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 central and 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 central galaxies scale as $\langle \log L \rangle \propto A_L \log (M_{200b})$, with $A_L=0.39\pm0.04$, and that the scatter of the central--galaxy luminosity at fixed $M_{200b}$ ( $\sigma_{\log L|M}$) is $0.23 ^{+0.05}_{-0.04}$ dex, with the error bar including systematics due to miscentering of the cluster finder, photometry, and photometric redshift estimation. Our data prefers a positive correlation between the luminosity of central galaxies and the observed richness of clusters at a fixed halo mass, with an effective correlation coefficient $d_{\rm{eff}}=0.36^{+0.17}_{-0.16}$. The characteristic luminosity of satellites becomes dimmer from $z=0.3$ to $z=0.1$ by $\sim 20\%$ after accounting for passive evolution. We estimate the fraction of galaxy clusters where the brightest galaxy is not the central to be $P_{\rm{BNC}} \sim 20\%$. We discuss implications of these findings in the context of galaxy evolution and the galaxy--halo connection.