On the formation of cluster radio relics

In several merging clusters of galaxies so-called cluster radio relics have been observed. These are extended radio sources which do not seem to be associated with any radio galaxies. Two competing physical mechanisms to accelerate the radio-emitting electrons have been proposed: (i) diffusive shock acceleration and (ii) adiabatic compression of fossil radio plasma by merger shock waves. Here the second scenario is investigated. We present detailed three-dimensional magneto-hydrodynamical simulations of the passage of a radio plasma cocoon filled with turbulent magnetic fields through a shock wave. Taking into account synchrotron, inverse Compton and adiabatic energy losses and gains, we evolved the relativistic electron population to produce synthetic polarization radio maps. On contact with the shock wave the radio cocoons are first compressed and finally torn into filamentary structures, as is observed in several cluster radio relics. In the synthetic radio maps the electric polarization vectors are mostly perpendicular to the filamentary radio structures. If the magnetic field inside the cocoon is not too strong, the initially spherical radio cocoon is transformed into a torus after the passage of the shock wave. Very recent, high-resolution radio maps of cluster radio relics seem to exhibit such toroidal geometries in some cases. This supports the hypothesis that cluster radio relics are fossil radio cocoons that have been revived by a shock wave. For a late-stage relic the ratio of its global diameter to the filament diameter should correlate with the shock strength. Finally, we argue that the total radio polarization of a radio relic should be well correlated with the three-dimensional orientation of the shock wave that produced the relic.