We present results from two high-resolution hydrodynamical simulations of proto-cluster regions at z~2.1. The simulations have been compared to observational results for the socalled Spiderweb galaxy system, the core of a putative proto-cluster region at z = 2.16, found around a radio galaxy. The simulated regions have been chosen so as to form a poor cluster with M200~10^14 h-1 Msun (C1) and a rich cluster with M200~2x10^15 h-1 Msun (C2) at z = 0. The simulated proto-clusters show evidence of ongoing assembly of a dominating central galaxy. The stellar mass of the brightest cluster galaxy (BCG) of the C2 system is in excess with respect to observational estimates for the Spiderweb galaxy, with a total star formation rate which is also larger than indicated by observations. We find that the projected velocities of galaxies in the C2 cluster are consistent with observations, while those measured for the poorer cluster C1 are too low compared to the observed velocities. We argue that the Spiderweb complex resemble the high-redshift progenitor of a rich galaxy cluster. Our results indicate that the included supernovae feedback is not enough to suppress star formation in these systems, supporting the need of introducing AGN feedback. According to our simulations, a diffuse atmosphere of hot gas in hydrostatic equilibrium should already be present at this redshift, and enriched at a level comparable to that of nearby galaxy clusters. The presence of this gas should be detectable with future deep X-ray observations.
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