MOA-2007-BLG-197: Exploring the brown dwarf desert
C. Ranc, A. Cassan, M. D. Albrow, D. Kubas, I. A. Bond, V. Batista, J.-P. Beaulieu, D. P. Bennett, M. Dominik, Subo Dong, P. Fouqué, A. Gould, J. Greenhill, U. G. Jørgensen, N. Kains, J. Menzies, T. Sumi, E. Bachelet, C. Coutures, S. Dieters, D. Dominis Prester, J. Donatowicz, B. S. Gaudi, C. Han, M. Hundertmark, K. Horne, S. R. Kane, C.-U. Lee, J.-B. Marquette, B.-G. Park, K. R. Pollard, K. C. Sahu, R. Street, Y. Tsapras, J. Wambsganss, A. Williams, M. Zub, F. Abe, A. Fukui, Y. Itow, K. Masuda, Y. Matsubara, Y. Muraki, K. Ohnishi, N. Rattenbury, To. Saito, D. J. Sullivan, W. L. Sweatman, P. J. Tristram, P. C. M. Yock, A. Yonehara
AAstronomy & Astrophysics manuscript no. draft c (cid:13)
ESO 2018March 5, 2018
MOA-2007-BLG-197: Exploring the brown dwarf desert
C. Ranc , , A. Cassan , , M. D. Albrow , , D. Kubas , , I. A. Bond , , V. Batista , , J.-P. Beaulieu , ,D. P. Bennett , , M. Dominik , , Subo Dong , , P. Fouqué , , , A. Gould , , J. Greenhill † , ,U. G. Jørgensen , , N. Kains , , , J. Menzies , , T. Sumi , , E. Bachelet , , C. Coutures , , S. Dieters , ,D. Dominis Prester , , J. Donatowicz , , B. S. Gaudi , , C. Han , , M. Hundertmark , , K. Horne , ,S. R. Kane , , C.-U. Lee , , J.-B. Marquette , , B.-G. Park , , K. R. Pollard , , K. C. Sahu , , R. Street , ,Y. Tsapras , , , J. Wambsganss , , A. Williams , , , M. Zub , , F. Abe , , A. Fukui , , Y. Itow , ,K. Masuda , , Y. Matsubara , , Y. Muraki , , K. Ohnishi , , N. Rattenbury , , To. Saito , ,D. J. Sullivan , , W. L. Sweatman , , P. J. Tristram , , P. C. M. Yock , , and A. Yonehara , (A ffi liations can be found after the references) Received < date > / accepted < date > ABSTRACT
We present the analysis of MOA-2007-BLG-197Lb, the first brown dwarf companion to a Sun-like star detected through gravitationalmicrolensing. The event was alerted and followed-up photometrically by a network of telescopes from the PLANET, MOA, and µ FUN collaborations, and observed at high angular resolution using the NaCo instrument at the VLT. From the modelling of themicrolensing light curve, we derived basic parameters such as, the binary lens separation in Einstein radius units ( s (cid:39) . q = (4 . ± . × − and the Einstein radius crossing time ( t E (cid:39)
82 d). Because of this long time scale, we took annualparallax and orbital motion of the lens in the models into account, as well as finite source e ff ects that were clearly detected during thesource caustic exit. To recover the lens system’s physical parameters, we combined the resulting light curve best-fit parameters with( J , H , K s ) magnitudes obtained with VLT NaCo and calibrated using IRSF and 2MASS data. From this analysis, we derived a lenstotal mass of 0 . ± .
04 M (cid:12) and a lens distance of D L = . ± . ± J observed at a projected separation of a ⊥ = . ± . . ± .
04 M (cid:12)
G-K dwarf star. Wethen placed the companion of MOA-2007-BLG-197L in a mass-period diagram consisting of all brown dwarf companions detectedso far through di ff erent techniques, including microlensing, transit, radial velocity, and direct imaging (most of these objects orbitsolar-type stars). To study the statistical properties of this population, we performed a two-dimensional, non-parametric probabilitydensity distribution fit to the data, which draws a structured brown dwarf landscape. We confirm the existence of a region that isstrongly depleted in objects at short periods and intermediate masses ( P (cid:46)
30 d, M ∼ −
60 M J ), but also find an accumulation ofobjects around P ∼
500 d and M ∼
20 M J , as well as another depletion region at long orbital periods ( P (cid:38)
500 d) and high masses( M (cid:38)
50 M J ). While these data provide important clues on the di ff erent physical mechanisms of formation (or destruction) that shapethe brown dwarf desert, more data are needed to establish their relative importance, in particular as a function of host star mass.Future microlensing surveys should soon provide more detections, in particular for red dwarf hosts, thus uniquely complementing thesolar-type host sample. Key words.
Gravitational lensing: micro - Planets and satellites: detection - Brown dwarfs
1. Introduction
Gravitational microlensing is a powerful technique for detectingextrasolar planets (Mao & Paczynski 1991), and it holds greatpromise for detecting populations of brown dwarf companionsto stars. Compared to other detection techniques, microlensingprovides unique information on the population of exoplanets, be-cause it allows the detection of very low-mass planets (down tothe mass of the Earth) at long orbital distances from their hoststars (typically 0.5 to 10 AU). It is also the only technique thatallows discovery of exoplanets and brown dwarfs at distancesfrom the Earth greater than a few kiloparsecs, up to the Galacticbulge, which would have been hard to detect with other methods.Exoplanets are found to be frequent by all detection tech-niques (e.g., Cassan et al. 2012; Bonfils et al. 2013; Mayor et al.2011; Sumi et al. 2011; Gould et al. 2010b), and recent statisticalmicrolensing studies even imply that there are, on average, oneor more bound planets per Milky Way star (Cassan et al. 2012). Conversely, brown dwarfs appear to be intrinsically rare, to thepoint that shortly after the first exoplanet detections, it led to theidea of a “brown dwarf desert” (Marcy & Butler 2000) bridg-ing the two well-defined regions of binary stars and planetarysystems. While in the past, brown dwarfs were defined as ob-jects of mass within the deuterium- and hydrogen-burning limits(13 −
74 M J , Burrows et al. 2001), it appears today that di ff er-ent formation scenarios can build objects with similar massesbut with di ff erent natures (super-massive planets, or low-massbrown dwarfs). An object formed via core accretion and reach-ing 13 M J would, for example, be able to start deuterium burn-ing, as would an object of same mass formed by gravitationalcollapse of a cloud or in a protoplanetary disk (Mollière & Mor-dasini 2012).Despite their low occurrence, a number of brown dwarf com-panions to stars have been discovered by di ff erent methods: ra-dial velocity and transit (e.g., Moutou et al. 2013; Díaz et al.2013; Sahlmann et al. 2011; Johnson et al. 2011; Deleuil et al. Article number, page 1 of 16 a r X i v : . [ a s t r o - ph . E P ] M a y & A proofs: manuscript no. draft ± J brown dwarf locatedat 525 ±
40 pc in the thick disk of the Milky Way) was re-ported by Gould et al. (2009) in microlensing event OGLE-2007-BLG-224. Two brown dwarfs with planetary-mass companionswere discovered in events OGLE-2009-BLG-151 / MOA-2009-BLG-232 and OGLE-2011-BLG-0420 by Choi et al. (2013). Inboth cases, the planets were super Jupiters (7 . ± . J and9 . ± . J , respectively) with the hosts being low-mass browndwarfs (19 ± J and 26 ± J , respectively), with very tightorbits (below 0 . ± J field brown dwarf hosting a 1 . ± . J planet ina tight system after the analysis of the event OGLE-2012-BLG-0358.The first published microlensing detection of a brown dwarfcompanion to a star is OGLE-2008-BLG-510 / MOA-2008-BLG-369, which was first reported by Bozza et al. (2012) as an am-biguous case between a binary-lens and a binary-source event.The data were reanalysed by Shin et al. (2012a), who con-cluded that the binary-lens model involving a massive browndwarf orbiting an M dwarf was preferred. Shin et al. (2012b)conducted a database search for brown dwarf companions byfocusing on microlensing events that exhibit low mass ratios.Among seven good candidates with well-determined masses(combination of Einstein radius and parallax measurements),they found two events that involve brown dwarfs: OGLE-2011-BLG-0172 / MOA-2011-BLG-104 with mass 21 ±
10 M J aroundan M dwarf, and MOA-2011-BLG-149, a 20 ± J brown dwarfalso orbiting an M dwarf. Similarly, Bachelet et al. (2012) re-ported the detection of another ∼
52 M J brown dwarf orbitingan M dwarf in MOA-2009-BLG-411, although the lens masscould not be determined exactly, and was estimated through sta-tistical realisations of Galactic models. In microlensing eventMOA-2010-BLG-073, Street et al. (2013) find that the lenswas composed of a 11 . ± . J companion (hence near theplanet / brown boundary) orbiting an M dwarf of 0 . ± .
