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.
We have analyzed the parallelism between the properties of galaxy clusters and early-type galaxies (ETGs) by looking at the similarity between their light profiles. We find that the equivalent luminosity profiles of all these systems in the vfilt ban
d, once normalized to the effective radius re and shifted in surface brightness, can be fitted by the Sersics law Sers and superposed with a small scatter ($le0.3$ mag). By grouping objects in different classes of luminosity, the average profile of each class slightly deviates from the other only in the inner and outer regions (outside $0.1leq r/R_eleq 3$), but the range of values of $n$ remains ample for the members of each class, indicating that objects with similar luminosity have quite different shapes. The Illustris simulation reproduces quite well the luminosity profiles of ETGs, with the exception of in the inner and outer regions where feedback from supernovae and active galactic nuclei, wet and dry mergers, are at work. The total mass and luminosity of galaxy clusters as well as their light profiles are not well reproduced. By exploiting simulations we have followed the variation of the effective half-light and half-mass radius of ETGs up to $z=0.8$, noting that progenitors are not necessarily smaller in size than current objects. We have also analyzed the projected dark+baryonic and dark-only mass profiles discovering that after a normalization to the half-mass radius, they can be well superposed and fitted by the Sersics law.
