clusters observed by @2013ApJ...767..116M are reported with filled and open magenta circles, respectively. []{data-label="fig:a1"}](fig4){width="50.00000%"}

We present the comparison between our [[[agn]{}]{}]{} simulated scaling relations at $z=0$ and $z=0.5$ and those obtained from observations at $z\leq 0.25$ and at $0.25\leq z \leq 0.6$ in Figs. \[fig:1\] and \[fig:2\], respectively. Each figure shows four scaling relations: $M-M_{g}$, $M-{T_{\rm sl}}$, $M-{Y_{\rm X}}$, and $L-M$. In this Section, all properties are measured within $R_{500}$ without any core excision to enlighten the good match that we obtain even including the region which is the most difficult to model. For the comparison, the observational measurements of $M$, ${M_{\rm g}}$, ${Y_{\rm X}}$ and $L$, which depend on $h^{-1}, h^{-5/2}, h^{-5/2}$ and $h^{-2}$, have been rescaled according to the value of the Hubble parameter of the simulation. In general, we observe a satisfactory consistency between simulations and observations for all relations, especially considering that [@2013ApJ...767..116M] measurements of the masses should be increased by $\sim20\%$ accordingly to the revised work from the group [@hoekstra.etal.2015].

The perfect accordance in the normalization of both the $M-{M_{\rm g}}$ and $L-M$ relations assures that the simulated baryon fraction is realistic over the mass range investigated. The overall $M-T$ relation is also consistent at 