On the neutrino flux from gamma-ray bursts

Observations imply that γ-ray bursts (GRBs) are produced by the dissipation of the kinetic energy of a highly relativistic fireball. Photomeson interactions of protons with γ-rays within the fireball dissipation region are expected to convert a significant fraction of fireball energy to greater than 10¹⁴ eV neutrinos. We present an analysis of the internal shock model of GRBs, where production of synchrotron photons and photomeson neutrinos are self-consistently calculated, and show that the fraction of fireball energy converted to high-energy neutrinos is not sensitive to uncertainties in fireball model parameters, such as the expansion Lorentz factor and characteristic variability time. This is due, in part, to the constraints imposed on fireball parameters by observed GRB characteristics and, in part, to the fact that, for parameter values for which the photomeson optical depth is high (implying high proton energy loss to pion production), neutrino production is suppressed by pion and muon synchrotron losses. The neutrino flux is, therefore, expected to be correlated mainly with the observed γ-ray flux. The time-averaged neutrino intensity predicted by the model, ∼10^-8.5 GeV cm^-2 s^-1 sr^-1, is consistent with the flux predicted by the assumption that GRBs are the sources of greater than 10¹⁹ eV cosmic rays.