A flat faint end of the Fornax cluster galaxy luminosity function

We analyse the photometric properties of the early-type Fornax cluster dwarf galaxy population (M_V>-17 mag), based on a wide field imaging study of the central cluster area in V and I band-passes with IMACS/Magellan at Las Campanas Observatory. We create a fiducial sample of ~100 Fornax cluster dwarf ellipticals (dEs) with -16.6<M_V<-8.8 mag in the following three steps: (1) To verify cluster membership, we measured I-band surface brightness fluctuations (SBF) distances to candidate dEs known from previous surveys; (2) We re-assessed morphological classifications for those candidate dEs that are too faint for SBF detection; and (3) We searched for new candidate dEs in the size-luminosity regime close to the resolution limit of previous surveys. The resulting fiducial dE sample follows a well-defined surface brightness - magnitude relation, showing that Fornax dEs are about 40% larger than Local Group dEs. The sample also defines a colour-magnitude relation similar to that of Local Group dEs. The early-type dwarf galaxy luminosity function in Fornax has a very flat faint end slope alpha = -1.1 +/- 0.1. We compare the number of dwarfs per unit mass with those in other environments and find that the Fornax cluster fits well into a general trend of a lack of high-mass dwarfs in more massive environments.