Distribution functions for spherical galaxies

A family of anisotropic distribution functions is derived that correspond exactly to the spherical density law $$\varrho(r)\propto r^{-2}(1+r)^{-2}$$, suggested by Jaffe for describing giant elliptical galaxies. The family is characterized by a single free parameter that specifies the degree of velocity anisotropy, from isotropic to completely radial. Both the distribution functions, and the equations describing the radial variation of the velocity dispersion, can be expressed in terms of simple functions.