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We study the multi-dimensional properties of neutrino transfer inside supernova cores by solving the Boltzmann equations for neutrino distribution functions in genuinely six dimensional (6D) phase space. Adopting representative snapshots of the post-bounce core from other supernova simulations in three dimensions, we solve the temporal evolutions to stationary states of neutrino distribution functions by our Boltzmann solver. Taking advantage of the multi-angle and multi-energy feature realized by the S$_n$ method in our code, we reveal the genuine characteristics of spatially three dimensional (3D) neutrino transfer such as non-radial fluxes and non-diagonal Eddington tensors. In addition, we assess the ray-by-ray approximation, turning off the lateral-transport terms in our code. We demonstrate that the ray-by-ray approximation tends to propagate fluctuations in thermodynamical states around the neutrino-sphere along each radial ray and overestimate the variations between the neutrino distributions on different radial rays. We find that the difference in the densities and fluxes of neutrinos between the ray-by-ray approximation and the full Boltzmann transport becomes ~20%, which is also the case for the local heating rate, whereas the volume-integrated heating rate in the Boltzmann transport is found to be only slightly larger (~2%) than the counterpart in the ray-by-ray approximation due to cancellation among different rays. These results suggest that we had better assess carefully the possible influences of various approximations in the neutrino transfer employed in the current simulations on supernova dynamics. Detailed information on the angle and energy moments of neutrino distribution functions will be profitable for the future development of numerical methods in neutrino-radiation hydrodynamics.
Core-collapse supernovae, the culmination of massive stellar evolution, are spectacular astronomical events and the principle actors in the story of our elemental origins. Our understanding of these events, while still incomplete, centers around a ne
We report on a set of long-term general-relativistic three-dimensional (3D) multi-group (energy-dependent) neutrino-radiation hydrodynamics simulations of core-collapse supernovae. We employ a full 3D two-moment scheme with the local M1 closure, thre
We develop a numerical code to calculate the neutrino transfer with multi-energy and multi-angle in three dimensions (3D) for the study of core-collapse supernovae. The numerical code solves the Boltzmann equations for neutrino distributions by the d
We have made core-collapse supernova simulations that allow oscillations between electron neutrinos (or their anti particles) with right-handed sterile neutrinos. We have considered a range of mixing angles and sterile neutrino masses including those
We present multi-dimensional core-collapse supernova simulations using the Isotropic Diffusion Source Approximation (IDSA) for the neutrino transport and a modified potential for general relativity in two different supernova codes: FLASH and ELEPHANT