Simple distribution functions for stellar disks

Distribution functions (DFs) for dynamically warm thin stellar disks residing in arbitrary axisymmetric potentials are presented, which approximately reproduce predescribed surface density and velocity dispersion profiles. The functional form of the DFs is obtained by "warming up" a model made entirely of circular orbits. This can be done in various ways, giving different functional forms for the DF. In the best case, the DF reproduces the predescribed profiles to within a few percent for a typical case reminiscent of the old stellar disk in the Milky Way. This match may be improved to about 1% or better by a simple iterative method. An algorithm is given to draw phase-space points randomly from the DFs for the purpose of, e.g., N-body simulations. All the relevant computer programs are available from the author.