Luminosity Functions for Extra Galactic Radio Sources

The monochromatic luminosity function of radio sources (RLF) is the number of sources per unit volume as a function of the luminosity P at a frequency v and of the cosmic epoch (z). Symbol : n(P(v),z). It is often given per interval of log P, or Mr, the absolute radio magnitude. This function is determined only for sources associated with optical objects (galaxies and QSO's). It can be given for all kinds of associations, or for sources associated with a specific type of object. In this case the normalized, or fractional, RLF is sometimes used, Fi (P,z) = ni (P,z)/ρi (z), where ρi is the space density of type i objects. The word “bivariate” is used for the RLF defined per interval of the optical luminosity (or magnitude M). A RLF can be determined using either a radio–optically complete sample of identified sources, or the radio observation of an optically selected sample. The merits of methods used to estimate a RLF from a complete sample are discussed by Felten (1976). Translation of a RLF from one frequency to another must be done with care if, at the two frequencies, different radio components (like the extended and the compact) would be preferentially sampled. We shall review the estimates of local (z = 0) RLF's using Ho = 100 Kms−1 Mpc−1 and the unit WHz−1 for P.