redshift. Throughout the paper, the symbol $\log$ indicates the [*decimal*]{} logarithm and the uncertainty at 1 $\sigma$ on the best-fit parameters represents the 68.4 per cent confidence maximum-probability interval.

\[sec:cmrr\]

Simulations {#Simulation}
===========

Our analysis is based on three runs of simulated clusters. These are selected from a parent DM-only cosmological volume of 1 $h^{-3}$ Gpc$^3$ [@yoshida.etal.2001; @2011MNRAS.418.2234B] and re-simulated at higher resolution and with the inclusion of baryons.

The re-simulated Lagrangian regions are chosen around 24 massive clusters and five isolated groups and extend a radius equal to 5 times their virial radius. Their particles, identified at redshift $z=0$, are traced back to high redshifts [@2011MNRAS.418.2234B] and their number is increased to achieve a better spatial and mass resolution. The resimulations are carried out with an improved version of the GADGET-3 code [@springel05] where we activated the full set of SPH modifications as described in [@2015arXiv150207358B]. In short, these allow the SPH method to perform better in hydrodynamical standard tests including weak and strong shocks, gas mixing, and self-gravitating clouds.

We analyze three different runs of the same cluster sample. They differ on the level of sophistication on the description of the ICM physics. The joint analysis of the 