Luminosity 44790 218517416 2008-06-11T00:11:03Z Thingg 5924818 Reverted edits by [[Special:Contributions/71.121.212.190|71.121.212.190]] to last version by ClueBot (using [[WP:HG|Huggle]]) {{unreferenced|date=November 2006}} {{Wiktionary}} '''Luminosity''' has different meanings in several different fields of science. ==In photometry and color imaging== {{main|luminance}} In [[photometry]], ''luminosity'' is sometimes incorrectly used to refer to [[luminance]], which is the density of [[luminous intensity]] in a given direction. The [[SI]] unit for luminance is [[candela]] per [[square metre]]. {{main|luma (video)}} In [[Adobe Photoshop]]'s imaging operations, ''luminosity'' is the term used incorrectly to refer to the [[luma (video)|luma]] component of a color image signal; that is, a weighted sum of the nonlinear red, green, and blue signals. It seems to be calculated with the Rec. 601 luma co-efficients (Rec. 601: Luma (Y’) = 0.299 R’ + 0.587 G’ + 0.114 B’). {{main|HSL color space}} The "L" in [[HSL color space]] is sometimes said to stand for luminosity. "L" in this case is calculated as 1/2 (MAX + MIN), where MAX and MIN refer to the highest and lowest of the R'G'B' components to be converted into HSL color space. ==In astronomy== In [[astronomy]], '''luminosity''' is the amount of energy a body radiates per unit time. The luminosity of stars is measured in two forms: apparent (counting visible light only) and bolometric (total radiant energy); a [[bolometer]] is an instrument that measures radiant energy over a wide band by absorption and measurement of heating. When not qualified, luminosity means bolometric luminosity, which is measured in the [[SI]] units [[watt]]s, or in terms of [[solar luminosity|solar luminosities]], <math> L_{\odot} </math>; that is, how many times as much energy the object radiates than the [[Sun]], whose luminosity is 3.846×10<sup>26</sup> W. Luminosity is an intrinsic constant independent of distance, and is measured as [[absolute magnitude]] corresponding to apparent luminosity, or bolometric magnitude corresponding to bolometric luminosity. In contrast, apparent brightness is related to distance by an inverse square law. Visible brightness is usually measured by [[apparent magnitude]], which is on a logarithmic scale. In measuring star brightnesses, visible luminosity (not total luminosity at all wave lengths), [[apparent magnitude]] (visible brightness), and [[distance]] are interrelated parameters. If you know two, you can determine the third. Since the sun's luminosity is the standard, comparing these parameters with the sun's apparent magnitude and distance is the easiest way to remember how to convert between them. ===Computing between brightness and luminosity=== Imagine a point source of light of luminosity <math>L</math> that radiates equally in all directions. A hollow [[sphere]] centered on the point would have its entire interior surface illuminated. As the radius increases, the surface area will also increase, and the constant luminosity has more surface area to illuminate, leading to a decrease in observed brightness. :<math>b = \frac{L}{A}</math> where :<math>A</math> is the area of the illuminated surface. For stars and other point sources of light, <math>A = 4\pi r^2</math> so :<math>b = \frac{L}{4\pi r^2} \,</math> where :<math>r</math> is the distance from the observer to the light source. It has been shown that the luminosity of a star <math>L</math> (assuming the star is a [[black body]], which is a good approximation) is also related to temperature <math>T</math> and radius <math>R</math> of the star by the equation: :<math>L = 4\pi R^2\sigma T^4 \,</math> where :&sigma; is the [[Stefan-Boltzmann constant]] 5.67{{e|&minus;8}} [[Watt|W]]·m<sup>-2</sup>·K<sup>-4</sup> Dividing by the luminosity of the sun <math>L_{\odot}</math> and cancelling constants, we obtain the relationship :<math>\frac{L}{L_{\odot}} = {\left ( \frac{R}{R_{\odot}} \right )}^2 {\left ( \frac{T}{T_{\odot}} \right )}^4</math>. For stars on the [[main sequence]], luminosity is also related to mass: :<math>\frac{L}{L_{\odot}} \sim {\left ( \frac{M}{M_{\odot}} \right )}^{3.9}</math> It is easy to see that a star's luminosity, temperature, radius, and mass are all related. The magnitude of a star is a logarithmic scale of observed visible brightness. The [[apparent magnitude]] is the observed visible brightness from [[Earth]], and the [[absolute magnitude]] is the [[apparent magnitude]] at a distance of 10 [[parsecs]]. Given a visible luminosity (not total luminosity), one can calculate the [[apparent magnitude]] of a star from a given distance: :<math>m_{\rm star}=m_{\rm