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Assessing the Impact of Binary Systems on Microlensing Using SPISEA and PopSyCLE Population Simulations

T0 review · 3 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read Most microlensing events involve binary stars, not single stars alone.

desk verdict Credible simulation result that most OGLE-like events involve a multiple system, but the headline tE shift is driven by a total-mass approximation the paper itself flags. read the letter →

arxiv 2501.03506 v1 pith:APVDCFS3 submitted 2025-01-07 astro-ph.SR astro-ph.GA

Natasha S. Abrams , Jessica R. Lu , Casey Y. Lam , Michael S. Medford , Matthew W. Hosek , Jr. , Sam Rose This is my paper · ORCID
classification astro-ph.SRastro-ph.GA
keywords microlensingbinarystarsmultiplesystemsEinsteincrossingtimepopulationsynthesisOGLEgravitationallensingcompactobjects
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper argues that binary and triple star systems are not a minor correction to microlensing surveys but the majority of what such surveys actually see, and that neglecting them systematically distorts the inferred populations. By adding realistic multiple systems to the SPISEA stellar population code and injecting them into the PopSyCLE microlensing simulation, the authors find that 55% of events passing OGLE-like selection criteria contain a multiple lens, a multiple source, or both. Most of these events have light curves that look single, so they are routinely misclassified as single-star events. Including the multiples shifts the mean Einstein crossing time from 19.1 days to 21.3 days, bringing the simulated distribution into better agreement with observed OGLE data. If correct, this means that current single-star interpretations of microlensing surveys underestimate the prevalence of binaries and bias the inferred mass and event-duration distributions.

What carries the argument

The central machinery is the injection of physically motivated multiple-star systems into a Milky Way microlensing simulation. The paper extends SPISEA (a stellar population synthesis code) to generate companions with semi-major axes, eccentricities, and orbital orientations drawn from empirical distributions (e.g., a broken power law for separation versus primary mass based on Duchêne & Kraus 2013), and then matches these systems onto stars in PopSyCLE (a microlensing survey simulator built on the Galaxia Milky Way model). Each event's light curve is then computed for the multiple system, using a point-source–point-lens model for single events but a binary light-curve treatment for multiples, and OGLE-like detection cuts are applied to determine which events would actually be observed. The key step is that the Einstein crossing time for a multiple lens is computed using the total system mass, so adding companions directly lengthens $t_E$; this is what produces the shift from 19.1 to 21.3 days.

What would settle it

A direct test would be to compare the predicted fraction of multi-peaked events (3.1% of all events under OGLE cuts) with a large, completeness-corrected sample from OGLE or KMTNet that accounts for cadence gaps. If the observed multi-peaked fraction is significantly lower (or higher) than 3.1% after such corrections, or if the recovered $t_E$ distribution does not shift by the predicted 2.2 days when binaries are included, the assumed binary population parameters or the system-mass approximation would be ruled out.

Watch

Extended reading notes

Core claim

The paper's central claim is that, under OGLE-like observational cuts, over half (55%) of microlensing events involve a binary or triple system as the lens, source, or both, specifically 14.5% with a multiple lens and single source, 31.7% with a single lens and multiple source, and 8.8% with both multiple. The great majority (94.4%) of these multiple events have only a single observable peak in their light curves, so they are easily mistaken for ordinary point-source, point-lens events. When these single-peaked multiples are included in the simulated event population, the mean Einstein crossing time $t_E$ shifts from 19.1 days (singles only) to 21.3 days, and the distribution becomes significantly more consistent with the observed OGLE $t_E$ distribution (the Kolmogorov–Smirnov p-value improves from $3.06\times10^{-10}$ to $9.34\times10^{-4}$). The paper concludes that multiple systems are a substantial missing piece in microlensing population synthesis and that binary-source and binary-lens–binary-source models should be routinely included in event analysis.

Load-bearing premise

The paper assumes that the Einstein crossing time of an event with a multiple lens is accurately given by the total system mass, as if all the mass were concentrated at the primary's position, an assumption that the authors themselves note can bias events with a massive, distant, and unlensed companion.

