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

TL;DR

This study investigates how interactions with cold dark matter influence the evolution and merger rates of primordial black hole binaries, suggesting that dark matter clustering significantly increases expected gravitational wave event rates.

Contribution

It introduces a combined numerical and semi-analytical approach to model PBH binary evolution considering dark matter clustering effects, which were previously neglected.

Findings

Binary semimajor axis decreases by about 100 times

Angular momentum decreases by about 10 times

Merger rate increases by at least 6-8 times with dark matter effects

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.