Global Continuation of a Vlasov Model of Rotating Galaxies

TL;DR

This paper proves the existence of axisymmetric, possibly rapidly rotating galaxy models within the Vlasov-Poisson framework, showing that such models form a connected set with unbounded support or densities under certain conditions.

Contribution

It establishes an existence theorem for rotating galaxy states in the Vlasov model and characterizes the behavior of these states within a connected set.

Findings

The set of steady states is connected in an appropriate function space.

States in this set can have unbounded support or densities.

Conditions under which rotation speeds or densities become unbounded are identified.

Abstract

A typical galaxy consists of a huge number of stars attracted to each other by gravity. For instance, the Milky Way has about $10^{11}$ stars. Thus it is typically modeled by the Vlasov-Poisson system. We prove an existence theorem for axisymmetric steady states of galaxies that may rotate rapidly. Such states are given in terms of a fairly general function $\phi$ of the particle energy and angular momentum. The set $\mathcal K$ of such states form a connected set in an appropriate function space. Along the set $\mathcal K$, we prove under some conditions that either (a) the supports of the galaxies become unbounded or (b) both the rotation speeds and the densities somewhere within the galaxy become unbounded.