KMT-2022-BLG-0086: Another Binary-lens Binary-source Microlensing Event Sun-Ju Chung1aa, Kyu-Ha Hwang1aa, Jennifer C. Yee2aa, Andrew Gould3,4, Ian A. Bond5, Hongjing Yang6aa, (Leading Authors), Michael D. Albrow7aa, Youn Kil Jung1,8aa, Cheongho Han9aa, Yoon-Hyun Ryu1aa, In-Gu Shin2aa, Yossi Shvartzvald10aa, Weicheng Zang2aa, Sang-Mok Cha1,11, Dong-Jin Kim1aa, Seung-Lee Kim1aa, Chung-Uk Lee1aa, Dong-Joo Lee1, Yongseok Lee1,11, Byeong-Gon Park1,8aa, Richard W. Pogge3aa, (The KMTNet Collaboration), and Fumio Abe12, David P. Bennett13,14aa, Aparna Bhattacharya13,14, Akihiko Fukui15,16aa, Ryusei Hamada17, Yuki Hirao18aa, Stela Ishitani Silva13,19aa, Naoki Koshimoto17aa, Shota Miyazaki20aa, Yasushi Muraki12aa, Tutumi Nagai17, Kansuke Nunota17aa, Greg Olmschenk13aa, Clément Ranc21aa, Nicholas J. Rattenbury22aa, Yuki Satoh17aa, Takahiro Sumi17aa, Daisuke Suzuki17aa, Sean K. Terry13,14aa, Paul J. Tristram23, Aikaterini Vandorou13,14aa, Hibiki Yama17 (The MOA Collaboration) 1 Korea Astronomy and Space Science Institute, 776 Daedeokdae-ro, Yuseong-Gu, Daejeon 34055, Republic of Korea; sjchung@kasi.re.kr 2 Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA 3 Department of Astronomy, Ohio State University, 140 W. 18th Avenue, Columbus, OH 43210, USA 4Max-Planck-Institute for Astronomy, Königstuhl 17, D-69117 Heidelberg, Germany 5 Institute of Natural and Mathematical Science, Massey University, Auckland 0745, New Zealand 6 Department of Astronomy and Tsinghua Centre for Astrophysics, Tsinghua University, Beijing 100084, People’s Republic of China 7 Department of Physics and Astronomy, University of Canterbury, Private Bag, 4800 Christchurch, New Zealand 8 University of Science and Technology, Korea, (UST), 217 Gajeong-ro, Yuseong-gu, Daejeon 34113, Republic of Korea 9 Department of Physics, Chungbuk National University, Cheongju 361-763, Republic of Korea 10 Department of Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot 76100, Israel 11 School of Space Research, Kyung Hee University, Giheung-gu, Yongin, Gyeonggi-do, 17104, Republic of Korea 12 Institute for Space-Earth Environmental Research, Nagoya University, Nagoya 464-8601, Japan 13 Code 667, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA 14 Department of Astronomy, University of Maryland, College Park, MD 20742, USA 15 Department of Earth and Planetary Science, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan 16 Instituto de Astrofísica de Canarias, Vía Láctea s/n, 38205 La Laguna, Tenerife, Spain 17 Department of Earth and Space Science, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan 18 Institute of Astronomy, Graduate School of Science, The University of Tokyo, 2-21-1 Osawa, Mitaka, Tokyo 181-0015, Japan 19 Department of Physics, The Catholic University of America, Washington, DC 20064, USA 20 Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency, 3-1-1 Yoshinodai, Chuo, Sagamihara, Kanagawa 252-5210, Japan 21 Sorbonne Université, CNRS, UMR 7095, Institut d’Astrophysique de Paris, 98 bis bd Arago, 75014 Paris, France 22 Department of Physics, University of Auckland, Private Bag 92019, Auckland, New Zealand 23 University of Canterbury Mt. John Observatory, P.O. Box 56, Lake Tekapo 8770, New Zealand Received 2025 April 23; revised 2025 June 4; accepted 2025 June 5; published 2025 July 8 Abstract We present the analysis of a microlensing event KMT-2022-BLG-0086 of which the overall light curve is not described by a binary-lens single-source (2L1S) model, which suggests the existence of an extra lens or an extra source. We found that the event is best explained by the binary-lens binary-source (2L2S) model, but the 2L2S model is only favored over the triple-lens single-source (3L1S) model by Δχ2 ≃ 9. Although the event has noticeable anomalies around the peak of the light curve, they are not enough covered to constrain the angular Einstein radius θE, thus we only measure the minimum angular Einstein radius E,min. From the Bayesian analysis, it is found that that the binary lens system is a binary star with masses of ( ) ( )= + +m m M M, 0.46 , 0.751 2 0.25 0.35 0.55 0.67 at a distance of = +D 5.87L 1.79 1.21 kpc, while the triple lens system is a brown dwarf or a massive giant planet in a low-mass binary-star system with masses of ( ) (= + +m m m M M, , 0.43 , 0.0561 2 3 0.35 0.41 0.047 0.055 , )+ M20.84 17.04 20.20 J at a distance of = +D 4.06L 3.28 1.39 kpc, indicating a disk lens system. The 2L2S model yields the relative lens-source proper motion of μrel � 4.6 mas yr−1 that is consistent with the Bayesian result, whereas the 3L1S model yields μrel � 18.9 mas yr−1, which is more than three times larger than that of a typical disk object of ∼6 mas yr−1 and thus is not consistent with the Bayesian result. This suggests that the event is likely caused by the binary-lens binary-source model. The Astronomical Journal, 170:75 (10pp), 2025 August https://doi.org/10.3847/1538-3881/ade2e7 © 2025. The Author(s). Published by the American Astronomical Society. aaaaaaa Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. 1 https://orcid.org/0000-0001-6285-4528 https://orcid.org/0000-0002-9241-4117 https://orcid.org/0000-0001-9481-7123 https://orcid.org/0000-0003-0626-8465 https://orcid.org/0000-0003-3316-4012 https://orcid.org/0000-0002-0314-6000 https://orcid.org/0000-0002-2641-9964 https://orcid.org/0000-0001-9823-2907 https://orcid.org/0000-0002-4355-9838 https://orcid.org/0000-0003-1525-5041 https://orcid.org/0000-0001-6000-3463 https://orcid.org/0000-0002-4292-9649 https://orcid.org/0000-0003-0562-5643 https://orcid.org/0000-0003-0043-3925 https://orcid.org/0000-0002-6982-7722 https://orcid.org/0000-0003-1435-3053 https://orcid.org/0000-0001-8043-8413 https://orcid.org/0000-0002-4909-5763 https://orcid.org/0000-0003-4776-8618 https://orcid.org/0000-0003-2267-1246 https://orcid.org/0000-0003-2302-9562 https://orcid.org/0000-0001-9818-1513 https://orcid.org/0000-0003-1978-2092 https://orcid.org/0009-0005-3414-455X https://orcid.org/0000-0001-8472-2219 https://orcid.org/0000-0003-2388-4534 https://orcid.org/0000-0001-5069-319X https://orcid.org/0000-0002-1228-4122 https://orcid.org/0000-0002-4035-5012 https://orcid.org/0000-0002-5843-9433 https://orcid.org/0000-0002-5029-3257 