KMT-2019-BLG-0797: binary-lensing event occurring on a binary stellar system
Cheongho Han, Chung-Uk Lee, Yoon-Hyun Ryu, Doeon Kim, Michael D. Albrow, Sun-Ju Chung, Andrew Gould, Kyu-Ha Hwang, Youn Kil Jung, Hyoun-Woo Kim, In-Gu Shin, Yossi Shvartzvald, Jennifer C. Yee, Weicheng Zang, Sang-Mok Cha, Dong-Jin Kim, Seung-Lee Kim, Dong-Joo Lee, Yongseok Lee, Byeong-Gon Park, Richard W. Pogge
aa r X i v : . [ a s t r o - ph . S R ] F e b Astronomy & Astrophysicsmanuscript no. ms © ESO 2021February 4, 2021
KMT-2019-BLG-0797: binary-lensing event occurring on a binarystellar system
Cheongho Han , Chung-Uk Lee , Yoon-Hyun Ryu , Doeon Kim (Leading authors),Michael D. Albrow , Sun-Ju Chung , , Andrew Gould , , Kyu-Ha Hwang , Youn Kil Jung , Hyoun-Woo Kim ,In-Gu Shin , Yossi Shvartzvald , Jennifer C. Yee , Weicheng Zang , Sang-Mok Cha , , Dong-Jin Kim ,Seung-Lee Kim , , Dong-Joo Lee , Yongseok Lee , , Byeong-Gon Park , , and Richard W. Pogge (The KMTNet Collaboration), Department of Physics, Chungbuk National University, Cheongju 28644, Republic of Koreae-mail: [email protected] Korea Astronomy and Space Science Institute, Daejon 34055, Republic of Korea University of Canterbury, Department of Physics and Astronomy, Private Bag 4800, Christchurch 8020, New Zealand Korea University of Science and Technology, 217 Gajeong-ro, Yuseong-gu, Daejeon, 34113, Republic of Korea Max Planck Institute for Astronomy, Königstuhl 17, D-69117 Heidelberg, Germany Department of Astronomy, The Ohio State University, 140 W. 18th Ave., Columbus, OH 43210, USA Department of Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot 76100, Israel Center for Astrophysics | Harvard & Smithsonian 60 Garden St., Cambridge, MA 02138, USA Department of Astronomy, Tsinghua University, Beijing 100084, China School of Space Research, Kyung Hee University, Yongin, Kyeonggi 17104, Republic of KoreaReceived ; accepted
ABSTRACT
Aims.
We analyze the microlensing event KMT-2019-BLG-0797. The light curve of the event exhibits two anomalous features froma single-lens single-source model, and we aim to reveal the nature of the anomaly.
Methods.
It is found that a model with two lenses plus a single source (2L1S model) can explain one feature of the anomaly, butthe other feature cannot be explained. We test various models and find that both anomalous features can be explained by introducingan extra source to a 2L1S model (2L2S model), making the event the third confirmed case of a 2L2S event, following on MOA-2010-BLG-117 and OGLE-2016-BLG-1003. It is estimated that the extra source comprises ∼
4% of the I -band flux from the primarysource. Results.
Interpreting the event is subject to a close–wide degeneracy. According to the close solution, the lens is a binary consistingof two brown dwarfs with masses ( M , M ) ∼ (0 . , . M ⊙ , and it is located at a distance of D L ∼ . / brown-dwarf boundary and an M dwarf with masses( M , M ) ∼ (0 . , . M ⊙ located at D L ∼ . / early-K-dwarf primary and anearly-to-mid M-dwarf companion. Key words. gravitational microlensing
1. Introduction
Microlensing light curves can exhibit deviations from thesmooth and symmetric form of a single-lens single-source(1L1S) event. The most common causes for these anomaliesare the binary nature of the lens, 2L1S event (Mao & Paczy´nski1991), and the source, 1L2S event (Griest & Hu 1992). De-tections of such three-object (2L +
1S or 1L + ffi cient detections of microlensinganomalies, e.g., survey + follow-up mode observations for inten-sive coverage of short-lasting anomalies (Gould & Loeb 1992),and the development of methodologies for e ffi cient analyses of anomalous lensing events, e.g., ray-shooting method (Bond et al.2002; Dong et al. 2009; Bennett et al. 2010) and contour inte-gration algorithm (Gould & Gaucherel 1997; Bozza et al. 2018).Thanks to the accomplishments on both observational and the-oretical sides, more than a hundred anomalous events are cur-rently being detected each year, and they are promptly analyzedalmost in real time with the progress of events (Ryu et al. 2010;Bozza et al. 2012)With the great increase of the event detection rate to-gether with the dense coverage of lensing light curves by high-cadence lensing surveys, OGLE-IV (Udalski et al. 2015), MOA(Bond et al. 2001), and KMTNet (Kim et al. 2016), one is oc-casionally confronted with events for which observed lensinglight curves cannot be explained by interpretations with threeobjects. At the time of writing this article, there exist thir-teen confirmed cases of events, for which at least four objects(lenses plus sources) are required to interpret observed light Article number, page 1 of 9 & Aproofs: manuscript no. ms
Table 1.
