KMT-2016-BLG-1836Lb: A Super-Jovian Planet From A High-Cadence Microlensing Field
Hongjing Yang, Xiangyu Zhang, Kyu-Ha Hwang, Weicheng Zang, Andrew Gould, Tianshu Wang, Shude Mao, Michael D. Albrow, Sun-Ju Chung, Cheongho Han, Youn Kil Jung, Yoon-Hyun Ryu, In-Gu Shin, Yossi Shvartzvald, Jennifer C. Yee, Wei Zhu, Matthew T. Penny, Pascal Fouqué, Sang-Mok Cha, Dong-Jin Kim, Hyoun-Woo Kim, Seung-Lee Kim, Chung-Uk Lee, Dong-Joo Lee, Yongseok Lee, Byeong-Gon Park, Richard W. Pogge
DD RAFT VERSION D ECEMBER
25, 2019Typeset using L A TEX default style in AASTeX62
KMT-2016-BLG-1836Lb: A Super-Jovian Planet From A High-Cadence Microlensing Field H ONGJING Y ANG ,
1, 2 X IANGYU Z HANG , K YU -H A H WANG , W EICHENG Z ANG , A NDREW G OULD ,
4, 5 T IANSHU W ANG , S HUDE M AO ,
1, 6 M ICHAEL
D. A
LBROW , S UN -J U C HUNG ,
3, 8 C HEONGHO H AN , Y OUN K IL J UNG , Y OON -H YUN R YU , I N -G U S HIN , Y OSSI S HVARTZVALD , J ENNIFER
C. Y EE , W EI Z HU , M ATTHEW
T. P
ENNY , P ASCAL F OUQU ´ E ,
14, 15 S ANG -M OK C HA ,
3, 16 D ONG -J IN K IM , H YOUN -W OO K IM , S EUNG -L EE K IM ,
3, 8 C HUNG -U K L EE ,
3, 8 D ONG -J OO L EE , Y ONGSEOK L EE ,
3, 16 B YEONG -G ON P ARK ,
3, 17
AND R ICHARD
W. P
OGGE Department of Astronomy and Tsinghua Centre for Astrophysics, Tsinghua University, Beijing 100084, China Department of Astronomy, Xiamen University, Xiamen 361005, China Korea Astronomy and Space Science Institute, Daejon 34055, Republic of Korea Max-Planck-Institute for Astronomy, K¨onigstuhl 17, 69117 Heidelberg, Germany Department of Astronomy, Ohio State University, 140 W. 18th Ave., Columbus, OH 43210, USA National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100101, China University of Canterbury, Department of Physics and Astronomy, Private Bag 4800, Christchurch 8020, New Zealand University of Science and Technology, Korea, (UST), 217 Gajeong-ro Yuseong-gu, Daejeon 34113, Republic of Korea Department of Physics, Chungbuk National University, Cheongju 28644, Republic of Korea IPAC, Mail Code 100-22, Caltech, 1200 E. California Blvd., Pasadena, CA 91125, USA Center for Astrophysics | Havard & Smithsonian, 60 Garden St.,Cambridge, MA 02138, USA Canadian Institute for Theoretical Astrophysics, University of Toronto, 60 St George Street, Toronto, ON M5S 3H8, Canada Department of Astronomy, The Ohio State University, 140 W. 18th Avenue, Columbus, OH 43210, USA CFHT Corporation, 65-1238 Mamalahoa Hwy, Kamuela, Hawaii 96743, USA Universit´e de Toulouse, UPS-OMP, IRAP, Toulouse, France School of Space Research, Kyung Hee University, Yongin, Kyeonggi 17104, Republic of Korea Korea University of Science and Technology, 217 Gajeong-ro, Yuseong-gu, Daejeon 34113, Republic of Korea
ABSTRACTWe report the discovery of a super-Jovian planet in the microlensing event KMT-2016-BLG-1836, whichwas found by the Korea Microlensing Telescope Network’s high-cadence observations ( Γ ∼ − ). Theplanet-host mass ratio q ∼ . . A Bayesian analysis indicates that the planetary system is composed of asuper-Jovian M planet = 2 . +1 . − . M J planet orbiting an M or K dwarf M host = 0 . +0 . − . M (cid:12) , at a distanceof D L = 7 . +0 . − . kpc. The projected planet-host separation is . +1 . − . AU, implying that the planet is locatedbeyond the snowline of the host star. Future high-resolution images can potentially strongly constrain the lensbrightness and thus the mass and distance of the planetary system. Without considering detailed detectionefficiency, selection or publication biases, we find a potential “mass ratio desert” at − . (cid:46) log q (cid:46) − . forthe 31 published KMTNet planets. INTRODUCTIONSince the first robust detection of a microlens planet in 2003 (Bond et al. 2004), more than 70 extrasolar planets have beendetected by the microlensing method (Mao & Paczynski 1991; Gould & Loeb 1992). Unlike other methods that rely on the lightfrom the host stars, the microlensing method uses the light from a background source deflected by the gravitational potentialof an aligned foreground planetary system. Thus, microlensing can detect planets around all types of stellar objects at variousGalactocentric distances (e.g., Calchi Novati et al. 2015; Zhu et al. 2017).The