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We characterize the X-ray luminosity--temperature ($L_{\rm X}-T$) relationusing a sample of 353 clusters and groups of galaxies with temperatures inexcess of 1 keV, spanning the redshift range $0.1 < z < 0.6$, the largest everassembled for this purpose. All systems are part of the ${\it XMM-Newton}$Cluster Survey (XCS), and have also been independently identified in SloanDigital Sky Survey (SDSS) data using the redMaPPer algorithm. We allow forredshift evolution of the normalisation and intrinsic scatter of the $L_{\rmX}-T$ relation, as well as, for the first time, the possibility of atemperature-dependent change-point in the exponent of such relation. However,we do not find strong statistical support for deviations from the usualmodelling of the $L_{\rm X}-T$ relation as a single power-law, where thenormalisation evolves self-similarly and the scatter remains constant withtime. Nevertheless, assuming {\it a priori} the existence of the type ofdeviations considered, then faster evolution than the self-similar expectationfor the normalisation of the $L_{\rm X}-T$ relation is favoured, as well as adecrease with redshift in the scatter about the $L_{\rm X}-T$ relation.Further, the preferred location for a change-point is then close to 2 keV,possibly marking the transition between the group and cluster regimes. Ourresults also indicate an increase in the power-law exponent of the $L_{\rmX}-T$ relation when moving from the group to the cluster regime, and fasterevolution in the former with respect to the later, driving thetemperature-dependent change-point towards higher values with redshift.

The ${\it XMM}$ Cluster Survey: joint modelling of the $L_{\rm X}-T$ scaling relation for clusters and groups of galaxies