both redshifts. It should be noted that the temperature in [@2015arXiv151203857L] (brown circles in the Figures) is measured within the aperture of $300$ kpc rather than within $R_{500}$. To compare with them, we report in the plot the simulated $M-T_{\rm sl,300kpc}$ with a red line. Since the temperature level of the ICM is mostly reached through the shocks generated by mergers and accretion during the formation of the cluster, the good match found in the two Figures implies that these processes are realistically reproduced in our models.

To investigate in a deeper manner the influence of the central regions, we compare the $L-T$ relation measured in the two categories of cool-core and non cool-core (Fig. \[fig:a1\]) clusters. The two simulated classes are taken from [@2015ApJ...813L..17R] and refer to the main halos of the 29 re-simulated regions. The distinction between the two types was established on the basis of the pseudo entropy level of the objects. We find reassurance in that the simulated clusters reproduce the same behavior of real systems: at a given temperature CC objects appear more luminous than NCC systems because of the higher central gas density that boosts their X-ray luminosity. The separation between CC and NCC 