Exact solution for core-collapsed isothermal star clusters

TL;DR

This paper presents new density profiles for isothermal star clusters, analyzing their thermodynamic behavior during core collapse, and clarifies the stability of different phases in canonical and microcanonical ensembles.

Contribution

It introduces novel density profiles for collapsed phases and examines their thermodynamic properties, including energy distribution and stability in different ensembles.

Findings

New density profiles for collapsed star clusters

Formation of binaries carrying 13% of gravitational energy

Positive specific heats in canonical ensemble, metastable negative specific heat solutions

Abstract

Star clusters in isothermal spheres are studied from a thermodynamic point of view. New density profiles are presented, that describe the collapsed phase at low temperatures. At the transition a set of binaries is formed that carries 13 % of the gravitational energy, while also a huge latent heat is generated. The total energy of the binaries is fixed by thermodynamics. In the canonical ensemble all specific heats are positive, while previously discussed negative specific heat solutions are metastable. In a microcanonical ensemble the latter remain partly dominant.