Dictionary - Definition of EFFECTIVE TEMPERATURE

Effective temperature

Star

The effective temperature, or blackbody 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 ( $\mathcal{F}_{Bol}$ ) as the star and is defined according to the Stefan–Boltzmann law $\mathcal{F}_{Bol}=\sigma T_{eff}4$ . Notice that the total (bolometric) luminosity of a star is then $L=4 \pi R2 \sigma T_{eff}4$ , where $R$ 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 the Rosseland optical depth.^[1] ^[2]The effective temperature and the bolometric luminosity are the two fundamental physical parameters needed to place a star on the HR 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 kelvins (K).^[3]^[4] 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 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 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 T.

Take the case of a planet at a distance D from the star, of luminosity L.

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 r, which intercepts some of the power which is spread over the surface of a sphere of radius D. 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:

$P_{abs} = \frac {L r2 (1-A)}{4 D2}$

The next assumption we can make is that the entire planet is at the same temperature T, and that the planet radiates as a blackbody. This gives an expression for the power radiated by the planet:

$P r a d = 4π r 2 σ T 4$

Equating these two expressions and rearranging gives an expression for the effective temperature:

$T = \left (\frac{L (1-A)}{16 \pi \sigma D2} \right ){\tfrac{1}{4}}$

Note that the planet's radius has cancelled out of the final expression.

The effective temperature for Jupiter is 112 K and 51 Pegasi b (Bellerophon) is 1258 K. The actual temperature depends on albedo, atmosphere, and internal heat. The actual temperature from spectroscopic analysis for HD 209458 b (Osiris) is 1130 K, but the black body temperature is 1359 K. The internal heat within Jupiter of 40 K combined with the effective temperature of 112 K results in a total of 152 K as the actual temperature.

References

Böhm-Vitense, Erika. Introduction to Stellar Astrophysics, Volume 3, Stellar structure and evolution. Cambridge University Press, 14.
Baschek. "The parameters R and Teff in stellar models and observations".
"Section 14: Geophysics, Astronomy, and Acousticse", Handbook of Chemistry and Physics, 88, CRC Press.
Jones, Barrie William (2004). Life in the Solar System and Beyond. Springer, 7. ISBN 1852331011.

External links

Source: adapted by the editor from Wikipedia, the free encyclopedia; from the article "Effective temperature". Image Credit.

Expressions	Definition
Effective temperature	The effective temperature of a star is the temperature of its visible surface, as opposed to the core at which it generates its energy through thermonuclear reactions or the rarefied corona of great heat where electrons meet ionized gases with the radiation of heat but in so sparse a gas that it is invisible. The color of a star indicates its temperature along a spectrum 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 types known as O, B, A, F, G, K, and M. The effective temperature of a star's surface is identical with the ironically-named black-body temperature of the visible surface. (references)
Source: compiled by the editor from various references; see credits.		Top

Expressions	Domain	Definition
Belgian effective temperature	Mining	A temperature scale used in Belgium for measuring the environmental comfort in mines. (references)
Corrected effective temperature	Mining	The scales of effective temperature take into consideration the temperature, humidity, and speed of the air. The effects of radiant heat can be included in an assessment of effective temperature by using the globe thermometer temperature instead of the dry-bulb temperature in those cases when the reading of the globe thermometer is higher than the dry-bulb temperature. In such cases, the result is described as the corrected effective temperature. (references)
Effective temperature	Aerospace	1: An empirical thermal index that illustrates how combinations of dry bulb air temperature, wet bulb temperature, velocity of air, and clothing affect people. (references)
		2: 1. In astrophysics, a measure of the temperature of a star deduced by means of the Stefan-Boltzmann law, from the total energy emitted per unit area. Compare brightness temperature, color temperature. Effective temperature is always less than actual temperature. 2. In physiology, the temperature at which motionless, saturated air would induce, in a sedentary worker wearing ordinary indoor clothing, the same sensation of comfort as that induced by the actual conditions of temperature, humidity, and air movement. Compare sensible temperature, standard operative temperature, operative temperature. Effective temperature is used as a guide in air-conditioning practice, and, on the comfort chart (American Society of Heating and Air Conditioning Engineers) it appears as a family of curves which serves as one coordinate in defining comfort zones. (references)
Effective temperature	Mining	A measure of warmth that is often employed to assess the health and comfort conditions of mine workings, which are a function of dry- and wet-bulb temperatures and air velocity. See also: dehumidification; dry kata cooling power. (references)
Source: compiled by the editor from various references; see credits.			Top

Common Expressions: EFFECTIVE TEMPERATURE

Specialty Expressions: EFFECTIVE TEMPERATURE

Extended Definition: Effective temperature

Effective temperature

Star

Planet

See also

References

External links