A new multi-dimensional general relativistic neutrino hydrodynamics code for core-collapse supernovae. I. Method and code tests in spherical symmetry

TL;DR

This paper introduces a new general relativistic neutrino hydrodynamics code for supernova simulations, combining advanced hydrodynamics and neutrino transport methods, and demonstrates its accuracy and stability through various tests.

Contribution

The paper presents a novel GR hydrodynamics code with improved energy conservation and neutrino transport schemes, validated by comprehensive tests in spherical symmetry.

Findings

The code accurately reproduces 1D core collapse results.

It demonstrates robustness in long-term proto-neutron star cooling simulations.

Effective GR treatment via an approximate potential yields high accuracy in 1D.

Abstract

We present a new general relativistic (GR) code for hydrodynamic supernova simulations with neutrino transport in spherical and azimuthal symmetry (1D/2D). The code is a combination of the CoCoNuT hydro module, which is a Riemann-solver based, high-resolution shock-capturing method, and the three-flavor, energy-dependent neutrino transport scheme VERTEX. VERTEX integrates the neutrino moment equations with a variable Eddington factor closure computed from a model Boltzmann equation and uses the ray-by-ray plus approximation in 2D, assuming the neutrino distribution to be axially symmetric around the radial direction, and thus the neutrino flux to be radial. Our spacetime treatment employs the ADM 3+1 formalism with the conformal flatness condition for the spatial three-metric. This approach is exact in 1D and has been shown to yield very accurate results also for rotational stellar collapse. We introduce new formulations of the energy equation to improve total energy conservation in relativistic and Newtonian hydro simulations with Eulerian finite-volume codes. Moreover, a modified version of the VERTEX scheme is developed that simultaneously conserves energy and lepton number with better accuracy and higher numerical stability. To verify our code, we conduct a series of tests, including a detailed comparison with published 1D results for stellar core collapse. Long-time simulations of proto-neutron star cooling over several seconds both demonstrate the robustness of the new CoCoNuT-VERTEX code and show the approximate treatment of GR effects by means of an effective gravitational potential as in PROMETHEUS-VERTEX to be remarkably accurate in 1D. (abridged)