MOA-2008-BLG-379Lb: A Massive Planet from a High Magnification Event with a Faint Source
D. Suzuki, A. Udalski, T. Sumi, D. P. Bennett, I. A. Bond, F. Abe, C. S. Botzler, M. Freeman, M. Fukagawa, A. Fukui, K. Furusawa, Y. Itow, C. H. Ling, K. Masuda, Y. Matsubara, Y. Muraki, K. Ohnishi, N. Rattenbury, To. Saito, H. Shibai, D. J. Sullivan, K. Suzuki, W. L. Sweatman, S. Takino, P. J. Tristram, K. Wada, P. C. M. Yock, M.K. Szymański, M. Kubiak, I. Soszyński, G. Pietrzyński, R. Poleski, K. Ulaczyk, Ł. Wyrzykowski
aa r X i v : . [ a s t r o - ph . E P ] D ec MOA-2008-BLG-379Lb: A Massive Planetfrom a High Magnification Event with a Faint Source
D. Suzuki ,A , A. Udalski ,B , T. Sumi ,A , D.P. Bennett ,A , I.A. Bond ,A andF. Abe , C.S. Botzler , M. Freeman , M. Fukagawa , A. Fukui , K. Furusawa , Y. Itow ,C.H. Ling , K. Masuda , Y. Matsubara , Y. Muraki , K. Ohnishi , N. Rattenbury , To.Saito , H. Shibai , D.J. Sullivan , K. Suzuki , W.L. Sweatman , S. Takino , P.J.Tristram , K. Wada , and P.C.M. Yock (MOA Collaboration)M.K. Szyma´nski , M. Kubiak , I. Soszy´nski , G. Pietrzy´nski , , R. Poleski , , K.Ulaczyk , and L. Wyrzykowski , (OGLE Collaboration) 2 – ABSTRACT
We report on the analysis of high microlensing event MOA-2008-BLG-379,which has a strong microlensing anomaly at its peak, due to a massive planetwith a mass ratio of q = 6 . × − . Because the faint source star crosses the largeresonant caustic, the planetary signal dominates the light curve. This is unusualfor planetary microlensing events, and as a result, the planetary nature of thislight curve was not immediately noticed. The planetary nature of the event wasfound when the Microlensing Observations in Astrophysics (MOA) Collaborationconducted a systematic study of binary microlensing events previously identifiedby the MOA alert system. We have conducted a Bayesian analysis based on a Department of Earth and Space Science, Graduate School of Science, Osaka University, 1-1Machikaneyama, Toyonaka, Osaka 560-0043, Japan Warsaw University Observatory, Al. Ujazdowskie 4, 00-478 Warszawa, Poland Department of Physics, University of Notre Dame, Notre Dame, IN 46556, USA Institute of Information and Mathematical Sciences, Massey University, Private Bag 102-904, NorthShore Mail Centre, Auckland, New Zealand Solar-Terrestrial Environment Laboratory, Nagoya University, Furo-cho, Chikusa, Nagoya, Aichi 464-8601, Japan Department of Physics, University of Auckland, Private Bag 92019, Auckland, New Zealand Okayama Astrophysical Observatory, National Astronomical Observatory, 3037-5 Honjo, Kamogata,Asakuchi, Okayama 719-0232, Japan Department of Physics, Konan University, Nishiokamoto 8-9-1, Kobe 658-8501, Japan Nagano National College of Technology, Nagano 381-8550, Japan Tokyo Metropolitan College of Industrial Technology, Tokyo 116-8523, Japan School of Chemical and Physical Sciences, Victoria University, Wellington, New Zealand Mt. John University Observatory, University of Canterbury, P.O. Box 56, Lake Tekapo 8770, NewZealand Universidad de Concepci´on, Departamento de Astronomia, Casilla 160-C, Concepci´on, Chile Department of Astronomy, The Ohio State University, 140 West 18th Avenue, Columbus, OH 43210,USA Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK A Microlensing Observations in Astrophysics (MOA) Collaboration B Optical Gravitational Lensing Experiment (OGLE) Collaboration M L = 0 . +0 . − . M ⊙ orbited by a planet of mass m P = 4 . +1 . − . M Jup at an orbital separation of a = 3 . +1 . − . AU at a distance of D L = 3 . +1 . − . kpc. The faint source magnitude of I S = 21 .
30 and relatively highlens-source relative proper motion of µ rel = 7 . ± . − implies that highangular resolution adaptive optics or Hubble Space Telescope observations arelikely to be able to detect the source star, which would determine the masses anddistance of the planet and its host star.
