The MUSIC of Galaxy Clusters III: Properties, evolution and Y-M scaling relation of protoclusters of galaxies

In this work we study the properties of protoclusters of galaxies by employing the MUSIC set of hydrodynamical simulations, featuring a sample of 282 resimulated clusters with available merger trees up to high redshift, tracing the cluster formation back to z = 4. We study the features and redshift evolution of the mass and the spatial distribution for all the protoclusters, which we define as the most massive progenitors of the clusters identified at z = 0. A natural extension to redshifts larger than 1 is applied to the estimate of the baryon content also in terms of gas and stars budgets: no remarkable variations with redshift are discovered. Furthermore, motivated by the proven potential of Sunyaev-Zeldovich surveys to blindly search for faint distant objects, we focus on the scaling relation between total object mass and integrated Compton y-parameter.We find that the slope of this scaling law is steeper than what expected for a self-similarity assumption among these objects, and it increases with redshift mainly when radiative processes are includedWe use three different criteria to account for the dynamical state of the protoclusters, and find no significant dependence of the scaling parameters from the level of relaxation, excluding the dynamical state as the cause of the observed deviations from self-similarity.