arXiv subjects

Krzysztof A. Rybicki

Publications and source records attributed to Krzysztof A. Rybicki.

At least 19 recordsLinked to original sources

arXiv2026

OGLE-2016-BLG-0523: A Low-mass Brown Dwarf or super-Jupiter in a $>100$ au Orbit

To search for very wide-orbit binary-lens events, we cross-match microlensing events detected by OGLE-IV and KMTNet between 2011 and 2024. After removing contaminants from variable stars, we identify OGLE-2016-BLG-0523 as a microlensing event showing two short-lived bumps in its light curve, with the two separated by 8.36 yr. We investigate three scenarios to explain the two bumps, including a binary-lens single-source (2L1S), a single-lens binary-source (1L2S), and two unrelated single-lens single-source events (2$\times$1L1S). The 1L2S interpretation is excluded due to its poorer fit to the data, while the 2$\times$1L1S scenario is disfavored by the low event rate, unphysical total source flux, and unphysical color for one of the two putative sources. For the surviving 2L1S interpretation, the Einstein timescales of the two bumps are $8.343 \pm 0.076$ days and $3.231 \pm 0.047$ days, respectively, implying a binary mass ratio of $q = 0.15$. A Bayesian analysis indicates that the primary lens is most likely a low-mass M dwarf, while the companion is probably a low-mass brown dwarf or super-Jupiter. The inferred projected separation is about 450 au, making the companion the widest low-mass object discovered via microlensing to date. Our discovery highlights both the promise and challenges of identifying very wide, low-mass companions through microlensing. Although upcoming facilities such as Roman and Earth 2.0 space telescopes will improve sensitivity to such events, overcoming degeneracies and distinguishing them from variable phenomena will remain essential for building a robust statistical sample.

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arXiv2026

Two Low-Mass-Ratio Microlensing Planets from High-Magnification Events: KMT-2021-BLG-0247 and MOA-2023-BLG-169

We present an analysis of two planetary microlensing events, KMT-2021-BLG-0247 and MOA-2023-BLG-169, both of which exhibit high magnifications and low planet--host mass ratios, but with markedly different levels of parameter constraint. For KMT-2021-BLG-0247, the finite-source effect and microlens parallax are both clearly detected, leading to unusually tight constraints on the physical properties of the lens system. The host mass and lens distance are approximately $M_{\rm L}=0.9\pm0.1\,M_\odot$ and $D_{\rm L}=6.7^{+1.0}_{-0.3}\,\mathrm{kpc}$, respectively, and the planet mass is $M_{\rm p}=41\pm5\,M_\oplus$. The projected planet--host separations are $a_\perp=3.4^{+0.7}_{-0.3}\,\mathrm{au}$ and $3.0^{+0.6}_{-0.3}\,\mathrm{au}$ for the wide and close solutions, respectively. In contrast, MOA-2023-BLG-169 involves an extremely faint source, with $I_{S,{\rm OGLE}}=26.73$, such that the light curve permits a broad family of strongly correlated solutions. We therefore construct the physical-parameter likelihood using approximate invariant combinations of the light-curve parameters and supplement it with post-event Euclid/VIS imaging from the Euclid Q2 Galactic Bulge Survey (Beaulieu et al. 2026). The Euclid data reveal a component at the event position with ${\rm VIS}_{\rm AB}=23.05\pm0.09\,{\rm mag}$. Interpreting this component as the combined light from the source and any luminous lens, the resulting posterior gives $M_{\rm L}=0.48^{+0.23}_{-0.17}\,M_\odot$, $D_{\rm L}=3.50^{+2.82}_{-1.20}\,\mathrm{kpc}$, $a_\perp=1.62^{+0.77}_{-0.43}\,\mathrm{au}$, and $M_{\rm p}=143^{+103}_{-63}\,M_\oplus$. MOA-2023-BLG-169 demonstrates that, for an extreme faint-source event, even the event timescale and angular Einstein radius can remain strongly dependent on the Galactic prior and independent flux constraints.

