Wiggle Instability of Galactic Spiral Shocks: Effects of Magnetic Fields

It has been suggested that the wiggle instability (WI) of spiral shocks in a galactic disk is responsible for the formation of gaseous feathers observed in grand-design spiral galaxies. We perform both a linear stability analysis and numerical simulations to investigate the effect of magnetic fields on the WI. The disk is assumed to be infinitesimally-thin, isothermal, and non-self-gravitating. We control the strengths of magnetic fields and spiral-arm forcing using the dimensionless parameters $\beta$ and $\mathcal{F}$, respectively. By solving the perturbation equations as a boundary-eigenvalue problem, we obtain dispersion relations of the WI for various values of $\beta=1-\infty$ and $\mathcal{F}=5\%$ and $10\%$. We find that the WI arising from the accumulation of potential vorticity at disturbed shocks is suppressed, albeit not completely, by magnetic fields. The stabilizing effect of magnetic fields is not from the perturbed fields but from the unperturbed fields that reduce the density compression factor in the background shocks. When $\mathcal{F}=5\%$ and $\beta\lesssim 10$ or $\mathcal{F}=10\%$ and $\beta\sim5-10$, the most unstable mode has a wavelength of $\sim0.1-0.2$ times the arm-to-arm separation, which appears consistent with a mean spacing of observed feathers.