https://orcid.org/0000-0002-9881-4760 mailto:sjchung@kasi.re.kr https://doi.org/10.3847/1538-3881/ade2e7 https://crossmark.crossref.org/dialog/?doi=10.3847/1538-3881/ade2e7&domain=pdf&date_stamp=2025-07-08 https://creativecommons.org/licenses/by/4.0/ Unified Astronomy Thesaurus concepts: Gravitational microlensing (672) Materials only available in the online version of record: data behind figure 1. Introduction Planets detected by microlensing are 4% of over 580024 exoplanets discovered so far, but they are quite different from those detected by transit and radial velocity that detected 93% of all the exoplanets. All the microlensing planets are cold or ice planets widely separated from their host stars, while planets detected by the transit and radial velocity are mostly located close to their host stars. Microlensing is also an unique method capable of probing the Galactic distribution of planets because it does not depend on the brightness of objects, but their mass. Moreover, microlensing is sensitive to free-floating planets that are believed to have been ejected from their planetary systems (F. A. Rasio & E. B. Ford 1996; D. Malmberg et al. 2011; N. A. Kaib et al. 2013). Due to such advantages of microlensing, the space-based microlensing exoplanet survey (D. P. Bennett & S. H. Rhie 2002) was adopted for the Nancy Grace Roman Space Telescope (Roman) mission (D. Spergel et al. 2015; R. Akeson et al. 2019). From the Roman, it is expected that about 1400 bound planets with masses of 0.1–104 M⊕ (M. Penny et al. 2019) and about 250 free-floating planets with masses of 0.1–103 M⊕ (S. A. Johnson et al. 2020) would be discovered. Planets are expected to be revealed in microlensing by a short-duration perturbation in an otherwise normal single- lens single-source (1L1S) event (S. Mao & B. Paczyń- ski 1991; A. Gould & A. Loeb 1992). This expectation has been borne out in the great majority of over 200 planets discovered by microlensing over two decades. However, planets can also occur as short perturbations on binary-star microlensing events, where they can remain hidden or submerged in more complex light curves, until they are exhumed by careful analysis. For example, OGLE-2007- BLG-349 (D. P. Bennett et al. 2016) had two severely degenerate solutions between a star hosting two planets and a planet in a binary star, with Δχ2 = 0.39, but it turned out that it was caused by the planet in the binary star because the binary-star model is consistent with the flux limits from Hubble Space Telescope (HST). Including the planet of OGLE-2007-BLG-349, nine planets orbiting binary stars, OGLE-2013-BLG-0341 (A. Gould et al. 2014), OGLE-2008- BLG-092 (R. Poleski et al. 2014), OGLE-2016-BLG-0613 (C. Han et al. 2017), OGLE-2006-BLG-284 (D. P. Bennett et al. 2020), OGLE-2018-BLG-1700 (C. Han et al. 2020), KMT-2020-BLG-041 (W. Zang et al. 2021, K. Zhang et al. 2024), OGLE-2023-BLG-0836 (C. Han et al. 2024b), and KMT-2024-BLG-0404 (Han et al. 2025, submitted), have been discovered through microlensing so far. However, the residuals from stellar-binary models are not necessarily due to a planet. They could be due to a second source, such as OGLE-2018-BLG-0584, KMT-2018-BLG- 2119 (C. Han et al. 2023), KMT-2021-BLG-0284, KMT-2022- BLG-2480, or KMT-2024-BLG-0412 (C. Han et al. 2024a), or possibly other effects including the microlens parallax and lens orbital motion effects, such as MACHO-97-BLG-41 (D. P. Bennett et al. 1999, M. D. Albrow et al. 2000, Y. K. Jung et al. 2013), OGLE-2013-BLG-0723 (A. Udalski et al. 2015, C. Han et al. 2016), KMT-2021-BLG-0322 (C. Han et al. 2021). Hence, careful work is required to distinguish among the possibilities. The event KMT-2022- BLG-0086 also has a severe degeneracy between the binary- lens binary-source and the triple-lens interpretations. In this paper, we report the results of careful analyses for the event. 2. Observations and Data The microlensing event KMT-2022-BLG-0086 occurred on a background source star at equatorial coordinates (R.A., decl.) = (17:33:57.68, −27:06:02.52), corresponding to the Galactic coordinates ( ) ( )= ° °l b, 0 .19, 3 .15 . The event was first discovered by the Korea Microlensing Telescope Network (KMTNet; S.-L. Kim et al. 2016), which is an optimized system for detecting microlensing exopla- nets. KMTNet uses three identical 1.6 m telescopes with 4 deg2 field of view (FOV) cameras that are globally distributed at the Cerro Tololo Inter-American Observatory in Chile (KMTC), the South African Astronomical Observa- tory, and the Siding Spring Observatory in Australia. The KMTNet observations were carried out in the I and V bands. The event lies in the KMT subprime field BLG15 with a cadence of Γ ≃ 1 hr−1. The Microlensing Observations in Astrophysics (MOA; I. A. Bond et al. 2001) also independently found this event and it was designated as MOA-2022-BLG-130. MOA uses a 1.8 m telescope with 2.2 deg2 FOV at Mt. John Observatory in New Zealand. The MOA observations were carried out in the MOA- Red band RMOA that corresponds to the sum of the Cousins R and I bands. KMTNet data were reduced by the pySIS photometry pipeline (M. D. Albrow et al. 2009) based on difference image analysis (DIA; C. Alard & R. H. Lupton 1998). For light-curve modeling, the KMTNet data were re-reduced using tender-loving-care (TLC) PySIS pipeline that provides best quality data sets. From the TLC photometry, we checked that one highly magnified data point at ( )HJD 2450000 HJD 9665.5 is real (see Figure 1). In addition, KMTC I- and V-band images were reduced using the pyDIA code (M. D. Albrow 2017) in order to estimate the source color and construct the color–magnitude diagram (CMD) of stars around the source. MOA data were reduced with the MOA’s DIA photometry pipeline (I. A. Bond et al. 2001). According to the procedures of J. C. Yee et al. (2012), the errors of the photometric data obtained from each pipeline were rescaled to make them χ2/dof → 1, where dof represents the degrees of freedom. 3. Light-curve Analysis Figure 1 presents the observed light curve of KMT-2022- BLG-0086, which has a U-shape feature in the peak that appears to be caused by caustic crossing. We thus conduct a standard binary-lens single-source (2L1S) modeling. 