Percolation Analysis of a Wiener Reconstruction of the IRAS 1.2 Jy Redshift Catalog

We present percolation analyses of Wiener Reconstructions of the IRAS 1.2 Jy Redshift Survey. There are ten reconstructions of galaxy density fields in real space spanning the range $\beta= 0.1$ to $1.0$, where ${\beta}={\Omega^{0.6}}/b$, $\Omega$ is the present dimensionless density and $b$ is the bias factor. Our method uses the growth of the largest cluster statistic to characterize the topology of a density field, where Gaussian randomized versions of the reconstructions are used as standards for analysis. For the reconstruction volume of radius, $R {\approx} 100 h^{-1}$ Mpc, percolation analysis reveals a slight `meatball' topology for the real space, galaxy distribution of the IRAS survey. cosmology-galaxies:clustering-methods:numericalComment: Revised version accepted for publication in The Astrophysical Journal, January 10, 1997 issue, Vol.47

The Evolution of Voids in the Adhesion Approximation

We apply the adhesion approximation to study the formation and evolution of voids in the Universe. Our simulations -- carried out using 128$^3$ particles in a cubical box with side 128 Mpc -- indicate that the void spectrum evolves with time and that the mean void size in the standard COBE-normalised Cold Dark Matter (hereafter CDM) model with $h_{50} = 1,$ scales approximately as $\bar D(z) = {\bar D_0\over \sqrt {1+z}},$ where $\bar D_0 \simeq 10.5$ Mpc. Interestingly, we find a strong correlation between the sizes of voids and the value of the primordial gravitational potential at void centers. This observation could in principle, pave the way towards reconstructing the form of the primordial potential from a knowledge of the observed void spectrum. Studying the void spectrum at different cosmological epochs, for spectra with a built in $k$-space cutoff we find that, the number of voids in a representative volume evolves with time. The mean number of voids first increases until a maximum value is reached (indicating that the formation of cellular structure is complete), and then begins to decrease as clumps and filaments merge leading to hierarchical clustering and the subsequent elimination of small voids. The cosmological epoch characterizing the completion of cellular structure occurs when the length scale going nonlinear approaches the mean distance between peaks of the gravitational potential. A central result of this paper is thatComment: Plain TeX, 38 pages Plus 16 Figures (available on request from the first author), IUCAA-28 To appear in The Astrophysical Journal, July 199

A Test of the Adhesion Approximation for Gravitational Clustering

We quantitatively compare a particle implementation of the adhesion approximation to fully non--linear, numerical nbody simulations. Our primary tool, cross--correlation of nbody simulations with the adhesion approximation, indicates good agreement, better than that found by the same test performed with the Zel'dovich approximation (hereafter ZA). However, the cross--correlation is not as good as that of the truncated Zel'dovich approximation (TZA), obtained by applying the Zel'dovich approximation after smoothing the initial density field with a Gaussian filter. We confirm that the adhesion approximation produces an excessively filamentary distribution. Relative to the nbody results, we also find that: (a) the power spectrum obtained from the adhesion approximation is more accurate than that from ZA or TZA, (b) the error in the phase angle of Fourier components is worse than that from TZA, and (c) the mass distribution function is more accurate than that from ZA or TZA. It appears that adhesion performs well statistically, but that TZA is more accurate dynamically, in the sense of moving mass to the right place. Subject Heading: Galaxies, formation, clustering--large--scale structure of the UniverseComment: TeX, 7 pages excluding figures (contact [email protected]). submitted to Ap

Probing Large Scale Structure using Percolation and Genus Curves

We study topological properties of large scale structure in a set of scale free N-body simulations using the genus and percolation curves as topological characteristics. Our results show that as gravitational clustering advances, the density field shows an increasingly pronounced departure from Gaussianity reflected in the changing shape of the percolation curve and the changing amplitude and shape of the genus curve. Both genus and percolation curves differentiate between the connectedness of overdense and underdense regions if plotted against the density. When plotted against the filling factor the percolation curve alone retains this property. The genus curve shows a pronounced decrease in amplitude caused by phase correlations in the non-linear regime. Both genus and percolation curves provide complementary probes of large scale structure topology and can be used to discriminate between models of structure formation and the analysis of observational data such as galaxy catalogs and MBR maps.Comment: 8 pages (latex, aaspp) + 4 postscript figures. To appear in, Ap J Let

