Gravitational-wave signatures of primordial black hole clusters and the imprint of an early dense-core collapse
Using direct -body simulations, this paper proposes that primordial black hole clusters form with a short-lived, dense core and an extended halo, a two-regime structure that resolves the tension between generating observed black hole spins and ensuring cluster survival while predicting a distinct stochastic gravitational-wave background and specific spin-mass signatures for future detectors like LISA.
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
Black holes are often thought of as the final, collapsed remains of massive stars, but there is a second possibility that has intrigued physicists for decades: primordial black holes. These are objects that did not form from dying stars at all, but instead were born in the first fractions of a second after the Big Bang, squeezed into existence by the sheer density of the early universe. If they exist, they could make up the invisible "dark matter" that holds galaxies together. A crucial clue to their identity lies in how they spin. Stars spin as they collapse, so black holes born from them usually carry a significant amount of rotation. Primordial black holes, however, would be born with almost no spin at all. If we find a population of black holes that are spinning, it suggests they were forged in a different way, perhaps by colliding with one another long after their birth.
The question of whether these ancient objects exist and how they behave has moved from pure theory to a testable hypothesis, thanks to the ability of gravitational-wave detectors to "hear" the ripples in space-time caused by colliding black holes. Recent observations have revealed a mix of black hole masses and spins that are difficult to explain with standard stellar evolution alone. Some of these black holes are surprisingly heavy, while others spin rapidly, a trait that usually indicates they are the product of a previous collision. To understand if a population of primordial black holes could produce this specific mix of signals, researchers needed to simulate how these invisible objects would interact over billions of years, a task that requires tracking the complex dance of gravity between thousands of individual points of mass.
In a new study, Marc Barceló-Sastre and Juan García-Bellido have performed these simulations to trace the life story of a cluster of primordial black holes. They started with a simple premise: if these objects are born without spin, they must acquire it through collisions. However, their calculations revealed a sharp contradiction. To generate the amount of spin seen in some of the observed black holes, the cluster would need to be incredibly dense, packed into a space so small that the black holes would crash into each other almost immediately. Yet, a cluster that dense would be unstable; it would dissolve and scatter its members long before the universe reached its current age. A cluster large enough to survive for billions of years, on the other hand, is too loose to generate significant spin through collisions. The researchers found that a single, uniform cluster cannot satisfy both conditions.
To resolve this tension, the team proposed a two-part structure for these ancient clusters, consisting of a tiny, dense core hidden inside a much larger, diffuse halo. They simulated the life of the core separately, treating it as a compact group of four thousand black holes packed into a region roughly one hundred-thousandth of a light-year across. In this extreme environment, the black holes collapsed inward and began colliding violently within days or years of their formation. These collisions were not gentle spirals but near-radial plunges, where objects fell straight toward one another. The simulations showed that these specific types of crashes produce merger remnants with a moderate amount of spin, typically between 0.1 and 0.2, which matches the lower end of what is observed. Crucially, this entire process happens so quickly that the spin is "frozen in" before the cluster has a chance to expand or dissolve.
While the core burns out its energy in a cosmic blink, the surrounding halo survives. The researchers then simulated the long-term evolution of a much larger cluster, containing twenty thousand black holes spread over a region ten light-years across. Over the course of the universe's history, this loose group produces very few internal collisions, confirming that it cannot generate the spinning black holes on its own. Instead, its main contribution to the observable universe comes from binary pairs that are kicked out of the cluster. As these pairs drift away, they slowly lose energy and circularize their orbits, eventually merging billions of years later. The masses of these escaping pairs are heavily biased toward the heaviest black holes in the group, with most falling between thirty and fifty times the mass of our sun. This finding aligns with observations that suggest a cutoff in the number of black holes above fifty solar masses, a limit predicted by the physics of the early universe.
The study also explored what happens if a massive "intermediate-mass" black hole forms in the center of the cluster, a likely outcome of the core's rapid collapse. If this central object is too heavy, around two thousand solar masses, its gravity is so strong that it prevents other black holes from forming tight pairs, effectively shutting down the production of merging binaries. However, if the central black hole is slightly lighter, it is often ejected from the cluster within the first few billion years, leaving the rest of the system to evolve as if it had never been there. This dynamic suggests that the presence or absence of a central heavy object could dramatically alter the number of black hole mergers we detect today.
Finally, the researchers calculated the gravitational waves these systems would emit. The violent collisions in the early, dense core would have created a burst of waves that, stretched by the expansion of the universe, would now be detectable by space-based observatories like LISA in a specific low-frequency band. The slower, long-term evolution of the surviving halo would produce a different signal, dominated by the merging of the escaped binary pairs at higher frequencies. The paper concludes that the observed properties of black hole spins and masses can be explained if primordial black holes formed in these dual-layered clusters, with the spin determined in the first few years of the universe and the mergers we see today coming from the survivors of the outer halo. This scenario offers a consistent explanation for why some black holes spin while others do not, and why the heaviest ones seem to have a natural upper limit, providing a concrete path forward for testing the existence of these primordial relics.
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