The Luminosity Function of Nearby Galaxy Clusters II: Redshifts and   Luminosity Function for Galaxies in the Region of the Centaurus Cluster
  We acquired spectra for a random sample of galaxies within a 0.83 square degree region centered on the core of the Centaurus cluster. Radial velocities were obtained for 225 galaxies to limiting magnitudes of V < 19.5. Of the galaxies for which velocities were obtained, we find 35% to be member galaxies. Of the 78 member galaxies, magnitudes range from 11.8 < V < 18.5 (-21.6 < M_{V} < -14.9 for H_o = 70 km s^-1 Mpc^-1) with a limiting central surface brightness of \mu_o < 22.5 mag arcsec^-2. We constructed the cluster galaxy luminosity function by using these spectroscopic results to calculate the expected fraction of cluster members in each magnitude bin. The faint-end slope of the luminosity function using this method is shallower than the one obtained using a statistical method to correct for background galaxy contamination. We also use the spectroscopy results to define surface brightness criteria to establish membership for the full sample. Using these criteria, we find a luminosity function very similar to the one constructed with the statistical background correction. For both, we find a faint-end slope alpha ~ -1.4. Adjusting the surface brightness membership criteria we find that the data are consistent with a faint-end slope as shallow as -1.22 or as steep as -1.50. We describe in this paper some of the limitations of using these methods for constructing the galaxy luminosity function. 
K. Chiboucas and M. Mateo