Jet Luminosity from Neutrino-dominated Accretion Flows in Gamma-Ray Bursts

A hyperaccretion disk formed around a stellar-mass black hole is a plausible model for the central engine that powers gamma-ray bursts (GRBs). If the central black hole rotates and a poloidal magnetic field threads its horizon, a powerful relativistic jet may be driven by a process resembling the Blandford-Znajek (BZ) mechanism. We estimate the luminosity of such a jet as a function of mass accretion rate and other accretion parameters assuming that the poloidal magnetic field strength is comparable to the inner accretion disk pressure. We show that the jet efficiency attains its maximal value when the accretion flow is cooled via optically thin neutrino emission. The jet luminosity is much larger than the energy deposition through neutrino-antineutrino annihilation (\nu \bar{\nu }\rightarrow e^+e^-) provided that the black hole is spinning rapidly enough. When the accretion rate onto a rapidly spinning black hole is larger than 0.003-0.01 M _⊙ s^-1, the disk becomes optically thin to neutrinos, its pressure increases and the jet luminosity is sufficient to drive a GRB. The transition of the accretion rate above and below this limiting value may cause the large variability observed in GRB.