Space Distribution and Luminosity Functions of Quasi-Stellar Radio Sources

The distribution in space and both the optical and radio luminosity functions of quasi-stellar radio sources are derived The derivation is based on quasi-stellar sources in the Revised 3C Catalogue, in which they have been identified and observed with a high degree of completeness down to magnitude around 18k. The redshifts are assumed to be cosmological. The distribution in space is found to be strongly non-uniform. The space density, in co-moving coordinates, is increasing with redshift z, such that at z = 1 the density is around 150 and 80 times the local (z = 0) density, for qo = 0 and qo = 1, respectively. This density increase corresponds to a N(S) relation quite ~imi1ar to that exhibited by extragalactic radio sources. The optical luminosity function is relatively flat, i e., the numbers per magnitude depend little on the luminosity In contrast the radio luminosity function is rather steep, the number per magnitude increas- ing toward fainter radio luminosities by a factor of around three to four per magnitude. Extension of this radio luminosity function by 1~ magnitude is sufficient to account for the Sandage-Luyten estimate of the sky density of quasi-stellar objects. The local (z = 0) density of quasi-stellar objects can then be estimated at 7 X 1O~ and 12 X 1O-~ Mpc3, for qo = 0 and qo = 1, respectively. Unpublished spectra and redshifts of quasi-stellar sources are given in the Appendix