Substructure at High Speed. I. Inferring the Escape Velocity in the Presence of Kinematic Substructure

Abstract

The local escape velocity provides valuable inputs to the mass profile of the galaxy, and requires understanding the tail of the stellar speed distribution. Following Leonard & Tremaine, various works have since modeled the tail of the stellar speed distribution as $\propto {({v}_{\mathrm{esc}}-v)}^{k}$ , where v _esc is the escape velocity, and k is the slope of the distribution. In such studies, however, these two parameters were found to be largely degenerate and often a narrow prior is imposed on k in order to constrain v _esc. Furthermore, the validity of the power-law form can breakdown in the presence of multiple kinematic substructures or other mis-modeled features in the data. In this paper, we introduce a strategy that for the first time takes into account the presence of kinematic substructure. We model the tail of the velocity distribution as a sum of multiple power laws as a way of introducing a more flexible fitting framework. Using mock data and data from FIRE simulations of Milky Way-like galaxies, we show the robustness of this method in the presence of kinematic structure that is similar to the recently discovered Gaia Sausage. In a companion paper, we present the new measurement of the escape velocity and subsequently the mass of the Milky Way using Gaia eDR3 data.