|
|
| Line 1: |
Line 1: |
| The '''effective temperature''' of a body such as a star or planet is the [[temperature]] of a [[black body]] that would emit the same total amount of [[electromagnetic radiation]].<ref name="Archie2003">{{cite book | title = Astronomy | author = Archie E. Roy, David Clarke | publisher = CRC Press | year = 2003 | isbn = 978-0-7503-0917-2 | url = http://books.google.com/?id=v2S6XV8dsIAC&pg=PA216&dq=%22effective+temperature%22+%22black+body%22+radiates+same }}</ref> Effective temperature is often used as an estimate of a body's temperature when the body's [[emissivity]] curve (as a function of [[wavelength]]) is not known.
| | Oscar is how he's known as and he completely enjoys this name. Her family members life in Minnesota. To do aerobics is a thing that I'm totally addicted to. Managing individuals is what I do and the wage has been truly satisfying.<br><br>Here is my web-site ... [http://2Za.Co.za/dietmealdelivery74619 2za.co.za] |
| | |
| When the star's or planet's net [[emissivity]] in the relevant wavelength band is less than unity (less than that of a [[black body]]), the actual temperature of the body will be higher than the effective temperature. The net emissivity may be low due to surface or atmospheric properties, including [[greenhouse effect]].
| |
| | |
| == Star ==
| |
| | |
| [[File:EffectiveTemperature 300dpi e.png|thumb|250px|The effective temperature of the [[Sun]] (5777 K) is the temperature a black body of the same size must have to yield the same total emissive power.]]
| |
| | |
| The effective temperature of a [[star]] is the temperature of a [[black body]] with the same luminosity per ''surface area'' (<math>\mathcal{F}_{\rm Bol}</math>) as the star and is defined according to the [[Stefan–Boltzmann law]] <math>\mathcal{F}_{\rm Bol}=\sigma T_{\rm eff}^4</math>. Notice that the total ([[Absolute magnitude|bolometric]]) luminosity of a star is then <math>L=4 \pi R^2 \sigma T_{\rm eff}^4</math>, where <math>R</math> is the stellar radius.<ref>{{cite book
| |
| | first=Roger John | last=Tayler | year=1994
| |
| | title=The Stars: Their Structure and Evolution
| |
| | publisher=Cambridge University Press | isbn=0-521-45885-4
| |
| | page=16 }}</ref> The definition of the stellar radius is obviously not straightforward. More rigorously the effective temperature corresponds to the temperature at the radius that is defined by the Rosseland optical depth.<ref name="Bohm">{{Cite book|title=Introduction to Stellar Astrophysics, Volume 3, Stellar structure and evolution|first=Erika|last=Böhm-Vitense|page=14|publisher=[[Cambridge University Press]]}}</ref><ref>{{cite journal|title=The parameters R and Teff in stellar models and observations|last=Baschek|bibcode=1991A&A...246..374B
| |
| |journal = Astronomy and Astrophysics
| |
| | volume = 246 |issue= 2 |date= June 1991 |pages= 374–382}}</ref> The effective temperature and the bolometric luminosity are the two fundamental physical parameters needed to place a star on the [[Hertzsprung–Russell diagram]]. Both effective temperature and bolometric luminosity actually depend on the chemical composition of a star.
| |
| | |
| The effective temperature of our Sun is around 5780 [[kelvin]] (K).<ref name="Ref_">{{Cite book |chapter=Section 14: Geophysics, Astronomy, and Acousticse |publisher=[[CRC Press]]|title=Handbook of Chemistry and Physics; section=14-18: Solar Spectral Irradiance |url=http://www.scenta.co.uk/tcaep/nonxml/science/constant/details/effectivetempofsun.htm|edition=88}}</ref><ref name="Jones2004">{{cite book|title=Life in the Solar System and Beyond|first=Barrie William|last=Jones|page=7|publisher = [[Springer Science+Business Media|Springer]]|year=2004|isbn=1-85233-101-1| url=http://books.google.com/?id=MmsWioMDiN8C&pg=PA7&dq=%22effective+temperature+of+the+sun%22}}</ref>
| |
| Stars actually have a temperature gradient, going from their central core up to the atmosphere. The "core temperature" of the sun—the temperature at the centre of the sun where nuclear reactions take place—is estimated to be 15 000 000 K.
