The pattern speed of the Milky Way bar from transverse velocities

Understand

We use the continuity equation to derive a method for measuring the pattern speed of the Milky Way's bar/bulge from proper motion data.

• The method has minimal assumptions but requires complete coverage of the non-axisymmetric component in two of the three Galactic coordinates.
• We apply our method to the proper motion data from a combination of Gaia DR2 and VISTA Variables in the Via Lactea (VVV) to measure the pattern speed of the bar as $\Omega_\mathrm{p}=(41\pm 3)\,\mathrm{km\,s^{-1}\,kpc^{-1}}$ (where the error is statistical).
• This puts the corotation radius at $(5.7\pm0.4)\,\mathrm{kpc}$, under the assumptions of the standard peculiar motion of the Sun and the absence of non-axisymmetric streaming in the Solar neighbourhood.