6 Void population and void shell

By definition the voids identified in the present study are regions completely devoid of a certain type of objects. They, however, may be populated by other types of objects of lower richness class.

Studies of the voids in the distribution of galaxies like the large void in Boötes with a population of $\sim$ 60 galaxies discovered so far (Szomoru et al. [1996]), do not confirm the theoretical predictions for the presence of a significant population of dwarf galaxies or of giant, unevolved, low surface brightness galaxies in the voids. Voids are rather inhabited by galaxies which are similar to field galaxies of the same morphological type. They are not uniformly distributed in the voids but form filament or sheet-like structures which surround smaller voids (see e.g. Szomoru et al. [1996]; Weistrop et al. [1995]; Cruzen et al. [1997]; Sage et al. [1997]). This picture is in agreement with the idea of a void hierarchy. The latter has been studied in more detail and on a higher hierarchical level by Lindner et al. ([1995], [1996]) in the region of the Northern Local Supervoid. In an earlier investigation of the 40 h^-1 Mpc Pisces-Cetus void (Burns et al. [1988]) in the distribution of Abell clusters Willick et al. ([1990]) find that it contains filaments of galaxies which surround subvoids with sizes of 25-30 h^-1 Mpc.

Our study of the population in the voids of galaxy clusters is based on a joint treatment of the catalogues of voids (Sect. 4, Table 2) and samples of objects (clusters, groups, galaxies) extracted from the compilations CL, CN, and CG (see Sect. 2.1), by using AVSAS. AVSAS offers possibilities for: (1) complete identification of the population of a chosen type (sample) in each void of a chosen catalogue, (2) identification of the objects surrounding a void in a shell of chosen thickness, (3) construction of the radial distribution of the void and shell population (void profiles), (4) construction of the spatial distribution of the void and shell population. Let us note that by "shell'' we shall understand a zone of a chosen thickness around a void which strictly follows the void shape. Thus, the shell may have a very complicated shape if the void is composed of a large number of CS. The shell has a simple spherical form only in the case of a single-sphere void.

Since voids in our void catalogues may overlap we permit a given object to populate more than one void if it is in the overlapping zone. The same is naturally true for the shell when it divides two neighbouring voids.

Because of the large number of void catalogues and voids a complete study of the population of the individual voids is only possible in a separate investigation. Here we shall adduce only first results concerning the population in the voids of $R \geq$ 1 A/ACO clusters. Let us also note that because of the lower completeness limits of the samples of poorer clusters, groups, and galaxies in comparison with the samples of rich A/ACO clusters, the results in the present section should be considered as preliminary.

The joint processing in the volume defined by $b \geq +20^{\circ }$ and $z \leq$ 0.16 of (1) the void catalogue AR/Lp (60 voids, see Table 3), a sample of 1312 clusters and groups extracted from the compilation CL, and a sample of 19879 galaxies extracted from the compilation CG (see Sect. 2.1), and (2) the void catalogue AR/Np (65 voids, see Table 2), a sample of 1309 clusters and groups extracted from the compilation CN, and the same sample of galaxies as in (1), has led to the complete identification of the void population of poorer clusters (i.e. R = 0 A/ACO and non-A/ACO), groups, and galaxies, as well as of the shell population ($R \geq$ 1 A/ACO clusters, poorer clusters, groups, and galaxies), for each void of the two catalogues. A shell thickness of 10 h^-1 Mpc has been chosen. This is twice the typical thickness of the walls of the voids of galaxies (e.g., de Lapparent et al. [1991]; Doroshkevich et al. [1996]). The results from the identification procedure are output as lists of the void and shell populations of the individual voids, and as tables with the numbers of objects of different types in each void and its shell, and the number densities of the void populations. These data for the void catalogue AR/Lp are given in Table 8 where Col. (2) contains the distance from the observer to the centre of the largest void sphere (see Table 3), Cols. (3) and (4) contain the number and density of the void population of poorer clusters and groups, Cols. (5) and (6) contain the number and density of the population of galaxies in the voids, and Cols. (7), (8), and (9) contain the number of $R \geq$ 1 A/ACO clusters forming the void shell, the number of poorer clusters and groups in the shell, and the number of galaxies in the shell, respectively. A similar table has been obtained for void catalogue AR/Np. Table 8 contains only the voids whose centres lie in the near subvolume V1, because of the very high incompleteness outside of it. Even this volume, however, is deeper than the completeness limits of the populations of poorer clusters, groups, and galaxies. Therefore, several of the nearest (r $\stackrel{\textstyle <}{\sim}$ 150 h^-1 Mpc) voids show much higher number densities compared to the rest of the voids.

  

Table 8: Numbers and densities of the void populations and numbers of the shell populations for the voids of $R \geq$ 1 A/ACO clusters (catalogue AR/Lp, volume V1)

As seen from Table 8 we have divided roughly the void population into two categories: (1) poorer clusters (all types of clusters except the $R \geq$ 1 A/ACO) and groups, and (2) galaxies. For the shell population we add to these two categories the $R \geq$ 1 A/ACO clusters. Our grounds for not processing the population of groups separately from the poorer clusters are (1) the comparatively small number of groups with measured redshifts at the distances of the voids of rich clusters, and (2) the uncertainty in classifying a poor concentration of galaxies as "poor cluster'' or "group'' (see e.g. Noonan [1973]; Ledlow et al. [1996]).

