Isotropic steady states in galactic dynamics revised

TL;DR

This paper extends previous work on the nonlinear stability of isotropic, spherically symmetric steady states in galactic dynamics, demonstrating their stability under general perturbations within the Vlasov-Poisson framework.

Contribution

It constructs a broad class of stable steady states by energy minimization under constraints, including all finite-mass polytropes with decreasing energy dependence.

Findings

Established nonlinear stability of a large class of steady states

Included all finite-mass polytropes with decreasing energy dependence

Proved stability against general, non-symmetric perturbations

Abstract

The present paper completes our earlier results on nonlinear stability of stationary solutions of the Vlasov-Poisson system in the stellar dynamics case. By minimizing the energy under a mass-Casimir constraint we construct a large class of isotropic, spherically symmetric steady states and prove their nonlinear stability against general, i. e., not necessarily symmetric perturbations. The class is optimal in a certain sense, in particular, it includes all polytropes of finite mass with decreasing dependence on the particle energy.