Composite Luminosity Functions Based on the Sloan Digital Sky Survey “Cut and Enhance” Galaxy Cluster Catalog

We present here results on the composite luminosity functions (LF) of galaxies in the clusters of galaxies selected from the Cut and Enhance cluster catalog (CE) of the Sloan Digital Sky Survey. We constructed composite LFs in the five SDSS bands, $u, g, r, i$ , and $z$ , using 204 CE clusters ranging from $z = 0.02$ to $z = 0.25$ . Background and foreground galaxies were subtracted from the LF using an annular region around clusters to take large-scale, galaxy-number-count variances into consideration. A LF of each cluster was weighted according to the richness and number of contributing galaxies to construct the composite LF. Taking advantage of accurate photometry of SDSS, we used photometric redshifts to construct composite luminosity functions and thus study a large number of clusters. The robustness of the weighting scheme was tested using a Monte-Carlo simulation. The best-fit Schechter parameters are $(M^*, \alpha) = (-21.61 \pm 0.26,-1.40 \pm0.11), (-22.01 \pm 0.11,-1.00 \pm 0.06), (-22.21 \pm 0.05,-0.85 \pm 0.03), (-22.31 \pm 0.08,-0.70 \pm 0.05)$ , and $(-21.36 \pm 0.06,-0.58 \pm 0.04)$ in $u, g, r, i$ , and $z$ , respectively. We find that the slope of composite LFs becomes flatter toward a redder color band. Compared with the field LFs of the SDSS, the cluster LFs have brighter characteristic magnitude and flatter slopes in the $g, r, i$ , and $z$ bands. These results are consistent with the hypothesis that the cluster LF has two distinct underlying populations; i.e. the bright end of the LF is dominated by bright early types that follow a Gaussian-like luminosity distribution, while the faint-end of the cluster LF is a steep power-law like function dominated by star-forming (bluer) galaxies. We also studied the composite LFs for early-type and late-type galaxies using profile fits, a concentration parameter and $u-r$ color to classify galaxy morphology. A strong dependence of LF on galaxy morphology was found. The faint end slope of the LF is always flatter for early-type galaxies than late-type, regardless of the passband and methodology. These results are consistent with the hypothesis that the cluster regions are dominated by bright elliptical galaxies. This work also provides a good low-redshift benchmark for on-going multi-color photometric studies of high redshift clusters of galaxies using 4–8m class telescopes.