On the Neutrino Distributions in Phase Space for the Rotating Core-collapse Supernova Simulated with a Boltzmann-neutrino-radiation-hydrodynamics Code

TL;DR

This paper presents a detailed simulation of neutrino phase space distributions in a rotating core-collapse supernova, highlighting the limitations of the M1-closure approximation in capturing complex angular distributions.

Contribution

It introduces a Boltzmann-neutrino-radiation-hydrodynamics code that directly solves neutrino transport equations, revealing inaccuracies in common closure methods under rotation.

Findings

Eddington tensor errors reach ~20% in the simulation.

M1-closure fails near the shock due to complex angular neutrino distributions.

Rotation significantly distorts neutrino angular distributions in phase space.

Abstract

With the Boltzmann-radiation-hydrodynamics code, which we have developed to solve numerically the Boltzmann equations for neutrino transfer, the Newtonian hydrodynamics equations, and the Newtonian self-gravity simultaneously and consistently, we simulate the collapse of a rotating core of the progenitor with a zero-age-main-sequence mass of $11.2\,M_\odot$ and a shelluler rotation of $1\,{\rm rad\,s^{-1}}$ at the center. We pay particular attention in this paper to the neutrino distribution in phase space, which is affected by the rotation. By solving the Boltzmann equations directly, we can assess the rotation-induced distortion of the angular distribution in momentum space, which gives rise to the rotational component of the neutrino flux. We compare the Eddington tensors calculated both from the raw data and from the M1-closure approximation. We demonstrate that the Eddington tensor is determined by complicated interplays of the fluid velocity and the neutrino interactions and that the M1-closure, which assumes that the Eddington factor is determined by the flux factor, fails to fully capture this aspect, especially in the vicinity of the shock. We find that the error in the Eddington factor reaches $\sim 20\%$ in our simulation. This is due not to the resolution but to the different dependence of the Eddington and flux factors on the angular profile of the neutrino distribution function, and hence modification to the closure relation is needed.