Ultra-high energy cosmic ray propagation in the local supercluster

We present detailed numerical simulations and analytical approximations of the propagation of nucleons above 10(19) eV in the Local Supercluster, assu ming that the ambient magnetic field is turbulent, and its strength 0.01 mu G less than or similar to B-rms less than or similar to 1 mu G. In such st rong magnetic fields, protons in the low energy part of the spectrum, 10(19 ) eV less than or similar to E less than or similar to E-C, diffuse, while the higher energy particles, with E greater than or similar to E-C, propaga te 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 similar or equal to 0.1 mu G, a largest eddy of length similar to 10 Mpc, and a distance to the source simi lar to 10 Mpc, E-C similar or equal to 100 EeV. Our numerical treatment sub stantially 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 similar to 0.1 mu G, close t o 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 less than or similar to 10 Mpc, for the geometry o f the Local Supercluster, i.e. a sheet of thickness similar or equal to 10 Mpc. Diffusion, in this case, allows us to reproduce the high flux beyond t he Greisen Zatsepin Kuzmin cutoff, with a soft injection spectrum j(E) prop ortional to E-2.4. Moreover, the large deflection angles at the highest ene rgies observed, typically similar to 10 degrees for the above values, would explain why no close-by astrophysical counterpart could be associated with these events. (C) 1999 Elsevier Science B.V.