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Advances in Astronomy
Volume 2011, Article ID 412620, 10 pages
Research Article

Relativistic Milne-Eddington Type Solutions with a Variable Eddington Factor for Relativistic Spherical Winds

Astronomical Institute, Osaka Kyoiku University, Asahigaoka, Kashiwara, Osaka 582-8582, Japan

Received 22 December 2010; Accepted 19 March 2011

Academic Editor: Jerome Orosz

Copyright © 2011 Jun Fukue. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Relativistic radiative transfer in a relativistic spherical flow is examined in the fully special relativistic treatment. Under the assumption of a constant flow speed and using a variable (prescribed) Eddington factor, we analytically solve the relativistic moment equations in the comoving frame for several restricted cases, and obtain relativistic Milne-Eddington type solutions. In contrast to the plane-parallel case where the solutions exhibit the exponential behavior on the optical depth, the solutions have power-law forms. In the case of the radiative equilibrium, for example, the radiative flux has a power-law term multiplied by the exponential term. In the case of the local thermodynamic equilibrium with a uniform source function in the comoving frame, the radiative flux has a power-law form on the optical depth. This is because there is an expansion effect (curvature effect) in the spherical wind and the background density decreases as the radius increases.