Diffusive shock acceleration simulations of radio relics

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.