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Extending the $L_{\mathrm{X}}-T$ relation from clusters to groups-Impact of cool core nature, AGN feedback, and selection effects

We aim to investigate the bolometric $L_{\mathrm{X}}-T$ relation for galaxy groups, and study the impact of gas cooling, feedback from supermassive black holes, and selection effects on it. With a sample of 26 galaxy groups we obtained the best fit $L_{\mathrm{X}}-T$ relation for five different cases depending on the ICM core properties and central AGN radio emission, and determined the slopes, normalisations, intrinsic and statistical scatters for both temperature and luminosity. Simulations were undertaken to correct for selection effects (e.g. Malmquist bias) and the bias corrected relations for groups and clusters were compared. The slope of the bias corrected $L_{\mathrm{X}}-T$ relation is marginally steeper but consistent with clusters ($\sim 3$). Groups with a central cooling time less than 1 Gyr (SCC groups) show indications of having the steepest slope and the highest normalisation. For the groups, the bias corrected intrinsic scatter in $L_{\mathrm{X}}$ is larger than the observed scatter for most cases, which is reported here for the first time. Lastly, we see indications that the groups with an extended central radio source have a much steeper slope than those groups which have a CRS with only core emission. Additionally, we also see indications that the more powerful radio AGN are preferentially located in NSCC groups rather than SCC groups.