Constraining magnetic field strength in radio relics

Abstract

Radio relics are diffuse synchrotron sources generally located in the peripheries of galaxy clusters in merging state. According to the current leading scenario, relics trace gigantic cosmological shock waves that cross the intra-cluster medium where particle acceleration occurs. Under the assumption that particles are accelerated at the shock front and are subsequently deposited and then age downstream of the shock, the magnetic field strength in radio relics can be constrained by measuring the thickness of the relic at different radio frequencies. In this paper we adopt this methodology to the relics in the clusters A 521 and CIZA J2242.8+5301. In these relics we find that a pure radiative aging of electrons downstream is consistent with observations allowing us to constrain the magnetic field strength. These results, together with the lower limits to the magnetic field that we derive from the lack of inverse Compton X-ray emission from the sources, have been combined with Faraday rotation measurements of the Coma cluster to derive a global result. Results suggest that the spatial profile of the magnetic field energy density is broader than that of the thermal gas, implying that the ratio between the thermal and the magnetic field energy densities decreases with cluster radius. Alternatively, radio relics could trace dynamically active regions where the magnetic field strength is increased with respect to the average value in the cluster volume.