typical Einstein timescale t E for microlensing events is about days, and the half-duration of a planetary perturbation(Gould & Loeb 1992) is t p ∼ t E √ q → q/ − ) / hr , (1) Corresponding author: Weicheng [email protected] http://exoplanetarchive.ipac.caltech.edu as of 2019 July 17 a r X i v : . [ a s t r o - ph . E P ] D ec Y ANG ET AL .where q is the planet-host mass ratio. Assuming that about 10 data points are needed to cover the planetary perturbation, a cadenceof Γ ∼ − would be required to discover “Neptunes” and Γ ∼ − would be required to detect Earths (Henderson et al.2014). In addition, because the optical depth to microlensing toward the Galactic bulge is only τ ∼ − (Sumi et al. 2013;Mr´oz et al. 2019), a large area (10–100 deg ) must be monitored to find a large number of microlensing events and thus planetaryevents.For many years, most microlensing planets were discovered by a combination of wide-area surveys for finding microlensingevents and intensive follow-up observations for capturing the planetary perturbation (Gould & Loeb 1992). This strategy mainlyfocused on high-magnification events (e.g., Udalski et al. 2005) which intrinsically have high sensitivity to planets (Griest &Safizadeh 1998). Another strategy to find microlensing planets is to conduct wide-area, high-cadence surveys toward the Galacticbulge. The Korea Microlensing Telescope Network (KMTNet, Kim et al. 2016), continuously monitors a broad area at relativelyhigh-cadence toward the Galactic bulge from three 1.6 m telescopes equipped with 4 deg FOV cameras at the Cerro TololoInter-American Observatory (CTIO) in Chile (KMTC), the South African Astronomical Observatory (SAAO) in South Africa(KMTS), and the Siding Spring Observatory (SSO) in Australia (KMTA). It aims to simultaneously find microlensing events andcharacterize the planetary perturbation without the need for follow-up observations.In its 2015 commissioning season, KMTNet followed this strategy and observed four fields at a very high cadence of
Γ =6 hr − . Beginning in 2016, KMTNet monitors a total of (3, 7, 11, 2) fields at cadences of Γ ∼ (4 , , . , .
2) hr − . See Figure12 of Kim et al. (2018a). This new strategy mainly aims to support Spitzer microlensing campaign (Gould et al. 2013, 2014,2015a,b, 2016, 2018) and find more planets over a much broader area. So far, this new strategy has detected planets in 2016–2018 , including an Earth-mass planet found by a cadence of Γ ∼ − (Shvartzvald et al. 2017), and a super-Jovian planetfound by a cadence of Γ ∼ . − (Ryu et al. 2019a).Here we report the analysis of a super-Jovian planet KMT-2016-BLG-1836Lb, which was detected by KMTNet’s Γ ∼ − observations. The paper is structured as follows. In Section 2, we introduce the KMTNet observations of this event. We thendescribe the light curve modeling process in Section 3, the properties of the microlens source in Section 4, and the physicalparameters of the planetary system in Section 5. Finally, we discuss the mass ratio distributions of 31 published KMTNet planetsin Section 6. OBSERVATIONSKMT-2016-BLG-1836 was at equatorial coordinates ( α, δ ) J2000 = (17:53:00.08, − :02:26.70), corresponding to Galacticcoordinates ( (cid:96), b ) = ( − . , − . . It was found by applying the KMTNet event-finding algorithm (Kim et al. 2018a) to the2016 KMTNet survey data (Kim et al. 2018b), and the apparently amplified flux of a KMTNet catalog-star I = 19 . ± . derived from the OGLE-III star catalog (Szyma´nski et al. 2011) led to the detection of this microlensing event. KMT-2016-BLG-1836 was located in two slightly offset fields BLG02 and BLG42, with a nominal combined cadence of Γ = 4 hr − . Infact, the cadence of KMTA and KMTS was altered to Γ = 6 hr − from April 23 to June 16 ( < HJD (cid:48) < , HJD (cid:48) =HJD − ) to support the Kepler K2 C9 campaign (Gould & Horne 2013; Henderson et al. 2016; Kim et al. 2018c). Thishigher cadence block came toward the end of the event and after the planetary perturbation. The majority of observations weretaken in the I -band, with about of the KMTC images and of the KMTS images taken in the V -band for the colormeasurement of microlens sources. All data for the light curve analyses were reduced using the pySIS software package (Albrowet al. 2009), a variant of difference image analysis (Alard & Lupton 1998). For the source color measurement and the color-magnitude diagram (CMD), we additionally conduct pyDIA photometry for the KMTC02 data, which simultaneously yieldsfield-star photometry on the same system as the light curve. LIGHT CURVE ANALYSISFigure 1 shows the KMT-2016-BLG-1836 data together with the best-fit model. The light curve shows a bump (
