We present new Giant Metre-wave Radio Telescope (GMRT) observations of Hubble Deep Field (HDF)130, an inverse-Compton (IC) ghost of a giant radio source that is no longer being powered by jets. We compare the properties of HDF130 with the new and important constraint of the upper limit of the radio flux density at 240 MHz to an analytic model. We learn what values of physical parameters in the model for the dynamics and evolution of the radio luminosity and X-ray luminosity [due to IC scattering of the cosmic microwave background (CMB)] of a Fanaroff-Riley type II (FR II) source are able to describe a source with features (lobe length, axial ratio, X-ray luminosity, photon index and upper limit of radio luminosity) similar to those of the observations. HDF130 is found to agree with the interpretation that it is an IC ghost of a powerful double-lobed radio source, and we are observing it at least a few Myr after jet activity (which lasted 5-100 Myr) has ceased. The minimum Lorentz factor of injected particles into the lobes from the hotspot is preferred to be γ~ 103 for the model to describe the observed quantities well, assuming that the magnetic energy density, electron energy density and lobe pressure at time of injection into the lobe are linked by constant factors according to a minimum energy argument, so that the minimum Lorentz factor is constrained by the lobe pressure. We also apply the model to match the features of 6C0905+3955, a classical double FR II galaxy thought to have a low-energy cut-off of γ~ 104 in the hotspot due to a lack of hotspot IC X-ray emission. The models suggest that the low-energy cut-off in the hotspots of 6C0905+3955 is γ≳ 103, just slightly above the particles required for X-ray emission. © 2011 The Authors. Monthly Notices of the Royal Astronomical Society © 2011 RAS.