MOA-bin-29b : A Microlensing Gas Giant Planet Orbiting a Low-mass Host Star
We report the discovery of a gas giant planet orbiting a low-mass host star in the microlensing event MOA-bin-29 that occurred in 2006. We find five degenerate solutions with the planet/host-star mass ratio of . The Einstein radius crossing time of all models are relatively short ( days), which indicates that the mass of host star is likely low. The measured lens-source proper motion is depending on the models. Since only finite source effects are detected, we conduct a Bayesian analysis in order to obtain the posterior probability distribution of the lens physical properties. As a result, we find the lens system is likely to be a gas giant orbiting a brown dwarf or a very late M-dwarf in the Galactic bulge. The probability distributions of the physical parameters for the five degenerate models are consistent within the range of error. By combining these probability distributions, we conclude that the lens system is a gas giant with a mass of orbiting a brown dwarf with a mass of at a projected star-planet separation of . The lens distance is , i.e., likely within the Galactic bulge.
More than 3900 exoplanets have been discovered since the first discovery of an exoplanet orbiting a main sequence star in 1995 (Mayor & Queloz, 1995), including various planetary systems, such as hot Jupiters and super Jupiters.
Most known exoplanets have been found by the radial velocity (Butler et al., 2006; Pepe et al., 2011) and transit methods (Batalha et al., 2013), which are most sensitive to massive planets in close orbits. Direct imaging has found young giant planets in very wide orbits.
The gravitational microlensing method has a unique planet sensitivity to planets down to low masses (Bennett
& Rhie, 1996) in wide orbits, just beyond the snow line (Gould & Loeb, 1992). Exoplanet searches by using the microlensing were first proposed by Mao & Paczyński (1991), and over 90 planets have been discovered by this method to date.
Gravitational microlensing occurs when a foreground lens star crosses the line of sight between an observer and a background source star by chance.
The gravity of the lens star bends the light from the source star and magnifies its brightness. If the lens star has a companion, its gravity affects the magnification of the source star.
The microlensing method does not depend on the brightness of the lens objects. So we can discover low-mass companions around faint and/or distant host, such as M-dwarfs or even brown-dwarfs in the Galactic disk and bulge.
The formation theory of gas giants around the low-mass host remains to be fully elucidated.
According to the core accretion theory, it is difficult to form gas giant planets in the disks around low-mass stars (Pollack et al., 1996; Ida & Lin, 2004; Laughlin et al., 2004; Kennedy et al., 2006).
Gravitational instability in the protoplanetary disk may play the important role in the formation of gas giants (Boss, 2006). In order to constrain the formation theory, more observational samples with low-mass hosts are required.
By using the microlensing method, many planetary systems with low-mass stars have been discovered in orbital separation between au (Street et al., 2013; Skowron et al., 2015; Nagakane et al., 2017; Jung et al., 2018a). This is complementary to the other detection methods.
In this paper, we present the analysis of the planetary microlensing event MOA-bin-29 with a short Einstein radius crossing time of days, which suggests the host is a low-mass object. Section 2 explains observations and data.
Our light curve modeling method and result are shown in Section 3.
In Section 4, we derive an angular Einstein radius from the source magnitude and color.
In Section 5, physical parameters of the lens system are estimated with a Bayesian analysis.
Finally, we discuss our analysis and reach conclusions in Section 6.
The Microlensing Observations in Astrophysics (MOA; Bond et al., 2001; Sumi et al., 2003) collaboration conducts a microlensing exoplanet survey towards the Galactic bulge by using the 1.8m MOA-II telescope with a 2.2 wide field of view (FOV) CCD-camera, MOA-cam3 (Sako et al., 2008) at Mt. John University Observatory in New Zealand. Thanks to the wide FOV, a high cadence survey observation can be conducted.
MOA survey uses a custom wide-band filter referred as , corresponding to a Cousins - and -band.
