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torily. Looking at the upper panel of Fig. 13, we see that we might overestimate the ICL fraction if we significantly overpredict the number of very low mass or very massive galaxies. The former does not seem to be a problem as in- dicated by the distribution in the figure’s lower panel. The abundance of massive galaxies, however, is typically overpre- dicted in cosmological hydrodynamical simulations (see e.g. Oppenheimer et al. (2009)). This surely is the case in our simulations without AGN, but we can not be fully sure yet whether this is completely resolved when the AGN feedback model is included. Assessing this reliably requires a high res- olution simulation of a large cosmological box, which has not yet been done due to the large computational cost. 

Nevertheless, from exploring the cluster galaxy mass functions of our simulated clusters, we can be confident that the problem of overpredicting massive galaxies is rather strongly alleviated in runs with AGN, as also suggested by the much lower BCG luminosities shown in Fig. 8. However, the ICL fractions in our simulations with AGN feedback are even slightly higher than in the runs without it. This sug- gests that overpredicting massive galaxies is not the main reason why our ICL fractions are relatively high compared to the values typically inferred from observations. This also highlights that it is really far from obvious how a large ICL fraction can be avoided in the simulations of the formation of clusters in the ΛCDM cosmology. 

## 3.4 The fate of infalling galaxies 

Fig. 14 illustrates the infall of satellite galaxies and the origin of intracluster stars for a 10 $^{14}$h − $^{1}$M ⊙ cluster. The upper left panel shows all star particles residing in the cluster’s satellite galaxies, and the BCG and ICL components at z = 0. Here, Method 4 was used for making a distinction between BCG and ICL, and the figure illustrates the assignment of the star particles to the individual components. The upper right panel of Fig. 14 shows the same cluster at z = 1. All star particle are still coloured according to the component which they belong to at z = 0, allowing some insights into the assembly history of the cluster galaxy population and the origin of intracluster stars. 

Looking at some of the infalling galaxies, it can be eas- ily seen that already at z = 1 stars that later become part of the ICL are preferentially found in the outskirts of infalling galaxies, and are therefore comparatively weakly bound to them. Furthermore, the figure shows that only the most mas- sive infalling object (marked as A) contributes a significant number of stars to the BCG, as expected from our analy- sis in the previous section. Following the evolution of clus- ters in this way also nicely shows that galaxy mergers often create a loosely bound component of stars which is sub- sequently stripped when the merger remnant falls into the cluster. Unfortunately, it is a bit hard to illustrate this in a still image, but it confirms the finding of Murante et al. (2007) that mergers in the assembly history of the BCG and of other massive cluster galaxies are of critical importance for the formation of the ICL. 

We now consider the fate of some infalling galaxies in more detail. For this purpose we have selected two infalling objects marked as A and B in the upper right panel of Fig. 14 and followed them to redshift z = 0. The distribution of their stars at z = 0 is shown in the lower panels. The core of group-sized object A has basically merged with the BCG at this point. However, even after several passages of the cluster core one can still see significant tidal features both in the distribution of stars that at z = 0 are assigned to the BCG and the ICL. The infalling galaxy B, on the other hand, remains largely intact and becomes one of the cluster’s satellite galaxies at z = 0. Those stars that were stripped from it form a large tidal stream extending almost over the whole cluster. These two examples illustrate that the ICL really consists of many individual tidal streams and shell- like features. Only their superposition looks like a smooth distribution of intracluster stars. 

As discussed above, stars that later become part of the ICL are preferentially found in the outskirts of infalling galaxies (see also the upper right panel of Fig. 14). It also seems plausible that the most weakly bound stars are the ones most likely to be stripped from an infalling galaxy and to become intracluster stars. We have checked this explicitly by calculating the binding energy of stars in such infalling galaxies, and Fig. 15 illustrates the results of our analysis. We show the fraction of stars that at z = 0 reside in the cluster’s satellite galaxies, the BCG, and the ICL as a func- tion of their binding energy in objects A and B at z = 1. As expected, the fraction of stars that become part of the ICL strongly decreases with increasing binding energy. For object A, the most bound stars end up in the cluster’s cen- tral galaxy, while for object B, the most bound stars remain 