3.1. 2L1S Model The standard 2L1S modeling requires seven parameters: three single lensing parameters (t0, u0, tE), three binary lensing parameters (s, q, α), and ρ. Here, t0 is the time of the closest24 https://exoplanetarchive.ipac.caltech.edu/index.html 2 The Astronomical Journal, 170:75 (10pp), 2025 August Chung et al. http://astrothesaurus.org/uat/672 https://doi.org/10.3847/1538-3881/ade2e7 https://exoplanetarchive.ipac.caltech.edu/index.html source approach to the lens, u0 is the lens-source separation at t = t0 in units of θE (impact parameter), tE is the Einstein radius crossing time of the event, s is the projected separation of the binary-lens components in units of θE, q is the mass ratio of the two lens components, α is the angle between the binary axis and the source trajectory, and ρ is the normalized source radius θ�/θE, where θ� is the angular radius of the source. In addition, there are two flux parameters ( fs,i, fb,i) for each observatory, which are the source flux and blended flux of the ith observatory, respectively. The two flux parameters are modeled by Fi(t) = fs,iAi(t) + fb,i, where Ai is the magnification as a function of time at the ith observatory (S. H. Rhie et al. 1999). In order to find the binary-lens solution, we first carry out a grid search in the parameter space (s, q, α) to find local χ2 minima using a downhill approach based on the Markov chain Monte Carlo (MCMC) algorithm. The ranges of each parameter used in the grid search are s1 log 1, q4 log 0, and 0 � α � 2π, and they are uniformly divided with (50, 50, 50), respectively. In the grid search, s and q are fixed, while the other parameters are allowed to vary in the MCMC chain. From the grid search, we find two local solutions in the (s, q) plane due to a well-known close– wide degeneracy (K. Griest & N. Safizadeh 1998), in which they have similar (s, q) but different trajectories of α ≃ 3.7 and 2.4. We then refine the local solutions obtained from the grid search by allowing all parameters to vary. From the procedures, it is found that the best 2L1S solution is the close model with (s, q, α) = (0.47, 0.36, 2.4) (Model 1), which approximately describes the anomalies, but there are significant residuals from the model. This means that the standard model cannot explain the lensing light curve. We note that the χ2 of the wide model is much larger than the best close model by 110. For the other solution with α = 3.70 (Model 2), it fails to describe the second anomaly around the peak, thus it is worse than the best solution by Δχ2 = 97. Here we note that Model 2 has a severe close– wide degeneracy and the close model is favored over the wide model by Δχ2 = 4. Figure 2 shows the light curves of the two binary-lens models and residuals from the models. Model 1 has two caustic-crossing features around the peak, while Model 2 has both caustic-crossing and cusp-approach- ing features (see Figure 3). The lensing parameters of the two standard models are presented in Table 1. The anomalies of the event can be caused by the high- order effects including the microlens parallax and lens orbital motion, which are caused by the orbital motions of the Earth and binary lens, respectively. We thus conduct the binary- lens modeling including the microlens parallax and lens orbital parameters that are described by πE = (πE,N, πE,E) and (ds/dt, dα/dt). In this modeling, we restrict the lens systems to β < 1, where β is a ratio of the projected kinetic to the potential energy, (KE/PE)⊥. The parallax+orbital modeling is carried out based on the two 2L1S models. As a result, it is found that the parallax+orbital model explains the light curve better than the standard model by Δχ2 = 86, but it also cannot describe the light curve. Figure 2 shows Figure 1. Light curve of the microlensing event KMT-2022-BLG-0086. The black curve is the 1L1S model fit. Table 1 Best-fit Lensing Parameters of Two 2L1S Models Parameter Standard Parallax+Orbital Model 1 Model 2 Model 1 Model 2 χ2 1676.65 1763.34 1600.29 1708.62 t0 (HJD ) 9666.8008 ± 0.0385 9666.4049 ± 0.0314 9667.0999 ± 0.0732 9666.2740 ± 0.0457 u0 0.0592 ± 0.0025 0.0772 ± 0.0045 0.0333 ± 0.0058 0.0660 ± 0.0065 tE (days) 19.1909 ± 0.8423 18.6452 ± 0.8430 36.6228 ± 4.1230 21.1662 ± 1.3840 s 0.4684 ± 0.0094 0.4967 ± 0.0163 0.4335 ± 0.0169 0.4100 ± 0.0165 q 0.3569 ± 0.0276 0.3827 ± 0.0365 0.1384 ± 0.0377 1.6245 ± 0.1737 α (radians) 2.4089 ± 0.0175 3.7325 ± 0.0164 2.5607 ± 0.0352 3.6935 ± 0.0197 ρ <0.0005 <0.003 <0.002 <0.001 πE,N ⋯ ⋯ 9.9419 ± 2.4518 9.9873 ± 0.5678 πE,E ⋯ ⋯ −0.6201 ± 0.4840 0.1050 ± 0.5393 ds/dt (yr−1) ⋯ ⋯ 3.3107 ± 1.0847 −8.1957 ± 0.8869 dα/dt (radians yr−1) ⋯ ⋯ 5.2053 ± 2.1390 0.5964 ± 3.3737 fs,kmt 0.0628 ± 0.0030 0.0773 ± 0.0046 0.0323 ± 0.0069 0.0620 ± 0.0066 fb,kmt 0.1172 ± 0.0026 0.1022 ± 0.0042 0.1481 ± 0.0070 0.1183 ± 0.0064 Note. HJD = HJD–2450000. 3 The Astronomical Journal, 170:75 (10pp), 2025 August Chung et al. that there are still remarkable residuals from the models. This indicates that it is highly likely that the event would be caused by an extra source (2L2S) or an extra lens (3L1S). 3.2. 2L2S Model For the 2L2S modeling, four lensing parameters (t02, u02, qF, ρ2) are added to those of the 2L1S model. Here, t02 and u02 are the peak time and impact parameter of the secondary source star (S2), qF is the flux ratio between the secondary and primary source stars, and ρ2 is the normalized angular radius of the S2. The subscripts “1” and “2” represent the lensing parameters related to the primary source (S1) and secondary source, respectively. 2L2S modeling is generally conducted based on the best 2L1S solution. For this event, there are two 2L1S solutions with different source trajectories of α = 2.4 and α = 3.7, although the Δχ2 between the two models is 86. Such a significant Δχ2 was due to the α = 3.7 solution’s failure to describe the second anomaly around the peak. Since the second anomaly could be caused by the binary companion of the source, we carry out 2L2S modeling for the two 2L1S models. In the 2L2S modeling, we use the lensing parameters Figure 2. Light curves of two different 2L1S models with and without high-order effects. “Model 1” is the best-fit model and “Model 2” is the alternative model with a different source trajectory. The black solid and dashed curves represent the light curves of the “Model 1” with and without high-order effects, respectively, while the gray dotted and dashed–dotted curves represent the light curves for “Model 2.” The lower four panels present the residuals from the four models. Figure 3. Geometries of the two best-fit 2L1S models. The blue dots represent the lens components of each model and the black closed curve represents the caustic. The straight line with an arrow denotes the source trajectory. 