Ultra-high energy cosmic ray propagation in the local supercluster

Abstract

We present detailed numerical simulations and analytical approximations of the propagation of nucleons above 10 19 eV in the Local Supercluster, assuming that the ambient magnetic field is turbulent, and its strength 0.01 μG ≲ B rms ≲ 1 μG. In such strong magnetic fields, protons in the low energy part of the spectrum, 10 19 eV ≲ E ≲ E C, diffuse, while the higher energy particles, with E ≳ E C, propagate along nearly straight lines. The magnitude of the transition energy E C depends mainly on the strength of the magnetic field, the coherence length, and the distance to the source; for B rms ⋍ 0.1 μ G , a largest eddy of length ∼ 10 Mpc, and a distance to the source ∼ 10 Mpc, E C ⋍ 100 EeV . Our numerical treatment substantially improves on previous analytical approximations, as it allows one to treat carefully the transition between the two propagation regimes, as well as the effects due to inhomogeneities expected on scales of a few Mpc. We show that a turbulent magnetic field B rms ∼ 0.1 μG, close to equipartition, would allow us to reproduce exactly the observed spectrum of ultra high energy cosmic rays, up to the highest energy observed, for a distance to the source d ≲ 10 Mpc, for the geometry of the Local Supercluster, i.e. a sheet of thickness ⋍ 10 Mpc. Diffusion, in this case, allows us to reproduce the high flux beyond the Greisen Zatsepin Kuzmin cutoff, with a soft injection spectrum j( E) ∝ E −2.4. Moreover, the large deflection angles at the highest energies observed, typically ∼ 10 o for the above values, would explain why no close-by astrophysical counterpart could be associated with these events.