03 M (cid:12) .Jung et al. (2015) report the detection of a star at the limit of thebrown dwarf regime hosting a companion at the planet / browndwarf boundary (13 ± J ). More recently, Park et al. (2015)have reported the discovery of a binary system composed of a33 . ± . J brown dwarf orbiting a late-type M dwarf in mi-crolensing event OGLE-2013-BLG-0578.Here we report the first microlensing discovery of a browndwarf orbiting a Sun-like star. This new brown dwarf has a massof 42 M J and it was observed at a projected separation of 4 . ff erent methods using non-parametric probability density estimation tools. In sec. 6 we summarise ourresults, and underline the importance of future microlensing ob-servations to characterise the populations of objects in the massregion between planets and stars.
2. Observational data
MOA-2007-BLG-197 ( l = . b = − . = = -31:56:46.77) is a microlens-ing event that was alerted by the MOA collaboration (1.8m tele-scope located in Mount John, New Zealand) in 2007 May 28 (orTHJD (cid:39) on the photometric light curve shown Fig. 1).Soon after, between 1-5 June (THJD (cid:39) ff ected the qualityand reliability of the photometry, resulting in gaps in the timeseries. A magnification peak in the MOA light curve was passedaround June 6 (THJD (cid:39) (cid:39) . µ FUN collaboration collecteddata from CTIO 1.3m in Mount Cerro Tololo (Chile).On June 19 (THJD (cid:39) (cid:39) ff ected the quality of the observa-tions, a public alert was issued after Danish 1.54m data werefound to be above the single lens curve by more than 0.2 magfor more than five consecutive days. Intensive follow-up obser-vations from SAAO confirmed the rise in brightness, announcinga caustic crossing. While Perth was overclouded, Canopus thentook over, and was the only telescope to densely cover the caus-tic exit, which took place during the night of July 4 in Australia(THJD (cid:39) . The photometric data was reduced several times using di ff erentsoftware to check their consistency. The final lightcurve datafrom all telescopes were extracted with the PLANET pipelinePySIS (Albrow et al. 2009), which is a DIA-based algorithm(Di ff erence Image Analysis, Alard 2000; Alard & Lupton 1998).For images taken in particularly bad weather conditions, we ex-amined by eye each image in order to check whether the subtrac-tion was correct or not. In the latter case we had to exclude them,but on the basis of image quality only. In the post-processingof the reduced data, we applied a cut in seeing and sky back-ground, although in a very conservative way so that possiblelow-amplitude signals were not rejected. Not surprisingly, mostof the data taken by MOA during the very bad weather periodmentioned before (THJD (cid:39) ff ected the reliability of our models. THJD = HJD − , , Table 1.
Telescopes and photometric data sets.
Telescope Location Filter Data a f b MOA (1 . R Mc
504 1.4PLANET Danish (1 .
54 m) La Silla, Chile I
167 1.7PLANET Canopus (1 . I
45 3.0PLANET SAAO (1 . I
43 1.6 µ FUN CTIO (1 . I
28 1.3PLANET Perth (0 . I
15 1.4
Notes. ( a ) Number after data cleaning. ( b ) Error bar rescaling factor (Sect. 2.2). ( c ) MOA broad R / I filter.
HJD −
2, 450, 000-0.10.00.1 r e s i dua l s ( m ag ) m agn i t ude I ( M O A ) • SAAO • CTIO • MOA • Canopus • Perth • Danish
E1 E2 E3 E4
Fig. 1.
In the upper panel, the light curve of MOA-2007-BLG-197 and the best-fit model (solid line) are plotted with a zoom on the caustic exiton the right-hand side. On the left-hand side, the structure of the resonant caustic is drawn in red, as well as the trajectory of the source, in black(axes are in Einstein radius units). The source is too small to be distinguished. The four intervals E − indicate time intervals where possible sourcecaustic crossing (caustic entry) have been investigated. In the lower panel, the residuals of the best-fit model are shown. The final light curve data amounts to a total of 802 datapoints. They are summerised in Table 1. As seen in the table,all telescopes use a similar I -band filter, apart from the MOA1.8m telescope which is equipped with a broad R / I filter (re-ferred to as R M ). Additionally, a few V -band images were takenby PLANET and µ FUN to produce colour-magnitude diagrams(see Sect. 4.1).The last concern about the photometry was the estimationof the error bars of the data. Galactic bulge fields are highlycrowded with stars, and during a microlensing event, the fluxvariation can easily span two order of magnitudes for high-magnification events. These pose severe challenges to managea good estimation of the error bars. As a matter of fact, in mi-crolensing experiments it is long known that data reduction soft-ware usually underestimates error bars. Furthermore, error barscan vary significantly from one data set to another, with the risk that one data set dominates over the others at the modellingstage. A relatively robust method to prevent these drawbacks isto rescale the error bars, based on the best model fitting the data.For each data set, the (classical) χ is set up to the number of de-grees of freedom by adjusting a rescaling factor f in the formula σ (cid:48) = f σ + σ , where σ (cid:48) and σ are respectively the rescaledand initial error bars on the magnitudes, and σ = × − aconstant accounting for the data most highly magnified. The f factors are given in Table 1 for each data set. On the night 20 /
21 of August 2007 (THJD (cid:39) .
0) we ob-tained first epoch observations of high resolution adaptive op- ESO Programme ID 279.C-5044(A). Article number, page 3 of 16 & A proofs: manuscript no. draft tics (AO) images in the near-infrared bands J , H and K s usingthe NaCo instrument, mounted on 8.2m ESO VLT Yepun tele-scope (Fig. 2). The source star was then still magnified by a fac-tor of about A (cid:39) .
30. A year later, on the night 2008 August3 / (cid:39) . while the event was back to baseline magnitude. In princi-ple, when two epochs are obtained at di ff erent magnifications, itshould be possible to directly disentangle the lens flux from thesource flux. In our case, however, the combination of a relativelyhigh blending factor and low magnification did not support thisdirect measurement. Therefore, in the global analysis we usedonly the first epoch images. We reduced and calibrated the NaCoimages following the general method outlined in Kubas et al.(2012) and briefly described below. Fig. 2.
The image on the left shows a sub-region (94 (cid:48)(cid:48) × (cid:48)(cid:48) ) of anoriginal 3 (cid:48) × (cid:48) K s -band IRSF image used to calibrate the NaCo magni-tudes. The image on the right is the corresponding K s -band NaCo image(27 (cid:48)(cid:48) × (cid:48)(cid:48) ) used to cross-identify the stars. The night was clear and stable according to the observatorynight logs, and the target was observed at low airmass and ingood seeing conditions ( < . (cid:48)(cid:48) ). The data were taken in auto-jitter mode within a 10 (cid:48)(cid:48) jitter box including the target in orderto be able to correct for bad pixels and sky background. TheAO correction was done using a K = . ± .
02 mag star(2MASS 18070464-3156423) at an angular separation of about5 (cid:48)(cid:48) from the microlensing target. The data were dark subtracted,flat-fielded and co-added with the tools underlying the NaCopipeline software (Devillard 1999).To derive the photometry from the reduced data, the first stepwas to compute the zeropoints for the conversion of instrumentalmagnitudes to calibrated magnitudes. A first possibility was touse catalogued stars within the target frame field-of-view (FOV),in our case 28 (cid:48)(cid:48) × (cid:48)(cid:48) . While several cross-matches between theNaCo frames and the 2MASS catalogue were identified, only2MASS 18070520-3156409 ( J = . ± . H = . ± . K = . ± .
