Relics in galaxy clusters at high radio frequencies

We observed three radio relics in galaxy clusters and one radio relic candidate at 4.85 and 8.35 GHz in total emission and linearly polarized emission with the Effelsberg 100-m telescope and one radio relic candidate in X-rays with the Chandra telescope. The radio spectra of the integrated emission below 8.35 GHz can be well fitted by single power laws for all four relics. The flat spectra (spectral indices of 0.9 and 1.0) for the "Sausage" relic in cluster CIZA J2242+53 and the "Toothbrush" relic in cluster 1RXS 06+42 indicate that models describing the origin of relics have to include effects beyond the assumptions of diffuse shock acceleration. The spectra of the radio relics in ZwCl 0008+52 and in Abell 1612 are steep, as expected from weak shocks (Mach number $\approx 2.4$). We find polarization degrees of more than 50 % in the two prominent Mpc-sized radio relics, the Sausage and the Toothbrush. The high degree of polarization indicates that the magnetic field vectors are almost perfectly aligned along the relic structure. The polarization degrees correspond to Mach numbers of $>2.2$. Polarized emission is also detected in the radio relics in ZwCl 0008+52 and, for the first time, in Abell 1612. Abell 1612 shows a complex X-ray surface brightness distribution, indicating a recent major merger. No Faraday depolarization is detected between 4.85 GHz and 8.35 GHz, except for one component of the Toothbrush relic. Faraday depolarization between 1.38 GHz and 8.35 GHz varies with distance from the center of the host cluster 1RXS 06+42, which can be explained by a decrease in electron density and/or in strength of a turbulent magnetic field. Faraday rotation measures show large-scale gradients along the relics, which cannot be explained by variations in the Milky Way foreground. Large-scale regular fields appear to be present in intergalactic space around galaxy clusters.