RELATIONSHIP BETWEEN THE POLARIZED RADIATION-FIELDS IN EXTERNALLY ANDINTERNALLY ILLUMINATED HOMOGENEOUS PLANETARY-ATMOSPHERES

The Stokes parameters of the polarized radiation in a plane-parallel h omogeneous atmosphere, which is solely illuminated by homogeneously di stributed, isotropically radiating internal sources, are expressed in terms of moments of the Stokes parameters of the polarized radiation i n the same atmosphere, but now solely illuminated by unidirectional ra diation at its boundaries. This relationship holds for homogeneous atm ospheres with a general law of single scattering and with arbitrary op tical thickness. It has already been reported by Domke and Yanovitskij , but a different derivation is presented here. For that purpose we us e analytic solutions of the equation of radiative transfer in the pres ence of internal sources for conservative and non-conservative scatter ing. Further, we show that the relationship for conservative scatterin g can also be obtained from the non-conservative one, by using the eig ensolution of the homogeneous equation of radiative transfer for weak absorption and taking the limit towards conservative scattering. Final ly, we present some numerical illustrations of the accuracy of (i) the eigensolution of the homogeneous equation of radiative transfer for w eak absorption and (ii) an analytical expression for the radiation dee p inside an optically thick homogeneous conservative atmosphere contai ning internal sources.