Editorial extensions

If this is right

  • Surveys that fit only single-lens, single-source models will systematically misclassify the majority of microlensing events, biasing measurements of event rates and durations.
  • The Einstein crossing time distribution, a key observable for inferring the mass function of compact objects, is significantly different when binaries are included, so population-level conclusions from OGLE and similar surveys need to be revisited.
  • Binary lenses are preferentially found with separations of 1–10 AU, so microlensing samples will underrepresent wide binaries; the same applies to source binaries, which are biased toward larger separations.
  • Black hole astrometric candidate selection using the criteria $t_E > 120$ days and $\pi_E < 0.08$ is unaffected by the presence of multiples, so the search for isolated black holes is robust to this effect.
  • The fraction of obvious multi-peaked events (3.1% of all events) matches the 2–11% binary fraction reported by surveys, suggesting that the missing multiples are hiding in plain sight as single-peaked events.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the 55% multiple fraction holds for deeper surveys such as the Vera Rubin Observatory or the Roman Space Telescope, the implied bias in the inferred mass distribution of lenses could be even larger, because these surveys probe fainter sources where binary companions contribute a smaller fraction of the light.
  • The paper's treatment of triples by selecting the two-body pair with the largest magnification may underestimate the fraction of multi-peaked events; a full three-body simulation could turn some single-peaked triples into observable multi-peaked events, which would raise the 'obvious' binary fraction.
  • The systematic use of total system mass for $t_E$ in wide binaries is likely the weakest link; if that approximation is refined (e.g., computing $t_E$ from the primary's Einstein radius and adding a separate companion signal), the reported 2.2-day shift might shrink or change sign for extreme mass ratios.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. Abrams et al. extend the SPISEA/PopSyCLE population-synthesis pipeline to include binary and triple systems, simulate mock OGLE-IV microlensing surveys, and analyze how multiples affect event statistics. They report that 55% of events passing OGLE-like cuts involve a multiple lens, source, or both, that most such events are single-peaked and well fit by point-source-point-lens models, and that including multiples shifts the mean Einstein crossing time from 19.1 days to 21.3 days, improving agreement with the OGLE tE distribution (KS p = 9.34e-4 vs 3.06e-10). The paper also examines biases in light-curve fitting, the selection of binary parameters by microlensing, and the impact on black-hole astrometric follow-up selection.

Significance. If the central results hold, this is a valuable contribution. The authors provide a public, extensible simulation tool; they use external calibrations for binary statistics rather than fitting to the target distribution; and they make a concrete, falsifiable prediction that multiples are ubiquitous in microlensing samples and largely masquerade as single events. The external comparison to OGLE is appropriate, and the KS test provides a useful summary statistic. The negative result that binaries do not affect black-hole candidate selection is also useful. The main caveat is that the quantitative tE shift and the 55% fraction rest on modeling choices—total-system-mass tE for binary lenses and solar-neighborhood multiplicity statistics—that are acknowledged but not tested for robustness.

