  Massive stars generally end their lives as neutron stars (NSs) or black holes
(BHs), with NS formation typically occurring at the low mass end and collapse
to a BH more likely at the high mass end. In an intermediate regime, with a
mass range that depends on the uncertain details of rotation and mass loss
during the star's life, a NS is initially formed which then experiences
fallback accretion and collapse to a BH. The electromagnetic consequence of
such an event is not clear. Depending on the progenitor's structure,
possibilities range from a long gamma-ray burst to a Type II supernova (that
may or may not be jet-powered) to a collapse with a weak electromagnetic
signature. Gravitational waves (GWs) provide the exciting opportunity to peer
through the envelope of a dying massive star and directly probe what is
occurring inside. We explore whether fallback onto young NSs can be detected by
ground-based interferometers. When the incoming material has sufficient angular
momentum to form a disk, the accretion spins up the NS sufficiently to produce
non-axisymmetric instabilities and gravitational radiation at frequencies of
~700-2400 Hz for ~30-3000 s until collapse to a BH occurs. Using a realistic
excess cross-power search algorithm, we show that such events are detectable by
Advanced LIGO out to ~17 Mpc. From the rate of nearby core-collapse supernovae,
we estimate that there will be ~1-2 events each year that are worth checking
for fallback GWs. The observation of these unique GW signatures coincident with
electromagnetic detections would identify the transient events that are
associated with this channel of BH formation, while providing information about
the protoneutron star progenitor.
