Same Events, Weaker Bound: Model Dependence in Magellanic Microlensing Limits on Primordial Black Holes

arXiv:2610.30510 · astro-ph.CO, astro-ph.HE, hep-ph · Submitted 2026-10-21 · Read on arXiv

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Introduction to the show: ident: Astrophysics Radio. Generated commentary on the latest astrophysics papers.

Vera: We're looking at the paper: "Same Events, Weaker Bound".

Jocelyn: Here's the gist of the paper. The gist The OGLE microlensing of the Magellanic Clouds sets leading bounds on primordial black holes as dark matter from 10−8 to 103 M⊙, and changes to various modeling assumptions weaken these published strict limits by up to 6 or over an order of magnitude in extreme stress tests.

Vera: Model Dependence in Microlensing Limits The microlensing exclusion depends on two distinct inputs: the predicted event rate at fixed abundance fPBH, and the treatment of the detected events OGLE already brackets the second, publishing strict limits, which assume that no detected event is a PBH, and relaxed limits, in which stellar and PBH lenses both contribute to the detections; the two differ by at most a factor ≃ 4, near 0.25 M⊙ The study extends this comparison to OGLE field-level data and timescale likelihoods by varying halo and stellar-population ingredients together Because the likelihood treats event origin as OGLE’s relaxed analysis does, ratios to the relaxed curves isolate the rate model The research finds that at fixed data, the 20-year bound weakens relative to OGLE’s relaxed limit by up to ≃ 1.6 for a benchmark built from recent Galactic and LMC measurements, and by up to ≃ 3.4 for an extreme stress test Impact of Halo and Stellar Population Changes The weakening of the bound is mass-dependent because the MW halo, LMC halo and stellar populations reshape the efficiency-weighted timescale distribution differently at different masses The benchmark takes a flattened double power law for the Milky Way halo, adopting smaller qh values which lowers the density off the Galactic plane, through which the LMC sightline passes This flattening alone lowers the MW dark-matter column toward the LMC by 11.8% and the detected MW-halo PBH yield by 19% The stress test takes a lower density for the Milky Way halo, with qh = 0.60, deliberately beyond values favored by Ibata et al.

Jocelyn: This extreme case gives Vc(R⊙) = 200.1 km s−1 and Vc(50 kpc) = 132.9 km s−1, which lies well below the implied velocity of distant halo tracers Effects of Disequilibrium and Clustering LMC-induced disequilibrium is invoked qualitatively as a reason to distrust equilibrium halo models However, this effect raises, rather than lowers, the lensing-weighted MW-halo density If PBHs are primordially clustered, the planetary-mass bound at its tabulated minimum weakens by ≃ 3.4 (benchmark) to ≃ 6.0 (stress test) relative to the published limit once a Lyα bound on cluster shot noise is imposed The study also investigates how clustering affects different mass windows: it weakens the planetary-mass bound by up to a factor ≃ 3.4–6.0 relative to the published limit, bounded mainly by the Lyα forest, but moves the 20-year bound by at most 16% Key Findings on Mass Dependence and Likelihood The weakening is mass-dependent because the MW halo, LMC halo and stellar populations reshape the efficiency-weighted timescale distribution differently at different masses At MPBH = 0.45 M⊙, a typical stellar-lens mass at which PBH and stellar timescales overlap, every ingredient acts The likelihood comparison shows that both models attain their grid maxima at Mbest = 0.0316 M⊙ For the high-cadence survey, the limit tracks the halo column directly when considering a single detected event at MPBH = 2.00 × 10−6 M⊙, yielding f95 = 1.49 × 10−3 and 3.00 × 10−3, which are weaker by factors 1.19 and 2.39 Constraints from Clustered PBHs Spatial clustering leaves the ensemble-mean lens population unchanged but broadens the distribution of event counts across realizations For clusters of radius 30 pc and the adopted threshold fMcl ≤ 8.6 × 102 M⊙, the high-cadence conditional envelopes at MPBH = 2.00×10−6 M⊙ are weaker than the published limit by factors ≃ 3.44 and ≃ 6.03 for the benchmark and stress test The Lyα constraint maps to a threshold of fMcl ≤ 8.6 × 102 M⊙ as an approximate Lyα threshold The combined budget analysis shows that for the stress test, the combined limit is Acrit ≃ 2.53 Limitations and Caveats Five caveats bound our conclusions: First, halo parameters are fixed, not marginalized, and our values of ρ⊙, qh and the LMC core were selected to suppress the rate Second, we use monochromatic PBH masses; an extended mass function changes both the signal and the timescale likelihood and is not guaranteed to weaken the bound Third, we do not reanalyze the long-timescale SMC sample Fourth, field-specific source luminosity functions were available to us for only one LMC and one SMC field Fifth, the clustered envelopes impose the microlensing and Lyα thresholds separately and assume primordially formed, independently distributed clusters The final two rows in Table S4 restore the corresponding ingredients together, but these tests do not provide a multiplicative decomposition of the comparison with the published OGLE limit The IMF gives the largest individual change, RIMF = 0.68, whereas the adopted MW disks act in the opposite direction, Rdisk = 1.10 The paper concludes that applications of microlensing bounds on compact-object DM should state the halo and stellar-population assumptions behind the curve they use Where robustness to those assumptions matters, the benchmark limits presented here are a conservative alternative to the published curves The work is partly supported by the U.S.

