2015ApJ...812...49H

Radio relics detected in the outskirts of galaxy clusters are thought to trace radio-emitting relativistic electrons accelerated at cosmological shocks. In this study, using the cosmological hydrodynamic simulation data for the large-scale structure formation and adopting a diffusive shock acceleration (DSA) model for the production of cosmic-ray (CR) electrons, we construct mock radio and X-ray maps of simulated galaxy clusters that are projected in the sky plane. Various properties of shocks and radio relics, including the shock Mach number, radio spectral index, and luminosity, are extracted from the synthetic maps and compared with observations. A substantial fraction of radio and X-ray shocks identified in these maps involve multiple shock surfaces along lines of sight (LOSs), and the morphology of shock distributions in the maps depends on the projection direction. Among multiple shocks in a given LOS, radio observations tend to pick up stronger shocks with flatter radio spectra, while X-ray observations preferentially select weaker shocks with larger kinetic energy flux. As a result, in some cases the shock Mach numbers and locations derived from radio and X-ray observations could differ from each other. We also find that the distributions of the spectral index and radio power of the synthetic radio relics are somewhat inconsistent with those of observed real relics; a bit more radio relics have been observed closer to the cluster core and with steeper spectral indices. We suggest that the inconsistency could be explained if very weak shocks with M_s≲ 2 accelerate CR electrons more efficiently, compared with the DSA model adopted here.