Acceleration and radiation of ultra-high energy protons in galaxy clusters

Context. Clusters of galaxies are believed to be capable of accelerating protons at accretion shocks to energies exceeding 1018 eV. At these energies, the losses caused by interactions of cosmic rays with photons of the cosmic microwave background radiation (CMBR) begin to have an effect and determine the maximum energy of protons and the shape of the energy spectrum in the cutoff region. Aims: The aim of this work is to study both the formation of the energy spectrum of accelerated protons at accretion shocks of galaxy clusters and the characteristics of their broad band emission. Methods: The proton energy distribution is calculated self-consistently via a time-dependent numerical treatment of the shock acceleration process, which takes the proton energy losses due to interactions with the CMBR into account. 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. Results: 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. Conclusions: For an efficient acceleration, the expected emission components in the X-ray and gamma-ray bands are close to the detection threshold of current generation instruments, and will possibly be detected with the future generation of detectors. Remarkably, the acceleration of iron at these shocks can proceed up to a particle energy of ≈ 1020 eV, making clusters of galaxies possible contributors to the observed flux of ultra high energy cosmic rays