The parallelism between galaxy clusters and early-type galaxies: II. Clues on the origin of the scaling relations.

Context. This is the second work dedicated to the observed parallelism between galaxy clusters and early-type galaxies. The focus is on the distribution of these systems in the scaling relations (SRs) observed when effective radii, effective surface brightness, total luminosities and velocity dispersions are mutually correlated. Aims. Using the data of the Illustris simulation we try to speculate on the origin of the observed SRs. Methods. We compare the observational SRs extracted from the database of the WIde-field Nearby Galaxy-cluster Survey (WINGS) with the relevant parameters coming from the Illustris simulations. Then we use the simulated data at different redshift to infer the evolution of the SRs. Results. The comparison demonstrate that galaxy clusters (GCs) at z~0 follow the same log(L)-log(sigma) relation of early-type galaxies (ETGs) and that both in the log(Ie)-log(Re) and log(Re)-log(M*) planes the distribution of GCs is along the sequence defined by the brightest and massive early-type galaxies (BCGs). The Illustris simulation reproduces the tails of the massive galaxies visible both in the log(Ie)-log(Re) and log(Re)-log(M*) planes, but fail to give the correct estimate of the effective radii of the dwarf galaxies that appear too large and those of GCs that are too small. The evolution of the SRs up to z=4 permits to reveal the complex evolutionary paths of galaxies in the SRs and indicate that the line marking the Zone of Exclusion (ZoE), visible both in the log(Ie)-log(Re) and log(Re)-log(M*) planes, is the trend followed by virialized and passively evolving systems. Conclusions. We speculate that the observed SRs originate from the intersection of the virial theorem and a relation L=L_0 x sigma^beta where the luminosities depend on the star formation history.