Testing models of the individual and cosmological evolutions of powerful radio galaxies

We seek to develop an essentially analytical model for the evolution of Fanaroff-Riley Class II (FR II) radio galaxies as they age individually and as their numbers vary with cosmological epoch. Such modelling is required in order to probe in more detail the impact of radio galaxies on the growth of structures in the Universe, which appears likely to have been quite significant at z > 1. In this first paper of a series we compare three rather sophisticated analytical models for the evolution of linear size and lobe power of FR II radio galaxies, those of Kaiser et al., Blundell et al. and Manolakou & Kirk. We perform multidimensional Monte Carlo simulations in order to compare the predictions of each model for radio powers, sizes, redshifts and spectral indices with data. The observational samples used here are the low-frequency radio surveys, 3CRR, 6CE and 7CRS, which are flux limited and complete. We search for and describe the best parameters for each model, after doing statistical tests on them. We find that no existing model can give acceptable fits to all the properties of the surveys considered, although the Kaiser et al. model gives overall better results than do the Manolakou & Kirk or Blundell et al. models for most of the tests we performed. We suggest ways in which these models may be improved.