Extragalactic cosmic rays diffusing from two populations of sources

We consider the possibility of explaining the observed spectrum and composition of the cosmic rays with energies above 1017 eV in terms of two different extragalactic populations of sources in the presence of a turbulent intergalactic magnetic field (including also a fading galactic cosmic-ray component). The populations are considered to be the superposition of different nuclear species having rigidity-dependent spectra. The first extragalactic population is dominant in the energy range 1017-1018 eV and consists of sources having a relatively large density (>10-3 Mpc-3) and a steep spectrum. The second extragalactic population dominates the cosmic-ray flux above a few EeV; it has a harder spectral slope and has a high-energy cutoff at a few Z EeV (where eZ is the associated cosmic-ray charge). This population has a lower density of sources (