Oblique magnetohydrodynamic cosmic-ray-modified shocks: Two-fluid numerical simulations

We present the first results of time-dependent two-fluid cosmic-ray (CR) modified magnetohydrodynamic (MHD) shock simulations. The calculations were carried out with a new numerical code for one-dimensional ideal MHD. By coupling this code with the CR energy transport equation we can simulate the time-dependent evolution of MHD shocks, including the acceleration of the CR and their feedback on the shock structures. We report tests of the combined numerical method including comparisons with analytical steady state results published earlier by Webb, as well as internal consistency checks for more general MHD CR shock structures after they apppear to have converged to dynamical steady states. We also present results from an initial time-dependent simulation which extends the parameter space domain of previous analytical models. These new results support Webb's suggestion that equilibrium oblique shocks are less effective than parallel shocks in the acceleration of CR. However, for realistic models of anisotropic CR diffusion, oblique shocks may achieve dynamical equilibrium on shorter timescales than parallel shocks.