Microlensing events with more than four bodiesModel Event Reference3L1S OGLE-2008-BLG-092 Poleski et al. (2014)(planet in binary) OGLE-2007-BLG-349 Bennett et al. (2016)OGLE-2013-BLG-0341 Gould et al. (2014)OGLE-2016-BLG-0613 Han et al. (2017)OGLE-2018-BLG-1700 Han et al. (2020b)OGLE-2019-BLG-0304 Han et al. (2020g)3L1S OGLE-2006-BLG-109 Gaudi et al. (2008); Bennett et al. (2010)(two-planet system) OGLE-2012-BLG-0026 Han et al. (2013)OGLE-2018-BLG-1011 Han et al. (2019)1L3S OGLE-2015-BLG-1459 Hwang et al. (2018)2L2S MOA-2010-BLG-117 Bennett et al. (2018)OGLE-2016-BLG-1003 Jung et al. (2017)3L2S KMT-2019-BLG-1715 Han et al. (2020e)3L1S or 2L2S OGLE-2014-BLG-1722 Suzuki et al. (2018)OGLE-2018-BLG-0532 Ryu et al. (2020)KMT-2019-BLG-1953 Han et al. (2020a) curves. These events are listed in Table 1. Nine of these are3L1S events, in which the lensing system is composed of threelens masses and a single source star. Among them, the lensesof six events (OGLE-2008-BLG-092, OGLE-2007-BLG-349,OGLE-2013-BLG-0341, OGLE-2016-BLG-0613, OGLE-2018-BLG-1700, and OGLE-2019-BLG-0304) are planets in binaries,and the lenses of the other three events (OGLE-2006-BLG-109,OGLE-2012-BLG-0026, OGLE-2018-BLG-1011) are systemscontaining two planets. The lensing event OGLE-2015-BLG-1459 was identified as a 1L3S event, in which a single-lens masswas involved with three source stars. The events MOA-2010-BLG-117 and OGLE-2016-BLG-1003 were very rare cases, inwhich both the lens and source are binaries. Interpretation ofthe event KMT-2019-BLG-1715 is even more complex and re-quires five objects, in which the lens is composed of three masses(a planet plus two stars) and the source consists of two stars,that is, 3L2S event. Besides these events, there exist three addi-tional events (OGLE-2014-BLG-1722, OGLE-2018-BLG-0532,and KMT-2019-BLG-1953), in which four-object modeling isrequired to explain the observed light curves, but unique so-lutions cannot be firmly specified due to either degeneraciesamong di ff erent interpretations or not enough coverage of sig-nals. Accumulation of knowledge from modeling these multi-body events is important for future interpretations of lensinglight curves with complex anomalous features.In this paper, we present the analysis of the lensing eventKMT-2019-BLG-0797. The light curve of the event exhibits twoanomalous features, which cannot be explained by a usual 2L1Sor 1L2S model. We test various four-object models, in which anextra lens or source are considered in the interpretation of theevent.The anomalous nature of KMT-2019-BLG-0797 was foundfrom a project conducted to reanalyze previous KMTNetevents detected in and before the 2019 season. In the firstpart of this project, Han et al. (2020d) investigated events in-volved with faint source stars and found four planetary events(KMT-2016-BLG-2364, KMT-2016-BLG-2397, OGLE-2017-BLG-0604, and OGLE-2017-BLG-1375), for which no detailedinvestigation had been conducted. The second part of the projectwas focused on high-magnification events, aiming to find subtleplanetary signals, and this led to the discoveries of two plan-etary systems KMT-2018-BLG-0748L (Han et al. 2020c) andKMT-2018-BLG-1025L (Han et al. 2020h). The event KMT-2019-BLG-0797 was closely examined as a part of the project in- vestigating high-magnification events involved with faint sourcestars.For the presentation of the work, we organize the paper asfollows. In Sect. 2, we mention the data of the lensing event an-alyzed in this work and describe observations conducted to ac-quire the data. In Sect. 3, we depict the anomaly that appearedon the light curve and describe various tests conducted to inter-pret the anomaly. We estimate the angular Einstein radius of thelensing event in Sect. 4, and estimate the physical parametersof the lens and source in Sect. 5. We summarize the results andconclude in Sect. 6.
