# A Detailed Comparison of Multi-Dimensional Boltzmann Neutrino Transport Methods in Core-Collapse Supernovae

(arXiv)

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 sub-dominant 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 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 Monte Carlo random walk approximation.

2D Eddington Tensor (Off-Diagonal Components).  All plots show the energy-integrated lab-frame $r\theta$ component of the Eddington tensor. This is a sensitive probe of multi-dimensional anisotropy, as it is identically zero in 1D calculations. In each plot, we show the radiation moment computed using the 2D_HR DO calculation (top left quadrant, northern hemisphere data) and the 2D_HR_native MC calculation (bottom left quadrant, northern hemisphere data). The left plot shows electron neutrinos, the center shows electron anti-neutrinos, and the right shows heavy lepton neutrinos. The difference between the MC and DO results is shown in the right half of each plot, which shows data from both hemispheres. The shock front is drawn as a contour at entropy S=7 k_B/baryon and is colored for clarity. MC results show larger values of P^r\theta due to limited angular resolution in the DO calculation.

## The Sedonu Monte Carlo Radiation Transport Code

Sedonu is open source and available at https://bitbucket.org/srichers/sedonu. It was first described in Richers et al., Astrophys. J. 813, 38 (2015) and the version released together with this new, Richer et al. 2017 study, comes with a number of improvements, in particular a special relativistic implementation of the Monte Carlo random walk approximation to speed up transport at high optical depth.

## Provided Data and Scripts

We provide the output data of our highest-fidelity results, along with the full working Sedonu setup hosted by zenodo.org at the following URL: https://zenodo.org/record/807765. The data are citable with . They are licensed under the Creative Commons Attribution 4.0 license. When using the data, please also cite our paper.