The formation and evolution of M31 are closely related to its dynamical structures, which remain unclear due to its high inclination. Gas kinematics could provide crucial evidence for the existence of a rotating bar in M31. Using position-velocity diagrams of [OIII] and HI, we identify sharp velocity jumps (shocks) exceeding 100 km/s in the central region (4.6 kpc x 2.3 kpc, or 20' x 10'). These shock features, consistent between [OIII] and HI, are found mainly on the leading side of the bar/bulge, following a hallmark pattern expected from the bar-driven gas inflow.
We further construct a series of gas dynamical models based on barred M31 potentials, and provide constraints on the bar pattern speed by fitting shock features. For a fixed gas disk inclination of i = 77, a low pattern speed of 16-20 km/s/kpc is required to reproduce observed shock positions and amplitudes, as higher pattern speed models place shocks too close to the bar axis. 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 have a lower central inclination similar to the HI and ionized gas observations, gas models with a pattern speed of 38 km/s/kpc, which is consistent with stellar-dynamical models, can match both the shock features and the central gas features.
Radiation transfer simulations based on multi-phase gas models reproduce the observed spectral energy distribution well. An X-shaped residual pattern appears in both the mock and observed 3.6 um images, further supporting the presence of a bar in M31.