In this section we study the overall distribution of
superclusters. In Figs. 4 (click here) and 5 (click here) we show the distribution of
clusters in supergalactic coordinates. In Fig. 4 (click here) all clusters are
plotted in slices of 100 h
Mpc thickness. In Fig. 5 (click here) we plot only
clusters belonging to very rich superclusters, in the lower panels
of this figure clusters from the Southern and Northern sky are
given separately. Clusters with estimated redshifts (members of
the supercluster candidates) are also included.
Figures 4 (click here) and 5 (click here) show that the network of superclusters and voids extends over the entire volume displayed. Superclusters are separated by huge voids. For example, the Hercules (SCL 160) and the Shapley (SCL 124) superclusters border the Northern Local void; the Hercules, the Bootes (SCL 138) and the Corona Borealis (SCL 158) superclusters surround the Bootes void, that is bordered by the Draco supercluster (SCL 114) in its far side. In the Southern sky the Sculptor supercluster (SCL 9) forms the farther wall of the Sculptor void, to name only the most well-known voids.
The distribution of X-ray emitting clusters from the ROSAT survey (Romer et al. 1994) shows essentially the same structures. The excess of ROSAT clusters in the region of the Pisces-Cetus supercluster and in the Sculptor wall are seen particularly well.
Figures 4 (click here) and 5 (click here) suggest that superclusters are not distributed
homogeneously. Most of very rich superclusters are located
along rods of a quasi-regular rectangular cubic lattice with almost
constant step, and form elongated structures - chains. These
chains are almost parallel to axes of supergalactic coordinates.
The whole distribution of clusters along rods is essentially
one-dimensional. One possibility to give a quantitative
description of the supercluster chains is to use the fractal
dimension, 
, where 
is the slope of the correlation function expressed in log-log form
(Coleman & Pietronero 1992). On small scales the slope of the
cluster-cluster correlation function characterises the fractal
dimension of superclusters themselves, on larger scales up to about
90 h
Mpc the slope is determined by the shape of supercluster
systems. On these scales the fractal dimension determined for all
clusters is 
. This value coincides well
with the correlation fractal dimension for galaxies on large scales
outside clusters (Einasto 1991; Di Nella et al. 1996). The
correlation fractal dimension calculated for clusters that belong
to very rich superclusters is smaller, 
. Thus structures delineated by very rich superclusters
are more one-dimensional than two-dimensional as in the case of
structures defined by all clusters.
Several data sets suggest that giant structures seen in the Southern and Northern sky may be connected, and superclusters form sheets or planes in supergalactic coordinates. One example of such connection is the Supergalactic Plane, which contains the Local Supercluster, the Coma Supercluster, the Pisces-Cetus and the Shapley superclusters (Einasto & Miller 1983; Tully 1986 and 1987; Tully et al. 1992, EETDA). This aggregate separates two giant voids - the Northern and the Southern Local supervoids (EETDA).
Figure 6: The distribution of member clusters
of very rich superclusters along supergalactic
coordinates X, Y, and Z
The search of galaxies in the zone of avoidance has provided further evidence that some other very rich superclusters may be connected through the zone of avoidance. Kraan-Korteweg et al. (1995) found that there may be a chain of galaxies in the zone of avoidance forming a bridge between the Shapley concentration and the Horologium-Reticulum supercluster. This bridge, if real, borders the Southern Local supervoid and connects chains of superclusters parallel to the Supergalactic plane.
The visual impression from Fig. 5 (click here) is that the upper right panel
(sheet 
h
Mpc) contains most of the members of rich
superclusters. No such concentration is seen along other
coordinates although we see several peaks in the distribution of
clusters in both Z- and Y- directions. We checked this
quantitatively by calculating the distribution of member clusters of
very rich superclusters along supergalactic coordinates
(Fig. 6 (click here)). In this way we can see whether the clusters are
concentrated in a certain supergalactic interval (this approach was
chosen because of simplicity and also because several rich systems
of superclusters are located almost parallel to one or another
plane of supergalactic coordinate axes). The presence of the zone
of avoidance causes the absence of clusters around Y = 0,
therefore we can only compare the distributions of clusters along
the X and Z coordinates. In the case of uniform distribution
the distribution of clusters and superclusters along X and Z
axes should be statistically identical. However, the
Kolmogorov-Smirnov test shows that the zero hypothesis
(distribution of clusters along X and Z coordinates is
identical) is rejected at the 99% confidence level.
We compared the distribution of the members of very rich
superclusters from real and random catalogues. The results show
that of the 320 member clusters of observed very rich
superclusters 198 belong to the sheet 
h
Mpc. In the case of randomly located superclusters the
expected number of clusters in very rich superclusters in the sheet
is 80 if we do not take into account the selection effects, and
123, if the selection effects have been taken into account.
Therefore no such concentration of clusters is seen in the case of
randomly located superclusters.
The evidence that the structures may be connected through the zone of avoidance leads us to believe that superclusters in this supergalactic X interval form a Dominant Supercluster Plane. The figures show that this plane is almost perpendicular to the X-axis and crosses the Supergalactic plane almost at right angle.
In fact, already Tully et al. (1992) noted the presence of the supercluster structures that are almost orthogonal to the Supergalactic plane. Due to that they described the supercluster-void network as a three-dimensional chessboard. Our data show that structures delineated by rich superclusters are not only orthogonal but also located quite regularly (Sects. 6 and 7). Thus, although the description as a chessboard is a simplification it describes certain aspects of the supercluster-void network rather well.
We list the superclusters belonging to the Dominant Supercluster Plane: the Aquarius-Cetus, the Aquarius, the Aquarius B, the Pisces-Cetus, the Horologium-Reticulum, the Sculptor, the Fornax-Eridanus and the Caelum superclusters in the Southern sky, and the Corona Borealis, the Bootes, the Hercules, the Virgo-Coma, the Vela, the Leo, the Leo A, the Leo-Virgo and the Bootes A in the Northern sky. These superclusters do not form a featureless wall - the Dominant Supercluster Plane is formed by a number of intertwined chains of rich superclusters.
We showed that very rich superclusters are arranged in chains and walls, separated by huge voids. To study the distribution of poor superclusters and isolated clusters with respect to richer superclusters we used the nearest neighbour test as in EETDA. In this test we calculate the distribution of distances of the nearest neighbours between members of poor superclusters and isolated clusters, and clusters belonging to rich superclusters, and the distribution of distances between randomly located points and clusters from rich superclusters. In this way we can see whether these clusters are located close to rich superclusters, or they form a more or less randomly distributed smooth population in voids.
In order to obtain a hypothetical homogeneous void population we
generated a sample of random clusters which are located at a distance
Mpc from real clusters that belong to rich
superclusters and occupy the same volume as real clusters.
The number of these random
clusters was equal to the number of isolated clusters and poor
supercluster members.
The results of this test are shown in the Fig. 7 (click here). We see that the nearest neighbour distribution curves of these sample pairs deviate from each other - real isolated clusters and members of poor superclusters are located much closer to rich superclusters than randomly located test clusters. A Kolmogorov-Smirnov test shows that these distributions are different at the 99% confidence level. In other words, isolated clusters and clusters in poor superclusters belong to outlying parts of superclusters and do not form a random population in voids.
Figure 7: The integral probability distribution of the nearest
neighbour distances: cross distributions for the sample pairs of
clusters from rich
superclusters vs. isolated clusters (solid curve) and
clusters from rich superclusters vs. random points (dashed curve)
Table 1: Median diameters of voids