Recovering the gravitational potential in a rotating frame: Deep Potential applied to a simulated barred galaxy

Stellar kinematics provides a window into the gravitational field, and therefore into the distribution of all mass, including dark matter. Deep Potential is a method for determining the gravitational potential from a snapshot of stellar positions in phase space, using mathematical tools borrowed from deep learning to model the distribution function and solve the Collisionless Boltzmann equation. In this work, we extend the Deep Potential method to rotating systems, and then demonstrate that it can accurately recover the gravitational potential, density distribution, and pattern speed of a simulated barred disc galaxy, using only a frozen snapshot of the stellar velocities. We demonstrate that we are able to recover the bar pattern speed to within $15 \,\rm {per\, cent}$ in our simulated galaxy using stars in a 4 kpc subvolume centred on a Solar-like position, and to within $20 \,\rm{per\,cent}$ in a 2 kpc subvolume. In addition, by subtracting the mock 'observed' stellar density from the recovered total density, we are able to infer the radial profile of the dark matter density in our simulated galaxy. This extension of Deep Potential is an important step in allowing its application to the Milky Way, which has rotating features, such as a central bar and spiral arms, and may moreover provide a new method of determining the pattern speed of the Milky Way bar.