2001ApJ...546..157V

We analyze systematic effects in the determination of the galaxy luminosity function in clusters using a deep mock catalog constructed from a numerical simulation of a hierarchical universe. The results indicate a strong tendency to derive a rising faint end (α≲-1.5) in clusters selected in two dimensions, using a galaxy catalog constructed with a universal flat luminosity function with α≃-1.0. This is a result of the projection effects inherent in catalogs of clusters constructed using two-dimensional data. Many of the clusters found in two dimensions have no significant three-dimensional counterparts, and most suffer from massive background contamination that cannot be corrected for by subtracting random offset fields. The luminosity function of high surface brightness galaxies in the field and within small groups follows a Schechter function with a fairly flat faint-end slope, n(L)∝L^α, with α=-0.9 to -1.2. On the contrary, observational studies of clusters constructed using Abell, EDCC, and APM catalogs are systematically found to have steeper luminosity functions with α=-1.4 to -2.0. This may be attributed to projection effects rather than a dominant population of high surface brightness dwarf galaxies (M≳M^*+2) in clusters. It should be straightforward to confirm our results by measuring redshifts of these faint cluster galaxies.