Inverse-Compton ghosts and double-lobed radio sources in the X-ray sky

In this study we predict the total distributions of powerful [Fanaroff and Riley Class II (FR II)] active double-lobed radio galaxies and ghost sources, and their observable distribution in the X-ray sky. We develop an analytic model for the evolution of the lobe emission at radio and X-ray energies. During jet activity, a double radio source emits synchrotron radiation in the radio and X-ray emission due to inverse-Compton (IC) upscattering by γ∼ 10³ electrons of the cosmic microwave background. After the jets switch off, the radio luminosity (due to higher γ electrons) falls faster than the X-ray luminosity and for some time the source appears as an IC ghost of a radio galaxy before becoming completely undetectable in the X-ray. With our model, for one set of typical parameters, we predict radio lobes occupy a volume fraction of the Universe of 0.01, 0.03, 0.3 at z= 2 (during the quasar era) of the filamentary structures in which they are situated, for typical jet lifetimes 5 × 10⁷ yr, 10⁸ yr, 5 × 10⁸ yr; however since the inferred abundance of sources depends on how quickly they fall below the radio flux limit the volume filling factor is found to be a strong function of radio galaxy properties such as energy index and minimum γ factor of injected particles, the latter not well constrained by observations. We test the predicted number density of sources against the Chandra X-ray Deep Field North survey and also find the contribution to the unresolved cosmic X-ray background by the lobes of radio galaxies. 10-30 per cent of observable double-lobed structures in the X-ray are predicted to be IC ghosts. The derived X-ray luminosity function of our synthetic population shows that double-lobed sources have higher space densities than X-ray clusters at redshifts z≥ 2 and X-ray luminosities above 10⁴⁴ erg s^-1.