Abstract
Scaling relations trace the formation and evolution of galaxy clusters. We exploited multi-wavelength surveys -- the XXL survey at \emph{XMM-Newton} in the X-ray band, and the Hyper Suprime-Cam Subaru Strategic Program for optical weak lensing -- to study an X-ray selected, complete sample of clusters and groups. The scalings of gas mass, temperature, and soft-band X-ray luminosity with the weak lensing mass show imprints of radiative cooling and AGN feedback in groups. From the multi-variate analysis, we found some evidence for steeper than self-similar slopes for gas mass () and luminosity () and a nearly self-similar slope for the temperature (). Intrinsic scatters of X-ray properties appear to be positively correlated at a fixed mass (median correlation factor ) due to dynamical state and merger history of the halos. Positive correlations with the weak lensing mass (median correlation factor ) can be connected to triaxiality and orientation. Comparison of weak lensing and hydrostatic masses suggests a small role played by non-thermal pressure support ().
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