Morphology of the supercluster–void network in ΛCDM cosmology

Mon. Not. R. Astron. Soc. 353, 162–178 (2004) doi:10.1111/j.1365-2966.2004.08060.x Morphology of the supercluster–void network in ΛCDM cosmology Sergei F. Shandarin,1
Jatush V. Sheth2
and Varun Sahni2
1 Department of Physics and Astronomy, University of Kansas, KS 66045, USA Centre for Astronomy and Astrophysics, Pune, India 2 Inter-University Accepted 2004 May 21. Received 2004 May 14; in original form 2003 December 5 We report here the first systematic study of the supercluster–void network in the CDM concordance cosmology in which voids and superclusters are treated on an equal footing. We study the dark matter density field in real space smoothed on a scale of 5 h −1 Mpc. Superclusters are defined as individual members of an overdense excursion set, and voids are defined as individual members of a complementary underdense excursion set at the same density threshold. We determine the geometric, topological and morphological properties of the cosmic web at a large set of density levels by computing Minkowski functionals for every supercluster and void using SURFGEN (described recently by Sheth et al.). The properties of the largest (percolating) supercluster and the complementary void are found to be very different from those of the individual superclusters and voids. In total, the individual superclusters occupy no more than about 5 per cent of the volume and contain no more than 20 per cent of the mass if the largest supercluster is excluded. Likewise, in total, individual voids occupy no more than 14 per cent of the volume and contain no more than 4 per cent of the mass if the largest void is excluded. Although superclusters are more massive and voids are more voluminous, the difference in maximum volumes is no greater than an order of magnitude. The genus value of individual superclusters can be ∼5, while the genus of individual voids can reach ∼50, implying a significant amount of substructure in superclusters and especially in voids. One of our main results is that large voids, as defined through the dark matter density field in real space, are distinctly non-spherical. Key words: methods: numerical – galaxies: statistics – cosmology: theory – large-scale structure of Universe. 1 INTRODUCTION One of the great observational discoveries of recent times is the realization that we live on a ‘cosmic web’ that is embedded in an accelerating Universe. Evidence for the cosmic web goes back to the late 1970s when the first redshift surveys revealed the existence of superclusters and voids on scales
20 h −1 Mpc (Gregory & Thompson 1978; Einasto, Joeveer & Saar 1980; Zel’dovich, Einasto & Shandarin 1982; Einasto et al. 1984). The discovery by Kirshner et al. (1981) of a large empty region in Boötes having a diameter of 50 h −1 Mpc focused dramatically on the importance of voids in the Universe. Perhaps the first really convincing demonstration of the ubiquity of voids and superclusters and of the existence of a supercluster–void network resembling a cosmic web was given in de Lapparent, Geller & Huchra (1986), which was soon followed by data from the Southern Sky Redshift Survey (da Costa et al.
E-mail: (VS) (SFS); (JVS); 1988, 1994). These results have been borne out by more recent studies (Colless et al. 2003; Tegmark et al. 2004), which convincingly demonstrate that the supercluster–void distribution in the Universe is ‘foam-like’ and has tantalizing geometrical and topological characteristics. Since the 1970s, theory, N-body simulations and, most importantly, galaxy redshift surveys have strongly suggested that the components of the supercluster–void network (or ‘cosmic web’) can be roughly divided into three classes: compact quasi-spherical or slightly elliptical structures like Abell clusters; long filaments like the famous ‘bridge’ connecting the Coma cluster and A1367 (Gregory & Thompson 1978); and voids. There have also been claims that pancake-like concentrations of galaxies have been observed (Fairall 1998; Martinez & Saar 2001). From the theoretical side, the fact that gravitational instability is going to function ‘anisotropically’ giving rise to pancake-like and filamentary features was first discussed in the works of Zel’dovich and collaborators, first within the context of the Zel’dovich approximation (Zel’dovich 1970, 1982; Arnol’d, Shandarin & Zel’dovich 1982; Zel’dovich et al. 1982; Shandarin & Zeldovich 1983) and later extended to  C 2004 RAS ABSTRACT Supercluster–void network in CDM cosmology 1 In addition, voids have frequently been claimed to have quasi-spherical or slightly elliptical shapes. One might add a cautionary note at this point since many of these claims were based on visual impressions and the statistics used in the studies of voids often tacitly assumed that voids are either spherical or close to being spherical, thereby precluding any other possibility.  C 2004 RAS, MNRAS 353, 162–178 natural thresholds associated with percolation in overdense and underdense excursion sets. The sizes of individual superclusters and voids change dramatically at the corresponding percolation thresholds revealing the largest scales characterizing the cosmic web. Concretely, we study the large-scale structure of the Universe by considering the geometry and topology of isodensity surfaces δ(x) ≡ δρ(x)/ρ̄ = constant. At a given threshold, δ th , regions having higher than threshold density (δ > δ th ) will be called ‘superclusters’, while regions with δ < δ th will be called ‘voids’. Thus, we define superclusters and voids as overdense and underdense connected regions bounded by one (or several) surfaces of constant density. This definition broadly corresponds to other definitions of superclusters and voids used in the literature but differs in detail. Apart from obvious differences with superclusters and voids of galaxies in redshift space, our approach specifies neither a particular density threshold nor the shapes of the structures. Despite these differences we call the objects of our study superclusters and voids mainly because they are non-linear structures having sizes, volumes and masses roughly corresponding to superclusters and voids of galaxies. We study superclusters and voids at a large number of density thresholds and construct the isodensity surfaces at every threshold to best accuracy. In contrast to many studies (see e.g. Blumenthal et al. 1992; Goldberg & Vogeley 2004), we do not ‘cook up’ voids or superclusters with predefined shapes but instead isolate individual objects from the dark matter density field (obtained from N-body simulations) by constructing isodensity surfaces. Apart from uniformly smoothing the density field with a Gaussian filter, we do not introduce any factors that may affect the shapes or substructure in superclusters and voids of the cosmic density field. Filtering the density field obviously erases some small-scale features but it certainly does not introduce any new structures. (...truncated)