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

Abstract

Spherically symmetric (1D) and two-dimensional (2D) supernova simulations for progenitor stars between 11 M and 25 M are presented, making use of the Prometheus/Vertex neutrino-hydrodynamics code, which employs a full spectral treatment of neutrino transport and neutrino-matter interactions with a variable Eddington factor closure of the O(v/c) moments equations of neutrino number, energy, and momentum. Multi-dimensional transport aspects are treated by the "ray-by-ray plus" approximation described in Paper I. We discuss in detail the variation of the supernova evolution with the progenitor models, including one calculation for a 15 M progenitor whose iron core is assumed to rotate rigidly with an angular frequency of 0.5 rad s −1 before collapse. We also test the sensitivity of our 2D calculations to the angular grid resolution, the lateral wedge size of the computational domain, and to the perturbations which seed convective instabilities in the post-bounce core. In particular, we do not find any important differences depending on whether random perturbations are included already during core collapse or whether such perturbations are imposed on a 1D collapse model shortly after core bounce. Convection below the neutrinosphere sets in 30−40 ms after bounce at a density well above 10 12 g cm −3 in all 2D models, and encompasses a layer of growing mass as time goes on. It leads to a more extended proto-neutron star structure with reduced mean energies of the radiated neutrinos, but accelerated lepton number and energy loss and significantly higher muon and tau neutrino luminosities at times later than about 100 ms after bounce. While convection inside the nascent neutron star turns out to be insensitive to our variations of the angular cell and grid size, the convective activity in the neutrino-heated postshock layer gains more strength in better resolved models. We find that low (l = 1, 2) convective modes, which require the use of a full 180 degree grid and are excluded in simulations with smaller angular wedges, can qualitatively change the evolution of a model. In case of an 11.2 M star, the lowest-mass progenitor we investigate, a probably rather weak explosion by the convectively supported neutrino-heating mechanism develops after about 150 ms post-bounce evolution in a 2D simulation with 180 degrees, whereas the same model with 90 degree wedge fails to explode like all other models. This sensitivity demonstrates the proximity of our 2D calculations to the borderline between success and failure, and stresses the need to strive for simulations in 3D, ultimately without the constraints connected with the axis singularity of a polar coordinate grid.

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

“…(See Appendix A for a full definition and discussion of the thermal energy.) A ratio of 1 adv heat t t > indicates that matter passing from the shock to the gain surface will undergo substantial heating while in the gain region, and conditions will therefore become favorable for a thermal runaway and the revival of the shock (Janka 2001; Thompson et al 2005;Buras et al 2006a). As can be seen in Figure 10(c), adv heat t t exceeds unity at ∼100 ms after bounce for all models and exceeds three about 50 ms later.…”

“…Because of the complex flow patterns that develop behind the shock, an alternative approach that better quantifies the complexities of the multidimensional flows is to examine the evolution of the residency time distribution function of the included passive tracer particles (Murphy & Burrows 2008;Takiwaki et al 2012;Handy et al 2014), which we will examine in a later paper. We define an advection timescale, as suggested by Buras et al (2006a), to be the interval of time from the time, t M , shock ( ) the shock encloses a given mass shell, M, to the time, t M , gain ( ) the gain surface encloses the same mass While a fluid element resides in the heating layer, it is heated by neutrino energy deposition. We characterize this process by a heating timescale heat t defined as…”

“…The measure of the explosion energy most widely used in discussions of CCSN models is referred to as the diagnostic energy, E + , which is the volume integral of the total energy density, e e e e , tot kin th grav = + + over all zones for which e 0 tot > (Buras et al 2006a;Suwa et al 2010;Müller et al 2012b;Bruenn et al 2013). The thermal energy e th is the internal energy minus the rest mass energy of all "conserved" particles.…”

“…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.…”

“…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.)…”