We compute and study the infrared and sub-mm properties of high-redshift (z ≳ 1) simulated clusters and protoclusters. The results of a large set of hydrodynamical zoom-in simulations including active galactic nuclei (AGN) feedback, have been treated with the recently developed radiative transfer code GRASIL-3D, which accounts for the effect of dust reprocessing in an arbitrary geometry. Here, we have slightly generalized the code to adapt it to the present purpose. Then we have post-processed boxes of physical size 2 Mpc encompassing each of the 24 most massive clusters identified at z = 0, at several redshifts between 0.5 and 3, producing IR and sub-mm mock images of these regions and spectral energy distributions (SEDs) of the radiation coming out from them. While this field is in its infancy from the observational point of view, rapid development is expected in the near future thanks to observations performed in the far-IR and sub-mm bands. Notably, we find that in this spectral regime our prediction are little affected by the assumption required by this post-processing, and the emission is mostly powered by star formation (SF) rather than accretion on to super massive black hole (SMBH). The comparison with the little observational information currently available, highlights that the simulated cluster regions never attain the impressive star formation rates suggested by these observations. This problem becomes more intriguing taking into account that the brightest cluster galaxies (BCGs) in the same simulations turn out to be too massive. It seems that the interplay between the feedback schemes and the star formation model should be revised, possibly incorporating a positive feedback mode.