2. Observation and data
The lensing event KMT-2019-BLG-0797 occurred on a sourcelying toward the Galactic bulge. The equatorial and galacticcoordinates of the source are (RA , DEC)
J2000 = (17 : 53 :48 . , −
31 : 58 : 36 .
70) and ( l , b ) = ( − ◦ . , − ◦ . I base ∼ .
1, as measuredon the KMTNet scale, before the lensing magnification. Thelensing-induced magnification of the source flux lasted about 10days as measured by the duration beyond the photometric scatter.The event was detected on 2019 May 13 (HJD ′ ≡ HJD − ∼ .
6) by the Alert Finder System (Kim et al. 2018)of the KMTNet survey. The survey uses three identical wide-field telescopes that are globally located in three continents. Thelocations of the individual telescopes are the Siding Spring Ob-servatory (KMTA) in Australia, the Cerro Tololo Inter-AmericanObservatory (KMTC) in South America, and the South AfricanAstronomical Observatory (KMTS) in Africa. Each KMTNettelescope has a 1.6m aperture and is equipped with a camerayielding 2 ◦ × ◦ field of view. Images of the source were mainlyacquired in the I band, and about one tenth of images were ob-tained in the V band for the source color measurement. We willdescribe the detailed procedure of determining the source colorin Sect. 4.Figure 1 shows the lensing light curve of KMT-2019-BLG-0797. The curve plotted over the data points is a 1L1S modelwith ( t , u , t E ) ∼ (8617 . , . , . θ E ), and event timescale, respectively. The inset shows thezoomed-in view of the peak region, around which the data ex- Article number, page 2 of 9heongho Han et al.: KMT-2019-BLG-0797: binary-lensing event occurring on a binary stellar system
Fig. 1.
Light curve of KMT-2019-BLG-0797. The curve drawn overthe data points is a 1L1S model. The inset shows the region aroundthe peak. The colors of the data points match those of the telescopes,marked in the legend, used to acquire the data. hibit an anomaly relative to the 1L1S model. The date of theevent alert approximately corresponds to the peak of the lensingmagnification. The anomaly was already in progress at the timeof the event alert, but it was not noticed due to the subtlety of theanomaly together with the considerable photometric uncertain-ties of data caused by the faintness of the source. As a result, lit-tle attention was paid to the event when the event was found, andthus no alert for follow-up observations was issued. Neverthe-less, the peak region of the light curve was densely and contin-uously covered, because the source was located in the two over-lapping KMTNet fields of BLG01 and BLG41, toward whichobservations were conducted most frequently. The observationalcadence for each field was 30 min, and thus the event was cov-ered with a combined cadence of 15 min.Photometry of the event was conducted utilizing the KMT-Net pipeline (Albrow et al. 2009), which is a customized versionof pySIS code developed on the basis of the di ff erence imagingmethod (Tomaney & Crotts 1996; Alard & Lupton 1998). Addi-tional photometry is conducted for a subset of KMTC I - and V -band data using the pyDIA software (Albrow 2017) to mea-sure the color of the source and to construct a color-magnitudediagram (CMD) of ambient stars around the source. We read-just error bars of data estimated from the pipeline following thestandard routine described in Yee et al. (2012).
3. Anomaly
Figure 2 shows the detailed pattern of the anomaly in the peakregion. It shows that the anomaly consists of two distinctive fea-tures. The first is the caustic-crossing feature, which is composedof two spikes at HJD ′ ∼ . ′ ∼ . Fig. 2.
Zoomed-in view around the peak of the light curve. Drawn overthe data points are the 2L2S (wide), 3L1S, and 2L1S models. The lowerthree panels show the residuals from the individual models. ture, but the falling side was not covered until almost the end ofthe anomaly.
