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 photomeson production to a burst of $\sim {10}^{14}\mathrm{eV}$ neutrinos. A ${\mathrm{km}}^2$ 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.