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 galaxy. 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 3-dimensional magneto-hydrodynamical simulations of the passage of a radio plasma cocoon 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 radio maps in Stokes I-, Q-, and U-polarisation. On contact with the shock wave the radio cocoons are first compressed and finally torn into filamentary structures, as is indeed observed in cluster radio relics. In the synthetic radio maps the electric polarisation 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 exhibit such toroidal geometries. This can be regarded as a strong indication that cluster radio relics are indeed 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. We show how this ratio, in combination with independent estimates of the shock strength estimates based on X-ray observations, might lead to a measurement of the unknown equation of state of radio plasma. Finally, we argue that the total radio polarisation of a radio relic can be used to infer the 3-dimensional orientation of the shock wave that produced the relic.