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We investigate the evolution of superclusters and supercluster cocoons (basins of attraction), and the influence of cosmological parameters to the evolution. We perform numerical simulations of the evolution of the cosmic web for different cosmological models: the LCDM model with a conventional value of the dark energy (DE) density, the open model OCDM with no DE, the standard SCDM model with no DE, and the Hyper-DE HCDM model with an enhanced DE density value. We find ensembles of superclusters of these models for five evolutionary stages, corresponding to the present epoch z = 0, and to redshifts z = 1, 3, 10, 30. We use diameters of the largest superclusters and the number of superclusters as percolation functions to describe properties of the ensemble of superclusters in the cosmic web. We analyse the size and mass distribution of superclusters in models and in real Sloan Digital Sky Survey (SDSS) based samples. In all models numbers and volumes of supercluster cocoons are independent on cosmological epochs. Supercluster masses increase with time, and geometrical sizes in comoving coordinates decrease with time, for all models. LCDM, OCDM and HCDM models have almost similar percolation parameters. This suggests that the essential parameter, which defines the evolution of superclusters, is the matter density. The DE density influences the growth of the amplitude of density perturbations, and the growth of masses of superclusters, albeit significantly less strongly. The HCDM model has the largest speed of the growth of the amplitude of density fluctuations, and the largest growth of supercluster masses during the evolution. Geometrical diameters and numbers of HCDM superclusters at high threshold densities are larger than for LCDM and OCDM superclusters. SCDM model has about two times more superclusters than other models; SCDM superclusters have smaller diameters and masses., Comment: 14 pages, 10 figures (accepted by Astronomy & Astrophysics). arXiv admin note: text overlap with arXiv:1901.09378

{We study biasing as a physical phenomenon by analysing geometrical and clustering properties of density fields of matter and galaxies.} {Our goal is to determine the bias function using a combination of geometrical and power spectrum analysis of simulated and real data.} {We apply an algorithm based on local densities of particles, $\delta$, to form simulated biased models using particles with $\delta \ge \delta_0$. We calculate the bias function of model samples as functions of the particle density limit $\delta_0$. We compare the biased models with Sloan Digital Sky Survey (SDSS) luminosity limited samples of galaxies using the extended percolation method. We find density limits $\delta_0$ of biased models, which correspond to luminosity limited SDSS samples.} {Power spectra of biased model samples allow to estimate the bias function $b(>L)$ of galaxies of luminosity $L$. We find the estimated bias parameter of $L_\ast$ galaxies, $b_\ast =1.85 \pm 0.15$. } {The absence of galaxy formation in low-density regions of the Universe is the dominant factor of the biasing phenomenon. Second largest effect is the dependence of the bias function on the luminosity of galaxies. Variations in gravitational and physical processes during the formation and evolution of galaxies have the smallest influence to the bias function. }, Comment: 20 pages, 16 figures. Submitted to Astronomy & Astrophysics

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 LambdaCDM model in box sizes L0 = 1024, 512, 256 Mpc/h. 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., Comment: 13 pages, 6 figures. Astronomy & Astrophysics (accepted)

Aims. We develop an extended percolation method to allow the comparison of geometrical properties of the real cosmic web with the simulated dark matter web for an ensemble of over- and under-density systems. Methods. We scan density fields of dark matter (DM) model and SDSS observational samples, and find connected over- and underdensity regions in a large range of threshold densities. Lengths, filling factors and numbers of largest clusters and voids as functions of the threshold density are used as percolation functions. Results. We find that percolation functions of DM models of different box sizes are very similar to each other. This stability suggests that properties of the cosmic web, as found in the present paper, can be applied to the cosmic web as a whole. Percolation functions depend strongly on the smoothing length. At smoothing length 1 $h^{-1}$ Mpc the percolation threshold density for clusters is $\log P_C = 0.718 \pm 0.014$, and for voids is $\log P_V = -0.816 \pm 0.015$, very different from percolation thresholds for random samples, $\log P_0 = 0.00 \pm 0.02$. Conclusions. The extended percolation analysis is a versatile method to study various geometrical properties of the cosmic web in a wide range of parameters. Percolation functions of the SDSS sample are very different from percolation functions of DM model samples. The SDSS sample has only one large percolating void which fills almost the whole volume. The SDSS sample contains numerous small isolated clusters at low threshold densities, instead of one single percolating DM cluster. These differences are due to the tenuous dark matter web, present in model samples, but absent in real observational samples., Comment: 15 pages, 10 figures, Astronomy & Astrophysics (accepted)

