Shocks are ubiquitous in astrophysical environments and cosmic-rays (CRs) are known to be accelerated at collisionless shocks via diffusive shock acceleration. It is believed that the CR pressure is important in the evolution of the interstellar medium of our galaxy and most of galactic CRs with energies up to ~ 1015 eV are accelerated by supernova remnant shocks. In this contribution we have studied the CR acceleration at shocks through numerical simulation of 1D, quasi-parallel shocks for a wide range of shock Mach numbers and shock speeds. We show that CR modified shocks evolve to time-asymptotic states by the time injected particles are accelerated to moderately relativistic energies, and that two shocks with the same Mach number, but with different shock speeds, evolve qualitatively similarly when the results are presented in terms of a characteristic diffusion length and diffusion time. We find that 10-4 - 10-3 of the particles passed through the shock are accelerated to form the CR population, and the injection rate is higher for shocks with higher Mach number. The time asymptotic value for the CR acceleration efficiency is controlled mainly by shock Mach number, and high Mach number shocks all evolve towards efficiencies ~ 50%, regardless of the injection rate and upstream CR pressure. We conclude that the injection rates in strong quasi-parallel shocks are sufficient to lead to significant nonlinear modifications to the shock structures, implying the importance of the CR acceleration at astrophysical shocks.

In order to explore the cosmic ray acceleration at the cosmological shocks, we have performed numerical simulations of one-dimensional, plane-parallel, cosmic ray (CR) modified shocks with the newly developed CRASH (Cosmic Ray Amr SHock) numerical code. Based on the hypothesis that strong Alfven waves are self-generated by streaming CRs, the Bohm diffusion model for CRs is adopted. The code includes a plasma-physics-based 'injection' model that transfers a small proportion of the thermal proton flux through the shock into low energy CRs for acceleration there. We found that, for strong accretion shocks with Mach numbers greater than 10, CRs can absorb most of shock kinetic energy and the accretion shock speed is reduced up to 20%, compared to pure gas dynamic shocks. Although the amount of kinetic energy passed through accretion shocks is small, since they propagate into the low density intergalactic medium, they might possibly provide acceleration sites for ultra-high energy cosmic rays of E > 10 18eV. For internal/merger shocks with Mach numbers less than 3, however, the energy transfer to CRs is only about 10-20% and so nonlinear feedback due to the CR pressure is insignificant. Considering that intracluster medium (ICM) can be shocked repeatedly, however, the CRs generated by these weak shocks could be sufficient to explain the observed non-thermal signatures from clusters of galaxies.

Nonthermal particles can be produced due to incomplete thermalization at collisionless shocks and further accelerated to very high energies via diffusive shock acceleration. In a previous study we explored the cosmic ray (CR) acceleration at cosmic shocks through numerical simulations of CR modified, quasi-parallel shocks in 1D plane-parallel geometry with the physical parameters relevant for the shocks emerging in the large scale structure formation of the universe (Kang & Jones 2002). Specifically we considered pancake shocks driven by accretion flows with Uo = 1500 km s-l and the preshock gas temperature of To = 10 4 - 10 8K. In order to consider the CR acceleration at shocks with a broader range of physical properties, in this contribution we present additional simulations with accretion flows with Uo = 75 - 1500 km s-l and To = 10 4K. We also compare the new simulation results with those reported in the previous study. For a given Mach number, shocks with higher speeds accelerate CRs faster with a greater number of particles, since the acceleration time scale is tacc ∝ Uo-2. However, two shocks with a same Mach number but with different shock speeds evolve qualitatively similarly when the results are presented in terms of diffusion length and time scales. Therefore, the time asymptotic value for the fraction of shock kinetic energy transferred to CRs is mainly controlled by shock Mach number rather than shock speed. Although the CR acceleration efficiency depends weakly on a well-constrained injection parameter, є, and on shock speed for low shock Mach numbers, the dependence disappears for high shock Mach numbers. We present the 'CR energy ratio', Φ(Ms), for a wide range of shock parameters and for є = 0.2 - 0.3 at terminal time of our simulations. We suggest that these values can be considered as time-asymptotic values for the CR acceleration efficiency, since the time-dependent evolution of CR modified shocks has become approximately self-similar before the terminal time.

A numerical scheme that incorporates a self-consistent cosmic-ray (CR, hereafter) injection model into the combined gas dynamics and CR diffusion-convection code has been developed. The hydro/CR code can follow in a very cos-effective way the evolution of CR modified shocks by adopting subzone shock-tracking and multi-level Adaptive Mesh Refinement techniques. The injection model is based on interactions of the suprathermal particles with self-generated MHD waves in quasi-parallel shocks. The particle injection is followed numerically by filtering the diffusive flux of suprathermal particles across the shock to upstream region according to a velocity-dependent transparency function, which represents the fraction of leaking suprathermal particles. In the strong shock limit of Mach numbers ≥ 20, significant physical processes such as the injection and acceleration seem to become independent of M, while they are sensitively dependent on M for M < 10. Although some particles injected early in the evolution continue to be accelerated to higher energies, the postshock CR pressure reaches a time asymptotic value due to balance between acceleration and diffusion of the CR particles.

In order to explore the time dependence of the closure parameters of the two-fluid calculations for supernova remnants and the terminal shocks of stellar winds, we have considered a simple model in which the time evolution of the cosmic-ray distribution function was followed in the test-particle limit using the Bohm diffusion model. The particles are mostly accelerated to relativistic energy either in the free expansion phase of the SNRs or in the early phase of the stellar winds, so the evolution of the closure parameters during these early stages is substantial and should be followed correctly. We have also calculated the maximum momentum which is limited by either the age or the curvature of these spherical shocks. We found that SNRs expanding into the medium where the gas density decreases with the distance from the explosion center might be necessary to explain the observed power-law distribution of the galactic cosmic rays. The energy loss due to the escaping energetic particles has been estimated for the terminal shocks of the stellar winds.

Most of high energy cosmic rays (CRs) are thought to be produced by diffusive shock acceleration (DSA) at supernova remnants (SNRs) within the Galaxy. Fortunately, nonthermal emissions from CR protons and electrons can provide direct observational evidence for such a model and place strong constraints on the complex nonlinear plasma processes in DSA theory. In this study we calculate the energy spectra of CR protons and electrons in Type Ia SNRs, using time-dependent DSA simulations that incorporate phenomenological models for some wave-particle interactions. We demonstrate that the timedependent evolution of the self-amplified magnetic fields, Alfvénic drift, and escape of the highest energy particles affect the energy spectra of accelerated protons and electrons, and so resulting nonthermal radiation spectrum. Especially, the spectral cutoffs in X-ray and γ-ray emission spectra are regulated by the evolution of the highest energy particles, which are injected at the early phase of SNRs. Thus detailed understandings of nonlinear wave-particle interactions and time-dependent DSA simulations of SNRs are crucial in testing the SNR hypothesis for the origin of Galactic cosmic rays.