  The induced gravitational collapse (IGC) paradigm has been successfully
applied to the explanation of the concomitance of gamma-ray bursts (GRBs) with
supernovae (SNe) Ic. The progenitor is a tight binary system composed by a
carbon-oxygen (CO) core and a neutron star (NS) companion. The explosion of the
SN leads to hypercritical accretion onto the NS companion which reaches the
critical mass, hence inducing its gravitational collapse to a black hole (BH)
with consequent emission of the GRB. The first estimates of this process were
based on a simplified model of the binary parameters and the
Bondi-Hoyle-Lyttleton accretion rate. We present here the first full numerical
simulations of the IGC phenomenon. We simulate the core-collapse and SN
explosion of CO stars to obtain the density and ejection velocity of the SN
ejecta. We follow the hydrodynamic evolution of the accreting material falling
into the Bondi-Hoyle surface of the NS all the way up to its incorporation to
the NS surface. The simulations go up to BH formation when the NS reaches the
critical mass. For appropriate binary parameters the IGC occurs in short
timescales (100-1000s) owing to the combined effective action of the photon
trapping and the neutrino cooling near the NS surface. We also show that the
IGC scenario leads to a natural explanation for why GRBs are associated only to
SN Ic with totally absent or very little helium.
