Fig. 4.30.3. The maximum predicted diffuse flux from GRBs and AGN with super-luminal shock fronts (the curve). The normalization is based on current neutrino flux limits (Munich and IceCube Collaboration, 2005). The flux is compared to the measured CR spectrum (small squares). From Meli et al. (2005).

Meli et al. (2005) conclude that described simulations are relevant to models of highly relativistic particle shock acceleration in sources as AGN jets and GRBs, and that:

(i) Large angle scattering is unrealistic -as expected- (our test spectra gave a steep sudden cutoff) in such high plasma velocities and the pitch angle diffusion scheme resembling the high turbulence upstream the shock was simulated, keeping the scattering cone angle within 0.1/r at crossing the shock front (Protheroe et al., 2002).

(ii) There is no decrease observed in the acceleration rate, comparing to results of diffusive relativistic shock acceleration (e.g. Lieu et al., 1994; Meli and Quenby, 2003a,b).

(iii) In order to keep a power-law spectra the angular distribution at crossing the shock is highly anisotropic and 'beamed'.

(iv) The energy gain of the CR in super-luminal shocks seems limited comparing to highly relativistic shocks.

(v) The possible contribution to the CR spectrum from super-luminal shock sources is predicted around to the knee of the measured CR spectrum.

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