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| - Gamma-ray emission from galaxy cluster outskirts versus radio relics
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| - Context. Galaxy cluster peripheries provide important information on the nature of ICM/IGM linkage. In this paper we consider potential future observations in the gamma-ray domain at cluster edges involving the radio relic phenomenon. Aims. We focus on the spectral signature of gamma radiation that should be evident in the energy range of Fermi-LAT, i.e. ≳10 -1 GeV and the CTA energy range ~10 2 GeV. The spectral signature results from a comparable gamma-ray flux due to the IC and π0 decay on the edge of the cluster, and its spectral position is a function of the magnetic field and relative efficiency of the acceleration of protons and electrons. We aim to draw attention to the dependence of the gamma-ray structure on the magnetic field value. Methods. As an example, we carried out analyses of two types of non-thermal diffuse radio emission: the radio relic of A 2256 and the radio halo of Coma cluster. We suggest that in both cases the expected spatially correlated gamma-ray spectrum should have a characteristic structure that depends on the strength of the local magnetic field. In both of the clusters we calculated the combined flux of gamma radiation from the actual observational values of the used observables. Results. The revealed spectral dependence on the magnetic field would allow us to relate the future spectral observations, in particular the position of the gamma-ray signature, to the value of the magnetic field in the border area between galaxy clusters and their connecting filaments, possibly constraining the estimated relative efficiency of particle acceleration at the edge of the cluster.
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