Subject headings: gravitational lensing, planetary systems
1. Introduction
Since the first discovery of an extrasolar planet orbiting an ordinary star in 1995(Mayor & Queloz 1995), more than 1000 planets have been found to date. Most of theplanets discovered were through the radial velocity (Butler et al. 2006; Bonfils et al. 2011)and transit (Borucki et al. 2011) methods, which are the most sensitive to the planets or-biting close to their host stars. In contrast, direct imaging is the most sensitive to youngplanets in orbits wider than that of Saturn (Marois et al. 2008). The gravitational mi-crolensing method has unique sensitivity to the planets orbiting just outside of the snow linewith masses down to Earth mass (Bennett & Rhie 1996). The snow line (Ida & Lin 2005;Lecar et al. 2006; Kennedy et al. 2006; Kennedy & Kenyon 2008) plays a critical role in thecore accretion theory of planet formation. Ices, including water ice, can condense beyondthe snow line, which increases the density of solid material in the proto-planetary disk bya factor of a few, compared to the disk just inside the snow line. The higher density ofsolids means that the solid planetary cores can form more quickly beyond the snow line, somicrolensing is unique in its ability to probe the planetary mass function at the separationwhere planet formation is thought to be the most efficient.To date, the primary contribution of the microlensing method to the study of exoplan-ets is the statistical results indicating that cold planets in wide orbits are quite common(Sumi et al. 2010; Gould et al. 2010b; Cassan et al. 2012). Relatively low-mass cold Nep-tunes or super-Earths are found to be more common than gas giants, which is in roughagreement with the core accretion theory expectation. Microlensing is also unique in itssensitivity to planets orbiting stars that are too faint to detect (Bennett 2008; Gaudi 2012).In fact, planetary mass objects can be detected even in cases when there is no indication ofa host star (Sumi et al. 2011). 4 –The microlensing events that are monitored for the signals of extrasolar planets aremainly identified by the two main microlensing survey groups, the Microlensing Observationsin Astrophysics (MOA; Bond et al. 2001; Sumi et al. 2003) and the Optical GravitationalLensing Experiment (OGLE; Udalski 2003). The MOA survey uses the MOA-II 1.8m tele-scope with a 2.2 deg field-of-view (FOV) CCD camera MOA-cam3 (Sako et al. 2008) at Mt.John University Observatory in New Zealand. With this large FOV camera, MOA is ableto observe > of the central Galactic Bulge fields every hour, with a higher cadencefor the fields with the largest microlensing rate. MOA identifies about 600 microlensingevents in progress each year and issues public alert messages as each new event is identi-fied. The OGLE survey has been conducted with the 1.3m Warsaw Telescope at the LasCampanas Observatory in Chile, which is currently equipped with a 1.4 deg CCD mosaiccamera. However, in 2008, when the microlensing event MOA-2008-BLG-379 took place,OGLE was operating the OGLE-III survey using a camera with a 0.35 deg FOV. OGLE-IIItypically identified ∼
100 more events than MOA-II, but observed at a lower cadence withmost fields only being observed once per night. Currently, the OGLE-IV survey operatesat a relatively high cadence in the central Galactic bulge, but covers a much wider areaof sky at a lower cadence, which yields nearly 2000 microlensing event discoveries per year.Most recently, the Wise microlensing survey (Shvartzvald & Maoz 2012) has conducted highcadence observations using a 1.0 deg CCD mosaic camera on the 1.0m Wise Telescope inIsrael. They fill the gap in longitude between MOA and OGLE, but due to their Northerlylocation, they can only observe the Galactic bulge for a limited amount of time each night.Microlensing follow-up groups, such as µ FUN, PLANET, RoboNet, and MINDSTEp,observe microlensing events that have been previously identified by one or more of the sur-vey groups. They aim to ensure dense, 24 hr light curve coverage on the highest prioritymicrolensing events, and they contribute to planet discoveries in a number of ways. Theycan identify planetary signals in some of the microlensing events with relatively bright sourcestars (Beaulieu et al. 2006; Batista et al. 2011), densely monitor high magnification mi-crolensing events (Udalski et al. 2005; Gould et al. 2010b; Miyake et al. 2011; Bachelet et al.2012; Yee et al. 2012; Han et al. 2013) that are known to have high sensitivity to planets(Griest & Safizadeh 1998; Rhie et al. 2000), or follow-up on events once potential plane-tary anomalies have been found by the survey teams (Sumi et al. 2010; Muraki et al. 2011;Kains et al. 2013). In addition, some events have been identified based on higher cadenceobservations by the survey groups prompted by the real-time identification of potential plan-etary anomalies (Bond et al. 2004). However, if the survey cadence is high enough, it ispossible to identify planets from survey observations alone without the benefit of follow-up observations from either the survey or follow-up teams. The event we present here,MOA-2008-BLG-379, is the planetary microlensing event that was found based on sur- 5 –vey observations alone, similar to MOA-2007-BLG-192 (Bennett et al. 2008), MOA-bin-1(Bennett et al. 2012) and MOA-2011-BLG-322 (Shvartzvald et al. 2013). We should notethat there are many more planetary events, such as MOA-2011-BLG-293 (Yee et al. 2012)and OGLE-2012-BLG-0406 (Poleski et al. 2013), that could have been discovered based uponsurvey observations alone. And in fact, the primary reason for the lack of follow-up obser-vations for MOA-2007-BLG-192 and MOA-2008-BLG-379 is the lack of experience in themicrolensing community with the full range of possible planetary signals.In this paper, we report on the analysis of a planetary microlensing event MOA-2008-BLG-379. Section 2 describes the observations of this event, and Section 3 describes thereduction of the data and the light curve modeling. In Section 4, source magnitude and colormeasurement using color-magnitude diagram (CMD) is discussed, and the derived angularEinstein radius is discussed in Section 5. In Section 6, we use a Bayesian analysis based ona standard Galactic model to estimate the masses and distances of the lens system based onthe angular Einstein radius. Discussion and our conclusions are presented in Section 7.
