Two-integral distribution functions for axisymmetric systems

Understand

Some formulae are presented for finding two-integral distribution functions (DFs) which depends only on the two classical integrals of the energy and the magnitude of the angular momentum with respect to the axis of symmetry for stellar systems with known axisymmetric densities.

• They come from an combination of the ideas of Eddington and Fricke and they are also an extension of those shown by Jiang and Ossipkov for finding anisotropic DFs for spherical galaxies.
• The density of the system is required 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 about the axis of symmetry.