Pith. sign in

REVIEW 4 major objections 4 minor 74 references

By re-analyzing 8,081 historic microlensing events and crossing them with Galactic models, this paper computes for each the probability that its lens is already resolvable from its source in Euclid images, and ranks them for follow-up.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

A ranked catalog of ~8000 historic microlensing events with predicted lens-source separation probabilities identifies the best targets for resolving lenses in Euclid images.

T0 review reviewed 2026-08-03 challenge →

load-bearing objection A genuinely useful ranked catalog for Euclid microlensing follow-up, but the headline probabilities are prior-dominated for many top targets and need sensitivity analysis and error bars before being used quantitatively. the 4 major comments →

arxiv 2511.03307 v2 pith:YL2GJTNR submitted 2025-11-05 astro-ph.EP astro-ph.GA

Historic microlensing events in the euclid Galactic Bulge Survey

classification astro-ph.EP astro-ph.GA
keywords gravitational microlensingGalactic bulgelens-source resolutionproper motionEuclidexoplanetsevent catalogBayesian priors
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper tries to establish that for every one of 8,081 historic microlensing events that fall in the Euclid Galactic Bulge Survey footprint, it is possible to compute a meaningful probability that the lens is now separated from the source by more than any chosen angular threshold, and thus to rank events for follow-up. It matters because resolving the lens star (and any planets around it) after 10–20 years is the cheapest way to convert microlensing's statistical mass-distance estimates into precise measurements of individual systems. The authors achieve this by re-fitting all events with one homogeneous light-curve model, then crossing the measured Einstein time, baseline brightness, and occasional parallax with a Galactic stellar population model to obtain posterior lens-source proper motions. For the 51 known planetary events, the paper also lists explicit expected separations, giving planet-hunters a concrete target list.

Core claim

The central claim is that the single observable t_E is too degenerate to predict whether a lens will be resolved from its source, but once a Galactic-model prior is applied, the resulting posterior distribution of relative proper motion—multiplied by the 6–20 year baseline between event peak and the Euclid observations—yields a defensible per-event probability of lens-source separation. The paper states this as: taking into account all uncertainties, for each microlensing event we are able to estimate the probability that the lens is separated from the source by more than a given angular distance threshold. Applied to 8,081 events, the method produces a ranked catalog, and a sub-table for 51

What carries the argument

The central object is the per-event posterior probability distribution of lens-source relative proper motion, built by combining the measured Einstein time, I-band baseline magnitude (an upper bound on lens/source brightness), and microlensing parallax where measurable, with a Galactic model that predicts the stellar density and kinematics along the sight-line. The posterior is converted into a separation probability by multiplying proper motion by the time elapsed since the event's peak; four thresholds are offered, from one full pixel (0.11") down to a quarter pixel (0.0275"). This is the engine that turns a degenerate set of light-curve parameters into a ranked, decision-ready list.

Load-bearing premise

The ranking is trustworthy only if the Galactic stellar population model used as a prior is a fair description of the real bulge and disk along each line of sight; for most events the data themselves (mainly t_E) are too weak to override that prior.

What would settle it

Look at the top-ranked events in the catalog and measure the actual lens-source separation in the Euclid images (or with adaptive optics on large telescopes). If the fraction of events resolved at a given threshold falls well below the predicted probability for that threshold, the prior-based proper-motion estimates are wrong.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • Astronomers can immediately prioritize which of the 8,081 events to search first in the Euclid images, starting at the top of the ranked list.
  • For the 51 known planetary microlensing events, the paper gives a dedicated table of predicted lens-source separations, with two events expected to exceed one pixel and about thirty exceeding a quarter pixel.
  • The four thresholds (one pixel, half pixel, quarter pixel, and average PSF size) let different observing strategies choose their own criterion for 'resolved'.
  • For short, fast events where the lens is expected to be well separated, a non-detection would support free-floating-planet or dark-lens explanations rather than a slow stellar lens.
  • Joint analysis with future high-resolution surveys can convert these probabilities into actual lens detections, sharpening mass and distance estimates for hundreds of events.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the Galactic-model prior is systematically wrong, the ranking inherits that error; checking the actual resolution rate in the top-ranked events is a direct test of the prior's validity.
  • The same prior-driven method could be re-run with future space surveys, where longer baselines shift the whole distribution toward higher separations.
  • The catalog's 'misclassified binary' events—nearly half of the sample—are an artifact of online photometry rather than real binaries, so users should treat model categories with caution, as the paper itself warns.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