2. Observations
Prior to 2009, the MOA-II observing strategy called for the observations of the twofields with the highest lensing rate every 10 minutes and observations of the remaining 20fields every hour using the custom wide-band MOA-Red filter, which is roughly the sum ofthe Cousins R - and I -bands. MOA-2008-BLG-379 was discovered in field gb8, which wasobserved with an hourly cadence in 2006–2008.The microlensing event MOA-2008-BLG-379 was identified by the MOA alert system(Bond et al. 2001) at (R . A ., decl . )(J2000) = (17 h m s .
44, -30 ◦ ′ ′′ . ′ = 4688 . ∼ ′′ resolution. The source star, MOA-2008-BLG-379S, happens to be located atan unusually large distance from the nearest star in the OGLE catalog, and as a result, itcould only be found via the “new object” channel of the OGLE EWS. In 2008 this channel 6 –was not run as often as the regular “resolved star” channel of the OGLE EWS. As a result,both the MOA and OGLE collaboration groups observed this event with normal cadence.
3. Data Reduction and Modeling
The MOA and OGLE data for MOA-2008-BLG-379 were reduced using the respectiveMOA (Bond et al. 2001) and OGLE (Udalski 2003) photometry pipelines. The initial re-ductions used the normal photometry available on the respective MOA and OGLE alert websites, and these data were used to show that the correct model involved a planet. However,it was possible to obtain improved photometry for both the MOA and OGLE data sets.The improved MOA photometry used “cameo” sub-images centered on the target, and theimproved OGLE photometry was redone with source position determined from differenceimages and a careful selection of reference images.Both the OGLE and MOA photometry were found to have systematic errors at thebeginning and/or end of each observing season when observations are only possible at highairmass. This may be due to low-level variability for a very bright star about 3 arc secondsfrom the source, MOA-2008-BLG-379S. So we removed the MOA data prior to HJD ′ =HJD − < HJD ′ < I -band observations and 7 V -band observations, as shown inTable 1.The error bar estimates from the photometry codes are normally accurate to a factorof 2 or better, and they provide a good estimate of the relative photometry errors for eachdata set. These are sufficient to find the best light curve model, but in order to estimate thefit parameter uncertainties, we need more accurate error bars, which have χ / dof ≃ σ ′ i = k q σ i + e (1)where σ i is the input error bar estimate (in magnitudes) for the i th data point, k is thenormalization factor, and e min is the minimum error. The modified error bars, σ ′ i , are usedfor all subsequent modeling and parameter uncertainty determination.The factors k and e min are estimated for each data set with the following procedure.First, we plot the cumulative distribution of χ as a function of the size of the input errorbars, σ i . Then, we chose the value of e min ≥ k is chosen to give χ / dof ≃ e min = 0 for all data sets. The values of k and e min for all three data sets are listed in Table 1.This event was identified in a systematic modeling of all anomalous events (i.e. thosenot well fit by a point source, single lens model without microlensing parallax) from theMOA alert pages (https://it019909.massey.ac.nz/moa/) from the 2007-2010 seasons. A sim-ilar analysis of OGLE-III binary events was conducted by Jaroszy´nski et al. (2010). Thelight curve calculations for this systematic analysis were done using the image centered ray-shooting method (Bennett & Rhie 1996; Bennett 2010). All the events that have anomalousdeviation from a point source, single lens model were fitted with the binary lens model ac-cording to the following procedure. Binary lens models have three parameters that are incommon with single lens models. These parameters are the time of the closest approach tothe lens system center of mass t , the Einstein radius crossing time, t E , and the impact pa-rameter u , in units of the angular Einstein radius θ E . Binary lens models also require threeadditional parameters. These are the lens system planet-star mass ratio, q , the planet-starseparation, s , projected into the plane perpendicular to the line-of-sight, and the angle of thesource trajectory relative to the binary lens axis α . Another parameter, the source radiuscrossing time, t ∗ is also included in the binary lens model because this parameter is importantfor most of planetary microlensing light curves. We carefully searched to find the best fitbinary lens model over a wide range of values of microlensing parameters using a variation ofthe Markov Chain Monte Carlo (MCMC) algorithm (Verde et al. 2003). Because the shapeof anomaly features in the light curve well depends on q , s and α , these three parametersare fixed in the first search. Next, we searched χ minima of the 100 models in order of χ in the first search with each parameter free and found the best fit model.This analysis indicated a planetary mass ratio for the MOA-2008-BLG-379L lens system.Figure 1 shows the light curve of this event and the best fit models. There are five distinctcaustic crossing and cusp approach features in the light curve. The first caustic crossing issandwiched between a single observation by OGLE and five MOA observations beginning96 minutes later at HJD ′ = 4686 .
