Stable models of elliptical galaxies

We construct stable axially symmetric models of elliptical galaxies. For these models the particle density on phase space is a function of the particle energy and the third component of the angular momentum and is decreasing in the former. They are obtained as minimizers of suitably defined energy–Casimir functionals, and this implies their non-linear dynamical stability against axisymmetric perturbations. Since our analysis proceeds from a rigorous but purely mathematical point of view, it should be interesting to determine if any of our models match observational data in astrophysics. The main purpose of this paper is to initiate some exchange of information between the astrophysics and the mathematics communities.