Extragalactic cosmic rays diffusing from two populations of sources

Abstract

We consider the possibility of explaining the observed spectrum and composition of the cosmic rays with energies above ${10}^{17}\text{ }\text{ }\mathrm{eV}$ 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 ${10}^{17}\ensuremath{-}{10}^{18}\text{ }\text{ }\mathrm{eV}$ and consists of sources having a relatively large density ($>{10}^{\ensuremath{-}3}\text{ }\text{ }{\mathrm{Mpc}}^{\ensuremath{-}3}$) 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 ($<{10}^{\ensuremath{-}4}\text{ }\text{ }{\mathrm{Mpc}}^{\ensuremath{-}3}$), so that the typical intersource separation is larger than few tens of Mpc, being significantly affected by a magnetic horizon effect that strongly suppresses its flux for energies below $\ensuremath{\sim}Z$ EeV. We discuss how this scenario could be reconciled with the values of the cosmic-ray source spectral indices that are expected to result from the diffusive shock acceleration mechanism.