The evolution of a primordial binary black hole due to interaction with cold dark matter and the formation rate of gravitational wave events

Abstract

In this Paper we consider a problem of formation and evolution of orbital parameters of a binary primordial black hole (PBH) due to gravitational interaction with clustering cold dark matter (CDM). Mass and initial separation have values, which are appropriate for the problem of explanation of the LIGO/Virgo events by coalescing binary PBHs. We consider both radiation dominated and CDM dominated stages of the evolution using numerical and semi-analytical means. We show that at the end time of our numerical simulations binary's semimajor axis decreases by approximately one hundred times, while its angular momentum decreases by ten times, in comparison to the standard values, which do not take into account effects associated with CDM clustering. We check that our conclusions are hardly affected by numerical artefacts. We estimate the merger rate of binary PBHs due to emission of gravitational wave at the present time both in the standard case when the effects associated with clustering are neglected and in the case when they are taken into account and show, that these effects could increase the merger rate at least by 6 − 8 times in comparison to the standard estimate. This, in turn, means, that a mass fraction of PBHs, f , should be smaller than it was assumed before.

Gravitational waves from the merger of two primordial black hole clusters

“…But at the last stage, when the clusters intersect, they merge quickly. This effect was previously noted in the works [19,20], where the PBHs surrounded by dark matter halos were considered. In some respects, these systems resemble the clusters we are considering.…”

“…As a rule, it is assumed that mergers of single PBHs in pairs can be responsible for the LIGO/Virgo events. Some studies have considered the mergers of PBHs surrounded by dark matter halos [19,20]. However, there is a model [6,7], in which clusters are formed rather than single PBHs.…”

“…This issue could be studied by direct numerical modelling, which is beyond the scope of this work. For the cluster case, no corresponding simulations have been done yet, but in [19] and [20], the interaction of PBHs surrounded by dark matter halos has been studied. Such systems resemble the clusters, so one can expect similar features of evolution.…”

“…Such systems resemble the clusters, so one can expect similar features of evolution. In [19] and [20], an important result was obtained that the merger of such PBHs is very effective, and their merger actually occurs at the first intersection.…”

Hot Primordial Regions with Anomalous Hydrogenless Chemical Composition

“…The cluster of primordial black holes (PBH) can be responsible for such regions. Formation of PBH clusters and their possible observational effects are now of special interest [2][3][4][5][6][7][8][9][10][11][12][13], but we do not constrain possibility of such regions appearance by PBH clusters only. PBH and their cluster formation can be the consequence of existence and breaking of some new symmetry in quantum field theory [2,14,15].…”