Structure and formation of superclusters VII. Supercluster-void topology

Supercluster-void topology is investigated for observed and model samples using density field method. Observed samples have cube size L=20 Mpc/h around the Virgo cluster. Model samples are calculated with 64^3 cells and particles: for standard CDM spectrum (cube size 32 Mpc/h) by Melott, for LambdaCDM spectrum (cube size 40 Mpc/h, Omega_m=0.2, Omega_Lambda=0.8) by Gramann. For model samples two cases are studied: unbiased samples with all test particles included, and biased samples where non-clustered particles in low-density regions are removed. High-resolution density fields are calculated for all observed and model samples using grid size 1.25 Mpc/h, close to the radius of real clusters/groups of galaxies. Connected cells having at least one common sidewall are considered as systems; the systems are found for a wide range of threshold density from 0.01 to 100 in mean density units. Galaxy/particle systems divided into 'empty' or 'filled', if the density is lower or equal/higher than the threshold density. As tests the length of the largest system, its filling factor, and the number of 'empty' and 'filled' systems are used. Results show that the supercluster-void topology depends on the density threshold: at low threshold the topology is cellular or sponge-like, at medium threshold it is sponge-like, at high threshold it is of the type 'islands in ocean'. The filling factor of the largest system and the number of filled system tests show that the biased LambdaCDM model has the closest similarity with observations.