HJD (cid:48) ∼ )after the peak of an otherwise normal Paczy´nski (1986) point-lens light curve. The bump could be a binary-lensing (2L1S)anomaly that is generally produced by caustic-crossing (e.g., Street et al. 2016) or cusp approach (e.g., Shvartzvald et al. 2017) ofthe lensed star, or the second peak of a binary-source event (1L2S), which is the superposition of two point-lens events generatedby two source stars (Gaudi 1998; Han 2002). Thus, we perform both binary-lens and binary-source analyses in this section. OGLE-2016-BLG-0263Lb (Han et al. 2017a), OGLE-2016-BLG-0596Lb (Mr´oz et al. 2017), OGLE-2016-BLG-0613Lb (Han et al. 2017b), OGLE-2016-BLG-1067Lb (Calchi Novati et al. 2019), OGLE-2016-BLG-1190Lb (Ryu et al. 2018), OGLE-2016-BLG-1195Lb (Shvartzvald et al. 2017), OGLE-2016-BLG-1227Lb (Han et al. 2019a), KMT-2016-BLG-0212Lb (Hwang et al. 2018a), KMT-2016-BLG-1107Lb (Hwang et al. 2019), KMT-2016-BLG-1397Lb (Zang et al.2018a), KMT-2016-BLG-1820Lb (Jung et al. 2018a), MOA-2016-BLG-319Lb (Han et al. 2018a), OGLE-2017-BLG-0173Lb (Hwang et al. 2018b), OGLE-2017-BLG-0373Lb (Skowron et al. 2018), OGLE-2017-BLG-0482Lb (Han et al. 2018b), OGLE-2017-BLG-1140Lb (Calchi Novati et al. 2018), OGLE-2017-BLG-1434Lb (Udalski et al. 2018), OGLE-2017-BLG-1522Lb (Jung et al. 2018b), KMT-2017-BLG-0165Lb (Jung et al. 2019a), KMT-2017-BLG-1038Lb (Shinet al. 2019), KMT-2017-BLG-1146Lb (Shin et al. 2019), OGLE-2018-BLG-0532Lb (Ryu et al. 2019c), OGLE-2018-BLG-0596Lb (Jung et al. 2019b), OGLE-2018-BLG-0740Lb (Han et al. 2019d), OGLE-2018-BLG-1011Lbc (Han et al. 2019b), OGLE-2018-BLG-1700Lb (Han et al. 2019c), KMT-2018-BLG-0029Lb(Gould et al. 2019), KMT-2018-BLG-1292Lb (Ryu et al. 2019a), and KMT-2018-BLG-1990Lb (Ryu et al. 2019b). MichaelDAlbrow/pyDIA: Initial Release on Github, doi:10.5281/zenodo.268049
Binary-lens (2L1S) Modeling
A standard binary lens model has seven parameters to calculate the magnification, A ( t ) . Three ( t , u , t E ) of these parametersdescribe a point-lens event (Paczy´nski 1986): the time of the maximum magnification, the minimum impact parameter in unitsof the angular Einstein radius θ E , and the Einstein radius crossing time. The next three ( q , s , α ) define the binary geometry:the binary mass ratio, the projected separation between the binary components normalized to the Einstein radius, and the anglebetween the source trajectory and the binary axis in the lens plane. The last parameter is the source radius normalized by theEinstein radius, ρ = θ ∗ /θ E . In addition, for each data set i , two flux parameters ( f S ,i , f B ,i ) represent the flux of the source starand the blend flux. The observed flux, f i ( t ) , calculated from the model is f i ( t ) = f S ,i A ( t ) + f B ,i . (2)We locate the χ minima by a searching over a grid of parameters ( log s, log q, α ). The grids consist of 21 values equallyspaced between − ≤ log s ≤ , 10 values equally spaced between ◦ ≤ α < ◦ , and 51 values equally spaced between − ≤ log q ≤ . For each set of ( log s, log q, α ), we fix log q , log s , ρ = 0 . , and free t , u , t E , α . We find the minimum χ by Markov chain Monte Carlo (MCMC) χ minimization using the emcee ensemble sampler (Foreman-Mackey et al. 2013).The upper panel of Figure 2 shows the χ distribution in the ( log s, log q ) plane from the grid search, which indicates the distinctminima are within − . ≤ log s ≤ . and − ≤ log q ≤ − . We therefore conduct a denser grid search, which consists of 61values equally spaced between − . ≤ log s ≤ . , 10 values equally spaced between ◦ ≤ α < ◦ , and 41 values equallyspaced between − ≤ log q ≤ − . As a result, we find four distinct minima and label them as “A”, “B”, “C” and “D” in thelower panel of Figure 2. We then investigate