Merger History of Clustered Primordial Black Holes

TL;DR

This paper develops a new formalism to analyze how initial clustering of primordial black holes affects their merger rates and gravitational wave signals, providing distinctive predictions for future observations.

Contribution

It introduces a novel approach to model the impact of PBH clustering on merger dynamics and gravitational wave background features, advancing understanding of PBH dark matter.

Findings

Merger rate evolution differs from isolated binaries due to clustering.

Clustering alters the gravitational-wave background spectral slope.

Predictions are testable with future gravitational wave detectors.

Abstract

Primordial black hole (PBH) binaries experience strong gravitational perturbations in the case of their initial clustering, which significantly affects the dynamics of their mergers. In this work, we develop a new formalism to account for these perturbations and track the evolution of the binary orbital parameters distribution. Based on this approach, we calculate the merger rate of PBH binaries and demonstrate that its temporal evolution differs greatly from that of isolated binary systems. Moreover, PBH clustering produces distinctive features in the stochastic gravitational-wave background: the canonical $2/3$ spectral slope transforms to $\Omega_{\rm gw} \propto \nu^{-65/28}$ in a certain frequency band. These predictions can be probed in future gravitational wave observations, opening up new opportunities to test the clustering of PBHs and their contribution to dark matter.