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

This paper demonstrates that the leading constraints on primordial black holes as dark matter, derived from OGLE microlensing of the Magellanic Clouds, are highly model-dependent and can be significantly weakened—by up to an order of magnitude—when incorporating recent data-driven updates to the Milky Way and Large Magellanic Cloud halo structures and stellar populations.

Original authors: David Morales-Zapien, Lucas Brown, Stefano Profumo

Published 2026-10-23

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CC BY 4.0

Original authors: David Morales-Zapien, Lucas Brown, Stefano Profumo

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Dark matter is the invisible scaffolding of the universe, a mysterious substance that holds galaxies together but refuses to reveal its true nature. For decades, scientists have hunted for clues, and one leading suspect is the primordial black hole. Unlike the black holes formed by dying stars, these are theoretical relics from the very first moments after the Big Bang, potentially existing in a vast range of sizes, from smaller than an atom to heavier than our sun. If they exist in large numbers, they could make up the missing mass of the cosmos. To find them, astronomers look for a specific cosmic trick called microlensing. When a dark object passes in front of a distant star, its gravity acts like a lens, briefly brightening the star's light. By counting how often this happens toward the Magellanic Clouds, two satellite galaxies orbiting our own Milky Way, researchers can set strict limits on how many of these invisible black holes could be hiding in our galactic neighborhood.

For years, data from the Optical Gravitational Lensing Experiment, known as OGLE, has provided the most stringent rules on this game. The standard analysis, which assumed a specific, smooth distribution of stars and dark matter, suggested that primordial black holes could make up no more than a tiny fraction of the universe's dark matter across a wide range of masses. These limits have become a fixed reference point for cosmologists, a boundary that any new theory of the early universe must respect. However, the reliability of these limits depends entirely on the models used to describe the invisible structures of our galaxy. If the shape of the Milky Way's dark halo or the population of its stars is slightly different from what was assumed, the rules of the game change.

A new study by David Morales-Zapien, Lucas Brown, and Stefano Profumo revisits these limits by holding the actual observed events constant while changing the underlying models of the galaxy. Instead of questioning the data itself, the researchers asked what would happen if the Milky Way and its neighbor, the Large Magellanic Cloud, looked different than the standard textbook versions. They tested a "benchmark" model built from recent, precise measurements of our galaxy's structure, including a flatter shape for the Milky Way's dark matter halo and updated estimates for the mass of stars in the Magellanic Clouds. They also ran an "extreme stress test," pushing these parameters to the very edge of what is physically plausible to see how fragile the original limits truly were.

The results show that the previous strict boundaries are not as unbreakable as once thought. When the researchers applied their benchmark model, which incorporates modern data on the shape of our galaxy and the distribution of its stars, the upper limit on the abundance of primordial black holes weakened by a factor of roughly 1.6 compared to the standard relaxed limit. In the extreme stress test, where the galaxy was modeled with a significantly flatter shape and lower density, the limit weakened by a factor of about 3.4. When compared to the most conservative strict limit, which assumes none of the detected events are caused by black holes, the weakening is even more dramatic, reaching factors of over 13 in the extreme case. This means that a much larger population of primordial black holes could exist without contradicting the observed data, provided the galaxy is shaped in these specific ways.

The study also looked at a different scenario where primordial black holes are not spread out evenly but are grouped together in clusters. In this case, the limits on the smallest, planetary-mass black holes weaken even further, by a factor of between 3.4 and 6, depending on the model used. This is because clustered black holes create a different statistical pattern of events that is harder to rule out with the current data. The researchers found that a phenomenon often cited as a reason to distrust simple models—the gravitational wake created by the Large Magellanic Cloud as it moves through the Milky Way—actually makes the signal stronger, not weaker, further tightening the constraints rather than loosening them.

Ultimately, this work does not prove that primordial black holes exist or that they make up all the dark matter. Instead, it demonstrates that the current limits are highly sensitive to the assumptions made about the structure of our galaxy. The authors argue that future studies must stop treating these limits as absolute facts and start reporting them alongside the specific models used to derive them. They recommend that scientists adopt more conservative assumptions when setting these boundaries, ensuring that the search for the universe's hidden mass remains robust against the inevitable updates in our understanding of the Milky Way's shape and composition.

