Thermodynamics of rotating self-gravitating systems

TL;DR

This paper explores the equilibrium states of rotating self-gravitating systems, revealing how rotation influences phase transitions and symmetry breaking, leading to complex structures like double clusters.

Contribution

It introduces a mean-field approach to analyze the thermodynamics and phase diagram of rotating gravitational systems, highlighting the effects of angular momentum on equilibrium configurations.

Findings

Low angular momentum systems undergo gravitational collapse.

High angular momentum induces spontaneous symmetry breaking.

Complex equilibrium states like double clusters emerge at high rotation.

Abstract

We investigate the statistical equilibrium properties of a system of classical particles interacting via Newtonian gravity, enclosed in a three-dimensional spherical volume. Within a mean-field approximation, we derive an equation for the density profiles maximizing the microcanonical entropy and solve it numerically. At low angular momenta, i.e. for a slowly rotating system, the well-known gravitational collapse ``transition'' is recovered. At higher angular momenta, instead, rotational symmetry can spontaneously break down giving rise to more complex equilibrium configurations, such as double-clusters (``double stars''). We analyze the thermodynamics of the system and the stability of the different equilibrium configurations against rotational symmetry breaking, and provide the global phase diagram.