Anatomy of luminosity functions: the 2dFGRS example
  Aims. We use the 2dF Galaxy Redshift Survey to derive the luminosity function (LF) of the first-ranked (brightest) group/cluster galaxies, the LF of second-ranked, satellite and isolated galaxies, and the LF of groups of galaxies.   Methods. We investigate the LFs of different samples in various environments: in voids, filaments, superclusters and supercluster cores. We compare the derived LFs with the Schechter and double-power-law analytical expressions. We also analyze the luminosities of isolated galaxies.   Results. We find strong environmental dependency of luminosity functions of all populations. The luminosities of first-ranked galaxies have a lower limit, depending on the global environment (higher in supercluster cores, and absent in voids). The LF of second-ranked galaxies in high-density regions is similar to the LF of first-ranked galaxies in a lower-density environment. The brightest isolated galaxies can be identified with first-ranked galaxies at distances where the remaining galaxies lie outside the observational window used in the survey.   Conclusions. The galaxy and cluster LFs can be well approximated by a double-power-law; the widely used Schechter function does not describe well the bright end and the bend of the LFs. Properties of the LFs reflect differences in the evolution of galaxies and their groups in different environments. 
Elmo Tempel, Jaan Einasto, Maret Einasto, Enn Saar and Erik Tago