The parallelism between galaxy clusters and early-type galaxies: I. The
  light and mass profiles
  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\ band, once normalized to the effective radius \re\ and shifted
in surface brightness, can be fitted by the S\'ersic's 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 $0.1\leq
r/R_e\leq 3$), 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 S\'ersic's law.