4 The Astronomical Journal, 170:75 (10pp), 2025 August Chung et al. Figure 4. Light curves of the best-fit 2L2S and 3L1S models. The black solid and gray dashed curves represent the close and wide solutions of the 2L2S model, while the black dotted curve represents the light curve of the 3L1S model. The individual light curves and model residuals are available as the Data behind the Figure. (The data used to create this figure are available in the online article.) Table 2 Best-fit Lensing Parameters of 2L2S Models Parameter Model 1 Model 2 Close Wide Close Wide χ2 1513.42 1517.248 1493.68 1491.74 t01 (HJD ) 9666.6661 ± 0.0563 9667.5836 ± 0.0698 9665.2832 ± 0.0566 9665.5305 ± 0.0599 t02 (HJD ) 9665.5403 ± 0.1298 9665.3797 ± 0.1765 9668.0693 ± 0.0712 9668.2471 ± 0.0390 u01 0.0844 ± 0.0032 0.0829 ± 0.0051 0.0667 ± 0.0109 −0.0340 ± 0.0039 u02 0.2329 ± 0.0135 −0.3788 ± 0.0355 −0.0964 ± 0.0139 0.0499 ± 0.0058 tE (days) 12.7327 ± 0.5302 12.6105 ± 0.7420 15.9137 ± 1.1454 24.2254 ± 2.8416 qF 0.8718 ± 0.1296 2.4190 ± 0.5403 1.3410 ± 0.0696 1.2420 ± 0.0540 s 0.5416 ± 0.0094 2.4874 ± 0.0799 0.4047 ± 0.0232 4.3619 ± 0.2169 q 0.3673 ± 0.0331 0.5819 ± 0.1398 0.4229 ± 0.0703 1.9082 ± 0.9697 α (radians) 2.3757 ± 0.0291 2.6656 ± 0.0337 3.0356 ± 0.0523 −3.0565 ± 0.0379 ρ1 <0.0013 <0.0013 <0.003 <0.002 ρ2 <0.010 ⋯ <0.022 <0.014 fs,kmt 0.1189 ± 0.0068 0.2347 ± 0.0373 0.0845 ± 0.0108 0.0842 ± 0.0096 fb,kmt 0.0627 ± 0.0065 −0.0541 ± 0.0372 0.0962 ± 0.0104 0.0963 ± 0.0093 5 The Astronomical Journal, 170:75 (10pp), 2025 August Chung et al. https://doi.org/10.3847/1538-3881/ade2e7 of the 2L1S model to obtain initial values of the primary source, i.e., (t01, u01, tE, s, q, α, ρ1), while we set the initial values of the secondary source, (t02, u02, qF), by considering the peak time and second anomaly magnification. We then refine the initial parameters by allowing all parameters to vary. Here we consider four degenerate solutions due to the unknown sign of (±u01, ±u02), i.e., the well-known “ecliptic degeneracy” (G. Jiang et al. 2004; S. Poindexter et al. 2005). We also consider the close and wide solutions for each 2L1S model. From the modeling, we find that the best-fit 2L2S solution is the wide model based on “Model 2,” and it describes all the anomalies in the lensing light curve better than the best model based on “Model 1” by Δχ2 = 22. The χ2 improvement mainly appears around the peak with the remarkable anomalies. Therefore, we dismiss the 2L2S models based on “Model 1.” The close and wide models for “Model 2” have Δχ2 < 2. Thus, they are severely degenerate. Table 2 presents the best-fit 2L2S lensing parameters. As shown in Figure 4, the 2L2S model describes well the anomaly range 9660 HJD 9672 that could not be explained by the 2L1S model. The Δχ2 improvement of the 2L2S model relative to the standard model is 185. 3.3. 3L1S Model The two major anomalies of KMT-2022-BLG-0086 appear around the peak, which means that they were caused by the caustic close to the primary star. In this case, the anomalies induced by the triple-lens systems can be approximated by the superposition of those induced by two binary-lens systems (V. Bozza 1999; C. Han et al. 2001; C. Han 2005). We thus search for two binary-lens models that can explain the overall light curve. The two anomalies are individually in the ranges of < <9664 HJD 9666.3 (anomaly region 1; hereafter AR1) and < <9666.5 HJD 9670.0 (anomaly region 2; hereafter AR2). After excluding each anomaly, we perform the same procedure as described in Section 3.1. From this, we find that the best solution for the AR1 excluded is a binary-star model with q ∼ 0.1–0.3, while for the AR2 excluded it is likely a planetary model with q ∼ 0.03–0.08. This implies that the tertiary lens component would be a massive planet or a brown dwarf (BD). The two best solutions each have a severely degenerate model with Δχ2 < 1 (for AR1 excluded) or Δχ2 < 7 (for AR2 excluded) due to the close–wide degeneracy. Figure 5 shows the best-fit light curves for each case, and the resulting lensing parameters are presented in Table 3. For the triple-lens modeling, three parameters related to an extra lens component are added, and they are (s3, q3, ψ), where s3 is the separation between the primary and the tertiary components, q3 is the tertiary-primary mass ratio (M3/M1), and ψ is the angle between the primary-secondary and the primary- tertiary axes. In conformity with the notation of the subscript “3” for the primary-tertiary parameters, we set the primary-secondary parameters to the subscript “2,” that is, (s2, q2). In order to find the 3L1S solution, we perform a grid search in the parameter space (s3, q3, ψ). The parameters (s3, q3, ψ) have the ranges of s1 log 13 , q4 log 03 , and 0 � ψ � 2π and they are uniformly divided with (50, 50, 50). In this grid search, (s2, q2, α) are fixed, while the other lensing parameters are allowed to vary. The initial lensing parameters are set to the close (s2 < 1) and wide (s2 > 1) solutions for the AR1 excluded (i.e., binary-star model), respectively. Each grid search produces two locals that represent the close and wide solutions. We then refine the local solutions by allowing all parameters to vary. As a result, we find that the best-fit 3L1S solution is (s2, q2, s3, q3) = (1.72, 0.13, 0.90, 0.05). Here we note that the solution for s2 > 1 and s3 < 1 is denoted as the “Wide–Close” model, while for s2 < 1 and s3 < 1 it is denoted as the “Close–Close” model. The “Close–Close” model is disfavored by Δχ2 = 14 relative to Table 3 Best-fit Lensing Parameters of 2L1S Model for AR1 or AR2 Excluded AR1 Excluded AR2 Excluded Parameter s < 1 s > 1 s < 1 s > 1 t0 (HJD ) 9666.9960 ± 0.0832 9667.1565 ± 0.0464 9666.4533 ± 0.0502 9666.3440 ± 0.0464 u0 0.2324 ± 0.0332 0.1914 ± 0.0345 0.2546 ± 0.0303 0.2654 ± 0.0284 tE (days) 9.8812 ± 0.6568 12.2625 ± 1.1579 9.9918 ± 0.6317 9.8712 ± 0.6257 s 0.8113 ± 0.0485 2.1347 ± 0.1331 0.9294 ± 0.0325 1.5721 ± 0.0484 q 0.1043 ± 0.0276 0.3319 ± 0.0705 0.0327 ± 0.0103 0.0793 ± 0.0193 α (radians) 1.1654 ± 0.0203 1.2254 ± 0.0220 1.9435 ± 0.0021 1.9238 ± 0.0243 ρ <0.02 <0.015 <0.011 <0.006 Note. The anomaly regions AR1 and AR2 represent the ranges of < <9664 HJD 9666.3 and < <9666.5 HJD 9670.0, respectively. 