Stationary and static stellar dynamic models with axial symmetry

TL;DR

This paper demonstrates the existence of stationary solutions to the Vlasov-Poisson system with axial symmetry, extending known spherical solutions to more general geometries, including static and dynamic stellar models.

Contribution

The authors show that spherically symmetric solutions can be embedded into families of axially symmetric solutions, broadening the understanding of stellar equilibrium states.

Findings

Existence of axially symmetric stationary solutions with finite radius and mass.

Construction of static solutions with vanishing velocity fields.

Extension of known spherical solutions to non-spherical geometries.

Abstract

We study the existence of stationary solutions of the Vlasov-Poisson system with finite radius and finite mass in the stellar dynamics case. So far, the existence of such solutions is known only under the assumption of spherical symmetry. Using the implicit function theorem we show that certain stationary, spherically symmetric solutions can be embedded in one parameter families of stationary, axially symmetric solutions with finite radius and finite mass. In general, these new steady states have non-vanishing average velocity field, but they can also be constructed such that their velocity field does vanish, in which case they are called static.