2021MNRAS.507.2714D

Radio relics are diffuse radio sources in galaxy clusters that are associated with merger shock waves. Detailed observations of radio relics in total intensity and in polarization show complex structures on kiloparsec scales. The relation between the observed features and the underlying morphology of the magnetic field is not clear. Using 3D magneto-hydrodynamical simulations, we study the polarized emission produced by a shock wave that propagates through a turbulent medium that resembles the intracluster medium. We model the polarized synchrotron emission on the basis of diffusive shock acceleration of cosmic ray electrons. We find that the synchrotron emission produced in a shocked turbulent medium can reproduce some of the observed features in radio relics. Shock compression can give rise to a high polarization fraction at the shock front and a partial alignment of the polarization E-vectors with the shock normal. Our work confirms that radio relics can also be formed in an environment with a tangled magnetic field. We also discuss the effect of Faraday rotation intrinsic to the source, and how our results depend on the angular resolution of observations.