The MOA photometry is reduced by using the MOA’s implementation of the Difference Image Analysis (DIA) pipeline (Bond et al., 2001).
The Optical Gravitational Lensing Experiment (OGLE; Udalski, 2003 ) also conducts a microlensing survey at the Las Campanas Observatory in Chile. The third phase of the survey, OGLE-III used the 1.3m Warsaw telescope with a 0.35 FOV CCD-camera. Currently, its forth phase, OGLE-IV (Udalski et al., 2015) started its high cadence survey in 2010 with a 1.4 FOV CCD-camera. The OGLE photometry is reduced by the OGLE’s implementation of the DIA photometry pipeline (Udalski, 2003).
The gravitational microlensing event MOA-bin-29 reached to near peak on 2006 July 14 ( ), at the J2000 equatorial coordinates = ( . ) corresponding to Galactic coordinates = . Figure 1 shows the MOA and OGLE-III light curves.
This event was not detected in the real-time analysis, but found only after the off-line analysis of MOA database during (Sumi et al. in prep.).
There are several possible reasons why this event was not detected by the MOA Alert system.
First, this was a short duration event.
Second, the alert system had just started since 2006 and the baseline was not long enough to distinguish from other variables.
In this off-line analysis, the MOA Galactic bulge data have been re-analyzed and the events were detected using a criteria that is different from MOA alert system.
Since this event was not alerted, there were no follow-up observation and only the survey data is available.
Fortunately, however, the event is located in MOA field gb9, which was observed with the highest cadence of 10 minutes, so we have good coverage of this short event.
The event is also located in the OGLE-III field BLG102 and we could get data covering some part of the light curve during its magnification.
Consequently, we must characterize the anomaly with only the survey groups’ observations.
Figure 2 shows the reference image around MOA-bin-29.
The green cross indicates the position of the event detected on the difference images. We found that the source star is much fainter than a nearby bright star upper left from the event location.
The photometric error bars produced by the data pipelines can be underestimated (or more rarely overestimated). We should consider other systematic errors caused by observational conditions and so on. In order to get proper errors of the parameters in the light curve modeling, we empirically normalize the error bars by using the standard method of (Bennett et al., 2008). We use the formula,
where is the th renormalized error, is the th error obtained from DIA, and and are the renormalizing parameters.
We set to account for flat fielding errors, and we adjust the value of and . The normalization parameters and the number of data of each telescope are given in Table 1.
|Telescope||Filter||Number of Data|
3 Light Curve Models
The single lens light curve model depends on three parameters: the time of lens-source closest approach , the Einstein ring crossing time , and the impact parameter in units of the Einstein radius . Binary lens models require four additional parameters: the planet-host mass ratio, , the planet-host separation in units of the Einstein radius, , the angle between the trajectory of the source and the planet-host axis, , and the ratio of the angular source size to the angular Einstein radius. If were to include microlensing parallax, we would need two additional parameters. The model flux of magnified source as a function of time can be given by,
where is a magnification of the source flux at , is the baseline flux of the source star and is the baseline flux of any unresolved light.
The large number of the parameters of the microlensing event and correlations with each parameter make it difficult to search for the best-fit model parameters.
The effective method of fitting is Markov Chain Monte Carlo (MCMC) algorithm (Verde et al., 2003) combined with the image-centered ray-shooting method (Bennett
& Rhie, 1996; Bennett, 2010).
First, we performed a broad grid search over the at 9680 different grid points, over space with other parameters free.
Next, we refined all parameters for the best 100 models with the smallest to search for the global best-fit model.
3.2 Limb Darkening
Binary lens events usually have caustic crossings of cusp approaches that resolve the finite angular size of the source, so we must include the limb-darkening of the source star. In order to take these effects into account, we adopt the following linear limb darkening law,
where is a limb darkening surface brightness.
The effective temperature of the source star estimated from the extinction-free source color presented in Section 4 is (González Hernández
& Bonifacio, 2009).
