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We present a hierarchical Bayesian method for estimating the total mass and mass profile of the Milky Way Galaxy. The new hierarchical Bayesian approach further improves the framework presented by Eadie et al. and Eadie and Harris and builds upon the preliminary reports by Eadie et al. The method uses a distribution function to model the Galaxy and kinematic data from satellite objects, such as globular clusters (GCs), to trace the Galaxy’s gravitational potential. A major advantage of the method is that it not only includes complete and incomplete data simultaneously in the analysis, but also incorporates measurement uncertainties in a coherent and meaningful way. We first test the hierarchical Bayesian framework, which includes measurement uncertainties, using the same data and power-law model assumed in Eadie and Harris and find the results are similar but more strongly constrained. Next, we take advantage of the new statistical framework and incorporate all possible GC data, finding a cumulative mass profile with Bayesian credible regions. This profile implies a mass within 125 kpc of with a 95% Bayesian credible region of . Our results also provide estimates of the true specific energies of all the GCs. By comparing these estimated energies to the measured energies of GCs with complete velocity measurements, we observe that (the few) remote tracers with complete measurements may play a large role in determining a total mass estimate of the Galaxy. Thus, our study stresses the need for more remote tracers with complete velocity measurements. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]