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

Wiggle Instability of Galactic Spiral Shocks: Effects of Magnetic Fields