tokens: luminosity function for bright galaxies and numerous papers (e.g., Vogelsberger et al. 2014 ; Crain et al. 2015 ) detail their success. So, whether the CDM paradigm is right or wrong, the physical processes that they implement give them a luminosity function, above and below the L * break, that matches real data. We have looked at the publicly available output from these groups to see if their results do or do not match observations on statistical expectations with regard to the Tremaine Richstone ( 1977 ) t 1 statistics. We use r -band magnitudes throughout this study. 3.1. EAGLE Simulation The EAGLE simulation is a publicly available (McAlpine et al. 2016 ) suite of cosmological hydrodynamical simulations (Crain et al. 2015 ; Schaye et al. 2015 ). It assumes a standard Λ cold dark-matter cosmology from the Planck-1 (Planck Collaboration et al. 2014 ), Ω m = 1 − Ω Λ = 0.307, Ω b = 0.04825, h = 0.6777, σ 8 = 0.8288, and n S = 0.9611. The simulation suite is run with a modified version of the GADGET-3 N -body Tree-PM smoothed particle hydrodynamics (SPH) code (Springel 2005 ), and includes an updated formulation of SPH, new time stepping, and sub-grid physics (see Schaye et al. 2015 , for details). In this study, we use RefL0100, which has a cosmological volume of (100 comoving Mpc) 3 and a baryonic mass resolution of . We refer the readers to the introductory papers Crain et al. ( 2015 ) and Schaye et al. ( 2015 ) for complete descriptions of the sub-grid physics models. We bin EAGLE simulation results into different size galaxy groups from smallest (12–24 objects), with stellar mass greater than , to more massive systems, with 75–150 galaxies (see Table 1 ). The red lines in Figures 1 and 2 show the average magnitude gap between first-brightest and second-brightest galaxies, , in each group and the brightness of the first-brightest galaxy . Overall, simulated galaxies in EAGLE show a ∼1.7 mag gap between first-brightest and second-brightest galaxies, which is similar to the gap reported by van den Bosch et al. ( 2007 ) with 2° Field Galaxy Redshift Survey data. Figure 1. M 12 presented in the EAGLE simulation (red) and in the “randomized” data (blue). Figure 2. Average first-ranked r magnitude as a function of number of galaxy members in the EAGLE simulation. Table 1 EAGLE Simulation Note. a Average halo mass of the first-brightest galaxies in solar mass. Next, we put all the groups in one bin and randomly repopulate each group from the collective bin, keeping the same number of galaxies in each galaxy group or cluster (See Table 2 ). By construction, this keeps the overall luminosity function invariant. Then, we recompute , and σ ( M 1 ) for each of Figures 1 and 2 . Table 2 EAGLE “Randomized” Simulation Note how the gap is systematically larger in the original () than in the randomized groups (), and the first-brightest galaxy is brighter by over a magnitudes in each original set of galaxy groups than in the randomized versions of
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