The radio relic in Abell 2256: overall spectrum and implications for electron acceleration

Abstract: The galaxy cluster Abell 2256 hosts one of the most intriguing examples in the class of radio relics. It has been found that this radio relic has a rather flat integrated spectrum at low frequencies that would imply an injection spectral index for the electrons that is inconsistent with the flattest allowed by the test particle diffusive shock acceleration (DSA). We performed new high-frequency observations at 2273, 2640, and 4850 MHz. Combining these new observations with images available in the literature, we constrain the radio integrated spectrum of the radio relic in Abell 2256 over the widest sampled frequency range collected so far for this class of objects (63 -10450 MHz). Moreover, we used X-ray observations of the cluster to check the temperature structure in the regions around the radio relic. We find that the relic keeps an unusually flat behavior up to high frequencies. Although the relic integrated spectrum between 63 and 10450 MHz is not inconsistent with a single power law with $\alpha_{63}^{10450}= 0.92\pm 0.02$, we find hints of a steepening at frequencies > 1400 MHz. The two frequency ranges 63-1369 MHz and 1369-10450 MHz are, indeed, best represented by two different power laws, with $\alpha_{63}^{1369}= 0.85\pm 0.01$ and $\alpha_{1369}^{10450}= 1.00\pm 0.02$. This broken power law would require special conditions to be explained in terms of test-particle DSA, e.g., non-stationarity of the spectrum and/or non-stationarity of the shock. On the other hand, the single power law would make of this relic the one with the flattest integrated spectrum known so far, even flatter than what allowed in the test-particle approach to DSA. We find a rather low temperature ratio of $T_2/T_1 \sim 1.7$ across the G region of the radio relic and no temperature jump across the H region.