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The analytical results of Chandrasekhar’s semi-infinite diffuse reflection problem is crucial in the context of the stellar or planetary atmosphere. However, the atmospheric emission effect was not taken into account in this model, and the solutions are applicable only for diffusely scattering atmosphere in absence of emission. In this talk I show how to extend the model of semi-infinite diffuse reflection problem by including the effects of thermal emission B(T ), and present how this affects Chandrasekhar’s analytical results. Thus I generalize Chandradekhar’s model to provide a complete picture of this problem. I use the Invariance Principle Method to find the radiative transfer equation accurate for diffuse reflection in presence of B(T ). Then I show the modified scattering function S for different kinds of phase functions. It can be noted that, the scattering function S and diffusely reflected specific intensity I for different phase functions are modified due to the emission B(T ) from layer τ = 0. In both cases, B(T) is added to the results of only the scattering case derived by Chandrasekhar, with some multiplicative factors. Thus the diffusely reflected spectra will be enriched and carry the temperature information of τ = 0 layers. As the effects are additive in nature, hence our model reduces to the sub-case of Chandrasekhar’s scattering model in case of B(T ) = 0.  I conclude that our generalized model provides more accurate results due to the inclusion of the thermal emission effect in Chandrasekhar’s semi-infinite atmosphere problem.

Effects of thermal emission on Chandrasekhar’s semi-infinite diffuse reflection problem