Cosmic rays and neutrinos from GRBs: predictions versus acceleration modeling

Abstract

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 pγ-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.

Which acceleration process for ultra high energy cosmic rays in gamma ray bursts?

“…However, in a recent paper (Gialis & Pelletier 2003), we have shown that this assumption is not realistic regarding the magnetic energy depletion time. Moreover, the Fermi acceleration time depends on the mean free path,¯ , of the particle in an irregular magnetic field.…”

“…There are two possible types of neutrino emission due to the generation of cosmic rays (Gialis & Pelletier 2003). The most expected one results from the pγ-process where the total energy radiated by neutrinos in the co-moving flow is given by…”

“…According to a Kolmogorov scaling with β = 5/3, we have shown (Gialis & Pelletier 2003) that GRBs are unable to produce UHECRs with this acceleration process because of a strong expansion limitation in energy …”

“…This limitation is far more important than the transverse escape. We also have neglected the synchrotron losses for protons because the synchrotron limitation, in the co-moving frame R Γ , is over 10 5 GeV at r b and next, increases like r 2 for B ∝ r −2 and r 11/8 for B ∝ r −3/2 (Gialis & Pelletier 2003). …”

“…As for the internal shocks, first and second order Fermi processes would achieve this goal with the extreme assumption of a cosmic ray mean free path of the order of its Larmor radius (so-called Bohm's scaling). In a previous paper (Gialis & Pelletier 2003), we have shown that such scaling is physically inconsistent for two reasons; first, the law is not validated by numerical simulations (Casse et al 2001) and second, even if inappropriately used, it would lead to tremendously fast magnetic energy depletion in the fireball. We also have considered a more realistic Kolmogorov scaling but a severe expansion loss limitation does not make it possible.…”