8, The subsequent, very bright, caustic exit was observedwith a single OGLE observation on the subsequent night, but the central cusp approachfeature and the next caustic entrance feature were reasonably well sampled by 9 and 7 MOAobservations, respectively, on the next two nights. It is the sampling of these two featuresthat allow the parameters of the planetary lens model for this event to be determined.For many binary events and most planetary events, the light curve has very sharpfeatures due to caustic crossings or cusp approaches that resolve the finite size of the sourcestar. Such features require an additional parameter, the source radius crossing time, t ∗ .Since the MOA-2008-BLG-379 includes caustic crossings and a close cusp approach, it is 8 –necessary to include finite source effects in its light curve model, and a proper accounting offinite source effects requires that limb darkening be included.For the limb darkening coefficients, we adopted a linear limb-darkening model for thesource star based on the source color estimate of ( V − I ) S , = 0 . ± .
13, which is discussedbelow in Section 4. This color implies that the source is a late G-star, with an effective tem-perature of T eff ≃ T eff = 5500 K, surface gravitylog g = 4 . − , and metallicity log [M / H] = 0 .
0. Girardi’s isochrones (Girardi et al.2002) suggest that the source may be a metal poor star if it is located at the distance ofthe Galactic center, but log [M / H] = 0 . σ error bar. The list ofthe coefficients used for the linear limb-darkening model are as follows, 0.7107 for V , 0.5493for I , and 0.5919 for MOA-Red, which is the mean of the coefficients for the Cousins R and I -bands. These are listed in Table 1.As is commonly the case for high magnification events, there are two degenerate lightcurve solutions that can explain the observed light curve. This is the well-known “close-wide”degeneracy, where the solutions have nearly identical parameters except that the separationis modified by the s ↔ /s transformation. Figure 2 shows the two caustic configurationsfrom the close and wide models for this event. Sometimes, when the planetary causticshave merged with the central caustic to form a so-called resonant caustic curve, as in thiscase, the light curve data can resolve this close-wide degeneracy. We can see in Figure 1that the close and wide light curves do have substantial differences, such as the time ofthe final caustic exit. However, the observations for this event are too sparse to samplethese light curve features, and the degeneracy remains. Fortunately, the parameters forthese two solutions differ by only ∼ s = 0 . ± . q = (6 . ± . × − and u = (6 . ± . × − for the close model, which is preferred by ∆ χ = 0 .
7, and s = 1 . ± . q = (6 . ± . × − , and u = (6 . ± . × − for the wide model.The full set of fit parameters are listed in Table 2.Higher order effects such as microlens parallax, xallarap (source star orbital motion) andorbital motion in the lens system have been detected in some previous events(Alcock et al.1995; Gaudi et al. 2008; Bennett et al. 2010; Sumi et al. 2010; Muraki et al. 2011; Kains et al.2013). The measurement of finite source effects or microlensing parallax effects can partiallybreak the degeneracies of the physical parameters that can be inferred from the microlens-ing light curve, and the measurement of both microlensing parallax and finite source effectsyields a direct measurement of the lens system mass (Bennett 2008; Gaudi 2012). For thisevent, however, the source is too faint for a reliable microlensing parallax measurement for 9 –an event of its duration, and the relatively sparse data sampling leaves some uncertaintyin the measurement of the source radius crossing time. Therefore, we use the light curveconstraints on the source radius crossing time to constrain the physical parameters of thelens system using a Bayesian analysis based on a standard Galactic model, as discussed inSection 6. If the lens star can be detected in high angular resolution follow-up observations,it will then be possible to directly determine the physical parameters of the lens system(Bennett et al. 2006, 2007; Dong et al. 2009).
