Spherical stellar systems with spheroidal velocity distributions

Abstract

A new method is described for deriving families of anisotropic distribution functions consistent with any spherically symmetric density profile. The algorithm is straightforward and sufficiently simple that analytic solutions can often be obtained. Each solution is defined by a single free parameter r/sub a/, the ''anisotropy radius''; the ratio of radial to tangential velocity dispersions is given by sigma/sup 2//sub r/ /sigma/sup 2//sub t/ = 1 +- r/sup 2//r/sup 2//sub a/. The models are isotropic in the center, and become either radially or tangentially anisotropic at large radii. Superposition of two or more solutions with different degrees of anisotropy allows one to construct models with almost any desired velocity structure. The algorithm is applied to a model galaxy with a de Vaucouleurs density law, and families of line-of-sight velocity dispersion profiles are obtained. The algorithm produces physically acceptable solutions that are nearly as radially anisotropic as those found by the more general linear programming method, and with considerably less computational effort.