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.
I discuss the formation of the modern cosmological paradigm. In more detail I describe the early study of dark matter and cosmic web and the role of Yakov Zeldovich in the formation of the present concepts on these subjects.
Shocks and turbulence generated during large-scale structure formation are predicted to produce large-scale, low surface-brightness synchrotron emission. On the largest scales, this emission is globally correlated with the thermal baryon distribution, and constitutes the "Synchrotron Cosmic- Web". I present the observational prospects and challenges for detecting this faint emission with upcoming SKA pathfinders.
We use the Bolshoi Simulation to find the most probable location of the Local Group (LG) in the cosmic web. Our LG simulacra are pairs of halos with isolation and kinematic properties consistent with observations. The cosmic web is defined using a tidal tensor approach. We find that the LG's preferred location is regions with a dark matter overdensity close to the cosmic average. This makes filaments and sheets the preferred environment. We also find a strong alignment between the LG and the cosmic web. The orbital angular momentum is preferentially perpendicular to the smallest tidal eigenvec…
Dark matter halos can be defined as smooth distributions of dark matter placed in a non-smooth cosmic web structure. This definition of halos demands a precise definition of smoothness and a characterization of the manner in which the transition from smooth halos to the cosmic web takes place. We introduce entropic measures of smoothness, related to measures of inequality previously used in economy and with the advantage of being connected with standard methods of multifractal analysis already used for characterizing the cosmic web structure in cold dark matter N-body simulations. These entrop…
The cosmic web structure is studied with the concepts and methods of fractal geometry, employing the adhesion model of cosmological dynamics as a basic reference. The structures of matter clusters and cosmic voids in cosmological N-body simulations or the Sloan Digital Sky Survey are elucidated by means of multifractal geometry. A non-lacunar multifractal geometry can encompass three fundamental descriptions of the cosmic structure, namely, the web structure, hierarchical clustering, and halo distributions. Furthermore, it explains our present knowledge of cosmic voids. In this way, a unified …
A quantitative study of the clustering properties of the cosmic web as a function of absolute magnitude and colour is presented using the SDSS Data Release 7 galaxy survey. Mark correlations are included in the analysis. We compare our results with mock galaxy samples obtained with four different semi-analytical models of galaxy formation imposed on the merger trees of the Millenium simulation. The clustering of both red and blue galaxies is studied separately.
The cosmic web contains a large fraction of the total gas mass in the universe but is difficult to detect at most wavelengths. Synchrotron emission from shock-accelerated electrons may offer the chance of imaging the cosmic web at radio wavelengths. In this work we use 3D cosmological ENZO-MHD simulations (combined with a post-processing renormalisation of the magnetic field to bracket for missing physical ingredients and resolution effects) to produce models of the radio emission from the cosmic web. In post-processing we study the capabilities of 13 large radio surveys to detect this emissio…
The cosmic web defines the large scale distribution of matter we see in the Universe today. Classifying the cosmic web into voids, sheets, filaments and nodes allows one to explore structure formation and the role environmental factors have on halo and galaxy properties. While existing studies of cosmic web classification concentrate on grid based methods, this work explores a Lagrangian approach where the V-web algorithm proposed by Hoffman et al. (2012) is implemented with techniques borrowed from smoothed particle hydrodynamics. The Lagrangian approach allows one to classify individual obje…
Voids form a prominent aspect of the Megaparsec distribution of galaxies and matter. Not only do they represent a key constituent of the Cosmic Web, they also are one of the cleanest probes and measures of global cosmological parameters. The shape and evolution of voids are highly sensitive to the nature of dark energy, while their substructure and galaxy population provides a direct key to the nature of dark matter. Also, the pristine environment of void interiors is an important testing ground for our understanding of environmental influences on galaxy formation and evolution. In this paper,…
We study the effect of baryons on the cosmic web -- halos, filaments, walls, and voids. To do so, we apply a modified version of NEXUS, a cosmic web morphological analysis algorithm, to the IllustrisTNG simulations. We find that halos lose more than $10\%$ of their mass due to baryons, mostly to filaments and a small portion to walls and voids. However, the mass transfer does not significantly shift the boundaries of structures, leaving the volume fractions of the cosmic structures largely unaffected. We quantify the effects of baryonic feedback on the power spectrum and the probability densit…
