Improved Leakage-Equilibration-Absorption Scheme (ILEAS) for Neutrino Physics in Compact Object Mergers

We present a new, computationally efficient, energy-integrated approximation for neutrino effects in hot and dense astrophysical environments such as supernova cores and compact binary mergers and their remnants. Our new method, termed ILEAS for Improved Leakage-Equilibration-Absorption Scheme, improves the lepton-number and energy losses of traditional leakage descriptions by a novel prescription of the diffusion time-scale based on a detailed energy integral of the flux-limited diffusion equation. The leakage module is supplemented by a neutrino-equilibration treatment that ensures the proper evolution of the total lepton number and medium plus neutrino energies as well as neutrino-pressure effects in the neutrino-trapping domain. Moreover, we employ a simple and straightforwardly applicable ray-tracing algorithm for including re-absorption of escaping neutrinos especially in the decoupling layer and during the transition to semi-transparent conditions. ILEAS is implemented on a three-dimensional (3D) Cartesian grid with a minimum of free and potentially case-dependent parameters and exploits the basic physics constraints that should be fulfilled in the neutrino-opaque and free-streaming limits. We discuss a suite of tests for stationary and time-dependent proto-neutron star models and post-merger black-hole-torus configurations, for which 3D ILEAS results are demonstrated to agree with energy-dependent 1D and 2D two-moment (M1) neutrino transport on the level of 10--15 percent in basic neutrino properties. This also holds for the radial profiles of the neutrino luminosities and of the electron fraction. Even neutrino absorption maps around torus-like neutrino sources are qualitatively similar without any fine-tuning, confirming that ILEAS can satisfactorily reproduce local losses and re-absorption of neutrinos as found in sophisticated transport calculations.