A comparison of two approaches for estimating local stellar kinematics: The Projection Method versus Maximum Likelihodd

Abstract: We test a new approach to calculate the mean velocity and velocity dispersion for a sample of nearby stars when their radial velocities are not available. The most commonly used method (here called the projection method, PM) was introduced in a paper by Dehnen & Binney (1998). That method is here compared, theoretically and numerically, with an application of the Maximum Likelihood (ML) method. The two methods are tested on synthetically generated samples as well as on real samples from the Hipparcos Catalogue. In general it turns out that ML is not significantly more accurate than PM, except that ML allows to take into account observational errors and therefore gives more correct dispersions when the uncertainty in the proper motions is significant. Applying PM and ML to samples from the Geneva-Copenhagen survey (Nordström et al. 2004), we find that both methods give very similar results as when the published three-dimensional velocities are used.