2010ApJ...722..543E

The statistical distribution of energies among particles responsible for long gamma-ray burst (GRB) emission is analyzed in light of recent results of the Fermi Observatory. The all-sky flux, F_γ, recorded by the Gamma-Ray Burst Monitor (GBM) is shown, despite its larger energy range, to be not significantly larger than that reported by the Burst and Transient Explorer, suggesting a relatively small flux in the 3-30 MeV energy range. The present-day energy input rate in γ-rays recorded by the GBM from long GRBs is found, assuming star formation rates in the literature, to be {dot}W(0)=0.5 F_γ H/c = 5 ×10^42 erg Mpc^-3  yr^-1. The Large Area Telescope fluence, when observed, is about 5%-10% per decade of the total, in good agreement with the predictions of saturated, nonlinear shock acceleration. The high-energy component of long GRBs, as measured by Fermi, is found to contain only ∼10^–2.5 of the energy needed to produce ultrahigh-energy cosmic rays (UHECRs) above 4 EeV, assuming the latter to be extragalactic, when various numerical factors are carefully included, if the cosmic-ray source spectrum has a spectral index of -2. The observed γ-ray fraction of the required UHECR energy is even smaller if the source spectrum is softer than E ^–2. The AMANDA II limits rule out such a GRB origin for UHECRs if much more than 10^–2 of the cosmic-ray energy goes into neutrinos that are within, and simultaneous with, the γ-ray beam. It is suggested that "orphan" neutrinos out of the γ-ray beam might be identifiable via orphan afterglow or other wide angle signatures of GRBs in lieu of coincidence with prompt γ-rays, and it is recommended that feasible single neutrino trigger criteria be established to search for such coincidences.