Self-gravitating Brownian systems and bacterial populations with two or more types of particles

TL;DR

This paper investigates the equilibrium and dynamical properties of multi-species self-gravitating Brownian systems, revealing how particle mass ratios influence stability, collapse behavior, and segregation, with applications to astrophysics and biology.

Contribution

It introduces a comprehensive analysis of multi-component self-gravitating gases, including stability criteria, collapse solutions, and segregation phenomena, extending previous single-species models.

Findings

Critical temperature and energy depend on particle mass ratios.

Analytic self-similar collapse solutions are derived.

Particle segregation occurs during collapse with non-universal scaling.

Abstract

We study the thermodynamical properties of a self-gravitating gas with two or more types of particles. Using the method of linear series of equilibria, we determine the structure and stability of statistical equilibrium states in both microcanonical and canonical ensembles. We show how the critical temperature (Jeans instability) and the critical energy (Antonov instability) depend on the relative mass of the particles and on the dimension of space. We then study the dynamical evolution of a multi-components gas of self-gravitating Brownian particles in the canonical ensemble. Self-similar solutions describing the collapse below the critical temperature are obtained analytically. We find particle segregation, with the scaling profile of the slowest collapsing particles decaying with a non universal exponent that we compute perturbatively in different limits. These results are compared with numerical simulations of the two-species Smoluchowski-Poisson system. Our model of self-attracting Brownian particles also describes the chemotactic aggregation of a multi-species system of bacteria in biology.