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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Optical depth (astrophysics) ： ウィキペディア英語版 Optical depth (astrophysics) Optical depth in astrophysics refers to a specific level of transparency. Optical depth and actual depth, $\backslash tau$ and $z$ respectively, can vary wildly depending on the absorptivity of the stellar interior. Because of this $\backslash tau$ is able to show the relationship between these two quantities and can lead to a greater understanding of the structure inside a star. Optical depth is a measure of the extinction coefficient or absorptivity up to a specific 'depth' of a star's makeup. :$\backslash tau\; \backslash equiv\; \backslash int\_0^z\; (\backslash alpha)\; dz\; =\; \backslash sigma\; N$ 〔http://scienceworld.wolfram.com/physics/OpticalDepth.html〕 This equation assumes that the extinction coefficient $\backslash alpha$ is known, or that N, the column number density, is known. These can generally be calculated from other equations if a fair amount of information is known about the chemical makeup of the star. $\backslash alpha$ can be calculated using the transfer equation. In most astrophysics problems this is exceptionally difficult to solve, since the equations assume one knows the incident radiation as well as the radiation leaving the star and these values are usually theoretical. In some cases the Beer-Lambert Law can be useful in finding $\backslash alpha$. :$\backslash alpha=e^\backslash frac$ where $\backslash kappa$ is the refractive index, and $\backslash lambda\_0$ is the wavelength of the incident light before being absorbed or scattered.〔http://www.files.chem.vt.edu/chem-ed/spec/beerslaw.html〕 Note that the Beer-Lambert Law is only appropriate when the absorption occurs at a specific wavelength, $\backslash lambda\_0$, for a gray atmosphere it is most appropriate to use the Eddington Approximation. Therefore, it is straightforward to see that $\backslash tau$ is simply a constant that depends on the physical distance from the outside of a star. To find $\backslash tau$ at a particular depth z, one simply uses the above equation with $\backslash alpha$ and integrates from $z=0$ to $z=z$. ==The Eddington Approximation and the Depth of the Photosphere== Because it is difficult to define where the photosphere of a star ends and the chromosphere begins astrophysicists rely on the Eddington Approximation to derive the formal definition of $\backslash tau=\backslash frac$ Devised by Sir Arthur Eddington the approximation takes into account the fact that $H^-$ produces a "gray" absorption in the atmosphere of a star, that is, it is independent of any specific wavelength and absorbs along the entire electromagnetic spectrum. In that case, :$T^4\; =\; \backslash fracT\_e^4\backslash left(\backslash tau\; +\; \backslash frac\backslash right)$ :Where $T\_e$ is the effective temperature at that depth and $\backslash tau$ is the optical depth. This illustrates not only that the observable temperature and actual temperature at a certain physical depth of a star vary, but that the optical depth plays a crucial role in understanding the stellar structure. It also serves to demonstrate that the depth of the photosphere of a star is highly dependent upon the absorptivity of its environment. The photosphere extends down to a point where $\backslash tau$ is about 2/3, which corresponds to a state where a photon would experience, in general, less than 1 scattering before leaving the star. One should also note that the above equation can be rewritten in terms of $\backslash alpha$ in the following way: :$T^4\; =\; \backslash fracT\_e^4\backslash left(\backslash int\_0^z\; (\backslash alpha)\; dz\; +\; \backslash frac\backslash right)$ Which is useful if $\backslash tau$ is not known but $\backslash alpha$ is. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Optical depth (astrophysics)」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.