Cosmology from Angular Size Counts of Extragalactic Radio Sources

In this paper the cosmological implications of the observed angular sizes of extragalactic radio sources are investigated using (i) the log N-log θ relation, where N is the number of sources with an angular size greater than a value θ, for the complete sample of 3CR sources, and (ii) the $$\theta_\text{median} \,\upsilon s$$ flux density (S) relation derived from the 3CR, the All-sky, and the Ooty occultation surveys, spanning a flux density range of about 300 : 1. The method of estimating the expected N(θ) and θ_m(S) relations for a uniform distribution of sources in space is outlined. Since values of $$\theta \gtrsim 100^{\prime\prime}$$ arc in the 3C sample arise from sources of small z, the slope of the N(θ) relation in this range is practically independent of the world model and the distribution of source sizes, but depends strongly on the radio luminosity function (RLF). From the observed slope, we derive the RLF in the luminosity range of about $$10^{23} \lt P_{178} \lt 10^{26} \,\text{W} \,\text{Hz}^{-1} \,\text{sr}^{-1} \,\text{to be of the form} \,\rho(P) dP \propto P^{-2 \cdot 1} dP.$$ It is shown that the angular size data provide independent evidence of evolution in source properties with epoch. It is difficult to explain the data with the simple steady-state theory even if identified QSOs are excluded from the source samples and a local deficiency of strong sources is postulated. The simplest evolutionary scheme that fits the data in the Einstein–de Sitter cosmology indicates that (a) the local RLF steepens considerably at high luminosities, (b) the comoving density of high luminosity sources increases with z in a manner similar to that implies by the log N–log S data and by the V/V_m test for QSOs, and (c) the mean physical sizes of radio sources evolve with z approximately as (1 + z)^–1. Similar evolutionary effects appear to be present for QSOs as well as radio galaxies.