The Ursa Major cluster of galaxies - III. Optical observations of dwarf galaxies and the luminosity function down to MR=-11

Results are presented of a deep optical survey of the Ursa Major cluster, a spiral-rich cluster of galaxies at a distance of 18.6Mpc which contains about 30 per cent of the light but only 5 per cent of the mass of the nearby Virgo cluster. Fields around known cluster members and a pattern of blind fields along the major and minor axes of the cluster were studied with mosaic CCD cameras on the Canada-France-Hawaii Telescope. The dynamical crossing time for the Ursa Major cluster is only slightly less than a Hubble time. Most galaxies in the local Universe exist in similar moderate-density environments. The Ursa Major cluster is therefore a good place to study the statistical properties of dwarf galaxies, since this structure is at an evolutionary stage representative of typical environments, yet has enough galaxies that reasonable counting statistics can be accumulated. The main observational results of our survey are as follows. (i) The galaxy luminosity function is flat, with a logarithmic slope α=-1.1 for -17<M_R<-11 from a power-law fit. The error in α is likely to be less than 0.2 and is dominated by systematic errors, primarily associated with uncertainties in assigning membership to specific galaxies. This faint-end slope is quite different from what was seen in the Virgo cluster, where α=-2.26+/-0.14. (ii) Dwarf galaxies are as frequently found to be blue dwarf irregulars as red dwarf spheroidals in the blind cluster fields. The density of red dwarfs is significantly higher in the fields around luminous members than in the blind fields. The most important result is the failure to detect many dwarfs. If the steep luminosity function claimed for the Virgo cluster were valid for Ursa Major, then in our blind fields we should have found ~10³ galaxies with -17<M_R<-11 whereas we have found two dozen. There is a clear deficiency of dwarfs compared with the expectations of hierarchical clustering theory. It is speculated that the critical difference between the Virgo and Ursa Major clusters is the very different dynamical collapse times, which probably straddle the time-scale for reionization of the Universe. Dwarf galaxies in the proto-Virgo environment probably formed before the epoch of reionization. The equivalent dwarf haloes in the proto-Ursa Major environment probably formed only after the epoch of reionization, when the conditions for star formation were inhospitable.