4 major / 4 minor

Summary. The paper compiles a catalog of historic microlensing events in the Euclid Galactic Bulge Survey (EGBS) footprint from OGLE, MOA, and KMTNet, re-models all events homogeneously with RTModel, and then uses the genulens Galactic model as a prior to derive posterior distributions of the lens-source relative proper motion. From these posteriors, the authors compute, for each event, the probability that the lens is separated from the source by more than four angular thresholds (0.18", 0.11", 0.055", 0.0275"), and rank the events by these probabilities (Sec. 4.3). The catalog is public, and special attention is paid to 51 known planetary events, whose independently published proper-motion constraints are compared with the new predictions (Sec. 5, Table 3). The central claim is that this ranking provides a useful prioritization tool for future high-resolution follow-up observations with Euclid, HST, and Roman.

Significance. If the ranking is robust, this is a valuable community resource: it is the first homogeneous, footprint-complete prioritization of historic microlensing targets for lens-source resolution, and the public catalog and scripts are a concrete deliverable. The authors correctly emphasize that the approach is Bayesian and prior-dependent, but the paper does not quantify how sensitive the ranking is to the adopted Galactic prior. The consistency check against 51 planetary events using independent finite-source/parallax/high-resolution-imaging constraints is a genuinely useful validation for that subset. However, because ~99% of events have no parallax measurement and t_E alone is degenerate in mass, distance, and velocity, the ranking for most events is a projection of the Galactic prior rather than a data-driven measurement. The absence of a prior-sensitivity analysis and of uncertainties on the reported probabilities leaves the headline ranking vulnerable, even though the methodology is sound in principle.

major comments (4)
  1. [Sec. 4.2, Fig. 7, Table 2] The posterior driving the ranking is prior-dominated for most events. Sec. 4.2 states that for most events the only constraints are t_E and I_base, and Fig. 7 shows that parallax is measured in only ~1% of events. Under Eqs. (1)-(3), t_E alone is degenerate among mass, distance, and proper motion. Table 2 includes top-ranked events with sigma_tE > t_E (OB020139: t_E=4.115±10.949 d; OB030120: 8.578±28.214 d; OB020372: 13.956±15.628 d). For these, the reported P(>55 mas)>96% is essentially drawn from the genulens prior, not from the data. No alternative-prior test is provided. I request a sensitivity analysis (e.g., varying the mass function, bulge kinematics, or extinction map) and a statement of how much the top-ranked list changes. Without this, the central deliverable — the ranked list — is not robust.
  2. [Sec. 4.3, Table 2] The probabilities are quoted to three decimal places with no uncertainties or credible intervals. Even assuming the Galactic model is correct, the probability is a point estimate from a posterior sample; events in Table 2 differ by fractions of a percent (e.g., P(>55 mas)=98.798 vs 98.502). The paper should provide error bars on P(>threshold) or otherwise demonstrate that the ranking is stable under resampling of the posterior draws. Without this, follow-up programs cannot judge whether the top-ranked events are significantly better targets than slightly lower-ranked ones.
  3. [Sec. 4.1, Fig. 6] The decision to preserve all outliers in the online photometry is load-bearing. Nearly half of the events are classified as binary-lens or binary-source (Fig. 6), and the text acknowledges that this is partly an artifact of outliers. The paper argues that such 'false anomalies do not spoil the measurement of the Einstein time,' but no test supports this. If the misclassification biases t_E for a significant fraction of events, the entire ranking inherits the bias. A recovery test on simulated light curves with outliers would quantify the bias in t_E and validate the modeling choice.
  4. [Abstract / Sec. 4.2 / Fig. 11] The abstract says the catalog contains 7801 entries, while the main text and Fig. 11 state 8081 events. This is a factual inconsistency that must be reconciled. Since the full catalog is the primary product, the event count needs to be exact and consistent across abstract, body, and figures.
minor comments (4)
  1. [Sec. 4.3] The epoch of the EGBS is given as 'HJD≃2460758±1'; please define this epoch explicitly (or cite the survey description) so the separation baseline is reproducible.
  2. [Table 3] The table lists 51 planetary events, but the excerpt shows only a subset; consider indicating clearly which events have multiple models and how the model probabilities are weighted.
  3. [Sec. 2] The text says the EGBS fields 'were rotated by 17° from the north'; it would be clearer to state the position angle, since rotation direction matters for the field footprint.
  4. [Fig. 6] The figure caption labels the y-axis as 'Incidence' but the units (counts or percentages) should be stated explicitly.

