The patchiness of radio relics

Abstract

Famous radio relics have been observed to be very patchy up to 19 GHz and very smooth at lower frequencies. We focus on studying reasonable conditions under which this trend can be theoretically reproduced. We performed three-dimensional magnetohydrodynamical simulations of merger shock waves propagating through a turbulent magnetized intracluster medium and use on-the-fly Lagrangian particles to study the differences in radio substructure observed at high and low frequencies. We use two cosmic-ray electron acceleration models: fresh injection (electrons from the thermal pool) and re-acceleration (mildly relativistic electrons). We show that the higher the frequency, the larger the degree of patchiness. Nevertheless, if radio relics are patchy at very high frequencies (e.g. 18.6 GHz), they necessarily also are at lower frequencies (e.g. 150 MHz). Therefore, we demonstrate that under simple modelling, neither the fresh injection model nor the re-acceleration model can reproduce the observed discrepancies between very low and high frequencies.