# The pattern speed of the Milky Way bar from transverse velocities

## TL;DR

This paper introduces a new method to measure the Milky Way's bar pattern speed using proper motion data, providing a more direct and assumption-minimal approach, and applies it to Gaia and VVV data to obtain consistent results.

## Contribution

The paper develops a novel method based on the continuity equation for measuring the bar's pattern speed from proper motions, with minimal assumptions and demonstrated robustness.

## Key findings

- Measured pattern speed as 41±3 km/s/kpc using near-side data.
- Including far-side data lowers the pattern speed estimate to 31±1 km/s/kpc.
- Method robustly recovers pattern speed in simulated bar/bulge models.

## 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 $\Omega_\mathrm{p}=(41\pm 3)\,\mathrm{km\,s^{-1}\,kpc^{-1}}$ (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. 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.