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

## TL;DR

This paper compares two advanced neutrino transport methods, discrete ordinates and Monte Carlo, in simulating core-collapse supernovae, highlighting their agreement, differences, and the impact of various approximations.

## Contribution

First detailed multi-dimensional comparison of DO and MC neutrino transport methods in supernovae, including an improved Sedonu code with relativistic capabilities.

## Key findings

- Good spectral and angular agreement between methods
- DO excels in optically thick regions for heating/cooling rates
- MC provides sharper angular features but has higher noise

## 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 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.