Kinematic analysis of a sample of X-ray luminous distant galaxy clusters. The $L_X$ - $σ_v$ relation in the $z>0.6$ universe

Observations and cosmological simulations show galaxy clusters as a family of nearly self-similar objects with properties that can be described by scaling relations as a function of e.g. mass and time. Here we study the scaling relations between the galaxy velocity dispersion and X-ray quantities like X-ray bolometric luminosity and temperature in galaxy clusters at high redshifts (0.64 $\leq$ z $\leq$ 1.46). We also compare our results with the similar study of the local HIFLUGCS sample. For the analysis, we use a set of 15 distant galaxy clusters extracted from the literature plus a sample of 10 newly discovered clusters selected in X-rays by the \XMM Distant Cluster Project (XDCP) with more than 10 confirmed spectroscopic members per cluster. We also study the evolution of this scaling relation by comparing the high redshift results with the data from the local HIFLUGCS sample. We also investigated the $L_X - T_X$ and the $σ_v - T_X$ relations for the 15 clusters in the literature sample. We report the results of the X-ray and kinematic analysis of 10 newly detected high redshift clusters and provide their spectroscopic and kinematic details. For the entire, distant sample we find a slope fully consistent with the one typical of local clusters, albeit with a large associated uncertainty. The study on the evolution of the amplitude reveals a positive offset if the self-similar evolution is neglected, hence possibly indicating the need for including evolutionary effects. However, the $L_X - T_X$ relation is found to be in good agreement with the local relation without any significant redshift evolution. Finally, the $σ_v - T_X$ relation appears to slightly deviate from the theoretical expectation that galaxies and gas particles have a similar specific kinetic energy. However, the associated uncertainty is currently too large for making any conclusive statement in this regard.