Only about 10% of the baryons in the universe lie in galaxies as stars or cold gas, with the remainder predicted to exist as a dilute gaseous filamentary network known as the Cosmic Web. Some of this gas is detected through UV absorption line studies, but half of the gas remains undetected. Growth of structure simulations suggest that these "missing" baryons were shock heated in unvirialized cosmic filaments to temperatures of 10^5.5-10^7 K, and that the gas is chemically enriched by galactic superwinds. Most of the gas in this temperature regime can be detected only by X-ray observations thro…
On the largest scales, galaxies are pulled together by gravity to form clusters, which are connected by filaments making a web-like pattern. Radio emission is predicted from this cosmic web, which should originate from the strong accretion shocks around the cosmic structures. We present the first observational evidence that Fermi-type acceleration from strong shocks surrounding the filaments of the cosmic web, as well as in peripherals of low-mass clusters, is at work in the Universe. Using all-sky radio maps and stacking on clusters and filaments, we have detected the polarization signature o…
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 evol…
The large-scale structure of the Universe is characterised by a web-like structure made of voids, sheets, filaments, and knots. The structure of this so-called cosmic web is dictated by the local velocity shear tensor. In particular, the local direction of a filament should be strongly aligned with e3, the eigenvector associated with the smallest eigenvalue of the tensor. That conjecture is tested here on the basis of a cosmological simulation. The cosmic web delineated by the halo distribution is probed by a marked point process with interactions (the Bisous model), detecting filaments direct…
The concept of the cosmic web, viewing the Universe as a set of discrete galaxies held together by gravity, is deeply engrained in cosmology. Yet, little is known about the most effective construction and the characteristics of the underlying network. Here we explore seven network construction algorithms that use various galaxy properties, from their location, to their size and relative velocity, to assign a network to galaxy distributions provided by both simulations and observations. We find that a model relying only on spatial proximity offers the best correlations between the physical char…
We propose an alternative physical mechanism to explain the observed accelerated expansion of the Universe based on the configuration entropy of the cosmic web and its evolution. We show that the sheets, filaments and clusters in the cosmic web act as sinks whereas the voids act as the sources of information. The differential entropy of the cosmic velocity field increases with time and also acts as a source of entropy. The growth of non-linear structures and the emergence of the cosmic web may lead to a situation where the overall dissipation rate of information at the sinks are about to domin…
Studies of cosmological objects should take into account their positions within the cosmic web of large-scale structure. Unfortunately, the cosmic web has only been extensively mapped at low-redshifts ($z<1$), using galaxy redshifts as tracers of the underlying density field. At $z>1$, the required galaxy densities are inaccessible for the foreseeable future, but 3D reconstructions of Lyman-$α$ forest absorption in closely-separated background QSOs and star-forming galaxies already offer a detailed window into $z\sim2-3$ large-scale structure. We quantify the utility of such maps for studying …
This work investigates the alignment of galactic spins with the cosmic web across cosmic time using the cosmological hydrodynamical simulation Horizon-AGN. The cosmic web structure is extracted via the persistent skeleton as implemented in the DISPERSE algorithm. It is found that the spin of low-mass galaxies is more likely to be aligned with the filaments of the cosmic web and to lie within the plane of the walls while more massive galaxies tend to have a spin perpendicular to the axis of the filaments and to the walls. The mass transition is detected with a significance of 9 sigmas. This gal…
Using a set of $Λ$CDM simulations of cosmic structure formation, we study the evolving connectivity and changing topological structure of the cosmic web using state-of-the-art tools of multiscale topological data analysis (TDA). We follow the development of the cosmic web topology in terms of the evolution of Betti number curves and feature persistence diagrams of the three (topological) classes of structural features: matter concentrations, filaments and tunnels, and voids. The Betti curves specify the prominence of features as a function of density level, and their evolution with cosmic epoc…
We describe how the dynamics of cosmic structure formation defines the intricate geometric structure of the spine of the cosmic web. The Zeldovich approximation is used to model the backbone of the cosmic web in terms of its singularity structure. The description by Arnold et al. (1982) in terms of catastrophe theory forms the basis of our analysis. This two-dimensional analysis involves a profound assessment of the Lagrangian and Eulerian projections of the gravitationally evolving four-dimensional phase-space manifold. It involves the identification of the complete family of singularity clas…
