Annu. Rev. Astron. Astrophys. 1991. 29: 499-541 Copyright © 1991 by Annual Reviews. All rights reserved

3.4 Sparse Surveys

The power-law behavior of the two-point correlation function of the galaxian distribution is well established. However, the clustering signature carried by this statistical procedure becomes weak at the larger scales, say in excess of 20 h^-1 Mpc. With increasing scale, structures tend to be found in the linear regime (small / ); they are therefore more likely to have retained memory of initial conditions. The determination of (r) over very large scales ideally requires both deep and wide-angle redshift surveys. Kaiser (1986) has convincingly argued that a sparse, rather than a complete survey approach, can provide the required accuracy in the determination of (r) at substantial observational economy. Although such an approach has been adopted in the past, Kaiser's note quantifies the parameters desired for optimal sampling. Kirshner et al (1987) took advantage of the pencil-beam and sparse sampling approach in effectively surveying a huge volume with a rather small number of observations, and Metcalfe et al (1989) observed only every third galaxy in their sample. However, the full advantage of the technique can be obtained when a very deep, wide-angle and homogeneous catalog is available, such as those generated by the APM (Maddox et al 1990) and COSMOS (Heydon-Dumbleton et al 1989) machines. The coverage of 4300 square degrees in the south galactic cap by the APM survey has produced a catalog of 2 x 10⁶ galaxies brighter than b_J ~ 20.5. A sparse survey aimed at obtaining redshifts for one of every 20 APM galaxies in selected areas is currently under way at the AAT (Loveday 1990, personal communication).