Circularity Check

0 steps flagged

No significant circularity: the separation probabilities are a Bayesian posterior from an external Galactic model conditioned on measured light-curve parameters, with independent validation against published planetary separations.

full rationale

The paper's central deliverable is a ranked list of P(separation > threshold) values obtained by conditioning an external Galactic-model prior (genulens; Koshimoto & Ranc 2022, based on Koshimoto et al. 2021) on per-event constraints t_E, I_base, and, when available, pi_E. The method is stated explicitly rather than hidden: 'we must rely on prior expectations from our knowledge of the Galactic stellar populations... Crossing this prior expectation with the constraints coming from our measured parameters, we can derive posterior probability distributions.' No parameter is fitted to reproduce a target separation; the reported probabilities are tail probabilities of the posterior separation distribution after multiplying the posterior proper motion by the time baseline. The consistency check in Sec. 5 compares the general re-modeling against independently published separations obtained via finite-source effects, parallax, or high-resolution imaging; this is validation, not circularity. Self-citations to RTModel, VBMicrolensing, and genulens refer to public modeling codes whose assumptions (stellar density and kinematics from Gaia, OGLE, and radial-velocity surveys) are external and are not fitted to the EGBS sample. The main weakness is prior dominance for events with poorly constrained t_E (e.g., Table 2 events with sigma_tE > tE), but that is a robustness/calibration concern rather than a circular derivation; the paper openly acknowledges reliance on prior expectations. The abstract/full-text count mismatch (7801 vs 8081) is an internal quality-control issue, not evidence of circularity.

Axiom & Free-Parameter Ledger

2 free parameters · 4 axioms · 0 invented entities

The central product is a catalog; its main inputs are measured t_E and I_base plus an external Galactic prior. The only hand-chosen constants are the four separation thresholds. The paper introduces no new physical entities. The main burden is prior-dependence and the assumption that online photometry yields unbiased t_E.

free parameters (2)
  • Einstein time t_E per event = Catalog values (e.g., Table 2)
    Fitted with RTModel from each light curve; it is the main observable entering the proper-motion posterior. For a number of events the fitted uncertainty exceeds the value itself.
  • Reference separation thresholds = 0.0275, 0.055, 0.11, 0.18 arcsec
    Hand-chosen angular thresholds that define P(>threshold); the reported probabilities and ranking depend on these choices.
axioms (4)
  • domain assumption genulens/Koshimoto et al. (2021) Galactic model correctly describes lens and source populations (mass function, density, kinematics) in the EGBS fields.
    Section 4.2 uses genulens to convert t_E and I_base into proper-motion posteriors; without this prior, t_E alone does not constrain lens-source separation.
  • domain assumption Online photometry from OGLE/MOA/KMTNet yields unbiased Einstein times for 8081 events.
    Section 4.1 asserts re-reduction has 'very little impact' on t_E; high chi-squared tails for KMTNet online photometry show this is not guaranteed for all events.
  • ad hoc to paper Preserving all data, including outliers that create binary-lens/source artifacts, preserves correct t_E more often than it corrupts it.
    Section 4.1 explicitly states the choice: 'we choose to have correct Einstein times on misclassified events rather than wrong Einstein times on short events.' This preference is untested and affects short-event probabilities.
  • domain assumption Large-scale extinction maps (Schlegel et al. 1998; Schlafly & Finkbeiner 2011) are accurate enough for baseline-magnitude constraints.
    Section 4.2 applies I_base as a mass upper limit for lens and source; small-scale extinction variations could bias this.

