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

Radio observations prove the existence of relativistic particles and magnetic field associated with the intra-cluster-medium (ICM) through the presence of extended synchrotron emission in the form of radio halos and peripheral relics. This observational evidence has fundamental implications on the physics of the ICM. Non-thermal components in galaxy clusters are indeed unique probes of very energetic processes operating within clusters that drain gravitational and electromagnetic energy into cosmic rays and magnetic fields. These components strongly affect the (micro-)physical properties of the ICM, including viscosity and electrical conductivities, and have also potential consequences on the evolution of clusters themselves. The nature and properties of cosmic rays in galaxy clusters, including the origin of the observed radio emission on cluster-scales, have triggered an active theoretical debate in the last decade. Only recently we can start addressing some of the most important questions in this field, thanks to recent observational advances, both in the radio and at high energies. The properties of cosmic rays and of cluster non-thermal emissions depend on the dynamical state of the ICM, the efficiency of particle acceleration mechanisms in the ICM and on the dynamics of these cosmic rays. In this review we discuss in some detail the acceleration and transport of cosmic rays in galaxy clusters and the most relevant observational milestones that have provided important steps on our understanding of this physics. Finally, looking forward to the possibilities from new generations of observational tools, we focus on what appear to be the most important prospects for the near future from radio and high-energy observations.

We investigate the generation and distribution of high-energy electrons in the cosmic structure environment and their observational consequences by carrying out the Ðrst cosmological simulation that includes directly cosmic-ray (CR) particles. Starting from cosmological initial conditions, in addition to the gas and dark matter related quantities, we follow the evolution of CR electrons (primary and secondary) and CR ions along with a passive magnetic Ðeld. CR ions and primary electrons are injected in accordance with the thermal leakage model and accelerated in the test-particle limit of di †usive shock acceleration at shocks associated with large-scale structure formation. Secondary electrons are continuously generated through p-p inelastic collisions of the CR ions with the thermal nuclei of the intergalactic medium. The evolution of the CR electrons accounts for spatial transport, adiabatic expansion/compression, and losses due to Coulomb collisions, bremsstrahlung, synchrotron and inverseCompton emission. The magnetic Ðeld is seeded at shocks according to the Biermann battery model, and thereafter ampliÐed by shear Ñow and gas compression. We compute the emission due to the inverseCompton scattering of the simulated primary and secondary electrons o † cosmic microwave background photons and compare it with the published values of the detected radiation excesses in the hard X-ray and extreme-ultraviolet wavebands. We Ðnd that the few instances of detection of hard X-ray radiation excess could be explained in the framework of IC emission from primary electrons in clusters characterized by high accretion/merger activity. On the other hand, with the only exception of measured Ñux from the Coma Cluster by Bowyer, Berghoefer & Korpela, both primary and secondary CR electrons associated with the cosmic structure formation account at most for a small fraction of the radiation excess detected in the extreme-ultraviolet waveband. Next, we calculate the synchrotron emission after normalizing the magnetic Ðeld strength so that for a Coma-like cluster the volume-averaged SB2T1@2^3 kG.Our results indicate that the synchrotron emission from the secondary CR electrons reproduces several general properties observed in radio halos. These include the recently found versus relation-P 1.4 GHz T X ship, the morphology and polarization of the emitting region, and, to some extent, even the spectral index. In addition, radio synchrotron emission from primary electrons turns out to be large enough to power extended regions of radio emission, resembling radio relics observed at the outskirts of clusters. Once again we Ðnd a striking resemblance between the general properties of morphology, polarization, and spectral index of our synthetic maps and those of reported in the literature.

Recent radio observations have identified a class of structures, so-called radio relics, in clusters of galaxies. The radio emission from these sources is interpreted as synchrotron radiation from GeV electrons gyrating in μG-level magnetic fields. Radio relics, located mostly in the outskirts of clusters, seem to associate with shock waves, especially those developed during mergers. In fact, they seem to be good structures to identify and probe such shocks in intracluster media (ICMs), provided we understand the electron acceleration and re-acceleration at those shocks. In this paper, we describe time-dependent simulations for diffusive shock acceleration at weak shocks that are expected to be found in ICMs. Freshly injected as well as pre-existing populations of cosmic-ray (CR) electrons are considered, and energy losses via synchrotron and inverse Compton are included. We then compare the synchrotron flux and spectral distributions estimated from the simulations with those in two well-observed radio relics in CIZA J2242.8+5301 and ZwCl0008.8+5215. Considering that CR electron injection is expected to be rather inefficient at weak shocks with Mach number M a few, the existence of radio relics could indicate the pre-existing population of low-energy CR electrons in ICMs. The implication of our results on the merger shock scenario of radio relics is discussed.

