A method for estimating the dynamical age of FR II- type radio sources from multi-frequency data

Context. Determining the ages of powerful radio sources is crucial for understanding galaxy evolution, the activity cycle of galactic nuclei, and their influence on the surrounding intergalactic medium. So far, several different methods for estimating the age of classical double radio galaxies have been proposed and widely used in the literature, although each of them faces difficulty due to observational limitations and/or freedom in choosing the underlying model assumptions. Aims. We propose a new approach to determining the ages of FR II type radio sources that, on one hand exploits a dynamical model developed for these objects by Kaiser et al. ( 1997, MNRAS, 292, 723) and, on the other hand, uses multifrequency radio observations not necessarily restricted to the high-resolution ones. Methods. In particular, we applied the assumed dynamical model to a number of FR II type radio galaxies observed at di.erent radio frequencies and fit - for each frequency separately - the model's free parameters to the quantities of the observed sources. Such a procedure, which in fact enlarged a number of observables, enabled us to determine relatively precise ages and other crucial characteristics ( like the jets' kinetic power) for the analyzed sources. Results. The resulting age estimates agree very well with those obtained with the classical spectral aging method for objects not older than 10 Myr, for which good-quality spectral data are available. However, this method is also applicable in the case of older sources than this and/or those for which the only available low-resolution radio data do not allow for detailed spectral aging studies. Interestingly, the estimated ages always correspond to the realistic values of the jets' advance velocity of similar to 0.01-0.1 c. Conclusions. Our analysis indicates that the main factor precluding precise age determination for FR II type radio galaxies is related to the poorly known shape of the initial electron energy distribution injected by the jet's terminal shocks to the expanding lobes/cocoons. We briefly considered this issue and conclude that the broad-band single power-law form assumed here may be accurate enough for the age estimates, although most likely it does not strictly correspond to some well-defined realistic particle acceleration process. Instead, it should be considered as the simplest model approximation of the initial electron continuum, averaged over a very broad energy range and over the age of the source, with the effective spectral index that may be different for different sources, but within the relatively narrow range of p = 2.0-2.4 suggested by our modeling.