Radiative Transfer in spherically symmetricsystems--II: The Non-Conservative case and Linearly Polarized Radiation

The method for the solution of transfer problems in spherically symmetric systems developed recently by Hummer and Rybicki is here generalized to the non-conservative case. This procedure, which depends on the iterative determination of the Eddington factor f = K / J , handles in a natural way the outward peaking of the radiation field which occurs in extended atmospheres. To illustrate the present extension of this method, solutions are obtained for the problem of scattering of linearly polarized radiation by an extended electron-scattering atmosphere. Although the transfer of radiation through such an atmosphere is conservative, each of the component equations is not. For opacity laws of the form $$k\rho \,=\,{r}^{-n},\,o\,\lt\,r\,\lt\,R,\,n\,=2\,\text{and}\,3$$ , very large values of the polarization are found as a general feature arising from the strong peaking of the radiation field. It is found that the temperature distribution in such extended electron-scattering atmospheres differs negligibly from that computed on the assumption of isotropic scattering, with the neglect of polarization. The procedure used for the polarization problem can also be applied directly to problems with a non-grey opacity involving many frequencies simultaneously.