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arXiv2026

A Search For Stellar-mass Black Holes Via Astrometric Microlensing II: 2012-2015 Keck Candidates

The Milky Way is expected to host $\sim$10$^8$ stellar-mass black holes with an uncertain binary fraction. The only proven method to detect isolated stellar mass black holes is gravitational microlensing. Here we report the results of a microlensing search for black holes with photometry and astrometry. By combining 10 years of seeing-limited photometry from OGLE and MOA with diffraction-limited photometry and astrometry from adaptive optics imagers at the W.~M.~Keck Observatory, we constrain lens masses for OGLE-2012-BLG-0169, OGLE-2014-BLG-0613/MOA-2015-BLG-041, OGLE-2015-BLG-0029/MOA-2015-BLG-170, and OGLE-2015-BLG-0211. Of the four long-duration microlensing events monitored, we ruled out black hole lenses in 3 events, which likely have stellar or white dwarf lenses. OGLE-2015-BLG-0211 remains a black hole candidate with a poorly constrained lens mass with a 1$σ$ upper mass limit of 3.2$M_\odot$ and a 3$σ$ upper mass limit of 21.6$M_\odot$. This event suffered from poor observing conditions and significant astrometric reference frame uncertainties, but its analysis may benefit from additional astrometric data in the upcoming Gaia Data Release 4. Of the six long-timescale ($t_E>100$ days) microlensing events from this work and previous studies, one black hole has been confirmed with a second not ruled out. We briefly examine Galactic model simulations and find that our result agrees with current expectations. Ultimately, we need a larger sample of isolated black holes to constrain their formation processes. This will be possible in the coming years with Rubin and Roman, as well as improved astrometry from JWST and large, ground-based telescopes equipped with adaptive optics.

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arXiv2026

KMT-2026-BLG-0083L: A Two-Jovian-Planet System Orbiting an M Dwarf Discovered by Microlensing

We present the analysis of the microlensing event KMT-2026-BLG-0083, which was independently detected by the KMTNet, OGLE, and PRIME surveys and also monitored by the DREAMS survey. The combined data provide dense coverage of two distinct short-duration anomalies in the light curve that cannot be reproduced by a standard binary-lens model. Independent analyses of the two anomalies indicate that each is produced by a planetary companion to the lens, motivating a triple-lens interpretation. The modeling yields two pairs of degenerate solutions arising from the well-known inner--outer degeneracy, with each pair exhibiting two local solutions depending on whether the source passes above or below the distant planetary companion. The preferred model indicates two giant planets with mass ratios $q_2=(5.25\pm 0.08)\times 10^{-3}$ and $q_3=(3.04\pm 0.24)\times10^{-3}$ orbiting a common host. Bayesian analysis indicates that the host is an M-dwarf star with a mass of $0.48^{+0.36}_{-0.28}~M_\odot$, hosting two giant planets with masses of $2.65^{+1.96}_{-1.55}~M_{\rm J}$ and $1.54^{+1.14}_{-0.90}~M_{\rm J}$. The projected planet--host separations are $10.6^{+1.7}_{-2.2}$~au and $1.7^{+0.3}_{-0.3}$~au, placing the inner planet near the host's snow line and the outer planet at a substantially larger separation. Thus, KMT-2026-BLG-0083L becomes the seventh confirmed multiple-planet system discovered through gravitational microlensing, providing another example of a cold giant planetary system orbiting a subsolar-mass star.

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arXiv2026

KMT-2025-BLG-0975Lb and KMT-2025-BLG-1160Lb: Two Uranus-Mass Planets Beyond the Snow Line Discovered by Microlensing

We present the analysis of two planetary microlensing events, KMT-2025-BLG-0975 and KMT-2025-BLG-1160, discovered during the 2025 Galactic bulge microlensing season through high-cadence survey observations. In both events, short-duration anomalies near the peaks of the lensing light curves reveal the presence of planetary companions. Light-curve modeling yields planet-to-host mass ratios of $q = 8.6 \times 10^{-4}$ for KMT-2025-BLG-0975 and $1.3 \times 10^{-4}$ for KMT-2025-BLG-1160. For KMT-2025-BLG-0975, finite-source effects are detected, enabling a measurement of the angular Einstein radius, whereas only a lower limit on this quantity is obtained for KMT-2025-BLG-1160. We estimate the physical parameters of the lens systems through Bayesian analyses constrained by the measured microlensing observables. The results indicate that the planetary companions have masses of $M_{\rm p}=29.8^{+50.5}_{-16.0}~M_\oplus$ for KMT-2025-BLG-0975Lb and $25.4^{+15.5}_{-14.1}~M_\oplus$ for KMT-2025-BLG-1160Lb. Both planets have masses comparable to that of Uranus. The host stars are inferred to be a low-mass M dwarf with a mass of $M_{\rm h}=0.10^{+0.18}_{-0.06}~M_\odot$ for KMT-2025-BLG-0975L and a late K dwarf with a mass of $M_{\rm h}=0.58^{+0.35}_{-0.32}~M_\odot$ for KMT-2025-BLG-1160L. The projected planet--host separations are $a_\perp=0.81^{+0.10}_{-0.11}$~au for KMT-2025-BLG-0975Lb and $a_\perp=2.56^{+0.48}_{-0.71}$~au and $3.29^{+0.61}_{-0.92}$~au for the inner and wide solutions, respectively, of KMT-2025-BLG-1160Lb. In both systems, the planets are located beyond the expected snow-line distances of their hosts, placing them in the cold ice-giant regime.

