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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]

The Cosmic Web is a complicated highly-entangled geometrical object. Remarkably it has formed from practically Gaussian initial conditions, which may be regarded as the simplest departure from exactly uniform universe in purely deterministic mapping. The full complexity of the web is revealed neither in configuration no velocity spaces considered separately. It can be fully appreciated only in six-dimensional (6D) phase space. However, studies of the phase space is complicated by the fact that every projection of it on a three-dimensional (3D) space is multivalued and contained caustics. In addition phase space is not a metric space that complicates studies of geometry. We suggest to use Lagrangian submanifold i.e., x = x(q), where both x and q are 3D vectors instead of the phase space for studies the complexity of cosmic web in cosmological N-body dark matter simulations. Being fully equivalent in dynamical sense to the phase space it has an advantage of being a single valued and also metric space. [ABSTRACT FROM PUBLISHER]

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]

Cold dark matter haloes are populated by high-density structures with sharply peaked profiles known as caustics, which have not yet been resolved by three-dimensional numerical simulations. Here, we derive semi-analytic expressions for the density profiles near caustics in haloes that form by self-similar accretions of dark matter with infinitesimal velocity dispersion. A simple rescaling shows that, similarly to the case of absolutely cold medium, these profiles are universal: they are valid for all caustics irrespective of the physical parameters of the halo. We derive the maximum density of the caustics and show that it depends on the velocity dispersion and the caustic location. We show that both the absolute and relative thickness of the caustic decrease monotonically towards the centre of the halo while the maximum density grows. This indicates that the radial component of the thermal velocities decreases in the inner streams, i.e. the collisionless medium cools down in the radial direction descending to the centre of the halo. Finally, we demonstrate that there can be a significant contribution to the emission measure from dark matter particle annihilation in the caustics. [ABSTRACT FROM AUTHOR]

We study a sample of 112 galaxies of various Hubble types imaged in the Two Micron All Sky Survey (2MASS) in the near-infrared (NIR; 1–2μm)J,Handbands. The sample contains (optically classified) 32 ellipticals, 16 lenticulars and 64 spirals acquired from the 2MASS Extended Source Catalogue (XSC).We use a set of non-parametric shape measures constructed from the Minkowski functionals (MFs) for galaxy shape analysis. We use ellipticity (ε) and orientation angle (Φ) as shape diagnostics. With these parameters as functions of area within the isophotal contour, we note that the NIR elliptical galaxies withshow a trend of being centrally spherical and increasingly flattened towards the edge, a trend similar to images in optical wavelengths. The highly flattened elliptical galaxies show strong change in ellipticity between the centre and the edge. The lenticular galaxies show morphological properties resembling either ellipticals or disc galaxies. Our analysis shows that almost half of the spiral galaxies appear to have bar-like features while the rest are likely to be non-barred. Our results also indicate that almost one-third of spiral galaxies have optically hidden bars.The isophotal twist noted in the orientations of elliptical galaxies decreases with the flattening of these galaxies, indicating that twist and flattening are also anticorrelated in the NIR, as found in optical wavelengths. The orientations of NIR lenticular and spiral galaxies show a wide range of twists. [ABSTRACT FROM AUTHOR]

We report here the first systematic study of the supercluster–void network in the ΛCDM 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. [ABSTRACT FROM AUTHOR]

ABSTRACT We suggest a set of morphological measures that we believe can help in quantifying the shapes of two-dimensional cosmological images such as galaxies, clusters and superclusters of galaxies. The method employs non-parametric morphological descriptors known as the Minkowski functionals in combination with geometric moments widely used in the image analysis. For the purpose of visualization of the morphological properties of image contour lines, we introduce three auxiliary ellipses representing the vector and tensor Minkowski functionals. We study the discreteness, seeing and noise effects on elliptic contours as well as their morphological characteristics such as the ellipticity and orientation. In order to reduce the effect of noise, we employ a technique of contour smoothing. We test the method by studying simulated elliptic profiles of toy spheroidal galaxies ranging in ellipticity from E0 to E7. We then apply the method to real galaxies, including eight spheroidals, three disc spirals and one peculiar galaxy, as imaged in the near-infrared K [sub s] -band (2.2 μm) with the Two Micron All Sky Survey. The method is numerically very efficient and can be used in the study of hundreds of thousands of images obtained in modern surveys. [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.

The assumption of the Gaussianity of primordial perturbations plays an important role in modern cosmology. The most direct test of this hypothesis consists of testing the Gaussianity of cosmic microwave background (CMB) maps. Counting the pixels with the temperatures in given ranges and thus estimating the one-point probability function of the field is the simplest of all the tests. Other usually more complex tests of Gaussianity generally use a great deal of the information already contained in the probability function. However, the most interesting outcome of such a test would be the signal of non-Gaussianity independent of the probability function. It is shown that the independent information has purely morphological character i.e. it depends on the geometry and topology of the level contours only. As an example we discuss in detail the quadratic model v=u+α(u2-1) (u is a Gaussian field with ū=0 and =1 , α is a parameter) that may arise in slow-roll or two-field inflation models. We show that in the limit of small amplitude α the full information about the non-Gaussianity is contained in the probability function. If other tests are performed on this model they simply recycle the same information. A simple procedure allowing us to assess the sensitivity of any statistics to the morphological information is suggested. We provide an analytic estimate of the statistical limit for detecting the quadratic non-Gaussianity αc as a function of the map size in the ideal situation when the scale of the field is resolved. This estimate is in a good agreement with the results of the Monte Carlo simulations of 2562 and 10242 maps. The effect of resolution on the detection quadratic non-Gaussianity is also briefly discussed. [ABSTRACT FROM AUTHOR]

We suggest novel statistics for the CMB maps that are sensitive to non-Gaussian features. These statistics are natural generalizations of the geometrical and topological methods that have been already used in cosmology such as the cumulative distribution function and genus. We compute the distribution functions of the Partial Minkowski Functionals for the excursion set above or bellow a constant temperature threshold. Minkowski Functionals are additive and are translationally and rotationally invariant. Thus, they can be used for patchy and/or incomplete coverage. The technique is highly efficient computationally (it requires only O(N) operations, where N is the number of pixels per one threshold level). Further, the procedure makes it possible to split large data sets into smaller subsets. The full advantage of these statistics can be obtained only on very large data sets. We apply it to the 4-year DMR COBE data corrected for the Galaxy contamination as an illustration of the technique. [ABSTRACT FROM AUTHOR]