The active galactic nuclei (AGN) lobe radio luminosities modelled in hydrodynamical simulations and most analytical models do not address the redistribution of the electron energies due to adiabatic expansion, synchrotron radiation and inverse-Compton scattering of CMB photons. We present a synchrotron emissivity model for resolved sources which includes a full treatment of the loss mechanisms spatially across the lobe, and apply it to a dynamical radio source model with known pressure and volume expansion rates. The bulk flow and dispersion of discrete electron packets is represented by tracer fields in hydrodynamical simulations; we show that the mixing of different aged electrons strongly effects the spectrum at each point of the radio map in high-powered FR-II sources. The inclusion of this mixing leads to a factor of a few discrepancy between the spectral age measured using impulsive injection models (e.g. JP model) and the dynamical age. The observable properties of radio sources are predicted to be strongly frequency dependent: FR-II lobes are expected to appear more elongated at higher frequencies, while jetted FR-I sources appear less extended. The emerging FR0 class of radio sources, comprising gigahertz peaked and compact steep spectrum sources, can potentially be explained by a population of low-powered FR-Is. The extended emission from such sources is shown to be undetectable for objects within a few orders of magnitude of the survey detection limit and to not contribute to the curvature of the radio SED.
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