Neutrino oscillations within the induced gravitational collapse paradigm of long gamma-ray bursts

The specific class of binary-driven hypernovae within the induced gravitational collapse scenario for the explanation of the long Gamma-Ray Bursts indicates as progenitor a binary system composed of a carbon-oxygen core and a neutron star in a tight orbit. The supernova explosion of the core triggers a hypercritical (highly super-Eddington) accretion process onto the NS companion, making it reach the critical mass with consequent formation of a Kerr black hole. Recent numerical simulations of the above system show that a part of the ejecta keeps bound to the newborn Kerr black hole with enough angular momentum to generate a new process of hypercritical accretion, i.e. an accretion disk. Throughout this entire process, we focus on two contexts of neutrino emission leading to two different systems in which an analysis of neutrino flavour oscillations (or flavour transformations) not only constitutes a novel extension of the induced gravitational collapse paradigm literature but also can have an impact on a wide range of astrophysical phenomena: from $e^{-}e^{+}$ plasma production in the vicinity of neutron stars or black holes in GRB models, to r-process nucleosynthesis in disk winds and characterization of astrophysical MeV neutrino sources. In particular, we study neutrino oscillations in: egin{enumerate} - extit{Spherical accretion onto a neutron star:} During this process, copious amounts of neutrino--anti-neutrino pairs ($ uar{ u}$) are emitted at the neutron star surface. The neutrino emission can reach luminosities of up to $10^{57}$~MeV~s$^{-1}$, mean neutrino energies 20~MeV, and neutrino densities $10^{31}$~cm$^{-3}$. Along their path from the vicinity of the NS surface outward, such neutrinos experience flavour transformations dictated by the neutrino to electron density ratio. We determine the neutrino and electron on the accretion zone and use them to compute the neutrino flavour evolution. For normal and inverted neutrino-mass hierarchies and within the two-flavour formalism ($ u_{e} u_{x}$), we estimate the final electronic and non-electronic neutrino content after two oscillation processes: (1) neutrino collective effects due to neutrino self-interactions where the neutrino density dominates and, (2) the Mikheyev-Smirnov-Wolfenstein effect, where the electron density dominates. We find that the final neutrino content is composed by $sim$55% ($sim$62%) of electronic neutrinos, i.e. $ u_{e}+ar{ u}_{e}$, for the normal (inverted) neutrino-mass hierarchy. - extit{Neutrino-cooled disks around a Kerr black hole:} In this phase of the binary-driven hypernovae, given the extreme conditions of high density (up to $10^{12}$~g~cm$^{-3}$) and temperatures (up to tens of MeV) inside this disk, neutrinos can reach densities of $10^{33}$~cm$^{-3}$ and energies of $50$~MeV. Although the geometry of the disk is significantly different from that of spherical accretion, these conditions provide an environment that allows neutrino flavour transformations. We estimate the evolution of the electronic and non-electronic neutrino content within the two-flavour formalism ($ u_{e} u_{x}$) under the action of neutrino collective effects by neutrino self-interactions. We find that neutrino oscillations inside the disk can have frequencies between $sim (10^{5}$--$10^{9})$~s$^{-1}$, leading the disk to achieve flavour equipartition. This implies that the energy deposition rate by neutrino annihilation ($ u + ar{ u} o e^{-} + e^{+}$) in the vicinity of the Kerr black hole is smaller than previous estimates in the literature not accounting by flavour oscillations inside the disk. The exact value of the reduction factor depends on the $ u_{e}$ and $ u_{x}$ optical depths but it can be as high as $sim 5$. This work has allowed us to identify key theoretical and numerical features involved in the study of neutrino oscillations and our results are a first step toward the analysis of neutrino oscillations in unique astrophysical settings other than core-collapse supernovae. As such, they deserve further attention.