Many approaches to galaxy dynamics assume that the gravitational potential is simple and the distribution function is time-invariant. Under these assumptions there are traditional tools for inferring potential parameters given observations of stellar kinematics (e.g., Jeans models). However, spectroscopic surveys measure many stellar properties beyond kinematics. Here we present a new approach for dynamical inference, Orbital Torus Imaging, which makes use of kinematic measurements and element abundances (or other invariant labels). We exploit the fact that, in steady state, stellar labels vary systematically with orbit characteristics (actions), yet must be invariant with respect to orbital phases (conjugate angles). The orbital foliation of phase space must therefore coincide with surfaces along which all moments of all stellar label distributions are constant. Both classical-statistics and Bayesian methods can be built on this; these methods will be more robust and require fewer assumptions than traditional tools because they require no knowledge of the (spatial) survey selection function and they do not involve second moments of velocity distributions. We perform a classical-statistics demonstration with red giant branch stars from the APOGEE surveys: We model the vertical orbit structure in the Milky Way disk to constrain the local disk mass, scale height, and the disk--halo mass ratio (at fixed local circular velocity). We find that the disk mass can be constrained (naively) at the few-percent level with Orbital Torus Imaging using only eight element-abundance ratios, demonstrating the promise of combining stellar labels with dynamical invariants.
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