The Drag Instability in a 1D Isothermal C-shock

We investigate whether the drag instability, proposed by Gu et al., occurs in a one-dimensional (1D) C-shock. The 1D background model proposed by Chen and Ostriker for a steady isothermal C-shock is adopted, and a 1D isothermal linear analysis is performed. We confirm the postulation of Gu et al. that the drift velocity between the ions and the neutrals is sufficiently high within a C-shock to allow for the drag instability. We also study the underlying physics of the decaying modes in the shock and post-shock regions. The drag instability is an overstability phenomenon associated with an exponentially growing mode of a propagating wave. We find that the growing wave mode can only propagate downstream 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 is estimated in typical environments of star-forming clouds, which is approximately 10-30 times larger than the initial perturbation at the modest shock velocities and can be significantly enhanced several hundred times for a stronger C-shock with a larger width.