9665.5 17 16.5 16 Figure 5. Light curves of the 2L1S solutions where the anomaly regions 1 and 2 (AR1 and AR2) are individually excluded. The AR1 and AR2 represent the ranges of < <9664 HJD 9666.3 and < <9666.5 HJD 9670.0, respectively 6 The Astronomical Journal, 170:75 (10pp), 2025 August Chung et al. “Wide–Close” model. The lensing parameters of the best-fit 3L1S model, “Wide–Close” model, is presented in Table 4 with the other three models, and its light curve is shown in Figure 4 together with those of the 2L2S models. Figure 4 shows that the triple-lens model also describes the light curve well. However, the 2L2S model is preferred over the triple-lens model by Δχ2 = 8.6. Figure 6 is the cumulative Δχ2 distribution between the 3L1S and 2L2S models and shows that the χ2 improvement is due to dominant KMTC data sets of the light curve that provide a better fit throughout the light curve, including the anomaly regions. This implies that KMT-2022-BLG-0086 is likely caused by the 2L2S model. The geometries of the 2L2S and 3L1S models are presented in Figure 7. We also check the 3L1S models based on the two 2L1S models, i.e., “Model 1” and “Model 2.” All the 3L1S models based on the two models have still severe residuals from each model. The 3L1S models for the “Model 1” and “Model 2” are worse than the best- fit 3L1S model by Δχ2 = 79 and 106, respectively. Hence, they also cannot explain the light curve of the event. 4. Angular Einstein Radius The angular Einstein radius is one of two key parameters to measure the physical lens parameters including the lens mass (ML) and distance to the lens (DL) and is defined by θE = θ�/ρ. For the event, the two major anomalies around the peak were not well covered. Thus, we only measured the upper limit of ρ, i.e., 0.002max,s1 within the 3σ level (see Figure 8). We thus can only obtain the lower limit of the θE. The angular source radius is obtained from the dereddened color and magnitude of the source that are determined from the offset between the source star and the red giant clump positions on the CMD ( ) ( ) ( ) ( )= +V I I V I I V I I, , , , 1s,0 cl,0 Table 4 Best-fit Lensing Parameters of 3L1S Model s2 < 1 s2 > 1 Parameter Close–Close Close–Wide Wide–Close Wide–Wide (s3 < 1) (s3 > 1) (s3 < 1) (s3 > 1) χ2 1514.17 1523.09 1500.30 1517.88 t0 (HJD ) 9666.6985 ± 0.0497 9666.6381 ± 0.0649 9666.9538 ± 0.0414 9666.9663 ± 0.0470 u0 0.2765 ± 0.0241 0.2581 ± 0.0300 0.2369 ± 0.0203 0.1900 ± 0.0273 tE (days) 9.5319 ± 0.5523 10.1363 ± 0.6729 10.4896 ± 0.5886 12.8868 ± 1.0883 s2 0.9172 ± 0.0323 0.8920 ± 0.0383 1.7224 ± 0.0635 1.8765 ± 0.0890 q2 0.0221 ± 0.0052 0.0239 ± 0.0093 0.1320 ± 0.0247 0.1825 ± 0.0304 α (radians) 1.0202 ± 0.0214 0.9445 ± 0.0216 1.0566 ± 0.0168 1.0268 ± 0.0203 s3 0.9410 ± 0.0256 1.5220 ± 0.0328 0.9031 ± 0.0200 1.3983 ± 0.0365 q3 0.0381 ± 0.0065 0.0635 ± 0.0117 0.0465 ± 0.0057 0.0556 ± 0.0104 ψ (radians) 0.9675 ± 0.0367 1.0617 ± 0.0452 1.1104 ± 0.0333 1.2017 ± 0.0365 ρ <0.007 <0.006 <0.003 <0.004 fs,kmt 0.2323 ± 0.0239 0.2208 ± 0.0316 0.2211 ± 0.0199 0.1743 ± 0.0326 fb,kmt −0.0504 ± 0.0236 −0.0393 ± 0.0313 −0.0397 ± 0.0197 0.0061 ± 0.0323 Figure 6. Cumulative Δχ2 distribution between the 3L1S and 2L2S models. Figure 7. Geometries of the best-fit 2L2S and 3L1S models. For the 2L2S model, S1 and S2 denote the primary and secondary sources. The dotted circle represents the Einstein ring and the other notations are the same as Figure 3. 7 The Astronomical Journal, 170:75 (10pp), 2025 August Chung et al. where Δ(V − I, I) = (V − I, I)s − (V − I, I)cl represents the offset between the source and the centroid of the red giant clump. This is based on the assumption that the source and clump experience the same amount of reddening and extinction (J. Yoo et al. 2004). From the KMTC CMD constructed from stars around the source star, we find that the centroid of the clump is (V − I, I)cl = (3.48 ± 0.17, 17.38 ± 0.43). The measured magnitudes of the primary and secondary source stars are Is1 = 21.56 ± 0.13 and Is2 = 21.33 ± 0.12, which are obtained from the source fluxes of the best-fit 2L2S wide model. Due to only two low- magnified KMTC V-band data points, the source color was not securely measured. We thus combine the KMCT CMD and the CMD constructed by HST toward Baade’s window (J. A. Holtzman et al. 1998). The combination of the two CMDs is conducted by calibrating the clump positions on the individual CMDs. Figure 9 shows the combined CMD. The source color is estimated from the mean value of the HST stars with similar magnitudes to the source star. From the combined CMD, we obtain the primary and secondary source colors of (V − I)s1 = 3.182 ± 0.066 and (V − I)s2 = 3.167 ± 0.061. The dereddened color and magnitude of the clump are adopted by (V − I)cl,0 = 1.06 and Icl,0 = 14.43 from T. Bensby et al. (2011) and D. M. Nataf et al. (2013), respectively. As a result, it is found that the dereddened colors and magnitudes of the two sources are (V − I, I)s1,0 = (0.758 ± 0.066, 18.62 ± 0.13) and (V − I, I)s2,0 = (0.743 ± 0.061, 18.38 ± 0.12). This means that both stars are late G dwarf stars. Using the VIK color–color relation of M. S. Bessell & J. M. Brett (1988) and color-surface brightness of P. Kervella et al. (2004), we obtain the angular radius of the primary source of θ�,s1 = 0.615 ± 0.056 μas. We then determine the lower limit of θE {= = 0.209 mas for close 0.308 mas for wide.E,min ,s1 max,s1 The lower limit of the relative lens-source proper motion is obtained as µ = = t 4.79 mas yr for close 4.64 mas yr for wide.rel,min E,min E 1 1 For the 3L1S model, by following the same procedure as the binary-source model, we find that the dereddened color and magnitude of the source are (V − I, I)0 = (0.81 ± 0.16, 16.69 ± 0.10), indicating that the source is an early G-type subgiant or a turn-off star. The color and magnitude derive the angular source radius of θ� = 1.63 ± 0.31 μas. For this model, the upper limit of the normalized source radius is 0.003max . With the upper limit, we estimate the lower limits of the angular Einstein radius and relative lens-source proper motion, = 0.542 masE,min and µ = 18.89 mas yrrel,min 1, respectively. 