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

TL;DR

This work develops MuDBaTH, a two-dimensional, spectrally resolved neutrino transport framework built as an extension of a validated 1D Vertex code, employing a ray-by-ray plus coupling with axial symmetry and an approximate GR potential. The authors apply it to a nonrotating 15 $M_\odot$ progenitor to assess how detailed neutrino-matter interactions and velocity-dependent transport terms influence core collapse, neutrino emission, and the neutrino-heated explosion mechanism. Across 1D and 2D runs with varied opacities, gravity treatments, and transport terms, they find that full spectral transport does not yield explosions for this progenitor, while omitting certain velocity-dependent terms can artificially trigger explosions, underscoring the critical role of transport physics in determining outcomes. The study highlights the limitations of 2D ray-by-ray transport, the importance of accurate neutrino-nucleon physics (recoil, weak magnetism, and flavor interactions), and the need for fully multidimensional transport to robustly assess the viability of neutrino-driven explosions, setting the stage for Paper II with broader progenitors, rotation, and higher angular resolution.

Abstract

Supernova models with a full spectral treatment of the neutrino transport are presented, employing the Prometheus/Vertex neutrino-hydrodynamics code with a ``ray-by-ray plus'' approximation for treating two- (or three-) dimensional problems. The method is described in detail and critically assessed with respect to its capabilities, limitations, and inaccuracies in the context of supernova simulations. In this first paper of a series, 1D and 2D core-collapse calculations for a (nonrotating) 15 M_sun 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 with a 90 degree lateral wedge. The success of previous 2D simulations with grey, flux-limited neutrino diffusion can therefore not be confirmed. Omitting the radial velocity terms in the neutrino momentum equation leads to ``artificial'' explosions by increasing 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. (abbreviated)

Figures (49)

• Figure 1: a Component of the linear momentum in polar axis direction of all matter on the computational grid. The solid line shows its time evolution for Model s15Gio_32.b, in which a lateral wedge around the equator and with periodic boundary conditions was used (this model is described in detail in Sect. \ref{['sec:acme']}). The dotted line belongs to Model s11.2Gio_128.b, which is a model with a full 180$\degr$ grid and thus with reflecting boundary conditions at the poles (in lateral direction); this model will be described in burram05:II. b Distance between the center of the grid and the center of mass for the same two models.
• Figure 2: a Standard deviation of the density $\sigma_\rho$ (see Eq. \ref{['eq:sigma']}) indicating convective activity inside the neutron star. The 1D Model s15Gio_1d.b was mapped to 2D (16 zones with a resolution of $2.7\degr$) $27\mathrm{ms}$ after core bounce and the density distribution $\rho$ was perturbed. The plot shows the situation after 3.6ms of dynamical evolution computed with different implementations of the 2D transport equations. The dotted line is the initial value of $\sigma_\rho$, the thick solid line shows the standard deviation $\sigma_\rho$ when the lateral terms are included in our scheme as described in Sects. \ref{['sec:2dmomequ']} and \ref{['sec:2dcoupling']}. For comparison, the thin solid line shows $\sigma_\rho$ when running with pure ray-by-ray transport (i.e., without all boldface terms in Eqs. (\ref{['eq:momeqe1']}--\ref{['eq:momeqn2']}) and without the lateral component of neutrino pressure gradients), and the dash-dotted line corresponds to a simulation where the lateral terms of Sect. \ref{['sec:2dmomequ']} and Appendix \ref{['app:momeq3d']} were taken into account but not the neutrino momentum transfer to the fluid discussed in Sect. \ref{['sec:2dcoupling']}. b Brunt-Väisälä frequency for the same model at the beginning of the test calculations, derived from the Quasi-Ledoux criterion, Eq. (\ref{['eq:quasi_ledoux']}), using $s=s+s_\nu$ and $Y=Y_\mathrm{lep}$. Negative $\omega_\mathrm{BV}$ indicates convectively stable regions.
• Figure 3: The upper panel compares total (volume integrated) neutrino heating rates in the gain layer $\delta_t E_\mathrm{gl}$. The bold upper solid line shows the evolution of $\delta_t E_\mathrm{gl}$ for the $11.2M_{\sun}$ supernova model of burram03. The post-processed heating rate obtained by averaging the neutrino densities over all latitudes is represented by diamond-like symbols. For a consistency check crosses are drawn for the post-processed neutrino heating rate without using the lateral averages of the specific neutrino density. Ideally the latter post-processed results should be equal to the values returned from the model run. Remaining differences result from the fact that the post-processing may yield a gain radius shifted by one radial zone. For drawing the second curve (thin solid line) and the corresponding symbols the analysis was restricted to downflows in the gain layer, i.e. for regions with velocity $v<1.5\left<v\right>_{\vartheta}<0$. The middle panel shows the average net heating rate per baryon (the symbols have the same meaning as in the upper panel), i.e. the total neutrino heating rate in the gain layer divided by the total mass $M_\mathrm{gl}$ contained in this region. The lower panel shows the maximum neutrino flux as measured slightly above the gain radius normalized to the flux average over all latitudes at the same radius, $F_\mathrm{max}^\mathrm{N} = \max_{\vartheta} \left(F\right) / \left<F\right>_\vartheta$. The values indicate the relative strength of localized luminosity outbursts.
• Figure 4: Comparison of the LS EoS (thick lines) with the four-species NSE table introduced here (thin lines), for ${Y_\mathrm{e}}=0.3$ and $T=1$ (solid), 2 (dotted), and 3 (dashed) MeV. $X_\alpha$ and $X_\mathrm{h}$ are the mass fractions of $\alpha$-particles and of the representative heavy nucleus, respectively.
• Figure 5: Shock positions for the two dynamical simulations of the post-bounce evolution of an $11.2M_{\sun}$ star with the LS EoS (dashed) and the four-species NSE table (solid) used in the density regime below $10^{11}~\mathrm{g}\,\mathrm{cm}^{-3}$.