Considering that both anomalous features are likely to be in-volved with source star’s crossing over or approaching a caus-tic, we first model the observed light curve under the assumptionthat the lens is a binary. In addition to the 1L1S lensing param-eters, a 2L1S modeling requires one to include the three addi-tional parameters ( s , q , α ), which represent the projected separa-tion (normalized to θ E ), mass ratio between the binary lens com-ponents, M and M , and the angle between the source trajec-tory and the M – M axis (source trajectory angle), respectively.In the 2L1S modeling, we conduct thorough grid searches forthe binary parameters ( s , q ) with multiple starting points of α evenly distributed in the range of 0 ≤ α ≤ π . For the compu-tations of finite-source magnifications, we use the ray-shootingmethod described in Dong et al. (2009). From this investigation,we find that the 2L1S modeling does not yield a plausible modelexplaining the observed anomalous features.We then conduct another 2L1S modeling, this time, by ex-cluding the data around one of the two anomaly features. Themodeling conducted by removing the data around the secondanomalous feature does not yield a reasonable solution either. However, the modeling with the exclusion of the first anomalousfeature yields a solution that well describes the second anoma-lous feature. As we will show in the following subsection, the first anomalousfeature is produced by an extra source. This source comprises a veryminor fraction of the primary source, and the most flux comes from theprimary source. As a result, the contribution of the second source tothe lensing light curve is confined only to the time of the first anomaly,and thus the 2L1S modeling conducted excluding the second anomalousfeature does not yield a model describing the overall light curve.Article number, page 3 of 9 & Aproofs: manuscript no. ms
Fig. 3.
Lens system configurations of the 2L1S solutions. The upperand lower panels are for the close and wide solutions, respectively. Theinset in each panel shows the enlarged view around the caustic locatedclose to the source trajectory (line with an arrow). The blue dots markedby M and M denote the positions of the binary lens components, andthe bigger dot represents the heavier lens mass. Lengths are scaled tothe Einstein radius. The small magenta circle on the source trajectoryrepresents the source size scaled to the Einstein radius: ρ = θ ∗ /θ E . Table 2.
Best-fit parameters of 2L1S solutionsParameter Close Wide t (HJD ′ ) 8617 . ± .
007 8617 . ± . u / u ′ . ± .
005 0 . ± . / . ± . t E / t ′ E (days) 4 . ± .
09 12 . ± . / . ± . s . ± .
008 3 . ± . q . ± .
068 5 . ± . α (rad) 6 . ± .
013 4 . ± . ρ / ρ ′ (10 − ) 12 . ± .
73 3 . ± . / . ± . Notes.
HJD ′ ≡ HJD − u ′ , t ′ E , ρ ′ ) of the widesolution are the values scaled to the angular Einstein radius correspond-ing to M , i.e., θ ′ E = θ E / (1 + q ) / . The model curve of the 2L1S solution obtained by exclud-ing the first anomalous feature is plotted over the data points inFigure 2, and the lensing parameters of the solution are listedin Table 2. We find two sets of solutions, in which one has abinary separation smaller than unity ( s < .
0) and the othersolution has a separation greater than unity ( s > . s , q , α ) close ∼ (0 . , . , − . ◦ ) and ( s , q , α ) wide ∼ (3 . , . , − . ◦ ), respectively. We note that M denotes thelens component located closer to the source trajectory, not theheavier mass component, and thus the mass ratio q of thewide solution is greater than unity. For the wide solution, wepresent additional parameters ( u ′ , t ′ E , ρ ′ ), which represent thevalues scaled to the angular Einstein radius corresponding to M , θ ′ E = θ E / (1 + q ) / , and thus u ′ = u (1 + q ) / , t ′ E = t E / (1 + q ) / ,and ρ ′ = ρ (1 + q ) / . It is found that the parameters ( u ′ , t ′ E , ρ ′ ) of Fig. 4.
Lens system configuration of the 2L2S model. Notations aresame as those in Fig. 3 except that there is an additional source trajec-tory of the second source, S . Table 3.
Best-fit parameters of 2L2S solutionsParameter Close Wide χ . . t , (HJD ′ ) 8617 . ± .
008 8617 . ± . u , / u ′ , . ± .
006 0 . ± . / . ± . t , (HJD ′ ) 8616 . ± .
007 8616 . ± . u , / u ′ , . ± .
002 0 . ± . / . ± . t E / t ′ E (days) 4 . ± .
08 12 . ± . / . ± . s . ± .
008 3 . ± . q . ± .
052 5 . ± . α (rad) 6 . ± .
011 4 . ± . ρ / ρ ′ (10 − ) 14 . ± .
33 4 . ± . / . ± . ρ / ρ ′ (10 − ) 3 . ± .
50 1 . ± . / . ± . q F , I . ± .
003 0 . ± . the wide solution are similar to the corresponding parameters ofthe close solution.Figure 3 shows the configuration of the lens system corre-sponding to the 2L1S solutions. The upper and lower panels arethe configurations of the close and wide solutions, respectively.According to these solutions, the second feature of the anomalyis produced by the source crossing over the tip of the four-cuspcaustic induced by a binary. We note that the binary separa-tion, s ∼ .
52 for the close solution and s ∼ . Article number, page 4 of 9heongho Han et al.: KMT-2019-BLG-0797: binary-lensing event occurring on a binary stellar system
Fig. 5.
