSE bursts are too distant (but see below).

Consider now giant flares from relatively “old” magnetars. The giant flare from SGR 1806–20 of Dec 27, 2004 emitted an energy $E\sim 10^{46}$ erg in less than a second. The radio afterglow convincingly demonstrated the formation of a (at least mildly) relativistic fireball. With the current hard X–ray instruments, such flares can be detected up to $\sim$30–40 Mpc (Hurley et al. 2005). Eq. \[rate\], with $D_{c,100}=0.3$, and $<E>=10^{46}$erg, would require $R\sim 1$ event per galaxy per year, while an approximate limit to the rate is $R< 1/30$ yr$^{-1}$ (see e.g. Lazzati et al. 2005).

Finally, consider fastly spinning newly born magnetars, whose rotational energy can exceed $10^{52}$ erg, with a rate of $R=10^{-4}$ events per galaxy per year (Arons 2003). With the estimated galaxy density ($n_{\rm g, -2}\sim 0.7$ with $L\sim L_*$; Blanton et al. 2001) there should be 1 event per year within 100 Mpc. If each magnetar produces $10^{50}$ erg in UHECRs, then this class of sources can be the progenitor of the Auger events (Eq. \[rate\]). This is independent of collimation, since the reduced rate of events pointing at us is compensated by an increase of the apparent energetics. But if an equal amount of energy is released in electromagnetic form, at energies detectable by BATSE, then they should be a significant fraction of all BATSE GRBs. Since the birth of a magnetar should be accompanied by a supernova, [*these events should be associated with long, rather than short GRBs,*]{} for which no associated supernova has been seen. If the radiative output is isotropic, they will all be nearby, sub–energetic, GRBs.

The required fluence of these sub–energetic nearby long GRBs, to match the UHECRs flux, should be $$<{\cal F}>\, \sim\,  3.15\times 10^{-4} \epsilon_{\rm CR} \, {F_{\rm A, -11} \over \eta N}
\,\,\, {\rm erg\,\, cm^{-2}}$$ where $\epsilon_{\rm CR}$ is the ratio of the emitted energy in radiation and UHECR. If $\eta\sim \epsilon_{\rm CR}\sim 1$, these events constitute a sizeable fraction of the total fluence of all long BATSE GRBs in one year (which is ${\cal F} \sim 0.024/9\sim  2.7\times 10^{-3}$ erg cm$^{-2}$).

Since we know that the large majority of long GRBs are not nearby, newly born magnetars should not constitute conspicuous events in hard X–rays. Their fluence must be mostly emitted in another energy range. GRB 060218 (Campana et al. 2006) with an energy of a few $\times 10^{49}$ erg, at a distance of 145 Mpc, could be one of these events, and Soderberg et al. (2006) and Toma et al. (2007) already suggested that this GRB was powered by a newly born magnetar. The spectrum of its prompt emission peaked at $\sim$5 keV, i.e. its fluence in relatively soft X–rays exceeded the 15–150 keV fluence. It was also very long, slowly rising, and would not have been detected by BATSE. Soderberg et al. (2006) pointed out that these sub–energetic long GRBs should not be strongly beamed (not to exceed the rate of SN Ib,c), and should occur at a rate of $230^{+490}_{190}$ Gpc$^{-3}$ yr$^{-1}$, corresponding to $R \approx 10^{-5}$ events per $L_*$ galaxy per year, about ten times larger than for classical long GRBs whose radiation is collimated into 1% of the sky. According to this rate, Eq. \[rate\] would then demand $<E>\sim 6\times 10^{50}$ erg in UHECRs to match the observed flux.

Conclusion
==========

We have correlated the cosmic rays with $E>57$ EeV detected by the Auger Observatory with a complete, absorption–free sample of  selected galaxies. We found a significant correlation when correlating the  [*flux*]{} of galaxies of our sample.

When considering the largest 95HIPASS catalogue and the 27 UHECRs we find a weak correlation (probability of 72%), while a larger significance (87.8%) is reached if we consider the most complete 99HICAT sample of galaxies (though with 25 UHECRs). These probabilities are maximised by cutting the  sample in distance or luminosity bins: it becomes 99% when considering the 500 most luminous (or most  massive) galaxies (1/4 of the sample), and 98% when considering the 500 galaxies lying between 38 and 54 Mpc, where the Centaurus cluster of galaxies is.

Thus there is the possibility that the UHECRs coming from the direction of Cen A are instead coming from the more distant Centaurus cluster. Galaxies of this cluster are richer in  than Virgo galaxies, explaining why there is no UHECR event from the direction of Virgo.

This sample is formed by  emitting galaxies, therefore it is biased against ellipticals. The found correlation with these galaxies, per se, is not disproving the found correlation with AGNs (Abraham et al. 2007, 2008; George et al. 2008), since they also trace the local distribution of matter, as spiral galaxies do. On the other hand, it opens up the possibility, on equal foot, that UHECRs are produced by GRBs or newly born magnetars (see also Singh et al. 2004 who used AGASA events). With the caveat that it is premature, with so few events and big theoretical uncertainties, to draw strong conclusions, we have pointed out that although classical (i.e. energetic) long GRBs and short GRBs have difficulties in producing the required UHECR flux, newly born magnetars can. If so, they could also be a subclass of [*long*]{} GRBs, possibly sub–energetic and relatively nearby, powered by fastly spinning, newborn magnetars. The future increased statistics of UHECRs arrival directions will help to discriminate among the different proposed progenitors, especially if there will be (or not) an excess of events close to the radio core and/or lobes of Cen A.

Acknowledgments {#acknowledgments .unnumbered}
===============

We thank the referee for constructive comments. We thank the ASI I/088/06/0 and the 2007 PRIN–INAF grants and Ivy Wong and Martin Zwaan for providing the NHICAT catalogue. The Parkes telescope is part of the Australia Telescope which is funded by the Commonwealth of Australia for operation as a National Facility managed by CSIRO.

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[^1]: Email: gabriele.ghisellini@brera.inaf.it
