ESTIMATING THE GALACTIC MASS PROFILE IN THE PRESENCE OF INCOMPLETE DATA

A powerful method to measure the mass profile of a galaxy is through the velocities of tracer particles distributed through its halo. Transforming this kind of data accurately to a mass profile , however, is not a trivial problem. In particular, limited or incomplete data may substantially affect the analysis. In this paper we develop a Bayesian method to deal with incomplete data effectively; we have a hybrid-Gibbs sampler that treats the unknown velocity components of tracers as parameters in the model. We explore the effectiveness of our model using simulated data and then apply our method to the Milky Way (MW) using velocity and position data from globular clusters and dwarf galaxies. We find that, in general, missing velocity components have little effect on the total mass estimate. However, the results are quite sensitive to the outer cluster Pal 3. Using a basic Hernquist model with an isotropic velocity dispersion, we obtain credible regions for the cumulative mass profile of the MW and provide estimates for the model parameters with 95% Bayesian credible intervals. The mass contained within 260 kpc is , with a 95% credible interval of . The Hernquist parameters for the total mass and scale radius are and kpc, where the uncertainties span the 95% credible intervals. The code we developed for this work, Galactic Mass Estimator (GME), will be available as an open source package in the R Project for Statistical Computing.