reviewed 2026-08-03 · how reviews work

0 comments
Cite this review

Pith. "Pith review of Historic microlensing events in the euclid Galactic Bulge Survey." pith.science (2026). https://pith.science/paper/YL2GJTNR

@misc{pith2026251103307,
  author       = {Pith},
  title        = {Pith review of: Historic microlensing events in the euclid Galactic Bulge Survey},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YL2GJTNR}},
  note         = {Machine review of arXiv:2511.03307}
}
Share X Bluesky LinkedIn Reddit HN
read the original abstract

Microlensing campaigns have a long history of observations covering the Galactic bulge, where thousands of detections have been obtained, including many exoplanetary systems. The Euclid Galactic Bulge Survey represents a unique opportunity to revisit a large number of past events and attempt the lens-source resolution of known events falling in the covered area. As the analysis of individual events requires non-negligible efforts, it is important to establish priorities among all possible targets, identifying those candidates with the higher chance for a successful resolution of the lens from the source and with the highest scientific interest. Drawing from the databases of the three main microlensing surveys (OGLE, MOA and KMTNet), we compile the complete catalog of past microlensing events in the Euclid survey footprint up to year 2023, containing 7801 entries. By re-modeling all events and cross-checking with Galactic models, we estimate the relative lens-source proper motions for all events. Taking into account all uncertainties, for each microlensing event we are able to estimate the probability that the lens is separated from the source by more than a given angular distance threshold. Hence, we rank all events by their resolution probability, providing additional useful information that will guide future analyses on the most promising candidates. A particular attention is dedicated to the 51 known planetary microlensing events.

Figures

Figures reproduced from arXiv: 2511.03307 by A.A. Cole, A. Bhattacharya, A. Idei, A. Udalski, A. Vandorou, C. Ranc, D.P. Bennett, D. Suzuki, E. Bachelet, E. Kerins, E. Thygesen, F. Abe, G. Olmschenk, H. Verma, H. Yama, I.A. Bond, I. McDonald, I. Soszy\'nski, J.C. Cuillandre, J.-P. Beaulieu, J. Skowron, K.A. Rybicki, K. Nunota, K. Ulaczyk, L. Salmeri, M. Gromadzki, M.J. Mr\'oz, M. K. Szyma\'nski, M. Penny, M. Wrona, N.J. Rattenbury, N. Rektsini, P. Iwanek, P.J. Tristram, P. Mr\'oz, P. Pietrukowicz, P. Rota, R. Hamada, R. Poleski, S. Ishitani Silva, S. Koz{\l}owski, S.K. Terry, S. Miyazaki, T. Nagai, T. Sumi, T. Tamaoki, V. Bozza, Y. Hirao, Y.K. Satoh, Y. Muraki.