A new approach for the classification of the cosmic web is presented. In extension of the previous work of Hahn et al. (2007) and Forero-Romero et al. (2009) the new algorithm is based on the analysis of the velocity shear tensor rather than the gravitational tidal tensor. The procedure consists of the construction of the the shear tensor at each (grid) point in space and the evaluation of its three eigenvectors. A given point is classified to be either a void, sheet, filament or a knot according to the number of eigenvalues above a certain threshold, 0, 1, 2, or 3 respectively. The threshold …
Learning cosmic web environments with diffusion models
Université Paris-Saclay（巴黎萨克雷大学）；CNRS（法国国家科学研究中心）；Institut d’Astrophysique Spatiale（空间天体物理研究所）；Centre national d’études spatiales (CNES)（法国国家太空研究中心）；Laboratoire de Physique de l’École normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris Cité（巴黎高等师范学院物理实验室，ENS，巴黎文理研究大学，CNRS，索邦大学，巴黎西岱大学）；Escuela Técnica Superior de Ingenieros Industriales, Universidad Politécnica de Madrid（马德里理工大学工业工程师高等学院）；GISC - Grupo Interdisciplinar de Sistemas Complejos（复杂系统跨学科小组）
Aims. We investigate how properties of the ensemble of superclusters in the cosmic web evolve with time. Methods. We perform numerical simulations of the evolution of the cosmic web using the LambdaCDM model in box sizes L0 = 1024, 512, 256 Mpc/h. We find supercluster ensembles of models for four evolutionary stages, corresponding to the present epoch z = 0, and to redshifts z = 1, z = 3, and z = 10. We calculate fitness diameters of superclusters defined from volumes of superclusters divided to filling factors of over-density regions. Geometrical and fitness diameters of largest superclusters…
We present results of analysis of the dark matter (DM) pairwise velocity statistics in different Cosmic Web environments. We use the DM velocity and density field from the Millennium 2 simulation together with the NEXUS+ algorithm to segment the simulation volume into voxels uniquely identifying one of the four possible environments: nodes, filaments, walls or cosmic voids. We show that the PDFs of the mean infall velocities $v_{12}$ as well as its spatial dependence together with the perpendicular and parallel velocity dispersions bear a significant signal of the large-scale structure environ…
We describe the Bayesian BARCODE formalism that has been designed towards the reconstruction of the Cosmic Web in a given volume on the basis of the sampled galaxy cluster distribution. Based on the realization that the massive compact clusters are responsible for the major share of the large scale tidal force field shaping the anisotropic and in particular filamentary features in the Cosmic Web. Given the nonlinearity of the constraints imposed by the cluster configurations, we resort to a state-of-the-art constrained reconstruction technique to find a proper statistically sampled realization…
Galaxy cluster mass halos ("clusters") in a dark matter simulation are matched to nodes in several different cosmic webs found using the Disperse cosmic web finder. The webs have different simulation smoothings and Disperse parameter choices; for each, 4 methods are considered for matching Disperse nodes to clusters. For most of the webs, Disperse nodes outnumber clusters, but not every cluster has a Disperse node match (and sometimes $>1$ cluster matches to the same Disperse node). The clusters frequently lacking a matching Disperse node have a different distribution of local shear trends and…
We follow the evolution of galaxy systems in numerical simulation. Our goal is to understand the role of density perturbations of various scales in the formation and evolution of the cosmic web. We perform numerical simulations with the full power spectrum of perturbations, and with spectrum cut at long wavelengths. Additionally, we have one model, where we cut the intermediate waves. We analyze the density field and study the void sizes and density field clusters in different models. Our analysis shows that the fine structure (groups and clusters of galaxies) is created by small-scale density…
The detection of the diffuse gas component of the cosmic web remains a formidable challenge. In this work we study synchrotron emission from the cosmic web with simulated SKA1 observations, which can represent an fundamental probe of the warm-hot intergalactic medium. We investigate radio emission originated by relativistic electrons accelerated by shocks surrounding cosmic filaments, assuming diffusive shock acceleration and as a function of the (unknown) large-scale magnetic fields. The detection of the brightest parts of large ($>10 \rm Mpc$) filaments of the cosmic web should be within rea…
We set limits on the presence of the synchrotron cosmic web through the cross-correlation of the 2.3 GHz S-PASS survey with a model of the local cosmic web derived from constrained magnetohydrodynamic (MHD) simulations. The MHD simulation assumes cosmologically seeded magnetic fields amplified during large-scale structure formation, and a population of relativistic electrons/positrons from proton-proton collisions within the intergalactic medium. We set a model-dependent 3$σ$ upper limit on the synchrotron surface brightness of 0.16 mJy arcmin$^{-2}$ at 2.3 GHz in filaments. Extrapolating from…
