  The association of long-duration gamma-ray bursts (LGRBs) with Type Ic
supernovae presents a challenge to supernova explosion models. In the collapsar
model for LGRBs, gamma rays are produced in an ultrarelativistic jet launching
from the magnetosphere of the black hole that forms in the aftermath of the
collapse of a rotating progenitor star. The jet is collimated along the star's
rotation axis, but the concomitant luminous supernova should be
relatively--though certainly not entirely--spherical, and should synthesize a
substantial mass of 56Ni. Our goal is to provide a qualitative assessment of
the possibility that accretion of the progenitor envelope onto the black hole,
which powers the LGRB, could also deposit sufficient energy and nickel mass in
the envelope to produce a luminous supernova. For this, the energy dissipated
near the black hole during accretion must be transported outward, where it can
drive a supernova-like shockwave. Here we suggest that the energy is
transported by convection and develop an analytical toy model, relying on
global mass and energy conservation, for the dynamics of stellar collapse. The
model suggests that a ~10,000 km/s shock can be driven into the envelope and
that ~10^51 erg explosions are possible. The efficiency with which the
accretion energy is being transferred to the envelope is governed by the
competition of advection and convection at distances ~100-1,000 km from the
black hole and is sensitive to the values of the convective mixing length, the
magnitude of the effective viscous stress, and the specific angular momentum of
the infalling envelope. Substantial masses of 56Ni may be synthesized in the
convective accretion flow over the course of tens of seconds from the initial
circularization of the infalling envelope around the black hole. The
synthesized nickel is convectively mixed with a much larger mass of unburned
ejecta.
