  We model explosions driven by the coalescence of a black hole or neutron star
with the core of its massive-star companion. Upon entering a common envelope
phase, a compact object may spiral all the way to the core. The concurrent
release of energy is likely to be deposited into the surrounding common
envelope, powering a merger-driven explosion. We use hydrodynamic models of
binary coalescence to model the common envelope density distribution at the
time of coalescence. We find toroidal profiles of material, concentrated in the
binary's equatorial plane and extending to many times the massive star's
original radius. We use the spherically-averaged properties of this
circumstellar material (CSM) to estimate the emergent light curves that result
from the interaction between the blast wave and the CSM. We find that typical
merger-driven explosions are brightened by up to three magnitudes by CSM
interaction. From population synthesis models we discover that the brightest
merger-driven explosions, $M_V \sim -18$ to $-19$, are those involving black
holes because they have the most massive and extended CSM. Black hole
coalescence events are also common; they represent about 50% of all
merger-driven explosions and approximately 0.3% of the core-collapse rate.
Merger-driven explosions offer a window into the highly-uncertain physics of
common envelope interactions in binary systems by probing the properties of
systems that merge rather than eject their envelopes.
