Inferring the Mass of Spherical Stellar Systems from Velocity Moments

The usefulness of line-of-sight velocity distributions for constraining the potential and kinematics of a nonrotating spherical system when nothing is known a priori about its radial mass distribution is discussed. A formalism, based on velocity moments, is developed in order to make use of the additional information contained within the distribution of line-of-sight velocities at every projected radius. It is shown that, if the potential Phi(r) is known, and the distribution function of the observed sample is of the form f(E, L-squared), the joint distribution of positions and velocities nu_p(r sub p, v_p) uniquely determines that distribution function. It is shown that most assumed potentials are inconsistent with a given nu_p(r sub p, v_p) since they imply intrinsic velocity moments that are negative at some radii, and hence a distribution function that is negative in some regions of phase space.