Detection of Network Structure in the Las Campanas Redshift Survey

We employ a percolation technique developed for pointwise distributions to analyze two-dimensional projections of the three northern and three southern slices in the Las Campanas Redshift Survey. One of the goals of this paper is to compare the visual impressions of the structure within distributions with objective statistical analysis. We track the growth of the largest cluster as an indicator of the network structure. We restrict our analysis to volume limited subsamples in the regions from 200 to 400 $h^{-1}$ Mpc where the number density of galaxies is the highest. As a major result, we report a measurement of an unambiguous signal, with high signal-to-noise ratio (at least at the level of a few $\sigma$), indicating significant connectivity of the galaxy distribution which in two dimensions is indicative of a filamentary distribution. This is in general agreement with the visual impression and typical for the standard theory of the large-scale structure formation based on gravitational instability of initially Gaussian density fluctuations

Behaviour of Lagrangian Approximations in Spherical Voids

We study the behaviour of spherical Voids in Lagrangian perturbation theories L(n), of which the Zel'dovich approximation is the lowest order solution L(1). We find that at early times higher order L(n) give an increasingly accurate picture of Void expansion. However at late times particle trajectories in L(2) begin to turnaround and converge leading to the {\em contraction} of a Void, a sign of pathological behaviour. By contrast particle trajectories in L(3) are well behaved and this approximation gives results in excellent agreement with the exact top-hat solution as long as the Void is not too underdense. For very underdense Voids, L(3) evacuates the Void much too rapidly leading us to conclude that the Zel'dovich approximation L(1), remains the best approximation to apply to the late time study of Voids. The behavior of high order approximations in spherical voids is typical for asymptotic series and may be generic for Lagrangian perturbation theory.Comment: 6 pages, latex, two figures. Better quality figures are available upon request from [email protected]

Evidence for Filamentarity in the Las Campanas Redshift Survey

We apply Shapefinders, statistical measures of `shape' constructed from two dimensional partial Minkowski functionals, to study the degree of filamentarity in the Las Campanas Redshift Survey (LCRS). In two dimensions, three Minkowski functionals characterise the morphology of an object, they are: its perimeter (L), area (S), and genus. Out of L and S a single dimensionless Shapefinder Statistic, F can be constructed (0 <=F <=1). F acquires extreme values on a circle (F = 0) and a filament (F = 1). Using F, we quantify the extent of filamentarity in the LCRS by comparing our results with a Poisson distribution with similar geometrical properties and having the same selection function as the survey. Our results unambiguously demonstrate that the LCRS displays a high degree of filamentarity both in the Northern and Southern galactic sections a result that is in general agreement with the visual appearance of the catalogue. It is well known that gravitational clustering from Gaussian initial conditions gives rise to the development of non-Gaussianity reflected in the formation of a network-like filamentary structure on supercluster scales. Consequently the fact that the smoothed LCRS catalogue shows properties consistent with those of a Gaussian random field (Colley 1997) whereas the unsmoothed catalogue demonstrates the presence of filamentarity lends strong support to the conjecture that the large scale clustering of galaxies is driven by gravitational instability.Comment: Accepted for publication in Ap

Disentangling the Cosmic Web I: Morphology of Isodensity Contours

We apply Minkowski functionals and various derived measures to decipher the morphological properties of large-scale structure seen in simulations of gravitational evolution. Minkowski functionals of isodensity contours serve as tools to test global properties of the density field. Furthermore, we identify coherent objects at various threshold levels and calculate their partial Minkowski functionals. We propose a set of two derived dimensionless quantities, planarity and filamentarity, which reduce the morphological information in a simple and intuitive way. Several simulations of the gravitational evolution of initial power-law spectra provide a framework for systematic tests of our method.Comment: 26 pages including 12 figures. Accepted for publication in Ap