The faint end of the galaxy luminosity function

We present and discuss optical measurements of the faint end of the galaxy luminosity function down to M-R = 10 in five different local environments of varying galaxy density and morphological content. The environments we studied, in order of decreasing galaxy density, are the Virgo Cluster, the NGC 1407 Group, the Coma I Group, the Leo Group and the NGC 1023 Group. Our results come from a deep wide-angle survey with the National Astronomical Observatories of Japan Subaru 8-m Telescope on Mauna Kea and are sensitive down to very faint surface-brightness levels. Galaxies were identified as group or cluster members on the basis of their surface brightness and morphology. The faintest galaxies in our sample have R similar to 22.5. There were thousands of fainter galaxies but we cannot distinguish cluster members from background galaxies at these faint limits so do not attempt to determine a luminosity function fainter than M-R = -10. In all cases, there are far fewer dwarfs than the numbers of low-mass haloes anticipated by cold dark matter theory. The mean logarithmic slope of the luminosity function between M-R = 18 and M-R = 10 is alpha similar or equal to -1.2, far shallower than the cold dark matter mass function slope of alpha similar or equal to -1.8. We would therefore need to be missing about 90 per cent of the dwarfs at the faint end of our sample in all the environments we study to achieve consistency with CDM theory. It is unlikely that such large numbers of dwarfs are missed because (i) the data are deep enough that we are sensitive to very low surface brightness galaxies, and (ii) the seeing is good enough that we can have some confidence in our ability to distinguish high surface brightness dwarfs from background galaxies brighter than R = 22.5. One caveat is that we miss compact members taken to be background galaxies, but such objects (like M32) are thought to be rare.