Magnetic diffusion effects on the ultra-high energy cosmic ray spectrum and composition

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 )√( l c /Mpc)( d s /70Mpc) in terms of the magnetic field RMS strength B , its coherence length l c and the typical separation between sources d s . We apply this to scenarios in which the sources produce a mixed composition and have a relatively low maximum rigidity ( E max ∼ (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 l c these effects can help to reproduce the composition trends observed by the Auger Collaboration for source spectra compatible with Fermi acceleration.