4. Source Color and Magnitude
The source star magnitude and color estimated from the light curve modeling are affectedby extinction and reddening due to interstellar dust. These effects must be removed in orderto infer the intrinsic brightness and color of the source star. In order to estimate extinctionand reddening, we use the centroid of the red clump giant (RCG) distribution, which is anapproximate standard candle. The CMD, shown in Figure 3 was made from stars from theOGLE-III catalog (Szyma´nski et al. 2011) within 2 ′ from the source star. From this CMD,we have found the RCG centroid to be at( V − I, I ) RCG = (2 . , . ± (0 . , . . (2)We adopt the intrinsic RCG centroid V − I color and magnitude from Bensby et al.(2011) and Nataf et al. (2013), respectively, which gives( V − I, I ) RCG , = (1 . , . ± (0 . , . . (3)Comparing the our measured RCG centroid from Equation (2) with the intrinsic dereddenedmagnitude and extinction from Equation (3), we find that the reddening and extinction are( E ( V − I ) , A I ) RCG = (1 . , . ± (0 . , .
06) (4), where E ( V − I ) is the average reddening and A I is the average extinction.The models presented in Table 2 give the source magnitude and color of I S = 21 . ± . V − I ) S = 2 . ± .
09 from the OGLE observations, calibrated to the OGLE-IIIphotometry map (Szyma´nski et al. 2011). This color is bluer than most of the bulge mainsequence stars at this magnitude, but with the error bars, it is marginally consistent with abulge main sequence star, as shown in Figure 3. This could be due to the fact that there isonly a single bright OGLE V -band image that might be affected by a nearby bright variablestar. 10 –Because the MOA-Red passband is centered at a slightly shorter wavelength than theOGLE I -band, we can use the MOA-Red and OGLE I passbands to derive the sourcecolor (Gould et al. 2010a). Although the color difference between these two passbands isrelatively small, we have a large number of data points at significant magnification in bothof these passbands. So, this method should yield a color that is less sensitive to systematicphotometry errors than the determination based on the single magnified OGLE V -bandmeasurement. In order to calibrate the MOA-Red measurements to the OGLE-III ( V , I )system, we use the OGLE-III photometry map (Szyma´nski et al. 2011) and a DoPHOT(Schechter et al. 1993) reduction of the MOA reference frame. Because the seeing in theMOA reference frame is significantly worse than the seeing images used for the OGLE-IIIcatalog, we choose isolated OGLE stars for the comparison with MOA to avoid problemsdue to blending in the MOA images. In order to select the stars with small uncertainty inmagnitude and color, we remove faint stars with I >
19 and stars with a V − I error bar > .
1. In order to obtain an accurate linear relation, we only fit stars in the color range2 < V − I <
4. We recursively reject 2 . σ outliers and find R M, DoPHOT − I OGLE − III = (0 . ± . V − I ) OGLE − III (5), where I OGLE − III and V OGLE − III are the OGLE-III catalog magnitudes, and R M, DoPHOT isthe calibrated MOA-Red band magnitude. (The MOA-Red calibration has a zero-pointuncertainty of 0.0144 mag.) The MOA light curve photometry (Bond et al. 2001) is donewith the difference imaging analysis (DIA; Tomaney & Crotts 1996; Alard & Lupton 1998),which is usually significantly more precise than DoPHOT, but DIA only measures changes inbrightness, which is why DoPHOT photometry is used to derive the relation in Equation 5between the R M − I OGLE and standard V − I colors. Thus, it is important that the MOA-Redband photometry from the DIA and DoPHOT codes have identical magnitude scales. This isaccomplished by using the DoPHOT point-spread function for the DIA photometry. Usingthe source magnitudes from the light curve modeling, this procedure yields ( V − I, I ) S =(2 . , . ± (0 . , .
03) for the best fit model. As shown in Figure 3, this source magnitudeand color are more reasonable for a bulge source than the less precise color derived fromOGLE V -band measurements, and it is the one that we use in our analysis.Combining the extinction from Equation (4) with the source magnitudes and colorsfrom the best fit wide and close models, we have( V − I, I ) S , = (0 . , . ± (0 . , .
06) for the wide model (6)( V − I, I ) S , = (0 . , . ± (0 . , .
06) for the close model . (7)Also, from the light curve models, we have determined the magnitude of the unlensedflux at the location of the source. This is the flux of the stars with images blended with the 11 –source. The flux from the blend stars is often used as an upper limit for the magnitude ofthe lens star. In this event, however, we found that the blending flux in the light curve isdominated by the flux from a bright star 0 . ′′ > ∼ σ limit of blend magnitude I b , > .
87 mag (8), which will be used as an upper limit for the magnitude of the planetary host star in Section6.
5. Angular Einstein Radius θ E With the use of ( V − I, I ) S , , we can determine the source angular radius with the colorsurface-brightness relation of Kervella & Fouqu´e (2008),log (2 θ ∗ ) = 0 . . V − I ) − . V − I ) − . V . (9)This yields an angular source radius of θ ∗ = 0 . ± . µ as. θ ∗ is also able to be derivedfrom the method of Kervella et al. (2004) with ( V − K ) S , estimated from the dwarf starcolor-color relations from Bessell & Brett (1988) , but the result is consistent with the abovevalue. We can combine this value of θ ∗ with the fit source radius crossing time, t ∗ , valuesfrom the light curve models to determine the lens-source relative proper motion, µ rel = θ ∗ t ∗ = θ E t E = 7 . ± .
