论文标题
大气热排放对Chandrasekhar的有限大气问题
Atmospheric Thermal Emission Effect on Chandrasekhar's Finite Atmosphere Problem
论文作者
论文摘要
\ textit {diffuse反射有限大气问题的解决方案在天体物理环境中非常有用。 Chandrasekhar是第一个通过考虑大气散射来分析该问题的人。这些结果在行星气氛的建模中具有广泛的应用。但是，它们不能用于建模具有发射的气氛。我们通过在散射和热发射的存在下包括\ textit {热发射效应}以及散射来解决这个问题。为此，我们使用不变性原理方法采用一种分析方法来解决在存在大气热发射的情况下弥漫反射有限大气问题。我们建立了修改散射函数$ s（τ;μ，ϕ;μ_0，ϕ_0）$的一般积分方程，传输函数$ t（τ;μ，ϕ;μ_0，ϕ_0）$及其相对于热辐射气氛的$τ$。我们将这些方程式定制为各向同性散射的情况，并引入两个新功能$ V（μ）$和$ W（μ）$，类似于Chandrasekhar $ x（μ）$和$ y（μ）$函数。我们还得出了修改后的S-T功能之间的转换关系，并给出了$ V（μ）$和$ W（μ）$函数的物理帐户。我们的最终结果与Chandrasekhar在低排放极限（即仅散射）下的结果一致。从我们的结果的一致性来看，我们得出的结论是，在弥漫反射有限大气问题中，对热排放效应的考虑比仅考虑散射更具通用和准确的结果。
The solutions of the \textit{diffuse reflection finite atmosphere problem} are very useful in the astrophysical context. Chandrasekhar was the first to solve this problem analytically, by considering atmospheric scattering. These results have wide applications in the modeling of planetary atmospheres. However, they cannot be used to model an atmosphere with emission. We solved this problem by including \textit{thermal emission effect} along with scattering.Here, our aim is to provide a complete picture of generalized finite atmosphere problem in presence of scattering and thermal emission, and to give a physical account of the same. For that, we take an analytical approach using the invariance principle method to solve the diffuse reflection finite atmosphere problem in the presence of atmospheric thermal emission. We established the general integral equations of modified scattering function $S(τ; μ, ϕ; μ_0, ϕ_0)$, transmission function $T(τ; μ, ϕ; μ_0, ϕ_0)$ and their derivatives with respect to $τ$ for a thermally emitting atmosphere. We customize these equations for the case of isotropic scattering and introduce two new functions $V(μ)$ and $W(μ)$, analogous to Chandrasekhar $X(μ)$, and $Y(μ)$ functions respectively. We also derive a transformation relation between the modified S-T functions and give a physical account of $V(μ)$ and $W(μ)$ functions. Our final results are consistent with those of Chandrasekhar at low emission limit (i.e. only scattering). From the consistency of our results, we conclude that the consideration of thermal emission effect in diffuse reflection finite atmosphere problem gives more general and accurate results than considering only scattering.
