The cluster distribution as a test of dark matter models - IV. Topology and geometry

Abstract

We study the geometry and topology of the large-scale structure traced by galaxy clusters in numerical simulations of a box of side 320 h −1 Mpc, and compare them with available data on real clusters. The simulations we use are generated by the Zel'dovich approximation, using the same methods as we have used in the first three papers in this series. We consider the following models to see if there are measurable differences in the topology and geometry of the superclustering they produce: (i) the standard CDM model (SCDM); (ii) a CDM model with Ω 0 = 0.2 (OCDM); (iii) a CDM model with a 'tilted' power spectrum having n = 0.7 (TCDM); (iv) a CDM model with a very low Hubble constant, h = 0.3 (LOWH); (v) a model with mixed CDM and HDM (CHDM); (vi) a flat low-density CDM model with Ω 0 = 0.2 and a non-zero cosmological Λ term (ΛCDM). We analyse these models using a variety of statistical tests based on the analysis of: (i) the Euler-Poincaré characteristic; (ii) percolation properties; (iii) the Minimal Spanning Tree construction. Taking all these tests together we find that the best fitting model is ΛCDM and, indeed, the others do not appear to be consistent with the data. Our results demonstrate that despite their biased and extremely sparse sampling of the cosmological density field, it is possible to use clusters to probe subtle statistical diagnostics of models which go far beyond the low-order correlation functions usually applied to study superclustering.

The size distribution of void filaments in a ΛCDM cosmology

“…In most of the previous works, where the large‐scale filaments were the targets to find by means of the MST technique, the values of p and l c were empirically determined as p = 9 or 10 (Barrow et al 1985; Bhavsar & Ling 1988a,b) and (Barrow, Bhavsar & Sonoda 1985; Bhavsar & Ling 1988b; Plionis, Valdarnini & Jing 1992; Pearson & Coles 1995; Krzewina & Saslaw 1996; Coles et al 1998) where is the mean edge length of the unreduced tree. And there were some authors who preferred or (Bhavsar & Ling 1988a; Zucca et al 1991).…”

Perturbative Analysis of Adaptive Smoothing Methods in Quantifying Large‐Scale Structure

“…But the genus density for contours around the mean density d D 0 would be positive as they would look like a highly connected spongelike structure (Gott, Melott, & Dickinson 1986). The genus density as a function of the matter density threshold is called the genus statistics and has been widely investigated both numerically and observationally Melott, Weinberg, & Gott 1988 ;Gott et al 1989 ;Park & Gott 1991 ;Park, Gott, & da Costa 1992 ;Weinberg & Cole 1992 ;Moore et al 1992 ;Vogeley et al 1994 ;Rhoads, Gott, & Postman 1994 ;Matsubara & Suto 1996 ;Coles, Davies, & Pearson 1996 ;Sahni, Sathyprakash, & Shandarin 1997 ;Protogeros & Weinberg 1997 ;Coles et al 1998 ;Canavezes et al 1998 ;Springel et al 1998). …”

ARGO Cosmic Microwave Background Anisotropy Measurement Constraints on Open and Flat‐Λ Cold Dark Matter Cosmogonies

“…These low density models are consistent with most current observational constraints. For discussions see Coles et al (1998), Bartelmann et al (1998), Jenkins et al (1998), Park et al (1998), Merchán et al (1998), Cole et al (1998), Cavaliere, Menci, &Tozzi (1998), andSomerville &Primack (1998).…”