The ultra-high energy cosmic ray spectrum and Fermi shock acceleration

International audienceThe energy spectrum of ultra-high energy cosmic rays (UHECR) is usually calculated for sources with identical properties. Assuming that all sources can accelerate UHECR protons to the same extremely high maximal energy E_max > 1020 eV and have the steeply falling injection spectrum 1/E2.7, one can reproduce the measured cosmic ray flux above E > 1018 eV. We show that relaxing the assumption of identical sources and using a power-law distribution of their maximal energy allows one to explain the observed UHECR spectrum with the injection 1/E2 predicted by Fermi shock acceleration. We study possible ways to distinguish between these two cases with future experiments