The Clustering Dynamics of Primordial Black Holes in N-Body Simulations

Abstract

We explore the possibility that Dark Matter (DM) may be explained by a nonuniform background of approximately stellar mass clusters of Primordial Black Holes (PBHs) by simulating the evolution 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 q¯B=0.154, and total masses of m¯T,B=303M⊙. Merged PBHs are rare, about 0.0023% of all PBHs at present, with mass ratios of q¯B=0.965 with total and chirp masses of m¯T,B=1670M⊙ and m¯c,M=642M⊙, 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 one-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∼1000M⊙), with ΓS=(1.2+5.9−0.9)×107yr−1Gpc−3 and mergers with ΓM=1337±41yr−1Gpc−3.

Consistency of Primordial Black Hole Dark Matter with LIGO/Virgo Merger Rates

“…Building on prior results [29,[33][34][35] (cf. also to [36]), we have argued in Ref. [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-Boltzmann energy distribution.…”

Constraining changes in the merger history of (P)BH binaries with the stochastic gravitational wave background

“…We expect the fraction of BH in binaries to be quite small. In some simulations of BH clusters it has been shown that f b O(10 −3 ) [25]. If we adopt this as a fiducial value, and because f BH ≤ 1 then it holds that…”

“…This is also a problem for clustered distributions, with the additional complication that the initial distribution could also depend on an enlarged set of parameters (given by -in principle-independent N-point correlations functions). Despite these dificulties, some interesting results have been obtained in determining the merger rate for some families of clustered distributions, with the use of numerical simulations [25,26]. For example, BBHs merging inside globular clusters can exhibit α = 2.3 +1.3 −1.0 [26].…”

Tracking the origin of black holes with the stochastic gravitational wave background popcorn signal

“…We note that the normalization of PBH merger rate has nothing to do with the fraction of CDM as our merger rate model described in Eq. ( 7) depends on the combination R clust f tot 2 PBH , which is the known degeneracy between clustering and abundance of PBHs (Raidal et al 2017;Clesse & Garcia-Bellido 2020;Vaskonen & Veermäe 2020;Young & Byrnes 2020;Trashorras et al 2021;Atal et al 2020;De Luca et al 2020b).…”