We analyze systematic effects in the determination of the galaxy luminosity function in clusters using a deep mock catalogue constructed from a numerical simulation of a hierarchical universe .
The results indicate a strong tendency to derive a rising faint end ( \alpha \lower 3.225 pt \hbox { $ \sim$ } \hbox to 0.0 pt { \raise 1.161 pt \hbox { $ < $ } } -1.5 ) in clusters selected in two dimensions , using a galaxy catalogue constructed with a universal flat luminosity function with \alpha \simeq - 1.0 .
This is due to the projection effects inherent in catalogues of clusters constructed using 2 dimensional data .
Many of the clusters found in 2d have no significant 3d counterparts , and most suffer from massive background contamination that can not 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 ) \propto L ^ { \alpha } with \alpha = -0.9 to -1.2 .
On the contrary , observational studies of clusters constructed using Abell , EDCC and APM catalogues 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 \lower 3.225 pt \hbox { $ \sim$ } \hbox to 0.0 pt { \raise 1.161 pt \hbox { $ > $ } } M ^ { * } +2 ) in clusters .
It should be straighforward to confirm our results by measuring redshifts of these faint cluster galaxies .