major comments (3)
  1. [Sec. 2.2.2, Eq. (7), Table 9, Table 6, Sec. 5.2] The central tE-shift result depends on assigning binary-lens events a tE based on the total system mass, Msys = M1 + M2, for all systems. This is unphysical for the ~50% of binaries whose projected separation exceeds the Einstein radius, as the paper itself notes in Sec. 2.2.2. For such wide binaries the companion does not contribute to the magnification of a source passing near the primary, so the event timescale should be set by the primary mass (or by the component actually responsible for the lensing), not by the total mass. Using Msys inflates tE by a factor sqrt(1+q), and Table 6 shows that M Run Mult Lens events have mean tE = 37.8 d versus 16.8 d for M Run Sing Lens events, so this approximation drives the reported shift from 19.1 d to 21.3 d and the improved KS p-value. The caveat in Sec. 6.2 about a 'massive, distant, and unlensed companion' is not sufficient; the paper needs a quantitative estimate. I request a rerun or post-processing correction in which wide binaries (projected separation > thetaE) are assigned tE based on the primary mass, and the resulting mean tE, Fig. 6, and KS p-value be reported.
  2. [Sec. 2.1, Table 5] The multiplicity fractions and companion statistics are taken from the solar neighborhood (Lu et al. 2013; Duchene & Kraus 2013) and applied to the Galactic bulge. The quantitative breakdown in Table 5 (14.5% PSBL, 31.7% BSPL, 8.8% BSBL) is therefore only as reliable as that extrapolation. The paper acknowledges that the parameters are uncertain but does not explore how the 55% total or the tE shift respond to plausible variations in the multiplicity-fraction normalization (A, alpha), the companion-star-fraction normalization (B, beta), or the mass-ratio index (gamma). Since 'over half of observable events involve a multiple system' is a headline claim, a sensitivity analysis over these input parameters is needed to establish robustness.
  3. [Appendix B, Appendix C, Sec. 6.2] The treatment of triple systems is approximate: for triples, the paper simulates only the primary-companion pair with the largest Delta m, rather than the full triple lens/source configuration. This approximation can affect the single-peaked versus multi-peaked classification and thus the comparison of the simulated tE distribution to OGLE in Sec. 5.2. Appendix C provides a partial test, but it assumes that correctly treated triples would yield multi-peaked or unobservable events, and it does not propagate the resulting classification changes through the KS test. Given that triples contribute about 10% of events and about half of the tE > 30 d difference between M Runs and S Runs, a more rigorous treatment, or at least a bracketing calculation, would materially strengthen the main conclusion.
minor comments (4)
  1. [Sec. 5.2] The KS p-value for M Runs (9.34e-4) is still very small, indicating that the simulated distribution remains statistically inconsistent with OGLE even after including multiples; the text should acknowledge this and not overstate the level of agreement.
  2. [Sec. 2.1] Typo: 'standard Keplarian distributions' should read 'standard Keplerian distributions.'
  3. [Sec. 5.3] The sentence 'we accept that the estimates we use for tE, which are based on system mass, are sufficient' seems to preempt the very concern raised in Sec. 6.2; this statement should be revised to reflect the quantitative caveat.
  4. [Fig. 3 caption] The caption lists triple fractions for PSBL/BSPL/BSBL but does not reference Table 10; adding a cross-reference would improve clarity.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; the tE shift is a stated modeling consequence of using total system mass, and the OGLE comparison is an external benchmark.

full rationale

The paper's quantitative claims are generated by a forward population-synthesis model whose inputs (multiplicity fractions, companion star frequencies, mass-ratio and separation distributions from Lu et al. 2013 and Duchene & Kraus 2013) are external empirical calibrations, not fitted to the OGLE tE distribution it compares against. The comparison dataset (Mroz et al. 2017/2019) is independent of the simulation, and the KS test, event-rate, and Nstars comparisons are external benchmarks. The tE shift for multiple-lens events follows from the explicitly stated rule that tE is computed from the total system mass (Sec. 2.2.1, Table 9); this is a transparent modeling approximation, and Sec. 6.2 flags the corresponding bias for massive, distant, unlensed companions. Although PopSyCLE, SPISEA, and the Lu et al. (2013) calibrations are authored or co-authored by the present authors, they are independently published, externally constrained tools and measurements, and are not invoked as a uniqueness theorem or as a substitute for comparison to data. The paper does not fit any parameter to the target tE distribution and does not rename a known result; the central claims could in principle be falsified by the OGLE comparison or by changing the assumed multiplicity inputs. No circular step is present.

Assumptions & free parameters 12 free parameters · 7 assumptions · 0 invented entities

The central numbers (55% multiple events, tE shift) inherit all of the uncertainty in the SPISEA multiplicity prescriptions and the PopSyCLE modeling choices; none of these are fitted to the OGLE tE distribution, which keeps the comparison external, but the input distributions themselves are weakly constrained for the bulge.

