The Luminosity Distribution of Local Group Galaxies

From a rediscussion of Local Group membership, and of distances to individualgalaxies, we obtain $M_V$ values for 35 probable and possible Local Groupmembers. The luminosity function of these objects is well fitted by a Schechterfunction with faint end slope $\alpha = -1.1 \pm 0.1$. The probability that theluminosity distribution of the Local Group is a single Schechter function with$\alpha$ steeper than -1.3 is less than 1 per cent. However, more complicatedluminosity functions, such as multi-component Schechter functions with steepfaint-end slopes, cannot be ruled out. There is some evidence that theluminosity distribution of dwarf spheroidal galaxies in the Local Group issteeper than that of dwarf irregular galaxies.Comment: 13 pages, 2 figures, accepted for publication in The Astronomical Journal. Figure 2 replaced, conclusion based on this figure change