Percolation Analysis of a Wiener Reconstruction of the<i>IRAS</i>1.2 Jy Redshift Catalog

Yess, Capp; Shandarin, Sergei F.; Fisher, Karl B.

doi:10.1086/303496

Cited by 13 publications

(12 citation statements)

References 30 publications

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“…Very recently the catalogue has also been examined with topological methods. Yess, Shandarin & Fisher (1997) Our approach is similar to that of the latter authors. We also work with mock catalogues to derive the statistical properties of the genus statistics.…”

Section: The 12-jy Redshift Survey Datamentioning

confidence: 78%

Genus statistics of the Virgo N-body simulations and the 1.2-Jy redshift survey

Springel

White

Colberg

et al. 1998

Monthly Notices RAS

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A B S T R A C TWe study the topology of the Virgo N-body simulations and compare it with the 1.2-Jy redshift survey of IRAS galaxies by means of the genus statistic. Four high-resolution simulations of variants of the CDM cosmology are considered: a flat standard model (SCDM), a variant of it with higher large-scale power ( tCDM), and two low-density universes, one open (OCDM, Q 0 ¼ 0:3) and one flat (LCDM, Q 0 ¼ 0:3, L ¼ 0:7). In all cases, the initial fluctuation amplitudes are chosen so that the simulations approximately reproduce the observed abundance of rich clusters of galaxies at the present day. The fully sampled N-body simulations are examined down to strongly non-linear scales, both with spatially fixed smoothing and with an adaptive smoothing technique. While the tCDM, LCDM and OCDM simulations have very similar genus statistics in the regime accessible to fixed smoothing, they can be separated with adaptive smoothing at small mass scales. In order to compare the N-body models with the 1.2-Jy survey, we extract large ensembles of mock catalogues from the simulations. These mock surveys are used to test for various systematic effects in the genus analysis and to establish the distribution of errors of the genus curve. We find that a simple multivariate analysis of the genus measurements is compromised both by non-Gaussian distributed errors and by noise that dominates the covariance matrix. We therefore introduce a principal components analysis of the genus curve. With a likelihood ratio test we find that the 1.2-Jy data favour the LCDM, tCDM and OCDM models compared with SCDM. When genus measurements for different smoothing scales are combined, the SCDM model can be excluded at a 99 per cent confidence level, while the other three models fit the 1.2-Jy data well. These results are unlikely to be significantly modified if galaxies are biased tracers of the mass, provided that biasing preserves a monotonic relation between galaxy density and mass density. Figure 17. Genus curves of the 1.2-Jy redshift survey of IRAS galaxies. The left column shows high-resolution genus curves obtained with fixed smoothing, while the middle and right columns give the results for the two adaptive smoothing schemes. In each row the same smoothing scale is considered, rising from 5 h ¹1 Mpc to 20 h ¹1 Mpc. Note however that the vertical scale is different for individual panels. The adaptively smoothed genus curves exhibit a considerably higher genus amplitude. The dashed lines are random-phase genus curves with amplitudes determined from the first principal component of the measured genus curves. In the case of adaptive smoothing, l sets the mass per smoothing volume via equation (20).

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Section: The 12-jy Redshift Survey Datamentioning

confidence: 78%

Genus statistics of the Virgo N-body simulations and the 1.2-Jy redshift survey

Springel

White

Colberg

et al. 1998

Monthly Notices RAS

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“…Percolation analysis gives similar results for Gaussian distributions but significantly differs from the genus statistic for the nonGaussian distributions (Sahni, Sathyaprakash & Shandarin 1997). In studies of geometry and topology, the major limiting factors were the shot noise in the analysis of pointwise distributions, or resolution in the analysis of density fields derived from galaxy positions (Yess, Shandarin & Fisher 1997) and the small size of the survey. The relatively high galaxy number density in the Las Campanas Redshift Survey (LCRS) reduces the discreteness effects.…”

Section: Introductionmentioning

confidence: 99%

Detection of Network Structure in the Las Campanas Redshift Survey

Shandarin

Yess

1998

ApJ

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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 $\sigma$), 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.Comment: The main body of the text (17 pages) is followed by the captions file plus 4 postscript figures. Submitted to Ap

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“…Thus, the percolation transition presents a natural threshold at which to study the shapes of individual clusters (Sathyaprakash, Sahni & Shandarin 1996 and in our study we shall employ this threshold to study clusters in the IRAS survey. (A comprehensive analysis of the IRAS 1.2Jy redshift survey using percolation theory was carried out in Yess, Shandarin & Fisher (1997). )…”

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confidence: 99%

“…1 we only show clusters having volume larger than 8 grid cells, consequently, the randomized catalogue is seen to contain fewer large clusters than the IRAS catalogue, even though the total number of clusters in both catalogues is roughly the same. (Details of Gaussian randomisation of the IRAS density field can be found in Yess, Shandarin & Fisher 1997. ) In Fig.…”

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confidence: 99%

Filaments and Pancakes in the [ITAL]IRAS[/ITAL] 1.2 J[CLC]y[/CLC] Redshift Catalog

Sathyaprakash¹,

Sahni²,

Shandarin³

et al. 1998

The Astrophysical Journal

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We explore shapes of clusters and superclusters in the IRAS 1.2Jy redshift survey with three reconstructions spanning the range β = 0.1, 0.5, 1.0, where β = Ω 0.6 /b, b is the bias factor and Ω the present value of the dimensionless matter density. Comparing our results to Gaussian randomized reconstructions of the IRAS catalogue, we find structures having both planar and filamentary properties. For β = 0.5, 1.0 the largest structures in the survey have a distinct tendency to be filament-like in general agreement with the results of N-body simulations.

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Percolation Analysis of a Wiener Reconstruction of theIRAS1.2 Jy Redshift Catalog

Cited by 13 publications

References 30 publications

Genus statistics of the Virgo N-body simulations and the 1.2-Jy redshift survey

Genus statistics of the Virgo N-body simulations and the 1.2-Jy redshift survey

Detection of Network Structure in the Las Campanas Redshift Survey

Filaments and Pancakes in the [ITAL]IRAS[/ITAL] 1.2 J[CLC]y[/CLC] Redshift Catalog

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