Neutrino treatment in multidimensional astrophysical simulations : a new spectral scheme

Neutrinos play a central role in modern physics and astrophysics. Their extremely weak interaction rate with baryons and other leptons makes their detection on the Earth difficult and challenging. At the same time, it implies that the emission and the absorption of neutrinos are the dominant radiative processes in hot and dense astrophysical environment (such as core-collapse supernovae and the merger of binary compact objects), where photons are completely trapped and diffuse out on much longer timescales. The implementation of neutrino-transport schemes in hydrodynamics simulations is a subtle problem, especially in multi-dimensions, where an accurate solution of the transport equations can be, computationally speaking, extremely expensive. In this work, we have developed a new approximate neutrino-radiation treatment, the Advanced Spectral Leakage (ASL) scheme; after having tested and calibrated it, we have shown a variety of applications, both in the context of core-collapse supernovae and of binary neutron star mergers. The ASL scheme was derived from previous grey leakage schemes, and it retains the conceptual and the computational simplicity that characterize leakage schemes. Different from its predecessors, the new treatment is spectral (i.e. it retains information on the particle energy), and it includes the modeling of a neutrino trapped component in optically thick conditions and of neutrino absorption terms in optically thin conditions. The scheme has been tested against detailed neutrino-transport in the context of spherically symmetric models of collapsing stellar cores. We have shown that it is able to capture, with reasonable accuracy, the main expected features during the collapse phase, at core bounce and in the first hundreds of millisecond after bounce, both for the fundamental hydrodynamics and neutrino quantities. The optical depth is a central quantity in leakages schemes. We have also developed a new algorithm to compute the optical depth in multi-dimensional domains, without any symmetry constraint. We called it Multidimensional Optical Depth Algorithm (MODA). The major application of the ASL scheme in this work has been the study of the development of a neutrino-driven wind from the hot and dense disc resulting from the merger of two neutron star. This process has been studied for the first time in 3D Cartesian simulations, performed with the FISH code. The intense (10^53 erg/s) neutrino emission coming from the (probably, unstable) hyper massive neutron star and from the disc itself is partially re-absorbed by low density (< 10^10 g/cm^3), neutron-rich (Y_e < 0.1) matter inside disc. This energy deposition drives a baryonic wind, mainly perpendicular to the disc plane, on a timescale of ~50 ms. Neutrino-matter interactions in the wind modify significantly the electron fraction of matter: the resulting distribution shows a broad range of Y_e, from 0.2 to 0.4, with larger values along the polar directions than along the equatorial one. At ~100ms after the merger, the amount of ejecta is of the order of 2% the initial mass of the disc, thus it represents a significant channel for mass ejection from binary neutron star mergers. The broad range in Y_e represents an interesting signature in the context of r-process nucleosynthesis. Furthermore, we have shown other applications of the ASL scheme. First, we have implemented it in the MHD version of the FISH code to study the electron fraction in jets resulting from magneto-rotationally driven supernovae. In the case of strong and fast jet formation (~30 ms after core bounce), the electron fraction in the ejecta is low enough (Y_e < 0.3) to produce robust r-process nucleosynthesis. Second, we have implemented the ASL scheme inside the SPH code SPHYNCS, to perform core-collapse simulations. The results we have obtained are compatible with what we have obtained with grid codes. This model shows that the scheme is of easy implementation also in Lagrangian, multidimensional SPH codes. Finally, we have designed a new prescription to explode artificially spherically symmetric core-collapse models, using the IDSA scheme for electron neutrinos and the ASL scheme for mu and tau neutrinos. The extra energy deposition required to trigger the explosion is obtained by the parametrized absorption of heavy flavour neutrinos inside the gain region. The model has shown promising results and it is well suited to study the explosive nucleosynthesis for broad stellar progenitor samples, including detailed neutrino treatment.