arXiv subjects

Sergei F. Shandarin

Publications and source records attributed to Sergei F. Shandarin.

44 records · Page 3Linked to original sources

arXiv1997

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 Mpc/h 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 $σ$), 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.

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arXiv1996

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 $β= 0.1$ to $1.0$, where $β={Ω^{0.6}}/b$, $Ω$ 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:numerical

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arXiv1996

Modeling Gravitational Clustering without Computing Gravitational Force

The large-scale structure in the Universe is believed to arise out of small random density perturbations generated in the very early Universe, that are amplified by gravity. Large and usually intricate N-body simulations are typically employed to model the complex nonlinear dynamics in a self gravitating medium. We suggest a very simple model which predicts, on large scales, the correct density and velocity distributions. The model does not involve an explicit computation of the gravitational force. It is based on a simple transformation of the variables and local conservation laws of mass and {\it generalized} linear momentum. The model demonstrates that the overall appearance of large-scale structure in the Universe is explicitly determined by the initial velocity field and it reveals the most significant large-scale effects of gravity on the formation of structure.

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arXiv1995

Three-dimensional Burgers' Equation as a Model for the Large-Scale Structure Formation in the Universe

As galaxy redshift surveys probe deeper into the universe, they uncover ever more dramatic structures in the large-scale distribution of galaxies. In particular, the CfA2 and SSRS2 surveys to an apparent magnitude limit of 15.5 exhibit an impressive complex of sheets, filaments, and clusters. The formation of the large-scale structure in the universe results from the gravitational amplification of the primordial small perturbations of density. The primordial density perturbations, as quantum fluctuations at the very early stage, may reveal important information about the early universe and the laws of fundamental physics. One of the major obstacles to understanding the formation of the large-scale structure is the complexity of the evolution of the density inhomogeneities at the nonlinear stage when the observable structures form. One way of addressing this problem is to run three-dimensional numerical simulations. Here we review another approach based on the approximate analytic model of the nonlinear gravitational instability utilizing Burgers' equation of the nonlinear diffusion.

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arXiv1995

Universality of the Network and Bubble Topology in Cosmological Gravitational Simulations

Using percolation statistics we, for the first time, demonstrate the universal character of a network pattern in the real space, mass distributions resulting from nonlinear gravitational instability of initial Gaussian fluctuations. Percolation analysis of five stages of the nonlinear evolution of five power law models reveals that all models show a shift toward a network topology if seen with high enough resolution. However, quantitatively, the shift is significantly different in different models: the smaller the spectral index ,n, the stronger the shift. On the contrary, the shift toward the "bubble" topology is characteristic only for the n <= -1 models. We find that the mean density of the percolating structures in the nonlinear density distributions generally is very different from the density threshold used to identify them and corresponds much better to a visual impression. We also find that the maximum of the number of structures (connected regions above or below a specified density threshold) in the evolved, nonlinear distributions is always smaller than in Gaussian fields with the same spectrum, and is determined by the effective slope at the cutoff frequency.

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arXiv1995

Topology of the Galaxy Distribution

The history and the major results of the study of the topology of the large-scale structure are briefly reviewed. Two techniques based on percolation theory and the genus curve are discussed. The preliminary results of the percolation analysis of the Wiener reconstruction of the IRAS $1.2 Jy$ redshift catalog are reported.

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arXiv1994

Biased Power Spectrum and Bispectrum for an Ensemble of Three-Dimensional Scale Free Numerical Simulations

We examine the effect of a threshold bias on the power spectrum and the bispectrum in an ensemble of numerical simulations (Gaussian initial perturbations with power law spectra P(k) \sim k^n, n=+1, 0, -1, -2) and compare our results with theoretical predictions. Our simulations are evolved sufficiently that on the scale where we apply the threshold the rms fluctuation has developed significantly into the nonlinear regime. Thus, predictions based on perturbation theory do not necessarily apply. Nevertheless, we find our results for the power spectrum, biased power simply amplified by a numerical factor, follow predicted trends, far beyond the regime where perturbation theory is expected to be valid. We find that the biased bispectrum continues to follow the so-called hierarchical form, with reduced three-point amplitude Q \approx 1 in the strongly nonlinear regime, independent of initial spectrum. In the quasi-linear perturbative regime the three-point amplitude depends on configuration shape, a behavior that is found to give useful information about the amount of bias without information about the unbiased matter distribution.

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arXiv1994

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 that

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