We introduce a method of identifying evidence of shocks in the X-ray emitting gas in clusters of galaxies. Using information from synthetic observations of simulated clusters, we do a blind search of the synthetic image plane. The locations of likely shocks found using this method closely match those of shocks identified in the simulation hydrodynamic data. Though this method assumes nothing about the geometry of the shocks, the general distribution of shocks as a function of Mach number in the cluster hydrodynamic data can be extracted via this method. Characterization of the cluster shock distribution is critical to understanding production of cosmic rays in clusters and the use of shocks as dynamical tracers.

I briefly review the current theoretical status of the origins of ultrahigh energy cosmic rays with special emphasis on models associated with galaxy clusters. Some basic constraints on models are laid out, including those that apply both to so-called 'top-down' and 'bottom-up' models. The origins of these UHECRs remain an enigma; no model stands out as a clear favorite. Large scale structure formation shocks, while very attractive conceptually in this context, are unlikely to be able to accelerate particles to energies much above 1018eV. Terminal shocks in relativistic AGN jets seem to be more viable candidates physically, but suffer from their rarity in the local universe. Several other, representative, models are outlined for comparison.

Cosmological shocks form as an inevitable consequence of gravitational collapse during the large scale structure formation and cosmic-rays (CRs) are known to be accelerated at collisionless shocks via diffusive shock acceleration (DSA). We have calculated the evolution of CR modified shocks for a wide range of shock Mach numbers and shock speeds through numerical simulations of DSA in 1D quasi-parallel plane shocks. The simulations include thermal leakage injection of seed CRs, as well as pre-existing, upstream CR populations. Bohm-like diffusion is assumed. We show that CR modified shocks evolve to time-asymptotic states by the time injected particles are accelerated to moderately relativistic energies (p/mc ≳ 1), 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 CR acceleration efficiency increases with shock Mach number, but it asymptotes to ~50% in high Mach number shocks, regardless of the injection rate and upstream CR pressure. On the other hand, in moderate strength shocks (Ms ≲ 5), the pre-existing CRs increase the overall CR energy. We conclude that the CR acceleration at cosmological shocks is efficient enough to lead to significant nonlinear modifications to the shock structures.

Cosmological hydrodynamic simulations of large scale structure in the universe have shown that accretion shocks and merger shocks form due to flow motions associated with the gravitational collapse of nonlinear structures. Estimated speed and curvature radius of these shocks could be as large as a few 1000 km/s and several Mpc, respectively. According to the diffusive shock acceleration theory, populations of cosmic-ray particles can be injected and accelerated to very high energy by astrophysical shocks in tenuous plasmas. In order to explore the cosmic ray acceleration at the cosmic shocks, we have performed nonlinear numerical simulations of cosmic ray (CR) modified shocks with the newly developed CRASH (Cosmic Ray Amr SHock) numerical code. We adopted the Bohm diffusion model for CRs, based on the hypothesis that strong Alfven waves are self-generated by streaming CRs. The shock formation simulation 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, CRs can absorb most of shock kinetic energy and the accretion shock speed is reduced up to 20%, compared to pure gas dynamic shocks. For merger shocks with small Mach numbers, however, the energy transfer to CRs is only about 10-20% with an associated CR particle fraction of 10-3. Nonlinear feedback due to the CR pressure is insignificant in the latter shocks. Although detailed results depend on models for the particle diffusion and injection, these calculations show that cosmic shocks in large scale structure could provide acceleration sites of extragalactic cosmic rays of the highest energy.

Compressible, magnetohydrodynamic (MHD) turbulence in two dimension is studied through high-resolution, numerical simulations with the isothermal equation of state. First, hydrodynamic turbulence with Mach number (M)rms ~ 1 is generated by enforcing a random force. Next, initial, uniform magnetic field of various strengths with Alfvenic Mach number Ma ≫ 1 is added. Then, the simulations are followed until MHD turbulence is fully developed. Such turbulence is expected to exist in a variety of astrophysical environments including clusters of galaxies. Although no dissipation is included explicitly in our simulations, truncation errors produce dissipation which induces numerical resistivity. It mimics a hyper-resistivity in our second-order accurate code. After saturation, the resulting flows are categorized as SF (strong field), WF (weak field), and VWF (very weak field) classes respectively, depending on the average magnetic field strength described with Alfvenic Mach number, (Ma)rms ~1, (Ma)rms≥1, and (Ma)rms ≫ 1. The characteristics of each class are discussed.

Cosmic-ray acceleration, although physically important in many astrophysical contexts, is difficult to incorporate into numerical models,. because it involves microphysics that is generally far from thermodynamic equilibrium, and also because the length and time scales for that physics typically range over many orders of magnitude, reflecting the huge range of particle rigidities that must be represented. The most common accelerator models are stochastic in nature and involve nonequilibrium plasma properties that are also often poorly understood. Still, nature clearly finds a way to produce simple, robust and almost scale-free energy distributions for the cosmic-rays. Their importance has inspired a number of approaches to examining the production and transport of cosmic-ray particles in numerical simulations. I offer here a brief comparison of some of the methods that have been introduced.

Rarefied cosmic plasmas generally do not achieve thermodynamic equilibria, and a natural consequence of this is the presence of a significant population of charged particles with energies well above those of the bulk population. These are exemplified by the galactic cosmic rays, but the importance of these high energy populations extends well beyond that context. I review here some of the basic issues associated with the propagation and acceleration of cosmic rays, especially in the context of collisionless plasma shocks.