The Supercluster-Void Network I. The Supercluster Catalogue and Large-Scale Distribution

We investigate the distribution of superclusters and voids using a new catalogue of superclusters of rich clusters of galaxies which extends up to a redshift of z=0.12. The new catalogue contains 220 superclusters of rich clusters, of which 90 superclusters have been determined for the first time. Two thirds of those superclusters with eight or more member clusters are concentrated to a Dominant Supercluster Plane almost perpendicular to the plane of the Local Supercluster. Several independent methods indicate consistently the presence of a quite regular supercluster-void network with scale of approx. 120 Mpc. We determine the selection function of the sample of clusters and suggest that the mean true space density of Abell clusters is 2.6 x 10^-5 h^3 Mpc^-3, or twice the conventionally used value.Comment: AA LaTex style, 14 pages, 1 Tex Table, 6 PostScript figures embedded, l-aa.sty added. Figures 4 and 5, 1 ASCII Table with readme.doc (and the complete paper) are available by anonymous ftp at ftp://ftp.aai.ee/pub/publications/astro, accepted by AAS on August 21, 199

Evolution of skewness and kurtosis of cosmic density fields

Methods. We perform numerical simulations of the evolution of the cosmic web for the conventional LCDM model. The simulations cover a wide range of box sizes L = 256 - 4000 Mpc/h, mass and force resolutions and epochs from very early moments z = 30 to the present moment z = 0. We calculate density fields with various smoothing lengths to find the dependence of the density field on smoothing scale. We calculate PDF and its moments - variance, skewness and kurtosis. Results. We focus on the third (skewness S) and fourth (kurtosis K) moments of the distribution functions: their dependence on the smoothing scale, the amplitude of fluctuations and the redshift. During the evolution the reduced skewness $S_3= S/\sigma$ and reduced kurtosis $S_4=K/\sigma^2$ present a complex behaviour: at a fixed redshift curves of $S_3(\sigma)$ and $S_4(\sigma)$ steeply increase with $\sigma$ at $\sigma\le 1$ and then flatten out and become constant at $\sigma\ge2$. If we fix the smoothing scale $R_t$, then after reaching the maximum at $\sigma\approx 2$, the curves at large $\sigma$ start to gradually decline. We provide accurate fits for the evolution of $S_{3,4}(\sigma,z)$. Skewness and kurtosis approach at early epochs constant levels, depending on smoothing length: $S_3(\sigma) \approx 3$ and $S_4(\sigma) \approx 15$. Conclusions. Most of statistics of dark matter clustering (e.g., halo mass function or concentration-mass relation) are nearly universal: they mostly depend on the $\sigma$ with the relatively modest correction to explicit dependence on the redshift. We find just the opposite for skewness and kurtosis: the dependence of moments on evolutionary epoch $z$ and smoothing length $R_t$ is very different, together they determine the evolution of $S_{3,4}(\sigma)$ uniquely. The evolution of $S_3$ and $S_4$ cannot be described by current theoretical approximations.Comment: 17 pages, 14 figures, revised version accepted by Astronomy and Astrophysic