The spectra and energies of classical double radio lobes

We compare two temporal properties of classical double radio sources: i) radiative lifetimes of synchrotron-emitting particles and ii) dynamical source ages. We discuss how these can be quite discrepant from one another, rendering use of the traditional spectral ageing method inappropriate: we contend that spectral ages give meaningful estimates of dynamical ages only when these ages are << 10^7 years. In juxtaposing the fleeting radiative lifetimes with source ages which are significantly longer, a refinement of the paradigm for radio source evolution is required. The changing spectra along lobes are explained, not predominantly by synchrotron ageing but, by gentle gradients in a magnetic field mediated by a low-gamma matrix which illuminates an energy-distribution of particles, controlled largely by classical synchrotron loss in the high magnetic field of the hotspot. The energy in the particles is an order of magnitude higher than that inferred from the minimum-energy estimate, implying that the jet-power is of the same order as the accretion luminosity produced by the quasar central engine. This refined paradigm points to a resolution of the findings of Rudnick et al (1994) and Katz-Stone & Rudnick (1994) that both the Jaffe-Perola and Kardashev-Pacholczyk model spectra are invariably poor descriptions of the curved spectral shape of lobe emission, and indeed that for Cygnus A all regions of the lobes are characterised by a `universal spectrum'. [abridged]