The time evolution of giant lobe-dominated radio galaxies (with projected linear size D>1 Mpc if H_{0}=50 km/s/Mpc and q_{0}=0.5 is analysed on the basis of dynamical evolution of the entire FRII-type population. Two basic physical parameters, namely
the jet power Q_{0} and central density of the galaxy nucleus rho0 are derived for a sample of giants with synchrotron ages reliably determined, and compared with the relevant parameters in a comparison sample of normal-size sources consisting of 3C, B2, and other sources. Having the apparent radio luminosity P and linear size D of each sample source, Q_{0} and rho_{0} are obtained by fitting the dynamical model of Kaiser et al. (1997). We find that: (i) there is not a unique factor governing the source size; they are old sources with temperate jet power (Q_{0}) evolved in a relatively low-density environment (rho_{0}). The size is dependent, in order of decreasing partial correlation coefficients, on age; then on Q_{0}; next on rho_{0}. (ii) A self-similar expansion of the sources cocoon seems to be feasible if the power supplied by the jets is a few orders of magnitude above the minimum-energy value. In other cases the expansion can only initially be self-similar; a departure from self-similarity for large and old sources is justified by observational data of giant sources. (iii) An apparent increase of the lowest internal pressure value observed within the largest sources cocoon with redshift is obscured by the intrinsic dependence of their size on age and the age on redshift, which hinders us from making definite conclusions about a cosmological evolution of intergalactic medium (IGM) pressure.
The time evolution of `fiducial radio sources derived from fitting the dynamical model of Kaiser et al. (1997) is compared with the observational data for the `clan sources found in the sample of giant and normal-size FRII-type sources published Pape
r I (Machalski et al. 2004). Each `clan comprises 3, 4 or 5 sample sources having similar values of the two basic physical parameters: the jet power Q_{0} and central density of the galaxy nucleus rho_{0} (determined in Paper I) but different ages, radio luminosities and axial ratios. These sources are considered as the `same source observed at different epochs of its lifetime and used to fit the evolutionary luminosity-size (P-D) and energy density-total energy (u_{c}-E_{tot}) tracks derived from the model for a `fiducial source with Q0 and rho_{0} equal to the means of relevant values obtained for the `clan members, as well as to constrain the evolutionary model of the source dynamics used. In the result we find that (i) The best fit is achieved when the Kaiser et al.s model is modified by allowing an evolution of the sources cocoon axial ratio with time as suggested by Blundell et al. (1999). (ii) A slow acceleration of the average expansion speed of the cocoon along the jet axis is suggested by the `clan sources. We argue that this acceleration, although minor, may be real and some supporting arguments come from the well known hydrodynamical considerations.
We present an analytical model for the cosmological evolution of the FRII source population. Based on an earlier model for the intrinsic radio luminosity - linear size evolution of these objects, we construct theoretical source samples. The source di
stributions in the radio power - linear size plane of these samples are then compared with that of an observed flux-limited sample. We find that the source parameters determining the radio luminosity of FRII objects can not be independent of each other. The best-fitting models predict the jet power to be correlated either with the life time of the source or with the shape of the density distribution of the source environment. The latter case is consistent with the observed tendency of the most luminous radio sources at high redshift to be located in richer and more extended environments than their low redshift counterparts. We also find evidence for a class of FRII sources distinctly different from the main population. These sources are extremely old and/or are located in very underdense environments. The luminosity function of FRII sources resulting from the model is in good agreement with previous results for high luminosity sources. The apparent luminosity evolution of the radio luminosity function is not reproduced because of the high flux limit of the used comparison sample. The cosmological evolution of the median linear size of FRII sources is found to be mild.
In this paper we show normalized differential source counts n(S) at 408 MHz and 1.4 GHz of radio sources separately for FRI and FRII classes with extended and compact morphologies. The maps from the FIRST, NVSS, and WENSS surveys are used to define t
he source morphology and flux density. The counts provide a basis for a direct test as well as constraining the cosmological evolution of powerful extragalactic radio sources in terms of the dual-population model (Jackson & Wall 1999), where radio sources of Fanaroff-Riley (1974) types I and II are regarded as two physically separate types of active galactic nuclei (AGN). The predicted count values are compared with the observational data to find the best fits for the evolution and beaming parameters, and to further refine the model.
Dynamical ages of the opposite lobes determined {sl independently} of each other suggest that their ratios are between $sim$1.1 to $sim$1.4. Demanding similar values of the jet power and the radio core density for the same GRS, we look for a {sl self
-consistent} solution for the opposite lobes, which results in different density profiles along them found by the fit. A comparison of the dynamical and spectral ages shows that their ratio is between $sim$1 and $sim$5, i.e. is similar to that found for smaller radio galaxies. Two causes of this effect are pointed out.