Truncated Moment Formalism for Radiation Hydrodynamics in Numerical Relativity

TL;DR

This paper develops a truncated moment formalism for general relativistic radiation hydrodynamics, enabling more accurate modeling of neutrino transfer in astrophysical phenomena by deriving covariant equations with a variable Eddington factor.

Contribution

It introduces a new formalism based on Thorne's moments, defining radiation moments in the fluid rest frame and deriving covariant equations with a closure relation.

Findings

Formalism applicable to optically thin and thick regimes

Derived equations in a closed covariant form

Effective closure relation with variable Eddington factor

Abstract

A truncated moment formalism for general relativistic radiation hydrodynamics, based on the Thorne's moment formalism, is derived. The fluid rest frame is chosen to be the fiducial frame for defining the radiation moments. Then, zeroth-, first-, and second-rank radiation moments are defined from the distribution function with a physically reasonable assumption for it in the optically thin and thick limits. The source terms are written, focusing specifically on the neutrino transfer and neglecting higher harmonic angular dependence of the reaction angle. Finally, basic equations for a truncated moment formalism for general relativistic radiation hydrodynamics in a closed covariant form are derived assuming a closure relation among the radiation stress tensor, energy density, and energy flux, and a variable Eddington factor, which works well.