Local Supercluster Structure via Voronoi Tessellation


The Local Supercluster (LS) of galaxies, like other superclusters, has no well-defined boundaries. The volume of the nearby Universe filled with galaxies with radial velocities approximately up to 3000 km/s is meant by the LS. The LS structure has been actively studied for more than 30 years since Vaucouleurs’s works. Tully (1982) found the LS to have three main components:

20 % of the luminous galaxies are located in the Virgo cluster (the central part of the LS), 40 % are concentrated in the disk, and 40 % form a ”halo”; the LS has an irregular shape. The studies by Einasto et al. (1984) showed that the LS has a filamentary structure; strings of galaxies join the dominant clusters (groups) of galaxies. A series of works aimed at revealing the internal 2D and 3D structure of the LS as a whole and its individual clusters and groups appeared in the 1980s. These works, which became classical ones, primarily include the group catalog by Geller and Huchra (1983) and the nearest group catalog by Tully (1987).

The goal of our paper Melnyk, Elyiv & Vavilova (2006) “The structure of the local supercluster of galaxies detected by three-dimensional Voronoi’s tessellation method” was to identify LS galaxy groups by 3D Voronoi tessellation method and to compare these with groups detected by the Karachentsev (1994) method. This will allow us to ascertain how the clustering criteria affect the characteristics of the groups selected from the same catalog of galaxies, on the one hand, and how the two different methods (dynamical and geometrical) agree, on the other hand. We preferred the geometrical Voronoi tessellation method because it had not yet been applied to the clustering of galaxy groups in 3D space and is sensitive to the detection of both prolate and spherical structures (see Fig. 2).

Example of a 2D Voronoi tessellation. (Fig. 1 in Melnyk, Elyiv & Vavilova 2006).
Fig. 2. Example of a 2D Voronoi tessellation. (Fig. 1 in Melnyk, Elyiv & Vavilova 2006).

As the result, we identified groups of galaxies in the Local Supercluster and compared their propertis with MK groups (Makarov & Karachentsev, 2000) using the same catalog of LS galaxies (N = 7064). The 3D Voronoi tessellation method is a geometrical method based only on the positions of galaxies in space. The method reveals regions with an enhanced galaxy density compared to the background (i.e., a density contrast compared to a random distribution). Since the LS catalog is inhomogeneous (there is a strong selection of dwarf galaxies with depth), we artificially rescaled the distances in such a way that the concentration of galaxies varied with sample depth as a power law with the same index as that for the full homogeneous catalog.

The fraction of the obtained groups and MK groups that coincided by all components is 22 %, which is quite acceptable. For example, when the hierarchical and percolation methods were compared, 25 % of the groups coincided (Garcia 1993). It was shown that the Voronoi tessellation method tend to identify rich populated groups contrary to the dynamical method by Karachentsev (1994) which likes to detect sparsely populated groups. The advantage of the Voronoi tessellation method is its simplicity, since only the coordinates and velocities of galaxies must be known. Thus, the method can be useful in a preliminary (initial) study of the structure of a supercluster or when there is no information about the individual properties of galaxies. The distance rescaling method is also of great importance, since any other geometrical clustering method can be used after its application