Symplectic coarse graining approach to the dynamics of spherical self-gravitating systems

TL;DR

This paper introduces a symplectic coarse graining method to analyze the dynamics of spherical self-gravitating systems, providing analytical insights into their relaxation processes and validating results with N-body simulations.

Contribution

It presents a novel symplectic coarse graining approach to derive effective evolution equations for self-gravitating systems, linking frequency scaling and damping times to Fourier modes.

Findings

Analytical scaling laws for frequencies around stationary states.

Damping times of Fourier modes depend on the magnitude of wave vectors.

Validation of analytical predictions with N-body simulation results.

Abstract

We investigate the evolution of the phase-space distribution function around slightly perturbed stationary states and the process of violent relaxation in the context of the dissipationless collapse of an isolated spherical self-gravitating system. By means of the recently introduced symplectic coarse graining technique, we obtain an effective evolution equation that allows us to compute the scaling of the frequencies around a stationary state, as well as the damping times of Fourier modes of the distribution function, with the magnitude of the Fourier $k-$vectors themselves. We compare our analytical results with $N$-body simulations.