K-band Properties of Galaxy Clusters and Groups: Luminosity Function,   Radial Distribution and Halo Occupation Number
  We explore the near-infrared (NIR) $K$-band properties of galaxies within 93 galaxy clusters and groups using data from the 2MASS. We use X-ray properties of these clusters to pinpoint cluster centers and estimate cluster masses. By stacking all these systems, we study the shape of the cluster luminosity function and the galaxy distribution within the clusters. We find that the galaxy profile is well described by the NFW profile with a concentration parameter c~3, with no evidence for cluster mass dependence of the concentration. Using this sample, whose masses span the range from $3\times10^{13}M_\odot$ to $2\times10^{15}M_\odot$, we confirm the existence of a tight correlation between total galaxy NIR luminosity and cluster binding mass, which indicates that NIR light can serve as a cluster mass indicator.   From the observed galaxy profile, together with cluster mass profile measurements from the literature, we find that the \mlr is a weakly decreasing function of cluster radius, and that it increases with cluster mass. We also derive the mean number of galaxies within halos of a given mass. We find that the mean number scales as $N\propto M^{0.84\pm0.04}$ for galaxies brighter than $M_K=-21$, indicating high mass clusters have fewer galaxies per unit mass than low mass clusters. Using published observations at high redshift, we show that higher redshift clusters have higher mean occupation number than nearby systems of the same mass. By comparing the luminosity function & radial distribution of galaxies in low mass and high mass clusters, we show that there is a marked decrease in the number density of galaxies fainter than $M_*$ as one moves to higher mass clusters; in addition, extremely luminous galaxies are more probable in high mass clusters. 
Yen-Ting Lin (1), Joseph J. Mohr (1) and S. Adam Stanford (2,3) ((1)   Illinois (2) LLNL (3) UC Davis)