Hyperaccreting Black Holes and Gamma-Ray Bursts

A variety of current models of gamma-ray bursts (GRBs) suggest a common engine: a black hole of several solar masses accreting matter from a disk at a rate of 0.01 to 10 M_☉ s^-1. Using a numerical model for relativistic disk accretion, we have studied steady state accretion at these high rates. Outside about 10⁸ cm, the disk is advection dominated; energy released by dissipation is carried in by the optically thick gas, and the disk does not cool. Inside this radius, for accretion rates greater than about 0.01 M_☉ s^-1 a global state of balanced power comes to exist between neutrino losses, chiefly pair capture on nucleons, and dissipation. As a result of these losses, the temperature is reduced, the density is raised, and the disk scale height is reduced compared to the advective solution. The sudden onset of neutrino losses (due to the high temperature dependence) and photodisintegration leads to an abrupt thinning of the disk that may provide a favorable geometry for jet production. The inner disk remains optically thin to neutrinos for accretion rates of up to about 1 M_☉ s^-1. The energy emitted in neutrinos is less, and in the case of low accretion rates, very much less, than the maximum efficiency factor for black hole accretion (0.057 for no rotation; 0.42 for extreme Kerr rotation) times the accretion rate, c². Neutrino temperatures at the last stable orbit range from 2 MeV (no rotation, slow accretion) to 13 MeV (Kerr geometry, rapid accretion), and the density ranges from 10⁹ to 10¹² g cm^-3. The efficiency for producing a pair fireball along the rotational axis by neutrino annihilation is calculated and found to be highly variable and very sensitive to the accretion rate. For some of the higher accretion rates studied, it can be several percent or more; for accretion rates less than 0.05 M_☉ s^-1, it is essentially zero. The efficiency of the Blandford-Znajek mechanism in extracting rotational energy from the black hole is also estimated. In light of these results, the viability of various gamma-ray burst models is discussed, and the sensitivity of the results to disk viscosity, black hole rotation rate, and black hole mass is explored. A diverse range of GRB energies seems unavoidable, and neutrino annihilation in hyperaccreting black hole systems can explain bursts of up to 10⁵² ergs. Larger energies can be inferred for beaming systems.