05) turned out as suitable (other potential calibra-tors in the NaCo images were either saturated or in the nonlinearregime of the detector). We finally checked that this star was notvariable, by comparing a series of H -band images taken withAndicam at CTIO, which is well calibrated to 2MASS thanksto its 2 . (cid:48) × . (cid:48) FOV. A second option for calibration was touse the zeropoints derived from the photometric standards takenwith NaCo directly before the observations on the night 20 /
21 ofAugust and at similar airmass. For calibration we used J , H , K ESO Programme ID 381.C-0425(A). magnitudes of star 9160-S870-T in the listed standards of Pers-son et al. (1998), which had the following advantages: this starwas brighter than the previous 2MASS reference, and the smallerpixel scale made it less sensitive to blending contamination inour crowded field. For consistency, however, we measured themagnitude of 2MASS 18070520-3156409 in the NaCo frame,and found an agreement to better than 3%.The second step was to extract accurate photometry from AOimages in the infrared. This was not a straightforward task, sincethe shape of the point-spread function (PSF) often is not wellfitted by analytical profiles, and also depends on the position ofthe target with respect to the star used for AO correction. Follow-ing Kubas et al. (2012), we constructed a PSF reference directlyfrom stars in the NaCo frame, using the StarFinder package (Di-olaiti et al. 2000). This software was especially designed for AOimages of crowded stellar fields. We found J = . ± . H = . ± .
05 and K s = . ± .
05. The quoted errorbars are dominated by the uncertainties in determining the truePSF shape and the scatter of the sky and unresolved backgroundsources. The measurements obtained with StarFinder are sum-marised in Table 2.Band Epoch Magnitude Date [THJD] FWHM J . ± .
06 4333.03906250 0.19” J . ± .
05 4682.12500000 0.17” H . ± .
05 4333.05468750 0.14” H . ± .
04 4682.14453125 0.11” K s . ± .
05 4333.02343750 0.11” K s . ± .
04 4682.10546875 0.11”
Table 2.
Derived NaCo magnitudes of the microlensing event target inthe ( J , H , K s ) filters for the two epochs 2007 August 20 /
21 (epoch 1) and2008 August 3 / The final step consisted in correcting the target for inter-stellar extinction, by fitting the position of the red clump giants(RCG) in the three colour-magnitude diagrams (CMD) involvingthe measured J , H , K s reddened magnitudes. Because the nomi-nal range in magnitudes from NaCo is above the 2MASS faintlimit, we performed InfraRed Survey Facility (IRSF) observa-tions at SAAO to extend the available 2MASS star list into theregime of stars measured within the NaCo frame. We used Katoet al. (2007) to obtain the calibration of IRSF images with re-spect to the 2MASS reference-star catalogue, noting that Janczaket al. (2010) found that no additional colour term is needed be-tween NaCo and IRSF filters (the full process to build the cal-ibration ladder is detailed in Kubas et al. 2012). Data to con-struct the NaCo + IRSF CMD are extracted from 2304 stars iden-tified within a 3 (cid:48) circle around the target in IRSF images, and135 stars identified in the NaCo images (Fig. 2). The result-ing de-reddened and calibrated CMD is plotted in Fig. 3, witha fit of the Red Clump Giant (RCG) position using a 10 Gyr, Z = .
019 isochrone from Bressan et al. (2012), and assuminga RCG distance modulus of µ = . A J = . ± .
05 mag, A H = . ± .
05 mag and A K s = . ± .
05 mag. These data are used in Sect. 4.2 to con-strain the lens and mass distance. Note that the di ff erence in the transmission profile between K and Ksbands is less than 1%, so negligible in the present case.Article number, page 4 of 16. Ranc et al.: MOA-2007-BLG-197: Exploring the brown dwarf desert J − Ks J NACOIRSF
Fig. 3. ( J , J − K s ) colour-magnitude diagram in the 2MASS system com-bining NaCo and IRSF data (respectively, in blue and black). The reddot is the magnitude / colour of the source derived from the source char-acterisation (Sect. 4.1). The values are not corrected for interstellar ex-tinction. The red clump (RCG) is fitted by the red over-plotted 10 Gyr,solar-metallicity isochrone from Bressan et al. (2012).
3. Light curve modelling
We start by modelling the light curve of MOA-2007-BLG-197with a static binary-lens model, in order to identify broad classesof possible solutions. In this model, the lens is characterised byits binary mass ratio q , and s , the projected separation of thebinary lens in angular Einstein radius units θ E . Here, θ E = (cid:115) GMc D S (cid:32) D S D L − (cid:33) , (1)where G is the gravitational constant, c the speed of light, D L and D S are respectively the observer-lens and observer-sourcedistances and M the total mass of the lens. Four additional pa-rameters describe the source mean rectilinear motion: the mini-mum impact distance u between the source and the origin (here,the centre of mass of the system, with the more massive body onthe right-hand side), t , the date at which the source reaches u , t E , the time it takes for the source to travel one Einstein angularradius, and α , the angle between the source trajectory and thelens symmetry axis.When the source approaches a caustic, finite-source e ff ectscannot be neglected and substantial deviations from a point-source model are expected. Finite-source e ff ects are included inthe modelling through ρ = θ S θ E , (2)where θ S is the angular radius of the source, and ρ the same quan-tity but in Einstein radius units. Here and in the following, apoint-source model is used when the source is far enough fromthe caustics ( t ≤ . t ≥ . t ∈ [4240 . , . ∪ [4260 . , . ∪ [4287 . , . ∼ ρ from the caustics. In this case, a fullintegration along the source images contours (Dominik 2007;Bozza 2010; Gould & Gaucherel 1997) or ray-shooting of theimages are required (Dong et al. 2006, 2009; Bennett 2010)to compute the magnification. Since finite-source e ff ects dra-matically increase the computational cost, these time intervalsare reduced as much as possible (here, t ∈ [4247 . , . ∪ [4286 . , . I ( r ) = π (cid:34) − Γ (cid:32) − √ − r (cid:33)(cid:35) , (3)where 0 ≤ r ≤ Γ the linearlimb-darkening (LLD) coe ffi cient. While in special cases limb-darkening laws beyond the linear law may slightly improve themodel (e.g., Cassan et al. 2004; Kubas et al. 2005), in the case ofMOA-2007-BLG-197L (relatively sparse data coverage of thecaustic crossings) it is an excellent approximation. As seen inthe right inset of Fig. 1, only Canopus data are sensitive to limbdarkening, although the light curve sampling is not dense enoughto provide strong constraints on the LLD coe ffi cient. We there-fore use Claret & Bloemen (2011) for the source surface grav-ity and e ff ective temperature found in Sect. 4.1 (log g ∼ . T e ff ∼ ffi -cients, and found ∼ . I filter and ∼ . R filter.We checked that refining the Canopus- I LLD coe ffi cient with afit to the data leads to Γ I = .
48. We then adopted Γ I = .
48 forall I -band data and Γ R M = . Γ R M filter is a broad R / Ifilter).Finally, two additional parameters, F i S (source flux) and F i B (blended flux), are included per individual observatory or filter,so that for a given individual data set i the total flux of the mi-crolensing target reads F i ( t ) = A ( t ) F i S + F i B , (4)where A ( t ) is the time-dependent source flux magnification fac-tor. The blending flux F B accounts for all luminous contribu-tions other than the source, in particular, it includes the flux fromthe lens. For the best model presented in Table 3, the blendingflux ratios F B / F S are respectively 17 .
79 (MOA), 38 .
14 (SAAO),12 .
85 (CTIO), 3 .
97 (Canopus), 66 .
97 (Perth), 12 .
10 (Danish).The high value for Perth is easily explained by the fact that theaperture of the telescope is small and the seeing was relativelyhigh, which results in a higher blend fraction.
The shape of the MOA-2007-BLG-197 light curve (Fig. 1)clearly indicates that the source crosses ( i.e. , exits) a fold caus-tic at THJD (cid:39) .
