Clustering statistics in cosmology

The main tools in cosmology for comparing theoretical models with the observations of the galaxy distribution are statistical. We will review the applications of spatial statistics to the description of the large-scale structure of the universe. Special topics discussed in this talk will be: description of the galaxy samples, selection effects and biases, correlation functions, Fourier analysis, nearest neighbor statistics, Minkowski functionals and structure statistics. Special attention will be devoted to scaling laws and the use of the lacunarity measures in the description of the cosmic texture.Comment: 15 pages, 7 figures, uses spie.cls (included). This paper will be published in SPIE Proceedings Vol. 4847, 2002, "Astronomical Data Analysis II," J.-L. Stark and F. Murtagh, eds., and is made available as an electronic preprint with permission of SPI

Multi-scale morphology of the galaxy distribution

Many statistical methods have been proposed in the last years for analyzing the spatial distribution of galaxies. Very few of them, however, can handle properly the border effects of complex observational sample volumes. In this paper, we first show how to calculate the Minkowski Functionals (MF) taking into account these border effects. Then we present a multiscale extension of the MF which gives us more information about how the galaxies are spatially distributed. A range of examples using Gaussian random fields illustrate the results. Finally we have applied the Multiscale Minkowski Functionals (MMF) to the 2dF Galaxy Redshift Survey data. The MMF clearly indicates an evolution of morphology with scale. We also compare the 2dF real catalog with mock catalogs and found that Lambda-CDM simulations roughly fit the data, except at the finest scale.Comment: 17 pages, 19 figures, accepted for publication in MNRA

Joint constraints on galaxy bias and σ8\sigma_8 through the N-pdf of the galaxy number density

We present a full description of the N-probability density function of the galaxy number density fluctuations. This N-pdf is given in terms, on the one hand, of the cold dark matter correlations and, on the other hand, of the galaxy bias parameter. The method relies on the assumption commonly adopted that the dark matter density fluctuations follow a local non-linear transformation of the initial energy density perturbations. The N-pdf of the galaxy number density fluctuations allows for an optimal estimation of the bias parameter (e.g., via maximum-likelihood estimation, or Bayesian inference if there exists any a priori information on the bias parameter), and of those parameters defining the dark matter correlations, in particular its amplitude ($\sigma_8$). It also provides the proper framework to perform model selection between two competitive hypotheses. The parameters estimation capabilities of the N-pdf are proved by SDSS-like simulations (both ideal log-normal simulations and mocks obtained from Las Damas simulations), showing that our estimator is unbiased. We apply our formalism to the 7th release of the SDSS main sample (for a volume-limited subset with absolute magnitudes $M_r \leq -20$). We obtain $\hat{b} = 1.193 \pm 0.074$ and $\hat{\sigma_8} = 0.862 \pm 0.080$, for galaxy number density fluctuations in cells of a size of $30h^{-1}$Mpc. Different model selection criteria show that galaxy biasing is clearly favoured.Comment: 25 pages, 9 figures, 2 tables. v2: Substantial revision, adding the joint constraints with \sigma_8 and testing with Las Damas mocks. Matches version accepted for publication in JCA

Unusual A2142 supercluster with a collapsing core: distribution of light and mass

We study the distribution, masses, and dynamical properties of galaxy groups in the A2142 supercluster. We analyse the global luminosity density distribution in the supercluster and divide the supercluster into the high-density core and the low-density outskirts regions. We find galaxy groups and filaments in the regions of different global density, calculate their masses and mass-to-light ratios and analyse their dynamical state with several 1D and 3D statistics. We use the spherical collapse model to study the dynamical state of the supercluster. We show that in A2142 supercluster groups and clusters with at least ten member galaxies lie along an almost straight line forming a 50 Mpc/h long main body of the supercluster. The A2142 supercluster has a very high density core surrounded by lower-density outskirt regions. The total estimated mass of the supercluster is M_est = 6.2 10^{15}M_sun. More than a half of groups with at least ten member galaxies in the supercluster lie in the high-density core of the supercluster, centered at the rich X-ray cluster A2142. Most of the galaxy groups in the core region are multimodal. In the outskirts of the supercluster, the number of groups is larger than in the core, and groups are poorer. The orientation of the cluster A2142 axis follows the orientations of its X-ray substructures and radio halo, and is aligned along the supercluster axis. The high-density core of the supercluster with the global density D8 > 17 and perhaps with D8 > 13 may have reached the turnaround radius and started to collapse. A2142 supercluster with luminous, collapsing core and straight body is an unusual object among galaxy superclusters. In the course of the future evolution the supercluster may be split into several separate systems.Comment: 13 pages, 9 figures, Astronomy and Astrophysics, in press. References update