The network of filaments with embedded clusters surrounding voids seen in maps derived from redshift surveys and reproduced in simulations has been referred to as the cosmic web. A complementary description is provided by considering the shear in the velocity field of galaxies. The eigenvalues of the shear provide information on whether a region is collapsing in three dimensions, the condition for a knot, expanding in three-dimensions, the condition for a void, or in the intermediate condition of a filament or sheet. The structures that are quantitatively defined by the eigenvalues can be appr…
We used magneto-hydrodynamical cosmological simulations to investigate the cross-correlation between different observables (i.e. X-ray emission, Sunyaev-Zeldovich signal at 21 cm, HI temperature decrement, diffuse synchrotron emission and Faraday Rotation) as a probe of the diffuse matter distribution in the cosmic web. We adopt an uniform and simplistic approach to produce synthetic observations at various wavelengths, and we compare the detection chances of different combinations of observables correlated with each other and with the underlying galaxy distribution in the volume. With present…
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 b…
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,…
Evidence repeatedly suggests that cosmological sheets, filaments and voids may be substantially magnetised today. The origin of magnetic fields in the intergalactic medium is however currently uncertain. We discuss a magnetogenesis mechanism based on the exchange of momentum between hard photons and electrons in an inhomogeneous intergalactic medium. Operating near ionising sources during the epoch of reionisation, it is capable of generating magnetic seeds of relevant strengths over scales comparable to the distance between ionising sources. Furthermore, when the contributions of all ionising…
Halos, filaments, sheets and voids in the cosmic web can be defined in terms of the eigenvalues of the smoothed shear tensor and a threshold $λ_{\rm th}$. Using analytic methods, we construct mean maps centered on these types of structures for Gaussian random fields corresponding to cosmological initial conditions. Each map also requires a choice of shear at the origin; we consider three possibilities. We find characteristic sizes, shapes and other properties of the central objects in these mean maps and explore how these properties change with varying the threshold and smoothing scale, i.e. v…
The intergalactic medium (IGM) accounts for ~90% of baryons at all epochs and yet its three dimensional distribution in the cosmic web remains mostly unknown. This is so because the only feasible way to observe the bulk of the IGM is through intervening absorption line systems in the spectra of bright background sources, which limits its characterization to being one-dimensional. Still, an averaged three dimensional picture can be obtained by combining and cross-matching multiple one-dimensional IGM information with three-dimensional galaxy surveys. Here, we present our recent and current effo…
We describe an innovative statistical approach for the ab initio simultaneous analysis of the formation history and morphology of the large-scale structure of the inhomogeneous Universe. Our algorithm explores the joint posterior distribution of the many millions of parameters involved via efficient Hamiltonian Markov Chain Monte Carlo sampling. We describe its application to the Sloan Digital Sky Survey data release 7 and an additional non-linear filtering step. We illustrate the use of our findings for cosmic web analysis: identification of structures via tidal shear analysis and inference o…
Recent application of the Bayesian algorithm BORG to the Sloan Digital Sky Survey (SDSS) main sample galaxies resulted in the physical inference of the formation history of the observed large-scale structure from its origin to the present epoch. In this work, we use these inferences as inputs for a detailed probabilistic cosmic web-type analysis. To do so, we generate a large set of data-constrained realizations of the large-scale structure using a fast, fully non-linear gravitational model. We then perform a dynamic classification of the cosmic web into four distinct components (voids, sheets…
We explore the information theory entropy of a graph as a scalar to quantify the cosmic web. We find entropy values in the range between 1.5 and 3.2 bits. We argue that this entropy can be used as a discrete analogue of scalars used to quantify the connectivity in continuous density fields. After showing that the entropy clearly distinguishes between clustered and random points, we use simulations to gauge the influence of survey geometry, cosmic variance, redshift space distortions, redshift evolution, cosmological parameters and spatial number density. Cosmic variance shows the least importa…
We study the cosmic web at redshifts 1.0 <= z <= 1.8 using quasar systems based on quasar data from the SDSS DR7 QSO catalogue. Quasar systems were determined with a friend-of-friend (FoF) algorithm at a series of linking lengths. At the linking lengths l <= 30 Mpc/h the diameters of quasar systems are smaller than the diameters of random systems, and are comparable to the sizes of galaxy superclusters in the local Universe. The mean space density of quasar systems is close to the mean space density of local rich superclusters. At larger linking lengths the diameters of quasar systems are comp…