5. Lens Properties The lens mass and distance to the lens are given by ( )= = + M D; au , 2L E E L E E S where ( )/G c M4 au 8.14 mas2 1 and πS = au/DS denotes the parallax of the source. Hence, we can directly Figure 8. χ2 distributions of u0 and ρ for the best-fit 2L2S and 3L1S models. The ρ of the 2L2S model represents the value of the primary source. Figure 9. Instrumental CMD of stars in the observed field, which is constructed from combining KMTC and HST observations. The KMTC and HST CMDs are plotted as black and green dots, respectively. The blue and cyan dots represent the positions of the primary and secondary sources for the 2L2S model, and the brown dot represents the source position for the 3L1S model. The red dot denotes the red giant clump centroid. 8 The Astronomical Journal, 170:75 (10pp), 2025 August Chung et al. determine the physical lens parameters by measuring θE and πE, but it is generally hard to measure them. For this event, only the lower limit of θE was measured. We thus carry out a Bayesian analysis to estimate the physical lens parameters with the measured two parameters ( )t ,E E,min . The Bayesian analysis is conducted by using the Galactic model proposed by Y. K. Jung et al. (2021). We randomly create about 2 × 107 simulated microlensing events. Then, we weight each simulated event, i, by ( ) ( )= =w t t t exp 2 ; , 3i i i i 2 2 E, E E 2 where σ(tE) is the uncertainty of the measured value. We set wi = 0 if iE, E,min. Figure 10 shows the Bayesian posteriors for the physical parameters of the primary lens star for close and wide solutions. The estimated mass and distance of the primary star are = + + M M M 0.35 for close 0.50 for wide, 1 0.19 0.34 0.27 0.36 and = + + D 6.24 kpc for close 5.75 kpc for wide. L 1.62 1.13 1.85 1.24 Then, the mass of the secondary component is = + + M M M 0.15 for close 0.96 for wide. 2 0.09 0.15 0.71 0.85 The projected separation of the lens components is = + + a 0.53 au for close 7.71 au for wide. 0.59 0.58 6.06 5.77 The results indicate that KMT-2022-BLG-0086L is likely to be a binary star composed of M and G dwarfs or two M dwarfs. However, the primary star could be also a K dwarf and the secondary companion could be also a BD, a K, or an A dwarf. Figure 10 shows that the lens system for the close and wide solutions is located in the disk and bulge with equal probability. This is consistent with the relative lens-source proper motion of μrel � 4.6 mas yr−1. We also carry out the Bayesian analysis for the 3L1S model. From the Bayesian analysis, it is found that the lens is a low-mass dwarf binary of ( ) ( )= + +M M M M, 0.43 , 0.0561 2 0.35 0.41 0.047 0.055 hosting a BD or a massive giant planet with a mass of = +M M20.843 17.04 20.20 J. The result is shown in Figure 10. The projected separations of the individual components from the primary star are = +a 3.79 au,2 2.48 3.72 and = +a 1.99 au,3 1.30 1.95 , respectively. If the tertiary component is a giant planet, it orbits beyond the snow line of the primary star. The lens system is located at a distance of = +D 4.06 kpcL 3.28 1.39 , which indicates that the lens is located in the disk of our Galaxy. The proper motion of the triple-lens model of μrel ≳ 18.9mas yr−1 is more than three times larger than a typical bulge-source disk-lens proper motion of ∼6mas yr−1, so it does not seem to be a valid solution. In order to check the unlikeness of the 3L1S solution, we estimate the relative weights of the 3L1S solution (A. Gould et al. 2022). The weights are the product of the two factors: the first is simply the total weight from the Bayesian analysis and the second is exp(−Δχ2/2), where Δχ2 is the χ2 difference relative to the best solution. The two factors are presented at the right side of each row in Table 5. For the 3L1S model, the relative weight is 0.00004, indicating that this solution is extremely unlikely. We also estimate the relative weights of the close and wide solutions for the 2L2S model. With the relative weights, we combine the physical parameters of the close and wide solutions and provide a single “adopted” value for each parameter, which is simply the weighted average of the two solutions. For a⊥, we follow a similar approach, provided that either the individual solutions are strongly overlapping or one Table 5 Physical Lens Parameters Physical Parameters Relative Weights Models M1 M2 Mp DL a⊥ a⊥,3 Gal. Mod. χ2 (M⊙) (M⊙) (MJ) (kpc) (au) (au) 2L2S ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ Close +0.35 0.19 0.34 +0.15 0.09 0.15 ⋯ +6.24 1.62 1.13 +0.53 0.59 0.58 ⋯ 0.90 0.38 Wide +0.50 0.27 0.36 +0.96 0.71 0.85 ⋯ +5.75 1.85 1.24 +7.71 6.06 5.77 ⋯ 1.00 1.00 Adopted +0.46 0.25 0.35 +0.75 0.55 0.67 ⋯ +5.87 1.79 1.21 (bi-modal) ⋯ ⋯ ⋯ 3L1S +0.43 0.35 0.41 +0.056 0.047 0.055 +20.84 17.04 20.20 +4.06 3.28 1.39 +3.79 2.48 3.72 +1.99 1.30 1.95 0.004 0.01 Figure 10. Bayesian posteriors for the mass and distance of the host lens star for the 2L2S and 3L1S models. The red and blue lines for the 2L2S model represent the distributions of the close and wide solutions. 9 The Astronomical Journal, 170:75 (10pp), 2025 August Chung et al. solution is strongly dominant. If neither condition is met, we enter “bi-model” instead. The “adopted” values are presented in Table 5. 