Lens system configuration of the models obtained by confiningthe source trajectory angle around ∼ α + ◦ from the best-fit solutionswith α . We conduct another modeling under the interpretation that boththe lens and source are binaries (2L2S model). The lensing mag-nification of a 2L2S event is the superposition of those involvedwith the individual source stars, S and S , that is, A = A F S + A F S F S + F S = A + A q F + q F . (1)Here ( F S , F S ) and ( A , A ) denote the baseline flux values andthe magnifications associated with the individual source stars,respectively, and q F = F S / F S represents the flux ratio betweenthe source stars. The consideration of an extra source requiresone to include additional parameters in modeling. These param-eters are ( t , , u , , ρ , q F ), which represent the time of the closestapproach of S to the lens, and the lens-source separation at thattime, the normalized radius of S , and the flux ratio between S and S , respectively (Hwang et al. 2013). As initial values of theparameters related to the S , ( t , , u , , t E , s , q , α, ρ ), we use thevalues obtained from the 2L1S modeling. We set the initial val-ues of ( t , , u , , ρ , q F ) considering the time and strength of thefirst anomaly feature.It is found that the 2L2S modeling yields solutions that welldescribe the observed data including both anomalous features.We find two sets of solutions resulting from the close–wide de-generacy, and the best-fit lensing parameters of the individualsolutions are listed in Table 3. It is found that the wide solu-tion yields a slightly better fit to the data than the close solution,especially in the region around the second anomalous feature.However, the χ di ff erence between the two solutions is merely ∆ χ = .
5, and thus we consider the close solution as a viablemodel. The model curves of the wide solution and the residualfrom the model are shown in Figure 2.In Figure 4, we present the lens system configurations corre-sponding to the close (upper panel) and wide (lower panel) 2L2Ssolutions. From the comparison of the lensing parameters with
Fig. 6.
Lens system configuration of the 3L1S model. We note that thereare three lens components, marked by M , M , and M . The dotted cir-cle with a radius unity and centered at the M – M barycenter representsthe Einstein ring. Table 4.
Best-fit parameters of 3L1S solutionParameter Value χ t (HJD ′ ) 8617 . ± . u . ± . t E (days) 6 . ± . s . ± . q . ± . α (rad) 4 . ± . s . ± . q (10 − ) 2 . ± . ψ (rad) 1 . ± . ρ (10 − ) 2 . ± . those of the 2L1S solutions, presented in Table 2, it is found thatthe parameters related to S ( t , , u , , t E , s , q , α ) for the 2L1S and2L2S solutions are similar to each other. The main di ff erence be-tween the two solutions is the presence of an additional source S that approaches M closer than S does. The second sourcepasses over the caustic producing a caustic-crossing feature inthe light curve, and this explains the first anomalous feature thatcould not be explained by the 2L1S model. According to the2L2S solutions, the companion source comprises about 4% ofthe I -band flux from the primary source, that is, q F , I ∼ . α and α ± ◦ have a similar shape. See Figure 4 of Hwang et al.(2010) for the illustration of this degeneracy. We find that KMT-2019-BLG-0797 is not subject to this degeneracy because thesource trajectory of the solution with α ± ◦ is approximatelyaligned with the line connecting the central and peripheral caus-tics of the binary lens. To demonstrate this, in Figure 5, we plot Article number, page 5 of 9 & Aproofs: manuscript no. ms
Fig. 7.
Cumulative distribution of χ di ff erence between the 3L1S and2L2S models, that is, ∆ χ = χ − χ . The two dotted vertical linesare drawn to indicate the region of the anomalies. the lens system configurations of the solutions obtained by con-fining the source trajectory angle around ∼ α ± ◦ from thebest-fit solution. It shows that these solutions result in source tra-jectories passing close to the peripheral caustic lying away fromthe central caustic. The source approach to the peripheral causticresults in an additional bump in the lensing light curve before themain peak. To avoid such a bump, the source trajectory angle ofthese solutions has less freedom in α , and this leads to a worsefit than the solutions presented in Table 3. We also test a model, in which the lens has three components(3L1S model). We test this model because the anomalous fea-tures appear around the peak of the light curve, and thus athird mass, if it exists, may induce an additional caustic and ex-plain the first anomalous feature that is not explained by a 2L1Smodel, for example, OGLE-2016-BLG-0613 (Han et al. 2017),OGLE-2018-BLG-1700 (Han et al. 2020f), OGLE-2019-BLG-0304 (Han et al. 2020g). In the 3L1S modeling, we conduct athorough grid search for the parameters describing the third lensmass, M . These parameters include ( s , q , ψ ), which denote thenormalized M – M separation, mass ratio q = M / M , and theposition angle of M as measured from the M – M axis and witha center at M .The 3L1S modeling also yields a solution that appears to de-pict both anomalous features. In Figure 2, we present the modelcurve and residual in the peak region of the light curve. Thebest-fit lensing parameters of the model are listed in Table 4,and the corresponding lens system configuration is shown in Fig-ure 6. According to this solution, the first anomalous feature isproduced by the crossing of the source over an additional caus-tic induced by a low-mass third lens component. The estimatedmass ratio of the third mass to the primary is q = M / M = (2 . ± . × − , indicating that M is a planetary mass object. Fig. 8.
