Two-dimensional hydrodynamic core-collapse supernova simulations with spectral neutrino transport -: I.: Numerical method and results for a 15 M⊙ star

Supernova models with a full spectral treatment of the neutrino transport are presented, employing the prometheus/vertex neutrinohydrodynamics code with a variable Eddington factor closure of the O(v/c) moments equations of neutrino number, energy, and momentum. Our ray-by-ray plus approximation developed for two-( or three-)dimensional problems assumes that the local neutrino distribution function is azimuthally symmetric around the radial direction, which implies that the nonradial flux components disappear. Other terms containing the angular velocity components are retained in the moments equations and establish a coupling of the transport at different latitudes by lateral derivatives. Also lateral components of the neutrino pressure gradients are included in the hydrodynamics equations. This approximative approach for neutrino transport in multi-dimensional environments is motivated and critically assessed with respect to its capabilities, limitations, and inaccuracies in the context of supernova simulations. In this first paper of a series, one- (1D) and two-dimensional (2D) core-collapse calculations for a ( nonrotating) 15 M-. star are discussed, uncertainties in the treatment of the equation of state - numerical and physical - are tested, Newtonian results are compared with simulations using a general relativistic potential, bremsstrahlung and interactions of neutrinos of different flavors are investigated, and the standard approximation in neutrino-nucleon interactions with zero energy transfer is replaced by rates that include corrections due to nucleon recoil, thermal motions, weak magnetism, and nucleon correlations. Models with the full implementation of the ray-by-ray plus spectral transport were found not to explode, neither in spherical symmetry nor in 2D when the computational grid is constrained to a lateral wedge (< +/- 45 degrees) around the equator. The success of previous two- dimensional simulations with grey, flux-limited neutrino diffusion can therefore not be confirmed. An explosion is obtained in 2D for the considered 15 M-. progenitor, when the radial velocity terms in the neutrino momentum equation are omitted. This manipulation increases the neutrino energy density in the convective gain layer by about 20-30% and thus the integral neutrino energy deposition in this region by about a factor of two compared to the non-exploding 2D model with the full transport. The spectral treatment of the transport and detailed description of charged-current processes leads to proton-rich neutrino-heated ejecta, removing the problem that previous explosion models with approximate neutrino treatment overproduced N = 50 closed neutron shell nuclei by large factors.