Precise cosmic web classification of observed galaxies in massive spectroscopic surveys can be either highly uncertain or computationally expensive. As an alternative, we explore a fast Machine Learning-based approach to infer the underlying dark matter tidal cosmic web environment of a galaxy distribution from its $β$-skeleton graph. We develop and test our methodology using the cosmological magnetohydrodynamic simulation Illustris-TNG at $z=0$. We explore three different tree-based machine-learning algorithms to find that a random forest classifier can best use graph-based features to classi…
We study the alignment of dark matter haloes with the cosmic web characterized by the tidal and velocity shear fields. We focus on the alignment of their shape, angular momentum and peculiar velocities. We use a cosmological N-body simulation that allows to study dark matter halos spanning almost five orders of magnitude in mass ($10^{9}$-$10^{14}$) $h^{-1}$$M_{\odot}$ and spatial scales of $(0.5$-$1.0)$ $h^{-1}$ Mpc to define the cosmic web. We find that the halo shape presents the strongest alignment along the smallest tidal eigenvector, e.g. along filaments and walls, with a signal that get…
Gravitational collapse in cosmological context produces an intricate cosmic web of voids, walls, filaments and nodes. The anisotropic nature of collisionless collapse leads to the emergence of an anisotropic velocity dispersion, or stress, that absorbs most of the kinetic energy after shell-crossing. In this paper, we measure this large-scale velocity dispersion tensor $σ^2_{ij}$ in $N$-body simulations using the phase-space interpolation technique. We study the environmental dependence of the amplitude and anisotropy of the velocity dispersion tensor field, and measure its spatial correlation…
We produce the first low to mid frequency radio simulation that incorporates both traditional extragalactic radio sources as well as synchrotron cosmic web emission. The FIlaments \& GAlactic RadiO (FIGARO) simulation includes ten unique \SI{4x4}{\degree} fields, incorporating active galactic nucleii (AGNs), star forming galaxies (SFGs) and synchrotron cosmic web emission out to a redshift of $z = 0.8$ and over the frequency range 100-1400 MHz. To do this, the simulation brings together a recent $100^3$ Mpc$^3$ magneto-hydrodynamic simulation (Vazza et al., 2019), calibrated to match observed …
The initial shear field plays a central role in the formation of large-scale structures, and in shaping the geometry, morphology, and topology of the cosmic web. We discuss a recent theoretical framework for the shear tensor, termed the `peak/dip picture', which accounts for the fact that halos/voids may form from local extrema of the density field - rather than from random spatial positions; the standard Doroshkevich's formalism is generalized, to include correlations between the density Hessian and shear field at special points in space around which halos/voids may form. We then present the …
Aims. Our goal is to find the relation between the two-point correlation functions (CFs) of projected and spatial density fields of galaxies in the context of the cosmic web. Methods. To investigate relations between spatial (3D) and projected (2D) CFs of galaxies we used density fields of two simulations: a $Λ$-dominated cold dark matter (LCDM) model with known particle data, and the Millennium simulation with know data on simulated galaxies. We compare 3D and 2D correlation functions. In the 2D case, we use samples of various thickness to find the dependence of 2D CFs on the thickness of sam…
The cosmic web is one of the most striking features of the distribution of galaxies and dark matter on the largest scales in the Universe. It is composed of dense regions packed full of galaxies, long filamentary bridges, flattened sheets and vast low density voids. The study of the cosmic web has focused primarily on the identification of such features, and on understanding the environmental effects on galaxy formation and halo assembly. As such, a variety of different methods have been devised to classify the cosmic web -- depending on the data at hand, be it numerical simulations, large sky…
Filament-Arm Node Systems (FANS): A new probe of the winding and chirality of the cosmic web
Center for Cosmology and Computational Astrophysics, Institute for Advanced Study in Physics, Zhejiang University（浙江大学高等物理研究院宇宙学与计算天体物理学中心）；Institute of Astronomy, School of Physics, Zhejiang University（浙江大学物理学院天文学研究所）
We introduce the NEXUS algorithm for the identification of Cosmic Web environments: clusters, filaments, walls and voids. This is a multiscale and automatic morphological analysis tool that identifies all the cosmic structures in a scale free way, without preference for a certain size or shape. We develop the NEXUS method to incorporate the density, tidal field, velocity divergence and velocity shear as tracers of the Cosmic Web. We also present the NEXUS+ procedure which, taking advantage of a novel filtering of the density in logarithmic space, is very successful at identifying the filament …
The phase space distribution of matter out to $\sim 100 \rm Mpc$ is probed by two types of observational data: galaxy redshift surveys and peculiar motions of galaxies. Important information on the process of structure formation and deviations from standard gravity have been extracted from the accumulating data. The remarkably simple Zel'dovich approximation is the basis for much of our insight into the dynamics of structure formation and the development of data analyses methods. Progress in the methodology and some recent results is reviewed.
