Untitled - Laboratoire d'Astrophysique de l'Observatoire de Grenoble

Figure 15.3: The spectrum of cosmic rays at a relativistic shock. This spectrum appears as the envelope of
Fermi cycles (i.e. cosmic rays of large mean free path cross the shock front back and forth several times and gain
energy at each crossing cycle downstream-upstream-downstream), the first corresponding to an amplification of
the cosmic ray energy from its initial value ɛ0 by a factor Γ 2 , and the subsequent ones to an amplification by a
factor 2.
Because we crucially need to know them in the strong turbulence regime, especially in relation with the new
investigations concerning the Ultra-High-Energy Cosmic Rays, we have undergone a systematical study of the
transport, by combining theoretical and semi-analytical approaches with Monte-Carlo numerical simulations
(Casse, Lemoine & Pelletier 2002). We have generalized the result of weak turbulence for the pitch angle diffusion
and for the spatial diffusion along the magnetic field, as a function of the characteristics of the turbulence
spectrum and the particle rigidity. But, as for the transverse diffusion with respect to the mean field, the
behavior is deeply different and controlled by the chaotic aspect of the field lines. Furthermore, the diffusion
at Larmor radii larger than the coherence length of the magnetic field does not stop suddenly, the diffusion
coefficient increases proportionally to the square of the particle energy.
Fermi acceleration in relativistic regime with magnetic fronts and shocks.
The enigma of the existence of Ultra High Energy Cosmic rays can be solved along two different but not
exclusive ways : either by a ”bottom up” scenario where the UHECRs are generated by an acceleration process
in the high energy astrophysical sources, or by a ”top down” scenario where some quantum objects, proposed by
a new physics beyond the standard model of particle physics, decay and produce particles in this energy range.
The Pierre Auger Observatory will soon provide a crucial answer to this question. Indeed we will soon know
whether there exists a particle spectrum beyond the ”GZK limit” (which is the energy threshold beyond which
protons loose energy by producing mesons through collisions with the CMB-photons), revealing a generation of
Cosmic Rays that would not come from extragalactic sources. We have contributed to the ”bottom up” scenario
by studying the relativistic regime of Fermi acceleration, necessary for the Cosmic Rays to reach energies of
order 10 20 eV in the considered sources (AGNs and Gamma-Ray Bursts or GRBs). We have developed the
Fermi acceleration in relativistic regime along two different ways : with relativistic fronts and with relativistic
shocks. When an ensemble of magnetic relativistic fronts propagate with relative speeds that are mildly relativistic,
like in GRBs, the elastic scattering of magnetic fronts generates an efficient Fermi acceleration that
we applied to GRBs (see next paragraph). As for the case of a relativistic shock, Martin Lemoine and G.P.
have developed a combined theoretical and numerical study. The formation of the energy spectrum has been
analyzed confirming a recent analysis proposed by Achterberg and Gallant (1999, MNRAS, 305, L6) and the
time scales of the process have been determined. Reliable laws for the generation of Cosmic Rays in relativistic
flows have therefore been provided (Fig. 15.3).
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