Neutrino-driven explosions in gamma-ray bursts and hypernovae

We study the physics behind the neutrino-driven mechanism for gamma-ray bursts (GRBs) and hypernovae, deriving the critical density at which these outbursts occur in the collapsar model. The agreement between this derivation and results from past collapsar simulations (MacFadyen & Woosley) is excellent, implying that we have captured the essential physics. We then use this derivation to study a range of progenitors for collapsar GRBs. We derive how much of the star will accrete onto the black hole core before the infall density drops below this critical density, leading to an estimate of the remnant black hole mass for GRBs and hypernovae. We also estimate the time delays between gravity-wave or neutrino signals and the onset of the explosion or burst event. This derivation, combined with future observational constraints, provides a physical insight into the structure of the GRB progenitor.