The cumulative mass profile of the Milky Way as determined by globular cluster kinematics from Gaia DR2

Abstract

We present new mass estimates and cumulative mass profiles (CMPs) with Bayesian credible regions for the Milky Way (MW) Galaxy, given the kinematic data of globular clusters as provided by (1) the $\textit{Gaia}$ DR2 collaboration and the HSTPROMO team, and (2) the new catalog in Vasiliev (2019). We use globular clusters beyond 15kpc to estimate the CMP of the MW, assuming a total gravitational potential model $\Phi(r) = \Phi_{\circ}r^{-\gamma}$, which approximates an NFW-type potential at large distances when $\gamma=0.5$. We compare the resulting CMPs given data sets (1) and (2), and find the results to be nearly identical. The median estimate for the total mass is $M_{200}= 0.70 \times 10^{12} M_{\odot}$ and the $50\%$ Bayesian credible interval is $(0.62, 0.81)\times10^{12}M_{\odot}$. However, because the Vasiliev catalog contains more complete data at large $r$, the MW total mass is slightly more constrained by these data. In this work, we also supply instructions for how to create a CMP for the MW with Bayesian credible regions, given a model for $M(<r)$ and samples drawn from a posterior distribution. With the CMP, we can report median estimates and $50\%$ Bayesian credible regions for the MW mass within any distance (e.g., $M(r=25\text{kpc})= 0.26~(0.20, 0.36)\times10^{12}M_{\odot}$, $M(r=50\text{kpc})= 0.37~(0.29, 0.51) \times10^{12}M_{\odot}$, $M(r=100\text{kpc}) = 0.53~(0.41, 0.74) \times10^{12}M_{\odot}$, etc.), making it easy to compare our results directly to other studies.