Spherical Relativistic Radiation Flows with Variable Eddington Factor

TL;DR

This paper develops a method to model spherically symmetric relativistic radiation flows using a variable Eddington factor, enabling the simulation of gas acceleration to near-light speeds by radiation pressure.

Contribution

It introduces a flow-dependent variable Eddington factor to improve the closure relation in relativistic radiation hydrodynamics, avoiding singularities of traditional methods.

Findings

Gas reaches near the speed of light due to radiation pressure.

The variable Eddington factor effectively models relativistic radiation flows.

The method improves stability and accuracy of relativistic flow simulations.

Abstract

We solve spherically symmetric radiation flows under full special relativity with the help of a variable Eddington factor $f(\tau, \beta)$, where $\tau$ is the optical depth and $\beta$ is the flow velocity normalized by the speed of light. Relativistic radiation hydrodynamics under the moment formalism has several complex problems, such as a closure relation. Conventional moment equations closed with the traditional Eddington approximation in the comoving frame have singularity, beyond which the flow cannot be accelerated. In order to avoid such a pathological behavior inherent in the relativistic moment formalism, we propose a variable Eddington factor, which depends on the flow velocity as well as the optical depth, for the case of the sperically symmertic one-dimensional flow. We then calculate the relaticistic spherical flow with such variable Eddington factors to investigate the case that gas is accelerated by radiative force. As a result, it is shown that the gas speed reaches around the speed of light by radiation pressure.