SPH Simulations of the Induced Gravitational Collapse Scenario of Long Gamma-Ray Bursts Associated with Supernovae

We present the first three-dimensional smoothed particle hydrodynamics simulations of the induced gravitational collapse scenario of long-duration gamma-ray bursts (GRBs) associated with supernovae (SNe). We simulate the SN explosion of a carbon-oxygen core (COcore) forming a binary system with a neutron star (NS) companion. We follow the evolution of the SN ejecta, including their morphological structure, subject to the gravitational field of both the new NS ( NS) formed at the center of the SN and the one of the NS companion. We compute the accretion rate of the SN ejecta onto the NS companion, as well as onto the NS from SN matter fallback. We determine the fate of the binary system for a wide parameter space including different COcore and NS companion masses, orbital periods, and SN explosion geometry and energies. We identify, for selected NS nuclear equations of state, the binary parameters leading the NS companion, by hypercritical accretion, either to the mass-shedding limit or to the secular axisymmetric instability for gravitational collapse to a black hole (BH), or to a more massive, fast-rotating, stable NS. We also assess whether the binary remains gravitationally bound after the SN explosion, hence exploring the space of binary and SN explosion parameters leading to NS-NS and NS-BH binaries. The consequences of our results for the modeling of long GRBs, i.e., X-ray flashes and binary-driven hypernovae, are discussed.