2, mainly thanks to Canopus data denselycovering this part of the light curve. On the other hand, the dateof the caustic entry is ambiguous. In fact, for such a small angu-lar source size as suggested by the caustic exit, the caustic entrycould easily fit in one of the several gaps in the data coverage, inparticular those marked as E − in Fig. 1. Article number, page 5 of 16 & A proofs: manuscript no. draft
One of the modelling challenges for this event was to findall possible local minima involving all possible caustic entrydates. The problem with the set of parameters ( u , α, t E , t ) de-scribed in the previous section is that it is not well suited toexplore e ffi ciently the parameter space. In fact, only very spe-cial combinations of these parameters produce caustic crossingsat the right locations on the light curve. Albrow et al. (1999a)proposed for the first time to introduce specific parameters tomodel a caustic crossing. Cassan (2008) developed further thisapproach, and generalised it to a pair of caustic crossings (entryand exit) by introducing a specific parametrisation of the caus-tic curves. This method is particularly e ffi cient for an event likeMOA-2007-BLG-197.In this formalism, two alternative parameters t in and t out areused to fit for the dates of the source entry (in) and exit (out),while two other parameters s in and s out (which are curvilin-ear distances along the caustic curve) are used to fit for thesource centre ingress and egress points on the caustic. It hasbeen demonstrated that this parametrisation is more e ffi cient inlocating all possible fitting source-lens trajectories (Kains et al.2009, 2012), because they all produce caustic-crossing featuresat the observed dates. Cassan et al. (2010) later derived Bayesianpriors on parameters ( t in , t out , s in , s out ) to explore even more e ffi -ciently the parameter space. The best-fit values derived from theminimisation process are finally converted back to the classicalparameters.We explored all static binary-lens models using thisparametrisation for all possible source caustic crossing dateswithin the E to E intervals displayed in Fig. 1, and for a regular(log s , log q ) grid of 30 ×
30 spanning log(0 . ≤ log s ≤ log(4)and − ≤ log q ≤
0. The minimisation was performed us-ing a classical Markov Chain Monte Carlo (MCMC) algorithm.The best model involves a caustic entry in the time interval E ,the longest of the four gaps explored. The best-fit values of themodel parameters and the corresponding χ are listed in columnESBL (Extended-Source, Binary-Lens) of Table 3, and posteriorprobability densities (correlation plots) are presented in Fig. 9. Given the long timescale found previously for the static binarylens model ( t E ∼
80 days), this event is a priori likely to exhibitannual parallax e ff ects. The relative lens-source (annual) paral-lax is expressed as π rel = AU D L − AU D S , (5)so that the Einstein angular radius Eq. (1) also reads θ E = (cid:112) κ M π rel , (6)where κ (cid:39) .
144 mas / M (cid:12) . The Einstein parallax vector π E hasan amplitude π E = π rel θ E , (7)and a direction along the lens-source proper motion. As fittingparameters, it is convenient to decompose π E into a northwardscomponent π E , N and an eastwards component π E , E (An et al.2002), with advantages discussed in Gould (2004). These very intensive computations were performed on the Tasmaniancluster TPAC (Tasmanian Partnership for Advanced Computing).
The best-fit model including parallax only (besides the pa-rameters described in Sect. 3.1) is presented in column ESBL + Pof Table 3, and correlation plots are shown in Fig. 10. It can benoticed that the binary mass ratio q and separation s change lit-tle by including parallax compared to ESBL, resulting in a verysimilar resonant caustic structure. As expected, including par-allax in the model improves the χ , by around 100. Neverthe-less, we found that several solutions with very di ff erent valuesof parallax (between 0 . .
5) give almost identical χ di ff eringby only one or two units. The di ff erences between these modelscome from di ff erences in the caustic entry date t in , i.e. preciselywhere no data are available to constrain the model. Hence, al-though parallax improves the fit, it is unlikely that a workablemeasurement can be obtained (we discuss this further later). Orbital motion of the lens is also a priori likely to produce no-ticeable e ff ects, because the event is fairly long and the causticresonant. The orbital rotation of the two lens components a ff ectsthe caustic in two ways: it changes the projected binary separa-tion s and the orientation of the caustic in the plane of the sky. Tofirst order, one can write s ( t ) (cid:39) s + ˙ s ( t − t r ) and α ( t ) (cid:39) α + ˙ α ( t − t r ),where t r is an arbitrary reference date chosen close or equal to t .These two e ff ects are included in the model through parameters γ (cid:107) = ˙ s / s and γ ⊥ = ˙ α , with γ = γ (cid:107) + γ ⊥ .The best-fit model including lens orbital motion with ESBLis presented in column ESBL + LOM of Table 3 (correlation plotsare shown in Fig. 11). According to this model, the changes inthe caustic geometry are very slow, which should result in a poorsignature on the light curve. Therefore, while this model alsoprovides a better fit than ESBL alone ( ∆ χ = ∆ χ between this model and ESBL + P (parallax alone)is only lower than 10 although two more parameters have beenincluded in the model. We conclude that the key time intervalsfor disentangling orbital motion from parallax are not covereddensely enough by the data.
As (annual) parallax and orbital motion individually lead to asimilar improvement of the ESBL χ , we now include both ef-fects in the model to check whether a better χ can be found. Par-allax and orbital motion are known to be very correlated (Batistaet al. 2011; Skowron et al. 2011).We investigate the two cases u > u < + P + LOM of Table 3) to check for possible ecliptic degen-eracy (Skowron et al. 2011), and find that u > ∆ χ = .
9. The ESBL best-fit parameters, again, are rela-tively stable. The correlation plots of the best model are shown inFig. 12. As expected, the overall fit is not significantly better thanESBL + P ( ∆ χ = .
2) or ESBL + LOM alone ( ∆ χ = . A model with (annual) parallax improves the goodness-of-fit by ∆ χ ∼
100 compared to a static binary lens, but several modelswith very di ff erent values of π E give comparable values of χ .Moreover, models with parallax or orbital motion alone lead to Article number, page 6 of 16. Ranc et al.: MOA-2007-BLG-197: Exploring the brown dwarf desert
Table 3.
Best-fit solutions for the di ff erent models of MOA-2007-BLG-197. Parameter [unit] ModelESBL a ESBL + P b ESBL + LOM c ESBL + P + LOM u < u > χ / d.o.f. (942 . / = .
19 (840 . / = .
06 (849 . / = .
07 (840 . / = .
06 (828 . / = . ∆ χ = χ − χ . . . . s . ± . . ± . . ± . . ± . . ± . q / − . ± .
043 4 . ± .
080 3 . ± .
25 4 . ± .
044 4 . ± . t E [days] 80 . ± .
21 78 . ± .
61 79 . ± . . ± . . ± . u / − . ± .
10 5 . ± .
15 7 . ± . − . ± .
12 5 . ± . t [THJD] 4259 . ± .
10 4259 . ± .
40 4258 . ± .
70 4259 . ± .
10 4258 . ± . α/ − [rad] 9 . ± .
056 8 . ± .
20 7 . ± . − . ± .
14 9 . ± . ρ/ − . ± .
23 5 . ± .
30 5 . ± .
27 6 . ± .
33 5 . ± . π E , N – 0 . ± .
25 – 1 . ± . − . ± . π E , E – − . ± .
15 – 0 . ± . − . ± . s / − [rad / year] – – 1 . ± . − . ± . − . ± . α/ − [rad / year] – – 0 . ± . − . ± .
60 2 . ± . Notes. ( a ) Extended-source binary-lens model. ( b ) Microlensing parallax. ( c ) Lens orbital motion. comparable χ . This is not surprising for two reasons. Firstly, thecaustic entry is not well covered by the data and it appears thata high value of parallax tends to change substantially the time ofthe caustic entry inside E . Secondly, parallax e ff ects are partlydegenerate with lens orbital motion, and the available data setsare not su ffi cient to disentangle these two e ff ects.We therefore adopt the ESBL parameters ( s , q , u , α, t E , t )found for model ESBL + P + LOM and u >
0. Following the ar-guments summarised in the previous paragraph, other parame-ters such as parallax or orbital motion parameters cannot be usedto constrain the lens mass and distance.
