翻訳と辞書 Words near each other ・ Spectral estimation of multidimensional signals ・ Spectral evidence ・ Spectral expansion solution ・ Spectral flatness ・ Spectral flux ・ Spectral flux density ・ Spectral gap ・ Spectral Gene ・ Spectral Genomics ・ Spectral geometry ・ Spectral glide ・ Spectral graph theory ・ Spectral Hash ・ Spectral hole burning ・ Spectral imaging ・ Spectral index ・ Spectral induced polarisation ・ Spectral invariants ・ Spectral layout ・ Spectral leakage ・ Spectral line ・ Spectral line ratios ・ Spectral line shape ・ Spectral mask ・ Spectral method ・ Spectral modeling synthesis ・ Spectral Mornings ・ Spectral music ・ Spectral mutability ・ Spectral network Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Spectral index ： ウィキペディア英語版 Spectral index In astronomy, the spectral index of a source is a measure of the dependence of radiative flux density on frequency. Given frequency $\backslash nu$ and radiative flux $S$, the spectral index $\backslash alpha$ is given implicitly by :$S\backslash propto\backslash nu^\backslash alpha.$ Note that if flux does not follow a power law in frequency, the spectral index itself is a function of frequency. Rearranging the above, we see that the spectral index is given by :$\backslash alpha\; \backslash !\; \backslash left(\; \backslash nu\; \backslash right)\; =\; \backslash frac.$ Spectral index is also sometimes defined in terms of wavelength $\backslash lambda$. In this case, the spectral index $\backslash alpha$ is given implicitly by :$S\backslash propto\backslash lambda^\backslash alpha,$ and at a given frequency, spectral index may be calculated by taking the derivative :$\backslash alpha\; \backslash !\; \backslash left(\; \backslash lambda\; \backslash right)\; =\backslash frac.$ The opposite sign convention is sometimes employed,〔Burke, B.F., Graham-Smith, F. (2009). ''An Introduction to Radio Astronomy, 3rd Ed.'', Cambridge University Press, Cambridge, UK, ISBN 978-0-521-87808-1, page 132.〕 in which the spectral index is given by :$S\backslash propto\backslash nu^.$ The spectral index of a source can hint at its properties. For example, using the positive sign convention, a spectral index of 0 to 2 at radio frequencies indicates thermal emission, while a steep negative spectral index typically indicates synchrotron emission. ==Spectral Index of Thermal emission== At radio frequencies (i.e. in the low-frequency, long-wavelength limit), where the Rayleigh–Jeans law is a good approximation to the spectrum of thermal radiation, intensity is given by :$B\_\backslash nu(T)\; \backslash simeq\; \backslash frac.$ Taking the logarithm of each side and taking the partial derivative with respect to $\backslash log\; \backslash ,\; \backslash nu$ yields :$\backslash frac\; \backslash simeq\; 2.$ Using the positive sign convention, the spectral index of thermal radiation is thus $\backslash alpha\; \backslash simeq\; 2$ in the Rayleigh-Jeans regime. The spectral index departs from this value at shorter wavelengths, for which the Rayleigh-Jeans law becomes an increasingly inaccurate approximation, tending towards zero as intensity reaches a peak at a frequency given by Wien's displacement law. Because of the simple temperature-dependence of radiative flux in the Rayleigh-Jeans regime, the ''radio spectral index'' is defined implicitly by〔(【引用サイトリンク】publisher=Wolfram Research )〕 :$S\; \backslash propto\; \backslash nu^\; T.$ 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「Spectral index」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.