Unstable Galaxy Models

TL;DR

This paper investigates the stability of spherically symmetric galaxy models described by the Vlasov-Poisson system, providing examples of unstable models where the distribution function is not monotone in energy.

Contribution

It constructs new examples of unstable galaxy models with non-monotonic energy distribution functions, extending stability analysis beyond classical monotone cases.

Findings

Identifies conditions under which galaxy models become unstable.

Provides explicit examples of unstable models with non-monotonic energy dependence.

Extends the understanding of stability criteria for collisionless galaxy models.

Abstract

The dynamics of collisionless galaxy can be described by the Vlasov-Poisson system. By the Jean's theorem, all the spherically symmetric steady galaxy models are given by a distribution of {\Phi}(E,L), where E is the particle energy and L the angular momentum. In a celebrated Doremus-Feix-Baumann Theorem, the galaxy model {\Phi}(E,L) is stable if the distribution {\Phi} is monotonically decreasing with respect to the particle energy E. On the other hand, the stability of {\Phi}(E,L) remains largely open otherwise. Based on a recent abstract instability criterion of Guo-Lin, we constuct examples of unstable galaxy models of f(E,L) and f(E) in which f fails to be monotone in E.