Assuming the surface gravity , and metallicity of , we find limb-darkening coefficient of and from the ATLAS model (Claret & Bloemen, 2011). For the passband, we use the coefficient for , which is the mean of and .
3.3 Best fit model and Degenerate models
Our grid search found that the best binary lens model is favored over the single lens model by .
Figure 1 shows a clear anomaly in light curve from single lens model, and the best fit binary lens model can explain the anomaly near the peak.
Figure 3 shows locations of these degenerate models in space from our five Markov chains of the distribution of the planet/host mass ratio , and the planet-host separation, , in the range of and . The points are color-coded based on from the best of the best model, which is the wide1 model.
We find that there are some local minima.
Thus we took a closer look at these models.
Figure 4 shows the caustic geometries of each model and Figure 5 shows the light curves of all degenerate models. The parameters of models are listed in Table 2. Figures 6 shows zooms of the characteristic part of the light curves.
This value indicates a upper limit on . The close1 model and the close2 model are favored by only and , respectively, over models with . Because of the weak measurements of for the close models, we put upper limits on .
The five competing models are divided into wide models, with , and close models, with . The Einstein radii crossing times are short ( days) for all models, and all models have a planetary mass ratio.
We now describe each of these degenerate models.
The wide1 model: This is the best fit model with a planetary mass ratio of and a separation of . Figure 4 (a) and 5 shows the light curve and the caustic of this model. The Einstein radius crossing time is only 4 days. We can see a bump around around due to cusp crossing in Figure 6 (b) followed by the main peak due to the caustic exit where the MOA data have a good coverage in Figure 6 (a). Thanks to its caustic crossing feature, the clear finite source effects are detected by .
The wide2 model: Because the parameters such as and are slightly different from those of the wide1 model, the shape of the caustic are similar to those of the wide1 model in Figure 4 (b). We can see a similar bump as that of the wide1 model on because the source crosses the similar cusps as shown in Figure 6 (b). Although the source courses different part of caustic from that of model 1, the features of the light curves of both models are alike during the data coverage.
The wide3 model: This model has a clearly different feature in the caustic shape and the light curve from those of the wide1 model. This model is disfavored again the model 1 by .
The mass ratio is and the separation is , which is larger than that of the wide1 model. Additionally, the Einstein radius crossing time is about 7 days, which is twice as long as that of the wide1 model. From the light curve in Figure 6 (c), we find another bump around due to a cusp approach to a planetary caustic, and the main magnification arise by approaching to a cusp of the central caustic.
The close1 and close2 model: These two models have star-planet separations of . The close1 and the close2 model are disfavored by and , respectively.
These two models have similar parameters, so the shapes of caustic geometry of both models are similar in Figure 4 (d), (e). As for the close1 model, the mass ratio is and the separation is , which is smaller than that of the wide1 model. The Einstein radius crossing time is about 5 days. The light curves of both models are characterized by a cusp approach of the central caustic.
The difference between the models is the source trajectory, and regarding close2 model, a bump around comes from a planetary caustic crossing (Figure 6 (d)).
According to Figure 5, the light curve differences between the models mainly arise from the light curve wings, where the wide1 and the wide2 have a bump at , as well as where the data coverage is poor such as .
The differences due to these bumps are small, at most. We can see a lot of outliers which can cause similar bumps on the baseline data. The visual inspection of difference images during the bumps do not indicate any strange features such as saturation images. Although the effects of the airmass, the seeing and the differential refraction for each data point have been corrected during the data reduction, it is not surprising that such small systematics remain in that dense stellar field. We investigated a possibility that these small bumps are the systematics on the baseline rather than the real caustic feature as follows.
