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 < B_rms < 1 micro-Gauss. 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 micro-Gauss, a largest eddy of length 10 Mpc, and a distance to the source of 10 Mpc, E_C=100 EeV. Our numerical treatment substantially improves on previous analytical approximations, as it allows 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 micro-Gauss, close to equipartition, would allow to reproduce exactly the observed spectrum of ultra high energy cosmic rays, up to the highest energy observed, for a distance to the source below 10 Mpc, for the geometry of the Local Supercluster, i.e. a sheet of thickness 10 Mpc. Diffusion, in this case, allows to reproduce the high flux beyond the Greisen Zatsepin Kuzmin cut-off, with a soft injection spectrum proportional to E**(-2.4). Moreover, the large deflection angles at the highest energies observed, typically 10 degrees for the above values, would explain why no close-by astrophysical counterpart could be associated with these events.