Spectroscopic Determination of the Faint End of the Luminosity Function in the Nearby Galaxy Clusters A2199 and Virgo

We report a new determination of the faint end of the galaxy luminosity function in the nearby clusters Virgo and Abell 2199 using data from SDSS and the Hectospec multifiber spectrograph on the MMT. The luminosity function of A2199 is consistent with a single Schechter function to M_r=-15.6 + 5 log h_70 with a faint-end slope of alpha=-1.13+/-0.07. The LF in Virgo extends to M_r=-13.5= M^*+8 and has a slope of alpha=-1.28+/-0.06. The red sequence of cluster members is prominent in both clusters, and almost no cluster galaxies are redder than this sequence. We show that selecting objects on the red sequence and blueward produces a steeply rising faint-end. A large fraction of photometric red-sequence galaxies lie behind the cluster. We compare our results to previous estimates and find poor agreement with estimates based on statistical background subtraction but good agreement with estimates based on photometric membership classifications (e.g., colors, morphology, surface brightness). We conclude that spectroscopic data are critical for estimating the faint end of the luminosity function in clusters. The faint-end slope we find is consistent with values found for field galaxies, weakening any argument for environmental evolution in the relative abundance of dwarf galaxies. However, dwarf galaxies in clusters are significantly redder than field galaxies of similar luminosity or mass, indicating that star formation processes in dwarfs do depend on environment.