Milne-Eddington Solutions for Relativistic Spherical Flows

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Relativistic radiative transfer in a relativistic spherical flow is examined using a fully special relativistic treatment. Under the assumption of a constant flow speed, we obtain analytical solutions of radiative moment equations in the case of a constant comoving luminosity, and in the streaming limit. In the case of a constant comoving luminosity, in the non-relativistic regime the luminosity in the inertial frame is constant, whereas in the relativistic regime there appears a term proportional to the velocity and the optical depth. The spherical pressure in the relativistic regime is also enhanced compared with that in the non-relativistic regime. In the case of the streaming limit, we can also integrate moment equations analytically to obtain the luminosity and the spherical pressure in the inertial frame. In this case the inertial luminosity increases with the optical depth, but the comoving one reduces. On the other hand, the spherical pressure in the inertial frame, which is proportional to the optical depth in the non-relativistic regime, reduces as the flow speed increases. These properties are similar to the plane-parallel case, if the luminosity and the spherical pressure are exchanged by the flux and the usual pressure, respectively.

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