New mass estimators for tracer populations

We introduce the "tracer mass estimator". This is a new and simple way to estimate the enclosed mass from the projected positions and line-of-sight velocities of a tracer population (such as globular clusters, halo stars, and planetary nebulae). Like the projected mass estimator, it works by averaging (projected distance) (radial velocity)(2)/G over the sample. However, it applies to the commonest case of all, in which the tracer population does not follow the overall dark matter density. The method is verified against simulated data sets drawn from Monte Carlo realizations of exact solutions of the collisionless Boltzmann equation and applied to the M31 globular cluster data set of Perrett and coworkers, as well as to M31's satellite galaxies.