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

Following the induced gravitational collapse (IGC) paradigm of gamma-ray bursts (GRBs) associated with type Ib/c supernovae, we present numerical simulations of the explosion of a carbon-oxygen (CO) core in a binary system with a neutron-star (NS) companion. The supernova ejecta trigger a \emph{hypercritical} accretion process onto the NS thanks to a copious neutrino emission and the trapping of photons within the accretion flow. We show that temperatures 1--10~MeV develop near the NS surface, hence electron-positron annihilation into neutrinos becomes the main cooling channel leading to accretion 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 higher the accretion rate). We estimate the maximum orbital period, $P_{\rm max}$, as a function of the NS initial mass, up to which the NS companion can reach by hypercritical accretion the critical mass for gravitational collapse leading to black-hole (BH) formation. We then estimate the effects of the accreting and orbiting NS companion onto a novel geometry of the supernova ejecta density profile. We present the results of a $1.4\times 10^7$~particle simulation which show that the NS induces accentuated asymmetries in the ejecta density around the orbital plane. We elaborate on the observables associated with the above features of the IGC process. We apply this framework to specific GRBs: we find that X-ray flashes (XRFs) and binary-driven hypernovae (BdHNe) are produced in binaries with $P>P_{\rm max}$ and $P < P_{\rm max}$, respectively. We analyze in detail the case of XRF 060218.