Order-disorder phase transition in black-hole star clusters. II. A scale-free cluster

TL;DR

This paper investigates phase transitions in dense star clusters around supermassive black holes, revealing conditions under which clusters shift from spherical to eccentric configurations, with implications for cluster stability and formation.

Contribution

It introduces a self-similar model showing a phase transition in black-hole star clusters, highlighting the effects of relativistic precession on cluster equilibrium states.

Findings

Identifies a first-order phase transition without relativistic effects.

Shows a continuous phase transition when relativistic effects are significant.

Suggests lopsided equilibria may naturally form in diverse black-hole star clusters.

Abstract

The supermassive black holes found at the centers of galaxies are often surrounded by dense star clusters. The ages of these clusters are generally longer than the resonant-relaxation time and shorter than the two-body relaxation time over a wide range of radii. We explore the thermodynamic equilibria of such clusters using a simple self-similar model. We find that the cluster exhibits a phase transition between a high-temperature spherical equilibrium and a low-temperature equilibrium in which the stars are on high-eccentricity orbits with nearly the same orientation. In the absence of relativistic precession, the spherical equilibrium is metastable below the critical temperature and the phase transition is first-order. When relativistic effects are important, the spherical equilibrium is linearly unstable below the critical temperature and the phase transition is continuous. A similar phase transition has recently been found in a model cluster composed of stars with a single semimajor axis. The presence of the same phenomenon in two quite different cluster models suggests that lopsided equilibria may form naturally in a wide variety of black-hole star clusters.