Spherical Relativistic Radiation Flows with Variable Eddington Factor

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.