free parameters (12)
  • A (multiplicity fraction normalization) = 0.44
    MF(M)=A M^alpha (Eq. 1); sets binary fraction as function of primary mass; from Lu et al. 2013, applied to Galactic bulge.
  • alpha (multiplicity fraction exponent) = 0.51
    Eq. 1; mass dependence of binary fraction.
  • B (companion star fraction normalization) = 0.5
    CSF(M)=B M^beta (Eq. 2); sets mean number of companions per multiple system.
  • beta (companion star fraction exponent) = 0.45
    Eq. 2; mass dependence of companion star fraction.
  • gamma (mass-ratio index) = -0.4
    P(q)=q^gamma (Eq. 4); sets companion mass distribution; from Lu et al. 2013.
  • q_min = 0.01
    Lower limit of mass ratio in Eq. 4; sets minimum companion mass.
  • Semi-major axis broken power law (A, M_break, alpha1, alpha2) = A=379.8 AU, M_break=4.9 Msun, alpha1=-1.8, alpha2=4.2
    Eq. 5; fitted to Duchêne & Kraus (2013) data; sets binary separations as function of primary mass.
  • sigma_log(a) coefficients (m, b) = m=0.84, b=0.31
    Eq. 6; fitted to Duchêne & Kraus (2013); width of the log-normal separation distribution.
  • Eccentricity distribution = thermal f(e)=2e
    Section 2.1; chosen over flat distribution; affects projected binary separation and lensing probability.
  • Secondary peak detection threshold = Delta_m >= 0.02 mag
    Section 3; estimated from mean OGLE photometric uncertainty; determines which events count as multi-peaked.
  • Flux-magnitude relation constants = F=350 counts x 10^((m-16)/-2.5); F_err=F^0.85
    Eqs. 30-31; fitted to 100 OGLE lightcurves; used to generate mock photometric errors.
  • Mass-match tolerance = 20%
    Section 2.2.2; SPISEA primaries matched to Galaxia stars within 20% in mass; affects which companions are retained in the final population.
assumptions (7)
  • standard math Kepler's third law and Thiele-Innes orbital projection (Eqs. 16, 20-29)
    Standard celestial mechanics used to assign binary separations, periods, and projected companion positions.
  • standard math Paczynski point-lens magnification formula (Eq. 10)
    Standard formula used to compute lightcurves for single-lens events and as the basis for binary lightcurve simulations.
  • domain assumption Local solar neighborhood binary statistics apply to the Galactic bulge
    SPISEA defaults (Lu et al. 2013, Duchêne & Kraus 2013) are used for bulge populations; the paper notes these are uncertain but does not validate them against bulge-specific binary statistics.
  • domain assumption Binaries are static over the microlensing survey, no orbital motion
    Section 2.2.4 ignores xallarap, which can create or suppress peaks; acknowledged in Sec 6.2 as a limitation.
  • domain assumption Stars evolve as singles, no binary mass exchange, mergers, or ejections
    Section 2.1 and 6.2: all compact objects remain in their original multiples, so every simulated black hole is in a binary; natal kicks and supernovae would disrupt many binaries.
  • ad hoc to paper Triple systems are approximated by the primary-companion pair giving the largest Delta_m
    Section 2.2.5 and Appendix B: full triple lens/source lightcurves are not simulated; 10.4% of events involve triples; this approximation may misclassify peak counts.
  • ad hoc to paper Binary lens tE is computed from total system mass
    Section 2.2.1 and Table 9: tE for multiple lenses uses M_sys = sum of masses, treating a separated binary as a point mass; acknowledged to bias events with massive distant companions.

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Cite this review

Pith. "Pith review of Assessing the Impact of Binary Systems on Microlensing Using SPISEA and PopSyCLE Population Simulations." pith.science (2026). https://pith.science/paper/APVDCFS3

@misc{pith2026250103506,
  author       = {Pith},
  title        = {Pith review of: Assessing the Impact of Binary Systems on Microlensing Using SPISEA and PopSyCLE Population Simulations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/APVDCFS3}},
  note         = {Machine review of arXiv:2501.03506}
}
read the original abstract

Gravitational microlensing provides a unique opportunity to probe the mass distribution of stars, black holes, and other objects in the Milky Way. Population simulations are necessary to interpret results from microlensing surveys. The contribution from binary objects is often neglected or minimized in analysis of observations and simulations despite the high percentage of binary systems and microlensing's ability to probe binaries. To simulate the population effects we added multiple systems to Stellar Population Interface for Stellar Evolution and Atmospheres (SPISEA), which simulates stellar clusters. We then inject these multiples into Population Synthesis for Compact-object Lensing Events (PopSyCLE), which simulates Milky Way microlensing surveys. When making OGLE observational selection criteria, we find that 55% of observed microlensing events involve a binary system. Specifically, 14.5% of events have a multiple-lens and a single source, 31.7% have a single lens and a multiple-source, and 8.8% have a multiple-lens and a multiple-source. The majority of these events have photometric lightcurves that appear single and are fit well by a single-lens, single-source model. This suggests that binary source and binary lens-binary source models should be included more frequently in event analysis. The mean Einstein crossing time shifts from 19.1 days for single events only to 21.3 days for singles and multiple events, after cutting binary events with multiple peaks. The Einstein crossing time distribution of singles and single-peaked multiple events is better aligned with observed distributions from OGLE (arXiv:1707.07634) than singles alone, indicating that multiple systems are a significant missing piece between simulations and reality.

