High Energy Neutrinos from Cosmological Gamma-Ray Burst Fireballs

Observations suggest that $\gamma$-ray bursts (GRBs) are produced by the dissipation of the kinetic energy of a relativistic fireball. We show that a large fraction, $\ge 10%$, of the fireball energy is expected to be converted by photo-meson production to a burst of $\sim10^{14} eV$ neutrinos. A km^2 neutrino detector would observe at least several tens of events per year correlated with GRBs, and test for neutrino properties (e.g. flavor oscillations, for which upward moving $\tau$'s would be a unique signature, and coupling to gravity) with an accuracy many orders of magnitude better than is currently possible.