Phase-space structure analysis of self-gravitating collisionless spherical systems

TL;DR

This paper investigates the phase-space evolution of self-gravitating spherical systems, revealing distinct dynamical phases and the impact of radial instabilities through high-resolution simulations.

Contribution

It provides the first detailed numerical analysis distinguishing multiple dynamical phases and the role of radial instabilities in collisionless gravitational systems.

Findings

Identification of three dynamical phases: violent relaxation, quasi-steady state, and non-spherical relaxation.

Demonstration that radial instabilities can disrupt phase-space spiral structures without altering coarse-grained properties.

Radial orbit instabilities lead to non-spherical states in cool systems with steep density profiles.

Abstract

In the mean field limit, isolated gravitational systems often evolve towards a steady state through a violent relaxation phase. One question is to understand the nature of this relaxation phase, in particular the role of radial instabilities in the establishment/destruction of the steady profile. Here, through a detailed phase-space analysis based both on a spherical Vlasov solver, a shell code and a $N$-body code, we revisit the evolution of collisionless self-gravitating spherical systems with initial power-law density profiles $\rho(r) \propto r^n$, $0 \leq n \leq -1.5$, and Gaussian velocity dispersion. Two sub-classes of models are considered, with initial virial ratios $\eta=0.5$ ("warm") and $\eta=0.1$ ("cool"). Thanks to the numerical techniques used and the high resolution of the simulations, our numerical analyses are able, for the first time, to show the clear separation between two or three well known dynamical phases: (i) the establishment of a spherical quasi-steady state through a violent relaxation phase during which the phase-space density displays a smooth spiral structure presenting a morphology consistent with predictions from self-similar dynamics, (ii) a quasi-steady state phase during which radial instabilities can take place at small scales and destroy the spiral structure but do not change quantitatively the properties of the phase-space distribution at the coarse grained level and (iii) relaxation to non spherical state due to radial orbit instabilities for $n \leq -1$ in the cool case.