4. Space distribution
Examples of variation of the supercluster space density with distance R for are presented in Figs. 10-11, together with Poisson errors and linear fits. The linear regression coefficients, corresponding correlation coefficients and st. dev. of regressions are given in Table 6. Generally the regression is
Merged samples for both galactic caps are denoted with (N+S).
Table 6. Linear regressions
The coefficient a defines the supercluster space density at redshift . Denoting whence , which is connected with the distance selection function and could be used to generate mock catalogs of superclusters.
Thus for 3N40.10, for 3S40.10, and the mean density (N+S) is .
Correspondingly for , we have and for N, S and (N+S).
For , we have mean density and for - .
Samples 3(N+S)40 (Fig. 10) demonstrate the decrease of when density contrast increases. The slope b, however does not depend on density contrast. A test with sample 3(N+S)40z.10 definitely shows that if we exclude superclusters with members whose redshift is estimated, then the distance selection will be stronger. Samples 3N40 and 3S40 (Fig. 11) allows us to establish the difference between north and south caps. Obviously the distance selection for the south cap is stronger and the space density is unrealistically high. Since the number of superclusters in the south cap are presumably found among ACO-clusters of galaxies, one has to conclude that the superclusters found among A-clusters form a more representative sample. The mean coefficient for samples 3N40.10-40, while for S samples. The conclusion is supported by samples 3N40.10 and 3S40.10.
It is curious to look at the space density variation of superclusters with multiplicity . Keeping in mind the supercluster searching procedure, we could assume that many doublets are illusory superclusters. But this is not the case, since the regression for the sample 2(N+S)40.10 is almost parallel to the regression for the sample 3(N+S)40.10 (Table 6).
© European Southern Observatory (ESO) 1998
Online publication: March 3, 1998