The bright end of the luminosity function of red sequence galaxies

We study the bright end of the luminosity distribution of galaxies in fields with luminous red galaxies (LRG) from the Sloan Digital Sky Survey ( SDSS). Using 2099 deg(2) of SDSS imaging data, we search for luminous ( greater than or similar to L*) early-type galaxies within 1.0 h(-1) Mpc of a volume-limited sample of 12 608 spectroscopic LRG in the redshift range 0.12 < z < 0.38. Most of these objects lie in rich environments, with the LRG being the brightest object within 1.0 h(-1) Mpc. The luminosity gap, M-12, between the first- and second-ranked galaxies within 1.0 h(-1) Mpc is large (similar to 0.8 mag), substantially larger than can be explained with an exponentially decaying luminosity function of galaxies. The brightest member is less luminous ( by 0.1-0.2 mag) and shows a larger gap in LRG selected groups than in cluster-like environments. The large luminosity gap shows little evolution with redshift to z = 0.4, ruling out the scenario that these LRG selected brightest cluster or group galaxies grow by recent cannibalism of cluster members.