The different growth pathways of Brightest Cluster Galaxies and the Intra-Cluster Light

We study the growth pathways of Brightest Central Galaxies (BCGs) and Intra-Cluster Light (ICL) by means of a semi-analytic model. We assume that the ICL forms by stellar stripping of satellite galaxies and violent processes during mergers, and implement two independent models: (1) one considers both mergers and stellar stripping (named {\small STANDARD} model), and one considers only mergers (named {\small MERGERS} model). We find that BCGs and ICL form, grow and overall evolve at different times and with different timescales, but they show a clear co-evolution after redshift $z \sim 0.7-0.8$. Around 90\% of the ICL from stellar stripping is built-up in the innermost 150 Kpc from the halo centre and the dominant contribution comes from disk-like galaxies (B/T$<$0.4) through a large number of small/intermediate stripping events ($M_{strip}/M_{sat}<0.3$). The fractions of stellar mass in BCGs and in ICL over the total stellar mass within the virial radius of the halo evolve differently with time. At high redshift, the BCG accounts for the bulk of the mass, but its contribution gradually decreases with time and stays constant after $z\sim 0.4-0.5$. The ICL, instead, grows very fast and its contribution keeps increasing down to the present time. The {\small STANDARD} and the {\small MERGERS} models make very similar predictions in most of the cases, but predict different amounts of ICL associated to other galaxies within the virial radius of the group/cluster other than the BCG, at $z=0$. We then suggest that this quantity is a valid observable that can shed light on the relative importance of mergers and stellar stripping for the formation of the ICL.