Analysis of instability of systems composed by dark and baryonic matter

TL;DR

This paper investigates the stability and collapse conditions of systems with dark and baryonic matter using collisionless Boltzmann and Poisson equations, revealing how dark matter velocity dispersion influences instability regions.

Contribution

It introduces a model analyzing the combined dynamics of dark and baryonic matter, extending previous dark matter-only models to include baryonic effects on instability.

Findings

Unstable region size increases with dark matter dispersion velocity.

Dark matter presence extends the instability limit compared to dark matter-only models.

The model predicts enhanced structure formation due to higher instability limits.

Abstract

In this work the dynamics of self-gravitating systems composed by dark and baryonic matter is analyzed. Searching for a description of this dynamics, a system of collisionless Boltzmann equations for the two constituents and the Poisson equation for the gravitational field are employed. Through the solution of these equations the collapse criterion is determined from a dispersion relation. The collapse occurs in an unstable region where the solutions grow exponentially with time. It is shown that the unstable region becomes larger if the dispersion velocity of dark matter becomes larger than the one of the baryonic matter. The results obtained are also compared with the case where only the dark matter is present. The model of the present work has a higher limit of instability and therefore, exhibited an advantage in the structure formation.