We study the properties of cosmological shock waves identified in high-resolution, N-body/hydrodynamic simulations of a ÃCDM universe and their role on thermalization of gas and acceleration of nonthermal, cosmic-ray (CR) particles. External shocks form around sheets, filaments, and knots of mass distribution when the gas in void regions accretes onto them. Within those nonlinear structures, internal shocks are produced by infall of previously shocked gas to filaments and knots and during subclump mergers, as well as by chaotic flow motions. Due to the low temperature of the accreting gas, the Mach number of external shocks is high, extending up to M $ 100 or higher. In contrast, internal shocks have mostly low Mach numbers. For all shocks of M ! 1:5, the mean distance between shock surfaces over the entire computed volume is $4 h À1 Mpc at present, or $1 h À1 Mpc for internal shocks within nonlinear structures. Identified external shocks are more extensive, with their surface area $2 times larger than that of identified internal shocks at present. However, especially because of higher preshock densities but also due to higher shock speeds, internal shocks dissipate more energy. Hence, the internal shocks are mainly responsible for gas thermalization as well as CR acceleration. In fact, internal shocks with 2dMd4 contribute about one-half of the total dissipation. Using a nonlinear diffusive shock acceleration model for CR protons, we estimate the ratio of CR energy to gas thermal energy dissipated at cosmological shock waves to be about one-half through the history of the universe. Our result supports scenarios in which the intracluster medium contains energetically significant populations of CRs. Subject headings: large-scale structure of universe -methods: numerical -shock waves

The nature and origin of turbulence and magnetic fields in the intergalactic space are important problems that are yet to be understood. We propose a scenario in which turbulent-flow motions are induced via the cascade of the vorticity generated at cosmological shocks during the formation of the large-scale structure. The turbulence in turn amplifies weak seed magnetic fields of any origin. Supercomputer simulations show that the turbulence is subsonic inside clusters and groups of galaxies, whereas it is transonic or mildly supersonic in filaments. Based on a turbulence dynamo model, we then estimated that the average magnetic field strength would be a few microgauss (microG) inside clusters and groups, approximately 0.1 muG around clusters and groups, and approximately 10 nanogauss in filaments. Our model presents a physical mechanism that transfers the gravitational energy to the turbulence and magnetic field energies in the large-scale structure of the universe.