Oscillating solutions of the Vlasov-Poisson system -- A numerical investigation

TL;DR

This paper provides numerical evidence that perturbations of stable steady states in the gravitational Vlasov-Poisson system cause oscillations, with periods related to central density, relevant for understanding galaxy dynamics.

Contribution

It introduces an Eddington-Ritter type relation linking oscillation periods to central density in the Vlasov-Poisson system, supported by numerical simulations.

Findings

Oscillations can be periodic or damped.

A relation between period and central density is established.

Estimated oscillation periods for elliptical galaxies are provided.

Abstract

Numerical evidence is given that spherically symmetric perturbations of stable spherically symmetric steady states of the gravitational Vlasov-Poisson system lead to solutions which oscillate in time. The oscillations can be periodic in time or damped. Along one-parameter families of polytropic steady states we establish an Eddington-Ritter type relation which relates the period of the oscillation to the central density of the steady state. The numerically obtained periods are used to estimate possible periods for typical elliptical galaxies.