Vera: Department of Energy grant number DE-SC0010107 (SP) Page 5 --- The OGLE microlensing of the Magellanic Clouds sets the leading bounds on primordial black holes as dark matter from 10−8 to 103 M⊙, and changes to various modeling assumptions weaken these published strict limits by up to 6 or over an order of magnitude in extreme stress tests.

Title and authors: Vera: So we're looking at this paper today: "Same Events, Weaker Bound: Model Dependence in Magellanic Microlensing Limits on Primordial Black Holes," by Morales-Zapien, Lucas Brown, and Stefano Profumo. It’s a study that looks at how much those strict limits on primordial black holes change when you tweak the assumptions about the Milky Way halo and the Large Magellanic Cloud structures.

Jocelyn: Right, so it's not just about finding more events; it’s about making sure we aren't over-constraining PBH dark matter if our models of what surrounds us are a bit off. It touches on how those limits shift based on the ingredients we plug in for the Milky Way and LMC halos, and that’s pretty interesting because those ingredients are often just educated guesses.

Subrahmanyan: I find it compelling because it moves the discussion from just observing an event rate to understanding how much uncertainty is baked into those predictions, especially when you're looking at very small masses like ten-eight to ten cubed solar masses. That mass range is where we’re hoping to find primordial black holes as dark matter.

Vera: Exactly. The paper dives into how changing the halo ingredients—like using a flattened double power law for the Milky Way halo instead of something else—can weaken those published strict twenty-year bounds by up to a factor of six and in extreme stress tests, it can weaken them by over an order of magnitude <ref:2610.30510#pg1>by over an order of magnitude>.

Jocelyn: That’s a big jump, so what exactly does that mean for the numbers we’re working with? It seems like just changing how you model the Milky Way's mass distribution has such a huge impact on the final constraint on PBHs.

Subrahmanyan: Well, it shows that if we don't fix those halo models, our bounds aren't as tight as they look. The study uses a benchmark where they adopt a flattened double power law for the Milky Way halo and some specific values for q h, which is at the one sigma lower edge of the Ibata et al <ref:2610.30510#pg2> range <ref:2610.30510#pg2>.

Vera: And that flattening alone, just using that one assumption for the Milky Way's halo structure, lowers the dark matter column toward the LMC by about eleven point eight percent and the detected MW-halo PBH yield by about nineteen percent <ref:2610.30510#pg2>by eleven point eight percent and the detected MW-halo PBH yield by>. That’s a concrete change in what we observe.

Jocelyn: So, it means that when we look at those event rates, if our model of where the dark matter is concentrated around us is slightly different, the statistical limits we set on PBHs also shift significantly.

