Wiggle Instability of Magnetized Spiral Shocks

Galactic spiral arms are abundant with interesting gaseous substructures. It has been suggested that arm substructures arise from the wiggle instability (WI) of spiral shocks. While the nature of the WI remained elusive, our recent work without considering magnetic fields shows that the WI is physically originated from the accumulation of potential vorticity (PV) generated by deformed shock fronts. To elucidate the characteristics of the WI in more realistic galactic situations, we extend our previous linear stability analysis of spiral shocks by including magnetic fields. We find that magnetic fields reduce the amount of density compression at shocks, making the shock fronts to move toward the upstream direction. Magnetic tension forces from bent field lines stabilize the WI by prevent the generation of PV. When the spiral-arm forcing is F=5% of the centrifugal force of galaxy rotation, the maximum growth rate of the WI is found to be about 1.0, 0.4, and 0.2 times the orbital angular frequency for the plasma parameter ${\beta}=100$, 10, and 5, respectively. Shocks with ${\beta}=1$ are stable to the WI for F=5%, while becoming still unstable when F=10%.