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 $\sim Z$ 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 $E< Z\, {\rm EeV}\,(B/{\rm G})\sqrt{l_c/{\rm Mpc}}(d_s/70\ {\rm Mpc})$ 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 ($E_{max}\sim (2$--$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.