Global continuation of a Vlasov model of rotating galaxies

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. In the astrophysics literature such a galaxy 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 suitable 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.