Modified Virial Formulae and the Theory of Mass Estimators
  We show how to estimate the enclosed mass from the observed motions of an
ensemble of test particles. Traditionally, this problem has been attacked
through virial or projected mass estimators. Here, we examine and extend these
systematically, and show how to construct an optimal estimator for any given
assumption as to the potential. The estimators do not explicitly depend on any
properties of the density of the test objects, which is desirable as in
practice such information is dominated by selection effects. As particular
examples, we also develop estimators tailored for the problem of estimating the
mass of the Hernquist or NFW dark matter haloes from the projected positions
and velocities of stars.