We removed these questionable data points during the bumps and conducted a grid search. We found only similar models to the original best five models, but with a bump at different part of the baseline. The distributions of the MCMC chains of these new models are almost same as the those of original models. So we conclude that it is likely that these small bumps are due to the systematics on the baseline rather than the real caustic feature and the best fit model parameters are not affected by these systematics. Therefore, we will use these original five models without removing the data points but recognize them as best fit models equally, not weighting by .
We could detect clear signals of the finite source effects in the three wide models, but we got very weak measurements of for the close models. The best fit close models are favored by only and , respectively, over models with . We detect strong signals of the finite source effects for the other models.
3.4 Binary source model
There is a possible degeneracy between single-lens, binary-source model (1L2S) and binary-lens, single-source model (2L1S) (Griest & Hu, 1993). For the 1L2S model, the magnification is expressed in the following equation,
where and are the magnification of the two sources with flux , respectively, and is the flux ratio between the two sources ().
For 1L2S model, the magnification depends on the wavelength unless the two source stars have the same color. By using the color difference expected for the two sources of unequal luminosity, the 2L1S/1L2S degeneracy could be solved (Gaudi, 1998).
For some microlensing events, the 2L1S/1L2S degeneracy is broken with this method, and this confirms the planetary models (Zang et al., 2018; Shvartzvald et al., 2014).
We searched for the best 1L2S model and found the best 1L2S model is disfavored over 2L1S model by . Figure 7 shows the comparison between 2L1S/1L2S. Table 3 shows the parameters of the best-fit 1L2S model.
Due to the poor data coverage for this event, the model parameters are uncertain, and this makes it difficult to use this color shift method to confirm the planetary interpretation more strongly.
3.5 Microlensing parallax model
The microlensing parallax is an effect caused by the orbital motion of the Earth.
Although it is known that there is little possibility of the detection of the parallax effect for such a short duration event (Gould & Loeb, 1992; Gaudi, 2012), we also considered a parallax model for completeness. Then we find the parallax model improve the fit only by and the value of the parameters are and , which are quite larger than the ordinary value (). Therefore we ruled out the parallax model.
4 Angular Einstein Radius
Thanks to the detection of the finite source effects, we can constrain the lens physical properties by estimating the angular Einstein radius . We can get from the light curve modeling and the angular source radius by using empirical relation of , the intrinsic source color and magnitude (Boyajian et al., 2014). Because there is no -band data during the magnification, we estimated the source color as follows. We cross-referenced stars in MOA DoPHOT catalog of the reference image with the stars in OGLE-III photometry map (Szymański et al., 2011) within around the source star. By using 91 cross-referenced stars, we derived the following color-color relation (see Figure 8),
If we have a good measurement of OGLE -band source magnitude, , we could derive the from this formula. However, from the light curve fitting has very large uncertainty because only a few data points during the low magnification are available.
Therefore, by following Bennett et al. (2008), we estimated the source color by taking the average color of main sequence stars in Baade’s window observed by the , (, Holtzman et al. (1998)). In the color-magnitude diagram (CMD) (Figure 9), black dots show the OGLE stars within around the source star and the green dots show the stars which are adjusted for the reddening and extinction by using the the Red Clump Giants (RGC) color and magnitude, (Bennett et al., 2008). Because we do not have any good calibrated -band source magnitude, we derived its magnitude and color as follows. We solve for and using an iterative procedure. First, we estimate the initial source color, from the average color of the main sequence stars with the input value. We then determine the new values from this color and the values from the light curve model. After a few iterations, this converges. We used the value from the light curve model for the initial value.
We derive the extinction-free magnitude and color of source so as to calculate an angular Einstein radius by following a method similar to that of Yoo et al. (2004). The extinction-corrected magnitude can be determined from the magnitude and color of the centroid of the RGC feature in the CMD. In figure 9, the red point shows the centroid of RCG color and magnitude, around the target. Assuming that the source star suffers the same reddening and extinction as the RGCs, we compare these values to the expected extinction-free RCG color and magnitude at this field of (Bensby et al., 2013; Nataf et al., 2013), and as a result, we got the reddening and extinction by using the RCG color and magnitude, (Bennett et al., 2008).
