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The Herschel Gould Belt Survey showed that stars form in dense filaments innearby molecular clouds. Recent studies suggest that massive filaments arebound by the slow shocks caused by accretion flows onto the filaments. The slowshock is known to be unstable to the corrugation deformation of the shockfront. The corrugation instability could convert the accretion flow's rampressure into turbulent pressure that influences the width of the filament,which, according to theory, determines the self-gravitational fragmentationscale and core mass. In spite of its importance, the effect of slow shockinstability on star-forming filaments has not been investigated. In addition,the linear dispersion relation obtained from the ideal magnetohydrodynamics(MHD) analysis shows that the most unstable wavelength of shock corrugation isinfinitesimally small (or mean free path). In the scale of dense filaments, theeffect of ambipolar diffusion can suppress the instability at small scales.This study investigates the influence of ambipolar diffusion on the instabilityof the slow shock. We perform two-dimensional MHD simulations to examine thelinear growth of the slow shock instability, considering the effect ofambipolar diffusion. The results demonstrate that the most unstable scale ofslow shock instability is approximately five times the length scale ofambipolar diffusion l_AD calculated using post-shock variables, where, l_ADcorresponds to the scale where the magnetic Reynolds number for ambipolardiffusivity is unity.

Growth of Massive Molecular Cloud Filament by Accretion Flows I: Slow Shock Instability v.s. Ambipolar Diffusion