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

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 qB = 0.154, and total masses of mT,B = 303 M . Merged PBHs are rare, about 0.0023% of all PBHs at present, with mass ratios of qM = 0.965 with total and chirp masses of mT,M = 1670 M and mc,M = 642 M 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 ∼ 1000 M ), with Γ S = (1.2 +5.9 −0.9 ) × 10 7 yr −1 Gpc −3 and mergers with Γ M = 1337 ± 41 yr −1 Gpc −3 .

Evidence for primordial black hole dark matter from LIGO/Virgo merger rates

“…Building on prior results [29,[33][34][35] (cf. also to [36]), we have argued in [32] that PBHs form clusters at very high redshifts which evaporate later due to the continuous loss of PBHs in the high energy tail of the Maxwell-Boltzman energy distribution. We have found that clusters of N cl ≈ 1300 with approximate densities n cl ≈ 3.6/pc 3 having formed at redshifts z ≈ 85 are evaporating at the current epoch.…”

Bayesian analysis of LIGO-Virgo mergers: Primordial vs. astrophysical black hole populations

“…Some of the uncertainty in the precise formation mechanism is bracketed by the cases S = 1 and the full expressions of Equations ( 9) and (10). More precise numerical simulations of PBH binary formation and evolution will be required for a more quantitative investigation of the sensitivity of our results to the formation model [15,[52][53][54][55].…”

Dark Matter Simulations with Primordial Black Holes in the Early Universe

“…However, despite the fact that the result for this PBH fraction matches the estimation of the merger rate by the LIGO collaboration (Abbott et al 2016c) and by other groups (Ali-Haïmoud 2018; Raidal et al 2019), such an extrapolation might not be well suited for the estimation of the merger rates for PBH fractions fP BH > 0.001 and it merely represents a qualitative result here. As we discussed in Section 3.3, the formation of large gravitationally-bound structures (such as DM halos) might prevent merger events from occurring altogether, while on the other hand, a choice of a more realistic model (for example, the one with the proper account of GR effects in dense clusters, as discussed in a recent paper by Trashorras et al (2020)) may complicate things even further.…”

“…A reliable estimate of the GW signatures from PBH binary mergers requires a good understanding of the process of formation of PBH binaries and their subsequent interactions with the surrounding matter that may disrupt the binaries (for example, see Raidal et al (2019) or Trashorras et al (2020)). Despite the fact that the bulk of this work is dedicated to PBH binaries, we also consider the effects of hyperbolic 2 close encounters (as suggested by Garc à a-Bellido & Nesseris (2017)), and how a proper account of these events could affect our final results.…”