65 mas yr − for the wide model (10)= 7 . ± .
56 mas yr − for the close model . (11)Note that this is the relative proper motion in the instantaneously geocentric inertial ref-erence frame that moved with the Earth when the event reached peak magnification. Themeasurement of t ∗ also yields the angular Einstein radius θ E = θ ∗ t E t ∗ = 0 . ± .
19 mas for the wide model (12)= 0 . ± .
18 mas for the close model , (13)which can be used to help constrain the lens mass.As we discuss in Section 7, follow-up observations might be able to detect the lens sep-arating the source and measure the lens-source relative proper motion. However, this would 12 –be in the heliocentric reference frame rather than the instantaneously geocentric inertialframe used for Equations (10) and (11). Fortunately, the follow-up observations and lightcurve model provide enough information to convert between these two reference frames.For this paper, however, we have not been able to distinguish the wide and close models,so to obtain our final predictions, we combine the values from the wide and close modelswith weights given by e − ∆ χ / . This gives an angular Einstein radius and lens-source relativeproper motion of θ E = 0 . ± .
19 mas (14) µ rel = 7 . ± .
61 mas yr − , (15)with the lens-source relative proper motion in the same instantaneous geocentric inertialreference frame used for Equations (10) and (11).
6. Bayesian Analysis
A microlensing light curve for a single lens event normally has the lens distance, mass,and angular velocity with respect to the source constrained by only a single measured pa-rameter, the Einstein radius crossing time, t E . But, like most planetary microlensing events,MOA-2008-BLG-379 has finite source effects that allow t ∗ , and therefore θ E , to be measured.If we could have also measured the microlensing parallax effect, we could determine the totallens system mass (Bennett 2008; Gaudi 2012).Without a microlensing parallax measurement, we are left with the relation θ = κM (cid:18) D L − D S (cid:19) (16)where κ = 8 .
14 mas /M ⊙ , M is the mass of the lens system, and D S is the distance to thesource star. This can be interpreted as a lens mass–distance relation, since D S is approxi-mately known.We can now use this mass-distance relation, Equation (16), in a Bayesian analysis toestimate the physical properties of the lens system (Beaulieu et al. 2006). Our Bayesiananalysis used the Galactic model of Han & Gould (2003) with an assumed Galactic centerdistance of 8 kpc with model parameters selected from the MCMC used to find the best fitmodel. The lens magnitude is constrained to be less than the blend magnitudes presented inEquation (8). Since the best fit wide model is slightly disfavored by ∆ χ = 0 .
7, we weightthe wide model Markov chains by e − ∆ χ / with respect to the close model Markov chains. 13 –The probability distributions resulting from this Bayesian analysis are shown in Figures 4and 5.An important caveat to this Bayesian analysis is that we have assumed that stars of allmasses, as well as brown dwarfs, are equally likely to host a planet with the measured massratio and separation. Because of this assumption, the results of this Bayesian analysis cannot(directly) be used to determine the probability that stars will host planets as a function oftheir mass. With this caveat, the star and planet masses resulting from the Bayesian analysisare M L = 0 . +0 . − . M ⊙ and m P = 4 . +1 . − . M Jup , respectively. Their projected separation wasdetermined to be r ⊥ = 2 . +0 . − . AU, and the lens system is at a distance of D L = 3 . +1 . − . kpc.The three-dimensional star-planet separation is estimated to be a = 3 . +1 . − . AU, assuminga random inclination and phase. These values are listed in Table 3. Therefore, the mostlikely physical parameters from the Bayesian analysis, indicate that the planet has a massof nearly 4 Jupiter-masses and orbits a late K-dwarf host star at just over twice the distanceof the snow line.
7. Discussion and Conclusion
We reported on the discovery and analysis of a planetary microlensing event MOA-2008-BLG-379. As is often the case with high magnification microlensing events, there aretwo degenerate models: a close model with a planet-host separation of s = 0 .
903 and awide model with s = 1 . q ≃ × − . Our Bayesian analysisindicates that the lens system consists of a G, K, or M-dwarf orbited by a super-Jupiter massplanet. The most likely physical properties for the lens system, according to the Bayesiananalysis, are that the host is a late K-dwarf, and the planet has a mass of about 4 Jupitermasses with a projected separation of about 3 AU. However, these values are dependent onour prior assumption that stars of different masses have equal probabilities to host a planetof the observed mass ratio and separation.Fortunately, the parameters of this event are quite favorable for a direct determination ofthe lens system mass and distance by the detection of the lens separating from the source starin high angular resolution follow-up observations (Bennett et al. 2006, 2007). The source staris quite faint at I S = 21 . ± .
