Transverse kinematics of the Galactic bar-bulge from VVV and Gaia

We analyse the kinematics of the Galactic bar-bulge using proper motions from the ESO public survey Vista Variables in the Via Lactea (VVV) and the second Gaia data release. Gaia has provided some of the first absolute proper motions within the bulge and the near-infrared VVV multi-epoch catalogue complements Gaia in highly-extincted low-latitude regions. We discuss the relative-to-absolute calibration of the VVV proper motions using Gaia. Along lines of sight spanning $-10<\ell/\,\mathrm{deg}<10$ and $-10<b/\,\mathrm{deg}<5$, we probabilistically model the density and velocity distributions as a function of distance of $\sim45$ million stars. The transverse velocities confirm the rotation signature of the bar seen in spectroscopic surveys. The differential rotation between the double peaks of the magnitude distribution confirms the X-shaped nature of the bar-bulge. Both transverse velocity components increase smoothly along the near-side of the bar towards the Galactic centre, peak at the Galactic centre and decline on the far-side. The anisotropy is $\sigma_\ell/\sigma_b\approx1.1-1.3$ within the bulk of the bar, reducing to $0.9-1.1$ when rotational broadening is accounted for, and exhibits a clear X-shaped signature. The vertex deviation in $\ell$ and $b$ is significant $|\rho_{\ell b}|\lesssim0.2$, greater on the near-side of the bar and produces a quadrupole signature across the bulge indicating approximate radial alignment. We have re-constructed the 3D kinematics from the assumption of triaxiality, finding good agreement with spectroscopic survey results. In the co-rotating frame, we find evidence of bar-supporting x1 orbits and tangential bias in the in-plane dispersion field.