We determine the angular Einstein radius for each model with the following method that we demonstrate with the parameters of the wide1 model. Assuming that the source star suffers the same reddening and extinction as the RGCs, we compare these values to the expected extinction-free RCG color and magnitude at this field of (Bensby et al., 2013; Nataf et al., 2013), and as a result, we get the reddening and extinction to the source of for the best-fit model, wide1 model. Therefore, we determined the intrinsic source color and magnitude to be
Then, we find the angular source radius with the empirical formula (Boyajian et al., 2014),
where is the limb darkened stellar angular diameter, (Fukui et al., 2015). This relation is derived by using stars with colors corresponding to (Bennett et al., 2017). We found the angular source radius for the wide1 model, with the uncertainty dominated by the source color uncertainty rather than the uncertainly from the empirical formula.
Finally, we calculate the angular Einstein radius and the lens-source relative proper motion for the wide1 model.
Since the source star color and magnitude depend on the model, the angular source radius also depends on the model and we summarize the values of and for each model in Table 4.
As for the close models, we get only an upper limit for , so we get only the lower limits of and .
5 Lens Physical Parameters by Bayesian Analysis
Because a microlensing parallax effect was not measured for this event, the lens masss cannot be directly measured from the light curve models.
In order to estimate the probability distribution of the lens properties, we conducted a Bayesian analysis (Beaulieu et al., 2006; Gould et al., 2006; Bennett et al., 2008) assuming the Galactic model of Han & Gould (1995) as a prior probability.
We also assume a mass function used in Sumi et al. (2011) and extend it to low-mass brown dwarf regime ().
We use the measured and to constrain the lens physical parameters. The extinction-corrected blending flux, which includes the lens and unrelated ambient stars on the line of sight to the source star, is derived from the light curve modeling, and is set as the upper limit for the lens brightness.
-band magnitudes for the lens of all models are estimated from the color-color relation of the main sequence stars (Kenyon & Hartmann, 1995) and the isochrone model of 5 Gyr brown dwarfs (Baraffe et al., 2003). The extinctions are calculated from Cardelli et al. (1989).
Table 5 shows the summary of the lens physical parameters of each model and we found the results are divided into 2 types according to the mass of the host star. The median value of the probability distribution of host mass for all models except wide3 indicates the host star is a brown dwarf, and that for the wide3 indicates the host star is a late M-dwarf. As for the wide1 model, the lens system could be a gas giant with a mass of orbiting a brown-dwarf with a mass of , located at from the Earth, and a projected separation from the host star of . If we assume a circular and randomly oriented orbit for the planet, the three-dimensional semi-major axis is expected to be . Assuming the wide3 model is correct, the lens system is likely a gas giant with a mass of orbiting an M-dwarf with a mass of , located at kpc from the Earth, and a projected separation of and the three-dimensional semi-major axis is expected to be . Figure 10 shows the probability distribution of the lens parameters of the wide1 model and the wide3 model. The dark and light blue regions show the and confidence intervals, respectively, and the vertical blue lines show the median value. The probability distributions of -, -, and -band magnitudes with extinction of the host star of the wide1 model and the wide3 model are also shown in Figure 11.
Since the probability distributions of lens physical parameters for all five models are consistent within , we combined the distributions of these five models. Here, we combined these distributions with equal weight because all models are equally good within the uncertainty including the possible systematics. Figure 12 shows the combined probability distributions which indicates the lens system comprise a gas giant planet with a mass of orbiting a brown dwarf with mass of at and a projected separation of .
6 Discussion and Summary
We analyzed the short duration microlensing event MOA-bin-29, which was found only after conducting an off-line analysis of the MOA database using data from (Sumi et al. in prep.). Although we found five competing solutions, all degenerate models have a planetary mass ratio and an Einstein radius crossing time of days.
