en>BG19bot: WP:CHECKWIKI error fix for #61. Punctuation goes before References. Do general fixes if a problem exists. - using AWB (9440)

2013-08-23T18:16:36Z

WP:CHECKWIKI error fix for #61. Punctuation goes before References. Do general fixes if a problem exists. - using AWB (9440)

← Older revision		Revision as of 20:16, 23 August 2013
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	~~Hi there~~. ~~Let me start~~ by ~~introducing~~ the ~~writer~~, ~~her name~~ is ~~Myrtle Cleary~~. ~~Hiring~~ is ~~her day job now and she will not change it whenever soon~~. ~~His spouse doesn't like it [http~~://~~www~~.~~innovec~~.~~com~~/~~node~~/~~3171 over~~ the ~~counter std test~~] ~~std home test way he does but what he truly~~ [~~http://www~~.~~sexualhealth~~.~~com/std~~-~~testing~~-~~windows/ likes performing~~] is to ~~do aerobics and he's been doing it for fairly a while.~~ [~~http~~://~~www~~.~~medicalnewstoday.com~~/~~articles~~/~~155236~~.~~php Puerto Rico~~] is ~~exactly where he's been living for many years and he will~~ by ~~no means transfer.~~<br>~~<br>Here is my~~ [http://~~muzikoman~~.com/~~profile~~-~~682~~/~~info/ home std test kit] web at home std testing site ... [http~~:~~//www~~.~~hamcass.org~~/~~index.php?document_srl~~=~~268708&mid~~=~~gido www.hamcass.org~~]		In [[astronomy]], the '''spectral index''' of a source is a measure of the dependence of radiative flux density on [[frequency]]. Given frequency <math>\nu</math> and [[radiative flux]] <math>S</math>, the spectral index <math>\alpha</math> is given implicitly by
			:<math>S\propto\nu^\alpha.</math>
			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
			:<math>\alpha \! \left( \nu \right) = \frac{\partial \log S \! \left( \nu \right)}{\partial \log \nu}.</math>

			Spectral index is also sometimes defined in terms of [[wavelength]] <math>\lambda</math>. In this case, the spectral index <math>\alpha</math> is given implicitly by
			:<math>S\propto\lambda^\alpha,</math>
			and at a given frequency, spectral index may be calculated by taking the derivative
			:<math>\alpha \! \left( \lambda \right) =\frac{\partial \log S \! \left( \lambda \right)}{\partial \log \lambda}.</math>

			The opposite sign convention is sometimes employed,<ref>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.</ref> in which the spectral index is given by
			:<math>S\propto\nu^{-\alpha}.</math>

			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
			:<math>B_\nu(T) \simeq \frac{2 \nu^2 k T}{c^2}.</math>
			Taking the logarithm of each side and taking the partial derivative with respect to <math>\log \, \nu</math> yields
			:<math>\frac{\partial \log B_\nu(T)}{\partial \log \nu} \simeq 2.</math>
			Using the positive sign convention, the spectral index of thermal radiation is thus <math>\alpha \simeq 2</math> 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#Frequency-dependent_formulation\|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<ref>{{cite web\|title=Radio Spectral Index \|publisher=[[Wolfram Research]] \|url=http://scienceworld.wolfram.com/astronomy/RadioSpectralIndex.html \|accessdate=2011-01-19}}</ref>
			:<math>S \propto \nu^{\alpha} T.</math>

			==References==
			{{Reflist}}

			[[Category:Radio astronomy]]

			{{astronomy-stub}}

en>My very best wishes at 05:45, 24 February 2012

2012-02-24T05:45:35Z

New page

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Phi value analysis - Revision history

en>BG19bot: WP:CHECKWIKI error fix for #61. Punctuation goes before References. Do general fixes if a problem exists. - using AWB (9440)

en>My very best wishes at 05:45, 24 February 2012