Is the Luminosity Distribution of Field Galaxies Really Flat?

Abstract
Recent observations of the galaxy population within rich clusters have found a characteristic luminosity distribution described by a flat (alpha = -1.0) Schechter function which exhibits an upturn at faint absolute magnitudes (B Mag = -18). Here we discuss whether such a form for the field luminosity distribution is ruled out by local and/or faint magnitude limited redshift surveys (MLRS). Our conclusions are that existing redshift surveys provide little constraints on the volume-density distribution of field galaxies faintwards of B Mag = -18. The local MLRS suffer from poor statistics over inhomogeneous volumes, while the faint MLRS are ambiguous because of the unknown nature of the ``faint blue excess'' and the ``normalization'' problem. Adopting a functional form similar to that seen in rich clusters we find that the maximum allowable faint end slope, based on the Mt Stromlo-APM redshift survey, is \alpha \approx -1.8 faintwards of B Mag = -18.0 (Ho = 50 km/s/Mpc^{3})
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