The stability of cosmic-ray-dominated shocks: A secondary instability

Previous studies in one spatial dimension showed that the precursors of cosmic-ray - dominated shocks are unstable against traveling acoustic disturbances. Here we report that a secondary, Rayleigh-Taylor type instability can exist in cosmic-ray - dominated media influenced by the acoustic instability. Using the local WKB approximation, the growth rate of the secondary instability is shown to be comparable to that of the one-dimensional acoustic instability itself in the cases we have considered. The nonlinear development has been followed numerically with a two-dimensional PPM hydrodynamics code that also incorporates the two-fluid cosmic-ray energy equation. We show that the secondary instability may cause the precursor and postshock flows to become highly turbulent. However, neither the primary, one-dimensional acoustic instability nor the secondary instability has a significant effect on the cosmic-ray pressure around the shock. That is because cosmic ray diffusion through the perturbations is much faster than the growth rate of the instability. An examination of the conditions necessary to lead such shocks to become unstable in the above fashion leads us to conclude that it is likely when astrophysical shocks become CR-dominated that they will become effective amplifiers of preexisting hydrodynamical turbulence.