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 analyse the luminosities of isolated galaxies. Results. We find a strong environmental dependency by the 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 approximated by a double-power law. The widely used Schechter function does not describe the bright end and the bend of the LFs well. Properties of the LFs reflect differences in the evolution of galaxies and their groups in different environments.