Two-dimensional hydrodynamic core-collapse supernova simulations with spectral neutrino transport

Abstract

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• ) 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 protonrich neutrino-heated ejecta, removing the problem that previous explosion models with approximate neutrino treatment overproduced N = 50 closed neutron shell nuclei by large factors.

The Development of Explosions in Axisymmetric Ab Initio Core-Collapse Supernova Simulations of 12–25 Stars

“…Second, material advecting toward the gain surface is continually heated by neutrinos, gaining entropy as it moves inwards. As has been pointed out by many authors (e.g., Herant et al 1992Herant et al , 1994Janka & Müller 1993;Burrows et al 1995;Janka & Müller 1995;Thompson 2000;Janka 2001;Fryer & Warren 2004;Thompson et al 2005;Bruenn et al 2006;Buras et al 2006b;Murphy & Burrows 2008;Scheck et al 2008;Müller et al 2012a), convective flows enhance the conditions necessary for the revival of the shock. They increase the effective neutrino heating efficiency because rising fluid elements have lower neutrino emissivities after adiabatic expansion, reducing losses due to neutrino cooling, and the non-radial motions increase the dwell time of fluid elements in the gain region, thereby increasing the time they are subject to neutrino heating.…”

“…Another difference is our use of the revised Cooperstein EoS in the region between the neutrinosphere and the shock. The PROMETHEUS-VERTEX code (Rampp & Janka 2002;Marek et al 2006), with Newtonian hydrodynamics and the same psuedo-Newtonian (spherical GR corrections to Newtonian) gravity treatment implemented in CHIMERA, was used by Buras et al (2006aBuras et al ( , 2006b and Marek & Janka (2009) to evolve, in axisymmetry, the 15 M  progenitor s15s7b2 of Woosley & Weaver (1995). Müller et al (2012b) also evolved s15s7b2 using the COCONUT-VERTEX code , which employes the conformal flatness GR approximation rather than a pseudo-Newtonian approximation to the hydrodynamics, gravity, and RbR transport.…”

“…The simulations of this progenitor reported by Buras et al (2006aBuras et al ( , 2006b were of rather low resolution (32 or 64 angular zones) and did not incorporate a full 180°grid in latitude, which excludes the development of the low order (ℓ 1, 2 = ) convective and SASI modes, and did not lead to explosions. Marek & Janka (2009) employed a full 180°grid and finer angular resolution (128 and 192 angular zones).…”

“…Though two decades have passed, 2D models are only now beginning to fill in the CCSN landscape in a fashion done previously in 1D. Twodimensional simulations including spectral neutrino transport, general relativistic corrections to 2D Newtonian self gravity or approximate 2D general relativistic self gravity, all relevant neutrino weak interactions, including neutrino-energy-coupled scattering and electron capture on nuclei modeled to include nucleon-nucleon interactions, and sophisticated nuclear equations of statehave been performed with two codes thus far, VERTEX (Buras et al 2006a(Buras et al , 2006bMarek & Janka 2009;Müller et al 2012aMüller et al , 2012b and CHIMERA (Bruenn et al 2006;Messer et al 2007;Bruenn et al 2009aBruenn et al , 2013, though these codes use the "ray-by-ray" (RbR) approximation to neutrino transport rather than a fully 2D transport implementation. (We will discuss the RbR approximation in Sections 2 and 5.3.)…”

Neutrino-Nucleon Interactions in Supernova: Hartree Response & Approximations

“…However, at densities around 10 12 g cm −3 and temperatures above 10 MeV differences on the order of 10% appear between the two [13]. For nonrelativistic opacities with recoil such as in [10], a specific correction factor, based on the corresponding vacuum cross sections in [11], was deduced in [14] and included in the neutrino transport code VERTEX. Fig.…”