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

The Herschel Gould Belt Survey showed that stars form in dense filaments in nearby molecular clouds. Recent studies suggest that massive filaments are bound by the slow shocks caused by accretion flows onto the filaments. The slow shock is known to be unstable to the corrugation deformation of the shock front. The corrugation instability could convert the accretion flow's ram pressure into turbulent pressure that influences the width of the filament, which, according to theory, determines the self-gravitational fragmentation scale and core mass. In spite of its importance, the effect of slow shock instability 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 is infinitesimally small (or mean free path). In the scale of dense filaments, the effect of ambipolar diffusion can suppress the instability at small scales. This study investigates the influence of ambipolar diffusion on the instability of the slow shock. We perform two-dimensional MHD simulations to examine the linear growth of the slow shock instability, considering the effect of ambipolar diffusion. The results demonstrate that the most unstable scale of slow shock instability is approximately five times the length scale of ambipolar diffusion l_AD calculated using post-shock variables, where, l_AD corresponds to the scale where the magnetic Reynolds number for ambipolar diffusivity is unity.