Subrahmanyan: It really highlights how sensitive these constraints are to the assumed density profiles of our galactic environment. If you use an extreme stress test case with a lower density for the Milky Way halo, like q h = zero point six zero, the circular velocity at twenty-seven point three one kpc drops to about one hundred seventy-nine point one km s−one which is quite low compared to some other tracers <ref:2610.30510#pg2>.

Vera: That comparison shows that even a small change in the halo parameters—specifically how dense the Milky Way halo is—can lead to a substantial weakening of the bound on PBHs. We’re seeing effects on different observables, like the halo optical depth, which Mr´oz et al. report has only few-percent changes among alternative Gaia DR3 halo models <ref:2610.30510#pg2>.

Jocelyn: It makes you wonder how much weight we should actually put on those specific halo models when we are trying to constrain dark matter candidates like PBHs, especially since the paper mentions that the two inputs for microlensing exclusion—the predicted event rate and the treatment of detected events—can differ by a factor of about four near zero point two five solar mass <ref:2610.30510#pg2>.

Subrahmanyan: And that difference in input treatment is what leads to those variations, which the study explores when they look at field-level data and timescale likelihoods <ref:2610.30510#pg3>. It shows that how you treat the detected events—whether you assume no detected event is a PBH or let both stellar and PBH lenses contribute—changes the result by up to a factor of four in some cases, near zero point two five solar mass <ref:2610.30510#pg2>.

Vera: And when you combine that with varying the halo and stellar population ingredients together, the weakening of the bound relative to OGLE’s relaxed limit can go up to one point six for a benchmark built from recent Galactic and LMC measurements <ref:2610.30510#pg3>.

Jocelyn: So, the overall effect is that when you push the assumptions into extreme stress tests, you can see limits weaken by as much as over an order of magnitude, which is a strong warning for our current constraints on PBHs <ref:2610.30510#pg1>.

Subrahmanyan: I think the main implication here is that we need to be very explicit about the modeling assumptions when we quote these limits because robustness matters, and the paper explicitly states that those benchmark limits are a conservative alternative to published curves <ref:2610.30510#pg1>.

The paper's summary: Vera: So, to recap, this paper shows that the constraints we set on primordial black holes from microlensing are much more sensitive to our assumptions about where dark matter is located than we thought <ref:2610.30510#pg1>.

Jocelyn: Right. It’s not just finding more events; it’s seeing how much the limits shift when you tweak the models for the Milky Way halo and the Large Magellanic Cloud structure <ref:2610.30510#pg2>.

Subrahmanyan: I find that really important because it shows that these strict limits on PBHs from ten-eight to ten cubed solar masses can weaken by up to a factor of six, and in extreme cases, even over an order of magnitude <ref:2610.30510#pg2>.

Vera: That’s a big shift, so what it means is that if we don't fix our models for the surrounding dark matter—the halo and the LMC—our current bounds on PBHs might be way too tight <ref:2610.30510#pg1>.

Jocelyn: Exactly. The paper explores how different ways of treating detected events change the rate model, and how that interacts with our choices for halo ingredients <ref:2610.30510#pg3>.

Subrahmanyan: And they show that if you include primordial clustering, which is a way PBHs might be distributed, the planetary-mass bound weakens by a factor of three point four to six relative to the published limit <ref:2610.30510#pg1>.

Vera: That factor of six is pretty significant for constraining the smallest possible primordial black holes we are looking for <ref:2610.30510#pg2>.

Jocelyn: And they found that if you use LMC-induced disequilibrium—which is a way to say our halo models aren't perfectly in equilibrium—it actually raises, rather than lowers, the lensing-weighted MW-halo density <ref:2610.30510#pg2>.

Subrahmanyan: That’s counterintuitive because you’d think non-equilibrium effects would just confuse our density estimates, but it shows that the LMC environment has a specific influence on how we calculate the lensing effect <ref:2610.30510#pg2>.

