热辐射对半无限漫反射问题的影响
Effects of thermal emission on Chandrasekhar's semi-infinite diffuse reflection problem
摘要：
内容：在恒星或行星大气的背景下，半无限漫反射问题的解析结果是至关重要的。然而，该模型没有考虑大气辐射的影响，并且该解仅适用于无辐射的漫散射大气。目的：我们扩展了半无限漫反射问题的模型，包括热辐射B（T）的影响，并提出这是如何影响Eschrasekhar的分析结果。因此，我们的目标是推广Ekrasekhar的模型，以提供一个完整的图片这个问题。方法：利用不变性原理，推导出B（T）存在时漫反射的辐射转移方程。在此基础上，我们导出了不同相函数的修正散射函数S（$μ,ϕ; μ_0 , ϕ_0$）。结果如下：我们发现，散射函数S（$μ, ϕ; μ_0 , ϕ_0$）以及漫反射比强度$I(0, μ; μ_0 )$为不同的相位函数修改由于层$τ = 0$的发射$B(T)$。在这两种情况下，B（T）被添加到由Eschrasekhar导出的仅散射情况的结果中，具有一些乘法因子。因此，漫反射光谱将被丰富并携带$τ = 0$层的温度信息。由于这些效应本质上是加性的，因此我们的模型在$B(T) = 0$的情况下简化为Alasekhar散射模型的子情况。我们的结论是，我们的广义模型提供了更准确的结果，由于列入的热辐射效应在Eschrasekhar的半无限大气问题。
英文摘要：
Context: The analytical results of Chandrasekhar's semi-infinite diffuse reflection problem is crucial in the context of 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. Aim: We 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 end results. Hence, we aim to generalize Chandrasekhar's model to provide a complete picture of this problem. Method: We use Invariance Principle Method to find the radiative transfer equation accurate for diffuse reflection in presence of B(T ). Then we derive the modified scattering function S($μ,ϕ; μ_0 , ϕ_0$ ) for different kind of phase functions. Results: We find that, the scattering function S($μ, ϕ; μ_0 , ϕ_0$ ) as well as diffusely reflected specific intensity $I(0, μ; μ_0 )$ 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 scattering case derived by Chandrasekhar, with some multiplicative factors. Thus the diffusely reflected spectra will be enriched and carries the temperature information of $τ = 0$ layer. As the effects are additive in nature, hence our model reduces to the sub-case of Chandrasekhar's scattering model in case of $B(T) = 0$. We 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.
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