TIME-DEPENDENT EVOLUTION OF COSMIC-RAY MODIFIED SHOCK STRUCTURE - TRANSITION TO STEADY-STATE

Steady state solutions to the two-fluid equations of cosmic-ray-modifi ed shock structure were investigated first by Drury and Volk (198 1). Their analysis revealed, among other properties, that there exist regi ons of upstream parameter space where the equations possess three diff erent downstream solutions for a given upstream state. In this paper w e investigate whether or not all these solutions can occur as time-asy mptotic states in a physically realistic evolution. To do this, we inv estigate the time-dependent evolution of the two-fluid cosmic-ray equa tions in going from a specified initial condition to a steady state. O ur results indicate that the time-asymptotic solution is strictly sing le-valued, and it undergoes a transition from weakly to strongly cosmi c-ray-modified at a critical value of the upstream cosmic ray energy d ensity. The expansion of supernova remnant shocks is considered as an example, and it is shown that the strong to weak transition is in fact more likely. The third intermediate solution is shown to influence th e time-dependent evolution of the shock, but it is not found to be a s table time-asymptotic state. Timescales for convergence to these state s and their implications for the efficiency of shock acceleration are considered. We also investigate the effects of a recently introduced m odel for the injection of seed particles into the shock accelerated co smic-ray population. The injection is found to result in a more strong ly cosmic-ray-dominated shock, which supports our conclusion that for most classes of intermediate and strong cosmic-ray-modified shocks, th e downstream cosmic-ray pressure component is at least as large as the thermal gas pressure, independent of the upstream state. As a result, cosmic rays almost always play a significant role in determining the shock structure and dissipation and they cannot be regarded as test pa rticles.