Magnetic diffusion effects on the Ultra-High Energy Cosmic Ray spectrum and composition

Abstract

We discuss the effects of diffusion of high energy cosmic rays in turbulent extra-galactic magnetic fields. We find an approximate expression for the low energy suppression of the spectrum of the different mass components (with charge Z) in the case in which this suppression happens at energies below ∼ Z EeV, so that energy losses are dominated by the adiabatic ones. The low energy suppression appears when cosmic rays from the closest sources take a time comparable to the age of the Universe to reach the Earth. This occurs for energies E < Z EeV (B/nG)p lc/Mpc(ds/70 Mpc) in terms of the magnetic field RMS strength B, its coherence length lc and the typical separation between sources ds. We apply this to scenarios in which the sources produce a mixed composition and have a relatively low maximum rigidity (Emax ∼ (2–10)Z EeV), finding that diffusion has a significant effect on the resulting spectrum, the average mass and on its spread, in particular reducing this last one. For reasonable values of B and lc these effects can help to reproduce the composition trends observed by the Auger Collaboration for source spectra compatible with Fermi acceleration.