Intracluster stars in simulations with AGN feedback 9 within 200 kpc. However, in this case the simulated profile would then start to significantly underpredict the surface brightness at even larger radii. One should keep in mind though that for large radii this comparison may be quite sensitive to the accuracy of the correction for incomplete masking of satellite galaxies in Zibetti et al. (2005). Without a strong feedback mechanism, hydrodynamical sim- ulations of galaxy clusters suffer from excessive overcooling in cluster cores. Typically, the central galaxy is fed by a strong cooling flow and becomes too massive, too luminous and too blue compared to observations. One of the main aims of including AGN heating in cluster simulations was to offset cooling in cluster cores and produce more realis- tic central galaxies. Comparing the BCGs in runs with and without AGN feedback to observations should thus allow us to assess whether the employed AGN feedback model suc- cessfully regulates the central cooling flow. Fig. 8 shows the r-band luminosities of the BCGs in our simulations as a function of cluster mass. Results are shown for runs with and without AGN feedback and are compared to observational constraints from Popesso et al. (2007). Here Method 1 was used for finding the BCGs. The AGN heating successfully reduces the BCG luminosities for all halo masses and strongly improves the agreement with observations. For massive clusters the BCG luminosities ob- tained with AGN are still somewhat larger than observed. However, one should note that this depends somewhat on the details of the method used for making a distinction be- tween the BCG and ICL components in the simulations. When Method 3 or 4 is used, the resulting relation has much more scatter and the agreement with observations in runs with AGN is not as good as with Method 1 or 2 . Note that the reduced BCG mass in our runs with AGN also reduces the gravitational lensing efficiency of our galaxy clusters (see Mead et al. 2010). We now explore in what objects the stars have formed that are part of satellite galaxies, the BCG, and the ICL at red- shift z = 0. Using the IDs of the simulation particles, we can easily trace back every star particle in the simulation to the first snapshot after its formation. We then consider the SUBFIND (sub-)halo that the star particle is part of in this snapshot as its formation halo. Because we have saved sim- ulation snapshots very frequently, there is only a negligibly small number of particles that are not bound to any halo in the first snapshot after their creation. We can thus, in this way, assign formation halos to almost all star particles in the simulation. Fig. 9 shows the formation time of the star particles that are found in the BCG, the ICL, and the satellite mem- ber galaxies of a 10 $^{14}$h − $^{1}$M ⊙ cluster at z = 0. Results are shown for simulations of this cluster with and without AGN feedback. Comparing the two runs clearly shows that AGN efficiently suppress star formation at low redshift. The ef- fect is particularly strong for the BCG where star formation At radii larger than about 30 kpc, the surface brightness of the two more massive simulated groups exceeds the ob- served profile by roughly ∼ 1 mag / arcsec 2 or somewhat less when AGN are included. This is consistent with our previ- ous findings that we have a very significant ICL component in our simulated halos, which as this comparison confirms appears to exceed the observed amount of ICL. As illus- trated further in the figure, we would need to compare to a simulated group of significantly lower mass to get a sur- face brightness profile that is close to the mean observed one Without AGN, the surface brightness is typically too high in the central regions. In other words, the BCGs are overluminous in such simulations. When AGN are included, the central profile of one of the two groups, whose mass is close to the mean mass of the stacked clusters and groups, agrees very well with the observed central profile, indicating that a realistic BCG is formed in this simulation. The other massive group shown in the plot has a somewhat flatter central profile. However, given that there is object-to-object scatter, no perfect agreement for all halos close to the mean mass is expected. to the mean mass of the observational sample. The mass of each simulated group is indicated in the figure’s legend. Due to the removal of gas by AGN heating, the mass in the runs with AGN is typically slightly lower. In addition, we include results for a further, lower mass group. Figure 7. BCG+ICL surface brightness profiles of three groups simulated with and without AGN feedback are shown in the upper panel . For comparison observational constraints from Zibetti et al. (2005) obtained by stacking SDSS clusters and groups are shown. Also shown is the mean surface brightness profile they find without correcting for incomplete masking of satellite galaxies (assuming a constant fraction of ∼ 15% of un- masked galaxy light). For each simulated halo, the mass M mean 200 is given in the figure’s legend. The two groups shown in red and blue have masses very similar to the mean halo mass in Zibetti et al. (2005). The lower panel shows the difference to the profile ob- tained in Zibetti et al. (2005). The vertical dotted line indicates the gravitational softening. 3.2 When and where do the stellar populations of satellite galaxies, BCGs, and the ICL form? 3.1.4 How do AGN affect the central cluster galaxies? 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