We consider the explosion of supernovae and the possible production of a variety of high energy transients by delayed black hole formation in massive stars endowed with rotation .
Following the launch of a “ successful ” shock by the usual neutrino powered mechanism , the inner layers of the star move outwards , but lack adequate energy to eject all the matter exterior to the neutron star .
Over a period of minutes to hours a variable amount of mass , \sim 0.1 to 5 M _ { \scriptscriptstyle \odot } , falls back into the collapsed remnant , often turning it into a black hole and establishing an accretion disk .
The accretion rate , \sim 0.001 to 0.01 M _ { \scriptscriptstyle \odot } s ^ { -1 } , is inadequate to produce a jet mediated by neutrino annihilation , but similar to that invoked in magnetohydrodynamic ( MHD ) models for gamma-ray bursts ( GRBs ) .
We thus consider the effect of jets formed by “ fallback ” in stars that are already in the process of exploding .
We justify a parameterization of the jet power as a constant times the mass accretion rate , \epsilon \dot { M } c ^ { 2 } , and explore the consequences of \epsilon = 0.001 and 0.01 .
Adopting an initial collimation half-angle of 10 degrees , we find that the opening of the jet as it propagates through the exploding star is strongly influenced by the jet ’ s initial pressure and the stellar structure .
Cold jets tend to stay collimated , and become even more so , sometimes having an angle of only a few degrees when they reach the surface .
Jets having higher internal pressure than the stellar material through which they pass , or less initial collimation by the disk , spread out and tend to make energetic , asymmetric supernovae accompanied , in helium stars , by weak GRBs .
SN 1998bw may have been such an event .
In supergiants , shock breakout also produces bright x-ray transients that might be a diagnostic of the model , but even the most powerful jets ( equivalent isotropic energy 10 ^ { 54 } erg ) will not produce a GRB in a red supergiant .
For such Type II supernovae we find a limiting Lorentz factor of \Gamma \approx 2 .
Jets produced by fallback should be more frequent than those made by the prompt formation of a black hole and may power the most common form of gamma-ray transient in the universe , although not the most common form seen so far by BATSE .
Those are still attributed to prompt black hole formation , but it may be that the diverse energies observed for GRBs so far reflect chiefly the variable collimation of the jet inside the star and a consequently highly variable fraction of relativistic ejecta .
Indeed , these events may all have a common total energy near 10 ^ { 52 } erg .