Brightness temperature

Brightness temperature is the temperature a black body in thermal equilibrium with its surroundings would have to be to duplicate the observed intensity of a grey body object at a frequency ${\displaystyle \nu }$. This concept is extensively used in radio astronomy and planetary science.

The brightness temperature is not a temperature as ordinarily understood. It characterizes radiation, and depending on the mechanism of radiation can differ considerably from the physical temperature of a radiating body (though it is theoretically possible to construct a device which will heat up by a source of radiation with some brightness temperature to the actual temperature equal to brightness temperature). Nonthermal sources can have very high brightness temperatures. In pulsars the brightness temperature can reach 10²⁶ K. For the radiation of a typical helium–neon laser with a power of 60 mW and a coherence length of 20 cm, focused in a spot with a diameter of 10 µm, the brightness temperature will be nearly 7010140000000000000♠14×10⁹ K.

For a black body, Planck's law gives:

where

${\displaystyle I_{\nu }}$ (the Intensity or Brightness) is the amount of energy emitted per unit surface area per unit time per unit solid angle and in the frequency range between ${\displaystyle \nu }$ and ${\displaystyle \nu +d\nu }$; ${\displaystyle T}$ is the temperature of the black body; ${\displaystyle h}$ is Planck's constant; ${\displaystyle \nu }$ is frequency; ${\displaystyle c}$ is the speed of light; and ${\displaystyle k}$ is Boltzmann's constant.

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