4. Physical parameters
Combining Eq. (2) and Eq. (6) yields the following mass-distance relation for the lens M = θ S2 ρ κ π rel , (8)where M is the lens mass and π rel is a proxy to lens distance D L according to Eq. (5). In this equation, ρ is measured from thelight curve modelling (Sect. 3.6) and θ S is derived below.To characterise the source, we use a DoPHOT-based data re-duction (Schechter et al. 1993) of Danish I and V data to buildan instrumental ( I , ( V − I )) CMD (Fig. 4). Fitting the I -band datafor the best-fit model parameters provides I S , DK = . ± . ffi cult to locate precisely the mean instrumental RCGposition, ( I RCG , DK , ( V − I ) RCG , DK ). To overcome this problem, wecross-calibrate the Danish CMD with a CMD obtained at CTIOin a very similar I filter, by cross-identifying a few clump stars.We then measure I RCG , DK = .
09 and ( V − I ) RCG , DK = .
11. Thevalues of M I , RCG = − . ± .
09 and ( V − I ) RCG , = . ± . D GC = .
20 kpcand an angle between the Galactic bar and the line of sight fromthe Sun φ = ◦ . From these values, the distance to the RCG is D RCG = D GC sin φ cos ( b ) sin ( l + φ ) . (9)For the Galactic coordinates of MOA-2007-BLG-197, the RCGis in the far side of the bar at a distance D RCG = .
29 kpc. Weadopt a source at the same distance, corresponding to a distancemodulus of µ = . ± . I S , = I S , DK + M I , RCG + µ − I RCG , DK andobtain I S , = . ± .
31, which gives an absolute magnitudeof M I = . ± .
31. We use a 10 Gyr and solar metallicityisochrone from Bressan et al. (2012) to get the correspondingabsolute magnitude M V of the source from which we derive anintrinsic source colour of ( V − I ) S , = . ± .
1. This value can becompared to an independent estimate of the source colour basedon the method of Gould et al. (2010a). MOA R M -band imagesare reduced with DoPHOT, and stars are cross-matched betweenDanish I , V and MOA R M frames (lower panel of Fig. 4). Weobtain I S , DK − I S , MOA = − (0 . ± . − (0 . ± . × ( V − I ) S , DK , (10)where I S , MOA = . ± .
02 from the fit of the R M light curveusing the best-fit parameters. Hence, I S , DK − I S , MOA = − . ± .
02, which yields ( V − I ) S , DK = − . ± .
10. It follows thatthe estimated de-reddened source colour is ( V − I ) S , = ( V − I ) S , DK + ( V − I ) RCG − ( V − I ) RCG , DK = . ± .
2, which is ingood agreement with the previous estimate. In the following, weadopt ( V − I ) S , = . ± . I S , = . ± .
31. The source is thus a G6-K0 Main Sequence star.From Kervella & Fouqué (2008) brightness-colour relations,we estimate the angular radius of the source,log( θ S ) = . − . I S , + . V − I ) S , − . V − I ) , , (11)which yields θ S = . ± . µ as. With a source at D S = . R S = D S θ S = . R (cid:12) . From Article number, page 7 of 16 & A proofs: manuscript no. draft − − V − I )[ DK ]1314151617181920 I [ D K ] Fig. 4.
Upper panel: ( I , V − I ) Danish instrumental CMD of the fieldaround MOA-2007-BLG-197, not corrected for interstellar extinction.The red point marks the position of the RCG. The magnitude of themicrolensing target is in blue ( i.e. magnified source, lens and blendedlight). The orange point corresponds to the source alone. Lower panel:empirical linear relation between instrumental colours ( I DK − I MOA ) and( V − I ) DK (red and green points are astrometric matches that are un-crowded in the MOA image; after sigma-clipping, only red points areused for the fit). Carroll & Ostlie (2006), this radius is that of G8 Main Sequencestar, which is in very good agreement with the constraint fromthe colour.The lens mass-distance relation obtained from Eq. (8) where θ S = . µ as and ρ = . × − is plotted in Fig. 6. Calibrated ( J , H , K s ) NaCo magnitudes (Sect. 2.3) provide inde-pendently from Eq. (8) further lens mass-distance relations (writ-ten below for J only) through m J ( L ) = M J + D L − + A J , (12) J − Ks ) M J Fig. 5.
Colour-magnitude diagram ( M J , ( J − K s ) ) of the lens. The curvesare a set of isochrones from 2 Gyr (in pink) to 8 Gyr (in blue) with solarmetallicity (Bressan et al. 2012). The black cross indicates the range ofcolours and magnitudes explored by the MCMC at the 1- σ level. where m J ( L ) is the lens apparent reddened magnitude of the lens, A J the interstellar absorption (given in Sect. 2.3), and M J thelens absolute magnitude (which is a function of its mass M ).The source ( J , H , K s ) magnitudes are expressed as (e.g., for J ) m J ( S ) = M J + D S − + A J − . A ) , (13)where A = . J , H , K s ) magnitudes are then computed from the previous equa-tions.The absolute magnitudes M J , H , K s are computed using theisochrones by Bressan et al. (2012) for both the source and lens.For the source we use the same isochrone as in Sect. 4.1. Forthe lens, we assume an age of 2 . Z (cid:12) ± . M and distance D L asfitting parameters. The observed magnitudes serve as Gaussianprior distributions with standard deviation equal to the magni-tudes error bars; they are shown as filled curves in Fig. 7. In thesame figure, posterior distributions for the resulting magnitudes(lens, and source + lens) are shown in solid and dashed lines re-spectively. The final lens mass-distance relations are plotted inFig. 6. It can be seen that while in principle three relations areobtained, they are very strongly correlated and thus only corre-spond to one e ff ective independent mass-distance relation. In principle, when parallax is measured, a further independentlens mass-distance relation can be obtained by combining Eq. (7)with Eq. (6), M = π rel π κ , (14)where π E is derived from the light curve modelling. Neverthe-less, as discussed in Sect. 3.6, the parallax is degenerate with Article number, page 8 of 16. Ranc et al.: MOA-2007-BLG-197: Exploring the brown dwarf desert D L (kpc)0.60.70.80.91.01.1 M / M fl c o l o r s s o u r c e s i z e Fig. 6.
Lens mass-distance relations derived from the source size ρ (1- σ around the best value shown by the green shadow limited by the dashedlines) and NaCo ( J , H , K s ) colours constrains (respectively yellow, or-ange, red from top to bottom below the label “colours”). The blue con-tours (1 − σ ) represent the joint posterior probability density P ( M , D L )from the MCMC run. den s i t y JHKs
Fig. 7.
Probability densities of NaCo ( J , H , K s ) magnitudes, not cor-rected for interstellar extinction. Filled curves are Bayesian Gaussianpriors based on the NaCo measurements, which are compared to pos-terior distributions (solid lines). The dotted posterior distributions arethose of the lens magnitudes alone ( i.e. , disentangled from the source;respectivement J , H , K s from the right to the left). the lens orbital motion, which prevent us from using this con-straint. We however plot on Fig. 6 the typical behaviour of themass-distance relation obtained from parallax measurements, if π E had been measured. We discuss this problem further below. We combined the di ff erent mass-distance relations discussed inthe previous sections (and shown in Fig. 6) in a MCMC min-imisation process to recover the lens mass M and the observer-lens distance D L . We use the measurement and error bars for ρ ,( J , H , K s ) and π E to build up Gaussian priors for the Bayesiananalysis, and flat (uninformative) priors for M and D L . The val-ues of the parameters correspond to the solution u >
0, asdiscussed in Sect. 3.6. We used the convergence criterion ofGeweke (1992) to stop the MCMC and compute the posteriorprobability densities.As seen in Fig. 6, in principle this problem is over-constrained, with three relations for only two fitting parame-ters. This enabled us to check the consistency of the di ff erent measurements, and investigate further the degeneracy betweenparallax and lens orbital motion, which prevents π E from beingused as a constraint. We first noticed a clear discrepancy betweenthe value of π E derived from the fit (the prior) and the poste-rior value. This pointed out a strong tension between the threeconstraints from parallax, source size and infrared colours. Wethen successively removed the parallax, source size or coloursconstraints from the MCMC runs. Without the source size con-straint, a model with parallax values as large as π E ∼ . D L ∼ . θ E ∼ . ρ ∼ . × − ). This value of ρ is manysigma away from that measured from the light curve modelling.Such a di ff erence is very unlikely given the very strong con-straint on ρ obtained from the caustic exit modelling. This there-fore confirmed previous concerns that in this case, the degen-eracy between parallax and lens orbital motion does not allowus to use the parallax mass-distance relation. Consequently, theparallax constraints are removed from the MCMC to derived thefinal values for M and D L , thus constrained by the source sizeand the colours.The final values for M and D L are given in Table 4, with thecorrelation plot shown in Fig. 6. We also compute the mass ofthe lens companion, m BD = qM , and find m BD = ± J .The host mass is 0 . ± .
