🔭 astrophysics

Do Primordial Black Hole Clusters Survive the Galaxy? Collisional Disruption and Microlensing Implications

This study demonstrates that primordial black hole clusters in the Milky Way halo undergo significant collisional disruption over cosmic time, particularly during early halo assembly, resulting in a substantial conversion of clustered mass into a diffuse component that must be accounted for when interpreting microlensing constraints.

Original authors: M. V. Tkachev, S. V. Pilipenko

Published 2026-07-14

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CC BY 4.0

Original authors: M. V. Tkachev, S. V. Pilipenko

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

To understand the new findings, we must first look at the mystery of dark matter. Most of the matter in galaxies appears to be invisible "dark matter" that we detect only through its gravity. It holds galaxies together, yet we still do not know what it is made of. It is one of the biggest open problems in physics.

One leading candidate for this missing mass is Primordial Black Holes (PBHs). Unlike "normal" black holes that form when massive stars collapse at the end of their lives, primordial black holes would have formed in the very early universe from unusually dense patches of matter. They could come in a wide range of masses. If they exist in large enough numbers, PBHs could make up some or all of the dark matter.

However, PBHs are not a "silver bullet." There are strong observational limits on how much of the dark matter PBHs can constitute. Some of the strongest constraints come from microlensing surveys. If many PBHs were flying around freely, they would fairly often pass in front of background stars and briefly magnify (lens) their light. We do not observe nearly enough such events, and the ones we do see can be explained without PBHs. Consequently, free-floating PBHs are tightly constrained; if they made up all the dark matter, we would see far more brightening events than we currently do.

This is where the concept of clustering enters the picture. To evade these microlensing constraints, some theorists proposed that PBHs might not be scattered evenly throughout the galaxy. Instead, they could be bunched together into massive, invisible clusters. If PBHs are in clusters, microlensing events become much rarer and harder to spot, which could allow PBHs to mostly evade those strict observational limits.

But a new study by M.V. Tkachev and S.V. Pilipenko challenges this "clustered loophole." They asked: Could these black hole cities survive the chaotic history of our galaxy? Or would the constant gravitational bumps and grinds eventually tear them apart, scattering the black holes back into a smooth fog that would be detectable?

The Cosmic Dance Floor

Think of the Milky Way's dark matter halo as a giant, crowded dance floor. The black hole clusters are the dancers. As they spin and orbit, they occasionally bump into each other.

The authors ran a massive computer simulation (a "virtual universe") to see what happens when these clusters collide. They didn't just guess; they built a model where every single particle in their simulation represented one entire cluster of black holes. They watched this virtual galaxy evolve from the early universe (when it was just a baby at redshift $z = 9$ ) all the way to today ( $z = 0$ ).

They found that the dance floor is much bumpier than we realized. When two clusters pass close to each other, the gravitational tug-of-war strips away some of the black holes, sending them flying off into the void. These "escaped" black holes become part of a smooth, unclustered background—exactly the kind of distribution that microlensing surveys are designed to detect.

The "Slow and Steady" Destruction

Here is the twist: The clusters aren't getting destroyed by one giant, catastrophic crash. Instead, it's a death by a thousand cuts.

The study shows that the "perfect storm" for destroying a cluster happens when two clusters move at a very specific, slow speed relative to each other (around $12\text{--}20 \text{ km s}^{-1}$ ). But in the current, mature Milky Way, clusters usually zip past each other much faster (around $230 \text{ km s}^{-1}$ ). At these high speeds, a single bump barely scratches the paint.

However, the simulation revealed that the real damage happened early in the galaxy's life. Back when the galaxy was still being built (around redshift $z \approx 2$ ), the universe was "colder" and denser. The clusters were moving at those perfect, slow speeds, and the collisions were much more destructive.

The authors found that half of the total mass lost by these clusters happened before the universe was even half its current age. The smooth, modern galaxy we see today is actually a graveyard of clusters that were already being dismantled billions of years ago.

The Numbers: Who Survived?

The team looked at two sizes of black hole clusters:

Small clusters: Containing about $10^6$ solar masses ( $M_\odot$ ).
Big clusters: Containing about $10^7$ solar masses ( $M_\odot$ ).

