Star Clusters, Self-Interacting Dark Matter Halos and Black Hole Cusps: The Fluid Conduction Model and its Extension to General Relativity

TL;DR

This paper develops a fluid conduction model to study the evolution of star clusters and SIDM halos, including the effects of black holes, and extends the model to general relativity for relativistic systems.

Contribution

It introduces a fluid conduction approximation for weakly-collisional systems and extends this approach to general relativity, enabling analysis of black hole cusps in star clusters and SIDM halos.

Findings

The model accurately reproduces the Bahcall-Wolf cusp in star clusters with black holes.

It shows how black holes halt gravothermal catastrophe and induce re-expansion.

SIDM halos evolve into core-halo structures with density cusps depending on interaction cross section.

Abstract

We adopt the fluid conduction approximation to study the evolution of spherical star clusters and self-interacting dark matter (SIDM) halos. We also explore the formation and dynamical impact of density cusps that arise in both systems due to the presence of a massive, central black hole. The large N-body, self-gravitating systems we treat are "weakly-collisional": the mean free time between star or SIDM particle collisions is much longer than their characteristic crossing (dynamical) time scale, but shorter than the system lifetime. The fluid conduction model reliably tracks the "gravothermal catastrophe" in star clusters and SIDM halos without black holes. For a star cluster with a massive, central black hole, this approximation reproduces the familiar Bahcall-Wolf quasistatic density cusp for the stars bound to the black hole and shows how the cusp halts the "gravothermal catastrophe" and causes the cluster to re-expand. An SIDM halo with an initial black hole central density spike that matches onto to an exterior NFW profile relaxes to a core-halo structure with a central density cusp determined by the velocity dependence of the SIDM interaction cross section. The success and relative simplicity of the fluid conduction approach in evolving such "weakly-collisional", quasiequilibrium Newtonian systems motivates its extension to relativistic systems. We present a general relativistic extension here.