Properties of cosmic shock waves in large-scale structure formation

We have examined the properties of shock waves in simulations of large-scale structure formation. Two cosmological scenarios have been considered: a standard cold dark matter model with Ω_M = 1 (SCDM), and a cold dark matter model with cosmological constant and Ω_M + Ω_Λ = 1 (ΛCDM) having Ω_Λ = 0.55. Large-scale shocks result from accretion onto sheets, filaments, and knots of mass distribution on a scale of the order of ∼ 5 h^-1 Mpc in both scenarios. Energetic motions, partly residuals of past accretion processes and partly caused by current asymmetric inflow along filaments, end up generating additional shocks. These extend on a scale of the order of ∼ 1 h^-1 Mpc and envelop and penetrate deep inside the clusters. Collisions between substructures inside clusters also form merger shocks. Consequently, the topology of the shocks is very complex and highly connected. During cosmic evolution the comoving shock surface density decreases, reflecting the ongoing structure merger process in both scenarios. Accretion shocks have very high Mach numbers, typically between 10 and a few × 10³, when photoheating of the preshock gas is not included. The characteristic shock velocity is of the order of v_sh(z) = H(z)λ_nl(z), where λ_nl(z) is the wavelength scale of the nonlinear perturbation at the given epoch. However, the Mach number for merger and flow shocks (which occur within clusters) is usually smaller, in the range of ∼ 3-10, corresponding to the fact that the intracluster gas is hot (i.e., already shock heated). Statistical fits of shock velocities around clusters as a function of cluster temperature give power-law functions in accord with those predicted by one-dimensional solutions. On the other hand, a very different result is obtained for the shock radius, reflecting extremely complex shock structures surrounding clusters of galaxies in three-dimensional simulations. The amount of inflowing kinetic energy across the shocks around clusters, which represents the power available for cosmic-ray acceleration, is comparable to the cluster X-ray luminosity emitted from a central region of radius 0.5 h^-1 Mpc. Considering their large size and long lifetimes, those shocks are potentially interesting sites for cosmic-ray acceleration, if modest magnetic fields exist within them.