Scaling relations trace the formation and evolution of galaxy clusters .
We exploited multi-wavelength surveys – the XXL survey at 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 ( \beta _ { m _ { \text { g } } |m } = 1.73 \pm 0.80 ) and luminosity ( \beta _ { l|m } = 1.91 \pm 0.94 ) and a nearly self-similar slope for the temperature ( \beta _ { t|m } = 0.78 \pm 0.43 ) .
Intrinsic scatters of X-ray properties appear to be positively correlated at a fixed mass ( median correlation factor \rho _ { X _ { 1 } X _ { 2 } |m } \sim 0.34 ) due to dynamical state and merger history of the halos .
Positive correlations with the weak lensing mass ( median correlation factor \rho _ { m _ { \text { wl } } X|m } \sim 0.35 ) can be connected to triaxiality and orientation .
Comparison of weak lensing and hydrostatic masses suggests a small role played by non-thermal pressure support ( 9 \pm 17 \% ) .