Characterizing Diffused Stellar Light in simulated galaxy clusters
  [Abridged] In this paper, we carry out a detailed analysis of the performance
of two different methods to identify the diffuse stellar light in cosmological
hydrodynamical simulations of galaxy clusters. One method is based on a
dynamical analysis of the stellar component. The second method is closer to
techniques commonly employed in observational studies. Both the dynamical
method and the method based on the surface brightness limit criterion are
applied to the same set of hydrodynamical simulations for a large sample about
80 galaxy clusters.
  We find significant differences between the ICL and DSC fractions computed
with the two corresponding methods, which amounts to about a factor of two for
the AGN simulations, and a factor of four for the CSF set. We also find that
the inclusion of AGN feedback boosts the DSC and ICL fractions by a factor of
1.5-2, respectively, while leaving the BCG+ICL and BCG+DSC mass fraction almost
unchanged. The sum of the BCG and DSC mass stellar mass fraction is found to
decrease from ~80 per cent in galaxy groups to ~60 per cent in rich clusters,
thus in excess of what found from observational analysis.
  We identify the average surface brightness limits that yields the ICL
fraction from the SBL method close to the DSC fraction from the dynamical
method. These surface brightness limits turn out to be brighter in the CSF than
in the AGN simulations. This is consistent with the finding that AGN feedback
makes BCGs to be less massive and with shallower density profiles than in the
CSF simulations. The BCG stellar component, as identified by both methods, are
slightly older and more metal-rich than the stars in the diffuse component.