03, so it is unlikely that the lens will be very much fainter thanthe source. The brightness of the source is compared to the Bayesian analysis predictionsfor the lens (host) star in the V -, I -, H -, and K -bands in Figure 5. This indicates that thelens star is likely to have a similar brightness to the source in all of these passbands. Also,it is unlikely that the lens and source magnitudes will differ by more than 2 mag in any ofthese passbands, so both the source and lens should be detectable. 14 –The measured source radius crossing time indicates a relatively large lens-source relativeproper motion of µ rel = 7 . ± . − (measured in the inertial geocentric referenceframe moving at the velocity of the Earth at the peak of the event). This implies a separationof ∼ . ± . Hubble Space Telescope ( HST ). (Because the relative propermotion, µ rel , is measured in an instantaneously geocentric reference frame, it cannot bedirectly converted into a precise separation prediction, but the conversion to the heliocentricreference frame, which is more relevant to the follow-up observation, usually results in asmall change.) The results of these follow-up observations will be reported in a futurepublication, but it seems quite likely that the planetary host star will be detected, resultingin a complete solution of the lens system. That is, the lens masses, distance and separationwill all be determined in physical units.One unfortunate feature of this discovery is that MOA-2008-BLG-379 was not recognizedas a planetary microlensing event when it was observed. This was partly due to the faintnessof the source star, which rendered the relatively long planetary perturbation as the dominantportion of the magnified light curve. However, the lack of familiarity with the completevariety of binary lens and planetary microlensing light curves also played a role in this lackof recognition. The planetary nature of the event was discovered as a result of a systematiceffort to model all of the binary microlensing events that were found by the MOA alertsystem. Fortunately, the joint analysis of OGLE data and the high cadence MOA-II surveyobservations allowed the planetary nature of the event to be establish and the basic planetarylens parameters to be measured.The MOA-II high cadence survey was enabled by the wide, 2 . field MOA-cam3that enabled hourly survey observations. In 2010 March, the OGLE group started theOGLE-IV survey with their new 1 . CCD camera, and they now also conduct a highcadence survey of the central Galactic bulge. This new camera and the good seeing availableat the OGLE site (Las Campanas) has substantially increased the rate in which plane-tary deviations are discovered in survey observations. The combination of the MOA-II andOGLE-IV high cadence surveys greatly improves the light curve sampling of these surveymicrolensing planet discoveries due to the large separation in longitude between the MOAand OGLE telescopes. The capabilities of microlensing follow-up teams are also rapidlyimproving, most notably with the recent expansion (Brown et al. 2013) of the Las CumbresObservatory Global Telescope Network (LCOGT), which should result in much higher lightcurve sampling rates of planetary signals discovered in progress.We acknowledge the following sources of support: the MOA project was supportedby the Grant-in-Aid for Scientific Research (JSPS19015005, JSPS19340058, JSPS20340052, 15 –JSPS20740104). D.S. was supported by Grant-in-Aid for JSPS Fellows. D.P.B. was sup-ported by grants NASA-NNX12AF54G, jpl-rsa 1453175 and NSF AST-1211875. The OGLEproject has received funding from the European Research Council under the EuropeanCommunity’s Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement No.246678 to A.U.
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This preprint was prepared with the AAS L A TEX macros v5.2.
18 –Fig. 1.— Light curve of MOA-2008-BLG-379. The top panel shows the magnified part of thelight curve and the middle panel shows a close up of the anomaly. The red, blue, and greenpoints are for MOA-Red, OGLE- I , and OGLE- V , respectively. The black and magenta linesindicate the best close and wide model. The bottom panel shows the residual from the bestclose model. 19 –Fig. 2.— Caustic geometries for both close (left) and wide (right) models are indicated bythe red curves. The insets in each panel are close up around the center of the coordinate.The blue lines show the source star trajectory with respect to the lens system, with arrowsindicating the direction of motion. The small blue circles in the insets indicate the sourcestar size. 20 –Fig. 3.— Color–magnitude diagram (CMD) of the stars within 2 ′ of MOA-2008-BLG-379from the OGLE-III catalog is shown as black dots. The green dots show the HST
