The radio luminosity function and the luminosity diameter function of extragalactic radio sources

On the basis of a radio index-surface brightness diagram recently published, the luminosity function and the luminosity diameter function are obtained. The uncertainties due to the incompleteness of the sample are of the same order as the statistical uncertainties. The luminosity function differs considerably from a simple power law and supports the distinction of two populations. The density of the weak population (P<10³⁵ W Hz⁻¹ ster⁻¹ at 1400 MHz) follows nearly a power law in P and increases towards small diameters at least down to I kpc. The density of the strong population (the high luminosity and small diameter part of which is occupied by the quasars) has a maximum between 10²⁵ and 10²⁸ W Hz⁻¹ ster⁻¹ and around 100 kpc. A strong evolution effect is clearly present and is in a good agreement with the models obtained from the log N-log S counts.