Scatter plots in the MCMC chain on the ρ – ρ parameter planefor the close (left panel) and wide (right panel) solutions. The colorcoding is set to indicate points within 1 σ (red), 2 σ (yellow), 3 σ (green),4 σ (cyan), and 5 σ (blue). The planet is located close to the Einstein ring corresponding to M + M with a position angle of ψ ∼ ◦ . Due to the proximityof s to unity, the planet induces a single large resonant caustic,and the source passes through the planet-induced caustic, pro-ducing the first anomalous feature, before it approaches the cuspof the binary-induced caustic, producing the second anomalousfeature.Although the 3L1S model seemingly describes the anoma-lous features, it is found that the model fit is substantially worsethan the 2L2S model. The di ff erence in the fits between the twomodels as measured by χ di ff erence is ∆ χ = χ − χ = .
9, indicating that the 2L2S model is strongly preferred overthe 3L1S model. To show the di ff erence in the fits, we presentthe cumulative distribution of ∆ χ between the two models inFigure 7. The distribution shows that the 2L2S model providesa better fit than the 3L1S model not only in the region aroundthe peak but also throughout the lightcurve during the lensingmagnification.
4. Angular Einstein radius
In this section, we estimate the angular Einstein radius θ E . Inorder to estimate θ E , it is required to measure the normalizedsource radius, that is related to the angular Einstein radius by θ E = θ ∗ ρ . (2)Here θ ∗ represents the angular source radius. We find that thenormalized source radii of both S and S are constrained, al-though the uncertainties are considerable due to a partial cov-erage of the caustic crossings. This can be seen in Figure 8,in which we present scatter plots of the points in the MCMCchain on the ρ – ρ parameter plane for the close (left panel) andwide (right panel) solutions. We note that the uncertainty of ρ is greater than the uncertainty of ρ , because only the rising partof the second anomalous feature was covered by the data.Another requirement for the θ E measurement is estimatingthe angular source radius θ ∗ . We estimate θ ∗ from the color andbrightness of the source. In order to estimate calibrated color Article number, page 6 of 9heongho Han et al.: KMT-2019-BLG-0797: binary-lensing event occurring on a binary stellar system
Fig. 9.
Locations of the primary and companion source stars with re-spect to the centroid of the red giant clump (RGC) in the instrumentalcolor-magnitude diagram (CMD, grey dots). The determinations of thesource positions and the construction of the CMD are based on the py-DIA photometry of the KMTC data set. We also present the
HubbleSpace Telescope
CMD (Holtzman et al. 1998, brown dots) to show thesource locations on the main-sequence branch.
Table 5.
Source color and magnitudeQuantity Value( V − I , I ) RGC (2 . , . V − I , I ) RGC , (1 . , . S )( V − I , I ) (2 . ± . , . ± . V − I , I ) (0 . ± . , . ± . S )( V − I , I ) (3 . ± . , . ± . V − I , I ) (2 . ± . , . ± . and brightness from the instrumental values, we use the methodof Yoo et al. (2004). In this method, the centroid of red giantclump (RGC), with its known de-reddened color and magnitude,in the CMD serves as a reference for the color and magnitudecalibration.In the first step of the method, we estimate the combined (in-strumental) flux from the source stars, F S , p = F S , p + F S , p , andthe companion / primary flux ratio, q F , p , by fitting the KMTC pho-tometry data set processed using the pyDIA code. Here the sub-script “ p ” denotes the passband of observation. The measuredvalues are ( F S , I , F S , V ) = (0 . ± . , . ± . q F , I , q F , V ) = (0 . ± . , . ± . q F , I , which is derived from the pyDIA reduc-tion, is slightly di ff erent (less than 1 σ ) from the value presentedin Table 3, which is derived from the pySIS reduction, becausethey come from di ff erent reductions of the data. Then, the fluxvalues from S and S are estimated by F S , p = + q F , p ! F S , p ; F S , p = q F , p + q F , p ! F S , p , (3) Table 6.
