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Following the induced gravitational collapse (IGC) paradigm of gamma-raybursts (GRBs) associated with type Ib/c supernovae, we present numericalsimulations of the explosion of a carbon-oxygen (CO) core in a binary systemwith a neutron-star (NS) companion. The supernova ejecta trigger a\emph{hypercritical} accretion process onto the NS thanks to a copious neutrinoemission and the trapping of photons within the accretion flow. We show thattemperatures 1--10~MeV develop near the NS surface, hence electron-positronannihilation into neutrinos becomes the main cooling channel leading toaccretion rates $10^{-9}$--$10^{-1}~M_\odot$~s$^{-1}$ and neutrino luminosities$10^{43}$--$10^{52}$~erg~s$^{-1}$ (the shorter the orbital period the higherthe accretion rate). We estimate the maximum orbital period, $P_{\rm max}$, asa function of the NS initial mass, up to which the NS companion can reach byhypercritical accretion the critical mass for gravitational collapse leading toblack-hole (BH) formation. We then estimate the effects of the accreting andorbiting NS companion onto a novel geometry of the supernova ejecta densityprofile. We present the results of a $1.4\times 10^7$~particle simulation whichshow that the NS induces accentuated asymmetries in the ejecta density aroundthe orbital plane. We elaborate on the observables associated with the abovefeatures of the IGC process. We apply this framework to specific GRBs: we findthat X-ray flashes (XRFs) and binary-driven hypernovae (BdHNe) are produced inbinaries with $P>P_{\rm max}$ and $P < P_{\rm max}$, respectively. We analyzein detail the case of XRF 060218.

On the induced gravitational collapse scenario of gamma-ray bursts associated with supernovae