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arXiv2026

Four Cold Giant Planets Discovered by High-Cadence Microlensing Surveys

We report the discovery of four cold giant planets identified through the analysis of microlensing events detected by high-cadence surveys: OGLE-2016-BLG-0261, KMT-2025-BLG-0026, KMT-2025-BLG-0030, and KMT-2025-BLG-2272. The planetary signals appear as short-duration anomalies in the light curves and are well described by binary-lens single-source models with mass ratios between the lens components of order $q \sim 10^{-3}$. Finite-source effects are securely measured in three out of four events, enabling determinations of the angular Einstein radius. A Bayesian analysis incorporating the measured event timescale and angular Einstein radius yields host masses of $\sim 0.07$--$0.6~M_\odot$ and companion masses of $\sim 0.2$--$2.5~M_{\rm J}$, confirming that all companions lie in the giant-planet regime. The projected separations are ~ 0.7--6 au, placing all planets at or beyond the snow lines of their host stars. The inferred lens distances span $\sim 6.6$--$7.9$ kpc, with all systems consistent with bulge lenses. These detections expand the sample of cold giant planets from homogeneous high-cadence surveys and highlight the sensitivity of microlensing to planetary systems beyond the snow line, providing further constraints on the occurrence and properties of giant planets around low-mass stars.

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arXiv2026

Incorporating physical source parameters into microlensing modeling

Modeling of complex microlensing events suffers from many difficult-to-disentangle degeneracies. This is especially the case for orbital motion of the source in a binary system, the so-called xallarap effect. To address the degeneracies inherent in xallarap modeling, we developed a novel approach that directly samples the physical parameters of the source stars (initial mass, evolutionary phase, metallicity, distance, and reddening) during MCMC fitting. In our approach the physical parameters of the source are estimated using MIST stellar evolution models. This parametrization imposes astrophysical constraints that help identify the physically most probable solutions. We test our method on the complex microlensing event OGLE-2017-BLG-0114, which exhibits signatures that can be traced to the complexity of the source system. We successfully constrained the microlensing models, achieving improvements in the Einstein ring radius estimates by up to an order of magnitude in the case of binary source models.

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arXiv2026

Four-Body Gravitational Microlensing Events Involving Both a Binary Lens and a Binary Source

We present detailed analyses of three anomalous microlensing events--KMT-2021-BLG-0209, KMT-2021-BLG-0901, and OGLE-2025-BLG-0356--identified from a systematic re-examination of KMTNet light curves for which previous modeling attempts failed or left persistent residuals. Although all three events show caustic-related features consistent with binary-lens microlensing, we find that their full light-curve structures can be described by four-body configurations that required four-body configurations involving a binary lens and a binary source. In KMT-2021-BLG-0209, weak caustic-exit residuals arise from a faint companion source undergoing an additional caustic interaction. In KMT-2021-BLG-0901, a late-time re-brightening is produced when the secondary source encounters the resonant caustic long after the primary. For OGLE-2025-BLG-0356, we test the degeneracy between 3L1S and 2L2S interpretations of a short isolated anomaly and find that the 2L2S model provides a significantly better fit. Source colors and magnitudes indicate binary sources composed of (G8V, M3V), (G8V, K2V), and (G6V, G8V) stars for the three events, respectively. Bayesian inference suggests that the lenses are predominantly low-mass binaries, including one system (KMT-2021-BLG-0901) with a companion consistent with a brown dwarf. These events add to the growing sample of well-characterized 2L2S systems and underscore the importance of systematically testing complex models, particularly in anticipation of the high-precision microlensing data expected from the Roman Space Telescope survey.

