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We present a statistical study of the luminosity functions of galaxiessurrounding luminous red galaxies (LRGs) at average redshifts <z>=0.34 and<z>=0.65. The luminosity functions are derived by extracting source photometryaround more than 40,000 LRGs and subtracting foreground and backgroundcontamination using randomly selected control fields. We show that at bothstudied redshifts the average luminosity functions of the LRGs and theirsatellite galaxies are poorly fitted by a Schechter function due to aluminosity gap between the centrals and their most luminous satellites. Weutilize a two-component fit of a Schechter function plus a log-normaldistribution to demonstrate that LRGs are typically brighter than their mostluminous satellite by roughly 1.3 magnitudes. This luminosity gap implies thatinteractions within LRG environments are typically restricted to minor mergerswith mass ratios of 1:4 or lower. The luminosity functions further imply thatroughly 35% of the mass in the environment is locked in the LRG itself,supporting the idea that mass growth through major mergers within theenvironment is unlikely. Lastly, we show that the luminosity gap may be atleast partially explained by the selection of LRGs as the gap can be reproducedby sparsely sampling a Schechter function. In that case LRGs may represent onlya small fraction of central galaxies in similar mass halos.

Mass growth and mergers: direct observations of the luminosity function of LRG satellite galaxies out to z=0.7 from SDSS and BOSS images