Do Clusters Contain a Large Population of Dwarf Galaxies?

We analyze systematic effects in the determination of the galaxy luminosityfunction in clusters using a deep mock catalogue constructed from a numericalsimulation of a hierarchical universe. The results indicate a strong tendencyto derive a rising faint end ($\alpha \lsim -1.5$) in clusters selected in twodimensions, using a galaxy catalogue constructed with a universal flatluminosity function with $\alpha \simeq -1.0$. This is due to the projectioneffects inherent in catalogues of clusters constructed using 2 dimensionaldata. Many of the clusters found in 2d have no significant 3d counterparts, andmost suffer from massive background contamination that cannot be corrected forby subtracting random offset fields. The luminosity function of high surfacebrightness galaxies in the field and within small groups follows a Schechterfunction 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 clustersconstructed using Abell, EDCC and APM catalogues are systematically found tohave steeper luminosity functions with $\alpha = -1.4$ to -2.0. This may beattributed to projection effects rather than a dominant population of highsurface brightness dwarf galaxies ($M\gsim M^*+2$) in clusters. It should bestraighforward to confirm our results by measuring redshifts of these faintcluster galaxies.