The photoionization models for the narrow emission-line regions of powerful radio galaxies have yet to be tested in depth. To this end, we present high-quality long-slit spectroscopy of the powerful double-nucleus radio galaxy 3C 321. The data have good enough spatial resolution to be able to trace the variation in emission-line properties on kpc scales. Continuum modelling and subtraction enables the faint emission-line fluxes to be measured in several regions across the emission-line nebula. We plot diagnostic line-ratio diagrams and compare them with the predictions of various photoionization models, finding that the data are best fitted by models that assume a mixture of optically thin and thick clouds illuminated by a power-law continuum. The emission-line kinematics, line ratios and deduced physical conditions show remarkably little variation across the source. We deduce a mean electron density of 400±120 cm−3 and a mean temperature of 11 500±1500 K. Assuming a single population of optically thick line-emitting clouds, we calculate a mean photoionization parameter of (1.1±0.5)×10−2, and hence a photoionizing photon luminosity of Q∼1055–1056 photon s−1 sr−1. This indicates a central engine as luminous as that of the powerful quasar 3C 273, yet there is no evidence for such an energetically prolific central engine at either far-infrared or radio wavelengths. We therefore conclude that the mixed-medium models, which give Q∼5×1053–5×1054 photon s−1 sr−1 represent a more likely scenario. As a by-product of the continuum subtraction, we infer that young stellar populations account for ∼0.4 per cent of the visible stellar mass in the galaxy, and that these populations are spatially extended.
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