Occurrence of gravitational collapse in the accreting neutron stars of binary-driven hypernovae

The binary-driven hypernova (BdHN) model proposes long gamma-ray bursts (GRBs) originate in binaries composed of a carbon-oxygen (CO) star and a neutron star (NS) companion. The CO core collapse generates a newborn NS and a supernova that triggers the GRB by accreting onto the NSs, rapidly transferring mass and angular momentum to them. This article aims to determine the conditions under which a black hole (BH) forms from NS collapse induced by the accretion and the impact on the GRB observational properties and taxonomy. We perform three-dimensional, smoothed-particle-hydrodynamics simulations of BdHNe using up-to-date NS nuclear equations of state (EOS), with and without hyperons, and calculate the structure evolution in full general relativity. We assess the binary parameters leading either NS in the binary to the critical mass for gravitational collapse into a BH and its occurrence time, $t_{\rm col}$. We include a non-zero angular momentum of the NSs and find that $t_{\rm col}$ ranges from a few tens of seconds to hours for decreasing NS initial angular momentum values. BdHNe I are the most compact (about five minutes orbital period), promptly form a BH and release $\gtrsim 10^{52}$ erg. They form NS-BH binaries with tens of kyr merger timescale by gravitational-wave emission. BdHNe II and III do not form BHs, release $\sim 10^{50}$-$10^{52}$ erg and $\lesssim 10^{50}$ erg. They form NS-NS binaries with a range of merger timescales larger than for NS-BH binaries. In some compact BdHNe II, either NS can become supramassive, i.e., above the critical mass of a non-rotating NS. Magnetic braking by a $10^{13}$ G field can delay BH formation, leading to BH-BH or NS-BH of tens of kyr merger timescale.