the best-fit model with all free parameters. Table 1 shows best-fit parameters ofthe four solutions from MCMC. The MCMC results show that the solution “B” is the best-fit model, while the solution “A” isdisfavored by ∆ χ ∼ . We note that these two solutions are related by the so-called close-wide degeneracy and approximatelytake s ↔ s − (Griest & Safizadeh 1998; Dominik 1999), so we label them by “Close” (solution B, s < ) and “Wide” (solutionA, s > ) in the following analysis. The solutions “C” and “D” are disfavored by ∆ χ ∼ and ∆ χ ∼ , respectively, sowe exclude these two solutions. For both the solutions “Close” and “Wide”, the data are consistent with a point-source modelwithin ∼ σ level, and the upper limit for ρ is . × − for the solution “Close” and . × − for the solution “Wide”. Thebest-fit model curves for the two solutions are shown in Figure 1, and their magnification maps are shown in Figure 3.In addition, we check whether the fit further improves by considering the microlens-parallax effect, π E = π rel θ E µ rel µ rel , (3)where ( π rel , µ rel ) are the lens-source relative (parallax, proper motion), which is caused by the orbital acceleration of Earth(Gould 1992). We also fit u > and u < solutions to consider the “ecliptic degeneracy” (Skowron et al. 2011). To facilitatethe further discussion of these solutions, we label them by C ± or W ± . The letter stands for “Close” ( s < ) or “Wide” ( s > ),while the subscript refers to the sign of u . The addition of parallax to the model does not significantly improve the fit, providingan improvement of ∆ χ < . for the C ± solutions and ∆ χ < . for the W ± solutions. However, we find that the eastcomponent of the parallax vector π E , E is well constrained for all the solutions, while the constraint on the north component π E , N is considerably weaker. Table 2 shows best-fit parameters of the standard binary-lens model, C ± and W ± solutions, and Figure4 shows the likelihood distribution of ( π E , N , π E , E ) from MCMC.3.2. Binary-source (1L2S) Modeling
The total magnification of a binary-source event is the superposition of two point-lens events, A λ = A f ,λ + A f ,λ f ,λ + f ,λ = A + q f,λ A q f,λ , (4) q f,λ = f ,λ f ,λ , (5)where f i ,λ ( i = 1 , ) is the flux at wavelength λ of each source and A λ is total magnification. We search for 1L2S solutions usingMCMC, and the best-fit model is disfavored by ∆ χ ∼ compared to the binary-lens “Wide” model (see Table 3). Figure5 presents their cumulative distribution of χ differences, which shows the χ differences are mainly from ± days from thepeak, rather than outliers. We also consider the microlens-parallax effect, but the improvement is very minor with ∆ χ ∼ . .Thus, we exclude the 1L2S solution. Y ANG ET AL . SOURCE PROPERTIESWe conduct a Bayesian analysis in Section 5 to estimate the physical parameters of the lens systems, which requires theconstraints of the source properties. Thus, we estimate the angular radius θ ∗ and the proper motion of the source in this section.4.1. Color-Magnitude Diagram
To further estimate the angular Einstein radius θ E = θ ∗ /ρ , we estimate the angular radius θ ∗ of the source by locating thesource on a CMD (Yoo et al. 2004). We calibrate the KMTC02 pyDIA reduction to the OGLE-III star catalog (Szyma´nski et al.2011) and construct a V − I versus I CMD using stars within a (cid:48) × (cid:48) square centered on the event (see Figure 6). The red giantclump is at ( V − I, I ) cl = (2 . ± . , . ± . , whereas the source is at ( V − I, I ) S = (2 . ± . , . ± . for the Wide solution and ( V − I, I ) S = (2 . ± . , . ± . for the Close solution. We adopt the intrinsic color andde-reddened magnitude of the red giant clump ( V − I, I ) cl , = (1 . , . from Bensby et al. (2013) and Nataf et al. (2016),and then we derive the intrinsic color and de-reddened brightness of the source as ( V − I, I ) S , = (0 . ± . , . ± . for the Wide solution and ( V − I, I ) S , = (0 . ± . , . ± . for the close solution. These values suggest the sourceis either a late-G or early-K type main-sequence star. Using the color/surface-brightness relation for dwarfs and sub-giants ofAdams et al. (2018), we obtain θ ∗ = (cid:26) . ± . µ as for the Wide solution , (6) . ± . µ as for the Close solution . (7)4.2. Source Proper Motion
