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

TL;DR

This paper analyzes how turbulent extragalactic magnetic fields cause diffusion effects that suppress the low-energy spectrum of ultra-high energy cosmic rays, influencing their composition and observable features.

Contribution

It provides an approximate expression for low-energy suppression due to magnetic diffusion and explores its impact on cosmic ray spectrum and composition with low maximum rigidity sources.

Findings

Diffusion causes low-energy suppression of cosmic ray spectrum.

Magnetic diffusion affects the average mass and its spread.

Results can explain observed composition trends by Auger.

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.