🔭 astrophysics

Stellar microlensing surveys as a probe of Primordial Black Holes: status and prospects

This paper provides a comprehensive overview for theorists on the history, theory, observational status, and future prospects of using stellar microlensing surveys to constrain primordial black holes as a component of dark matter, noting that current data excludes them from comprising all dark matter in the mass range of $10^{-11}$ to $10^{4}$ solar masses.

Original authors: Anne M. Green

Published 2026-04-24

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Anne M. Green

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

The Cosmic "Flashlight" Hunt: How We Search for Invisible Black Holes

Imagine you are walking through a dark forest at night, holding a flashlight. You can't see the trees clearly, but every now and then, a beam of light from a distant lighthouse flickers and gets brighter for a split second before fading back to normal. You know there's no one else there to block the light, so you realize: something invisible must have passed right in front of the lighthouse, bending the light toward you.

This is the basic idea behind Stellar Microlensing, the subject of this paper by Anne Green. It is a cosmic game of "spot the invisible intruder."

Here is the story of how astronomers use this trick to hunt for Primordial Black Holes (PBHs)—ghostly, ancient black holes that might make up the "Dark Matter" holding our galaxy together.

1. The Invisible Ghosts (Dark Matter & PBHs)

We know our galaxy, the Milky Way, is held together by a mysterious, invisible glue called Dark Matter. We can't see it, but we know it's there because stars move faster than they should if only visible matter existed.

For a long time, scientists thought Dark Matter was made of tiny, subatomic particles. But another idea exists: What if Dark Matter is made of millions of tiny, invisible black holes? These aren't the super-massive ones at the center of galaxies; these are "Primordial Black Holes" (PBHs) that formed in the very first split-second after the Big Bang. They could be as small as a planet or as heavy as a star.

2. The Cosmic Magnifying Glass (Microlensing)

How do you find something you can't see? You look for how it messes with things you can see.

According to Einstein's theory of gravity, massive objects bend space. When a massive object (like a black hole) passes exactly between us and a distant star, it acts like a cosmic magnifying glass.

The Effect: The background star suddenly gets brighter (magnified) for a few days or weeks, then fades away.
The Catch: The black hole itself is invisible. We only see the "flash" of the star behind it.

This is called Microlensing. It's like seeing a car drive past a streetlamp at night; you don't see the car, but you see the light flicker as the car blocks and bends the beam.

3. The Great Detective Story (The History of the Hunt)

The paper reviews a 30-year detective story involving three main teams of astronomers: MACHO, EROS, and OGLE.

The Early Hopes (1990s): The MACHO team started watching millions of stars in the "Magellanic Clouds" (two small galaxies near ours). They saw a lot of flashes! At first, they thought, "Wow, maybe the whole galaxy is filled with these invisible black holes!" They estimated that up to 20% of our galaxy's invisible mass could be these black holes.
The Reality Check: Other teams (EROS and OGLE) started watching the same skies with better cameras. They didn't see as many flashes as MACHO predicted.
The Twist: As time went on, astronomers realized many of the "flashes" MACHO saw weren't actually black holes. Some were just variable stars (stars that naturally pulse like a heartbeat), and some were distant supernovas. When they cleaned up the data, the number of "black hole candidates" dropped significantly.

4. The Current Verdict (What We Know Now)

By combining all the data from these decades of watching the sky, the paper concludes a very strict rule:

If Primordial Black Holes exist, they cannot make up 100% of the Dark Matter.

The Mass Range: We have looked for black holes ranging from the mass of a small asteroid ( $10^{-11}$ times the Sun) to the mass of a giant star cluster ( $10^4$ times the Sun).
The Result: In almost every size category, the "flash count" is too low. If the galaxy were full of these black holes, we would see thousands of flashes every year. Instead, we see very few.
The Limit: The paper says that for most sizes, these black holes can make up less than 1% of the Dark Matter. They might exist, but they are the "minority report," not the main ingredient.

5. The Future: Sharper Eyes

So, is the hunt over? Not quite! The paper looks forward to new tools:

The Roman Space Telescope: A new space telescope that will act like a super-powered camera. It will be able to spot much fainter flashes and distinguish them from "fake" signals (like variable stars) much better than before.
Astrometry: This is a new technique. Instead of just measuring how bright a star gets, these telescopes will measure exactly where the star moves on the sky. It's like seeing the shadow of the invisible car move across the street, not just the flicker of the light.

The Big Picture Analogy

Imagine you are trying to figure out if a room is filled with invisible balloons.

The Old Way: You turn on a light and watch for shadows. You see a few shadows and guess there are a lot of balloons.
The Better Way: You realize some shadows were just people walking by, not balloons. You count again and find very few shadows.
The Conclusion: The room isn't full of balloons. Maybe there are a few, but mostly it's empty (or filled with something else, like invisible gas).

In summary: This paper tells us that while Primordial Black Holes are a fascinating idea, the evidence from looking at "flashing stars" suggests they are not the main solution to the Dark Matter mystery. However, with new, sharper telescopes coming soon, we will be able to look even deeper and be absolutely sure.

1. Problem Statement

The paper addresses the question of whether Primordial Black Holes (PBHs) or other Compact Objects (COs) in the planetary to stellar mass range ( $10^{-11} M_\odot \lesssim M \lesssim 10^4 M_\odot$ ) can constitute a significant fraction of the Dark Matter (DM) in the Milky Way (MW) halo.

While the discovery of gravitational waves from multi-solar mass black hole mergers by LIGO-Virgo reignited interest in PBHs as DM candidates, there is a tension between these discoveries and observational constraints. Specifically, if a significant fraction of the MW halo were composed of stellar-mass COs, stellar microlensing surveys should have detected a large excess of events ( $\gtrsim 10^2$ ) over two decades. The paper aims to review the history, theoretical framework, current observational status, and future prospects of using stellar microlensing to constrain the abundance of such objects.

