Mass-radius spirals for steady state families of the Vlasov-Poisson system

TL;DR

This paper investigates the mass-radius relationship of steady state solutions to the Vlasov-Poisson system, revealing spiral patterns in certain models like King and Woolley-Dickens, which describe equilibrium states of galaxies.

Contribution

It demonstrates that for specific microscopic equations of state, the mass-radius relation forms a spiral, extending understanding of equilibrium configurations in galactic models.

Findings

Mass-radius relation forms a spiral in King and Woolley-Dickens models.

Polytropic cases show monotone mass-radius relation.

Provides mathematical proof of spiral structure in certain models.

Abstract

We consider spherically symmetric steady states of the Vlasov-Poisson system, which describe equilibrium configurations of galaxies or globular clusters. If the microscopic equation of state, i.e., the dependence of the steady state on the particle energy (and angular momentum) is fixed, a one-parameter family of such states is obtained. In the polytropic case the mass of the state along such a one-parameter family is a monotone function of its radius. We prove that for the King, Woolley-Dickens, and related models this mass-radius relation takes the form of a spiral.