Orbital Torus Imaging: Using Element Abundances to Map Orbits and Mass
  in the Milky Way
  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 (na\"ively) 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.
