Bar-driven Gas Dynamics of M31

The large-scale gaseous shocks in the bulge of M31 can be naturally explained by a rotating stellar bar. We use gas dynamical models to provide an independent measurement of the bar pattern speed in M31. The gravitational potentials of our simulations are from a set of made-to-measure models constrained by stellar photometry and kinematics. If the inclination of the gas disk is fixed at $i = 77^{\circ}$, we find that a low pattern speed of $16-20\;\rm km\;s^{-1}\;kpc^{-1}$ is needed to match the observed position and amplitude of the shock features, as shock positions are too close to the bar major axis in high $\Omega_{b}$ models. The pattern speed can increase to $20-30\;\rm km\;s^{-1}\;kpc^{-1}$ if the inner gas disk has a slightly smaller inclination angle compared with the outer one. Including sub-grid physics such as star formation and stellar feedback has minor effects on the shock amplitude, and does not change the shock position significantly. If the inner gas disk is allowed to follow a varying inclination similar to the HI and ionized gas observations, the gas models with a pattern speed of $38\;\rm km\;s^{-1}\;kpc^{-1}$, which is consistent with stellar-dynamical models, can match both the shock features and the central gas features.