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We use deep archival  Chandra  and  XMM–Newton  observations of three of the brightest cluster‐centre radio galaxies in the sky, Cygnus A, Hercules A and Hydra A, to search for inverse‐Compton emission from the population of electrons responsible for the low‐frequency radio emission. Using simulated observations, we derive robust estimates for the uncertainties on the normalization of an inverse‐Compton component in the presence of the variations in background thermal temperature actually seen in our target objects. Using these, together with the pressures external to the lobes, we are able to place interesting upper limits on the fraction of the energy density in the lobes of Hydra A and Her A that can be provided by a population of relativistic electrons with standard properties, assuming that the magnetic field is not dominant; these limits are consistent with the long‐standing idea that the energy density in these lobes is dominated by a non‐radiating particle population. In Cygnus A, we find evidence in the spectra for an additional hard component over and above the expected thermal emission, which is plausibly a detection of inverse‐Compton emission; even in this case, though, some additional non‐radiating particles and/or a departure from our standard assumptions on the electron spectrum are necessary to allow pressure balance at the mid‐point of the lobes. As this is not the case in other Fanaroff–Riley class II radio galaxies, we suggest that the rich environment of Cygnus A may have some effect on its lobe particle content.

Searching for the inverse‐Compton emission from bright cluster‐centre radio galaxies