Further high-resolution observations of faint radio sources and the angular size–flux density relation

We present high-resolution radio observations of 37 5C 12 and four 5C 7 sources. Together with other sources from 5C 6 and 7, these make up two (overlapping) samples complete to 20 mJy at 1407 MHz (35 sources) and in flux density range 0.1–1 Jy at 408 MHz (43 sources). Both the radio structures and the small proportion of the sources which are identified suggest that many of the sources lie at redshifts z ≳ 1. The median angular sizes for the two samples are 7 and 7.5 arcsec respectively, with the distributions extending up to ∼ 2 arcmin at both frequencies. The observed angular sizes, combined with published data, are compared with the predictions of models of evolution of the radio-source population, using as alternative parent populations the 178-MHz 3CR sample and a sample of bright sources at 2700 MHz. For the flux density range 0.05–1 Jy at 408 MHz the best fits are obtained for linear size evolution as $$(1+z)^{-1.0\enspace\text {to}\enspace-1.5}$$, but a good fit is also obtained for no linear size evolution in an empty universe when the 2700-MHz parent sample is used. This is likely to be a result of the relatively larger number of steep-spectrum compact objects found in surveys at frequencies above ∼ 178 MHz. The quality of the fits does not depend strongly upon the form of the evolving radio luminosity functions considered here. We conclude that, contrary to claims in the literature (e.g. Kapahi & Subrahmanya 1982), the presently available data do not determine whether linear size evolution is required.