One major complication in void studies arises from the difficulty to obtain spatial distributions of the tracers of the LSS with spectroscopically measured redshifts which are fairly complete in volumes both wide and deep. From this point of view the use of rich clusters of galaxies as tracers allows to study the largest spatial volumes.
Wide-angle studies of the voids in the distribution of clusters of galaxies containing lists (catalogues) of the identified voids have been carried out so far by Batuski & Burns ([1985]), Tully ([1986]), Stavrev ([1990a], [1990b]), and Einasto et al. ([1994]). All of them are based on Abell/ACO clusters (Abell [1958]; Abell et al. [1989]) as tracers. Since then, new redshift data for the clusters have been accumulated. An important step in this direction is the MX Northern Abell Cluster Redshift Survey (Slinglend et al. [1998]), not only because of the increased number of clusters with measured redshifts, but also because of the reliable determination of the cluster redshifts excluding to a great extent the foreground/background contamination. The newly accumulated redshift data allows now for a more complete and correct mapping of the voids in the distribution of galaxy clusters.
Recent observational studies confirm a hierarchical structure of the voids, suggested from theoretical considerations for the void evolution by Dubinski et al. ([1993]), and van de Weygaert & van Kampen ([1993]). According to Einasto et al. ([1994]) the voids determined by rich clusters of galaxies are divided into smaller voids by filaments of very poor clusters and galaxies. Lindner et al. ([1995], [1996]) find a void hierarchy in the Northern Local Supervoid (Einasto et al. [1983]): voids defined by poor (Zwicky) clusters are divided into smaller voids by late-type galaxies. These voids contain fainter galaxies which define still smaller voids. The presence of the void hierarchy makes it reasonable to combine the observations of different types of tracers of the LSS - from rich clusters of galaxies down to poor clusters, groups, and single galaxies. The usefulness of this approach, however, is limited by the incompleteness of the samples of poor clusters, groups and galaxies with measured redshifts in volumes in which the rich clusters of galaxies form complete samples.
The choice of appropriate numerical techniques for void search and analysis is an important aspect of the void studies. The method of the largest empty sphere, nested in the void, has been most often used in searches for voids in the distribution of clusters. It has been first applied by Tully ([1986]), and later by Einasto et al. ([1989]) and Stavrev ([1990a], [1990b]). Tifft & Gregory ([1988]) and Stavrev ([1991]) have proposed an improvement of this method through approximation of a void by a system of intersecting spheres (spheroids). Such an approach allows for a more complete description of the void dimensions, volumes and shapes. An application of this version of the method is given in Stavrev ([1998]). Recently similar multi-sphere techniques were developed by El-Ad et al. ([1996]), as well as by Aikio & Mähönen ([1998]), and applied to the study of voids in the distribution of IRAS galaxies (El-Ad et al. [1997]) and southern sky galaxies (El-Ad & Piran [1997]).
The goals of this paper are (1) to map as completely as possible
the large voids in the distribution of clusters of galaxies in the
Northern Galactic Hemisphere out to medium-large distances
(
400 h-1 Mpc) combining redshift data from many sources,
and using estimated redshifts, (2) to define void parameters on the
basis of a more elaborate procedure for void search and analysis,
(3) to obtain estimates of the mean characteristics of voids
from a statistical analysis of homogeneous samples of voids, and
(4) to identify the void population and study its distribution
in the light of the concept of a void hierarchy. To achieve these
goals we have developed and applied an automated system for void
search and analysis.
The observational data used in this study are described in Sect. 2. The Automated Void Search and Analysis System is presented in Sect. 3, including the void-search algorithm and the void parameterization. Some functions of the system are explained also in Sects. 5 and 6. Section 4 presents the generated void catalogues, and Sect. 5 contains the results from their analysis, including an automated comparison of the catalogues obtained with different tracers, a comparison with voids known from previous investigations, and a statistical analysis. The void population and void shell are discussed in Sect. 6. Finally, Sect. 7 gives a summary of the results.
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