Line-of-sight velocity profiles in spherical galaxies: breaking the degeneracy between anisotropy and mass

A systematic study of the line profiles expected in the outer parts (RR c ) of non-rotating elliptical galaxies is reported. For a family of quasi-separable spherical models the line-of-sight velocity profiles l(v) are calculated analytically in both a Keplerian and a scale-free halo potential. These velocity profiles (VPs) can take a wide variety of shapes; they illustrate that tangentially anisotropic distribution functions (DFs) generally lead to VPs with flat tops, while radially anisotropic DFs lead to more nearly Gaussian VPs. Strongly radial DFs in a halo potential develop prominent wings. As a general rule these velocity profiles are sensitive to the anisotropy β of the model, less so to the stellar density profile and the potential, and least so to the form of the DF at fixed β