Should One Use the Ray-by-Ray Approximation in Core-Collapse Supernova Simulations?

Abstract

We perform the first self-consistent, time-dependent, multi-group calculations in two dimensions (2D) to address the consequences of using the ray-by-ray+ transport simplification in core-collapse supernova simulations. Such a dimensional reduction is employed by many researchers to facilitate their resource-intensive calculations. Our new code (Fornax) implements multi-D transport, and can, by zeroing out transverse flux terms, emulate the ray-by-ray+ scheme. Using the same microphysics, initial models, resolution, and code, we compare the results of simulating 12-, 15-, 20-, and 25-M ⊙ progenitor models using these two transport methods. Our findings call into question the wisdom of the pervasive use of the ray-by-ray+ approach. Employing it leads to maximum post-bounce/preexplosion shock radii that are almost universally larger by tens of kilometers than those derived using the more accurate scheme, typically leaving the post-bounce matter less bound and artificially more "explodable." In fact, for our 25-M ⊙ progenitor, the ray-by-ray+ model explodes, while the corresponding multi-D transport model does not. Therefore, in two dimensions the combination of ray-by-ray+ with the axial sloshing hydrodynamics that is a feature of 2D supernova dynamics can result in quantitatively, and perhaps qualitatively, incorrect results.

General-Relativistic Three-Dimensional Multi-Group Neutrino Radiation-Hydrodynamics Simulations of Core-Collapse Supernovae

“…Additionally, we employ a set of neutrino opacities that differ in detail from the opacities used by Tamborra et al (2014), which can result in a different evolution of entropy and lepton number gradients. It is also possible that the full 3D neutrino transport we employ, as opposed to the "ray-by-ray" approximation used by Tamborra et al (2014), washes out asymmetries in the neutrino field that drive LESA (Skinner et al 2015;Sumiyoshi et al 2015). We emphasize that there are many other differences between our neutrino transport scheme and the scheme used by Tamborra et al (2014), so the absence of LESA in our models cannot be unequivocally attributed to the difference between full 3D transport and the "ray-by-ray" approximation.…”

“…To date, 3D radiation-hydrodynamics simulations of CCSNe have employed spectral, one-moment or two-moment radiation transport schemes in the ray-by-ray approximation (e.g., Lentz et al 2015;Melson et al 2015). Some argue that this approximation may overestimate spatial variations in the neutrino field (e.g., Sumiyoshi et al 2015;Skinner et al 2015).…”

Crucial Physical Dependencies of the Core-Collapse Supernova Mechanism

“…2) simulations, the dependence of the outcome of collapse (most notably whether the model explodes) on neutrino-nucleon scattering rates (via modifications of in-medium response corrections due to many-body effects), pre-collapse convective perturbations, inelastic neutrino-electron scattering, and inelastic neutrino-nucleon scattering. We also continue our study, started in Skinner et al (2016), of the issues raised by the use of the ray-by-ray+ method. What we find is that when the proto-neutron star bounded by a stalled shock is close to the critical condition for explosion (Burrows and Goshy 1993), as it easily can be in the turbulent multi-D context, the sensitivity to explosion of small changes in the physical inputs is amplified.…”

“…Such a dimensional reduction for the transport, particularly manifest in 2D, ignores lateral, non-radial radiative transport, which has been shown to be of quantitative (Ott et al 2008;Brandt et al 2011;Burrows 2013;Dolence et al 2015;Sumiyoshi et al 2015) and qualitative (Skinner et al 2016) importance. To the point, Skinner et al (2016) have shown that the ray-by-ray anomalies in the angular distribution of the radiation field and corresponding neutrino heating rates can reinforce the axial sloshing motions in 2D and push the shock into explosion. 1 Bruenn et al (2013Bruenn et al ( , 2016 find explosions in 2D (axially symmetry) for all the progenitors they studied (the 12-, 15-, 20-, and 25-M models of Woosley and Heger 2007), but the models all explode at about the same post-bounce time (∼100 milliseconds) and the shock radii never decrease in value.…”

“…The ORNL group (Bruenn et al 2013(Bruenn et al , 2016, with their CHIMERA code, uses multi-group flux-limited diffusion (MGFLD) neutrino transport (Bruenn 1985), the VH-1 Newtonian hydrodynamics package, a monopole correction for general relativity (GR) (Marek et al 2006), but multiple one-dimensional solves for multi-dimensional transport using the so-called "ray-by-ray+" approach (Buras et al 2003;Burrows et al 1995). Such a dimensional reduction for the transport, particularly manifest in 2D, ignores lateral, non-radial radiative transport, which has been shown to be of quantitative (Ott et al 2008;Brandt et al 2011;Burrows 2013;Dolence et al 2015;Sumiyoshi et al 2015) and qualitative (Skinner et al 2016) importance. To the point, Skinner et al (2016) have shown that the ray-by-ray anomalies in the angular distribution of the radiation field and corresponding neutrino heating rates can reinforce the axial sloshing motions in 2D and push the shock into explosion.…”