Revealing the drag instability in one-fluid nonideal MHD simulations of a 1D isothermal C-shock

TL;DR

This study confirms the presence of drag instability in 1D non-ideal MHD simulations of isothermal C-shocks, demonstrating growth, damping, and nonlinear saturation consistent with linear theory predictions.

Contribution

First numerical confirmation of drag instability in 1D non-ideal MHD simulations of C-shocks, linking linear theory with nonlinear behavior in star-forming cloud environments.

Findings

Perturbations grow within the shock region and match linear mode profiles.

Growth rates and wave frequencies agree with linear analysis.

Nonlinear wave steepening leads to saturation of the instability.

Abstract

C-type shocks are believed to be ubiquitous in turbulent molecular clouds thanks to ambipolar diffusion. We investigate whether the drag instability in 1D isothermal C-shocks, inferred from the local linear theory of Gu & Chen, can appear in non-ideal magnetohydrodynamic simulations. Two C-shock models (with narrow and broad steady-state shock widths) are considered to represent the typical environment of star-forming clouds. The ionization-recombination equilibrium is adopted for the one-fluid approach. In the 1D simulation, the inflow gas is continuously perturbed by a sinusoidal density fluctuation with a constant frequency. The perturbations clearly grow after entering the C-shock region until they start being damped at the transition to the postshock region. We show that the profiles of a predominant Fourier mode extracted locally from the simulated growing perturbation match those of the growing mode derived from the linear analysis. Moreover, the local growth rate and wave frequency derived from the predominant mode generally agree with those from the linear theory. Therefore, we confirm the presence of the drag instability in simulated 1D isothermal C-shocks. We also explore the nonlinear behavior of the instability by imposing larger-amplitude perturbations to the simulation. We find that the drag instability is subject to wave steepening, leading to saturated perturbation growth. Issues concerning local analysis, nonlinear effects, one-fluid approach, and astrophysical applications are discussed.