Figure 1
Figure 1. Figure 1: Outline of the nine Euclid Galactic Bulge Survey point￾ings (red) overlaid on a Gaia image of the Milky Way. The total outlined sky coverage is 4.8 deg2 . tunity to make a much broader statistical study embracing all microlensing events for which we can detect the lens. Population studies can receive a validation by the real flux we see from the lens. Even the non-detection of the lens can be of great valu… view at source ↗
Figure 3
Figure 3. Figure 3: Distribution of events per survey. Some events have been observed by more than one survey [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Distribution of events per year. lens has already been detected by Keck and is a candi￾date planet in the habitable zone (Batista et al. 2014), OGLE-2005-BLG-390, a system with an icy 5.5 Earth￾masses planet (Beaulieu et al. 2006), the Earth-mass planet OGLE-2016-BLG-1195b (Bond et al. 2017; Shvartzvald et al. 2017; Vandorou et al. 2025b), OGLE-2017-BLG-0173, a planet in a “Hollywood” event Hwang et al. (2… view at source ↗
Figure 7
Figure 7. Figure 7: Events classified according to measured observables. for rejection of outliers, but this would put real short time￾scale events in danger. So, between the two alternatives, we choose to have correct Einstein times on misclassified events rather than wrong Einstein times on short events. We were not able to extract Ibase and πE for all mi￾crolensing events. As already anticipated, for MOA-only events we are… view at source ↗
Figure 6
Figure 6. Figure 6: Incidence of different model categories as found by RTModel. As explained in the text, we caution the reader that the abundance of binary lens/source events found in this analy￾sis is a natural consequence of the presence of occasional outliers in the online photometry, which has been adopted in this study and does not reflect the real distribution of microlensing events. signal (periodic or eruptive varia… view at source ↗
Figure 8
Figure 8. Figure 8: Distribution of events in terms of the baseline magnitude in I-band [PITH_FULL_IMAGE:figures/full_fig_p007_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Distribution of events in the Einstein time tE. coming from our measured parameters, we can derive pos￾terior probability distributions for the proper motion that can be used to infer the expected lens-source separation for each microlensing event. There are several Galactic models designed for such a Bayesian approach in microlensing analysis (see e.g. Robin et al. (2003); Han & Gould (2003); Dominik (200… view at source ↗
Figure 10
Figure 10. Figure 10: Three representative historic events. (a) Light curve for the single-lens-single-source event MOA-2002-BLG-61/OGLE￾2002-BLG-347 and (b) the probability distribution for the lens-source separation for this event as calculated by genulens using the Einstein time obtained by RTModel. We have also marked the four thresholds used in the compilation of [PITH_FULL_IMAGE:figures/full_fig_p008_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Number of events with detection probability higher than the given value in the abscissa. Each curve is drawn for a given reference detection threshold [PITH_FULL_IMAGE:figures/full_fig_p010_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Number of events with detection probability higher than 50% by year. The three colors refer to three different thresh￾olds reported in the legend. re-modeling of the original survey data, which makes us more confident with respect to our modeling. Consistently with our full sample of microlensing events, there are just 2 planetary events for which the lens should be separated by more than 0.11”, 18 events… view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

74 extracted references

  1. [1]

    N., Alard, C., et al

    Afonso, C., Albert, J. N., Alard, C., et al. 2003, A&A, 404, 145

  2. [2]

    W., Allsman, R

    Alcock, C., Akerlof, C. W., Allsman, R. A., et al. 1993, Nature, 365, 621

  3. [3]

    & Penny, M

    Bachelet, E. & Penny, M. 2019, ApJ, 880, L32

  4. [4]

    2022, A&A, 664, A136

    Bachelet, E., Specht, D., Penny, M., et al. 2022, A&A, 664, A136

  5. [5]

    P., Gould, A., et al

    Batista, V., Beaulieu, J. P., Gould, A., et al. 2014, ApJ, 780, 54

  6. [6]

    2018, Universe, 4, 61

    Beaulieu, J.-P. 2018, Universe, 4, 61

  7. [7]

    P., Bennett, D

    Beaulieu, J. P., Bennett, D. P., Fouqué, P., et al. 2006, Nature, 439, 437

  8. [8]

    P., Anderson, J., Bond, I

    Bennett, D. P., Anderson, J., Bond, I. A., Udalski, A., & Gould, A. 2006, ApJ, 647, L171

  9. [9]

    P., Bhattacharya, A., Anderson, J., et al

    Bennett, D. P., Bhattacharya, A., Anderson, J., et al. 2015, ApJ, 808, 169

  10. [10]

