RedMaPPer: Evolution and Mass Dependence of the Conditional Luminosity Functions of Red Galaxies in Galaxy Clusters

We characterize the luminosity distribution, halo-mass dependence, and redshift evolution of red galaxies in galaxy clusters using the SDSS Data Release 8 redMaPPer cluster sample. We propose a simple prescription for the relationship between the luminosity of both red central and red satellite galaxies and the mass of their host halos, and show that this model is well fit by the data. Using a larger galaxy cluster sample than previously employed in the literature, we find that the luminosities of red central galaxies scale as $\langle \mathrm{log}L\rangle \propto {A}_{L}\mathrm{log}({M}_{200b})$ , with A_L = 0.39 ± 0.04, and that the scatter of the red central galaxy luminosity at fixed M_200b ( ${\sigma }_{\mathrm{log}L| M}$ ) is ${0.23}_{-0.04}^{+0.05}$ dex, with the error bar including systematics due to mis-centering of the cluster finder, photometry, and photometric redshift estimation. Our data prefers a positive correlation between the luminosity of red central galaxies and the observed richness of clusters at a fixed halo mass, with an effective correlation coefficient ${d}_{\mathrm{eff}}={0.36}_{-0.16}^{+0.17}$ . The characteristic luminosity of red satellites becomes dimmer from z = 0.3 to z = 0.1 by ∼20% after accounting for passive evolution. We estimate the fraction of galaxy clusters where the brightest red galaxy is not the central to be P_BNC ∼ 20%. We discuss implications of these findings in the context of galaxy evolution and the galaxy-halo connection.