For KMT-2016-BLG-1836, the microlens source is too faint to measure its proper motion either from
Gaia (e.g., Li et al. 2019)or from ground-based data (e.g., Shvartzvald et al. 2019). However, we can still estimate the source proper motion by the proper-motion distribution of “bulge” stars in the
Gaia
DR2 catalog (Gaia Collaboration et al. 2016, 2018). We examine a
Gaia
CMDusing the stars within 1 arcmin and derive the proper motion (in the Sun frame) of red giant branch stars (
G < . B p − R p > . ). We remove one outlier and obtain (in the Sun frame) (cid:104) µ bulge ( (cid:96), b ) (cid:105) = ( − . , − . ± (0 . , . mas yr − , (8) σ ( µ bulge ) = (3 . , . ± (0 . , . mas yr − . (9) LENS PROPERTIES5.1.
Bayesian Analysis
For a lensing object, the total mass is related to θ E and π E by (Gould 1992, 2000) M L = θ E κπ E , (10)and its distance by D L = AU π E θ E + π S , (11)where κ ≡ G/ ( c AU) = 8 . mas /M (cid:12) , π S = AU /D S is the source parallax, and D S is the source distance. In the presentcase, neither θ E nor π E is unambiguously measured, so we conduct a Bayesian analysis to estimate the physical parameters ofthe lens systems.For each solution of C ± and W ± , we first create a sample of simulated events from the Galactic model of Zhu et al. (2017).We also choose the initial mass function of Kroupa (2001) and . M (cid:12) for the upper end of the initial mass function. The onlyexception is that we draw the source proper motions from a Gaussian distribution with the parameters that were derived in Section4.2. For each simulated event i of solution k , we then weight it by ω Gal ,i,k = Γ i,k L i,k ( t E ) L i,k ( π E ) L i,k ( θ E ) , (12)where Γ i,k ∝ θ E ,i,k × µ rel ,i,k is the microlensing event rate, L i,k ( t E ) , L i,k ( π E ) are the likelihood of its inferred parameters ( t E , π E ) i,k given the error distributions of these quantities derived from the MCMC for that solution L i,k ( t E ) = exp[ − ( t E ,i,k − t E ,k ) / σ t E ,k ] √ πσ t E ,k , (13) L i,k ( π E ) = exp[ − (cid:80) m,n =1 b km,n ( π E ,m,i − π E ,m,k )( π E ,n,i − π E ,n,k ) / π/ √ det b k , (14) b km,n is the inverse covariance matrix of π E ,k , and ( m, n ) are dummy variables ranging over ( N, E ), and L i,k ( θ E ) is the likelihoodderived from the minimum χ for the lower envelope of the ( χ vs. ρ ) diagram from MCMC and the measured source angularradius θ ∗ from Section 4.1. Finally, we weight each solution by exp( − ∆ χ k / , where ∆ χ k is the χ difference between the k thsolution and the best-fit solution.Table 4 shows the resulting lens properties and relative weights for each solution, and the combined results. We find that the“Wide” solutions are significantly favored because they are preferred by a factor of ∼ exp(14 / ∼ from the χ weight,while the “Wide” solutions also have slightly higher Galactic model likelihood. The net effect is that the resulting combinedsolution is basically the same as the wide solution. The Bayesian analysis yields a host mass of M host = 0 . +0 . − . M (cid:12) , aplanet mass of M planet = 2 . +1 . − . M J , and a host-planet projected separation r ⊥ = 3 . +1 . − . AU , which indicates the planet isa super-Jovian planet well beyond the snow line of an M/K dwarf star (assuming a snow line radius r SL = 2 . M/M (cid:12) ) AU,Kennedy & Kenyon 2008). For each solution, the resulting distributions of the lens host-mass M host and the lens distance D L are shown in Figures 7 and 8, respectively. The resulting combined distributions of the lens properties are shown in Figure 9.5.2. Blended Light