    P., Bhattacharya, A., Beaulieu, J.-P., et al

    Bennett, D. P., Bhattacharya, A., Beaulieu, J.-P., et al. 2020, AJ, 159, 68

  11. [11]

    P., Bhattacharya, A., Beaulieu, J.-P., et al

    Bennett, D. P., Bhattacharya, A., Beaulieu, J.-P., et al. 2024, AJ, 168, 15

  12. [12]

    P., Rhie, S

    Bennett, D. P., Rhie, S. H., Nikolaev, S., et al. 2010, ApJ, 713, 837

  13. [13]

    P., Rhie, S

    Bennett, D. P., Rhie, S. H., Udalski, A., et al. 2016, AJ, 152, 125

  14. [14]

    2019, BAAS, 51, 520

    Bhattacharya, A., Akeson, R., Anderson, J., et al. 2019, BAAS, 51, 520

  15. [15]

    P., Bennett, D

    Bhattacharya, A., Beaulieu, J. P., Bennett, D. P., et al. 2018, AJ, 156, 289

  16. [16]

    P., Beaulieu, J

    Bhattacharya, A., Bennett, D. P., Beaulieu, J. P., et al. 2023, AJ, 165, 206

  17. [17]

    P., Bond, I

    Bhattacharya, A., Bennett, D. P., Bond, I. A., et al. 2016, AJ, 152, 140

  18. [18]

    W., Beaulieu, J

    Blackman, J. W., Beaulieu, J. P., Cole, A. A., et al. 2021, AJ, 161, 279

  19. [19]

    A., Abe, F., Dodd, R

    Bond, I. A., Abe, F., Dodd, R. J., et al. 2001, MNRAS, 327, 868

  20. [20]

    A., Bennett, D

    Bond, I. A., Bennett, D. P., Sumi, T., et al. 2017, MNRAS, 469, 2434

  21. [21]

    A., Udalski, A., Jaroszyński, M., et al

    Bond, I. A., Udalski, A., Jaroszyński, M., et al. 2004, ApJ, 606, L155

  22. [22]

    2025, A&A, 694, A219

    Bozza, V., Saggese, V., Covone, G., Rota, P., & Zhang, J. 2025, A&A, 694, A219

  23. [23]

    P., Wegg, C., Gerhard, O., et al

    Clarke, J. P., Wegg, C., Gerhard, O., et al. 2019, MNRAS, 489, 3519

  24. [24]

    2016, in Society of Photo- Optical Instrumentation Engineers (SPIE) Conference Series, Vol

    Cropper, M., Pottinger, S., Niemi, S., et al. 2016, in Society of Photo- Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 9904, Space Telescopes and Instrumentation 2016: Optical, In- frared, and Millimeter Wave, ed. H. A. MacEwen, G. G. Fazio, M. Lystrup, N. Batalha, N. Siegler, & E. C. Tong, 99040Q

  25. [25]

    2006, MNRAS, 367, 669 Gaia Collaboration, Katz, D., Antoja, T., et al

    Dominik, M. 2006, MNRAS, 367, 669 Gaia Collaboration, Katz, D., Antoja, T., et al. 2018, A&A, 616, A11

  26. [26]

    Gaudi, B. S. 2012, ARA&A, 50, 411

  27. [27]

    S., Bennett, D

    Gaudi, B. S., Bennett, D. P., Udalski, A., et al. 2008, Science, 319, 927

  28. [28]

    G., et al

    Gould, A., Udalski, A., Shin, I. G., et al. 2014, Science, 345, 46

  29. [29]

    P., Udalski, A., et al

    Han, C., Bennett, D. P., Udalski, A., et al. 2019, AJ, 158, 114

  30. [30]

    & Gould, A

    Han, C. & Gould, A. 2003, ApJ, 592, 172

  31. [31]

