  It is firmly established that the stellar mass distribution is smooth,
covering the range 0.1-100 Msun. It is to be expected that the masses of the
ensuing compact remnants correlate with the masses of their progenitor stars,
and thus it is generally thought that the remnant masses should be smoothly
distributed from the lightest white dwarfs to the heaviest black holes.
However, this intuitive prediction is not borne out by observed data. In the
rapidly growing population of remnants with observationally determined masses,
a striking mass gap has emerged at the boundary between neutron stars and black
holes. The heaviest neutron stars reach a maximum of two solar masses, while
the lightest black holes are at least five solar masses. Over a decade after
the discovery, the gap has become a significant challenge to our understanding
of compact object formation. We offer new insights into the physical processes
that bifurcate the formation of remnants into lower mass neutron stars and
heavier black holes. Combining the results of stellar modeling with
hydrodynamic simulations of supernovae, we both explain the existence of the
gap, and also put stringent constraints on the inner workings of the supernova
explosion mechanism. In particular, we show that core-collapse supernovae are
launched within 100-200 milliseconds of the initial stellar collapse, implying
that the explosions are driven by instabilities with a rapid (10-20 ms) growth
time. Alternatively, if future observations fill in the gap, this will be an
indication that these instabilities develop over a longer (>200 milliseconds)
timescale.
