Do clusters contain a large population of dwarf galaxies?

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 (alpha less than or similar to -1.5) in clusters selected in two dimensions, using a galaxy catalog constructed with a universal flat luminosity function with alpha similar or equal to 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) proportional to L-alpha, with alpha = -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 alpha = -1.4 to -2.0. This may be attributed to projection effects rather than a dominant population of high surface brightness dwarf galaxies (M greater than or similar to M* + 2) in clusters. It should be straightforward to confirm our results by measuring redshifts of these faint cluster galaxies.