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.
