  Member galaxies within galaxy clusters nowadays can be routinely identified
in cosmological, hydrodynamical simulations using methods based on identifying
self bound, locally over dense substructures. However, distinguishing the
central galaxy from the stellar diffuse component within clusters is
notoriously difficult, and in the center it is not even clear if two distinct
stellar populations exist. Here, after subtracting all member galaxies, we use
the velocity distribution of the remaining stars and detect two dynamically,
well-distinct stellar components within simulated galaxy clusters. These
differences in the dynamics can be used to apply an un-binding procedure which
leads to a spatial separation of the two components into a cD and a diffuse
stellar component (DSC). Applying our new algorithm to a cosmological,
hydrodynamical simulation we find that -- in line with previous studies --
these two components have clearly distinguished spatial and velocity
distributions as well as different star formation histories. We show that the
DSC fraction -- which can broadly be associated with the observed intra cluster
light -- does not depend on the virial mass of the galaxy cluster and is much
more sensitive to the formation history of the cluster. We conclude that the
separation of the cD and the DSC in simulations, based on our dynamical
criteria, is more physically motivated than current methods which depend on
implicit assumptions on a length scale associated with the cD galaxy and
therefore represent a step forward in understanding the different stellar
components within galaxy clusters. Our results also show the importance of
analyzing the dynamics of the DSC to characterize its properties and understand
its origin.
