ClearPotential: Revealing Local Dark Matter in Three Dimensions

We present ClearPotential, a data-driven, three-dimensional measurement of the gravitational potential of the local Milky Way using unsupervised machine learning, without the symmetry assumptions, specific functional forms, and binning required in previous work. The potential is modeled as a neural network, optimized to solve the equilibrium collisionless Boltzmann equation for the observed phase space density of Gaia DR3 Red Clump stars within 4 kpc of the Sun. This density is obtained from data using normalizing flows, and our unsupervised solution to the Boltzmann equation automatically corrects for selection effects from crowding and the dust-driven extinction of starlight. Our fully-differentiable model of the gravitational potential allows us to map the acceleration and mass density of the Galaxy in the volume around the Sun, including in the dust-obscured disk towards the Galactic Center. We determine the dark matter density at the Solar radius to be $(0.84 \pm 0.08)\times 10^{-2}\,{M}_\odot/{\rm pc}^3$, and analyze the structure of the dark matter halo. We find strong evidence for a tilted oblate halo, weak preference for a cored inner profile, and the strongest constraints to date on a possible dark matter disk. We place a bound on the timescale of disequilibrium in the local Milky Way, and find mild evidence for disequilibrium using independent acceleration measurements from timings of binary pulsar systems. This work provides the clearest map of the local Galactic potential to date and marks an important step in the era of data-driven astrometry.