04 M (cid:12) . The companion is thus a browndwarf orbiting a solar-type star.Physical parameter [unit] ValueLens mass, M [M (cid:12) ] 0 . ± . (cid:12) ] 0 . ± . m BD [M J ] 41 ± a ⊥ [AU] 4 . ± . D L [kpc] 4 . ± . D S [kpc] 8 . ± . θ S [ µ as] 0 . ± . θ E [mas] 0 . ± . v ⊥ [km.s − ] 80 ± π E (calculated) [mas] 0 . ± . γ (new fit) [year − ] 0 . ± . β . ± . Table 4.
Physical parameters of MOA-2007-BLG-197L and its com-panion.
We finally perform additional consistency checks on theoverall parameters of MOA-2007-BLG-197L. First, we computethe projected lens-source relative velocity v ⊥ = θ E D L t E , (15)and find v ⊥ (cid:39)
80 km.s − , which is in very good agreement withprobability densities predicted by Dominik (2006) for the de-rived values of t E and D L . Moreover and as a supplementarycheck, we computed the probability distribution of π E from thedistributions of M and D L using Eq. (14), and derived its maxi-mum a posteriori (MAP) value. We then ran again the light curvemodelling with this value of π E kept fixed. For the overall consis-tency, all the parameters are fixed as well, except ˙ s and ˙ α (valuesare given in Table 3, model with u >
0) which yields the valueof the orbital motion parameter γ (see Table 4). From this, we Article number, page 9 of 16 & A proofs: manuscript no. draft compute β = (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) E kin , ⊥ E pot , ⊥ (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) = c π E s γ θ E ( π E + π S /θ E ) , (16)the ratio of the apparent kinetic to potential energy for the bi-nary lens orbit projected onto the plane of the sky (An et al.2002). Gravitationally bound systems should exhibit 0 < β < β = . π S = AU / D S , wefind β (cid:39) .
08, which is a value consistent with a bound sys-tem. In contrast, high parallax values of e.g., π E = . β (cid:39) . × − . As argued by Batista et al.(2011), a scenario with β (cid:28)
5. MOA-2007-BLG-197Lb in the brown dwarflandscape
While around 1900 exoplanets have been detected so far , lessthan a hundred brown dwarfs orbiting stars are known today. Thelack of brown dwarf companions to solar-type stars was noticedearly after the first exoplanets detections, and referred to as a“brown dwarf desert”. Using the radial velocity method, Marcy& Butler (2000) noted that at tight orbital separations ( a < J represented only a very lowfraction of the detected objects. This was not expected from therelatively high frequency ( ∼ . + . − . % for 13 −
75 M J companions located in the range25 −
250 AU from the Gemini Deep Planet Survey. Similarly,Metchev & Hillenbrand (2009) derived a frequency of 3 . ± . − ∼ −
10 at wide separations. Luhman et al. (2007) foundthat this ratio is comparable to the relative abundance of starsto substellar objects when they are found single, either in starforming regions or in the solar neighbourhood.The upper panel of Fig. 8 is a mass vs. period diagramwhich diplays the known brown dwarf companions of solar-type stars detected through microlensing, radial velocimetry,transit and direct imaging. For radial velocimetry and tran-sit, we included objects from Ma & Ge (2014) catalogue with(minimum) masses in the range 13 −
74 M J and orbital peri-ods below 2 × d. Furthermore, we have excluded objectswith mass uncertainties above 25 M J , and deleted (false posi-tive) TYC 1240-945-1. Microlensing brown dwarfs are shown asgreen points, they are: MOA-2011-BLG-149 and OGLE-2011-BLG-0172 / MOA-2011-BLG-104 (Shin et al. 2012b), MOA-2010-BLG-073 (Street et al. 2013), OGLE-2013-BLG-0578(Park et al. 2015) as well as MOA-2007-BLG-197 (this paper).For consistency with Doppler and transit data, we did not in-clude MOA-2009-BLG-411 (Bachelet et al. 2012) which has alarge uncertainty in the mass. In the case of microlensing objectsfor which only projected separations a ⊥ were measured (all ob-jects in this case), we estimate the (physical) semi-major axis a http://exoplanet.eu Period (days)010203040506070 M a ss ( M J ) Period (days)010203040506070 M a ss ( M J ) . . . . . . . . Fig. 8.
The upper panel shows a mass-period diagram with browndwarfs companions detected through radial velocity, transit and directimaging (blue filled circles for measured masses, and open circles forminimum masses; list adapted from Ma & Ge 2014), and microlensing(green diamonds). For reference, exoplanets detected so far are also dis-played (small black circles, http://exoplanets.org ). The red dot-ted line indicates the global radial velocity completeness limit, whilethe red dashed line marks the region above which data are included toperform the non-parametric, two-dimensional probability density distri-bution shown in the lower panel. as the median of the probability distribution of Gould & Loeb(1992), which we find to be equal to a = (2 / √ a ⊥ ≈ . a ⊥ .Kepler’s third law is then used to yield the estimated period. Theerror bar on measured a ⊥ is propagated to a following the previ-ous equation, and the error bar on the period is obtained througha MCMC run including uncertainties on a and primary mass M (Gaussian distributions are assumed).As seen in Fig. 8, the distribution of brown dwarfs is not uni-form, in particular it exhibits an increasing frequency of objectswith increasing orbital period. Furthermore, Ma & Ge (2014)argue that the driest part of the brown dwarf desert seems tobe confined within a region at close separation, namely within P <
100 d and for masses within 30 −
55 M J for Sun-like hoststars. They subsequently split the objects into two distinct popu-lations, whether their mass is higher or lower than 42 . J : themore massive brown dwarfs would mainly be the outcome ofgravitational fragmentation and collapse of a molecular cloud(star-like formation scenario, corroborated by an eccentricitydistribution similar to binary stars), while brown dwarfs below42 . J would mainly result from gravitational instability withinthe proto-planetary disk. But other authors such as Guillot et al.(2012), however, argue that the depletion of objects at tight or-bits may as well be explained by a loss of an initial population Article number, page 10 of 16. Ranc et al.: MOA-2007-BLG-197: Exploring the brown dwarf desert of close-in brown dwarfs due to tidal interactions with their hoststars. In this scenario, close-in, massive objects lose angular mo-mentum due to the slower rotation of the star relative to the plan-ets orbital motion, spiral in and fall into the star. This e ff ect ispredicted to peak for G-dwarf primaries and should not be im-portant for earlier-type stars, which is supported by the detectionof close-in brown dwarfs around F-type stars.Di ff erent mechanisms may overlap to shape the browndwarfs landscape, and lead to a more complex structure thanpreviously discussed. To analyse it further, we performed a non-parametric, two-dimensional probability density distribution fitto the data, only for objects above the red dashed line ( i.e. , abovethe radial velocity completeness limit, based on Mayor et al.(2011), and marked by the red dotted line in Fig. 8). The prob-ability density estimation is based on Scott (1992); in practicewe used a Gaussian kernel, and follow Silverman (1986) rule toestimate the bandwidth parameter. The resulting probability den-sity is shown in the lower panel of Fig. 8. We used two di ff erentmethods to compute the bandwidth parameter, Silverman (1986)or Scott (1992), and found that the resulting probability densityis relatively stable, even if a few data points are removed fromsparsely sampled regions.The first striking feature of the density profile (lower panelof Fig. 8) is a region of depletion of objects at intermediatemasses ( M ∼ −
60 M J ) and short orbital periods ( P (cid:46)
30 d).This matches the region referred to as the driest part of thebrown dwarf desert according to Ma & Ge (2014). Second, anaccumulation of objects can be seen around P ∼
500 d and M ∼
20 M J (following the apparent trend observed for giantplanets, black data points in Fig. 8). Third, we find another de-pletion of objects at long orbital periods ( P (cid:38)
500 d) and highmasses ( M (cid:38)
50 M J ). Since the brown dwarf sample is drawnfrom various surveys (mainly from radial velocities), the inter-pretation of these features should be taken with caution. Al-though all brown dwarfs in Fig. 8 are chosen above the radial ve-locity completeness limit from Mayor et al. (2011), it is not guar-anteed that these objects are not a ff ected by observational biases.In particular, a degeneracy between mass and period is increas-ingly a ff ecting very long-period brown dwarfs, and the di ff erentsurveys should be corrected from their sample size. Hence, whilea thorough analysis of all these factors is necessary to assess theexact shape of the brown dwarfs distribution, the gross featuresemerging from the lower panel of Fig. 8 may well be real. If wesplit the density profile into two regions of masses above and be-low 42 . J as discussed by Ma & Ge (2014), the distribution ofhigh-mass objects can be seen as shifted towards shorts orbitalperiods ( P ∼
30 d), while less massive objects appear to pile upat longer orbital periods ( P ∼
500 d). This supports the claimof Ma & Ge (2014) that massive objects would accumulate atshort periods as a result of gravitational collapse of a molecularcloud, contrary to less-massive objects built up by gravitationalinstability in the disk which would accumulate at longer periods.Nevertheless, the depletion at intermediate masses and short pe-riods would as well be a ff ected by a star-engulfing mechanismadvocated by Guillot et al. (2012), in particular because almostall brown dwarfs included here orbit Sun-like stars, for whichthis e ff ect peaks.The distribution of brown dwarfs as a function of mass andperiod still remains uncertain because of a lack of detections.It is thus di ffi cult to distinguish between the di ff erent mecha-nisms which shape the brown dwarf desert. Moreover, these de-tections are mostly objects orbiting Sun-like stars, which makesit di ffi cult to study their distribution as a function of host starmass. While the MOA-2007-BLG-197L companion orbits a G-K dwarf host, microlensing hosts are most frequently M-K dwarfs.Hence, future microlensing surveys will provide unique infor-mation on the brown dwarf distribution for low-mass hosts, thuso ff ering a complementary mass bin to other methods.
