Diffusive propagation of UHECR and the propagation theorem

Details Diffusive propagation of UHECR and the propagation theorem Diffusive propagation of UHECR and the propagation theorem

2004-03-03

arxiv.org/abs/astro-ph/0403095v3

Astrophys.J. 612 (2004) 900-913

Astronomy and Astrophysics

Astrophysics

16 pages, 13 eps figures, discussion of the absence of the GZK cut-off in strong magnetic field added, a misprint in figure 6

Scientific paper

10.1086/421869

We present a detailed analytical study of the propagation of ultra high energy (UHE) particles in extragalactic magnetic fields. The crucial parameter which affects the diffuse spectrum is the separation between sources. In the case of a uniform distribution of sources with a separation between them much smaller than all characteristic propagation lengths, the diffuse spectrum of UHE particles has a {\em universal} form, independent of the mode of propagation. This statement has a status of theorem. The proof is obtained using the particle number conservation during propagation, and also using the kinetic equation for the propagation of UHE particles. This theorem can be also proved with the help of the diffusion equation. In particular, it is shown numerically, how the diffuse fluxes converge to this universal spectrum, when the separation between sources diminishes. We study also the analytic solution of the diffusion equation in weak and strong magnetic fields with energy losses taken into account. In the case of strong magnetic fields and for a separation between sources large enough, the GZK cutoff can practically disappear, as it has been found early in numerical simulations. In practice, however, the source luminosities required are too large for this possibility.

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