Velocity profiles of Osipkov–Merritt models

A simple algorithm is presented for the calculation of the projected line-of-sight velocity profiles (VPs) of non-rotating anisotropic spherical dynamical models with a phase-space distribution function of the Osipkov–Merritt type. The velocity distribution in these models is isotropic inside the anisotropy radius r_a and becomes increasingly radially biased at larger radii. VP shape parameters are presented for a family of models in which the luminous mass density has a power-law cusp $$\rho_\text L\propto r^{-\gamma}$$ at small radii and a power-law fall-off $$\rho_\text L\propto r^{-4}$$ at large radii. Self-consistent models and models in which the luminous matter is embedded in a dark halo are discussed. The effects of changes in the cusp slope γ and in the anisotropy radius r_a are documented, and the area in the (γ, r_a)-plane that contains physical models is delineated. The shapes of the VPs of the models show a considerable (and observable) variation with projected galactocentric radius. These models will be useful for interpreting the data on the VP shapes of elliptical galaxies that are now becoming available.