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

We characterize the X-ray luminosity--temperature ($L_{\rm X}-T$) relation using a sample of 353 clusters and groups of galaxies with temperatures in excess of 1 keV, spanning the redshift range $0.1 < z < 0.6$, the largest ever assembled for this purpose. All systems are part of the ${\it XMM-Newton}$ Cluster Survey (XCS), and have also been independently identified in Sloan Digital Sky Survey (SDSS) data using the redMaPPer algorithm. We allow for redshift evolution of the normalisation and intrinsic scatter of the $L_{\rm X}-T$ relation, as well as, for the first time, the possibility of a temperature-dependent change-point in the exponent of such relation. However, we do not find strong statistical support for deviations from the usual modelling of the $L_{\rm X}-T$ relation as a single power-law, where the normalisation evolves self-similarly and the scatter remains constant with time. Nevertheless, assuming {\it a priori} the existence of the type of deviations considered, then faster evolution than the self-similar expectation for the normalisation of the $L_{\rm X}-T$ relation is favoured, as well as a decrease 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. Our results also indicate an increase in the power-law exponent of the $L_{\rm X}-T$ relation when moving from the group to the cluster regime, and faster evolution in the former with respect to the later, driving the temperature-dependent change-point towards higher values with redshift.