Cosmic Rays and Neutrinos from GRBs: Predictions versus Acceleration Modeling

The paper is devoted to the analysis of Fermi acceleration of protons in GRBs and its neutrino signature. We have compared the consequences of Bohm scaling and those of a Kolmogorov scaling, the latter being more reliable. The predictions about the energy limitation of UHE-protons by the various losses and the neutrino emissions turn out to be very sensitive to these scalings. We consider Kolmogorov scaling as the most realistic and predict a reasonable pp-neutrino emission around 100 GeV at the end of the radiative stage of the fireball expansion, for a large number of GRBs pending on their baryonic load. A second p$\gamma$-neutrino emission is expected with the acceleration of protons in the radiation free stage, but with a synchrotron loss limitation immediately followed by a severe expansion loss limitation. According to the Kolmogorov scaling, the protons could not reach the UHE-range. Anyway the large possibility of a two component neutrino emission would be an interesting clue of cosmic ray physics.