6. Summary and prospects
We have presented MOA-2007-BLG-197Lb, the first browndwarf discovered around a Sun-like star through gravitationalmicrolensing. The system is located at 4 . ± . ± J andwas observed at a projected distance of 4 . ± . ff erent (and perhaps competitive) formation or de-struction mechanisms. While it seems di ffi cult with the currentdata set to distinguish observationally which are the dominantmechanisms, an answer to this question appears to within thereach of further observations in the near to mid-term future.Gravitational microlensing is an exceptional tool to detectbrown dwarfs as free-floating objects, companions to stars or asbrown dwarfs binaries. It has a unique sensitivity to detect browndwarfs companions to stars of any type, in particular at long or-bital periods. Recent advances in using networks of robotic tele-scopes (e.g., Tsapras et al. 2009) will provide in a near futurean order of magnitudes more brown dwarfs detections throughmicrolensing. Future microlensing space missions (Penny et al.2013; Yee et al. 2014; Beaulieu et al. 2010) also carry importantpromises for providing unique information on the populations ofbrown dwarfs in their di ff erent configurations. Acknowledgements.
A.C. acknowledges financial support from the EmergenceUPMC 2012 grant. C.R. and A.C. are grateful to Bo Ma for providing us withthe brown dwarfs catalogue used in Ma & Ge (2014). We especially thank theUniversity of Tasmania for granting us access to their TPAC supercomputerfacilities where part of the calculations were carried out. Work by C.H. wassupported by Creative Research Initiative Program (2009-0081561) of NationalResearch Foundation of Korea. K.H., M.D. and M.H. are supported by NPRPgrant NPRP-09-476-1-78 from the Qatar National Research Fund (a memberof Qatar Foundation). M.H. acknowledges support from the Villum foundation.S.D. is supported by “the Strategic Priority Research Program- The Emergenceof Cosmological Structures” of the Chinese Academy of Sciences (grant No.XDB09000000).
References
Alard, C. 2000, A&AS, 144, 363Alard, C. & Lupton, R. H. 1998, ApJ, 503, 325Albrow, M. D., Beaulieu, J.-P., Caldwell, J. A. R., et al. 1999a, ApJ, 522, 1022Albrow, M. D., Beaulieu, J.-P., Caldwell, J. A. R., et al. 1999b, ApJ, 522, 1011Albrow, M. D., Horne, K., Bramich, D. M., et al. 2009, MNRAS, 397, 2099An, J. H., Albrow, M. D., Beaulieu, J.-P., et al. 2002, ApJ, 572, 521Bachelet, E., Fouqué, P., Han, C., et al. 2012, A&A, 547, A55Batista, V., Gould, A., Dieters, S., et al. 2011, A&A, 529, A102Beaulieu, J. P., Bennett, D. P., Batista, V., et al. 2010, in Astronomical Society ofthe Pacific Conference Series, Vol. 430, Pathways Towards Habitable Planets,ed. V. Coudé du Foresto, D. M. Gelino, & I. Ribas, 266Bennett, D. P. 2010, ApJ, 716, 1408Bonfils, X., Delfosse, X., Udry, S., et al. 2013, A&A, 549, A109Bozza, V. 2010, MNRAS, 408, 2188Bozza, V., Dominik, M., Rattenbury, N. J., et al. 2012, MNRAS, 424, 902Bressan, A., Marigo, P., Girardi, L., et al. 2012, MNRAS, 427, 127Burrows, A., Hubbard, W. B., Lunine, J. I., & Liebert, J. 2001, Reviews of Mod-ern Physics, 73, 719Carroll, B. W. & Ostlie, D. A. 2006, An introduction to modern astrophysics andcosmology (Addison-Wesley)Cassan, A. 2008, A&A, 491, 587Cassan, A., Beaulieu, J. P., Brillant, S., et al. 2004, A&A, 419, L1
Article number, page 11 of 16 & A proofs: manuscript no. draft
Cassan, A., Beaulieu, J.-P., Fouqué, P., et al. 2006, A&A, 460, 277Cassan, A., Horne, K., Kains, N., Tsapras, Y., & Browne, P. 2010, A&A, 515,A52Cassan, A., Kubas, D., Beaulieu, J.-P., et al. 2012, Nature, 481, 167Choi, J.-Y., Han, C., Udalski, A., et al. 2013, ApJ, 768, 129Claret, A. & Bloemen, S. 2011, A&A, 529, A75Deleuil, M., Deeg, H. J., Alonso, R., et al. 2008, A&A, 491, 889Devillard, N. 1999, in Astronomical Society of the Pacific Conference Series,Vol. 172, Astronomical Data Analysis Software and Systems VIII, ed. D. M.Mehringer, R. L. Plante, & D. A. Roberts, 333Díaz, R. F., Damiani, C., Deleuil, M., et al. 2013, A&A, 551, L9Diolaiti, E., Bendinelli, O., Bonaccini, D., et al. 2000, in Presented at the Societyof Photo-Optical Instrumentation Engineers (SPIE) Conference, Vol. 4007,Proc. SPIE Vol. 4007, p. 879-888, Adaptive Optical Systems Technology, Pe-ter L. Wizinowich; Ed., ed. P. L. Wizinowich, 879–888Dominik, M. 2006, MNRAS, 367, 669Dominik, M. 2007, MNRAS, 377, 1679Dong, S., DePoy, D. L., Gaudi, B. S., et al. 2006, ApJ, 642, 842Dong, S. et al. 2009, ApJ, 698, 1826Duquennoy, A. & Mayor, M. 1991, A&A, 248, 485Geweke, J. 1992, in Bernardo, J. M., Berger, J. O., Dawid, A. P. and Smith,A. F. M. (eds), Bayesian Statistics (Oxford University Press, New York), 169–193Gould, A. 2004, ApJ, 606, 319Gould, A. 2008, ApJ, 681, 1593Gould, A., Dong, S., Bennett, D. P., et al. 2010a, ApJ, 710, 1800Gould, A., Dong, S., Gaudi, B. S., et al. 2010b, ApJ, 720, 1073Gould, A. & Gaucherel, C. 1997, ApJ, 477, 580Gould, A. & Loeb, A. 1992, ApJ, 396, 104Gould, A., Udalski, A., Monard, B., et al. 2009, ApJ, 698, L147Guillot, T., Lin, D. N. C., & Morel, P. 2012, in American Astronomical SocietyMeeting Abstracts, Vol. 220, American Astronomical Society Meeting Ab-stracts arXiv:1109.2497 ]McCarthy, C. & Zuckerman, B. 2004, AJ, 127, 2871Metchev, S. A. & Hillenbrand, L. A. 2009, ApJS, 181, 62Mollière, P. & Mordasini, C. 2012, A&A, 547, A105Moutou, C., Bonomo, A. S., Bruno, G., et al. 2013, A&A, 558, L6Nataf, D. M., Gould, A., Fouqué, P., et al. 2013, ApJ, 769, 88Park, H., Udalski, A., Han, C., et al. 2015, ArXiv e-prints [ arXiv:1503.03197 ]Penny, M. T., Kerins, E., Rattenbury, N., et al. 2013, MNRAS, 434, 2Persson, S. E., Murphy, D. C., Krzeminski, W., Roth, M., & Rieke, M. J. 1998,AJ, 116, 2475Sahlmann, J., Ségransan, D., Queloz, D., et al. 2011, A&A, 525, A95Schechter, P. L., Mateo, M., & Saha, A. 1993, PASP, 105, 1342Scott, D. W. 1992, Multivariate Density Estimation: Theory, Practice, and Visu-alization (John Wiley & Sons, New York, Chicester)Shin, I.