Anisotropic distribution functions for spherical galaxies

TL;DR

This paper introduces a method to derive anisotropic distribution functions for spherical galaxies with known density profiles, using a sum-of-products approach based on classical integrals of motion.

Contribution

It presents a novel technique to construct anisotropic distribution functions from density profiles expressed as sums of potential and radius functions, including new examples.

Findings

Derived new anisotropic distribution functions for spherical galaxies.

Demonstrated the method with several explicit examples.

Outlined potential extension to axisymmetric galaxies.

Abstract

A method is presented for finding anisotropic distribution functions for stellar systems with known, spherically symmetric, densities, which depends only on the two classical integrals of the energy and the magnitude of the angular momentum. It requires the density to be expressed as a sum of products of functions of the potential and of the radial coordinate. The solution corresponding to this type of density is in turn a sum of products of functions of the energy and of the magnitude of the angular momentum. The products of the density and its radial and transverse velocity dispersions can be also expressed as a sum of products of functions of the potential and of the radial coordinate. Several examples are given, including some of new anisotropic distribution functions. This device can be extended further to the related problem of finding two-integral distribution functions for axisymmetric galaxies.