The light curve analysis shows the blended light for the pySIS light curve is I B ∼ . . To investigate the blend, we check thehigher-resolution i -band images (pixel scale . (cid:48)(cid:48) , FWHM ∼ . (cid:48)(cid:48) ) taken from the Canada-France-Hawaii Telescope (CFHT)located at the Maunakea Observatories in 2018 (Zang et al. 2018b). We identify the source position in the CFHT images from anastrometric transformation of the highly magnified KMTC02 images. We use DoPhot (Schechter et al. 1993) to identify nearbystars and do photometry. As a result, DoPhot identifies two stars within (cid:48)(cid:48) (see Figure 10): an I = 18 . ± . star offset fromthe source by . (cid:48)(cid:48) , and an I = 19 . ± . star offset by . (cid:48)(cid:48) . Thus, the blend of pySIS light curve is from unrelated ambientstars. In addition, the total brightness of the source and the lens is fainter than the nearby I = 19 . ± . star.From the CMD analysis and the Bayesian analysis, the source is a late-G or early-K dwarf and the lens is probably an M/Kdwarf. Thus, the lens and source may have approximately equal brightness in the near-infrared, therefore follow-up adaptive-optics (AO) observations can potentially strongly constrain the lens brightness and thus the mass and distance of the planetarysystem (Batista et al. 2015; Bennett et al. 2015; Bhattacharya et al. 2018). In addition, our Bayesian analysis shows that thelens-source relative proper motion is µ rel = 3 . +1 . − . mas yr − , so the lens and source will be separated by about 40 mas by 2028.Thus, the source and lens can be resolved by the first AO light on next-generation (30 m) telescopes, which have a resolution θ ∼ D/ − mas in H band. DISCUSSIONWe have reported the discovery and analysis of the microlens planet KMT-2016-BLG-1836Lb, for which the ∼ day, q ∼ . planetary perturbation was detected and characterized by KMTNet’s Γ ∼ − observations. Many previous works haveexplored the mass ratio distribution of microlens planets. Of particular note is the work of Suzuki et al. (2016) which discovereda break in the mass-ratio function of planets at log q ∼ − . In addition Mr´oz et al. (2017) tested whether observation strategy(survey vs. survey + followup) could affect the observed mass ratio distribution. A full analysis of the mass-ratio distribution forKMTNet planets is well beyond the scope of this work. However, we construct an initial distribution to emphasize the need forsuch a detailed analysis in the future.We conduct our analysis on published KMTNet planets discovered in the 2016–2018 seasons and also on the 2016 seasonalone, since the 2016 season is the most likely to be complete, i.e. have the least publication bias. Including KMT-2016-BLG-1836Lb, there are 13 published microlens planets with KMTNet data from 2016 and 31 published planets from 2016–2018, mostof which (19/31 for all the planets from 2016–2018, and 8/13 for planets from 2016) are located in KMTNet’s Γ > − fields .The upper and lower panels of Figure 11 show the cumulative distributions of planets by log mass ratio log q for 31 planets from2016–2018 and 13 planets from 2016, respectively. For each panel, we also show the cumulative distributions of log q for planetsobserved at cadences of Γ > − and Γ ≤ − . For events with n degenerate solutions, each solutions are included at aweight of 1/n.The KMTNet planet sample appears to have a “mass ratio desert” at − . (cid:46) log q (cid:46) − . . The only planet ( log q ∼ − . )that appears in this desert is one of the two degenerate solutions for OGLE-2017-BLG-0373Lb. This potential “mass ratiodesert” cannot be caused by the detection efficiency of KMTNet because eight planets with log q < − . have been detected by Actually, only OGLE-2018-BLG-0596Lb was observed at a cadence of Γ ∼ − , while other planets were observed at cadences of Γ ≥ − . Y ANG ET AL . Γ > − . However, the sample of planets from Suzuki et al. (2016), which was subject to a rigorous analysis, does not showany evidence for a mass ratio desert in this range. Likewise, Mr´oz et al. (2017) found that the cumulative distributions of log q are nearly uniformly distributed in − . < log q < − . (i.e., constant number of detections in each bin of equal log q ) for asample including 44 published microlensing planets before 2016 plus OGLE-2016-BLG-0596Lb.The most likely source of this discrepancy is incompleteness due to publication bias. For example, the number of planetswith log q ( < − . , > − . are (2, 11) in 2016, (4, 5) in 2017, and (3, 6) in 2018, which suggests that there are likely besome unpublished planets with log q > − . from 2017 and 2018. This publication bias could result in the missing planets at − . (cid:46) log q (cid:46) − . and thus the apparent “mass ratio desert”.The core accretion runaway growth scenario predicts that the planets in the mass range 30–100 M ⊕ are rare (Ida & Lin 2004).For the typical microlensing lens mass M host ∼ M (cid:12) , 30–100 M ⊕ corresponds to mass ratio − . (cid:46) log q (cid:46) − . .Thus, the mass ratio distribution from microlensing can be used to test predictions of core accretion theory. Suzuki et al. (2018)found that the MOA mass-ratio distribution from Suzuki et al. (2016) is inconsistent with those predictions. KMTNet enablesan independent measurement of this mass ratio distribution. If the potential “mass ratio desert” of the KMTNet planet sampleis real, it could be consistent with the core accretion theory of planet formation and potentially contradicts Suzuki et al. (2018).Verifying this apparent “mass ratio desert” requires a full statistical analysis of the KMTNet data including detection efficiencyand selection biases. Software: pySIS (Albrow et al. 2009), pyDIA (doi:10.5281/zenodo.268049), emcee (Foreman-Mackey et al. 2013), DoPhot(Schechter et al. 1993)This research has made use of the KMTNet system operated by the Korea Astronomy and Space Science Institute (KASI) andthe data were obtained at three host sites of CTIO in Chile, SAAO in South Africa, and SSO in Australia. This research uses dataobtained through the Telescope Access Program (TAP), which has been funded by the National Astronomical Observatories ofChina, the Chinese Academy of Sciences, and the Special Fund for Astronomy from the Ministry of Finance. H.Y., X.Z., W.Z.,W.T. and S.M. acknowledge support by the National Science Foundation of China (Grant No. 11821303 and 11761131004). Workby AG was supported by AST-1516842 and by JPL grant 1500811. AG received support from the European Research Councilunder the European Unions Seventh Framework Programme (FP 7) ERC Grant Agreement n. [321035]. Work by CH wassupported by the grant (2017R1A4A1015178) of National Research Foundation of Korea. Work by P.F. and W.Z. was supportedby Canada-France-Hawaii Telescope (CFHT). MTP was supported by NASA grants NNX14AF63G and NNG16PJ32C, as wellas the Thomas Jefferson Chair for Discovery and Space Exploration. Wei Zhu was supported by the Beatrice and VincentTremaine Fellowship at CITA. Partly based on observations obtained with MegaPrime/MegaCam, a joint project of CFHT andCEA/DAPNIA, at the Canada-France-Hawaii Telescope (CFHT) which is operated by the National Research Council (NRC) ofCanada, the Institut National des Science de lUnivers of the Centre National de la Recherche Scientifique (CNRS) of France, andthe University of Hawaii. REFERENCES
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Best-fit parameters and their uncertainty range from MCMC for four distinct minima shown in Figure 2Solutions A B C D t ( HJD (cid:48) ) 7487.58(4) 7487.67(4) 7487.39(4) 7487.26(5) u t E s q (10 − ) α (deg) 333.1(0.5) 333.3(0.5) 150.3(0.7) 266.3(0.8) ρ (10 − ) < . < . I S I B χ /dof Table 2.
Best-fit parameters and their uncertainty range for binary-lens model with parallaxWide CloseSolutions W + W − C + C − t ( HJD (cid:48) ) 7487.69(7) 7487.68(6) 7487.60(4) 7487.61(4) u − − t E s q (10 − ) α (deg) 335.1(2.0) 25.4(1.7) 335.1(1.3) 24.7(1.1) ρ (10 − ) < . < . < . < . π E , N − − π E , E I S I B χ /dof Table 3.
Best-fit parameters and their uncertainty range from MCMC for binary-source modelsParallax modelsSolution Standard u > u < t , ( HJD (cid:48) ) 7487.12(2) 7487.17(4) 7487.15(4) t , ( HJD (cid:48) ) 7494.73(3) 7493.78(3) 7493.77(3) u , − u , − t E (d) ρ ρ q f,I I S I B χ /dof I - M a g n i t u d e KMTA02( I )KMTA42( I )KMTC02( I )KMTC42( I )KMTS02( I )KMTS42( I ) WideClose1L2S
Wide R e s i d u a l s Close
HJD-2450000 I - M a g n i t u d e KMTA02( I )KMTA42( I )KMTC02( I )KMTC42( I )KMTS02( I )KMTS42( I ) WideClose1L2S
Wide R e s i d u a l s Close
HJD-2450000
Figure 1.
The data of KMT-2016-BLG-1836 together with the best-fit models of the binary-lens “Wide”, binary-lens “Close”, and binary-source (1L2S) model. The upper panel shows a zoom of the anomaly. The residuals for each model are shown separately. The light curve anddata have been calibrated to standard I -band magnitude. ANG ET AL . Table 4.
