Instability of Radiative and C-Type MHD Shock Waves

Radiative shocks with a cooling law Lambda ~ rho^2T^alpha can be subject to a global thermal instability which drives a periodic oscillation of the shock front. The stabilizing effect of a transverse magnetic field is examined. The two dimensionless parameters determining the stability of the system are alpha and the Alfven Mach number M_A. The stable and unstable regions of this two-dimensional parameter space are determined through linear analysis. For alpha > 0 even a relatively weak magnetic field (M_A < 8) can stabilize against all modes. The results are confirmed by means of numerical simulations. The simulations show saturation or secondary shock formation in the non-linear regime. Radiative shocks with v_{s } _sp{~}< 160km s^{-1} radiative shocks in the "warm ISM" may be magnetically stabilized. In higher density gas, however, the magnetic field is not strong enough to appreciably affect the shock stability. Next the dynamics of C-type MHD shocks in the partially ionized ISM are studied in the two-fluid approximation by an explicitly flux conserving two-dimensional Eulerian FCT code. A numerical instability intrinsic to two-fluid problems is discovered, and a fix to the problem is proposed. The code can successfully simulate a rippling instability of the shock front discovered by Wardle through linear analysis. Numerical simulations are presented to find the wave vector vec k_max and the growth rate s_max of the fastest growing modes. For perpendicular shocks the analytic calculations are confirmed, while for oblique shocks k_ {|} equiv k cos phi_k, the component of the wave vector lying in the plane of the magnetic field and the shock normal, is found to be the critical parameter determining s_max. The phi_max angle is only weakly constrained. These results confirm and generalize the predictions of the linear analysis. The simulation of a weak perpendicular shock shows that saturation of the Wardle-instability occurs only when the density perturbations reach an amplitude comparable to the total density jump through the shock front. The simulations show a strong transient amplification of the initial perturbations, thus to some extent the amplitude and spectrum of the seed perturbations in the ambient ISM will contribute to the selection of the dominant growing mode.