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 \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 s ^ { -1 } kpc ^ { -1 } } but requires a lower transverse velocity for the Galactic centre than observed .
This suggests systematics of 5 - 10 \mathrm { km s ^ { -1 } kpc ^ { -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 .