6. Summary We analyzed the microlensing event KMT-2022-BLG-0086 with remarkable anomalies around the peak. From the analysis, it was found that the event was best described by the 2L2S model, but the 3L1S model is only disfavored by Δχ2 ≃ 9. Unfortunately, the anomalies were not enough covered, we thus could only measure the minimum angular Einstein radius E,min. From the Bayesian analysis with the measured tE and E,min, it was estimated that the masses of the binary-lens components are ( ) ( )= + +M M M M, 0.46 , 0.751 2 0.25 0.35 0.55 0.67 , while those of the triple-lens components are (M M, ,1 2 ) ( )= + + +M M M M0.43 , 0.06 , 20.843 0.35 0.41 0.05 0.06 17.04 20.20 J . The rela- tive lens-source proper motion of the 2L2S model of μrel � 4.6 mas yr−1 corresponds to the Bayesian result with = +D 5.87L 1.79 1.21 kpc, whereas that of the 3L1S model of μrel � 18.9 mas yr−1 does not correspond to the Bayesian result with = +D 4.06 kpcL 3.28 1.39 , because it is >3 times larger than the typical disk object value. Therefore, it is likely that the event was caused by the 2L2S model. Acknowledgments The work by S.-J.C. was supported by the Korea Astronomy and Space Science Institute under the R&D program (project No. 2025-1-830-05) supervised by the Ministry of Science and ICT. The MOA project is supported by JSPS KAKENHI grant No. JP24253004, JP26247023, JP16H06287, and JP22H00153. J.C.Y., I.-G.S. acknowledge support from N.S.F grant No. AST-2108414. W.Z. and H.Y. acknowledge support by the National Natural Science Foundation of China (grant No. 12133005). Y.S. acknowledges support from BSF grant No. 2020740. This research has made use of the KMTNet system operated by the KASI and the data were obtained at three sites of CTIO in Chile, SAAO in South Africa, and SSO in Australia. Data transfer from the host site to KASI was supported by the Korea Research Environment Open NETwork (KREONET). ORCID iDs Sun-Ju Chungaa https://orcid.org/0000-0001-6285-4528 Kyu-Ha Hwangaa https://orcid.org/0000-0002-9241-4117 Jennifer C. Yeeaa https://orcid.org/0000-0001-9481-7123 Hongjing Yangaa https://orcid.org/0000-0003-0626-8465 Michael D. Albrowaa https://orcid.org/0000-0003-3316-4012 Youn Kil Jungaa https://orcid.org/0000-0002-0314-6000 Cheongho Hanaa https://orcid.org/0000-0002-2641-9964 Yoon-Hyun Ryuaa https://orcid.org/0000-0001-9823-2907 In-Gu Shinaa https://orcid.org/0000-0002-4355-9838 Yossi Shvartzvaldaa https://orcid.org/0000-0003-1525-5041 Weicheng Zangaa https://orcid.org/0000-0001-6000-3463 Dong-Jin Kimaa https://orcid.org/0000-0002-4292-9649 Seung-Lee Kimaa https://orcid.org/0000-0003-0562-5643 Chung-Uk Leeaa https://orcid.org/0000-0003-0043-3925 Byeong-Gon Parkaa https://orcid.org/0000-0002-6982-7722 Richard W. Poggeaa https://orcid.org/0000-0003-1435-3053 David P. Bennettaa https://orcid.org/0000-0001-8043-8413 Akihiko Fukuiaa https://orcid.org/0000-0002-4909-5763 Yuki Hiraoaa https://orcid.org/0000-0003-4776-8618 Stela Ishitani Silvaaa https://orcid.org/0000-0003-2267-1246 Naoki Koshimotoaa https://orcid.org/0000-0003-2302-9562 Shota Miyazakiaa https://orcid.org/0000-0001-9818-1513 Yasushi Murakiaa https://orcid.org/0000-0003-1978-2092 Kansuke Nunotaaa https://orcid.org/0009-0005-3414-455X Greg Olmschenkaa https://orcid.org/0000-0001-8472-2219 Clément Rancaa https://orcid.org/0000-0003-2388-4534 Nicholas J. Rattenburyaa https://orcid.org/0000-0001- 5069-319X Yuki Satohaa https://orcid.org/0000-0002-1228-4122 Takahiro Sumiaa https://orcid.org/0000-0002-4035-5012 Daisuke Suzukiaa https://orcid.org/0000-0002-5843-9433 Sean K. Terryaa https://orcid.org/0000-0002-5029-3257 Aikaterini Vandorouaa https://orcid.org/0000-0002- 9881-4760 References Akeson, R., Armus, L., Bachelet, E., et al. 2019, arXiv:1902.05569 Albrow, M. D. 2017, MichaelDAlbrow/pyDIA: Initial Release on Github, v1.0.0, Zenodo, doi:10.5281/zenodo.268049 Albrow, M. D., Beaulieu, J.-P., Caldwell, J. A. R., et al. 2000, ApJ, 534, 894 Albrow, M. D., Horne, K., Bramich, D. M., et al. 2009, MNRAS, 397, 2099 Alard, C., & Lupton, R. H. 1998, ApJ, 503, 325 Bennett, D. P., & Rhie, S. H. 2002, ApJ, 574, 985 Bennett, D. P., Rhie, S. H., Becker, A. C., et al. 1999, Natur, 402, 57 Bennett, D. P., Rhie, S. H., Udalski, A., et al. 2016, AJ, 152, 125 Bennett, D. P., Udalski, A., Bond, I. A., et al. 2020, AJ, 160, 72 Bensby, T., Adén, D., Meléndez, J., et al. 2011, A&A, 533, 134 Bessell, M. S., & Brett, J. M. 1988, PASP, 100, 1134 Bond, I. A., Abe, F., Dodd, R. J., et al. 2001, MNRAS, 327, 868 Bozza, V. 1999, A&A, 348, 311 Gould, A., Han, C., Zang, W., et al. 2022, A&A, 664, A13 Gould, A., & Loeb, A. 1992, ApJ, 396, 104 Gould, A., Udalski, A., Shin, I.-G., et al. 2014, Sci, 345, 46 Griest, K., & Safizadeh, N. 1998, ApJ, 500, 37 Han, C. 2005, ApJ, 629, 1102 Han, C., Bennett, D. P., Udalski, A., et al. 2016, ApJ, 825, 8 Han, C., Chang, H.-Y., An, J. H., et al. 2001, MNRAS, 328, 986 Han, C., Gould, A., Hirao, Y., et al. 2021, A&A, 655, A24 Han, C., Lee, C.-U., Udalski, A., et al. 2020, AJ, 159, 48 Han, C., Udalski, A., Bond, I. A., et al. 2024a, A&A, 692, A221 Han, C., Udalski, A., Gould, A., et al. 2017, AJ, 154, 223 Han, C., Udalski, A., Jung, Y. K., et al. 2023, A&A, 670, A172 Han, C., Udalski, A., Jung, Y. K., et al. 2024b, A&A, 685, A16 Holtzman, J. A., Watson, A. M., Baum, W. A., et al. 1998, AJ, 115, 1946 Jiang, G., Depoy, D. L., Gal-Yam, A., et al. 2004, ApJ, 617, 1307 Johnson, S. A., Penny, M., Gaudi, B. S., et al. 2020, AJ, 160, 123 Jung, Y. K., Han, C., Gould, A., et al. 2013, ApJL, 768, L7 Jung, Y. K., Han, C., Udalski, A., et al. 2021, AJ, 161, 293 Kaib, N. A., Raymond, S. N., & Duncan, M. 2013, Natur, 493, 381 Kervella, P., Thévenin, F., Di Folco, E., & Ségransan, D. 2004, A&A, 426, 297 Kim, S.-L., Lee, C.-U., Park, B.-G., et al. 2016, JKAS, 49, 37 Malmberg, D., Davies, M. B., & Heggie, D. C. 2011, MNRAS, 411, 859 Mao, S., & Paczyński, B. 1991, ApJ, 374, 37 Nataf, D. M., Gould, A., Fouqué, P., et al. 2013, ApJ, 769, 88 Penny, M., Gaudi, B. S., Kerins, E., et al. 2019, ApJS, 241, 3 Poindexter, S., Afonso, C., Bennett, D. P., et al. 2005, ApJ, 633, 914 Poleski, R., Skowron, J., Udalski, A., et al. 2014, ApJ, 795, 42 Rasio, F. A., & Ford, E. B. 1996, Sci, 274, 954 Rhie, S. H., Becker, A. C., & Bennett, D. P. 1999, ApJ, 522, 1037 Spergel, D., Gehrels, N., Baltay, C., et al. 2015, arXiv:1503.03757 Udalski, A., Jung, Y. K., Han, C., et al. 2015, ApJ, 812, 47 Yee, J. C., Shvartzvald, Y., Gal-Yam, A., et al. 2012, ApJ, 755, 102 Yoo, J., DePoy, D. L., Gal-Yam, A., et al. 2004, ApJ, 603, 139 Zang, W., Han, C., Kondo, I., et al. 2021, RAA, 21, 239 Zhang, K., Zang, W., El-Badry, K., et al. 2024, NatAs, 8, 1575 10 The Astronomical Journal, 170:75 (10pp), 2025 August Chung et