Estimating the Galactic Mass Profile in the Presence of Incomplete Data

TL;DR

This paper introduces a Bayesian method with a hybrid-Gibbs sampler to estimate the galactic mass profile from incomplete tracer data, effectively handling missing velocity components and applying it to the Milky Way.

Contribution

Developed a novel Bayesian approach with a hybrid-Gibbs sampler for estimating galaxy mass profiles from incomplete data, demonstrated on the Milky Way.

Findings

Missing velocity components minimally affect total mass estimates.

Mass within 260 kpc is estimated at 1.37x10^12 solar masses.

The method provides credible intervals for mass profile parameters.

Abstract

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 M(r), 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 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 globular cluster Pal 3. Using a basic Hernquist model with an isotropic velocity dispersion, we obtain credible regions for the cumulative mass profile M(r) of the Milky Way, and provide estimates for the model parameters with 95 percent Bayesian credible intervals. The mass contained within 260 kpc is 1.37x10^12 solar masses, with a 95 percent credible interval of (1.27,1.51)x10^12 solar masses. The Hernquist parameters for the total mass and scale radius are 1.55 (+0.18/-0.13)x10^12 solar masses and 16.9 (+4.8/-4.1) kpc, where the uncertainties span the 95 percent 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.