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Under the assumption of a simple and time-invariant gravitational potential,many Galactic dynamics techniques infer the Milky Way's mass and dark matterdistribution from stellar kinematic observations. These methods typically relyon parameterized potential models of the Galaxy and must take into accountnon-trivial survey selection effects, because they make use of the density ofstars in phase space. Large-scale spectroscopic surveys now supply informationbeyond kinematics in the form of precise stellar label measurements (especiallyelement abundances). These element abundances are known to correlate withorbital actions or other dynamical invariants. Here, we use the Orbital TorusImaging (OTI) framework that uses abundance gradients in phase space to maporbits. In many cases these gradients can be measured without detailedknowledge of the selection function. We use stellar surface abundances from theAPOGEE survey combined with kinematic data from the Gaia mission. Our methodreveals the vertical ($z$-direction) orbit structure in the Galaxy and enablesempirical measurements of the vertical acceleration field and orbitalfrequencies in the disk. From these measurements, we infer the total surfacemass density, $\Sigma$, and midplane volume density, $\rho_0$, as a function ofGalactocentric radius and height. Around the Sun, we find$\Sigma_{\odot}(z=1.1$ kpc)$=72^{+6}_{-9}$M$_{\odot}$pc$^{-2}$ and$\rho_{\odot}(z=0)=0.081^{+0.015}_{-0.009}$ M$_{\odot}$pc$^{-3}$ using the mostconstraining abundance ratio, [Mg/Fe]. This corresponds to a dark mattercontribution in surface density of $\Sigma_{\odot,\mathrm{DM}}(z=1.1$kpc)$=24\pm4$ M$_{\odot}$pc$^{-2}$, and in total volume mass density of$\rho_{\odot,\mathrm{DM}}(z=0)=0.011\pm0.002$ M$_{\odot}$pc$^{-3}$. Moreover,using these mass density values we estimate the scale length of thelow-$\alpha$ disc to be $h_R=2.24\pm0.06$kpc.

Orbital Torus Imaging: Acceleration, density, and dark matter in the Galactic disk measured with element abundance gradients