| |
| | |
| The [[color index]] of a star indicates its temperature from the very cool—by stellar standards, that is—red M stars that radiate heavily in the [[infrared]] to the very blue O stars that radiate largely in the [[ultraviolet]]. The effective temperature of a star indicates the amount of heat that the star radiates per unit of surface area. From the warmest surfaces to the coolest is the sequence of star [[stellar classification|types]] known as O, B, A, F, G, K, and M.
| |
| | |
| A red star could be a tiny [[red dwarf]], a star of feeble energy production and a small surface or a bloated giant or even [[supergiant]] star such as [[Antares]] or [[Betelgeuse]], either of which generates far greater energy but passes it through a surface so large that the star radiates little per unit of surface area. A star near the middle of the spectrum, such as the modest [[Sun]] or the giant [[Capella (star)|Capella]] radiates more heat per unit of surface area than the feeble red dwarf stars or the bloated supergiants, but much less than such a white or blue star as [[Vega]] or [[Rigel]].
| |
| | |
| == Planet ==
| |
| | |
| The effective temperature of a [[planet]] can be calculated by equating the power received by the planet with the power emitted by a blackbody of temperature <var>T</var>.
| |
| | |
| Take the case of a planet at a distance <var>D</var> from the star, of [[luminosity]] <var>L</var>.
| |
| | |
| Assuming the star radiates isotropically and that the planet is a long way from the star, the power absorbed by the planet is given by treating the planet as a disc of radius <var>r</var>, which intercepts some of the power which is spread over the surface of a sphere of radius <var>D</var> (the distance of the planet from the star). We also allow the planet to reflect some of the incoming radiation by incorporating a parameter called the [[albedo]]. An albedo of 1 means that all the radiation is reflected, an albedo of 0 means all of it is absorbed. The expression for absorbed power is then:
| |
| | |
| <math>P_{\rm abs} = \frac {L r^2 (1-A)}{4 D^2}</math>
| |
| | |
| The next assumption we can make is that the entire planet is at the same temperature <var>T</var>, and that the planet radiates as a blackbody. The [[Stefan–Boltzmann law]] gives an expression for the power radiated by the planet:
| |
| | |
| <math>P_{\rm rad} = 4 \pi r^2 \sigma T^4</math>
| |
| | |
| Equating these two expressions and rearranging gives an expression for the effective temperature:
| |
| | |
| <math>T = \left (\frac{L (1-A)}{16 \pi \sigma D^2} \right )^{\tfrac{1}{4}}</math>
| |
| | |
| Note that the planet's radius has cancelled out of the final expression.
| |
| | |
| The effective temperature for [[Jupiter]] from this calculation is 112 K and [[51 Pegasi b]] (Bellerophon) is 1258 K.{{Citation needed|date=December 2011}} A better estimate of effective temperature for some planets, such as Jupiter, would need to include the [[internal heating]] as a power input. The actual temperature depends on [[albedo]] and [[atmosphere]] effects. The actual temperature from [[spectroscopic analysis]] for [[HD 209458 b]] (Osiris) is 1130 K, but the effective temperature is 1359 K.{{Citation needed|date=December 2011}} The internal heating within Jupiter raises the effective temperature to about 152 K.{{Citation needed|date=December 2011}}
| |
| | |
| ==Surface temperature of a planet==
| |
| | |
| The surface temperature of a planet can be estimated by modifying the effective-temperature calculation to account for emissivity and temperature variation.
