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Register a new userExtended percolation analysis of the cosmic web
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Aims. We develop an extended percolation method to allow the comparison of geometrical properties of the real cosmic web with the simulated dark matter web for an ensemble of over- and under-density systems. Methods. We scan density fields of dark matter (DM) model and SDSS observational samples, and find connected over- and underdensity regions in a large range of threshold densities. Lengths, filling factors and numbers of largest clusters and voids as functions of the threshold density are used as percolation functions. Results. We find that percolation functions of DM models of different box sizes are very similar to each other. This stability suggests that properties of the cosmic web, as found in the present paper, can be applied to the cosmic web as a whole. Percolation functions depend strongly on the smoothing length. At smoothing length 1 $h^{-1}$ Mpc the percolation threshold density for clusters is $log P_C = 0.718 pm 0.014$, and for voids is $log P_V = -0.816 pm 0.015$, very different from percolation thresholds for random samples, $log P_0 = 0.00 pm 0.02$. Conclusions. The extended percolation analysis is a versatile method to study various geometrical properties of the cosmic web in a wide range of parameters. Percolation functions of the SDSS sample are very different from percolation functions of DM model samples. The SDSS sample has only one large percolating void which fills almost the whole volume. The SDSS sample contains numerous small isolated clusters at low threshold densities, instead of one single percolating DM cluster. These differences are due to the tenuous dark matter web, present in model samples, but absent in real observational samples.
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The $beta$-skeleton is a mathematical method to construct graphs from a set of points that has been widely applied in the areas of image analysis, machine learning, visual perception, and pattern recognition. In this work, we apply the $beta$-skeleton to study the cosmic web. We use this tool on observed and simulated data to identify the filamentary structures and characterize the statistical properties of the skeleton. In particular, we compare the $beta$-skeletons built from SDSS-III galaxies to those obtained from MD-PATCHY mocks, and also to mocks directly built from the Big MultiDark $N$-body simulation. We find that the $beta$-skeleton is able to reveal the underlying structures in observed and simulated samples without any parameter fine-tuning. A different degree of sparseness can be obtained by adjusting the value of $beta$; in addition, the statistical properties of the length and direction of the skeleton connections show a clear dependence on redshift space distortions (RSDs), cosmological effects and galaxy bias. We also find that the $N$-body simulation accurately reproduces the RSD effect in the data, while the MD-PATCHY mocks appear to underestimate its magnitude. Our proof-of-concept study shows that the statistical properties of the $beta$-skeleton can be used to probe cosmological parameters and galaxy evolution.
According to the modern cosmological paradigm galaxies and galaxy systems form from tiny density perturbations generated during the very early phase of the evolution of the Universe. Using numerical simulations we study the evolution of phases of density perturbations of different scales to understand the formation and evolution of the cosmic web. We apply the wavelet analysis to follow the evolution of high-density regions (clusters and superclusters) of the cosmic web. We show that the positions of maxima and minima of density waves (their spatial phases) almost do not change during the evolution of the structure. Positions of extrema of density perturbations are the more stable, the larger is the wavelength of perturbations. Combining observational and simulation data we conclude that the skeleton of the cosmic web was present already in an early stage of structure evolution.
We investigate the ability of three reconstruction techniques to analyze and investigate weblike features and geometries in a discrete distribution of objects. The three methods are the linear Delaunay Tessellation Field Estimator (DTFE), its higher order equivalent Natural Neighbour Field Estimator (NNFE) and a version of Kriging interpolation adapted to the specific circumstances encountered in galaxy redshift surveys, the Natural Lognormal Kriging technique. DTFE and NNFE are based on the local geometry defined by the Voronoi and Delaunay tessellations of the galaxy distribution. The three reconstruction methods are analysed and compared using mock magnitude-limited and volume-limited SDSS redshift surveys, obtained on the basis of the Millennium simulation. We investigate error trends, biases and the topological structure of the resulting fields, concentrating on the void population identified by the Watershed Void Finder. Environmental effects are addressed by evaluating the density fields on a range of Gaussian filter scales. Comparison with the void population in the original simulation yields the fraction of false void mergers and false void splits. In most tests DTFE, NNFE and Kriging have largely similar density and topology error behaviour. Cosmetically, higher order NNFE and Kriging methods produce more visually appealing reconstructions. Quantitatively, however, DTFE performs better, even while computationally far less demanding. A successful recovery of the void population on small scales appears to be difficult, while the void recovery rate improves significantly on scales > 3 h-1Mpc. A study of small scale voids and the void galaxy population should therefore be restricted to the local Universe, out to at most 100 h-1Mpc.
The cosmic web is the largest scale manifestation of the anisotropic gravitational collapse of matter. It represents the transitional stage between linear and non-linear structures and contains easily accessible information about the early phases of structure formation processes. Here we investigate the characteristics and the time evolution of morphological components since. Our analysis involves the application of the NEXUS Multiscale Morphology Filter (MMF) technique, predominantly its NEXUS+ version, to high resolution and large volume cosmological simulations. We quantify the cosmic web components in terms of their mass and volume content, their density distribution and halo populations. We employ new analysis techniques to determine the spatial extent of filaments and sheets, like their total length and local width. This analysis identifies cluster and filaments as the most prominent components of the web. In contrast, while voids and sheets take most of the volume, they correspond to underdense environments and are devoid of group-sized and more massive haloes. At early times the cosmos is dominated by tenuous filaments and sheets, which, during subsequent evolution, merge together, such that the present day web is dominated by fewer, but much more massive, structures. The analysis of the mass transport between environments clearly shows how matter flows from voids into walls, and then via filaments into cluster regions, which form the nodes of the cosmic web. We also study the properties of individual filamentary branches, to find long, almost straight, filaments extending to distances larger than 100Mpc/h. These constitute the bridges between massive clusters, which seem to form along approximatively straight lines.
We investigate the characteristics and the time evolution of the cosmic web from redshift, z=2, to present time, within the framework of the NEXUS+ algorithm. This necessitates the introduction of new analysis tools optimally suited to describe the very intricate and hierarchical pattern that is the cosmic web. In particular, we characterize filaments (walls) in terms of their linear (surface) mass density. This is very good in capturing the evolution of these structures. At early times the cosmos is dominated by tenuous filaments and sheets, which, during subsequent evolution, merge together, such that the present day web is dominated by fewer, but much more massive, structures. We also show that voids are more naturally described in terms of their boundaries and not their centres. We illustrate this for void density profiles, which, when expressed as a function of the distance from void boundary, show a universal profile in good qualitative agreement with the theoretical shell-crossing framework of expanding underdense regions.
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