The angular Einstein radius estimated from the detection of the finite source effects was used to constrain the lens parameters for some models.
As a result of a Bayesian analysis, we found that the lens system is likely to be a gas giant orbiting a brown-dwarf or a late M-dwarf.
Future high-resolution imaging with ground-based AO observations or space telescope could constrain the lens parameters (Bennett et al., 2006, 2007, 2015; Batista et al., 2014, 2015; Bhattacharya et al., 2017; Koshimoto et al., 2017; Bhattacharya et al., 2018). The source and the lens will be separated by mas for the wide1 model and mas for the wide3 model by 2025.
According to the Figure 11 and Table 5, the lens -band magnitude with extinction would be mag and mag for the wide1 and the wide3 model, respectively. These are mag and mag fainter compared to the source for the wide1 and the wide3, respectively. This indicates that there is only small chance to detect the lens flux even if the lens and sources are separated by mas.
However the source flux could be detected using Keck AO (Batista et al., 2014) or (Gardner et al., 2006) because the measured source magnitude with extinction is bright enough to be detected.
The source flux for each model is not well determined by the light curve modeling, so the improvement of the accuracy of the source flux would constrain the degenerate models.
According to Suzuki et al. (2016), the detection efficiency and the survey sensitivity of planetary systems with a short duration is relatively low, so only a few microlensing planets with a short duration have been found (Bennett et al., 2014), and therefore any inferences drawn from these data have large statistical errors.
It is therefore important to increase the number of samples of these planets.
However the determination of lens properties for short duration events is difficult because in such a short event the measurement of a significant microlensng parallax effect is almost impossible. In order to solve the relation between lens physical parameters, other constraints are important, for example follow-up observations with high-resolution imaging as described above.
Measuring the space parallax is also a powerful way to determine the lens parameters for short duration events (Shvartzvald et al., 2017; Chung et al., 2019). Especially, Earth-L2 separation between the ground and the telescope (Spergel et al., 2015) will be optimal for such short events with small Einstein radius.
The formation theory of a gas giant orbiting a brown dwarf and even that for a brown dwarf itself is still ambiguous.
As a result of analyzing the event MOA-bin-29, we found the lens system is most likely to be a gas giant orbiting a brown dwarf, which is hard to form according to the core accretion theory.
Therefore more and more accurate mass measurements of such systems are required.
The microlensing method is a powerful way to detect these systems and
some of such events have been discovered by the microlensing method (Han et al., 2013; Jung et al., 2018a, b; Albrow et al., 2018).
Figure 13 shows the mass distribution of discovered systems with a brown dwarf/a late M-dwarf hosting a gas giant (, ).
For most of these events, the lens physical parameters such as mass are derived through a Bayesian analysis, which uses the mass function as a prior. The mass probability distribution of low-mass host stars () depends strongly on the shape of the mass function which has large uncertainty.
In Albrow et al. (2018), the lens parameters are directly derived by combining measurements from Earth and from the telescope (Gould et al., 2014). The increase in number of the mass measurements by the space parallax effect and high resolution images are greatly anticipated by satellite in the near future, and would contribute significantly to clarification of the formation theory of a gas giant around a low-mass star.
T.S. acknowledges the financial support from the JSPS, JSPS23103002, JSPS24253004, and JSPS26247023. The MOA project is supported by the grant JSPS25103508 and 23340064. D.P.B., A.B., and D.S. were supported by NASA through grant NASA-NNX12AF54G. Work by N.K. is supported by JSPS KAKENHI Grant Number JP15J01676. Work by A.F. is supported by JSPS KAKENHI Grant Number JP17H02871. N.J.R. is a Royal Society of New Zealand Rutherford Discovery Fellow. A.S. is a University of Auckland Doctoral Scholar. The OGLE project has received funding from the National Science Centre, Poland, grant MAESTRO 2014/14/A/ST9/00121 to AU.
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