Cluster accretion shocks as possible acceleration sites for ultra-high-energy protons below the Greisen cutoff

Three-dimensional hydrodynamic simulations of large-scale structure in the universe have shown that accretion shocks form during the gravitational collapse of one-dimensional caustics, and that clusters of galaxies formed at intersections of the caustics are surrounded by these accretion shocks. Estimated speed and curvature radius of the shocks are 1000-3000 km s(-1) and about 5 Mpc, respectively, in the Omega = 1 cold dark matter universe, Assuming that energetic protons are accelerated by these accretion shocks via the first-order Fermi process and modeling particle transport around the shocks through Bohm diffusion, we suggest that protons can be accelerated up to the Greisen cutoff energy near 6 x 10(19) eV, provided the mean magnetic field strength in the region around the shocks is at least of order 1 mu G. We have also estimated the proton flux at Earth from the Virgo Cluster. Assuming that a few (1-10) percent of the ram pressure of the infalling matter would be transferred to the cosmic rays, the estimated flux for E similar to 10(19) eV is consistent with observations, so that such clusters could be plausible sources of the ultrahigh-energy cosmic rays.