Recently, the Pierre Auger Observatory has found strong evidence supporting the extragalactic origin of the most energetic cosmic rays. Despite several observed excesses in the distribution of arrival directions for the highest energy cosmic rays, the sources remain unidentified. Accretion shocks in galaxy clusters have been proposed as potential sources in the past. These immense shock waves, which can have radii on the order of megaparsecs, are generated by the infall of material from the intergalactic medium into the gravitational potential wells of galaxy clusters. In this work, we investigate the possibility that ultrahigh-energy cosmic rays are accelerated in these regions. Nearby massive galaxy clusters, including Virgo, are treated as a discrete component of the cluster mass distribution. Less massive galaxy clusters, as well as distant massive ones, are assumed to follow a continuous distribution in agreement with cluster mass statistics. We fit the flux at Earth and the composition profile measured by the Pierre Auger Observatory, assuming the injection of different nuclear species by these sources, to determine the values of the model parameters. Our results indicate that cosmic ray acceleration in cluster accretion shocks may account for at least a fraction of the observed UHECR flux at energies below the suppression scale. At higher energies, direct acceleration from the thermal pool would be feasible only if local fluctuations create favorable conditions, such as magnetic fields about an order of magnitude stronger than those typically expected in cluster accretion shocks, or for particular shock normal-magnetic field configurations. Moreover, in these scenarios, where the energy spectrum of accelerated cosmic rays is modeled as $\propto E^{-\gamma }$ with an exponential cutoff, the spectral index obtained from fitting the experimental data lies in the range $\gamma \sim 0.7–1.6$. This is smaller than 2, which is the value expected from the first-order Fermi acceleration mechanism for strong shocks.

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• Cosmic ray composition & spectra
• Cosmic ray propagation
• Cosmic ray sources