A Hubble Space Telescope lensing survey of X-ray luminous galaxy clusters -: IV.: Mass, structure and thermodynamics of cluster cores at z=0.2

We present a comprehensive space-based study of 10 X-ray luminous galaxy clusters (L-X >= 8 x 10(44) erg s(-1), 0.1 - 2.4 keV) at z = 0.2. Hubble Space Telescope (HST) observations reveal numerous gravitationally lensed arcs for which we present four new spectroscopic redshifts, bringing the total to 13 confirmed arcs in this cluster sample. The confirmed arcs reside in just half of the clusters; we thus obtain a firm lower limit on the fraction of clusters with a central projected mass density exceeding the critical density required for strong lensing of 50 per cent. We combine the multiple-image systems with the weakly sheared background galaxies to model the total mass distribution in the cluster cores ( R <= 500 kpc). These models are complemented by high-resolution X-ray data from Chandra and used to develop quantitative criteria to classify the clusters as relaxed or unrelaxed. Formally, ( 30 +/- 20) per cent of the clusters form a relatively homogeneous subsample of relaxed clusters; the remaining ( 70 +/- 20) per cent are unrelaxed and are a much more diverse population. Most of the clusters therefore appear to be experiencing a cluster - cluster merger or relaxing after such an event. We also study the normalization and scatter of scaling relations between the cluster mass, the X-ray luminosity and the temperature. The scatter in these relations is dominated by the unrelaxed clusters and is typically sigma similar or equal to 0.4. Most notably, we detect two to three times more scatter in the mass - temperature relation than theoretical simulations and models predict. The observed scatter is also asymmetric - the unrelaxed clusters are systematically 40 per cent hotter than the relaxed clusters at 2.5 sigma significance. This structural segregation should be a major concern for experiments designed to constrain cosmological parameters using galaxy clusters. Overall our results are consistent with a scenario of cluster - cluster merger-induced boosts to cluster X-ray luminosities and temperatures.