The new sample of giant radio sources III. Statistical trends and correlations

In this paper we analyse whether `giant' radio galaxies (GRGs) differ from `normal'-size galaxies (NSGs) except for the linear extent of their radio structure. We compare a number of properties of GRGs with the corresponding properties of NSGs, and analyse the statistical trends and correlations of physical parameters, homogeneously determined for the sources, with their `fundamental' parameters. Using the Pearson partial-correlation test on the correlation between two variables in the presence of one or two other variables, we examine which correlation is the strongest. The analysis clearly shows that GRGs do not form a separate class of radio sources. They most likely evolve with time from smaller sources, however under specific circumstances. Analysing properties of GRGs and NSGs together, we find that (i) the core prominence does not correlate with the total radio luminosity (as does the core power), but it anti-correlates with the surface brightness of the lobes of sources, (ii) the energy density (and possibly the internal pressure) in the lobes is independent of redshift for constant radio luminosity and size of the sources, (iii) the equipartition magnetic-field strength, transformed into constant source luminosity and redshift, strongly correlates with the source size. We argue that this B_{eq} - D correlation reflects a more fundamental correlation between B_{eq} and the source age, (iv) both the rotation and depolarisation measures suggest Faraday screens local to the lobes of sources, however their geometry and the composition of intervening material cannot be determined from the global polarisation characteristics.Comment: 10 pages, 8 figures, 6 tables. Accepted for publication in A&