Clusters of galaxies are believed to be capable to accelerate protons at accretion shocks to energies exceeding 10^18 eV. At these energies, the losses caused by interactions of cosmic rays with photons of the Cosmic Microwave Background Radiation (CMBR) become effective and determine the maximum energy of protons and the shape of the energy spectrum in the cutoff region. The aim of this work is the study of the formation of the energy spectrum of accelerated protons at accretion shocks of galaxy clusters and of the characteristics of their broad band emission. The proton energy distribution is calculated self-consistently via a time-dependent numerical treatment of the shock acceleration process which takes into account the proton energy losses due to interactions with the CMBR. We calculate the energy distribution of accelerated protons, as well as the flux of broad-band emission produced by secondary electrons and positrons via synchrotron and inverse Compton scattering processes. We find that the downstream and upstream regions contribute almost at the same level to the emission. For the typical parameters characterising galaxy clusters, the synchrotron and IC peaks in the spectral energy distributions appear at comparable flux levels. For an efficient acceleration, the expected emission components in the X-ray and gamma-ray band are close to the detection threshold of current generation instruments, and will be possibly detected with the future generation of detectors.
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