A complete redshift sample of galaxies
The role of complete redshift samples is discussed with particular attention focused on the need for new deeper and better controlled surveys for statistical clustering and dynamical studies. The compilation of one such catalogue, along with simulated samples, is described, this 'AARS' survey consisting of 322 accurate galaxy velocities and magnitudes in five small, well separated fields. An estimate of the galaxy luminosity function is made, with and without assuming spatial homogeneity, and fitted with a standard parameterised form the characteristic luminosity of which is found to be some 0.5 magnitudes brighter than from most previous samples. Evidence that the sample may be fairly representative comes from the number magnitude and redshift counts that are compared with models which assume spatial homogeneity. Plots of the galaxy distributions, though, vividly demonstrate the clustering of galaxies at small scales. The AARS and other surveys are used to estimate redshift two and three point galaxy correlation functions. The two point function is generally consistent with homogeneity at scales beyond 10 MPC although there is some evidence for anti-clustering. At smaller scales the projected form agrees well in shape and amplitude with the -0.8 powerlaw found from projected catalogues with a 'break' in the powerlaw also occurring at a similar scale. The unsmoothed spatial function, however, exhibits a strong rise above the usual powerlaw behaviour at scales smaller than the break. The two point function is also used to estimate the relative peculiar velocity dispersion between close galaxy pairs. The dispersion of ~ 200 km/sec, roughly independent of separation, is found to be considerably smaller than most previous estimates, however a reanalysis of these samples suggest the data may, in fact, be compatible. This dispersion along with the spatial correlation functions provides a 'Cosmic Virial Estimate' of the cosmic Density Parameter of 0.1 < Ω < 0.2, the universe only being closed if most of the matter is considerably less clustered than galaxies. The new statistical results are discussed in detail and used to constrain theories of galaxy formation.