A detailed investigation of radio power selection effects relevant to the study of classical double radio sources

A sample of powerful classical double radio sources, also known as FR II sources, has been assembled to study the properties of the radio sources and their gaseous environments, as well as the redshift evolution of these properties. The possibility that the observed redshift dependences of various parameters of interest are caused by radio power selection effects is investigated here using statistical tools such as two-parameter fitting and partial rank correlation analysis. It is found that the Mach number of lobe advance, the lobe propagation velocity, and the ambient gas density of the FR II sources are unlikely to be significantly affected by radio power selection effects. Hence, the observed redshift dependences of these parameters are likely to reflect real redshift evolution. A previous study by Wellman, Daly, & Wan indicates that the powerful FR II sources in this sample lie in cluster-like gaseous environments. The fact that the ambient gas density of the FR II sources is not affected by radio power selection means that these sources can be used to probe the evolution of their environments. Specifically, the observed decrease of the ambient gas density with redshift is likely to reflect real redshift evolution rather than being caused by radio power selection effects. It is interesting to note that the current data suggest that the Mach number of lobe advance is independent of redshift, while the lobe propagation velocity increases with redshift, as summarized in the final table in this paper. Radio power selection effects are likely to be quite weak, if present at all, in the study of the non-thermal pressure inside a classical double source, and the study of the characteristic size of a source. The two-parameter fitting and partial rank correlation analysis applied to the ambient gas temperature and luminosity in directed kinetic energy of the jet yield inconclusive results, so these direct analyses do not clearly indicate whether the redshift evolution of each of these two parameters is due to radio power selection effects. However, each parameter is estimated using other parameters such as the Mach number of lobe advance, the lobe propagation velocity, and the nonthermal pressure inside the radio lobe, which do not suffer significant radio power selection effects.