Implications of Liouville's theorem on the apparent brightness temperatures of solar radio bursts

Liouville's radiation theorem is discussed with respect to its consequences for the propagation of radio waves from the actual to the apparent sources in the solar corona. It is shown that the observed solid angle and apparent area of the source are compatible with the theorem only if the apparent source corresponds to the envelope of subsources with a small filling factor (f). The brightness temperature of the actual source is found to be greater than that of the apparent source by 1/f.