Vast cavities in the intergalactic medium are excavated by radio galaxies. The cavities appear as such in X-ray images because the external medium has been swept up, leaving a hot but low density bubble surrounding the radio lobes. We explore here the predicted thermal X-ray emission from a large set of high-resolution three dimensional simulations of radio galaxies driven by supersonic jets. We assume adiabatic non-relativistic hydrodynamics with injected straight and precessing jets of supersonic gas emitted from nozzles. Images of X-ray Bremsstrahlung emission tend to generate oval cavities in the soft keV bands and leading arcuate structures in hard X-rays. However, the cavity shape is sensitive to the jet-ambient density contrast, varying from concave-shaped at $eta = 0.1$ to convex for $eta = 0.0001$ where $eta$ is the jet/ambient density ratio. We find lateral ribs in the soft X-rays in certain cases and propose this as an explanation for those detected in the vicinity of Cygnus,A. In bi-lobed or X-shaped sources and in curved or deflected jets, the strongest X-ray emission is not associated with the hotspot but with the relic lobe or deflection location. This is because the hot high-pressure and dense high-compression regions do not coincide. Directed toward the observer, the cavity becomes a deep round hole surrounded by circular ripples. With short radio-mode outbursts with a duty cycle of 10% , the intracluster medium simmers with low Mach number shocks widely dissipating the jet energy in between active jet episodes.
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