Relativistic Variable Eddington Factor

Abstract

We analytically derive a relativistic variable Eddington factor in the relativistic radiative flow, and found that the Eddington factor depends on the {\it velocity gradient} as well as the flow velocity. When the gaseous flow is accelerated and there is a velocity gradient, there also exists a density gradient. As a result, an unobstructed viewing range by a comoving observer, where the optical depth measured from the comoving observer is unity, is not a sphere, but becomes an oval shape elongated in the direction of the flow; we call it a {\it one-tau photo-oval}. For the comoving observer, an inner wall of the photo-oval generally emits at a non-uniform intensity, and has a relative velocity. Thus, the comoving radiation fields observed by the comoving observer becomes {\it anisotropic}, and the Eddington factor must deviate from the value for the isotropic radiation fields. % In the case of a plane-parallel vertical flow, we examine the photo-oval and obtain the Eddington factor. In the sufficiently optically thick linear regime, the Eddington factor is analytically expressed as $f(\tau ,\beta ,\frac{d\beta }{d\tau })=1/3(1+16/15\frac{d\beta }{d\tau })$, where $\tau$ is the optical depth and $\beta$ ($=v/c$) is the flow speed normalized by the speed of light. %i.e., the Eddington factor depends on the velocity gradient. We also examine the linear and semi-linear regimes, and found that the Eddington factor generally depends both on the velocity and its gradient.

9 pages, 9 figures

References in corpus (7)

• Equations of General Relativistic Radiation Hydrodynamics from Tensor Formalism
• Relativistic Radiative Flow in a Luminous Disk
• Radiative Transfer and Limb Darkening of Accretion Disks
• Relativistic Radiative Flow in a Luminous Disk II
• Velocity-Dependent Eddington Factor in Relativistic Radiative Flow
• Equations of general relativistic radiation hydrodynamics in Kerr space-time
• Spherical Relativistic Radiation Flows with Variable Eddington Factor

Cited by in corpus (5)

• Variable Eddington Factor in a Relativistic Plane-Parallel Flow
• Relativistic Variable Eddington Factor in a Relativistic Plane-Parallel Flow
• Milne-Eddington Solutions for Relativistic Plane-Parallel Flows
• The radiation hydrodynamics of relativistic shear flows
• A Class of Physically Motivated Closures for Radiation Hydrodynamics