Brightness Temperature

Telescopes usually observe the flux density (in mJy) from the sky. Images themselves are usually in the units of Jy per beam. Brightness temperature is a way to convert this intensity into an equivalent temperature of a blackbody that would produce the same surface brightness at that frequency.

One can do this conversion by using Planck’s law. We have

Now, flux density per beam, is:

where is the beam solid angle. We can apply Rayleigh-Jeans approximation under which which reduces the exponent and gives a slightly simpler explanation