Vera: And they also looked at how different stellar populations affect things; for instance, when you replace standard Han-Gould disks with Ibata disks, the detected MW disk count can be raised by about thirty percent at fixed kinematics and initial mass function <ref:2610.30510#pg3>.

Jocelyn: That means the assumptions we make about what kind of stars are making those lenses really matter for our final constraint on PBHs <ref:2610.30510#pg3>.

Subrahmanyan: The paper concludes that applications of these microlensing bounds should always state the halo and stellar-population assumptions behind the curve they use, because robustness to those assumptions matters <ref:2610.30510#pg1>.

Vera: So, basically, if you want a real constraint on primordial black holes from microlensing data, you can't just take the number out of the equation without knowing exactly what model you are using <ref:2610.30510#pg3>.

Jocelyn: It’s a strong caution for us as we try to constrain dark matter with these methods <ref:2610.30510#pg3>.

Subrahmanyan: And they are suggesting that the benchmark limits presented here are a conservative alternative to the published curves <ref:2610.30510#pg1>.

The paper's improvements: Vera: So, to recap, this paper shows that we need to be much more explicit about our modeling choices when we quote constraints on primordial black holes from microlensing <ref:2610.30510#pg1>.

Jocelyn: Exactly. They're saying that if you want these limits to mean something, you have to state exactly what assumptions about the Milky Way halo and stellar populations are going into the calculation <ref:2610.30510#pg2>.

Subrahmanyan: I think that's important because it connects this directly to structure formation; if our constraints on dark matter candidates are changing based on our modeling choices, we need better ways to probe the actual dark matter distribution <ref:2610.30510#pg1>.

Vera: They also suggest that the benchmark limits they present are a conservative alternative to the published curves <ref:2610.30510#pg1>.

Jocelyn: Which means if you're looking at those published limits, you should be aware that they might be much tighter than what you get if you use their own conservative tests <ref:2610.30510#pg3>.

Subrahmanyan: And they’re pushing for a more thorough analysis of the ingredients; they show how the initial mass function, or IMF, gives one of the largest individual changes to the final upper limit <ref:2610.30510#pg1>.

Vera: So, if you want to see where those bounds might be weakest or strongest, you have to look at how changing those specific ingredients alters the result <ref:2610.30510#pg3>.

Jocelyn: They also touched on how different stellar populations affect the results; they found that when you swap out Han-Gould disks for Ibata disks, you get a thirty percent increase in the detected MW disk count at fixed kinematics and IMF <ref:2610.30510#pg3>.

Subrahmanyan: That’s a concrete result; it shows how changing the lens population structure directly impacts the constraint on PBHs <ref:2610.30510#pg1>.

Vera: And they also looked at primordial clustering, which we already talked about, showing that if PBHs are clustered, the planetary-mass bound weakens by a factor of three point four to six relative to the published limit <ref:2610.30510#pg1>.

Jocelyn: That confirms that spatial distribution matters; clustering definitely pushes those limits down when you include those cluster constraints <ref:2610.30510#pg2>.

Subrahmanyan: The paper also points out that the Lyman alpha constraint maps to a threshold of f Mcl at most eight point six times ten squared M as an approximate Lyman alpha threshold <ref:2610.30510#pg2>.

Vera: So, the overall message is that we need to use these bounds carefully and be aware of all those modeling assumptions when interpreting them <ref:2610.30510#pg1>.

Jocelyn: And they are saying that this work is a conservative way to think about these constraints on compact-object dark matter <ref:2610.30510#pg1>.

Subrahmanyan: So, the implication is that we need to move beyond just quoting the final number and start quoting the model behind it <ref:2610.30510#pg1>.

Conclusion: Vera: So, to wrap up, this paper shows that the constraints we set on primordial black holes from microlensing are much more sensitive to our assumptions about where dark matter is located <ref:2610.30510#pg1>.

Jocelyn: Yeah. It’s a big reminder that when we talk about these limits, you have to be super careful about the halo and stellar population models you're using <ref:2610.30510#pg3>.

