In this section we study the influence of selection effects on the distribution of clusters and superclusters, and on the space density of clusters.
The probability to detect a cluster at a certain location depends on the galactic obscuration and on the distance of the cluster. To investigate the selection effects we determined the volume density of clusters of galaxies in bins of spherical shells of thickness of 20 h Mpc and in bins of (b is the galactic latitude). Results are shown in Fig. 3 (click here), separately for all clusters and for the population of clusters in very rich superclusters with at least 8 members. The distributions are given for all clusters, but the selection effects are similar for only the clusters with measured redshifts (Einasto et al. 1997b).
This figure shows that the dependence of the space density of clusters on distance and on is almost linear. Thus we can represent the selection effects by linear laws: , and , where , , , and are constants, and is the limiting radius of the sample. Both for all clusters and for those in very rich superclusters, corrected for incompleteness and Galactic extinction, we find: , . The latitude dependence is given by the value , at which the density is equal to zero. For samples of all clusters and clusters in very rich superclusters we get , and , respectively.
These data were used also to derive the mean number density of clusters in space. In order to be left with 1304 clusters in the volume under investigation and with the above selection function, we actually need approximately 9000 clusters in a cube of side 700 h Mpc. Thus the mean density of Abell-ACO clusters in space, corrected for incompleteness and Galactic extinction, is 26 per cube of side-length 100 h Mpc, or , or approximately twice the estimate by Bahcall & Cen (1993). This estimate of the space density of clusters is consistent with the results by Postman et al. (1996) obtained from the study of distant clusters.
This calculation shows that selection effects are important in deriving the density of clusters in space. The comparison with random supercluster catalogues also shows that in low galactic latitudes the multiplicity of superclusters is distorted as some supercluster members are not visible. This explains the observed fact that the density of rich and very rich superclusters decreases toward galactic equator more rapidly than the density of poor superclusters, see Fig. 3 (click here).