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Microlensing by Cluster of Primordial Black Holes

This study demonstrates that while clustering primordial black holes can significantly evade current microlensing constraints by producing complex light curves that evade detection, the presence of isolated lenses within these clusters ensures that microlensing surveys still impose meaningful limits on the fraction of dark matter composed of primordial black holes.

Original authors: K. A. Toshchenko, P. V. Baklanov, K. M. Belotsky, S. I. Blinnikov

Published 2026-03-25

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CC BY 4.0

Original authors: K. A. Toshchenko, P. V. Baklanov, K. M. Belotsky, S. I. Blinnikov

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 Invisible Crowd: How Black Hole Clusters Hide from Our Telescopes

Imagine you are trying to count a crowd of people in a dark room using a flashlight. If the people are standing far apart, you can easily spot each one as you sweep the light across the room. This is how astronomers have been trying to find Dark Matter for decades.

For a long time, scientists suspected that Dark Matter might be made of invisible, compact objects like Primordial Black Holes (PBHs). To find them, they used a trick called gravitational microlensing.

The "Flashlight" Trick (Microlensing)

Think of a distant star as a lighthouse. If a black hole (the "lens") passes in front of it, the black hole's gravity bends the light, acting like a magnifying glass. The star suddenly gets brighter for a few days, then fades back to normal. This is a microlensing event.

For years, surveys like MACHO, EROS, and OGLE have scanned the sky looking for these brightening events. They found very few. Based on this, they concluded: "If black holes were the main ingredient of Dark Matter, we would have seen way more of these brightening events. Therefore, black holes can't be the whole story."

The Assumption: These surveys assumed the black holes were like lonely islands in the ocean—widely separated and acting alone.

The Twist: The "Crowded Party"

This new paper asks a simple but revolutionary question: What if the black holes aren't lonely islands? What if they are stuck together in massive, crowded clusters?

The authors imagine a scenario where billions of black holes are packed into a tight group, like a mosh pit at a concert. In this "cluster," the gravity isn't just coming from one object; it's a chaotic mix of many black holes pulling on each other.

The Analogy: The Solo Singer vs. The Choir

The Solo Singer (Isolated Black Hole): When a single black hole passes in front of a star, the light curve (the graph of brightness over time) is a smooth, symmetrical bell shape. It's easy to recognize, like a solo singer hitting a perfect note.
The Chaotic Choir (Clustered Black Holes): When a cluster of black holes passes by, the gravity is messy. The light doesn't just get brighter and fade; it flickers, spikes, and distorts in weird, jagged ways. It's like a choir singing out of sync, or a crowd shouting over each other. The signal is no longer a clean "bell curve."

The Great Escape

The researchers used powerful computer simulations to see what happens when these "crowded parties" of black holes pass in front of stars. They found something surprising:

The "Invisible" Majority: The weird, jagged light curves caused by the clusters do not look like the standard "solo singer" events that the telescopes are programmed to find. The search algorithms are tuned to spot the smooth bell curves. When they see the messy, chaotic curves, they often ignore them or mistake them for noise.
The Hiding Spot: Because the telescopes are looking for the "solo" pattern, they miss the "crowded" events. The authors calculated that in some of their models, up to 93% of the black hole mass could be hiding in these clusters, completely undetected by current surveys. It's as if the crowd is so loud and chaotic that the flashlight can't pick out the individual people.

The Catch: Not a Perfect Hiding Spot

However, the paper also delivers a reality check. Even in a crowded cluster, not everyone is hiding.

The Edge of the Party: On the very edges of these clusters, the black holes are far enough apart that they act like lonely islands again. They produce those clean, smooth "solo" light curves that the telescopes can detect.
The Conclusion: While clustering allows a lot of black holes to hide (up to 93% in the densest models), it doesn't hide all of them. A significant number still act alone and get caught by the surveys.

The Big Picture

So, does this mean black holes are definitely the answer to Dark Matter? Not yet.

Good News: This paper shows that previous "rules" saying "black holes can't be Dark Matter" might be too strict. If black holes are clustered, we might have missed most of them.
Bad News: The clustering doesn't hide them completely. The "lonely" black holes on the edges of the clusters are still visible, and the current limits still apply to them.

In short: The universe might be hiding a massive crowd of black holes in a chaotic dance that our current telescopes aren't tuned to see. But because some dancers are still standing on the sidelines, we can't say the mystery is fully solved. We need new, sharper eyes (like the upcoming Vera C. Rubin Observatory) to look for the messy, chaotic signals of these hidden crowds.

1. Problem Statement

Current observational constraints on Primordial Black Holes (PBHs) as a candidate for dark matter are derived primarily from microlensing surveys (e.g., MACHO, EROS, OGLE, POINT-AGAPE, HSC). These constraints assume that PBHs exist as isolated, widely separated objects acting as single lenses. The standard analysis relies on fitting observed light curves to the Point-Lens Point-Source (PLPS) model.

The central problem addressed by this paper is whether these constraints remain valid if PBHs are not isolated but instead exist in clusters. If PBHs are clustered, their mutual gravitational influence and the collective potential of the cluster could distort microlensing light curves, causing them to deviate from the standard PLPS profile. If such "complex" events are not detected or are misidentified by current algorithms, a significant fraction of PBH dark matter could remain "hidden" from observational limits.

