The Gravitational Force Field of the Galaxy Measured From the Kinematics of RR Lyrae in Gaia

From a sample of 15651 RR Lyrae with accurate proper motions in Gaia DR2, we measure the azimuthally averaged kinematics of the inner stellar halo between 1.5 kpc and 20 kpc from the Galactic centre. We find that their kinematics are strongly radially anisotropic, and their velocity ellipsoid nearly spherically aligned over this volume. Only in the inner regions $\lesssim$ 5 kpc does the anisotropy significantly fall (but still with $\beta >$ 0.25) and the velocity ellipsoid tilt towards cylindrical alignment. In the inner regions, our sample of halo stars rotates at up to 50 km s$^{-1}$, which may reflect the early history of the Milky Way, although there is also significant angular momentum exchange with the Galactic bar at these radii. We subsequently apply the Jeans equations to these kinematic measurements in order to non-parametrically infer the azimuthally averaged gravitational acceleration field over this volume, and by removing the contribution from baryonic matter, measure the contribution from dark matter. We find that the gravitational potential of the dark matter is nearly spherical with average flattening $q_\Phi=$ 1.01 $\pm$ 0.06 between 5 kpc and 20 kpc, and by fitting parametric ellipsoidal density profiles to the acceleration field, we measure the flattening of the dark matter halo over these radii to be $q_\rho=$ 1.00 $\pm$ 0.09.