    P., Ryu, Y.-H., et al

    Hirao, Y., Bennett, D. P., Ryu, Y.-H., et al. 2020, AJ, 160, 74

  32. [32]

    2016, ApJ, 824, 139

    Hirao, Y., Udalski, A., Sumi, T., et al. 2016, ApJ, 824, 139

  33. [33]

    K., Gould, A., Udalski, A., et al

    Jung, Y. K., Gould, A., Udalski, A., et al. 2019, AJ, 158, 28

  34. [34]

    K., Hwang, K.-H., Ryu, Y.-H., et al

    Jung, Y. K., Hwang, K.-H., Ryu, Y.-H., et al. 2018, AJ, 156, 208

  35. [35]

    2021, AJ, 162, 15

    Kim, H.-W., Hwang, K.-H., Gould, A., et al. 2021, AJ, 162, 15

  36. [36]

    2016, Journal of Korean Astronomical Society, 49, 37

    Kim, S.-L., Lee, C.-U., Park, B.-G., et al. 2016, Journal of Korean Astronomical Society, 49, 37

  37. [37]

    Koshimoto, N., Baba, J., & Bennett, D. P. 2021, ApJ, 917, 78

  38. [38]

    & Ranc, C

    Koshimoto, N. & Ranc, C. 2022, nkoshimoto/genulens: Release ver- sion 1.2

  39. [39]

    M., et al

    Kunder, A., Koch, A., Rich, R. M., et al. 2012, AJ, 143, 57

  40. [40]

    Y., Lu, J

    Lam, C. Y., Lu, J. R., Udalski, A., et al. 2022, ApJ, 933, L23

  41. [41]

    & Paczynski, B

    Mao, S. & Paczynski, B. 1991, ApJ, 374, L37

  42. [42]

    A., et al

    Mellier, Y., Abdurro’uf, Acevedo Barroso, J. A., et al. 2025, A&A, 697, A1 Mróz, P., Udalski, A., Bond, I. A., et al. 2017a, AJ, 154, 205 Mróz, P., Udalski, A., Skowron, J., et al. 2017b, Nature, 548, 183 Mróz, P., Udalski, A., Skowron, J., et al. 2019, ApJS, 244, 29 Mróz, P., Udalski, A., Szymański, M. K., et al. 2024a, ApJ, 976, L19 Mróz, P., Udalski, A...

  43. [43]

    M., Gould, A., Fouqué, P., et al

    Nataf, D. M., Gould, A., Fouqué, P., et al. 2013, ApJ, 769, 88

  44. [44]

    2019, Nature Astronomy, 3, 524

    Niikura, H., Takada, M., Yasuda, N., et al. 2019, Nature Astronomy, 3, 524

  45. [45]

    2025, ApJ, 979, 123

    Nunota, K., Sumi, T., Koshimoto, N., et al. 2025, ApJ, 979, 123

  46. [46]

    1986, ApJ, 304, 1

    Paczynski, B. 1986, ApJ, 304, 1

  47. [47]

    T., Kerins, E., Rattenbury, N., et al

    Penny, M. T., Kerins, E., Rattenbury, N., et al. 2013, MNRAS, 434, 2

  48. [48]

    D., Laureijs, R., Stagnaro, L., et al

    Racca, G. D., Laureijs, R., Stagnaro, L., et al. 2016, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Se- ries, Vol. 9904, Space Telescopes and Instrumentation 2016: Op- tical, Infrared, and Millimeter Wave, ed. H. A. MacEwen, G. G

  49. [49]

    P., Hirao, Y., et al

    Ranc, C., Bennett, D. P., Hirao, Y., et al. 2019, AJ, 157, 232

  50. [50]

    J., Bennett, D

    Rattenbury, N. J., Bennett, D. P., Sumi, T., et al. 2017, MNRAS, 466, 2710

  51. [51]

    1966, MNRAS, 134, 315

    Refsdal, S. 1966, MNRAS, 134, 315

  52. [52]