Angular source radius, Einstein radius, and proper motionQuantity Close Wide θ ∗ ( µ as) 0 . ± . ← θ E / θ ′ E (mas) 0 . ± .
005 0 . ± . / . ± . µ (mas yr − ) 4 . ± .
36 5 . ± . Notes.
The notation “ ← ” in the wide solution column implies that thevalue is same as the one in the left column. respectively. From the measured flux values in the I and V bands,it is estimated that the colors and magnitudes of S and S are( V − I , I ) S = (2 . ± . , . ± . V − I , I ) S = (3 . ± . , . ± . S and S with respect to the RGC centroidin the instrumental CMD constructed using the pyDIA photom-etry of the KMTC data (grey dots).Although the V -band flux of S has a relatively large frac-tional (i.e., magnitude) error, it is strongly constrained to be faintin an absolute sense. In particular, we find q F , I − q F , V = . ± . , (4)i.e., a 4 . σ di ff erence. This serves as a second line of evidencethat the 2L2S solution is correct. If, for example, we had some-how missed a 3L1S solution, and the derived 2L2S solution weremerely mimicking it, then q F , I − q F , V should be consistent withzero because there is only one source with just one color. How-ever, according to Equation (4) this possibility is excluded at4 . σ .In the second step, we calibrate the color and magnitude.With the measured instrumental color and brightness of thesource, ( V − I , I ), and the RGC centroid, ( V − I , I ) RGC = (2 . , . V − I , I ) RGC , = (1 . , . V − I , I ) = ( V − I , I ) RGC , + ∆ ( V − I , I ) , (5)where ∆ ( V − I , I ) denote the o ff sets in the color and brightness ofthe source from the RGC centroid measured on the instrumentalCMD. This results in( V − I , I ) = ( (0 . ± . , . ± . S , (2 . ± . , . ± . S . (6)In Table 5, we summarize the values of ( V − I , I ) RGC , ( V − I , I ) RGC , , ( V − I , I ), and ( V − I , I ) for the primary and com-panion source stars.According to the estimated color and magnitude, the faintersource, S , is clearly an early-to-mid M dwarf. On the otherhand, the brighter source, S , presents something of a puzzlebecause its best-fit position lies in a relatively unpopulated por-tion of the CMD (see Figure 9). The most likely explanation isthat its true position lies (1.5 – 2.0) σ blueward of the best-fit po-sition. That is, it is most likely a very late G dwarf or a very earlyK dwarf. Because the position of S is consistent with lying inthe normal bulge population at the (1 – 2) σ level, we evaluateits angular radius using the measured values and normal errorpropagation.In the third step, we estimate the angular source radius us-ing the measured source color and brightness. For this, we firstconvert V − I color into V − K color using the color–color re-lation of Bessell & Brett (1988), and then estimate θ ∗ using the Article number, page 7 of 9 & Aproofs: manuscript no. ms
Fig. 10.
Bayesian posteriors of the primary lens mass ( M ), and dis-tances to the lens ( D L ) and source ( D S ). Red and blue curves are distri-butions obtained from the close and wide solutions, respectively. ( V − K )– θ ∗ relation of Kervella et al. (2004). This process yieldsan angular source radius of θ ∗ = . ± . µ as . (7)We note that the source radius of S is uncertain due to its largecolor uncertainty, and thus we use θ ∗ of S for the θ E estimation,i.e., θ E = θ ∗ , /ρ . With the angular source radius, the angularEinstein radius is estimated using the relation in Equation (2),which yields θ E = ( . ± .
005 mas (close) , . ± .
006 mas (wide) . (8)Here the angular Einstein radius of the wide solution is scaledto θ ′ E . Together with the event timescale, the relative lens-sourceproper motion is estimated as µ = θ E t E = ( . ± .
36 mas yr − (close) , . ± .
46 mas yr − (wide) . (9)In Table 6, we summarize the values of θ ∗ , θ E , and µ correspond-ing to the close and wide solutions.
5. Physical parameters of the lens and source
For KMT-2019-BLG-0797, it is di ffi cult to uniquely determinethe physical lens parameters because the microlens parallax can-not be measured due to the short timescale of the event, which is . t E = θ E µ , θ E = ( κ M π rel ) / , π rel = AU D L − D S ! . (10) Table 7.