Because of the incompleteness problem the data in Table 8 cannot be used to obtain a reliable estimate of the mean number density of the void population. We may try to get rough estimates based on the nearest voids. From voids Nos. 31, 37, 52 (Table 8) and two additional voids (Nos. 35, 57) from the void catalogue AR/Np we obtain the mean number densities of the void population of poorer clusters and groups $\sim 40~10^{-6}~h^{3}~ \mathrm{Mpc}^{-3}$, and $\sim 1~10^{-3}~h^{3}~\mathrm{Mpc}^{-3}$ for the population of galaxies. (We do not use the nearest void No. 2 in Table 8 because of the exceptionally high number density of its population.) These values are much lower than the known estimates of the mean spatial number density for the two types of population. E.g., Frisch et al. ([1995]) give for the mean density of the near Zwicky clusters (which are only a part of the total population of poorer clusters and groups in our voids) the value 75.6 10^-6 h³ Mpc^-3, and Lin et al. ([1996]) estimate the mean number density of the galaxies with absolute magnitude $M \leq -17.5 + 5 \log h$ from the Las Campanas Redshift Survey as $\bar{n} = 0.029~h^{3}~ \mathrm{Mpc}^{-3}$. If our estimates are not strongly affected by the observational selection we may conclude that the voids of $R \geq$ 1 A/ACO clusters are also regions with underdensities of the poorer clusters and groups, and of the galaxies.

One of the important questions concerning the void population is how it is distributed inside the void. As a first step we have studied the radial distribution of the number density of the population, i.e. the void density profiles.

Profiles of voids observed in the distribution of galaxies have been obtained so far by Dey et al. ([1990]), Szomoru et al. ([1996]), and Lindner et al. ([1996]). Here, an attempt is made to construct radial profiles of voids in the distribution of clusters of galaxies.

The void radial profiles have been obtained from the population number densities in concentric spheres, centred in the void (on the centroid of all CS), increasing their radius by $\Delta d =$ 5 h^-1 Mpc, i.e. the profiles are cumulative functions. This approach has the disadvantage that it does not take into account the void shape if it is different from spherical. That leads to errors in the calculated densities, which are larger if the void sphericity is smaller. As a result, the zone of the void profile corresponding to the void shell appears artificially extended and flattened. Another disadvantage is that near the void centre the density is averaged over very small volumes.

Figure 14: Radial density profiles of voids of $R \geq$ 1 A/ACO clusters (catalogue AR/Lp, see Table 3) for the population of a) clusters and groups, and b) galaxies

The radial density profiles of three voids of $R \geq$ 1 A/ACO clusters selected from the void catalogue AR/Lp (Nos. 3, 31, 52 - see Tables 3 and 8) are shown in Figs. 14a and b for the population of clusters and groups, and of galaxies, respectively. It is seen that the profiles of the more distant void No. 3 are shallower than those of the nearer voids Nos. 31 and 52, probably due to the growing incompleteness with distance. Let us note that the inadequate completeness of the population in most of the voids in volume V1 makes difficult the construction of reliable mean radial profiles from the profiles of the individual voids.

The profile of void No. 31 for the population of clusters and groups shows a deep void with a dense shell. Its population of 79 poorer clusters and groups is concentrated near the void shell, which is formed by 16 $R \geq$ 1 A/ACO clusters and contains additionally 57 poorer clusters and groups. The maximum density of the shell is at radius $65-70\ h^{-1}$ Mpc and corresponds to the equivalent diameter D_e = 134 h^-1 Mpc of the void (see Table 3). The central part of the void with diameter $\sim$ 60 h^-1 Mpc is completely empty of poorer clusters and groups. However, from the profile of the same void for the population of galaxies (Fig. 14b) it is seen that this central part contains a population of galaxies, penetrating deep into the void. The local maximum of the profile at $\sim$ 20 h^-1 Mpc is an indication for the presence of a fine substructure in the void (concentrations and filaments of galaxies) and probably represents the shell of a subvoid of galaxies. This, however, should be confirmed by investigating the 3-D distribution of the void population.

Void No. 52 shows a somewhat different profile from void No. 31. It is shelf-like with the density of the void shell (composed of 5 $R \geq$ 1 A/ACO clusters, 28 poorer clusters and groups, 579 galaxies) being not much different from the density of the void population (32 poorer clusters and groups, 639 galaxies). The population of poorer clusters and groups penetrates deep into the void but leaves completely empty a subvoid of nearly 50 h^-1 Mpc (Fig. 14a), which as seen from Fig. 14b is populated by galaxies almost to the void centre.

The density profiles in Figs. 14a and b, as well as density profiles of some other voids that we have studied, suggest that the voids of $R \geq$ 1 A/ACO clusters contain smaller voids of poorer clusters and groups which contain still smaller voids or underdense regions in the distribution of galaxies. This suggestion supports the model of a void hierarchy.

A further, more complete study of the void substructure is possible by direct analysis of the 3-D distribution of the void population. We intend to consider this problem in a separate paper.