### Interpretation

It happens that when an astronomical source, whose angular extent fills exactly the main lobe, emits as a black-body in the Rayleigh-Jeans regime , the main-beam temperature is directly the physical temperature of the emitting source. However, this interpretation is only valid when the stated conditions are met. This almost never happens in (sub)-millimeter radio-astronomy because the emitting sources are often out of local thermodynamic equilibrium and . So this interpretation is mostly misleading for newcomers.

As the measured spectral power in radio-astronomy have very small values, it is easier to express them in term of temperatures that will be orders of magnitude larger because . As a matter of fact, most observed brightness temperatures have values close to 1 (within a factor 1000!)

So it's easier to interpret the above relationship as: expressing spectral powers in terms of temperature is just a useful convenience.