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We investigate whether the drag instability, proposed by Gu et al., occurs ina one-dimensional (1D) C-shock. The 1D background model proposed by Chen andOstriker for a steady isothermal C-shock is adopted, and a 1D isothermal linearanalysis is performed. We confirm the postulation of Gu et al. that the driftvelocity between the ions and the neutrals is sufficiently high within aC-shock to allow for the drag instability. We also study the underlying physicsof the decaying modes in the shock and post-shock regions. The drag instabilityis an overstability phenomenon associated with an exponentially growing mode ofa propagating wave. We find that the growing wave mode can only propagatedownstream within the shock and subsequently decay in the post-shock region.The maximum total growth (MTG) for such an unstable wave before it is damped isestimated in typical environments of star-forming clouds, which isapproximately 10-30 times larger than the initial perturbation at the modestshock velocities and can be significantly enhanced several hundred times for astronger C-shock with a larger width.

The Drag Instability in a 1D Isothermal C-Shock