2000A&A...362..447K

A 3-dimensional model of the synchrotron emissivity of the cocoons of powerful extragalactic radio sources of type FRII is constructed. Bulk backflow and energy losses of the relativistic electrons, radiative and adiabatic, are self-consistently taken into account. Thus the model is an extension of spectral aging methods including the underlying source dynamics into the age estimates. The discrepancies between spectral ages and dynamical ages arising from earlier methods are resolved. It is also shown that diffusion of relativistic particles within the cocoon is unlikely to significantly change the particle spectrum and thus the emitted radio spectrum. Projection along the line of sight yields 1 or 2-dimensional surface brightness distributions which can be compared with observations. From the model parameters constraints on the source age, the density of the source environment and the angle to the line of sight can be derived. Application of the method to Cygnus A, 3C 219 and 3C 215 show that the method provides robust estimates for the model parameters for sources with comparatively regularly shaped radio lobes. The resolution of the radio maps required is only moderate. Within the large uncertainties for the orientation angle, the three example sources are found to be consistent with orientation-based unification schemes of radio-loud AGN. In the case of Cygnus A the gas density of the environment is found to agree with independent X-ray measurements. For 3C 219 and 3C 215 the densities derived from the model are apparently too low. It is suggested that these discrepancies are caused by overestimates of slope and core radius of β-models for the gas density distribution from X-ray observations for clusters hosting powerful radio sources.