Using double radio relics to constrain galaxy cluster mergers: a model of double radio relics in CIZA J2242.8+5301

Galaxy clusters grow by mergers with other clusters and galaxy groups. These mergers create shock waves within the intracluster medium (ICM) that can accelerate particles to extreme energies. In the presence of magnetic fields, relativistic electrons form large regions emitting synchrotron radiation, the so-called radio relics. Behind the shock front, synchrotron and inverse Compton losses cause the radio spectral index to steepen away from the shock front. In a binary cluster merger, two shock waves are generated which move diametrically outwards along the merger axis. Two radio relics can then form on both sides of the cluster centre. An example of such a cluster is CIZA J2242.8+5301, where very clear spectral steepening in the downstream region is observed. The main relic has a total extent of 1700 kpc, while its width is only 55 kpc. Together with the high observed polarization fraction, this implies that the relic is seen very close to edge-on which makes it easier to constrain the merger geometry. Here we present hydrodynamical simulations of idealized binary cluster mergers with the aim of constraining the merger scenario for this cluster. From our simulations, we find that CIZA J2242.8+5301 is probably undergoing a merger in the plane of the sky (less than 10 degrees from edge-on) with a mass ratio (M1:M2) of about 2:1, and an impact parameter 400 kpc. We find that the core passage of the clusters happened about 1 Gyr ago. We conclude that double relics can set constraints on the mass ratios, impact parameters, time-scales and viewing geometry of binary cluster mergers, which is particularly useful when detailed X-ray observations are not available. In addition, the presence of large radio relics can be used to constrain the degree of clumping in the outskirts of the ICM, which is important to constrain the baryon fraction, density and entropy profiles, around the virial radius and beyond. We find that the amplitude of density fluctuations, with sizes of 200 kpc, in the relic in CIZA J2242.8+5301 is not larger than 30 per cent.