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Shock waves in Eulerian cosmological simulations: main properties and acceleration of cosmic rays

Large-scale shocks are responsible for the heating of the intracluster medium and can be important sources of cosmic rays (CRs) in the Universe. However, the occurrence and properties of these shocks are still poorly constrained from both a theoretical and an observational side.



In this work we analyse the properties of large-scale shocks in a (103 Mpc h−1)3 cosmological volume simulated with the public 1.0.1 release of the enzo code. Different methods to identify and characterize shocks in post-processing are discussed together with their uncertainties. Re-ionization affects the properties of shocks in simulations, and we propose a fitting procedure to model accurately the effect of re-ionization in non-radiative simulations, with a post-processing procedure. We investigate the properties of shocks in our simulations by means of a procedure which uses jumps in the velocity variables across the cells in the simulations and this allows us to have a viable description of shocks also in relatively underdense cosmic regions. In particular we derive the distributions of the number of shocks and of the energy dissipated at these shocks as a function of their Mach number, and discuss the evolution of these distributions with cosmological time and across different cosmic environments (clusters, outskirts, filaments, voids).



In line with previous numerical studies relatively weak shocks are found to dominate the process of energy dissipation in the simulated cosmic volume, although we find a larger ratio between weak and strong shocks with respect to previous studies. The bulk of energy is dissipated at shocks with Mach number M≈ 2 and the fraction of strong shocks decreases with increasing the density of the cosmic environments, in agreement with semi-analytical studies in the case of galaxy clusters.



We estimate the rate of injection of CR at large-scale shocks by adopting injection efficiencies taken from previous numerical calculations. The bulk of the energy is dissipated in galaxy clusters and in filaments and the flux dissipated in the form of CR within the whole simulated volume at the present epoch is ≈0.2 of the thermal energy dissipated at shocks; this fraction is smaller within galaxy clusters.



Finally, we discuss the properties of shocks in galaxy clusters in relation with their dynamical state. In these regions the bulk of the energy is dissipated at weak shocks, with Mach number ≈1.5, although slightly stronger shocks are found in the external regions of merging clusters.