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

Results are presented of a deep optical survey of the Ursa Major cluster, a spiral-rich cluster of galaxies at a distance of 18.6 Mpc which contains a bout 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 mosa ic CCD cameras on the Canada-France-Hawaii Telescope. The dynamical crossin g 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 envi ronments. The Ursa Major cluster is therefore a good place to study the sta tistical properties of dwarf galaxies, since this structure is at an evolut ionary stage representative of typical environments, yet has enough galaxie s that reasonable counting statistics can be accumulated. The main observat ional results of our survey are as follows. (i) The galaxy luminosity function is flat, with a logarithmic slope alpha = - 1.1 for - 17 < M-R < - 11 from a power-law fit. The error in alpha is l ikely 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 cl uster, where alpha = -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 dwarf s 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 stee p luminosity function claimed for the Virgo cluster were valid for Ursa Maj or, then in our blind fields we should have found similar to 10(3) galaxies with - 17 < M-R < -11 whereas we have found two dozen. There is a clear de ficiency of dwarfs compared with the expectations of hierarchical clusterin g theory. It is speculated that the critical difference between the Virgo a nd Ursa Major clusters is the very different dynamical collapse times, whic h 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 environm ent probably formed only after the epoch of reionization, when the conditio ns for star formation were inhospitable.