We provide flux-limited and volume-limited galaxy group and cluster catalogues, based on the spectroscopic sample of the SDSS data release 10 galaxies. We used a modified friends-of-friends (FoF) 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 588193 galaxies and 82458 groups. The volume-limited catalogues are complete for absolute magnitudes down to M_r = -18.0, -18.5, -19.0, -19.5, -20.0, -20.5, and -21.0; the completeness is achieved within different spatial volumes, respectively. Our analysis shows that flux-limited and volume-limited group samples are well compatible to each other, especially for the larger groups/clusters. Dynamical mass estimates, based on radial velocity dispersions and group extent in the sky, are added to the extracted groups. The catalogues can be accessed via http://cosmodb.to.ee and the Strasbourg Astronomical Data Center (CDS)., Comment: 16 pages, 18 figures, 2 tables, accepted for publication in A&A

Our goal is to see how density waves of different scale combine to form voids between galaxy systems of various scale. We perform numerical simulations of structure formation in cubes of size 100 and 256 Mpc/h, with resolutions 256^3 and 512^3 particles and cells. To understand the role of density perturbations of various scale we cut power spectra at scales from 8 to 128 Mpc/h, using in all series identical initial random realisations. We find that small haloes and short filaments form all over the simulation box, if perturbations only up to scale 8 Mpc/h are present. The phenomenon of large multi-scale voids in the cosmic web requires the presence of an extended spectrum of primordial density perturbations. The void phenomenon is due to the action of two processes: the synchronisation of density perturbations of medium and large scales, and the suppression of galaxy formation in low-density regions by the combined action of negative sections of medium- and large-scale density perturbations, so that their densities are less than the mean density, and thus during the evolution their densities decrease., Comment: 16 pages, 11 figures, revised version

We follow the evolution of galaxy systems in numerical simulation. Our goal is to understand the role of density perturbations of various scales in the formation and evolution of the cosmic web. We perform numerical simulations with the full power spectrum of perturbations, and with spectrum cut at long wavelengths. Additionally, we have one model, where we cut the intermediate waves. We analyze the density field and study the void sizes and density field clusters in different models. Our analysis shows that the fine structure (groups and clusters of galaxies) is created by small-scale density perturbations of scale $\leq 8$ \Mpc. Filaments of galaxies and clusters are created by perturbations of intermediate scale from $\sim 8$ to $\sim 32$ \Mpc, superclusters of galaxies by larger perturbations. We conclude that the scale of the pattern of the cosmic web is determined by density perturbations of scale up to $\sim 100$ \Mpc. Larger perturbations do not change the pattern of the web, but modulate the richness of galaxy systems, and make voids emptier. The stop of the increase of the scale of the pattern of the cosmic web with increasing scale of density perturbations can probably be explained as the freezing of the web at redshift $z\simeq 0.7$., Comment: 12 pages, 7 figures, accepted for publication in Astronomy and Astrophysics

According to the modern cosmological paradigm galaxies and galaxy systems form from tiny density perturbations generated during the very early phase of the evolution of the Universe. Using numerical simulations we study the evolution of phases of density perturbations of different scales to understand the formation and evolution of the cosmic web. We apply the wavelet analysis to follow the evolution of high-density regions (clusters and superclusters) of the cosmic web. We show that the positions of maxima and minima of density waves (their spatial phases) almost do not change during the evolution of the structure. Positions of extrema of density perturbations are the more stable, the larger is the wavelength of perturbations. Combining observational and simulation data we conclude that the skeleton of the cosmic web was present already in an early stage of structure evolution., Comment: 12 pages, 8 figures, revised version