A description is given for preserving ∇ · B = 0 in a magnetohydrodynamic (MHD) code that employs the upwind, Total Variation Diminishing (TVD) scheme and the Strang-type operator splitting for multi-dimensionality. The method is based on the staggered mesh technique to constrain the transport of magnetic field: the magnetic field components are defined at grid interfaces with their advective fluxes on grid edges, while other quantities are defined at grid centers. The magnetic field at grid centers for the upwind step is calculated by interpolating the values from grid interfaces. The advective fluxes on grid edges for the magnetic field evolution are calculated from the upwind fluxes at grid interfaces. Then, the magnetic field can be maintained with ∇ · B = 0 exactly, if this is so initially, while the upwind scheme is used for the update of fluid quantities. The correctness of the code is demonstrated through tests comparing numerical solutions either with analytic solutions or with numerical solutions from the code using an explicit divergence-cleaning method. Also the robustness is shown through tests involving realistic astrophysical problems.

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We investigate the production of cosmic ray (CR) protons at cosmological shocks by performing, for the first time, numerical simulations of large scale structure formation that include directly the acceleration, transport and energy losses of the high energy particles. CRs are injected at shocks according to the thermal leakage model and, thereafter, accelerated to a power-law distribution as indicated by the test particle limit of the diffusive shock acceleration theory. The evolution of the CR protons accounts for losses due to adiabatic expansion/compression, Coulomb collisions and inelastic p-p scattering. Our results suggest that CR protons produced at shocks formed in association with the process of large scale structure formation could amount to a substantial fraction of the total pressure in the intra-cluster medium. Their presence should be easily revealed by GLAST through detection of γ-ray flux from the decay of π 0 produced in inelastic p-p collisions of such CR protons with nuclei of the intra-cluster gas. This measurement will allow a direct determination of the CR pressure contribution in the intra-cluster medium. We also find that the spatial distribution of CR is typically more irregular than that of the thermal gas because it is more influenced by the underlying distribution of shocks. This feature is reflected in the appearance of our γ-ray synthetic images. Finally, the average CR pressure distribution appears statistically slightly more extended than the thermal pressure.

A numerical scheme that incorporates a thermal leakage injection model into a combined gasdynamics and cosmic-ray (CR) diffusion-convection code has been developed. The hydro/CR code can follow in a very cost-effective way the evolution of CR-modified planar quasi-parallel shocks by adopting subzone shock tracking and multilevel adaptive mesh refinement techniques. An additional conservative quantity, S ¼ P g = g À1 , is introduced to follow the adiabatic compression accurately in the precursor region, especially in front of strong, highly modified shocks. The '' thermal leakage '' injection model is based on the nonlinear 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 the upstream region according to a velocity-dependent transparency function that controls the fraction of leaking particles. This function is determined by a single parameter, , which should depend on the strength of postshock wave turbulence but is modeled as a constant parameter in our simulations. We have studied CR injection and acceleration efficiencies during the evolution of CR-modified planar shocks for a wide range of initial shock Mach numbers, M 0 , assuming a Bohm-like diffusion coefficient. For expected values of the injection process is very efficient when the subshock is strong, leading to fast and significant modification of the shock structure. As the CR pressure increases, the subshock weakens and the injection rate decreases accordingly so that the subshock does not disappear. Although some fraction of the particles injected early in the evolution continue to be accelerated to ever higher energies, the postshock CR pressure reaches an approximate time-asymptotic value because of a balance between fresh injection/acceleration and advection/diffusion of the CR particles away from the shock. In the strong shock limit of M 0 e30, the injection and acceleration processes are largely independent of the initial shock Mach number for a given , while they are sensitively dependent on M 0 for M 0 < 30. We conclude that the injection rates in strong parallel shocks are sufficient to lead to rapid nonlinear modifications to the shock structures and that self-consistent injection and time-dependent simulations are crucial to understanding the nonlinear evolution of CR-modified shocks.