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arXiv2026

Candidate Microlensing Brown Dwarfs in Binary Lens Systems from the 2023--2025 Observing Seasons

We present detailed light-curve analyses of ten binary-lens microlensing events observed during the 2023--2025 seasons and selected as candidates for hosting brown-dwarf companions. The sample includes OGLE-2023-BLG-0249, KMT-2023-BLG-1246, OGLE-2023-BLG-0079, KMT-2024-BLG-0072, KMT-2024-BLG-0897, KMT-2024-BLG-1876, KMT-2024-BLG-2379, KMT-2025-BLG-0922, KMT-2025-BLG-1056, and KMT-2025-BLG-2427. For each event, we carry out modeling of the light curve, explore relevant degeneracies, and, when finite-source effects are present, determine the angular Einstein radius. For OGLE-2023-BLG-0249, we additionally measure the microlens parallax, which allows a direct determination of the lens masses and distance. For the remaining events, we estimate the physical lens properties via Bayesian analyses incorporating Galactic priors. The resulting posteriors show that the lens companions in all systems have median masses in the brown-dwarf regime, and the lenses of two events (KMT-2025-BLG-0922 and KMT-2025-BLG-1056) are consistent with binaries in which both lens components fall within the brown-dwarf mass range. Spanning a wide range of projected separations and distances, these detections illustrate the power of high-cadence microlensing surveys to build a census of brown-dwarf companions, including faint and distant systems beyond the reach of flux-limited methods.

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arXiv2026

Mass Production of 2023 KMTNet Microlensing Planets. II: Two Planets and A Brown Dwarf

To expand the homogeneous microlensing planetary sample of the Korea Microlensing Telescope Network (KMTNet), we investigate six planetary candidates identified by the AnomalyFinder search in the 2023 prime-field data, namely KMT-2023-BLG-1592, OGLE-2023-BLG-0766, KMT-2023-BLG-0332, KMT-2023-BLG-0486, KMT-2023-BLG-0792, and OGLE-2023-BLG-1043. Light-curve modeling indicates that the first two events have planetary mass ratios of $\log q \sim -3.0$ and $-2.6$, while the third exhibits a brown dwarf mass ratio of $\log q \sim -1.4$. The remaining three events show the well-known degeneracy between the binary-lens single-source (2L1S) and single-lens binary-source (1L2S) interpretations. A Bayesian analysis yields companion masses of about 0.6 and 1.2 Jupiter masses for the two planetary systems, likely orbiting beyond the snow lines of M- or K-dwarf hosts. A review of the KMTNet planetary sample shows that candidates discovered by AnomalyFinder are significantly more likely to exhibit the 2L1S/1L2S degeneracy, consistent with the tendency of AnomalyFinder to detect subtler planetary signals.

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arXiv2026

Two Low Mass-Ratio Microlensing Planets and Two Types of Central-Resonant Degeneracy

We present observations and analysis of two low planet/host mass-ratio ($q$) microlensing planets discovered in high-magnification events. KMT-2025-BLG-0811Lb has $q \sim 4.5 \times 10^{-5}$, and a Bayesian analysis favors a super-Earth/mini-Neptune orbiting an M- or K-dwarf host at a projected separation of $\sim 3$ au. KMT-2025-BLG-0912Lb has $q = 2.6 \times 10^{-4}$ and likely hosts a super-Earth/mini-Neptune around either a low-mass M dwarf or a brown dwarf at $\sim 1$ au. Even with an observing cadence of $Γ> 30~{\rm hr}^{-1}$ during the planetary signal, KMT-2025-BLG-0811 still exhibits the "central-resonant" degeneracy. Reviewing nine such events, we find that the "central-resonant" degeneracy can be divided into two distinct types that occupy separate regions in the plane of $q$ and normalized source radius ($ρ$). Type~I events have similar $q$ but substantially different $ρ$ and are more difficult to resolve from the light curves. For Type~II events, the "resonant" solutions have relatively lower $q$ and larger $ρ$. Our review provides guidance for searching for the alternative solution once one solution has been identified.

