Determination of the escape velocity of the Milky Way using a proper motion selected halo sample

Abstract: The {\it Gaia} mission has provided the largest catalogue ever of sources with tangential velocity information. However, using this catalogue for dynamical studies is difficult because most of the stars lack line-of-sight velocity measurements. Recently, we presented a selection of $\sim 10^7$ halo stars with accurate distances that have been selected based on their photometry and proper motions. Using this sample, we model the tail of the velocity distribution with a power-law distribution, a commonly used approach first established by \cite{Leonard1990THESPEED}. For the first time ever we use tangential velocities measured accurately for an unprecedented number of halo stars to estimate the escape velocity. In the solar neighbourhood, we obtain a very precise estimate of the escape velocity which is $497^{+8}_{-8}~{\rm km/s}$. This estimate is most likely biased low, our best guess is by 10\%. As a result, the true escape velocity most likely is closer to $550~{\rm km/s}$. The escape velocity directly constrains the total mass of the Milky Way. To find the best fitting halo mass and concentration parameter we adjusted the dark (spherical NFW) halo of a realistic Milky Way potential while keeping the circular velocity at the solar radius fixed at $v_c(R_\odot) = 232.8~{\rm km/s}$. The resulting halo parameters are $M_{200}^{+10\%} = 1.11^{+0.08}_{-0.07} \cdot10^{12} ~{\rm M}\odot$ and concentration parameter $c^{+10\%} = 11.8^{+0.3}{-0.3}$, where we use the explicit notation to indicate that these have been corrected for the 10\% bias. The slope of the escape velocity with galactocentric distance is as expected in the inner Galaxy based on Milky Way models. Curiously, we find a disagreement beyond the solar radius which is likely an effect of a change in the shape of the velocity distribution and could be related to the presence of velocity clumps.