Physical parameters for KMT-2016-BLG-1836Physical Properties Relative WeightsSolutions M host [ M (cid:12) ] M planet [ M J ] D L [kpc] r ⊥ [AU] Gal.Mod. χ W + . +0 . − . . +1 . − . . +0 . − . . +1 . − . W − . +0 . − . . +1 . − . . +0 . − . . +1 . − . W Total . +0 . − . . +1 . − . . +0 . − . . +1 . − . C + . +0 . − . . +1 . − . . +1 . − . . +0 . − . C − . +0 . − . . +1 . − . . +0 . − . . +0 . − . C Total . +0 . − . . +1 . − . . +1 . − . . +0 . − . Total . +0 . − . . +1 . − . . +0 . − . . +1 . − . log s -5.0-4.0-3.0-2.0-1.00.0 l og q log s -5.0-4.5-4.0-3.5-3.0-2.5-2.0-1.5-1.0 l og q Figure 2. χ surface in the ( log s, log q ) plane drawn from the grid search. The upper panel shows the space that is equally divided on a( × ) grid with ranges of − . ≤ log s ≤ . and − . ≤ log q ≤ , respectively. The lower panel shows the space that is equally dividedon a ( × ) grid with ranges of − . ≤ log s ≤ . and − . ≤ log q ≤ − . , respectively. The labels “A”, “B”, “C” and “D” in the lowerpanel show four distinct minima. ANG ET AL . x s y s Host Planet
Wide x s y s Host Planet
Close L o g m a g n i f i c a t i o n Figure 3.
Magnification maps of the standard “Wide” (upper panel) and “Close” (lower panel) models shown in Table 1. In each panel, the blueline with arrow represents the trajectory of the source with direction. The red contours are the caustics. The dashed lines indicate the Einsteinring and both x S and y S are in unit of the Einstein radius. The grayscale indicates the magnification of a point source at each position, wherewhite means higher magnification. -0.50.00.5 E, E -2.0-1.5-1.0-0.50.00.51.01.52.0 E , N W + -0.50.00.5 E, E
W -0.50.00.5
E, E C + -0.50.00.5 E, E C Figure 4.
Likelihood distributions for π E derived from MCMC for W ± and C ± solutions (see Table 1 for the solution parameters). Red,yellow, and blue show likelihood ratios [ −
2∆ ln L / L max ] < (1 , , ∞ ) , respectively. ANG ET AL . I - M a g HJD-2450000 A cc u m u l a t e WideClose1L2S
Figure 5.
Cumulative distribution of χ differences ( ∆ χ = χ − χ ) between the “Close”, binary-source (1L2S), and the “Wide”models. V I I red clumpsource Figure 6.
Color-magnitude diagram of a × square centered on KMT-2016-BLG-1836. The black dots show the stars from pyDIA photometryof KMTC02 data which are calibrated to OGLE-III star catalog (Szyma´nski et al. 2011), and the green dots show the HST CMD of Holtzmanet al. (1998) whose red-clump centroid is adjusted to match pyDIAs using the Holtzman field red-clump centroid of ( V − I, I ) = (1 . , . (Bennett et al. 2008). The red asterisk shows the centroid of the red clump, and the blue dot indicates the position of the source. ANG ET AL . Figure 7.
Bayesian posterior distributions of the lens host-mass M host for each solution of C ± and W ± (top two rows) and the combineddistributions for C ± and W ± (bottom row). In each panel, the red solid vertical line represents the median value and the two red dashed linesrepresent 16th and 84th percentiles of the distribution. Figure 8.
Bayesian posterior distributions of the lens distance D L . The plot is similar to Figure 7. Figure 9.
The combined Bayesian distributions of the lens host-mass M host , the lens distance D L , the planet-mass M planet , and the projectedseparation r ⊥ of the planet. ANG ET AL . Figure 10. i -band CFHT images within . (cid:48)(cid:48) × . (cid:48)(cid:48) around the event. The red cross indicates the source position derived from an astrometrictransformation of the highly magnified KMTC02 images. The blue and magenta crosses indicate the I = 18 . ± . star and I = 19 . ± . star found by DoPhot (Schechter et al. 1993), respectively. Figure 11.
Cumulative distributions of 31 published KMTNet microlensing planets from 2016–2018 by log q (upper panel) and 13 publishedKMTNet microlensing planets from 2016 by log q (lower panel). In each panel, the red and green lines represent the distributions for planetsobserved at cadences of Γ > − , Γ ≤ −1