Physical lens parametersParameter Close Wide M ( M ⊙ ) 0 . + . − . . + . − . M ( M ⊙ ) 0 . + . − . . + . − . D L (kpc) 8 . + . − . . + . − . D S (kpc) 9 . + . − . . + . − . a L , ⊥ (AU) 0 . + . − . . + . − . a S , ⊥ (AU) 0 . + . − . . + . − . Notes. M denotes the lens component located closer to the source tra-jectory, not the heavier mass component. Here κ = G / ( c AU), π rel denotes the relative lens-source par-allax, D L and D S represent the distances to the lens and source,respectively.We estimate the physical lens parameters by conductinga Bayesian analysis. The analysis is done using the priors ofthe lens mass function and the physical and dynamical galac-tic models. We adopt the mass function models of Zhang et al.(2020) and Gould (2000), in which the former mass function in-cludes stellar and brown-dwarf lenses and the latter one accountsfor stellar remnants. The locations and motions of lenses andsource stars are assigned using the physical distribution modelof Han & Gould (2003) and the dynamical distribution model ofHan & Gould (1995), respectively. Based on these models, weproduce a large number (4 × ) of artificial lensing events byconducting a Monte Carlo simulation, and then construct the dis-tributions of the physical parameters. With the distributions, therepresentative values of the lens parameters are estimated as themedian values of the distributions, and the uncertainties are esti-mated as the 16% and 84% ranges of the distributions.Figure 10 shows the Bayesian posteriors of the primary lensmass and the distances to the lens and source. In Table 7, welist the estimated parameters M , M , D L , D S , a L , ⊥ , and a S , ⊥ .The last two parameters indicate the projected binary-lens andbinary-source separations, that is, a L , ⊥ = sD L θ E , a S , ⊥ = ∆ uD S θ E , (11)where ∆ u = { [( t , − t , ) / t E ] + ( u , − u , ) } / is the instanta-neous separation between S and S at the time of the lensingmagnification.According to the close solution, the lens is composed of twobrown dwarfs with masses ( M , M ) ∼ (0 . , . M ⊙ lo-cated in the bulge with a distance of D L = . + . − . kpc. Accord-ing to the wide solution, on the other hand, the lens is composedof an object at the star / brown-dwarf boundary and an M dwarfwith masses ( M , M ) ∼ (0 . , . M ⊙ , and it is located ata distance of D L = . + . − . kpc. The masses of M estimatedfrom the close and wide solutions are similar to each other, al-though the wide solution prefers somewhat larger mass due tothe larger value of the estimated θ E . On the other hand, themasses of M estimated from the two degenerate solutions arewidely di ff erent from each other. This is because M and M have similar masses, with q ∼ .
6, according to the close solu-tion, while M according to the wide solution is much heavierthan M , with q ∼ .
3. For both the close and wide solutions,the source is located slightly behind the galactic center at a dis-tance of D S ∼ . a L , ⊥ , a S , ⊥ ) ∼ (0 . , .
10) AUaccording to the close solution, and ∼ (2 . , .
06) AU accord-ing to the wide solution. We note that the expected orbital pe-
Article number, page 8 of 9heongho Han et al.: KMT-2019-BLG-0797: binary-lensing event occurring on a binary stellar system riod of the source, P & . P & M S = M S + M S ∼ . M ⊙ + . M ⊙ ∼ . M ⊙ , is short,and thus the orbital motion of the source may a ff ect the lensinglight curve. However, it is di ffi cult to constrain the orbital mo-tion first because the duration of the anomaly, which is ∼
6. Summary and conclusion
We investigated the lensing event KMT-2019-BLG-0797, forwhich the light curve was found to be anomalous from the reex-amination of events detected in and before the 2019 season. Forthis event, it was found that a 2L1S model could not explain theanomaly. From the tests with various models, it was found thatthe anomaly could be explained by introducing an extra sourcestar to a 2L1S model. The event is the third case of a confirmed2L2S event following on MOA-2010-BLG-117 (Bennett et al.2018) and OGLE-2016-BLG-1003 (Jung et al. 2017).The interpretation of the light curve was subject to a close–wide degeneracy. According to the close solution, the lens is abinary consisting of two brown dwarfs with masses ( M , M ) ∼ (0 . , . M ⊙ , and it is located at a distance of D L ∼ . / brown-dwarf boundary andan M dwarf with masses ( M , M ) ∼ (0 . , . M ⊙ located at D L ∼ . / K-dwarf boundary and an early-to-mid M dwarfcompanion.
Acknowledgements.
Work by C.H. was supported by the grants of National Re-search Foundation of Korea (2019R1A2C2085965 and 2020R1A4A2002885).This research has made use of the KMTNet system operated by the Korea As-tronomy and Space Science Institute (KASI) and the data were obtained at threehost sites of CTIO in Chile, SAAO in South Africa, and SSO in Australia.
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