Figures

Figures reproduced from arXiv: 2501.03506 by the authors.

Figure 1
Figure 1. Semi-major axis (a) as a function of primary mass (M). The orange points are the mean semi-major axis values averaged over mass bins in Duchene & Kraus ˆ (2013). We fit these points and corresponding standard deviations, shown in blue. At each mass, the semi-major axis distribution is modeled as a log-normal distri￾bution with a mean (indicated by the dark blue line) and standard deviation (indicated by the shaded b… view at source ↗
Figure 2
Figure 2. We show the matching process of the Galaxia stars and SPISEA primary stars. The orange circles represent SPISEA primary stars and the blue circles represent Galaxia stars. Circles with a dotted boarder and faint color represent unmatched objects and filled in circles represent objects with a confirmed match. Lines drawn between dotted circles are tentative matches which are either confirmed or rejected indicated wit… view at source ↗
Figure 3
Figure 3. Left shows the percentage of the intrinsic population with OGLE EWS observability cuts with a single source and single lens (PSPL), a single source and multiple lens (PSBL; 19% of which have a triple lens), a multiple source and single lens (BSPL; 15% of which have a triple source), and multiple source and multiple lens (BSBL; 31% of which have a triple lens or source) as indicated in [PITH_FULL_IMAGE:figures/full_… view at source ↗
Figures from the paper (8 more)
Figure 4
Figure 4. Figure 4: This is a set of random example lightcurves from the PopSyCLE simulation where time is in days where 0 corresponds to t0. In blue are PSPL events. Deviations from the prototypical microlensing shape in these lightcurves are due to parallax. Binary events with more than…
Figure 6
Figure 6. Figure 6: Number of events as a function of the Einstein crossing time in days with the distribution of events from S Runs in the yel￾low dashed line, single and single-peaked multiple events from M Runs in the blue solid line, and event distributions from Mroz et al. ´ (2017) d…
Figure 7
Figure 7. Figure 7: Simulated events fit by a PSPL model without parallax which first passed Mock OGLE EWS Cuts (see Section 4) and had significant signal beyond a straight line. 28% of the fit lightcurves had significant signal beyond a straight line, which are those shown in the pie cha…
Figure 8
Figure 8. Figure 8: Events that were fit by a PSPL model without parallax, which first passed Mock OGLE EWS Cuts (see Section 4). These are events that had a significant signal above a straight line and fit well by a PSPL model. Each panel shows the tE distributions of the input parameter…
Figure 9
Figure 9. Figure 9: We compare the distribution of semi-major axes of bi￾nary systems at the population synthesis stage before microlens￾ing (blue), binaries which are lenses (orange dashed), and bina￾ries which are sources (green dash-dotted). The distributions are smoothed with a Gaussi…
Figure 10
Figure 10. Figure 10: We compare the distribution of q (companion current mass/primary current mass) of binary systems at the population synthesis stage before microlensing (blue) and binaries which are lenses (orange dashed). For any systems where q > 1 due to mass loss such that the prim…
Figure 11
Figure 11. Figure 11: πE vs tE for S Runs (left) and single and single-peaked multiples events for M Runs (right). The blue contours are stars, the orange contours are WDs, the green contours are NSs, and the red squares are BHs. The contours are density contours. The grey box is the selec…
Figure 12
Figure 12. Figure 12: Fraction of events which are black holes as a function of the minimum tE (Eq. 8) per bin. The contours are 1σ Poisson errors. There is no significant difference in the fraction of black holes at any given tE between the M Runs and S Runs. include binaries, but in a ru…

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Pith tools

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