Dynamics and merger rate of primordial black holes in a cluster

TL;DR

This paper models the evolution and merger rate of primordial black holes in clusters over cosmic time, highlighting a distinctive increase at core collapse and a subsequent decline, with implications for gravitational wave observations.

Contribution

It introduces a Fokker-Planck based dynamic model of PBH clusters, predicting a unique time-dependent merger rate signature.

Findings

Merger rate increases by an order of magnitude at core collapse

Post-collapse, the merger rate decreases as t^{-1.48}

Results apply to monochromatic and power-law PBH mass distributions

Abstract

The PBHs clusters can be source of gravitational waves, and the merger rate depends on the spatial distribution of PBHs in the cluster which changes over time. It is well known that gravitational collisional systems experience the core collapse, that leads to significantly increase of the central density and shrinking of the core. After core collapse, the cluster expands almost self-similarly (i.e. density profile extends in size without changing its shape). These dynamic processes affect at the merger rate of PBHs. In this paper the dynamics of the PBH cluster is considered using the Fokker-Planck equation. We calculate the merger rate of PBHs on cosmic time scales and show that its time dependence has a unique signature. Namely, it grows by about an order of magnitude at the moment of core collapse which depends on the characteristic of the cluster, and then decreases according to the dependence $\mathcal{R} \propto t^{-1.48}$. It was obtained for monochromatic and power-law PBH mass distributions with some fixed parameters. Obtained results can be used to test the model of the PBH clusters via observation of gravitational waves at high redshift.