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arXiv2026

Mass Production of 2023 KMTNet Microlensing Planets I: Low Mass Ratio

We initiate the systematic search for planets in the 2023 data of the Korea Microlensing Telescope Network (KMTNet), focusing on those planets found by the KMTNet AnomalyFinder with low preliminary estimates of the mass-ratio, $q<2\times 10^{-4}$. The 2023 season is the first for which the photometry of all events was re-reduced prior to the AnomalyFinder search, potentially increasing its sensitivity to planets. We find three strong low-$q$ planet candidates, KMT-2023-BLG-0164 ($q\sim 1.3\times 10^{-4}$), KMT-2023-BLG-1286 ($q\sim 1.9\times 10^{-4}$), and KMT-2023-BLG-1746 ($q\sim 8\times 10^{-5}$). KMT-2023-BLG-0164 is notable in that the source is projected on a very bright ($I=16.0$) foreground star, which is either the planet's host or (more likely) a companion to the host. We obtain a spectrum, finding that its mass and distance are $M\sim 1.0\,M_\odot$ and $D\sim 1.5$ kpc, the latter being the distance of the lens ($D_L$) regardless of whether the spectroscopic target is the host or its companion. We also analyze two other candidates, KMT-2023-BLG-0614 and KMT-2023-BLG-1593, which are unlikely to enter the statistical sample due to their ambiguous interpretations as possible non-planetary events.

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arXiv2026

Three Saturn-mass Microlensing Planets Identified through Signals from Peripheral-caustic Perturbations

We present the discovery and analysis of three microlensing planets identified through brief positive anomalies on the wings of their light curves. The events, KMT-2021-BLG-0852, KMT-2024-BLG-2005, and KMT-2025-BLG-0481, were detected in high-cadence survey data from the KMTNet, OGLE, MOA, and PRIME collaborations. The anomaly morphologies are consistent with major-image perturbations induced by planetary-mass companions located near the peripheral caustic. A systematic exploration of model degeneracies, including binary-source scenarios, higher mass-ratio binary lenses, and the inner--outer caustic degeneracy, firmly establishes the planetary origin of each signal. Measurements of the angular Einstein radius and event timescale, combined with Bayesian priors from a Galactic model, yield the physical parameters of each system. The hosts are low-mass stars (0.12--0.75~$M_\odot$), while the companions are Saturn-mass planets (0.16--0.59 $M_{\rm J}$) projected at separations of 1.1--7.8 au, placing them beyond the snowline of their hosts. These results demonstrate the capability of microlensing to detect and characterize cold giant planets around low-mass stars at kpc distances, populating the critical transition region between ice giants and gas giants.

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arXiv2026

KMT-2016-BLG-1337L: A Saturn-mass planet orbiting within a binary system of low-mass stars

We report the discovery and characterization of a planetary companion in the microlensing event KMT-2016-BLG-1337, which was produced by a binary system of low-mass stars. The light curve of the event exhibits a short-term anomaly superposed on the profile of a binary-lens single-source (2L1S) model. To investigate the nature of this anomaly, we performed detailed modeling under both the binary-lens binary-source (2L2S) and triple-lens single-source (3L1S) interpretations. The 3L1S model provides a substantially better fit to the data, strongly favoring the presence of a planetary companion in the lens system. Two viable $3L1S$ solutions describe the event nearly equally well. In one solution, the planet has a mass of $M_3 \sim 0.3~M_{\mathrm{J}}$ and lies at a projected separation of $a_{\perp,3} \sim 4~{\rm au}$ from the heavier member of the host binary. In the alternative solution, the planet has a mass of $M_3 \sim 7~M_{\mathrm{J}}$ and a projected separation of $a_{\perp,3} \sim 1.5~{\rm au}$. The host binary consists of early M-type dwarfs with masses of $M_1 \sim 0.54~M_\odot$ and $M_2 \sim 0.40~M_\odot$, separated in projection by $a_{\perp,2} \sim 3.5~{\rm au}$. The system is located at a distance of $D_{\rm L} \sim 7~{\rm kpc}$ toward the Galactic bulge. This event demonstrates the sensitivity of microlensing to planets in dynamically complex stellar environments, including systems beyond the reach of other detection techniques. It thereby contributes to a more comprehensive understanding of planet formation in multiple-star systems.

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arXiv2025

A free-floating-planet microlensing event caused by a Saturn-mass object

A population of free-floating planets is known from gravitational microlensing surveys. None have a directly measured mass, owing to a degeneracy with the distance, but the population statistics indicate that many are less massive than Jupiter. We report a microlensing event -- KMT-2024-BLG-0792/OGLE-2024-BLG-0516, which was observed from both ground- and space-based telescopes -- that breaks the mass-distance degeneracy. The event was caused by an object with 0.219^{+0.075}_{-0.046} Jupiter masses that is either gravitationally unbound or on a very wide orbit. Through comparison with the statistical properties of other observed microlensing events and predictions from simulations, we infer that this object likely formed in a protoplanetary disk (like a planet), not in isolation (like a brown dwarf), and dynamical processes then ejected it from its birth place, producing a free-floating object.