Vera: Exactly. They’re saying that if you want those limits to mean something, you have to state exactly what assumptions about the Milky Way halo and the Large Magellanic Cloud structure are going into the calculation <ref:2610.30510#pg2>.

Jocelyn: And they’re also saying that if you want those limits to mean something, you have to state exactly what assumptions about the Milky Way halo and stellar population are going into the calculation <ref:2610.30510#pg3>.

Subrahmanyan: The paper also points out that the initial mass function, or IMF, gives one of the largest individual changes to the final upper limit <ref:2610.30510#pg1>.

David Morales-Zapien, Lucas Brown, Stefano Profumo

Department of Physics & Astronomy, California State University Long Beach · Santa Cruz Institute for Particle Physics · Department of Physics, University of California Santa Cruz

astro-ph.CO, astro-ph.HE, hep-ph

Submitted: 2026-10-21

Updated: 2026-10-21

Comments: 16 pages, 4 figures

License: http://creativecommons.org/licenses/by/4.0/

The gist: The gist The OGLE microlensing of the Magellanic Clouds sets leading bounds on primordial black holes as dark matter from 10−8 to 103 M⊙, and changes to various modeling assumptions weaken these

Key concepts

Model Dependence

The microlensing exclusion depends on two main inputs: the predicted event rate and how detected events are treated. The difference between assuming no detected event is a PBH versus allowing both stellar and PBH lenses to contribute can lead to limits differing by up to a factor of four, especially near 0.25 Msun.

Halo and Stellar Population Changes

Varying the models for the Milky Way halo and LMC halo significantly impacts the results because they change how efficiently dark matter is distributed at different masses. For example, flattening the MW halo model alone can lower the dark-matter column toward the LMC by 11.8%.

Clustering Constraints

If primordial black holes are clustered spatially, this effect weakens bounds on their mass. Including clustering in the modeling assumptions can reduce the planetary-mass bound by a factor of 3.4 to 6.0 relative to the published limit, provided a Ly$ ext{ ext{ extalpha}}$ bound on cluster shot noise is also imposed.

Terminology

• Microlensing — 1× in this paper · explained in 2 episodes
• Model Dependence — 1× in this paper · explained in 2 episodes

Summary

Improvements for AI systems

Abstract

Sources

• Primordial Black Holes as Dark Matter: Recent Developments
• Constraints on Primordial Black Holes
• Primordial Black Holes as a dark matter candidate
• Constraints on Earth-mass primordial black holes from OGLE 5-year microlensing events
• The OGLE View of Microlensing towards the Magellanic Clouds. III. Ruling out sub-solar MACHOs with the OGLE-III LMC data
• The OGLE View of Microlensing towards the Magellanic Clouds. IV. OGLE-III SMC Data and Final Conclusions on MACHOs
• No massive black holes in the Milky Way halo
• Limits on planetary-mass primordial black holes from the OGLE high-cadence survey of the Magellanic Clouds
• Microlensing optical depth, event rate, and limits on compact objects in dark matter based on 20 yr of OGLE observations of the Small Magellanic Cloud
• A critical analysis of the recent OGLE limits on stellar mass primordial black holes in the halo of the Milky Way
• Eppur non si trovano: Comments on the Primordial Black Hole Limits in the Galactic Halo
• Updating the MACHO fraction of the Milky Way dark halo with improved mass models
• Microlensing optical depth and event rate toward the Large Magellanic Cloud based on 20 years of OGLE observations
• The Milky Way total mass profile as inferred from Gaia DR2
• The total mass of the Large Magellanic Cloud from its perturbation on the Orphan stream
• Charting the Galactic acceleration field II. A global mass model of the Milky Way from the STREAMFINDER Atlas of Stellar Streams detected in Gaia DR3
• Dark matter in the Milky Way: Measurements up to 3 kpc from the Galactic plane above the Sun
• Galactic Accelerations from the GD-1 Stream Suggest a Tilted Dark Matter Halo
• The dark matter profile of the Milky Way inferred from its circular velocity curve
• The Circular Velocity Curve of the Milky Way from $5$ to $25$ kpc

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