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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]

We present mass and mass profile estimates for the Milky Way (MW) Galaxy using the Bayesian analysis developed by Eadie et al. and using globular clusters (GCs) as tracers of the Galactic potential. The dark matter and GCs are assumed to follow different spatial distributions; we assume power-law model profiles and use the model distribution functions described in Evans et al. and Deason et al. We explore the relationships between assumptions about model parameters and how these assumptions affect mass profile estimates. We also explore how using subsamples of the GC population beyond certain radii affect mass estimates. After exploring the posterior distributions of different parameter assumption scenarios, we conclude that a conservative estimate of the Galaxy’s mass within 125 kpc is , with a 50% probability region of . Extrapolating out to the virial radius, we obtain a virial mass for the MW of with 50% credible region of (. If we consider only the GCs beyond 10 kpc, then the virial mass is ( kpc). We also arrive at an estimate of the velocity anisotropy parameter β of the GC population, which is with a 50% credible region (0.21, 0.35). Interestingly, the mass estimates are sensitive to both the dark matter halo potential and visible matter tracer parameters, but are not very sensitive to the anisotropy parameter. [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]

We present new deep photometry of the rich globular cluster (GC) systems around the Brightest Cluster Galaxies UGC 9799 (Abell 2052) and UGC 10143 (Abell 2147), obtained with the Hubble Space Telescope (HST) ACS and WFC3 cameras. For comparison, we also present new reductions of similar HST/ACS data for the Coma supergiants NGC 4874 and 4889. All four of these galaxies have huge cluster populations (to the radial limits of our data, comprising from 12,000 to 23,000 clusters per galaxy). The metallicity distribution functions (MDFs) of the GCs can still be matched by a bimodal-Gaussian form where the metal-rich and metal-poor modes are separated by dex, but the internal dispersions of each mode are so large that the total MDF becomes very broad and nearly continuous from [Fe/H] ≃ −2.4 to solar. There are, however, significant differences between galaxies in the relative numbers of metal-rich clusters, suggesting that they underwent significantly different histories of mergers with massive gas-rich halos. Last, the proportion of metal-poor GCs rises especially rapidly outside projected radii , suggesting the importance of accreted dwarf satellites in the outer halo. Comprehensive models for the formation of GCs as part of the hierarchical formation of their parent galaxies will be needed to trace the systematic change in structure of the MDF with galaxy mass, from the distinctly bimodal form in smaller galaxies up to the broad continuum that we see in the very largest systems. [ABSTRACT FROM AUTHOR]