Luminous Red Galaxies in Clusters: Central Occupation, Spatial Distributions, and Mis-centering

Luminous red galaxies (LRG) from the Sloan Digital Sky Survey are among the best understood samples of galaxies and are employed in a broad range of cosmological studies. In this paper, we study how LRGs occupy massive haloes via counts in clusters and reveal several unexpected trends. Using the red-sequence Matched-filter Probabilistic Percolation (redMaPPer) cluster catalogue, we derive the central occupation of LRGs as a function richness. We show that clusters contain a significantly lower fraction of central LRGs than predicted from the two-point correlation function. At halo masses of 10^14.5 M_⊙, we find N_cen = 0.73 compared toN_cen = 0.89 from correlation studies. Our central occupation function for LRGs converges to 0.95 at large halo masses. A strong anticorrelation between central luminosity and cluster mass at fixed richness is required to reconcile our results with those based on clustering studies. We derive the probability that the brightest cluster member is not the central galaxy. We find P_BNC ≈ 20–30 per cent which is a factor of ∼2 lower than the value found by Skibba et al. Finally, we study the radial offsets of bright non-central LRGs from cluster centres and show that bright non-central LRGs follow a different radial distribution compared to red cluster members. This work demonstrates that even the most massive clusters do not always have an LRG at the centre, and that the brightest galaxy in a cluster is not always the central galaxy.