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 \leq \alpha \leq - 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 .