Efficiency of Nonlinear Particle Acceleration at Cosmic Structure Shocks

We have calculated the evolution of cosmic ray (CR) modified astrophysicalshocks for a wide range of shock Mach numbers and shock speeds throughnumerical simulations of diffusive shock acceleration (DSA) in 1D quasi-parallel plane shocks. The simulations include thermal leakage injection ofseed CRs, as well as pre-existing, upstream CR populations. Bohm-like diffusionis assumed. We model shocks similar to those expected around cosmic structurepancakes as well as other accretion shocks driven by flows with upstream gastemperatures in the range $T_0=10^4-10^{7.6}$K and shock Mach numbers spanning$M_s=2.4-133$. We show that CR modified shocks evolve to time-asymptotic statesby the time injected particles are accelerated to moderately relativisticenergies ($p/mc \gsim 1$), and that two shocks with the same Mach number, butwith different shock speeds, evolve qualitatively similarly when the resultsare presented in terms of a characteristic diffusion length and diffusion time.For these models the time asymptotic value for the CR acceleration efficiencyis controlled mainly by shock Mach number. The modeled high Mach number shocksall evolve towards efficiencies $\sim 50$%, regardless of the upstream CRpressure. On the other hand, the upstream CR pressure increases the overall CRenergy in moderate strength shocks ($M_s \sim {\rm a few}$). (abridged)Comment: 23 pages, 12 ps figures, accepted for Astrophysical Journal (Feb. 10, 2005