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 mass-limited sample of 282 resimulated clusters with available merger trees up to high redshift, and we trace the cluster formation back to $z$ = 1.5, 2.3 and 4. We study the features and redshift evolution of the mass and the spatial distribution for all the cluster progenitors and for 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-Zel'dovich surveys to blindly search for faint distant objects, we focus on the scaling relation between total object mass and integrated Compton $y$-parameter, and we check for the possibility to extend the mass-observable paradigm to the protocluster regime, far beyond the redshift of 1, to account for the properties of the simulated objects. 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 for the synthetic clusters where radiative processes, such as radiative cooling, heating processes of the gas due to UV background, star formation and supernovae feedback, are included. We 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. Based on this, we exclude that the dynamical state is the cause of the observed deviations from self-similarity.