RASS-SDSS galaxy cluster survey. II. A unified picture of the Cluster   Luminosity Function
  We constructed the composite luminosity function (LF) of clusters of galaxies in the five SDSS photometric bands u,g,r,i and z from the RASS-SDSS galaxy cluster catalog. Background and foreground galaxies are subtracted using both a local and a global background correction to take in account the presence of large scale structures and variations from field to field, respectively. The composite LF clearly shows two components: a bright-end LF with a classical slope of -1.25 in each photometric band, and a faint-end LF much steeper (-2.1 <= \alpha <= -1.6) in the dwarf galaxy region. The observed upturn of the faint galaxies has a location ranging from -16 +5log(h) in the g band to -18.5 +5log(h) in the z band. To study the universality of the cluster LF we compare the individual cluster LFs with the composite luminosity function. We notice that, in agreement with the composite LF, a single Schechter component is not a good fit for the majority of the clusters. We fit a Schechter function to the bright-end of the individual clusters LFs in the magnitude region brighter than the observed upturn of the dwarf galaxies. We observe that the distributions of the derived parameters is close to a Gaussian around the value of the composite bright-end LF parameters with a dispersion compatible with the statistical errors. We conclude that the bright-end of the galaxy clusters is universal. To study the behavior of the individual faint-end LF we define the Dwarf to Giant galaxy Ratio (DGR) of the single clusters. We notice that the distribution of DGR has a spread much larger than the statistical errors. Our conclusion is that the cluster luminosity function is not universal since the cluster faint-end, differently from the bright-end, varies from cluster to cluster. 
Paola Popesso, Hans Boehringer, Martino Romaniello, Wolfgang Voges