Nature of the Wiggle Instability of Galactic Spiral Shocks
  Gas in disk galaxies interacts nonlinearly with an underlying stellar spiral
potential to form galactic spiral shocks. While numerical simulations typically
show that spiral shocks are unstable to wiggle instability (WI) even in the
absence of magnetic fields and self-gravity, its physical nature has remained
uncertain. To clarify the mechanism behind the WI, we conduct a normal-mode
linear stability analysis as well as nonlinear simulations assuming that the
disk is isothermal and infinitesimally thin. We find that the WI is physical,
originating from the generation of potential vorticity at a deformed shock
front, rather than Kelvin-Helmholtz instabilities as previously thought. Since
gas in galaxy rotation periodically passes through the shocks multiple times,
the potential vorticity can accumulate successively, setting up a normal mode
that grows exponentially with time. Eigenfunctions of the WI decay
exponentially downstream from the shock front. Both shock compression of
acoustic waves and a discontinuity of shear across the shock stabilize the WI.
The wavelength and growth time of the WI depend on the arm strength quite
sensitively. When the stellar-arm forcing is moderate at 5%, the wavelength of
the most unstable mode is about 0.07 times the arm-to-arm spacing, with the
growth rate comparable to the orbital angular frequency, which is found to be
in good agreement with the results of numerical simulations.
