Constraining the Milky Way Mass Profile with Satellite Galaxies in Phase Space

The Milky Way (MW) halo mass and the detailed profile is crucial to astrophysical studies at various scales. The kinematics of satellite galaxies provides unique constraints on the gravitational potential of the MW outer halo and the total halo mass. Here we propose a versatile and accurate method to estimate the halo mass and concentration from satellite kinematics. Based on the similarity in halo structure implied by the NFW profile, we construct an non-parametric model for the 6D phase-space distribution function (DF) of satellites from cosmological simulations. Within the Bayesian statistical framework, not only can we infer the halo mass efficiently, but also handle various observational effects including the selection function and measurement errors in a rigorous and straightforward manner. Applied the method to 28 satellites with Gaia DR2 proper motion measurement, we report that the Milky Way halo mass is $M=1.23_{-0.18}^{+0.21}\times 10^{12} M_\odot$, and the concentration is $c=9.4_{ -2.1}^{ +2.8}$. The $20\%$ uncertainty level makes it the current best estimation to MW mass. The inferred mass profile is consistent with previous measurements from halo stars and globular clusters. With the DF model and inferred halo mass, we are able to reduce the uncertainty of kinematics for distant satellites, which will help to better infer their orbits and the assembly history of MW. This method can be also extended to any other extragalactic systems.