Population studies in groups and clusters of galaxies. I - The luminosity function of galaxies in the Fornax Cluster

We compare the luminosity functions of galaxies of various Hubble types in the central 2.4^deg^ radius core of the Fornax Cluster and the 6^deg^ radius core of the Virgo Cluster. The galaxy classifications for the two clusters are based on identical plate material, and are hence directly comparable. The properties (galaxy density, velocity dispersion, x-ray luminosity) of the two clusters are quite different, yet we find few significant differences in the luminosity functions, or in the morphological mix of galaxies between the two clusters. In particular, while there is some indication that the ratios of giants to dwarfs and early- to late-type galaxies in the two clusters differ, we cannot exclude the possibility that they are identical. We discuss the selection limits of our survey and the completeness corrections that must be applied to the faint end of the luminosity function. The effective surface brightness of early-type galaxies in our sample decreases with decreasing luminosity. We show that this correlation is not an artifact of our selection criteria for dwarf spheroidal galaxies and use it to determine the ratio of the distances to the Fornax and Virgo clusters. We also present evidence for a radial variation in the luminosity function of dwarf ellipticals within the two clusters in the sense that the faint end of the luminosity distribution is enhanced at the center of each cluster.