Cosmic evolution of the physical sizes of extragalactic radio sourcesand their luminosity-size correlation.

We have examined the cosmic evolution of physical sizes of extragalactic radio sources and also looked for any possible luminosity-size correlation among these. For this purpose we have formed a sample of 669 optically identified extragalactic radio sources, compiled from a number of published subsamples. Information on the flux density, angular size and redshift for each source has been obtained either from the original subsample or gathered from the other literature. By using this sample we have examined the size distribution of extragalactic radio sources in different luminosity-redshift bins, separately for galaxies and quasars. It appears that for radio galaxies the physical size increases with luminosity for redshifts ~<0.5, where reliable data are available. Moreover, it is found that the physical size decreases with increasing redshift for the radio galaxies with luminosity 10^26^<P_408_<10^27^ W Hz^-1^, where the median value of largest linear dimension drops from ~300 kpc for nearby sources to ~100 kpc at redshifts ~0.5. This drop in size can be represented by the size evolutionary models of type (1 + z)^-n^, for n~3. The observed size evolution can also be fairly well described by other models including one in which there is an exponential increase in the physical size of radio sources with cosmic time. For brighter radio galaxies (P_408_>10^27^W Hz^-1^), there is little evidence for size evolution, at least up to redshift ~0.5; at higher redshifts, data are lacking mainly because of the incompleteness of optical identifications. For quasars, unlike galaxies, there is no evidence of an increase in size with luminosity; in fact there is a hint of an inverse correlation between luminosity and size. Only a marginal size evolution seems to be present for different luminosity classes among quasars. The possibility of a differential size evolution for different luminosity classes among galaxies and/or that of an intrinsic difference in the size distribution among galaxies and quasars cannot be ruled out.