a distinction between the BCG and the ICL in simulated clusters. These are: zoom softening particle mass [ h − 1 M$_{⊙}$ ] factor [ h − $^{1}$kpc] DM gas stars 1 7.5 8 . 3 × 10 8 1 . 8 × 10 8 8 . 9 × 10 7 2 3.75 1 . 1 × 10 8 2 . 1 × 10 7 1 . 0 × 10 7 3 2.5 3 . 1 × 10 7 6 . 2 × 10 6 3 . 1 × 10 6 4 1.875 1 . 3 × 10 7 2 . 8 × 10 6 1 . 4 × 10 6 2.2 Identifying intracluster stars and cluster galaxies c ○ 0000 RAS, MNRAS 000 , 000–000 • Method 3: Analysis of the stellar velocity distribution. In relaxed simulated clusters, the distribution of the ve- locities v of the main halo stars can be well fit by a sum of two Maxwell-Boltzmann distributions (see Dolag et al. 2009). Here v is given by v = | $^{v}$star − v $_{clus}$| , where $^{v}$star is the velocity of the star particle and $^{v}$clus is the veloc- ity of the centre of mass of the cluster’s main halo. In this method, we perform such a fit for each cluster and define the BCG mass as the mass of the stars in the Maxwell- Boltzmann component with the lower velocity dispersion, while we associate the higher dispersion component with the ICL. This is illustrated in Fig. 2 for a cluster with mass M crit 200 = 2 . 2 × 10 $^{14}$h − $^{1}$M ⊙ . • Method 4: Analysis of the stellar velocity distribution and binding energies. While Method 3 allows an estimate of the total stellar BCG mass, it does not assign individual star particles to either the BCG or ICL component, as it yields, for each velocity bin, only the fraction of stars in each com- Starting from the particle distribution in the simulated clus- ters, we aim to identify the cluster’s central galaxy, all satel- lite member galaxies and the ICL component. As a first step, we run a friends-of-friends (FoF) group finder with a linking length of 0.2 in units of the mean interparti- cle distance, as well as the SUBFIND substructure finder (Springel et al. 2001). The FoF algorithm is applied only to the high-resolution dark matter particles, with the gas and stars linked to their nearest dark matter particle. This avoids biases in the group catalogue due to the very differ- ent spatial distribution of dark matter and baryonic parti- cles. We then use a version of SUBFIND that was specifically adapted to work robustly with hydrodynamical simulations (Dolag et al. 2008) for decomposing each FoF-group into a main halo and self-bound substructures. We consider the stellar content of each self-bound substructure of the cluster to be a satellite galaxy. All star particles that are part of the main halo are assumed to belong either to the BCG or to the ICL component. It is, however, not straightforward to unambiguously decide to which of these two components such a star particle should be assigned. In the following, we therefore employ several independent methods for making The complete surface brightness profile of BCG and ICL can typically be well fit by the sum of two de Vaucouleurs profiles (see e.g. Gonzalez et al. 2005). We perform such a two-component fit to the surface brightness profile of all stars residing in a simulated cluster’s main halo, as found by SUBFIND , and consider the component with the smaller effective radius as the BCG and the component with the larger effective radius as the ICL. This procedure is illus- trated for a cluster with M crit 200 = 2 . 2 × 10 $^{14}$h − $^{1}$M ⊙ in Fig. 1. We note that we obtain projected mass profiles for the BCG and the intracluster stars by assuming that in each radial bin both components have the same mass-to-light ra- tio. In order to compute surface brightness profiles we use the stellar population synthesis model library GALAXEV (Bruzual and Charlot 2003) to assign a r-band luminosity to each star particle according to its mass, age and metal- licity. Table 1 summarizes the different mass and force res- olutions that were used in our resimulations. For all halos with M crit 200 ⩽ 1 . 5 × 10 $^{14}$h − $^{1}$M ⊙ simulations with a zoom fac- tor of 3 (see Table 1) have been performed, while all more massive cluster were resimulated only with a zoom factor of 2. For some objects several resimulations have been per- formed, covering a wide range in mass and force resolution. This allows us to assess the convergence of the simulations. (based on Springel 2005), which employs an entropy- conserving formulation of smoothed particle hydrodynam- ics (SPH). Radiative cooling and heating was calculated for an optically thin plasma of hydrogen and helium, and for a time-varying but spatially uniform UV background. Star formation and supernovae feedback were modelled with a subresolution multi-phase model for the interstellar medium as in Springel and Hernquist (2003a). Black hole growth and associated feedback processes were followed as in Springel et al. (2005a) and Sijacki et al. (2007). • Method 2: Analysis of the surface brightness profiles. A de Vaucouleurs profile (de Vaucouleurs 1948) is usually a good fit to the surface brightness profile of an elliptical galaxy. For cD galaxies, however, one often finds a light ex- cess at large radii with respect to such a fit to the inner re- gion (Schombert 1986). This light excess can be attributed to intracluster stars. When using this method, all star particles of the main halo that are within the cut-off radius are considered to be part of the BCG, while all main halo star particles outside this radius are considered to be intracluster stars. • Method 1: A cut-off radius around the central galaxy. The simplest possible approach is to just cut off the BCG at a specific radius r cut . However, the size of BCGs corre- lates with cluster mass. We therefore choose to scale r cut with cluster mass. We obtain an appropriate scaling re- lation by combining an empirical relation between clus- ter mass and BCG luminosity (Popesso et al. 2007) with a relation between BCG luminosity and half-light radius r e (Bernardi et al. 2007). We decide to cut at r cut = 3 × r e , yielding r cut = 27 . 3 h − $^{1}$kpc × ( M crit 200 10 $^{15}$h − $^{1}$M ⊙ ) 0 . 29 . (1) Table 1. Force and mass resolutions used in the cluster and group simulations. The physical (Plummer-equivalent) softening lengths that were used for redshifts z < 5 are listed in Column 2. For z > 5, comoving softenings of 45 h − $^{1}$kpc, 22 . 5 h − $^{1}$kpc, 15 h − $^{1}$kpc, and 11 . 25 h − $^{1}$kpc were used for zoom factors 1, 2, 3, and 4, respectively. The masses of the dark matter (DM), gas and star particles in the simulations are tabulated in Columns 3-5. Intracluster stars in simulations with AGN feedback 3