Analysis of Jeans instability from the Boltzmann equation

TL;DR

This paper investigates Jeans instability using the collisionless Boltzmann equation, analyzing both static and expanding universe scenarios, revealing how dark matter influences collapse thresholds and the nature of density fluctuations.

Contribution

It provides a detailed analysis of Jeans instability directly from the Boltzmann equation, including effects of dark matter and universe expansion without the Jeans swindle.

Findings

Combined dark matter and baryonic system has a smaller Jeans mass.

In an expanding universe, small wavelengths oscillate, large wavelengths grow, indicating instability.

No need for Jeans swindle in the expanding universe case.

Abstract

The dynamics of self-gravitating fluids is analyzed within the framework of a collisionless Boltzmann equation in the presence of gravitational fields and Poisson equation. Two cases are analyzed: a system with baryonic and dark matter in a static universe and a single system in an expanding universe. The amplitudes of the perturbed distribution functions are considered as a linear combination of the collision invariants of the Boltzmann equation. For the system of baryonic and dark matter, the Jeans mass of the combined system is smaller than the one of the single system indicating that a smaller mass is needed to initiate the collapse. For the single system in an expanding universe it is not necessary to make use of Jeans "swindle"and it shown that for small wavelengths the density contrast oscillates while for large wavelengths it grows with time and the Jeans instability emerges.