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The effective temperature of a body such as a star or planet is the
temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer. Thermometers are calibrated in various temperature scales that historically have relied on ...
of a
black body A black body or blackbody is an idealized physical object, physical body that absorption (electromagnetic radiation), absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence (optics), angle of incidence. T ...
that would emit the same total amount of
electromagnetic radiation In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visible ...
. Effective temperature is often used as an estimate of a body's surface temperature when the body's emissivity curve (as a function of
wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tr ...
) is not known. 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 A black body or blackbody is an idealized physical object, physical body that absorption (electromagnetic radiation), absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence (optics), angle of incidence. T ...
), 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

The effective temperature of a
star A star is an astronomical object comprising a luminous spheroid of plasma held together by its gravity. The nearest star to Earth is the Sun. Many other stars are visible to the naked eye at night, but their immense distances from Earth make ...
is the temperature of a
black body A black body or blackbody is an idealized physical object, physical body that absorption (electromagnetic radiation), absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence (optics), angle of incidence. T ...
with the same luminosity per ''surface area'' () as the star and is defined according to the Stefan–Boltzmann law . Notice that the total ( bolometric) luminosity of a star is then , where is the stellar radius. 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 a certain value of the Rosseland optical depth (usually 1) within the stellar atmosphere. 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 depend on the chemical composition of a star. The effective temperature of the Sun is around 5780  kelvins (K). The value recommended by the
International Astronomical Union The International Astronomical Union (IAU; french: link=yes, Union astronomique internationale, UAI) is a nongovernmental organisation with the objective of advancing astronomy in all aspects, including promoting astronomical research, outreach ...
is Stars have a decreasing 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 In astronomy, the color index is a simple numerical expression that determines the color of an object, which in the case of a star gives its temperature. The lower the color index, the more blue (or hotter) the object is. Conversely, the larg ...
of a star indicates its temperature from the very cool—by stellar standards—red M stars that radiate heavily in the
infrared Infrared (IR), sometimes called infrared light, is electromagnetic radiation (EMR) with wavelengths longer than those of visible light. It is therefore invisible to the human eye. IR is generally understood to encompass wavelengths from aroun ...
to the very hot blue O stars that radiate largely in the
ultraviolet Ultraviolet (UV) is a form of electromagnetic radiation with wavelength from 10 nm (with a corresponding frequency around 30  PHz) to 400 nm (750  THz), shorter than that of visible light, but longer than X-rays. UV radiati ...
. Various colour-effective temperature relations exist in the literature. There relations also have smaller dependencies on other stellar parameters, such as the stellar metallicity and surface gravity. 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 stellar classifications known as O, B, A, F, G, K, M. A red star could be a tiny
red dwarf ''Red Dwarf'' is a British science fiction comedy franchise created by Rob Grant and Doug Naylor, which primarily consists of a television sitcom that aired on BBC Two between 1988 and 1999, and on Dave (TV channel), Dave since 2009, gaining a ...
, 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 radiates more energy 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 Vega is the brightest star in the northern Northern may refer to the following: Geography * North, a point in direction * Northern Europe, the northern part or region of Europe * Northern Highland, a region of Wisconsin, United Sta ...
or Rigel.


Planet


Blackbody temperature

To find the effective (blackbody) temperature of a
planet A planet is a large, rounded astronomical body that is neither a star nor its remnant. The best available theory of planet formation is the nebular hypothesis, which posits that an interstellar cloud collapses out of a nebula to create a ...
, it can be calculated by equating the power received by the planet to the known power emitted by a blackbody of temperature . Take the case of a planet at a distance from the star, of luminosity . 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 , which intercepts some of the power which is spread over the surface of a sphere of radius (the distance of the planet from the star). The calculation assumes the planet reflects some of the incoming radiation by incorporating a parameter called the albedo (a). 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: :P_ = \frac The next assumption we can make is that the entire planet is at the same temperature , and that the planet radiates as a blackbody. The Stefan–Boltzmann law gives an expression for the power radiated by the planet: :P_ = 4 \pi r^2 \sigma T^4 Equating these two expressions and rearranging gives an expression for the effective temperature: :T = \sqrt /math> Where \sigma is the Stefan–Boltzmann constant. Note that the planet's radius has cancelled out of the final expression. The effective temperature for
Jupiter Jupiter is the fifth planet from the Sun and the largest in the Solar System. It is a gas giant with a mass more than two and a half times that of all the other planets in the Solar System combined, but slightly less than one-thousandt ...
from this calculation is 88 K and 51 Pegasi b (Bellerophon) is 1,258 K. 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 An atmosphere () is a layer of gas or layers of gases that envelop a planet, and is held in place by the gravity of the planetary body. A planet retains an atmosphere when the gravity is great and the temperature of the atmosphere is low. ...
effects. The actual temperature from spectroscopic analysis for HD 209458 b (Osiris) is 1,130 K, but the effective temperature is 1,359 K. The internal heating within Jupiter raises the effective temperature to about 152 K.


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 which is some fraction of the total surface area , where is the radius of the planet. This area intercepts some of the power which is spread over the surface of a sphere of radius . 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: :P_ = \frac 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 over an area which is again some fraction of the total area of the planet. There is also a factor , which is the emissivity and represents atmospheric effects. 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: :P_ = A_ \varepsilon \sigma T^4 Equating these two expressions and rearranging gives an expression for the surface temperature: :T = \sqrt /math> Note the ratio of the two areas. Common assumptions for this ratio are for a rapidly rotating body and for a slowly rotating body, or a tidally locked body on the sunlit side. This ratio would be 1 for the
subsolar point The subsolar point on a planet is the point at which its sun is perceived to be directly overhead (at the zenith); that is, where the sun's rays strike the planet exactly perpendicular to its surface. It can also mean the point closest to th ...
, the point on the planet directly below the sun and gives the maximum temperature of the planet — a factor of (1.414) greater than the effective temperature of a rapidly rotating planet. 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.


Earth effective temperature

The Earth has an albedo of about 0.306. 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.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) The Earth is a fairly fast rotator so the area ratio can be estimated as . The other variables are constant. This calculation gives us an effective temperature of the Earth of . The average temperature of the Earth is . 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.


See also

* Brightness temperature * Color temperature * List of hottest stars *


References


External links


Effective temperature scale for solar type stars

Surface Temperature of Planets


{{DEFAULTSORT:Effective Temperature Stellar astronomy Planetary science Thermodynamic properties Electromagnetic radiation Concepts in astronomy