  We study the physics behind the neutrino-driven mechanism for gamma-ray
bursts 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 2000) is excellent,
implying that we have captured the essential physics. We then use this
derivation to study a range of progenitors for collapsar gamma-ray bursts. 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.
