Neutrino Scattering, Absorption and Annihilation above the accretion disks 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 disk 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 towards the disk axis. We present annihilation efficiencies and the momentum/energy transfers for a number of accretion disk models and compute the critical densities of infalling material below which the transfer of neutrino momentum/energy will lead to an explosion. Models in which the neutrinos and antineutrinos become trapped within the disk have noticeably different momentum and energy deposition structure compared to thin disk models that may lead to significant differences in the explosion dynamics.