We derive the luminosity and multiplicity functions of superclusters compiled for the 2dF Galaxy Redshift Survey, the Sloan Digital Sky Survey (Data Release 4), and for three samples of simulated superclusters. 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/masses of richness class 1 DF-clusters to calculate relative luminosity/mass functions. We show that the fraction of very luminous (massive) superclusters in real samples is more than tenfolds greater than in simulated samples. Superclusters are generated by large-scale density perturbations which evolve very slowly. The absence of very luminous superclusters in simulations can be explained either by non-proper treatment of large-scale perturbations, or by some yet unknown processes in the very early Universe., Comment: 6 pages, 3 Figures, submitted for Astronomy and Astrophysics

We investigate properties of superclusters of galaxies found on the basis of the 2dF Galaxy Redshift Survey, and compare them with properties of superclusters from the Millennium Simulation. We study the dependence of various characteristics of superclusters on their distance from the observer, on their total luminosity, and on their multiplicity. The multiplicity is defined by the number of Density Field (DF) clusters in superclusters. Using the multiplicity we divide superclusters into four richness classes: poor, medium, rich and extremely rich. We show that superclusters are asymmetrical and have multi-branching filamentary structure, with the degree of asymmetry and filamentarity being higher for the more luminous and richer superclusters. The comparison of real superclusters with Millennium superclusters shows that most properties of simulated superclusters agree very well with real data, the main differences being in the luminosity and multiplicity distributions., Comment: 15 pages, 13 Figures, submitted for Astronomy and Astrophysics

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. 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 Mpc/h. 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., Comment: 16 pages, 11 figures, submitted for Astronomy and Astrophysics. High-resolution pdf file and supplementary data can be found at http://www.aai.ee/~maret/2dfscl.html

We present a new fast method for simulating pencil-beam type light-cones, using the MLAPM-code (Multi Level Adaptive Particle Mesh) with light-cone additions. We show that by a careful choice of the light-cone orientation, it is possible to avoid extra periodicities in the light-cone. As an example, we apply the method to simulate a 6 Gpc deep light-cone, create the dark matter halo catalogue for the light-cone and study the evolution of haloes from $z=6$ up to the present time. We determine the spatial density of the haloes, their large-scale correlation function, and study the evolution of the mass function. We find a surprisingly simple relation for the dependence of halo maximum mass on redshift, and apply it to derive redshift limits for bright quasars., Comment: 9 pages, 9 figures, submitted for Astronomy and Astrophys

We study the properties of dark matter haloes of a LCDM model in different environments. Using the distance of the 5th nearest neighbour as an environmental density indicator, we show that haloes in a high density environment are more massive, richer, have larger radii and larger velocity dispersions than haloes in a low density environment. Haloes in high density regions move with larger velocities, and are more spherical than haloes in low density regions. In addition, low mass haloes in the vicinity of the most massive haloes are themselves more massive, larger, and have larger rms velocities and larger 3D velocities than low mass haloes far from massive haloes. The velocities of low mass haloes near massive haloes increase with the parent halo mass. Our results are in agreement with recent findings about environmental effects for groups and clusters of galaxies from deep (SDSS and LCRS) surveys., Comment: 9 pages, 7 figures, submitted for Astronomy and Astrophysics

We find clusters and superclusters of galaxies using the Data Release 1 of the Sloan Digital Sky Survey. We determine the luminosity function of clusters and find that clusters in a high-density environment have a luminosity a factor of ~5 higher than in a low-density environment. We also study clusters and superclusters in numerical simulations. Simulated clusters in a high-density environment are also more massive than those in a low-density environment. Comparison of the density distribution at various epochs in simulations shows that in large low-density regions (voids) dynamical evolution is very slow and stops at an early epoch. In contrast, in large regions of higher density (superclusters) dynamical evolution starts early and continues until the present; here particles cluster early, and by merging of smaller groups very rich systems of galaxies form., Comment: 12 pages, 8 figures, submitted for Astronomy and Astrophysics