A perfect power-law spectrum even at highest frequencies: The Toothbrush relic

Radio relics trace shock fronts generated in the intracluster medium (ICM) during cluster mergers. The particle acceleration mechanism at the shock fronts is not yet completely understood. We observed the Toothbrush relic with the Effelsberg and Sardinia Radio Telescope at 14.25 GHz and 18.6 GHz, respectively. Unlike previously claimed, the integrated spectrum of the relic closely follows a power law over almost three orders of magnitude in frequency, with a spectral index of $\alpha_{\rm 58\,MHz}^{\rm 18.6\,GHz}=-1.16\pm0.03$. Our finding is consistent with a power-law injection spectrum, as predicted by diffusive shock acceleration theory. The result suggests that there is only little magnetic field strength evolution downstream to the shock. From the lack of spectral steepening, we find that either the Sunyaev-Zeldovich decrement produced by the pressure jump is less extended than $\sim$ 600\,kpc along the line of sight or, conversely, that the relic is located far behind in the cluster. For the first time, we detect linearly polarized emission from the "brush" at 18.6 GHz. Compared to 8.3 GHz, the degree of polarization across the brush increases at 18.6 GHz, suggesting a strong Faraday depolarization towards lower frequencies. The observed depolarization is consistent with an intervening magnetized screen that arise from the dense ICM containing turbulent magnetic fields. The depolarization, corresponding to a standard deviation of the Rotation Measures as high as $\sigma_{\rm RM}= 212\pm23\rm \,rad\,m^{-2}$, suggests that the brush is located in or behind the ICM. Our findings indicate that the Toothbrush can be consistently explained by the standard scenario for relic formation