tokens: A MannWhitney U test of the distributions about this relation does not rule out at 95percent confidence the null hypothesis that the two redshift sub-samples have the same parent population. We do, however, acknowledge that weak evolution of the relation of equation ( 1 ) cannot be ruled out by our data, and this should be investigated with deep X-ray survey data and/or further deep X-ray observations of carefully selected samples. 2.3 Using pressure to predict X-ray luminosity We have demonstrated that we can reliably predict the ICM pressure at a single distance within the group/cluster surrounding an FRII radio galaxy. To be able to predict the overall group/cluster richness, we need to be able to translate this pressure measurement into an estimate of cluster mass and/or X-ray luminosity. We therefore examined whether the universal cluster pressure profile of Arnaud etal. ( 2010 , hereafter A10 ) could be applied to FRII environments. We first examined the sub-sample of I17 for which reliable spectral temperature estimates were available. Our pressure profiles have large uncertainties, and were obtained from either beta or double-beta model fits to the surface brightness profiles (see I17 ). The environments are also mainly galaxy groups ( L X 10 44 ergs 1 ), and so lower in mass than the sample of A10 ; however, Sun etal. ( 2011 ) have shown that the universal profile also applies on galaxy group scales. Fig. 2 (right-hand panel) shows that our scaled pressure profiles are in broad agreement with the A10 profile shape and normalization. We therefore tested whether the universal cluster pressure profile could be used to translate our single-radius pressure estimates, from our radio predictions, into cluster mass and X-ray luminosity. We used the profile of A10 (equations 1113 of that work) and our input values of distance and P ext to estimate M 500 for each radio-galaxy environment. We then applied the L X M 500 relation of Pratt etal. ( 2009 ) (using the relation for L X R 500 ) to obtain a predicted L X for each radio-galaxy environment. Finally, we compared our radio-predicted X-ray luminosities with the measured X-ray luminosities for our sample from Ineson etal. ( 2015 ). Fig. 3 (left-hand panel) shows the remarkable agreement between our radio-predicted X-ray luminosities and the measured values across more than three orders of magnitude in X-ray luminosity (from poor groups to moderate clusters) our method appears to predict ICM X-ray luminosity to within roughly a factor of 2 based only on the measured properties of the embedded radio galaxy. We have included four additional FRII sources from the sample of I17 for which external pressure distributions could not be measured, but which meet the morphological selection criteria, leading to a sample of 31 objects, as listed in Table 1 . Figure 3. Left-hand panel: the predicted group/cluster X-ray luminosities determined from the radio-measured pressures for the morphologically
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