sun}-2.5\log_{10}\left({ L_{\rm star} \over L_{\odot} } \cdot \left(\frac{ r_{\rm sun} }{ r_{\rm star} }\right)^2\right)</math> where :''m''<sub>star</sub> is the apparent magnitude of the star (a pure number) :''m''<sub>sun</sub> is the apparent magnitude of the sun (also a pure number) :''L''<sub>star</sub> is the visible luminosity of the star :<math>L_{\odot}</math> is the solar visible luminosity :''r''<sub>star</sub> is the distance to the star :''r''<sub>sun</sub> is the distance to the sun Or simplified, given m<sub>sun</sub> = &minus;26.73, dist<sub>sun</sub> = 1.58 &times; 10<sup>&minus;5</sup> lyr: : m<sub>star</sub> = &minus; 2.72 &minus; 2.5 &middot; log(L<sub>star</sub>/dist<sub>star</sub><sup>2</sup>) Example: :How bright would a star like the sun be from 4.3 light years away? (The distance to the next closest star [[Alpha Centauri]]) ::m<sub>sun</sub> (@4.3lyr) = &minus;2.72 &minus; 2.5 &middot; log(1/4.3<sup>2</sup>) = 0.45 :0.45 magnitude would be a very bright star, but not quite as bright as Alpha Centauri. Also you can calculate the luminosity given a distance and apparent magnitude: :L<sub>star</sub>/<math>L_{\odot}</math> = (dist<sub>star</sub>/dist<sub>sun</sub>)<sup>2</sup> &middot; 10<sup>[(m<sub>sun</sub> &minus;m<sub>star</sub>) &middot; 0.4]</sup> :L<sub>star</sub> = 0.0813 &middot; dist<sub>star</sub><sup>2</sup> &middot; 10<sup>(&minus;0.4 &middot; m<sub>star</sub>)</sup> &middot; <math>L_{\odot}</math> Example: What is the luminosity of the star [[Sirius]]? :Sirius is 8.6 lyr distant, and magnitude &minus;1.47. :L<sub>Sirius</sub> = 0.0813 &middot; 8.6<sup>2</sup> &middot; 10<sup>&minus;0.4&middot;(&minus;1.47)</sup> = 23.3 &times; <math>L_{\odot}</math> :You can say that Sirius is 23 times brighter than the sun, or it radiates 23 suns. A bright [[star]] with [[absolute magnitude|bolometric magnitude]] &minus;10 has a luminosity of 10<sup>6</sup> <math>L_{\odot}</math>, whereas a dim star with bolometric magnitude +17 has luminosity of 10<sup>&minus;5</sup> <math>L_{\odot}</math>. Note that [[absolute magnitude]] is directly related to luminosity, but [[apparent magnitude]] is also a function of distance. Since only apparent magnitude can be measured observationally, an estimate of distance is required to determine the luminosity of an object. ===Computing between luminosity and magnitude=== A magnitude difference is related to stellar luminosity ratio according to: :<math>M_1 - M_2 = -2.5 \log{\frac{L_1}{L_2}}</math> which makes by inversion: :<math>\frac{L_1}{L_2} = 10^{(M_2 - M_1)/2.5}.</math> ==In scattering theory and accelerator physics== In [[scattering theory]] and [[Particle accelerator|accelerator]] physics, '''luminosity''' is the number of particles per unit [[area]] per unit [[time]] times the [[Opacity (optics)|opacity]] of the target, usually expressed in either the [[cgs]] units [[centimetre|cm]]<sup>-2</sup>&nbsp;[[second|s]]<sup>-1</sup> or [[Barn (unit)|b]]<sup>-1</sub>&nbsp;s<sup>-1</sup>. The integrated luminosity is the [[integral]] of the luminosity with respect to time. The luminosity is an important value to characterize the performance of an accelerator. ===Elementary relations for luminosity=== The following relations hold : <math>L = \rho v \,</math> (if the target is perfectly opaque) : <math>\frac{dN}{dt} = L \sigma</math> : <math>\frac{d\sigma}{d\Omega} = \frac{1}{L} \frac{d^{2}N}{d\Omega dt}</math> where :<math>L</math> is the Luminosity. :<math>N</math> is the number of interactions. :<math>\rho</math> is the number density of a particle beam. :<math>\sigma</math> is the total [[Cross section (physics)|cross section]]. :<math>d\Omega</math> is the [[differential]] [[solid angle]]. :<math> \frac{d\sigma}{d\Omega}</math> is the differential [[cross section (physics)|cross section]]. For an intersecting storage ring collider: : <math>L = f n \frac{N_{1} N_{2}}{A}</math> where :<math>f</math> is the revolution frequency :<math>n</math> is the number of bunches in one beam in the storage ring. :<math>N_{i}</math> is the number of particles in each bunch :<math>A</math> is the cross section of the beam. [[Category:Astrophysics]] [[Category:Physical quantity]] [[Category:Photometry]] [[Category:Particle accelerators]] [[Category:Scattering theory]] [[bs:Luminozitet]] [[ca:Lluminositat]] [[cs:Zářivý výkon]] [[de:Leuchtkraft]] [[es:Luminosidad]] [[eo:Lumeco]] [[fr:Luminosité]] [[gl:Luminosidade]] [[hr:Luminozitet]] [[is:Ljósafl]] [[it:Luminosità (fisica)]] [[lt:Šviesis]] [[hu:Luminozitás]] [[nl:Lichtkracht]] [[ja:光度 (天文学)]] [[no:Luminositet]] [[pt:Luminosidade]] [[sk:Svietivosť]] [[sl:Izsev]] [[sh:Luminozitet]] [[fi:Luminositeetti]] [[sv:Luminositet]] [[zh:光度]]