Testing the neutrino annihilation model for launching GRB jets

The mechanism behind the launching of gamma-ray-burst (GRB) jets remains debated resulting in large uncertainty over the jet composition. Both magnetohydrodynamical and neutrino annihilation models have been proposed for the energy extraction in a black hole/accretion-disc central engine. In particular, for the extreme accretion rates $\dot M\sim 0.1-1$~ M$_\odot$s$^{-1}$ expected for bursts of duration $T\lesssim 100$~s, the disc can be an efficient neutrino emitter. Neutrino-antineutrino annihilation results in an energy deposition rate at the jet that can, in principle, account for the burst's energetics. Recent discoveries of X-ray flares hours after the burst and of ultra-long GRBs suggest that GRB activity can last for $\sim 10^4$~s or longer. These long-lived events have fluence similar to that of classical GRBs. In view of these findings, we re-evaluate the neutrino annihilation model. We derive the maximum possible energy of a neutrino-powered jet as a function of the burst duration and show that the available energy drops fast for longer bursts. For a standard choice of the parameters, the model falls short by three to four orders of magnitude in explaining the observed energetics of events that last longer than $\sim 10^3$~s.