They calculated how many clusters are left standing at our location in the galaxy (the "Solar circle," about $8.2 \text{ kpc}$ from the center):

For the small clusters ( $10^6 M_\odot$ ), about 50% ( $S \simeq 0.50$ ) of the original mass is still in clusters. The other half has been stripped away into a smooth fog.
For the big clusters ( $10^7 M_\odot$ ), it's a disaster. Only about 4% ( $S \simeq 0.04$ ) of the mass remains in clusters. The other 92% has been scattered into the smooth component.

Why This Matters for "Ghost Hunting"

This has profound implications for the microlensing constraints mentioned earlier. Scientists use microlensing to hunt for dark matter by watching stars in the Large and Small Magellanic Clouds (satellite galaxies of the Milky Way).

If the black holes are in clusters: They act like a single, giant, fuzzy lens. This changes the shape of the light curve and makes them harder to spot with standard searches.
If the black holes are smooth (scattered): They act like individual, sharp lenses, which is what current surveys (like EROS, OGLE, and Subaru) are designed to find.

The paper calculates exactly how much of the dark matter along the line of sight to these galaxies is "smooth" versus "clustered":

Looking at the Large Magellanic Cloud (LMC): About 49% of the mass is smooth for small clusters, and a whopping 92% is smooth for big clusters.
Looking at the Small Magellanic Cloud (SMC): The numbers are almost identical (49% and 92%).

The Bottom Line

The authors argue that we can no longer pretend dark matter is either all clusters or all smooth. It's a mix.

If you are trying to use microlensing data to prove or disprove that dark matter is made of primordial black holes, you can't just look at the whole picture. You have to split the data:

The smooth fraction (the scattered black holes) is directly constrained by current surveys.
The clustered fraction (the survivors) requires a different, more complex model to detect.

The study concludes that for the most massive clusters ( $10^7 M_\odot$ ), the "clustered" loophole is almost completely closed; they have been mostly destroyed by the galaxy's own history. Even for the smaller clusters, nearly half the population has been scattered, meaning a significant portion is now subject to the strict microlensing constraints that previously ruled out PBHs as the sole source of dark matter.

What the paper rules out:
The paper explicitly argues against the idea that we can simply assume all primordial black holes are safely tucked away in clusters to evade detection. The simulations show that the galaxy's history is too violent for that. The "clustered" explanation for dark matter is not a magic shield; the clusters get shredded over time. Consequently, the strategy of tucking PBHs into clusters does not lift the microlensing constraints, as most black holes are scattered and remain detectable.

How sure are they?
These results come from simulations, not direct observation of black hole clusters (which we haven't seen yet). The authors combined:

Analytic math models (equations predicting collision rates).
72 specific N-body simulations of two clusters crashing into each other to measure exactly how much mass gets stripped.
One massive cosmological simulation of a Milky Way-like galaxy evolving over 13 billion years.

The agreement between their math and their simulation at our solar location is within 40%, which they consider a solid match. They are confident that the process of disruption is real and significant, even if the exact numbers might shift slightly if we tweak the galaxy's mass or the black holes' sizes. They are not claiming to have found the clusters, but rather showing that if they were there, they wouldn't have survived the journey to today.

Problem Statement
The nature of dark matter (DM) remains an open question, with Primordial Black Holes (PBHs) as a viable candidate. A significant complication in interpreting observational constraints (such as microlensing surveys by EROS, OGLE, and Subaru HSC) arises if PBHs are not isolated but reside in gravitationally bound clusters. While clustering can alter microlensing signatures (shifting event timescales and optical depths), the survival of these clusters over the lifetime of the Galaxy is uncertain. Previous analytic estimates of cluster disruption relied on simplified models. This paper investigates whether PBH clusters, specifically those formed via the Carr et al. scenario with masses of $10^6$ and $10^7 M_\odot$ , can survive the cumulative history of gravitational encounters within a Milky Way-like halo. The core question is: what fraction of PBH mass remains clustered versus stripped into a smooth, diffuse component, and how does this affect microlensing constraints?

