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Observations and cosmological simulations show galaxy clusters as a family ofnearly self-similar objects with properties that can be described by scalingrelations as a function of e.g. mass and time. Here we study the scalingrelations between the galaxy velocity dispersion and X-ray quantities likeX-ray bolometric luminosity and temperature in galaxy clusters at highredshifts (0.64 $\leq$ z $\leq$ 1.46). We also compare our results with thesimilar study of the local HIFLUGCS sample. For the analysis, we use a set of15 distant galaxy clusters extracted from the literature plus a sample of 10newly discovered clusters selected in X-rays by the \XMM Distant ClusterProject (XDCP) with more than 10 confirmed spectroscopic members per cluster.We also study the evolution of this scaling relation by comparing the highredshift results with the data from the local HIFLUGCS sample. We alsoinvestigated the $L_X - T_X$ and the $\sigma_v - T_X$ relations for the 15clusters in the literature sample. We report the results of the X-ray andkinematic analysis of 10 newly detected high redshift clusters and providetheir spectroscopic and kinematic details. For the entire, distant sample wefind a slope fully consistent with the one typical of local clusters, albeitwith a large associated uncertainty. The study on the evolution of theamplitude 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 localrelation without any significant redshift evolution. Finally, the $\sigma_v -T_X$ relation appears to slightly deviate from the theoretical expectation thatgalaxies and gas particles have a similar specific kinetic energy. However, theassociated uncertainty is currently too large for making any conclusivestatement in this regard.

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