Three-dimensional Boltzmann-Hydro code for core-collapse in massive stars I. special relativistic treatments

TL;DR

This paper introduces a novel numerical method for simulating core-collapse supernovae using special relativistic Boltzmann equations, demonstrating improved accuracy over non-relativistic models.

Contribution

The paper presents a new approach to solve multi-dimensional relativistic Boltzmann equations with innovative energy grid handling, enabling comprehensive supernova simulations.

Findings

Successfully simulated core-collapse, bounce, and shock-stall phases.

Demonstrated the importance of relativistic effects in neutrino transfer.

Validated the method with basic tests and a 1D supernova model.

Abstract

We propose a novel numerical method for solving multi-dimensional, special relativistic Boltzmann equations for neutrinos coupled to hydrodynamics equations. It is meant to be applied to simulations of core-collapse supernovae. We handle special relativity in a non-conventional way, taking account of all orders of v/c. Consistent treatment of advection and collision terms in the Boltzmann equations is the source of difficulties, which we overcome by employing two different energy grids: Lagrangian remapped and laboratory fixed grids. We conduct a series of basic tests and perform a one-dimensional simulation of core-collapse, bounce and shock-stall for a 15M_{sun} progenitor model with a minimum but essential set of microphysics. We demonstrate in the latter simulation that our new code is capable of handling all phases in core-collapse supernova. For comparison, a non-relativistic simulation is also conducted with the same code, and we show that they produce qualitatively wrong results in neutrino transfer. Finally, we discuss a possible incorporation of general relativistic effects in our method.