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 field to field variations, 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 steeper faint-end LF (- 2.1 <= alpha <= - 1.6) in the dwarf galaxy region. The observed upturn of the faint galaxies has a location ranging from - 16 + 5 log( h) in the g band to - 18.5 + 5 log( h) in the z band. To study the universality of the cluster LF we compare the individual cluster LFs with the composite luminosity function. 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 cluster LFs in the magnitude region brighter than the observed upturn of the dwarf galaxies. The bright-end of the galaxy clusters shows the same shape in all the systems. To study the behavior of the individual faint-end LF we define the Dwarf to Giant galaxy Ratio (DGR) of the single clusters. The distribution of DGR has a spread much larger than the statistical errors. The DGR clearly anti-correlates with both X-ray and optical cluster luminosities. This anti-correlation is most likely due to the choice of a fixed metric aperture for all the clusters. Therefore, because of this effect, the different cluster physical sizes must be taken into account before comparing the LF of different clusters.