| |
| | |
| The area of the planet that absorbs the power from the star is <var>A<sub>abs</sub></var> which is some fraction of the total surface area <math>A_{\rm total} = 4 \pi r^2</math>, where <var>r</var> is the radius of the planet. This area intercepts some of the power which is spread over the surface of a sphere of radius <var>D</var>. We also allow the planet to reflect some of the incoming radiation by incorporating a parameter <var>a</var> called the [[albedo]]. An albedo of 1 means that all the radiation is reflected, an albedo of 0 means all of it is absorbed. The expression for absorbed power is then:
| |
| | |
| <math>P_{\rm abs} = \frac {L A_{\rm abs} (1-a)}{4 \pi D^2}</math>
| |
| | |
| The next assumption we can make is that although the entire planet is not at the same temperature, it will radiate as if it had a temperature <var>T</var> over an area <var>A<sub>rad</sub></var> which is again some fraction of the total area of the planet. There is also a factor <var>ε</var>, which is the [[emissivity]] and represents atmospheric effects. ε ranges from 1 to 0 with 1 meaning the planet is a perfect blackbody and emits all the incident power. The [[Stefan–Boltzmann law]] gives an expression for the power radiated by the planet:
| |
| | |
| <math>P_{\rm rad} = A_{\rm rad} \varepsilon \sigma T^4</math>
| |
| | |
| Equating these two expressions and rearranging gives an expression for the surface temperature:
| |
| | |
| <math>T = \left (\frac{A_{\rm abs}}{A_{\rm rad}} \frac{L (1-a)}{4 \pi \sigma \varepsilon D^2} \right )^{\tfrac{1}{4}}</math>
| |
| | |
| Note the ratio of the two areas. Common assumptions for this ratio are 1/4 for a rapidly rotating body and 1/2 for a slowly rotating body. This ratio would be 1 for the [[subsolar point]], the point on the planet directly below the sun and gives the maximum temperature of the planet.<ref>Swihart, Thomas. "Quantitative Astronomy". Prentice Hall, 1992, Chapter 5, Section 1.</ref>
| |
| | |
| Let's look at the Earth. The Earth has an albedo of about 0.367.<ref>http://nssdc.gsfc.nasa.gov/planetary/factsheet/earthfact.html</ref> The emissivity is dependent on the type of surface and many [[climate models]] set the value of the Earth's emissivity to 1. However, a more realistic value is 0.96.<ref>Jin, Menglin and Shunlin Liang, (2006) “An Improved Land Surface Emissivity Parameter for Land Surface Models Using Global Remote Sensing Observations” Journal of Climate, 19 2867-81. (www.glue.umd.edu/~sliang/papers/Jin2006.emissivity.pdf)</ref> The Earth is a fairly fast rotator so the area ratio can be estimated as 1/4. The other variables are constant. This calculation gives us an effective temperature of the Earth of 252K or -21°C. The average temperature of the Earth is 288K or 15°C. One reason for the difference between the two values is due to the [[Greenhouse effect]], which increases the average temperature of the Earth's surface.
| |
| | |
| Also note here that this equation does not take into account any effects from internal heating of the planet, which can arise directly from sources such as [[radioactive decay]] and also be produced from frictions resulting from [[tidal forces]].
| |
| | |
| == See also ==
| |
| {{Portal|Star}}
| |
| * [[Color temperature]]
| |
| * [[Brightness temperature]]
| |
| | |
| ==References==
| |
| <references/>
| |
| | |
| ==External links==
| |
| * [http://adsabs.harvard.edu/abs/2006astro.ph..8504C Effective temperature scale for solar type stars]
| |
| * [http://ijolite.geology.uiuc.edu/05SprgClass/geo116/8-1.pdf Surface Temperature of Planets]
| |
| * [http://www.astro.indiana.edu/~gsimonel/temperature1.html Planet temperature calculator]
| |
| | |
| {{Star}}
| |
| | |
| {{DEFAULTSORT:Effective Temperature}}
| |
| [[Category:Stellar astronomy]]
| |
| [[Category:Planetary science]]
| |
| [[Category:Thermodynamics]]
| |
| [[Category:Electromagnetic radiation]]
| |
Oscar is how he's known as and he completely enjoys this name. Her family members life in Minnesota. To do aerobics is a thing that I'm totally addicted to. Managing individuals is what I do and the wage has been truly satisfying.
Here is my web-site ... 2za.co.za