Methodology
The authors employ a hybrid approach combining analytic modeling, direct N-body simulations, and cosmological N-body simulations:

Analytic Collision-Rate Model: They derive a collision rate for clusters in an NFW halo, incorporating gravitational focusing and local velocity distributions. This model calculates the encounter rate $\Gamma(r)$ based on cluster density, cross-sections, and relative velocities.
Binary Collision Calibration (N-body): To determine the mass loss per encounter, the authors performed 72 direct N-body simulations of binary cluster collisions. They used a reference cluster with a Dehnen density profile ( $\gamma=3/2$ ) and scaled the results using the scale invariance of Newtonian gravity. This produced a universal, dimensionless mass-loss function $\tilde{f}(\tilde{v}, \tilde{b})$ , dependent on the relative velocity normalized to the cluster's internal velocity scale ( $\tilde{v} = v_{rel}/v_c$ ) and the impact parameter normalized to the half-mass radius ( $\tilde{b} = b/r_h$ ).
Cosmological Halo Simulations: They simulated a Milky Way-like halo ( $M_{200} \approx 8 \times 10^{11} M_\odot$ , $c_{200} \approx 11$ ) from redshift $z=9$ to $z=0$ . In these simulations, each particle represents a single PBH cluster. An "encounter logger" module recorded every pair of clusters passing within a specific threshold, capturing their relative velocities and impact parameters.
Integration: The recorded encounter histories from the cosmological simulation were integrated with the universal mass-loss calibration to compute the cumulative surviving mass fraction $S(r)$ as a function of galactocentric radius.

Key Results

Encounter Rates: At the Solar circle ( $R_\odot = 8.2$ kpc), the local encounter rate is $2.9 \times 10^{-3}$ Myr $^{-1}$ for $10^6 M_\odot$ clusters and $1.2 \times 10^{-2}$ Myr $^{-1}$ for $10^7 M_\odot$ clusters. These rates are consistent with the analytic model to within $\sim 40\%$ .
Disruption Mechanism: The peak disruption velocity for Carr-radius clusters ( $12\text{--}20$ km s $^{-1}$ ) is far below the typical halo encounter velocities ( $\sim 230$ km s $^{-1}$ median). Consequently, disruption does not occur via rare catastrophic collisions but accumulates through many weak, high-velocity fly-bys.
Survival Fractions:
- For $10^6 M_\odot$ clusters, the surviving mass fraction at the Solar circle is $S \simeq 0.50$ .
- For $10^7 M_\odot$ clusters, the surviving fraction is $S \simeq 0.04$ .
- Survival decreases further toward the Galactic center.
The "Assembly" Effect: A critical finding is that half of the total mass loss occurs before $z \approx 2$ (for $10^6 M_\odot$ ) and $z \approx 1.5$ (for $10^7 M_\odot$ ). During the early, cold phases of halo assembly, clusters encountered each other at velocities comparable to their internal velocity scales, maximizing disruption. Standard analytic estimates based on the present-day ( $z=0$ ) smooth halo miss this early channel entirely, leading to an overestimation of survival at large radii.
Smooth Fraction ( $f_{sm}$ ): The fraction of PBH mass stripped into a smooth, unclustered component along the line of sight to the Magellanic Clouds is:
- LMC/SMC ( $10^6 M_\odot$ ): $\langle f_{sm} \rangle_{LOS} \simeq 0.49$ .
- LMC/SMC ( $10^7 M_\odot$ ): $\langle f_{sm} \rangle_{LOS} \simeq 0.92$ .

Significance and Implications
The paper concludes that collisional disruption is a substantial process over the Galaxy's lifetime for PBH clusters in the $10^6\text{--}10^7 M_\odot$ range. The existence of a significant smooth component ( $f_{sm}$ ) implies that microlensing constraints cannot be applied solely to the clustered population.

Reanalysis of Constraints: Standard microlensing exclusion limits (which assume isolated point lenses) apply directly to the smooth fraction of the PBH population. The remaining clustered fraction requires a separate lensing model accounting for extended cluster geometry.
Partial Evasion: While clustering was proposed as a way to evade microlensing limits, the authors find this evasion is only partially realized. Even in the most optimistic case ( $10^6 M_\odot$ ), roughly half the PBH mass is in a smooth component subject to standard constraints. For $10^7 M_\odot$ clusters, the population is nearly fully disrupted, leaving almost all mass subject to standard point-lens limits.
Conservative Estimates: The authors note their results are conservative lower bounds on the smooth fraction. They did not account for dynamical friction (which would drive clusters inward to higher disruption rates) or the fact that even the periphery of "intact" clusters can produce microlensing signatures indistinguishable from isolated PBHs.

In summary, the study establishes that any PBH dark matter model involving clusters must account for a radially varying smooth fraction derived from the cumulative history of encounters, particularly those occurring during the early, cold assembly of the halo.

The Cosmic Dance Floor

The "Slow and Steady" Destruction

The Numbers: Who Survived?

Why This Matters for "Ghost Hunting"

The Bottom Line

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