D. The Collapsar Model

The evidence for the association of (long) GRBs with supernovae (see Bloom et al. [36] and Section IIC4) provides a strong support for the Collapsar model. Woosley [443] proposed that GRB arise from the collapse of a single Wolf-Rayet star endowed with fast rotation ('failed' Type Ib supernova). Paczynski [287] pointed out that there is tentative evidence that the GRBs 970228, 970508, and 970828 were close to star-forming regions and that this suggests that GRBs are linked to cataclysmic deaths of massive stars. MacFadyen and Woosley [242] begun a series of calculations [4, 243, 447] of a relativistic jet propagation through the stellar envelope of the collapsing star which is the most important ingredient unique to this model (other features like the accretion process onto the black hole, the corresponding particle acceleration and to some extend the collimation process are common to other models). The collimation of a jet by the stellar mantle was shown to occur analytically by Meszaros and Rees [240]. Zhang et al. [447] numerically confirmed and extended the basic features of this collimation process.

According to the Collapsar model the massive iron core of a rapidly rotating massive star, of mass M > 30 M, collapses to a black hole (either directly or during the accretion phase that follows the core collapse). An accretion disk form around this black hole and a funnel forms along the rotation axis, where the stellar material has relatively little rotational support. The mass of the accretion disk is around 0.1 M. Accretion of this disk onto the black hole takes place several dozen seconds and powers the GRB. Energy can be extracted via neutrino annihilation [242] or via the Bladford-Znajek mechanism. The energy deposited in the surrounding matter will preferably leak out along the rotation axis producing jets with opening angles of < 10°. If the jets are powerful enough they would penetrate the stellar envelope and produce the GRB.

Zhang et al. [447] find that relativistic jets are collimated by their passage through the stellar mantle. Starting with an initial half-angle of up to 20°, the jet emerges with half-angles that, though variable with time, are around 5°. The jet becomes very hot in this phase and it has only a moderate Lorentz factor, modulated by mixing, and a very large internal energy (more than 80% of the total energy). As the jet escapes, conversion of the remaining internal energy into kinetic energy gives terminal Lorentz factors along the axis of ~ 150 (depending, of course, on the initial conditions considered). Because of the large ratio of internal to kinetic energy in both the jet and its cocoon, the opening angle of the final jet is significantly greater than at breakout. A small amount of material emerges at large angles, but with a Lorentz factor still sufficiently large to make a weak GRB. When the jet breaks out from the star it may produce a thermal precursor (seen in several GRBs) [287, 329, 332]. Instabilities in the accretion process, or in the passage of the jet through the stellar envelope [3, 447] can produce the required variability in the Lorentz factor that is needed to produce internal shocks.

The processes of core collapse, accretion along the polar column (which is essential in order to create the funnel) and the jet propagation through the stellar envelope take together ~ 10 sec [242]. The duration of the accretion onto the black hole is expected to take several dozen seconds. These arguments imply that Collapsars are expected to produce long GRBs (see however, Zhang et al. [447] for a suggestion that the breakout of a relativistic jet and its collision with the stellar wind will produce a brief transient with properties similar to the class of "short-hard" GRBs.).