Evolution of the cluster of primordial black holes within the Fokker-Planck approach

TL;DR

This paper models the evolution of primordial black hole clusters using the Fokker-Planck equation, examining the impact of a central massive black hole and revealing a tenfold cluster expansion over 1 Gyr.

Contribution

It introduces a Fokker-Planck based approach to simulate primordial black hole cluster evolution, including the effects of a central massive black hole.

Findings

Negligible growth of central black hole over 1 Gyr

Tenfold expansion of the cluster observed

Central black hole influences cluster dynamics

Abstract

The calculation results of the evolution of the cluster of primordial black holes based on the Fokker-Planck equation with neglecting of the gas accretion onto black holes are presented. In addition, we consider how a massive black hole located within the cluster center affects on its evolution. Despite it creates an additional potential in the central region of the cluster and might capture surrounding black holes, a negligible growth rate of a central black hole was shown for 1 Gyr. Furthermore, we find a significant (approximately tenfold) expansion of the cluster.