-G., Han, C., Choi, J.-Y., et al. 2012a, ApJ, 755, 91Shin, I.-G., Han, C., Gould, A., et al. 2012b, ApJ, 760, 116Silverman, B. W. 1986, Density Estimation for Statistics and Data Analysis(Chapman and Hall, London)Skowron, J., Udalski, A., Gould, A., et al. 2011, ApJ, 738, 87Street, R. A., Choi, J.-Y., Tsapras, Y., et al. 2013, ApJ, 763, 67Sumi, T., Kamiya, K., Bennett, D. P., et al. 2011, Nature, 473, 349Tsapras, Y. et al. 2009, AN, 330, 4Yee, J. C., Albrow, M., Barry, R. K., et al. 2014, ArXiv e-prints[ arXiv:1409.2759 ]Zub, M., Cassan, A., Heyrovský, D., et al. 2011, A&A, 525, A15 Sorbonne Universités, UPMC Univ Paris 6 et CNRS, UMR 7095,Institut d’Astrophysique de Paris, 98 bis bd Arago, 75014 Paris,France University of Canterbury, Dept. of Physics and Astronomy, PrivateBag 4800, 8020 Christchurch, New Zealand Institute of Natural and Mathematical Sciences, Massey Univer-sity, Private Bag 102-904, North Shore Mail Centre, Auckland, NewZealand Department of Physics, University of Notre Dame, Notre Dame, IN46556, USA SUPA, School of Physics & Astronomy, North Haugh, Universityof St Andrews, KY16 9SS, Scotland, UK Kavli Institute for Astronomy and Astrophysics, Peking University,Yi He Yuan Road 5, Hai Dian District, Beijing 100871, China IRAP, CNRS - Université de Toulouse, 14 av. E. Belin, F-31400Toulouse, France CFHT Corporation, 65-1238 Mamalahoa Hwy, Kamuela, Hawaii96743, USA Department of Astronomy, Ohio State University, 140 W. 18th Ave.,Columbus, OH 43210, USA School of Math and Physics, University of Tasmania, Private Bag37, GPO Hobart, 7001 Tasmania, Australia Niels Bohr Institutet, Københavns Universitet, Juliane Maries Vej30, 2100 København Ø, Denmark Space Telescope Science Institute, 3700 San Martin Drive, Balti-more, MD 21218, USA South African Astronomical Observatory, PO Box 9, Observatory7935, South Africa Department of Earth and Space Science, Graduate School of Sci-ence, Osaka University, Toyonaka, Osaka 560-0043, Japan Qatar Environment and Energy Research Institute, Qatar Founda-tion, P.O. Box 5825, Doha, Qatar Department of Physics, University of Rijeka, Radmile Matej vci´c 2,51000 Rijeka, Croatia Technical University of Vienna, Department of Computing,WiednerHauptstrasse 10, 1040 Wien, Austria Department of Physics, Chungbuk National University, Cheongju371-763, Korea Department of Physics and Astronomy, San Francisco State Uni-versity, 1600 Holloway Avenue, San Francisco, CA 94132, USA Korea Astronomy and Space Science Institute, 776 Daedukdae-ro,Daejeon, Korea Las Cumbres Observatory Global Telescope Network, 6740 Cor-tona Drive, suite 102, Goleta, CA 93117, USA Astronomisches Rechen-Institut, Zentrum für Astronomie der Uni-versität Heidelberg (ZAH), Mönchhofstraße 12-14, 69120 Heidel-berg, Germany Perth Observatory, Walnut Road, Bickley, Perth 6076, Australia International Centre for Radio Astronomy Research, Curtin Univer-sity, Bentley, WA 6102, Australia Solar-Terrestrial Environment Laboratory, Nagoya University,Nagoya 464-8601, Japan Okayama Astrophysical Observatory, National Astronomical Ob-servatory of Japan, 3037-5 Honjo, Kamogata, Asakuchi, Okayama719-0232, Japan Nagano National College of Technology, Nagano 381-8550, Japan Department of Physics, University of Auckland, Private Bag 92019,Auckland, New Zealand Tokyo Metropolitan College of Aeronautics, Tokyo 116-8523,Japan School of Chemical and Physical Sciences, Victoria University,Wellington, New Zealand Institute of Information and Mathematical Sciences, Massey Uni-versity at Albany, Private Bag 102904, North Shore 0745, Auckland,New Zealand Mt. John University Observatory, P.O. Box 56, Lake Tekapo 8770,New Zealand Department of Physics, University of Auckland, Private Bag 92019,Auckland, New Zealand Department of Physics, Faculty of Science, Kyoto Sangyo Univer-sity, 603-8555, Kyoto, Japan PLANET / RoboNET Collaboration MOA Collaboration µ FUN CollaborationArticle number, page 12 of 16. Ranc et al.: MOA-2007-BLG-197: Exploring the brown dwarf desert . . t − ρ / − α q / − s t E u / − CD F . . u / − CD F . . t E CD F .
125 1 . s CD F .
80 4 . q / − CD F .
90 0 . α CD F . . ρ/ − CD F Fig. 9.
Correlations between the parameters derived from ESBL’s model discussed in Sect. 3.1. The red point refers to the best-fitting modelobtained. Article number, page 13 of 16 & A proofs: manuscript no. draft . . t − − π E , E π E , N ρ / − α q / − s t E u / − CD F . . u / − CD F . . t E CD F .
134 1 . s CD F .
50 4 . q / − CD F .
80 0 . α CD F ρ/ − CD F . . π E , N CD F − . . π E , E CD F Fig. 10.
Idem for ESBL + P’s model.Article number, page 14 of 16. Ranc et al.: MOA-2007-BLG-197: Exploring the brown dwarf desert − t − − ˙ α ˙ s ρ / − α q / − s t E u / − CD F . . u / − CD F
76 80 t E CD F .
15 1 .
16 1 . s CD F . . q / − CD F .
76 0 . α CD F . . ρ/ − CD F .
10 0 . ˙s CD F − . . ˙ α CD F Fig. 11.
Idem for ESBL + LOM’s model. Article number, page 15 of 16 & A proofs: manuscript no. draft − . − . t − ˙ α − ˙ s − − π E , E − π E , N ( ρ − ρ ) / − α q / − s t E u / − CD F . . u / − CD F
80 82 t E CD F .
12 1 . s CD F .
71 4 . q / − CD F .
960 0 . α CD F ( ρ − ρ ) / − CD F − . . π E , N CD F − . − . π E , E CD F − .
06 0 . ˙s CD F . . ˙ α CD F Fig. 12.
Idem for ESBL + P + LOM’s model ( u >
0) with ρ (cid:48) = . × −4