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

Problem Statement
Primordial black holes (PBHs) remain a viable dark matter (DM) candidate across a wide mass range. Gravitational microlensing surveys of the Magellanic Clouds by the Optical Gravitational Lensing Experiment (OGLE) currently provide the leading constraints on PBHs as DM, limiting their abundance ( $f_{\text{PBH}} = \Omega_{\text{PBH}}/\Omega_{\text{DM}}$ ) to a few percent over the mass range $10^{-8}$ to $10^3 M_\odot$ . These limits are routinely treated as fixed inputs in cosmological and particle physics analyses. However, the robustness of these limits against variations in astrophysical modeling has been disputed. While previous defenses argued that plausible changes to the Milky Way (MW) halo profile alter the optical depth by only a few percent, this paper investigates whether simultaneous, data-motivated changes to the MW halo, the Large Magellanic Cloud (LMC) halo, and stellar lens populations significantly weaken the published bounds.

Methodology
The authors reanalyze the 20-year OGLE-III+IV LMC survey and the high-cadence LMC/SMC survey, holding the detected events and survey efficiencies fixed. They employ an extended-Poisson likelihood that treats event origins as a mixture of stellar and PBH lenses (matching OGLE's "relaxed" analysis), allowing them to isolate the impact of rate model changes.

The study introduces two alternative modeling configurations:

Benchmark Model: Incorporates recent measurements including:
- MW Halo: A flattened double-power-law profile (Ibata et al.) with an axis ratio $q_h = 0.72$ and local density $\rho_\odot = 0.30 \text{ GeV cm}^{-3}$ .
- LMC Halo: A cored Burkert profile fitted to inner rotation curves, replacing the untruncated Hernquist profile.
- Stellar Populations: More massive MW disks (Ibata et al.) and a lower LMC stellar mass ( $2.1 \times 10^9 M_\odot$ ) with a shallower initial mass function (IMF).
- Disequilibrium: The model evaluates LMC-induced MW halo disequilibrium but conservatively sets the enhancement factor $\kappa_w = 1$ .
Stress Test Model: Deliberately extreme configurations, including a lower local density ( $\rho_\odot = 0.20 \text{ GeV cm}^{-3}$ ), a highly flattened MW halo ( $q_h = 0.60$ ), and a truncated, low-mass LMC halo.

The authors also investigate the impact of primordial PBH clustering, where PBHs reside in clusters of radius $R_{\text{cl}} = 30 \text{ pc}$ , subject to constraints from the Ly $\alpha$ forest on cluster shot noise.

Key Contributions and Results
The paper demonstrates that holding the observed data fixed, changes in astrophysical modeling motivated by recent data significantly weaken the published exclusion limits:

20-Year Survey Limits: Relative to OGLE's relaxed limit (which assumes a mix of stellar and PBH lenses), the benchmark model weakens the bound by a factor of $\simeq 1.6$ near $0.32 M_\odot$ , and the stress test weakens it by $\simeq 3.4$ near $0.05 M_\odot$ . Relative to the stricter "no PBH events" limit, these factors increase to $\simeq 6.2$ and $\simeq 13.2$ , respectively.
High-Cadence Planetary-Mass Limits: At the tabulated minimum of the published curve ( $M_{\text{PBH}} = 2.00 \times 10^{-6} M_\odot$ ), the benchmark weakens the limit by a factor of 1.19, and the stress test by 2.39.
Role of Disequilibrium: Contrary to qualitative arguments suggesting LMC-induced disequilibrium might lower the lensing signal, the authors find that the dipole response of the MW halo actually increases the lensing-weighted DM density along the sightline by $\simeq 6\%$ . Setting this to unity is a conservative choice.
Effect of Clustering: If PBHs are primordially clustered, the planetary-mass bound weakens further. Relative to the published limit, the bound weakens by factors of $\simeq 3.4$ (benchmark) to $\simeq 6.0$ (stress test) when Ly $\alpha$ constraints are imposed. For the 20-year survey, clustering has a minimal effect (at most 16%).
Ablation Studies: The weakening is mass-dependent. The initial mass function (IMF) is identified as the single largest individual contributor to the weakening (a factor of 1.46 tightening if restored to canonical values), followed by halo flattening and LMC halo profile changes.

Significance and Claims
The authors conclude that the robustness of compact-object dark matter limits is highly sensitive to modeling assumptions regarding the MW and LMC halos, as well as stellar populations. They do not claim that their benchmark restores compatibility with the anomalous bulge lens population or other specific PBH interpretations; rather, they demonstrate that the "fixed" limits used in the literature are not as model-independent as often assumed.

The paper strongly recommends that future limits on compact-object dark matter be quoted alongside their specific modeling assumptions (halo profiles, stellar masses, IMFs) and whether they represent strict or relaxed limits. Where robustness to these assumptions is critical, the benchmark limits presented here serve as a conservative alternative to the published curves. The authors note that a joint hierarchical analysis of bulge and Magellanic Cloud samples with common priors is necessary to fully confront the bulge preference for a PBH-like component with the Magellanic Cloud null results.

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