Neutrino scattering, absorption and annihilation above the accretion discs of gamma ray bursts

The central engine that drives gamma ray burst (GRB) explosions may derive from the ability of electrons/positrons and nucleons to tap into the momentum and energy from the large neutrino luminosity emitted by an accretion disc surrounding a black hole. This transfer of momentum and energy occurs due to neutrino absorption, scattering and annihilation, and the non-spherical geometry of the source both increases the annihilation efficiency and, close to the black hole, directs the momentum transfer toward the disc axis. We focus on the micro-physical aspects of this system and present annihilation efficiencies and the momentum/energy transfers for a number of accretion disc models. Models in which the neutrinos and antineutrinos become trapped within the disc have noticeably different momentum and energy deposition structure compared to thin disc models that may lead to significant differences in the explosion dynamics. Using these results we make estimates for the critical densities of infalling material below which the transfer of neutrino momentum/energy will lead to an explosion.