Bayesian Mass Estimates of the Milky Way: including measurement uncertainties with hierarchical Bayes

TL;DR

This paper introduces a hierarchical Bayesian method for estimating the Milky Way's mass profile that effectively incorporates measurement uncertainties and incomplete data, providing more constrained and comprehensive mass estimates.

Contribution

The paper develops a novel hierarchical Bayesian framework that improves mass estimation of the Milky Way by including measurement uncertainties and all available data types.

Findings

Mass within 125 kpc is estimated at 4.8 x 10^11 solar masses.

The method yields more constrained mass profiles compared to previous approaches.

Remote tracers with complete velocity data significantly influence mass estimates.

Abstract

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, Harris, & Widrow (2015) and Eadie & Harris (2016) and builds upon the preliminary reports by Eadie et al (2015a,c). The method uses a distribution function $f(\mathcal{E},L)$ 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 & Harris (2016), 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 $4.8\times10^{11}M_{\odot}$ with a 95\% Bayesian credible region of $(4.0-5.8)\times10^{11}M_{\odot}$. 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.