## Brightness Temperature

Often in radio astronomy brightness temperature (TB) is used as a measure of received intensity. For an understanding of the definition of brightness temperature it is necessary to analyse Plank's blackbody radiation law:

The specific intensity of the radiation, i.e. intensity per differential frequency element, is given by I.

The exponential can be expanded so that:

Hence we have:

These equations all relate to black bodies. Subsequently the formal definition of brightness temperature is the temperature at which a black body in thermal equilibrium with its surroundings would have to be in order to duplicate the observed specific intensity of an object at a frequency v.

A linked concept is that of antenna temperature. This is the temperature that a resistor would have to be to generate the same power density at a given frequency observed to be coming from the system as a whole. As such it contains contributions from all noise and interference sources.