Bayesian Mass Estimates of the Milky Way: Including Measurement Uncertainties with Hierarchical Bayes

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 et al. (2015b); Eadie & Harris (2016) and builds upon the preliminary reports by Eadie et al. (2015a,c). The method uses a distribution function f (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 125kpc of 4.8 × 1011 M with a 95% Bayesian credible region of (4.0 − 5.8) × 10 11 M . 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.

Parameters of Six Selected Galactic Potential Models

“…In the works of Eadie et al (2015Eadie et al ( , 2017; Watkins et al (2010), and as well as Sofue (2009Sofue ( , 2015, for estimating the Galactic mass data on globular clusters and dwarf…”

“…The analysis method applied in the works of Sofue (2009Sofue ( , 2015 is close to ours: there was constructed the Galactic rotation curve, then was improved the model of the Galactic gravitational potential, and finally the latter was used for the Galactic mass estimation. Eadie et al (2017) present a hierarchical Bayesian method, which uses a distribution function to model the Galaxy and kinematic data from companion objects, such as globular clusters, to trace the Galaxy's gravitational potential.…”

HALO7D II: The Halo Velocity Ellipsoid and Velocity Anisotropy with Distant Main-sequence Stars

“…The remnants of these accreted dwarfs are found in the Milky Way's stellar halo, and the velocities of these stars retain a link to their initial conditions because of their long dynamical times. The HALO7D project aims to investigate The velocity anisotropy parameter β plays a key role in the spherical Jeans (1915) Jeans modeling has been used to estimate the mass of the Galaxy in many studies (e.g., Dehnen et al 2006, Gnedin et al 2010, Watkins et al 2009, Deason et al 2012, Eadie et al 2017 and references therein). However, estimates of the MW's mass have long been plagued by the mass-anisotropy degeneracy, owing to the lack of constraints on the tangential velocity distributions.…”

Better Galactic Mass Models through Chemistry

“…Because of this limited information, our knowledge of the shape and mass of the MW's DM halo is equally limited: measurements of its total mass disagree by a factor of ∼4 [14] and our understanding of its shape and radial profile is still poorly constrained enough to be controversial [15,16] especially in light of new estimates of the mass of its largest companion, the Large Magellanic Cloud [17,18]. This makes it difficult to place our Galaxy in a cosmological context in order to use it as a test of DM theories, since many predictions from cosmological simulations scale with mass and concentration [19].…”