Self-gravitating clusters of Bose-Einstein gas with planar, cylindrical, or spherical symmetry: gaseous density profiles and onset of condensation

TL;DR

This paper investigates the density profiles and phase transitions of self-gravitating Bose-Einstein gas clusters with various symmetries and dimensions, revealing how geometry influences condensation and stability.

Contribution

It provides a comprehensive analysis of gaseous and condensed phases in self-gravitating Bose-Einstein clusters across different symmetries and dimensions, highlighting the onset of condensation at nonzero temperatures.

Findings

Density profiles are independent of total mass due to chosen scales.

Mixed-phase states feature a condensed core with a gaseous halo.

Multiple stable macrostates can coexist at thermal equilibrium.

Abstract

We calculate density profiles for self-gravitating clusters of an ideal Bose-Einstein gas with nonrelativistic energy-momentum relation and macroscopic mass at thermal equilibrium. Our study includes clusters with planar symmetry in dimensions $\mathcal{D}=1,2,3$, clusters with cylindrical symmetry in $\mathcal{D}=2,3$, and clusters with spherical symmetry in $\mathcal{D}=3$. Wall confinement is imposed where needed to prevent escape. The length scale and energy scale in use for the gaseous phase render density profiles for gaseous macrostates independent of total mass. Density profiles for mixed-phase macrostates have a condensed core surrounded by a gaseous halo. The spatial extension of the core is negligibly small on the length scale tailored for the halo. The mechanical stability conditions as evident in caloric curves permit multiple macrostates to coexist. Their status regarding thermal equilibrium is examined by a comparison of free energies. The onset of condensation takes place at a nonzero temperature in all cases. The critical singularities and the nature of the phase transition vary with the symmetry of the cluster and the dimensionality of the space.