The clustering dynamics of primordial black boles in $N$-body simulations

TL;DR

This study uses extensive N-body simulations to investigate primordial black holes as dark matter candidates, revealing their clustering behavior, binary formation, mergers, and distribution across cosmic structures, with implications for gravitational wave events.

Contribution

It provides the first detailed simulation-based analysis of PBH clustering, binary dynamics, and merger rates over cosmic history, supporting their viability as dark matter.

Findings

PBHs can constitute a viable dark matter candidate.

Binary systems make up about 9.5% of PBHs today.

Merger rate of PBHs is approximately 1337 per Gpc^3 per year.

Abstract

We explore the possibility that Dark Matter (DM) may be explained by a non-uniform background of approximately stellar-mass clusters of Primordial Black Holes (PBHs), by simulating the evolution them from recombination to the present with over 5000 realisations using a Newtonian $ N $-body code. We compute the cluster rate of evaporation, and extract the binary and merged sub-populations along with their parent and merger tree histories, lifetimes and formation rates; the dynamical and orbital parameter profiles, the degree of mass segregation and dynamical friction, and power spectrum of close encounters. Overall, we find that PBHs can constitute a viable DM candidate, and that their clustering presents a rich phenomenology throughout the history of the Universe. We show that binary systems constitute about 9.5\% of all PBHs at present, with mass ratios of $ \bar{q}_{\rm B} = 0.154 $, and total masses of $ \bar{m}_{\rm T,\,B} = 303\,M_\odot$. Merged PBHs are rare, about 0.0023\% of all PBHs at present, with mass ratios of $ \bar{q}_{\rm B}= 0.965 $ with total and chirp masses of $ \bar{m}_{\rm T,\,B}= 1670\,M_\odot$ and $ \bar{m}_{c,{\rm M}} = 642\,M_\odot $ respectively. We find that cluster puffing up and evaporation leads to bubbles of these PBHs of order 1 kpc containing at present times about 36\% of objects and mass, with hundred pc sized cores. We also find that these PBH sub-haloes are distributed in wider PBH haloes of order hundreds of kpc, containing about 63\% of objects and mass, coinciding with the sizes of galactic halos. We find at last high rates of close encounters of massive Black Holes ($ M \sim 1000\,M_\odot$), with $ \Gamma^{\mathrm{S}} = (1.2^{+5.9}_{-0.9}) \times 10^{7} \mathrm{yr^{-1} Gpc^{-3}}$ and mergers with $\Gamma^{\mathrm{M}} = 1337 \pm 41 \mathrm{yr^{-1} Gpc^{-3}} $.