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arXiv2025

Towards sub-milliarcsecond astrometric precision using seeing-limited imaging

The Earth's atmospheric turbulence degrades the precision of ground-based astrometry. Here, we discuss these limitations and propose that, with proper treatment of systematics and by leveraging the many epochs available from the Korean Microlensing Telescope Network (KMTNet), seeing-limited observations can reach sub-milliarcsecond precision. Such observations may be instrumental for the detection of Galactic black holes via microlensing. We present our methodology and pipeline for precise astrometric measurements using seeing-limited observations. The method is a variant of Gaia's Astrometric Global Iterative Solution (AGIS) that includes several detrending steps. Tests on 6,500 images of the same field, obtained by KMTNet with typical seeing condition of 1 arcsecond and pixel scale of 0.4 arcsecond, suggest that we can achieve, at the bright end (mag<17), per-epoch relative astrometric precision of ~5 and relative proper motion precision of 0.1-0.2 mas/yr over a baseline of approximately five years, using data from the Cerro Tololo Inter-American Observatory (CTIO) site. Time binning on 5--20 day cadences improves the bright-source precision to ~2 mas per coordinate on astrometric microlensing-relevant timescales. The precision is estimated using bootstrap simulations and further validated by comparing results from two independent KMTNet telescopes.

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arXiv2025

Four Giant Planets from 2024 KMTNet Microlensing Campaign

In this work, we present analyses of four newly discovered planetary microlensing events from the 2024 KMTNet survey season: KMT-2024-BLG-0176, KMT-2024-BLG-0349, KMT-2024-BLG-1870, and KMT-2024-BLG-2087. In each case, the planetary nature was revealed through distinct types of anomalies in the lensing light curves: a positive bump near the peak for KMT-2024-BLG-0176, an asymmetric peak for KMT-2024-BLG-0349, a short-duration central dip for KMT-2024-BLG-1870, and a caustic-crossing feature for KMT-2024-BLG-2087. Detailed modeling of the light curves confirms that these anomalies are produced by planetary companions with planet-to-host mass ratios in the range of $(1.5\text{--}17.9)\times 10^{-3}$. Despite the diversity of signal morphologies, all planets detected in these events are giant planets with masses comparable to or exceeding that of Jupiter in the Solar System. Each planet orbits a host star less massive than the Sun, emphasizing the strength of microlensing in uncovering planetary systems around low-mass stellar hosts.

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arXiv2025

Six binary brown dwarf candidates identified by microlensing

In this study, we analyze microlensing events from the 2023 and 2024 observing seasons to identify cases likely caused by binary systems composed of BDs. By applying criteria that the binary-lens events exhibit well-resolved caustics, short time scales ($t_{\rm E} \lesssim 9$ days), and have small angular Einstein radii ($θ_{\rm E} \lesssim 0.17$~mas), we identify six candidate binary BD events: MOA-2023-BLG-331, KMT-2023-BLG-2019, KMT-2024-BLG-1005, KMT-2024-BLG-1518, MOA-2024-BLG-181, and KMT-2024-BLG-2486. Analysis of these events leads to models that provide precise estimates for both lensing observables, $t_{\rm E}$ and $θ_{\rm E}$. We estimate the masses of the binary components through Bayesian analysis, utilizing the constraints from $t_{\rm E}$ and $θ_{\rm E}$. The results show that for the events KMT-2024-BLG-1005, KMT-2024-BLG-1518, MOA-2024-BLG-181, and KMT-2024-BLG-2486, the probability that both binary components lie within the BD mass range exceeds 50\%, indicating a high likelihood that the lenses of these events are binary BDs. In contrast, for MOA-2023-BLG-331L and KMT-2023-BLG-2019L, the probabilities that the lower-mass components of the binary lenses lie within the BD mass range exceed 50\%, while the probabilities for the heavier components are below 50\%, suggesting that these systems are more likely to consist of a low-mass M dwarf and a BD. The brown-dwarf nature of the binary candidates can ultimately be confirmed by combining the measured lens-source relative proper motions with high-resolution imaging taken at a later time.

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