The pattern speed of the Milky Way bar from transverse velocities

Abstract

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 ${\Omega }_{\mathrm{p}}=(41\pm 3)\mathrm{km}{\mathrm{s}}^{-1}\mathrm{kp}{\mathrm{c}}^{-1}$ (where the error is statistical). This puts the corotation radius at $(5.7\pm 0.4)\mathrm{kpc}$, under the assumptions of the standard peculiar motion of the Sun and the absence of non-axisymmetric streaming in the Solar neighbourhood. The obtained result uses only data on the near-side of the bar which produces consistent measurements of the distance and velocity of the centre of the Galaxy. Addition of the data on the far-side of the bar pulls the pattern speed down to ${\Omega }_{\mathrm{p}}=(31\pm 1)\mathrm{km}{\mathrm{s}}^{-1}\mathrm{kp}{\mathrm{c}}^{-1}$ but requires a lower transverse velocity for the Galactic centre than observed. This suggests systematics of $5-10\mathrm{km}{\mathrm{s}}^{-1}\mathrm{kp}{\mathrm{c}}^{-1}$ dominate the uncertainty. We demonstrate using a dynamically-formed bar/bulge simulation that even with the limited field of view of the VVV survey our method robustly recovers the pattern speed.

13 pages, 10 figures, updated to match MNRAS accepted version (new appendices on 1. generalising estimators to account for Sun's height above the plane and 2. validating choice of luminosity function)

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