On the formation of compact-object binaries from binary-driven hypernovae

We present smoothed-particle-hydrodynamics (SPH) simulations of the binary-driven hypernova (BdHN) scenario of long gamma-ray bursts (GRBs), focusing on the binary stability during the supernova (SN) explosion. The BdHN progenitor is a binary comprised of a carbon-oxygen (CO) star and a neutron star (NS) companion. The core collapse of the CO leads to an SN explosion and a newborn NS ($\nu$NS) at its center. Ejected material accretes onto the NS and the $\nu$NS. BdHNe of type I have compact orbits of a few minutes, the NS reaches the critical mass, forming a black hole (BH), and the energy release is $\gtrsim 10^{52}$ erg. BdHNe II have longer periods of tens of minutes to hours; the NS becomes more massive, remains stable, and the system releases $\sim 10^{50}$-$10^{52}$ erg. BdHN III have longer periods, even days, where the accretion is negligible, and the energy released is $\lesssim 10^{50}$ erg. We assess whether the system remains gravitationally bound after the SN explosion, leading to an NS-BH in BdHN I, an NS-NS in BdHN II and III, or if the SN explosion disrupts the system. The existence of bound systems predicts an evolutionary connection between the long and short GRB populations. We determine the binary parameters for which the binary remains bound after the BdHN event. For these binaries, we derive fitting formulas of the numerical results for the main parameters, e.g., the mass loss, the SN explosion energy, orbital period, eccentricity, center-of-mass velocity, and the relation between the initial and final binary parameters, which are useful for outlined astrophysical applications.