2. Methodology

The authors employed a numerical simulation approach to model microlensing by PBH clusters and analyze the resulting light curves.

Cluster Models: Five distinct PBH cluster models were constructed based on two formation mechanisms:
- Power-law profiles (M1–M3): Derived from stochastic clustering of PBHs formed during inflation. These models feature spherically symmetric density profiles $\rho(r) \propto r^{-\alpha}$ with indices $\alpha = 2.8, 2.5,$ and $2.0$.
- Plummer profiles (M4–M5): Derived from domain wall collapse mechanisms. These models feature a core radius ( $R_c$ ) of $0.1$ pc and $0.01$ pc, respectively.
- Common Parameters: All models share a total mass $M_{tot} = 4 \times 10^4 M_\odot$ , a cluster radius $R_{cl} = 1$ pc, and a PBH mass function following a power law ( $\propto M^{-2}$ ) in the range $10^{-4} \text{ to } 10^2 M_\odot$ .
Simulation Setup:
- Geometry: Simulations assumed a lens distance $D_l = 25$ kpc and a source distance $D_s = 50$ kpc (mimicking the Large Magellanic Cloud).
- Ray-Tracing: The Microlenscode (Wambsganss, 1999) was used to generate magnification maps for multiple lenses. The code accounts for optical depth ( $\kappa$ ) and external shear ( $\gamma$ ) derived from the cluster's density profile.
- Light Curve Generation: Background source trajectories were simulated across magnification maps. Source sizes were kept small ( $< 9 R_\odot$ ) to approximate point sources.
- Event Classification: Detected peaks (magnification $\mu > 1.34$ $μ > 1.34$ ) were fitted with the standard PLPS model. A goodness-of-fit criterion ( $\chi^2_{d.o.f}$ $χ_{d . o . f}^{2}$ ) was used to classify events:
  - PLPS: Events fitting the single-lens model well ( $\chi^2_{d.o.f} < \chi^2_{crit}$ ).
  - no-PLPS: Events with complex, asymmetric light curves that deviate significantly from the single-lens profile.
Statistical Analysis: The fraction of "hidden" mass ( $g_{PBH}$ ) was calculated by integrating the surface density weighted by the fraction of no-PLPS events across the cluster radius.

3. Key Contributions

Quantification of "Hidden" Dark Matter: The study provides the first rigorous quantification of how much PBH mass can evade detection in standard microlensing surveys due to clustering effects.
Refutation of Total Evasion: The paper demonstrates that while clustering significantly reduces the detectability of PBHs, it does not completely eliminate the constraints on the PBH fraction of dark matter ( $f_{PBH}$ ).
Dependence on Density Profiles: The authors establish a clear correlation between the steepness of the cluster density profile (or core compactness) and the fraction of undetected events. Steeper profiles and smaller core radii lead to higher fractions of undetected mass.

4. Key Results

Light Curve Deviation: In the central regions of dense clusters, mutual gravitational interactions between PBHs create complex caustic structures. This results in no-PLPS events that are asymmetric and distinct from standard microlensing curves.
Fraction of Hidden Mass ( $g_{PBH}$ ):
- Model M5 (Most Compact): The fraction of mass producing undetected (no-PLPS) events reaches 93%.
- Model M1 (Steepest Power-law): Approximately 60% of the mass is hidden.
- Models M2 & M3 (Flatter Profiles): The hidden fraction drops significantly to 22% and 11%, respectively.
- Peripheral Regions: In the outer regions of all clusters, the lens density is low enough that PBHs behave as isolated lenses. Consequently, a substantial population of PBHs still produces detectable PLPS events.
Constraints on $f_{PBH}$ : Because a significant number of events in all models still conform to the PLPS profile (especially in the cluster periphery), current microlensing constraints on $f_{PBH}$ are not fully lifted. The existence of PBH clusters relaxes the constraints but does not invalidate them entirely.
Observational Implications:
- Current surveys (MACHO, EROS, OGLE) likely missed the complex no-PLPS events, leading to an underestimation of the PBH contribution if they are clustered.
- Future wide-field surveys (e.g., Vera C. Rubin Observatory) targeting stars closer to the Galactic center (smaller $D_l$ ) will have lower optical depth ( $\kappa$ ) and shear ( $\gamma$ ) for a given cluster. This reduces mutual lens interference, making the "hidden" fraction ( $g_{PBH}$ ) even smaller and potentially tightening constraints further.

5. Significance

This work is significant for the field of dark matter research as it addresses a critical loophole in the exclusion limits for PBHs.

Theoretical Impact: It challenges the assumption that microlensing constraints apply universally to all PBH distributions, highlighting that clustering mechanisms (specifically those leading to compact, dense cores) can hide a majority of the PBH population from current detection methods.
Observational Strategy: It suggests that future searches must develop algorithms capable of identifying complex, non-standard light curves (no-PLPS) rather than relying solely on single-lens templates.
Cosmological Context: The results imply that while PBHs could still constitute a large fraction of dark matter if they are highly clustered (e.g., Model M5), the specific mass ranges and cluster configurations are tightly constrained by the fact that isolated-like events are still observed. The study effectively narrows the parameter space for viable PBH dark matter models.