2. Methodology

The paper employs a comprehensive review approach, synthesizing theoretical models with observational data from major microlensing surveys.

Theoretical Framework:
- Microlensing Physics: The review details the photometric magnification of a source star when a CO crosses the line of sight. Key parameters include the Einstein radius ( $R_E$ ), the event timescale ( $\hat{t}$ ), and the optical depth ( $\tau$ ).
- Differential Event Rate: The paper derives the differential event rate ( $d\Gamma/d\hat{t}$ ) as a function of CO mass, distance, and velocity distribution. It highlights that $\hat{t} \propto M^{1/2}$ , meaning long-duration surveys probe high masses, while high-cadence (frequent) observations probe low masses.
- Degeneracy and Constraints: It addresses the "microlensing degeneracy" (inability to measure mass from a single event's timescale alone) and explains how statistical analysis of event distributions, combined with halo models (e.g., standard isothermal sphere vs. NFW profiles), allows for constraints on the halo fraction ( $f$ ).
- Non-Standard Effects: The paper discusses deviations from the standard Paczyński light curve, including finite source effects, parallax, binary lenses, and wave optics (diffraction) for very low masses ( $M \lesssim 10^{-11} M_\odot$ ).
Observational Analysis:
- The paper reviews data from four major collaborations: MACHO, EROS, OGLE, and Kepler, as well as surveys targeting M31 (Andromeda) and the Galactic Bulge.
- It analyzes the selection criteria, detection efficiencies ( $\epsilon(\hat{t})$ ), and the re-evaluation of candidate events (distinguishing true microlensing from variable stars, supernovae, or self-lensing).
- It utilizes likelihood functions to calculate exclusion limits on the halo fraction $f$ for specific mass ranges.

3. Key Contributions

Comprehensive Review for Theorists: The paper serves as a bridge between observational astronomy and theoretical PBH research, providing a clear overview of how microlensing constraints are derived and their limitations.
Re-evaluation of Historical Data: It updates the status of candidate events from the MACHO collaboration. While MACHO initially suggested a significant halo fraction ( $f \approx 0.2$ ), subsequent follow-up and re-analysis (by OGLE and others) have reclassified many events as variable stars or self-lensing, significantly reducing the inferred halo fraction.
Synthesis of Mass Constraints: The paper consolidates constraints across a vast mass range, from $10^{-11} M_\odot$ (probed by high-cadence M31 and OGLE surveys) to $10^4 M_\odot$ (probed by long-duration surveys).
Identification of Systematic Uncertainties: It highlights critical uncertainties in the field, particularly the dependence of constraints on the local dark matter velocity distribution and the potential for PBH clustering (which could alter the differential event rate).

4. Key Results

Exclusion of 100% Dark Matter: Under standard assumptions (smooth distribution, Maxwellian velocity), current observations exclude COs in the mass range $10^{-11} M_\odot \lesssim M/M_\odot \lesssim 10^4$ from making up 100% of the Milky Way's dark matter.
Tight Constraints on Stellar Mass: For stellar-mass objects ( $\sim 1 M_\odot$ ), the fraction of the halo they can comprise is constrained to $f \lesssim 10\%$ (and likely much lower, $\sim 1\%$ , depending on the specific model and event re-classification).
Planetary Mass Constraints: High-cadence surveys (e.g., OGLE high-cadence, Subaru-HSC) have constrained planetary-mass COs ( $10^{-8} \lesssim M/M_\odot \lesssim 0.01$ ) to make up less than 1% of the halo.
Event Re-classification:
- MACHO: Of the 13 "Criteria A" events, follow-up suggests only a few are robust microlensing candidates; many are variable stars or lenses in the MW disk/LMC rather than the halo.
- EROS/OGLE: These surveys found very few events consistent with halo COs, with most observed events being consistent with self-lensing (stars in the LMC/SMC) or MW disk stars.
M31 Surveys: Surveys of M31 (e.g., HSC) have probed lower masses ( $10^{-9} - 10^{-5} M_\odot$ ), though results are debated regarding whether candidate events are variable stars or true microlensing.

5. Significance and Future Prospects

Current Status: The "MACHO era" suggestion that the halo is dominated by $\sim 0.5 M_\odot$ objects has been largely ruled out. The current consensus is that PBHs in the planetary-to-stellar mass range can only make up a small fraction ( $f \lesssim 1\% - 10\%$ ) of the total dark matter.
Future Observations:
- Roman Space Telescope: Will offer high resolution and cadence to reduce blending effects and probe the Galactic Bulge, potentially reaching sensitivities of $f \sim 10^{-3} - 10^{-4}$ .
- Vera C. Rubin Observatory: Will provide long-duration, wide-field coverage, sensitive to intermediate and high-mass COs.
- Astrometric Microlensing: Future telescopes capable of precise astrometry (measuring position shifts, not just brightness) will break the mass-distance degeneracy, allowing direct mass measurement of lenses.
Theoretical Challenges: The paper emphasizes that the robustness of these constraints depends on the spatial distribution of PBHs. If PBHs form compact clusters (due to non-Gaussian initial fluctuations), the microlensing constraints could shift to lower masses. Understanding the clustering and binary fraction of PBHs remains a critical outstanding theoretical issue.

In conclusion, the paper establishes that while stellar microlensing has successfully ruled out PBHs as the sole constituent of dark matter across a wide mass spectrum, it remains a powerful tool for probing sub-dominant populations, provided that systematic uncertainties regarding halo structure and PBH clustering are better understood.