The Merger Rate of Primordial Black Holes

TL;DR

This paper introduces a numerical framework to accurately calculate primordial black hole merger rates, accounting for environmental effects within dark matter halos, revealing a significant increase in merger rates at low redshifts compared to previous models.

Contribution

The authors develop a comprehensive numerical method that combines isolated binary evolution with halo dynamics, improving the accuracy of primordial black hole merger rate predictions.

Findings

Merger rate is suppressed at low redshifts in isolated binary models.

Environmental interactions in halos increase the merger rate by about 50% at redshifts below 2.

Total merger rates are now more consistent with gravitational-wave observations.

Abstract

The merger rate of primordial black hole (PBH) binaries can be used to understand the source population of the merging black hole binaries observable through gravitational-waves (GWs) and also to constrain the possible contribution of PBHs to dark matter. In the literature, the PBH merger rate is calculated analytically, assuming that PBH binaries stay in isolation (i.e. are unperturbed) and evolve solely via GW emission during their entire lifetime. However, if some or all of dark matter consists of PBHs, then as cosmic structures grow, PBH binaries and single PBHs fall inside dark matter halos. In those halos, the PBH binaries' interactions with their environment significantly affect the subsequent evolution of their orbital properties. In this paper, we present a numerical framework that accurately calculates the total PBH merger rate by combining the evolution of isolated binaries outside halos with the dynamics of binaries inside halos. In our work we have found that the isolated binary channel is suppressed at low redshifts and dynamical interactions in halos reshape the merger rate evolution with time, accelerating some mergers. At redshifts of $\lesssim 2$ the total merger rate is a factor of $\simeq 50 \%$ higher than the results assuming that all PBH binaries effectively stay unperturbed until their merger. Our simulations provide a definitive calculation on the total PBH merger rates, that are currently being probed and constrained from gravitational-wave observations. We make our merger rates publicly available at Zenodo