A Detailed Comparison of Multidimensional Boltzmann Neutrino Transport Methods in Core-collapse Supernovae

Abstract

The mechanism driving core-collapse supernovae is sensitive to the interplay between matter and neutrino radiation. However, neutrino radiation transport is very difficult to simulate, and several radiation transport methods of varying levels of approximation are available. We carefully compare for the first time in multiple spatial dimensions the discrete ordinates (DO) code of Nagakura, Yamada, and Sumiyoshi and the Monte Carlo (MC) code Sedonu, under the assumptions of a static fluid background, flat spacetime, elastic scattering, and full special relativity. We find remarkably good agreement in all spectral, angular, and fluid interaction quantities, lending confidence to both methods. The DO method excels in determining the heating and cooling rates in the optically thick region. The MC method predicts sharper angular features due to the effectively infinite angular resolution, but struggles to drive down noise in quantities where subtractive cancellation is prevalent, such as the net gain in the protoneutron star and off-diagonal components of the Eddington tensor. We also find that errors in the angular moments of the distribution functions induced by neglecting velocity dependence are subdominant to those from limited momentum-space resolution. We briefly compare directly computed second angular moments to those predicted by popular algebraic two-moment closures, and we find that the errors from the approximate closures are comparable to the difference between the DO and MC methods. Included in this work is an improved Sedonu code, which now implements a fully special relativistic, time-independent version of the grid-agnostic MC random walk approximation.

Fast-pairwise Collective Neutrino Oscillations Associated with Asymmetric Neutrino Emissions in Core-collapse Supernovae

“…The details of the code development of our Boltzmann solver are described in a series of papers Nagakura et al 2014Nagakura et al , 2017Nagakura et al , 2019d and its reliability has been well established by a detailed comparison to another Monte-Carlo neutrino transport code (Richers et al 2017). Some results of axisymmetric CCSN simulations by using our code can be seen in Nagakura et al (2018); Harada et al (2019); Nagakura et al (2019c).…”

“…This generates coherent lateral flux of ELN, and then induces the non-radial ELN crossings. It should be noted, however, that our Boltzmann solver suffers from the numerical diffusion in particular at larger radii as demonstrated in Richers et al (2017), which may artificially enhance the region of non-radial ELN crossing. For more quantitative discussions, we need to carry out higher-resolution simulations, which are beyond the scope of this paper, though.…”

Comparing Treatments of Weak Reactions with Nuclei in Simulations of Core-collapse Supernovae

“…We solve the Poisson equation for Newtonian gravity using the mass integration method. Details of the formulation and numerical methods in our code were presented in a series of our previous papers (Sumiyoshi & Yamada 2012;Nagakura et al 2014;Shibata et al 2014;Nagakura et al 2017) and the reliability of our code was established by a detailed comparison with Monte-Carlo transport method in Richers et al (2017a). For all simulations, we employ the same weak interaction rates as those used in (Nagakura et al 2018), except for electron and positron captures on nuclei.…”

Neutrino quantum kinetics in compact objects

“…Numerical simulations have become the primary tool for studying the nonlinear and multi-physics dynamics in CCSNe. Current state of the art simulations account for neutrino transport by treating neutrinos as classical radiation and employing a variety of implementations of the relativistic Boltzmann equation or approximations thereof (e.g., [4][5][6][7][8][9][10]). Over the years since the first numerical model of a neutrino-driven supernova by ?…”