en>David Eppstein: clean up the (single) reference, add a wikilink, and clarify description of Brauer

2013-03-27T21:33:39Z

clean up the (single) reference, add a wikilink, and clarify description of Brauer

← Older revision		Revision as of 23:33, 27 March 2013
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	If you present photography effectively, it helps you look much more properly at the globe around you. Offshore expert Word - Press developers high level of interactivity, accessibility, functionality and usability of our website can add custom online to using. * A community forum for debate of the product together with some other customers in the comments spot. They found out all the possible information about bringing up your baby and save money at the same time. Over a million people are using Wordpress to blog and the number of Wordpress users is increasing every day. <br><br>		{{About\|optical depth in astrophysics\|optical depth in general\|optical depth}}

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			Optical depth is a measure of the [[extinction coefficient]] or [[absorptivity]] up to a specific 'depth' of a star's makeup.

			:<math>\tau \equiv \int_0^z (\alpha) dz = \sigma N</math> <ref>http://scienceworld.wolfram.com/physics/OpticalDepth.html</ref>

			This equation assumes that the extinction coefficient <math>\alpha</math> is known, or that N, the column 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.

			<math>\alpha</math> can be calculated using the [[Radiative_transfer#Solutions_to_the_equation_of_radiative_transfer\|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 <math>\alpha</math>.

			:<math>\alpha=e^\frac{4 \pi \kappa}{\lambda_0}</math>

			where <math>\kappa</math> is the [[refractive index]], and <math>\lambda_0</math> is the [[wavelength]] of the incident light before being absorbed or scattered.<ref>http://www.files.chem.vt.edu/chem-ed/spec/beerslaw.html</ref> Note that the Beer-Lambert Law is only appropriate when the absorption occurs at a specific wavelength, <math>\lambda_0</math>, for a gray atmosphere it is most appropriate to use the Eddington Approximation.

			Therefore it is straightforward to see that <math>\tau</math> is simply a constant that depends on the physical distance from the outside of a star. To find <math>\tau</math> at a particular depth z, one simply uses the above equation with <math>\alpha</math> and integrates from <math>z=0</math> to <math>z=z</math>.

			==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 [[Radiative_transfer#The_Eddington_approximation\|Eddington Approximation]] to derive the formal definition of <math>\tau=\frac{2}{3}</math>

			Devised by [[Sir Arthur Eddington]] the approximation takes into account the fact that <math>H^-</math> 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,
			:<math>T^4 = \frac{3}{4}T_e^4\left(\tau + \frac{2}{3}\right)</math>

			:Where <math>T_e</math> is the [[effective temperature]] at that depth and <math>\tau</math> 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 <math>\tau</math> 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 <math>\alpha</math> in the following way:
			:<math>T^4 = \frac{3}{4}T_e^4\left(\int_0^z (\alpha) dz + \frac{2}{3}\right)</math>

			Which is useful if <math>\tau</math> is not known but <math>\alpha</math> is.

			== References ==

			{{Reflist}}

			[[Category:Astrophysics]]
			[[Category:Scattering, absorption and radiative transfer (optics)]]

en>Michael Shulman: Clarified language

2012-03-01T05:31:45Z

Clarified language

New page

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These websites can be easily customized and can appear in the top rankings of the major search engines. Infertility can cause a major setback to the couples due to the inability to conceive. A Wordpress plugin is a software that you can install into your Wordpress site. They provide many such popular products which you can buy for your baby. That's a total of 180$ for each Wordpress theme if you sell 3 links and keep the designer link for your own website, or 240$ if you sell all links. Digital photography is a innovative effort, if you removethe stress to catch every position and viewpoint of a place, you free yourself up to be more innovative and your outcomes will be much better. Now if we talk about them one by one then -wordpress blog customization means customization of your blog such as installation of wordpress on your server by wordpress developer which will help you to acquire the SEO friendly blog application integrated with your site design as well as separate blog administration panel for starting up your own business blog,which demands a experienced wordpress designer. Are you considering getting your website redesigned. Storing write-ups in advance would have to be neccessary with the auto blogs. Have you heard about niche marketing and advertising. A built-in widget which allows you to embed quickly video from popular websites. I didn't straight consider near it solon than one distance, I got the Popup Ascendancy plugin and it's up and lengthways, likely you make seen it today when you visited our blog, and I yet customize it to fit our Thesis Wound which gives it a rattling uncomparable visage and search than any different popup you know seen before on any added journal, I hump arrogated asset of one of it's quatern themes to make our own. A higher percentage of women are marrying at older ages,many are delaying childbearing until their careers are established, the divorce rate is high and many couples remarry and desire their own children. To read more info about [http://svo.ro/wordpressbackupplugin49261 wordpress dropbox backup] review the website. If you choose a blog then people will be able to post articles on your site and people will be able to make comments on your posts (unless you turn comments off). Look for experience: When you are searching for a Word - Press developer you should always look at their experience level. Internet is not only the source for information, it is also one of the source for passive income. I'm a large fan of using Word - Press to create pretty much any sort of web page. Offshore Wordpress development services from a legitimate source caters dedicated and professional services assistance with very simplified yet technically effective development and designing techniques from experienced professional Wordpress developer India. In addition, Word - Press design integration is also possible. The 2010 voting took place from July 7 through August 31, 2010.

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en>David Eppstein: clean up the (single) reference, add a wikilink, and clarify description of Brauer

en>Michael Shulman: Clarified language