We provide flux-and volume-limited galaxy group and cluster catalogues based on the spectroscopic sample of the galaxies of SDSS data release 10. We used a modified friends-of-friends method with a variable linking length in the transverse and radial directions to identify as many realistic groups as possible. The flux-limited catalogue incorporates galaxies down to m r = 17.77 mag. It includes 588 193 galaxies and 82 458 groups. The volume-limited catalogues are complete for absolute magnitudes down to M r,lim = −18.0, −18.5, −19.0, −19.5, −20.0, −20.5, and −21.0; the completeness is achieved within different spatial volumes. Our analysis shows that flux-and volume-limited group samples are well compatible, especially for the larger groups/clusters. Dynamical mass estimates based on radial velocity dispersions and group extent in the sky were added to the extracted groups.

Aims. We use the 2dF Galaxy Redshift Survey data to compile catalogues of superclusters for the Northern and Southern regions of the 2dFGRS, altogether 543 superclusters at redshifts 0.009 ≤ z ≤ 0.2. Methods. We analyse methods of compiling supercluster catalogues and use results of the Millennium Simulation to investigate possible selection effects and errors. We find that the most effective method is the density field method using smoothing with an Epanechnikov kernel of radius 8 h −1 Mpc. Results. We derive positions of the highest luminosity density peaks and find the most luminous cluster in the vicinity of the peak, this cluster is considered as the main cluster and its brightest galaxy the main galaxy of the supercluster. In catalogues we give equatorial coordinates and distances of superclusters as determined by positions of their main clusters. We also calculate the expected total luminosities of the superclusters.

We create a new catalogue of groups and clusters, applying the friends-of-friends method to the 2dF GRS final release. We investigate various selection effects due to the use of a magnitude limited sample. For this purpose we follow the changes in group sizes and mean galaxy number densities within groups when shifting nearby observed groups to larger distances. We study the distribution of sizes of dark matter haloes in N -body simulations and compare properties of these haloes and the 2dF groups. We show that at large distances from the observer luminous and intrinsically greater groups dominate, but in these groups only very bright members are seen, which form compact cores of the groups. These two effects almost cancel each other, so that the mean sizes and densities of groups do not change considerably with distance. Our final sample contains 10750 groups in the Northern part, and 14465 groups in the Southern part of the 2dF survey with membership N gal ≥ 2. We estimate the total luminosities of our groups, correcting for group members fainter than the observational limit of the survey. The cluster catalogue is available at our web-site

Aims. We compile a supercluster sample using the Sloan Digital Sky Survey Data Release 4, and reanalyse supercluster samples found for the 2dF Galaxy Redshift Survey and for simulated galaxies of the Millennium Run. Methods. We find for all supercluster samples Density Field (DF) clusters, which represent high-density peaks of the class of Abell clusters, and use median luminosities of richness class 1 DF-clusters to calculate relative luminosity functions. Results. We show that the fraction of very luminous superclusters in real samples is about five times greater than in simulated samples. Conclusions. Superclusters are generated by large-scale density perturbations that evolve very slowly. The absence of very luminous superclusters in simulations can be explained either by incorrect treatment of large-scale perturbations, or by some yet unknown processes in the very early Universe.

Aims. We investigate how properties of the ensemble of superclusters in the cosmic web evolve with time. Methods. We perform numerical simulations of the evolution of the cosmic web using the ΛCDM model in box sizes L 0 = 1024, 512, 256 h −1 Mpc. We find supercluster ensembles of models for four evolutionary stages, corresponding to the present epoch z = 0, and to redshifts z = 1, z = 3, and z = 10. We calculate fitness diameters of superclusters defined from volumes of superclusters divided to filling factors of over-density regions. Geometrical and fitness diameters of largest superclusters, and the number of superclusters as functions of the threshold density are used as percolation functions to describe geometrical properties of the ensemble of superclusters in the cosmic web. We calculate distributions of geometrical and fitness diameters and luminosities of superclusters, and follow time evolution of percolation functions and supercluster distributions. We compare percolation functions and supercluster distributions of models and samples of galaxies of the Sloan Digital Sky Survey (SDSS). Results. Our analysis shows that fitness diameters of superclusters have a minimum at certain threshold density. Fitness diameters around minima almost do not change with time in co-moving coordinates. Numbers of superclusters have maxima which are approximately constant for all evolutionary epochs. Geometrical diameters of superclusters decrease during the evolution of the cosmic web; luminosities of superclusters increase during the evolution. Conclusions. Our study suggests that evolutionary changes occur inside dynamical volumes of superclusters. The stability of fitness diameters and numbers of superclusters during the evolution is an important property of the cosmic web.