Tracing high redshift cosmic web with quasar systems

We trace the cosmic web at redshifts 1.0 <= z <= 1.8 using the quasar data from the SDSS DR7 QSO catalogue (Schneider et al. 2010). We apply a friend-of-friend (FoF) algorithm to the quasar and random catalogues to determine systems at a series of linking lengths, and analyse richness and sizes of these systems. At the linking lengths l <= 30 Mpc/h the number of quasar systems is larger than the number of systems detected in random catalogues, and systems themselves have smaller diameters than random systems. The diameters of quasar systems are comparable to the sizes of poor galaxy superclusters in the local Universe, the richest quasar systems have four members. The mean space density of quasar systems is close to the mean space density of local rich superclusters. At intermediate linking lengths (40 <= l <= 70 Mpc/h) the richness and length of quasar systems are similar to those derived from random catalogues. Quasar system diameters are similar to the sizes of rich superclusters and supercluster chains in the local Universe. At the linking length 70 Mpc/h the richest systems of quasars have diameters exceeding 500 Mpc/h. The percolating system which penetrate the whole sample volume appears in quasar sample at smaller linking length than in random samples (85 Mpc/h). Quasar luminosities in systems are not correlated with the system richness. Quasar system catalogues at our web pages http://www.aai.ee/~maret/QSOsystems.html serve as a database to search for superclusters of galaxies and to trace the cosmic web at high redshifts.Comment: 10 pages, 8 figures, accepted for publication in Astronomy and Astrophysic

Infalling groups and galaxy transformations in the cluster A2142

We study galaxy populations and search for possible merging substructures in the rich galaxy cluster A2142. Normal mixture modelling revealed in A2142 several infalling galaxy groups and subclusters. The projected phase space diagram was used to analyse the dynamics of the cluster and study the distribution of various galaxy populations in the cluster and subclusters. The cluster, supercluster, BCGs, and one infalling subcluster are aligned. Their orientation is correlated with the alignment of the radio and X-ray haloes of the cluster. Galaxies in the centre of the main cluster at the clustercentric distances $0.5~h^{-1}Mpc$ have older stellar populations (with the median age of $10 - 11$~Gyrs) than galaxies at larger clustercentric distances. Star-forming and recently quenched galaxies are located mostly in the infall region at the clustercentric distances $D_{\mathrm{c}} \approx 1.8~h^{-1}Mpc$, where the median age of stellar populations of galaxies is about $2$~Gyrs. Galaxies in A2142 have higher stellar masses, lower star formation rates, and redder colours than galaxies in other rich groups. The total mass in infalling groups and subclusters is $M \approx 6\times10^{14}h^{-1}M_\odot$, approximately half of the mass of the cluster, sufficient for the mass growth of the cluster from redshift $z = 0.5$ (half-mass epoch) to the present. The cluster A2142 may have formed as a result of past and present mergers and infallen groups, predominantly along the supercluster axis. Mergers cause complex radio and X-ray structure of the cluster and affect the properties of galaxies in the cluster, especially in the infall region. Explaining the differences between galaxy populations, mass, and richness of A2142, and other groups and clusters may lead to better insight about the formation and evolution of rich galaxy clusters.Comment: 16 pages, 13 figures, A&A, in pres