The XMM Cluster Survey: evolution of the velocity dispersion -- temperature relation over half a Hubble time

We measure the evolution of the velocity dispersion--temperature ($σ_{\rm v}$--$T_{\rm X}$) relation up to $z = 1$ using a sample of 38 galaxy clusters drawn from the \textit{XMM} Cluster Survey. This work improves upon previous studies by the use of a homogeneous cluster sample and in terms of the number of high redshift clusters included. We present here new redshift and velocity dispersion measurements for 12 $z > 0.5$ clusters observed with the GMOS instruments on the Gemini telescopes. Using an orthogonal regression method, we find that the slope of the relation is steeper than that expected if clusters were self-similar, and that the evolution of the normalisation is slightly negative, but not significantly different from zero ($σ_{\rm v} \propto T^{0.86 \pm 0.14} E(z)^{-0.37 \pm 0.33}$). We verify our results by applying our methods to cosmological hydrodynamical simulations. The lack of evolution seen in our data is consistent with simulations that include both feedback and radiative cooling.