CMD ofHoltzman et al. (1998) whose extinction is adjusted to match the MOA-2008-BLG-379 usingthe Holtzman field red clump giant (RCG) centroid of ( V − I, I ) RCG , Holtz = (15 . , . V I is indicated with a bluedot, while the source star color and magnitude derived from the MOA-Red and OGLE- I passbands is shown as a magenta dot. Although the error bars on the MOA-Red + OGLE- I color estimate are similar to the error bar from the OGLE V I estimate, we use the MOA-Red + OGLE- I estimate for the source color because it is subject to smaller systematicuncertainties. 21 –Fig. 4.— Probability distribution of lens parameters from the Bayesian analysis. The top-leftpanel shows the probability of the distance to the lens system. The bottom-left panel showsthe mass of the primary and secondary lenses (the star and planet) in units of Solar andJupiter masses, respectively. The top-right panel shows the projected separation r ⊥ . Thedark and light blue regions indicate the 68% and 95% confidence intervals, and the verticallines indicate the median value. 22 –Fig. 5.— Probability distribution of V -, I -, K - and H -band magnitudes for the extinction-free lens star from the Bayesian analysis. The dark and light blue regions indicate the 68%and 95% confidence intervals. The red solid lines show the source star magnitudes with theextinction estimated in Equation (4), and the red dashed lines are their 1 sigma errors. 23 –Table 1: The error bar corrections parameters and linear limb darkening parameters forthe data sets used to model the MOA-2008-BLG-379 light curve. The formula used tomodify the error bars is σ ′ i = k p σ i + e where σ i is the input error bar for the i th datapoint from the photometry code in magnitudes, and σ ′ i is the final error bar used for thedetermination of parameter uncertainties.Dataset k e min Limb-darkening Coefficients Number of DataMOA-Red 1.266 0 0.5919 951OGLE I -band 0.995 0 0.5493 294OGLE V -band 1.180 0 0.7107 7 24 –Table 2: The best fit model parameters for both the wide and close models. The second andfourth rows in each column are the 1- σ error bars for each parameter. HJD ′ ≡ HJD − t t E u q s θ t ∗ χ HJD ′ (days) 10 − − (rad) (days)Wide 4687.896 42.14 6.03 6.99 1.119 1.124 0.0219 1246.70.001 0.23 0.03 0.01 0.001 0.003 0.0020Close 4687.897 42.46 6.02 6.85 0.903 5.154 0.0212 1246.00.001 0.45 0.06 0.05 0.001 0.002 0.0017 25 –Table 3: Physical parameters of the lens system obtained from the Bayesian analysis.Primary Mass Secondary Mass Distance Projected Separation Separation M L ( M ⊙ ) m P ( M Jup ) D L (kpc) r ⊥ (AU) a (AU)0 . +0 . − . . +1 . − . . +1 . − . . +0 . − . . +1 ..
CMD ofHoltzman et al. (1998) whose extinction is adjusted to match the MOA-2008-BLG-379 usingthe Holtzman field red clump giant (RCG) centroid of ( V − I, I ) RCG , Holtz = (15 . , . V I is indicated with a bluedot, while the source star color and magnitude derived from the MOA-Red and OGLE- I passbands is shown as a magenta dot. Although the error bars on the MOA-Red + OGLE- I color estimate are similar to the error bar from the OGLE V I estimate, we use the MOA-Red + OGLE- I estimate for the source color because it is subject to smaller systematicuncertainties. 21 –Fig. 4.— Probability distribution of lens parameters from the Bayesian analysis. The top-leftpanel shows the probability of the distance to the lens system. The bottom-left panel showsthe mass of the primary and secondary lenses (the star and planet) in units of Solar andJupiter masses, respectively. The top-right panel shows the projected separation r ⊥ . Thedark and light blue regions indicate the 68% and 95% confidence intervals, and the verticallines indicate the median value. 22 –Fig. 5.— Probability distribution of V -, I -, K - and H -band magnitudes for the extinction-free lens star from the Bayesian analysis. The dark and light blue regions indicate the 68%and 95% confidence intervals. The red solid lines show the source star magnitudes with theextinction estimated in Equation (4), and the red dashed lines are their 1 sigma errors. 23 –Table 1: The error bar corrections parameters and linear limb darkening parameters forthe data sets used to model the MOA-2008-BLG-379 light curve. The formula used tomodify the error bars is σ ′ i = k p σ i + e where σ i is the input error bar for the i th datapoint from the photometry code in magnitudes, and σ ′ i is the final error bar used for thedetermination of parameter uncertainties.Dataset k e min Limb-darkening Coefficients Number of DataMOA-Red 1.266 0 0.5919 951OGLE I -band 0.995 0 0.5493 294OGLE V -band 1.180 0 0.7107 7 24 –Table 2: The best fit model parameters for both the wide and close models. The second andfourth rows in each column are the 1- σ error bars for each parameter. HJD ′ ≡ HJD − t t E u q s θ t ∗ χ HJD ′ (days) 10 − − (rad) (days)Wide 4687.896 42.14 6.03 6.99 1.119 1.124 0.0219 1246.70.001 0.23 0.03 0.01 0.001 0.003 0.0020Close 4687.897 42.46 6.02 6.85 0.903 5.154 0.0212 1246.00.001 0.45 0.06 0.05 0.001 0.002 0.0017 25 –Table 3: Physical parameters of the lens system obtained from the Bayesian analysis.Primary Mass Secondary Mass Distance Projected Separation Separation M L ( M ⊙ ) m P ( M Jup ) D L (kpc) r ⊥ (AU) a (AU)0 . +0 . − . . +1 . − . . +1 . − . . +0 . − . . +1 .. − ..