Data-driven Dynamics with Orbital Torus Imaging: A Flexible Model of the Vertical Phase Space of the Galaxy

The vertical kinematics of stars near the Sun can be used to measure thetotal mass distribution near the Galactic disk and to study out-of-equilibriumdynamics. With contemporary stellar surveys, the tracers of vertical dynamicsare so numerous and so well measured that the shapes of underlying orbits arealmost directly visible in the data through element abundances or even stellardensity. These orbits can be used to infer a mass model for the Milky Way,enabling constraints on the dark matter distribution in the inner galaxy. Herewe present a flexible model for foliating the vertical position-velocity phasespace with orbits, for use in data-driven studies of dynamics. The verticalacceleration profile in the vicinity of the disk, along with the orbitalactions, angles, and frequencies for individual stars, can all be derived fromthat orbit foliation. We show that this framework - "Orbital Torus Imaging"(OTI) - is rigorously justified in the context of dynamical theory, and does agood job of fitting orbits to simulated stellar abundance data with varyingdegrees of realism. OTI (1) does not require a global model for the Milky Waymass distribution, and (2) does not require detailed modeling of the selectionfunction of the input survey data. We discuss the approximations andlimitations of the OTI framework, which currently trades dynamicalinterpretability for flexibility in representing the data in some regimes, andwhich also presently separates the vertical and radial dynamics. We release anopen-source tool, torusimaging, to accompany this article.