    C., Reylé, C., Derrière, S., & Picaud, S

    Robin, A. C., Reylé, C., Derrière, S., & Picaud, S. 2003, A&A, 409, 523 ROTAC. 2025, arXiv e-prints, arXiv:2505.10574

  53. [53]

    C., Anderson, J., Casertano, S., et al

    Sahu, K. C., Anderson, J., Casertano, S., et al. 2022, ApJ, 933, 83

  54. [54]

    Schlafly, E. F. & Finkbeiner, D. P. 2011, ApJ, 737, 103

  55. [55]

    J., Finkbeiner, D

    Schlegel, D. J., Finkbeiner, D. P., & Davis, M. 1998, ApJ, 500, 525

  56. [56]

    C., Calchi Novati, S., et al

    Shvartzvald, Y., Yee, J. C., Calchi Novati, S., et al. 2017, ApJ, 840, L3

  57. [57]

    A., Udalski, A., Calchi Novati, S., et al

    Street, R. A., Udalski, A., Calchi Novati, S., et al. 2016, ApJ, 819, 93

  58. [58]

    A., et al

    Sumi, T., Abe, F., Bond, I. A., et al. 2003, ApJ, 591, 204

  59. [59]

    P., Bond, I

    Sumi, T., Bennett, D. P., Bond, I. A., et al. 2013, ApJ, 778, 150

  60. [60]

    P., et al

    Sumi, T., Koshimoto, N., Bennett, D. P., et al. 2023, AJ, 166, 108

  61. [61]

    K., Bachelet, E., Zohrabi, F., et al

    Terry, S. K., Bachelet, E., Zohrabi, F., et al. 2025, arXiv e-prints, arXiv:2510.13974

  62. [62]

    2007, A&A, 469, 387

    Tisserand, P., Le Guillou, L., Afonso, C., et al. 2007, A&A, 469, 387

  63. [63]

    2018, Geosciences, 8, 365

    Tsapras, Y. 2018, Geosciences, 8, 365

  64. [64]

    H., Sajadian, S., et al

    Udalski, A., Ryu, Y. H., Sajadian, S., et al. 2018, Acta Astron., 68, 1

  65. [65]

    1993, Acta Astron., 43, 289

    Udalski, A., Szymanski, M., Kaluzny, J., et al. 1993, Acta Astron., 43, 289

  66. [66]

    1992, Acta Astron., 42, 253

    Udalski, A., Szymanski, M., Kaluzny, J., Kubiak, M., & Mateo, M. 1992, Acta Astron., 42, 253

  67. [67]

    K., & Szymański, G

    Udalski, A., Szymański, M. K., & Szymański, G. 2015, Acta Astron., 65, 1

  68. [68]

    P., Beaulieu, J.-P., et al

    Vandorou, A., Bennett, D. P., Beaulieu, J.-P., et al. 2020, AJ, 160, 121

  69. [69]

    P., Beaulieu, J.-P., et al

    Vandorou, A., Bennett, D. P., Beaulieu, J.-P., et al. 2025a, arXiv e- prints, arXiv:2504.06347

  70. [70]

    Witt, H. J. & Mao, S. 1994, ApJ, 430, 505

  71. [71]

    2011, MNRAS, 416, 2949

    Wyrzykowski, L., Skowron, J., Kozłowski, S., et al. 2011, MNRAS, 416, 2949

  72. [72]

    2021, MNRAS, 502, 5631

    Yang, H., Mao, S., Zang, W., & Zhang, X. 2021, MNRAS, 502, 5631

  73. [73]

    C., Shvartzvald, Y., Gal-Yam, A., et al

    Yee, J. C., Shvartzvald, Y., Gal-Yam, A., et al. 2012, ApJ, 755, 102

  74. [74]

    E.R. Caianiello

    Zhang, X., Zang, W., Udalski, A., et al. 2020, AJ, 159, 116 1 Dipartimento di Fisica "E.R. Caianiello", Università di

This paper was first reviewed by deepseek-v4-flash on August 3, 2026.