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Mysterious dark matter constitutes about 85 per cent of all masses in the Universe. Clustering of dark matter plays a dominant role in the formation of all observed structures on scales from a fraction to a few hundreds of Mega-parsecs. Galaxies play a role of lights illuminating these structures so they can be observed. The observations in the last several decades have unveiled opulent geometry of these structures currently known as the cosmic web. Haloes are the highest concentrations of dark matter and host luminous galaxies. Currently the most accurate modelling of dark matter haloes is achieved in cosmological N-body simulations. Identifying the haloes from the distribution of particles in N-body simulations is one of the problems attracting both considerable interest and efforts. We propose a novel framework for detecting potential dark matter haloes using the field unique for dark matter-multistream field. The multistream field emerges at the non-linear stage of the growth of perturbations because the dark matter is collisionless. Counting the number of velocity streams in gravitational collapses supplements our knowledge of spatial clustering. We assume that the virialized haloes have convex boundaries. Closed and convex regions of the multistream field are hence isolated by imposing a positivity condition on all three eigenvalues of the Hessian estimated on the smoothed multistream field. In a single-scale analysis of high multistream field resolution and low softening length, the halo substructures with local multistream maxima are isolated as individual halo sites. [ABSTRACT FROM AUTHOR]

Topological connections in the single-streaming voids and multistreaming filaments and walls reveal a cosmic web structure different from traditional mass density fields. A single void structure not only percolates the multistream field in all the directions, but also occupies over 99 per cent of all the single-streaming regions. Sub-grid analyses on scales smaller than simulation resolution reveal tiny pockets of voids that are isolated by membranes of the structure. For the multistreaming excursion sets, the percolating structure is significantly thinner than the filaments in overdensity excursion approach. Hessian eigenvalues of the multistream field are used as local geometrical indicators of dark matter structures. Single-streaming regions have most of the zero eigenvalues. Parameter-free conditions on the eigenvalues in the multistream region may be used to delineate primitive geometries with concavities corresponding to filaments, walls and haloes. [ABSTRACT FROM AUTHOR]

We report the results of the first study of the multi-stream environment of dark matter haloes in cosmological N-body simulations in the A cold dark matter cosmology. The full dynamical state of dark matter can be described as a three-dimensional sub-manifold in six-dimensional phase space - the dark matter sheet. In our study we use a Lagrangian sub-manifold x = x (q,t) (where x and q are comoving Eulerian and Lagrangian coordinates, respectively), which is dynamically equivalent to the dark matter sheet but is more convenient for numerical analysis. Our major results can be summarized as follows. At the resolution of the simulation, i.e. without additional smoothing, the cosmic web represents a hierarchical structure: each halo is embedded in the filamentary framework of the web predominantly at the filament crossings, and each filament is embedded in the wall-like fabric of the web at the wall crossings. Locally, each halo or sub-halo is a peak in the number of streams field. The number of streams in the neighbouring filaments is higher than in the neighbouring walls. The walls are regions where number of streams is equal to three or a few. Voids are uniquely defined by the local condition requiring to be a single-stream flow region. The shells of streams around haloes are quite thin and the closest void region is typically within one and a half friends-of-friends radius from the centre of the halo. [ABSTRACT FROM AUTHOR]

Modeling and understanding the structure of the universe is one the most interesting problems in modern cosmology. It is also an extremely difficult problem. Despite spectacular achievements in observations and computational capabilities at present there is no comprehensive theory of the structure formation. There are successful theoretical models however most of them rely on assumptions and various fits which are not fully physically justified. The Zeldovich Approximation is a rare exception. Suggested more than forty years ago it remains one of the most successful and profound analytic models of structure formation. Some of results stemmed from the Zeldovich Approximation will be briefly reviewed. [ABSTRACT FROM PUBLISHER]

We have made a comparative study of morphological evolution in simulated dark matter (DM) haloes and X-ray brightness distribution, and in optical clusters. Samples of simulated clusters include star formation with supernovae feedback, radiative cooling and simulation in the adiabatic limit at three different redshifts, and 0.25. The optical sample contains 208 Abell, Corwin & Olowin (ACO) clusters within redshift, . Cluster morphology, within 0.5 and 1.0 h−1 Mpc from cluster centre, is quantified by multiplicity and ellipticity. We find that the distribution of the DM haloes in the adiabatic simulation appears to be more elongated than the galaxy clusters. Radiative cooling brings halo shapes in excellent agreement with observed clusters; however, cooling along with feedback mechanism makes the haloes more flattened. Our results indicate relatively stronger structural evolution and more clumpy distributions in observed clusters than in the structure of simulated clusters, and slower increase in simulated cluster shapes compared to those in the observed one. Within , we note an interesting agreement in the shapes of clusters obtained from the cooling simulations and observation. We also note that the different samples of observed clusters differ significantly in morphological evolution with redshift. We highlight a few possibilities responsible for the discrepancy in morphological evolution of simulated and observed clusters. [ABSTRACT FROM AUTHOR]

ABSTRACT Observations of the Universe reveal that matter within it clusters on a variety of scales. On scales between 10 and 100 Mpc, the Universe is spanned by a percolating network of superclusters interspersed with large and almost empty regions – voids. This paper, the first in a series, presents a new Ansatz that can successfully be used to determine the morphological properties of the supercluster–void network. The Ansatz is based on a surface modelling scheme (SURFGEN), developed explicitly for the purpose, which generates a triangulated surface from a discrete data set representing (say) the distribution of galaxies in real (or redshift) space. The triangulated surface describes, at progressively lower density thresholds, clusters of galaxies, superclusters of galaxies and voids. Four Minkowski functionals (MFs) – surface area, volume, extrinsic curvature and genus – describe the geometry and topology of the supercluster–void network. On a discretized and closed triangulated surface, the MFs are determined using SURFGEN. Ratios of the MFs provide us with an excellent diagnostic of three-dimensional shapes of clusters, superclusters and voids. MFs can be studied at different levels of the density contrast and therefore probe the morphology of large-scale structure on a variety of length-scales. Our method for determining the MFs of a triangulated isodensity surface is tested against both simply and multiply connected eikonal surfaces such as triaxial ellipsoids and tori. The performance of our code is thereby evaluated using density distributions that are pancake-like, filamentary, ribbon-like and spherical. Remarkably, the first three MFs are computed to better than 1 per cent accuracy while the fourth (genus) is known exactly. SURFGEN also gives very accurate results when applied to Gaussian random fields. We apply SURFGEN to study morphology in three cosmological models, ΛCDM, τCDM and SCDM, at the present epoch. Geometrical properties of the supercluster–void network are found to be sensitive to the underlying cosmological parameter set. For instance, the percolating supercluster in ΛCDM turns out to be more filamentary but topologically simpler than superclusters in τCDM and SCDM. It occupies just 0.6 per cent of the total simulation-box volume yet contains about 4 per cent of the total mass. Our results indicate that the surface modelling scheme to calculate MFs is accurate and robust and can successfully be used to quantify the topology and morphology of the supercluster–void network in the universe. [ABSTRACT FROM AUTHOR]

Studies the morphology of the secondary cosmic microwave background anisotropies. Galaxies; Intergalactic medium; Cosmology; Structure of the universe.