Self-gravitating isothermal sphere in an expanding background

TL;DR

This paper develops a gravitational thermodynamics framework for self-gravitating isothermal spheres in an expanding universe, revealing instabilities that could influence early cosmic baryonic structures.

Contribution

It introduces a consistent thermodynamic model for isothermal spheres in an expanding universe and identifies instabilities in both homogeneous and inhomogeneous equilibria.

Findings

Identifies instability in gravitational equilibria within an expanding background.

Suggests potential impact on high-redshift baryonic gas cloud formation.

Provides conditions for instability related to mass and radius of gas clouds.

Abstract

Spatially homogeneous thermal equilibria of self-gravitating gas, being impossible otherwise, are nevertheless allowed in an expanding background accounting for Universe's expansion. Furthermore, a fixed density at the boundary of a perturbation is a natural boundary condition keeping the mass finite inside without the need to invoke any unphysical walls. These facts allow us to develop a consistent gravitational thermodynamics of isothermal spheres inside an expanding Universe. In the canonical and grand canonical ensembles we identify an instability for both homogeneous and inhomogeneous equilibria. We discuss a potential astrophysical application. If such an instability is triggered on baryonic gas at high redshift $z > 137$ when the primary baryonic component, namely atomic hydrogen, was still thermally locked to the Cosmic Microwave Background radiation, then the corresponding destabilized gaseous clouds have baryonic mass $\geq 0.8\cdot 10^5 {\rm M}_\odot$ and radius $\geq 15{\rm pc}$.