al. https://orcid.org/0000-0001-6285-4528 https://orcid.org/0000-0002-9241-4117 https://orcid.org/0000-0001-9481-7123 https://orcid.org/0000-0003-0626-8465 https://orcid.org/0000-0003-3316-4012 https://orcid.org/0000-0002-0314-6000 https://orcid.org/0000-0002-2641-9964 https://orcid.org/0000-0001-9823-2907 https://orcid.org/0000-0002-4355-9838 https://orcid.org/0000-0003-1525-5041 https://orcid.org/0000-0001-6000-3463 https://orcid.org/0000-0002-4292-9649 https://orcid.org/0000-0003-0562-5643 https://orcid.org/0000-0003-0043-3925 https://orcid.org/0000-0002-6982-7722 https://orcid.org/0000-0003-1435-3053 https://orcid.org/0000-0001-8043-8413 https://orcid.org/0000-0002-4909-5763 https://orcid.org/0000-0003-4776-8618 https://orcid.org/0000-0003-2267-1246 https://orcid.org/0000-0003-2302-9562 https://orcid.org/0000-0001-9818-1513 https://orcid.org/0000-0003-1978-2092 https://orcid.org/0009-0005-3414-455X https://orcid.org/0000-0001-8472-2219 https://orcid.org/0000-0003-2388-4534 https://orcid.org/0000-0001-5069-319X https://orcid.org/0000-0001-5069-319X https://orcid.org/0000-0002-1228-4122 https://orcid.org/0000-0002-4035-5012 https://orcid.org/0000-0002-5843-9433 https://orcid.org/0000-0002-5029-3257 https://orcid.org/0000-0002-9881-4760 https://orcid.org/0000-0002-9881-4760 https://arxiv.org/abs/1902.05569 https://doi.org/10.5281/zenodo.268049 https://doi.org/10.1086/308798 https://ui.adsabs.harvard.edu/abs/2000ApJ...534..894A/abstract https://doi.org/10.1111/j.1365-2966.2009.15098.x https://ui.adsabs.harvard.edu/abs/2009MNRAS.397.2099A/abstract https://doi.org/10.1086/305984 https://ui.adsabs.harvard.edu/abs/1998ApJ...503..325A/abstract https://doi.org/10.1086/340977 https://ui.adsabs.harvard.edu/abs/2002ApJ...574..985B/abstract https://doi.org/10.1038/46990 https://ui.adsabs.harvard.edu/abs/1999Natur.402...57B/abstract https://doi.org/10.3847/0004-6256/152/5/125 https://ui.adsabs.harvard.edu/abs/2016AJ....152..125B/abstract https://doi.org/10.3847/1538-3881/ab9cb9 https://ui.adsabs.harvard.edu/abs/2020AJ....160...72B/abstract https://doi.org/10.1051/0004-6361/201117059 https://ui.adsabs.harvard.edu/abs/2011A&A...533A.134B/abstract https://doi.org/10.1086/132281 https://ui.adsabs.harvard.edu/abs/1988PASP..100.1134B/abstract https://doi.org/10.1046/j.1365-8711.2001.04776.x https://ui.adsabs.harvard.edu/abs/2001MNRAS.327..868B/abstract https://ui.adsabs.harvard.edu/abs/1999A&A...348..311B/abstract https://doi.org/10.1051/0004-6361/202243744 https://ui.adsabs.harvard.edu/abs/2022A&A...664A..13G/abstract https://doi.org/10.1086/171700 https://ui.adsabs.harvard.edu/abs/1992ApJ...396..104G/abstract https://doi.org/10.1126/science.1251527 https://ui.adsabs.harvard.edu/abs/2014Sci...345...46G/abstract https://doi.org/10.1086/305729 https://ui.adsabs.harvard.edu/abs/1998ApJ...500...37G/abstract https://doi.org/10.1086/431143 https://ui.adsabs.harvard.edu/abs/2005ApJ...629.1102H/abstract https://doi.org/10.3847/0004-637X/825/1/8 https://ui.adsabs.harvard.edu/abs/2016ApJ...825....8H/abstract https://doi.org/10.1046/j.1365-8711.2001.04973.x https://ui.adsabs.harvard.edu/abs/2001MNRAS.328..986H/abstract https://doi.org/10.1051/0004-6361/202141939 https://ui.adsabs.harvard.edu/abs/2021A&A...655A..24H/abstract https://doi.org/10.3847/1538-3881/ab5db9 https://ui.adsabs.harvard.edu/abs/2020AJ....159...48H/abstract https://doi.org/10.1051/0004-6361/202451806 https://ui.adsabs.harvard.edu/abs/2024A&A...692A.221H/abstract https://doi.org/10.3847/1538-3881/aa9179 https://ui.adsabs.harvard.edu/abs/2017AJ....154..223H/abstract https://doi.org/10.1051/0004-6361/202245525 https://ui.adsabs.harvard.edu/abs/2023A&A...670A.172H/abstract https://doi.org/10.1051/0004-6361/202348791 https://ui.adsabs.harvard.edu/abs/2024A&A...685A..16H/abstract https://doi.org/10.1086/300336 https://ui.adsabs.harvard.edu/abs/1998AJ....115.1946H/abstract https://ui.adsabs.harvard.edu/abs/1998AJ....115.1946H/abstract https://doi.org/10.1086/425678 https://ui.adsabs.harvard.edu/abs/2004ApJ...617.1307J/abstract https://doi.org/10.3847/1538-3881/aba75b https://ui.adsabs.harvard.edu/abs/2020AJ....160..123J/abstract https://doi.org/10.1088/2041-8205/768/1/L7 https://ui.adsabs.harvard.edu/abs/2013ApJ...768L...7J/abstract https://doi.org/10.3847/1538-3881/abf8bd https://ui.adsabs.harvard.edu/abs/2021AJ....161..293J/abstract https://doi.org/10.1038/nature11780 https://ui.adsabs.harvard.edu/abs/2013Natur.493..381K/abstract https://doi.org/10.1051/0004-6361:20035930 https://ui.adsabs.harvard.edu/abs/2004A&A...426..297K/abstract https://ui.adsabs.harvard.edu/abs/2004A&A...426..297K/abstract https://doi.org/10.5303/JKAS.2016.49.1.37 https://ui.adsabs.harvard.edu/abs/2016JKAS...49...37K/abstract https://doi.org/10.1111/j.1365-2966.2010.17730.x https://ui.adsabs.harvard.edu/abs/2011MNRAS.411..859M/abstract https://doi.org/10.1086/186066 https://ui.adsabs.harvard.edu/abs/1991ApJ...374L..37M/abstract https://doi.org/10.1088/0004-637X/769/2/88 https://ui.adsabs.harvard.edu/abs/2013ApJ...769...88N/abstract https://doi.org/10.3847/1538-4365/aafb69 https://ui.adsabs.harvard.edu/abs/2019ApJS..241....3P/abstract https://doi.org/10.1086/468182 https://ui.adsabs.harvard.edu/abs/2005ApJ...633..914P/abstract https://doi.org/10.1088/0004-637X/795/1/42 https://ui.adsabs.harvard.edu/abs/2014ApJ...795...42P/abstract https://doi.org/10.1126/science.274.5289.954 https://ui.adsabs.harvard.edu/abs/1996Sci...274..954R/abstract https://doi.org/10.1086/307697 https://ui.adsabs.harvard.edu/abs/1999ApJ...522.1037R/abstract https://arxiv.org/abs/1503.03757 https://doi.org/10.1088/0004-637X/812/1/47 https://ui.adsabs.harvard.edu/abs/2015ApJ...812...47U/abstract https://doi.org/10.1088/0004-637X/755/2/102 https://ui.adsabs.harvard.edu/abs/2012ApJ...755..102Y/abstract https://doi.org/10.1086/381241 https://ui.adsabs.harvard.edu/abs/2004ApJ...603..139Y/abstract https://doi.org/10.1088/1674-4527/21/9/239 https://ui.adsabs.harvard.edu/abs/2021RAA....21..239Z/abstract https://doi.org/10.1038/s41550-024-02375-9 https://ui.adsabs.harvard.edu/abs/2024NatAs...8.1575Z/abstract 1. Introduction 2. Observations and Data 3. Light-curve Analysis 3.1.2L1S Model 3.2.2L2S Model 3.3.3L1S Model 4. Angular Einstein Radius 5. Lens Properties 6. Summary References