Merger rates in primordial black hole clusters without initial binaries

TL;DR

This study reevaluates primordial black hole merger rates in small clusters without initial binaries, finding significantly lower rates than previously estimated, thus reducing the likelihood of detecting such mergers via gravitational waves.

Contribution

It demonstrates that in small primordial black hole clusters without initial binaries, merger rates are much lower than earlier predictions, impacting gravitational wave detection prospects.

Findings

Merger rates are at least an order of magnitude lower than previous estimates.

Binary formation through Newtonian interactions is inefficient for mergers.

Gravitational-wave detection of these mergers is unlikely in this scenario.

Abstract

Primordial black holes formed through the collapse of cosmological density fluctuations have been hypothesised as contributors to the dark matter content of the Universe. At the same time, their mergers could contribute to the recently observed population of gravitational-wave sources. We investigate the scenario in which primordial black holes form binaries at late times in the Universe. Specifically, we re-examine the mergers of primordial black holes in small clusters of ~30 objects in the absence of initial binaries. Binaries form dynamically through Newtonian gravitational interactions. These binaries act as heat sources for the cluster, increasing the cluster's velocity dispersion, which inhibits direct mergers through gravitational-wave two-body captures. Meanwhile, three-body encounters of tight binaries are too rare to tighten binaries sufficiently to allow them to merge through gravitational-wave emission. We conclude that in the absence of initial binaries, merger rates of primordial black holes in the Bird et al. (2016) initial cluster configuration are at least an order of magnitude lower than previously suggested, which makes gravitational-wave detections of such sources improbable.