Collapsars - Gamma-Ray Bursts and Explosions in "Failed Supernovae"
  Using a two-dimensional hydrodynamics code (PROMETHEUS), we study the continued evolution of rotating massive helium stars whose iron core collapse does not produce a successful outgoing shock, but instead forms a black hole. We study the formation of a disk, the associated flow patterns, and the accretion rate for disk viscosity parameter, alpha ~ 0.001 and 0.1. For the standard 14 solar mass model the average accretion rate for 15 s is 0.07 solar masses per second and the total energy deposited along the rotational axes by neutrino annihilation is (1 - 14) x 10**51 erg, depending upon the evolution of the Kerr parameter and uncertain neutrino efficiencies. Simulated deposition of this energy in the polar regions results in strong relativistic outflow - jets beamed to about 1.5% of the sky. The jets remain highly focused, and are capable of penetrating the star in 5 - 10 s. After the jet breaks through the surface of the star, highly relativistic flow can commence. Because of the sensitivity of the mass ejection and jets to accretion rate, angular momentum, and disk viscosity, and the variation of observational consequences with viewing angle, a large range of outcomes is possible ranging from bright GRBs like GRB 971214 to faint GRB-supernovae like SN 1998bw. X-ray precursors are also possible as the jet first breaks out of the star. While only a small fraction of supernovae make GRBs, we predict that all GRBs longer than a few seconds will make supernovae similar to SN 1998bw. However, hard, energetic GRBs shorter than a few seconds will be difficult to make in this model. 
A. MacFadyen and S. E. Woosley