arXiv subjects

Rien van de Weygaert

Publications and source records attributed to Rien van de Weygaert.

At least 37 records · Page 2Linked to original sources

arXiv2023

Persistent topology of the reionization bubble network. II: Evolution & Classification

We study the topology of the network of ionized and neutral regions that characterized the intergalactic medium during the Epoch of Reionization. Our analysis uses the formalism of persistent homology, which offers a highly intuitive and comprehensive description of the ionization topology in terms of the births and deaths of topological features. Features are identified as $k$-dimensional holes in the ionization bubble network, whose abundance is given by the $k$th Betti number: $β_0$ for ionized bubbles, $β_1$ for tunnels, and $β_2$ for neutral islands. Using semi-numerical models of reionization, we investigate the dependence on the properties of sources and sinks of ionizing radiation. Of all topological features, we find that the tunnels dominate during reionization and that their number is easiest to observe and most sensitive to the astrophysical parameters of interest, such as the gas fraction and halo mass necessary for star formation. Seen as a phase transition, the importance of the tunnels can be explained by the entanglement of two percolating clusters and the fact that higher-dimensional features arise when lower-dimensional features link together. We also study the relation between the morphological components of the bubble network (bubbles, tunnels, islands) and those of the cosmic web (clusters, filaments, voids), describing a correspondence between the $k$-dimensional features of both. Finally, we apply the formalism to mock observations of the 21-cm signal. Assuming 1000 observation hours with HERA Phase II, we show that astrophysical models can be differentiated and confirm that persistent homology provides additional information beyond the power spectrum.

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arXiv2023

Stellar mass-metallicity relation throughout the large-scale structure of the Universe: CAVITY mother sample

Void galaxies are essential for understanding the physical processes that drive galaxy evolution because they are less affected by external factors than galaxies in denser environments, that is, in filaments, walls, and clusters. The stellar metallicity of a galaxy traces the accumulated fossil record of the star formation through the entire life of the galaxy. A comparison of the stellar metallicity of galaxies in various environments, including voids, filaments, walls, and clusters can provide valuable insights into how the large-scale environment affects the chemical evolution of the galaxy. We present the first comparison of the relation of the total stellar mass versus central stellar metallicity between galaxies in voids, filaments, walls, and clusters with different star formation history (SFH) types, morphologies, and colours for stellar masses between $10^{8.0}$ to $10^{11.5}$ solar masses and redshift $0.01<z<0.05$. We applied non-parametric full spectral fitting techniques (pPXF and STECKMAP) to 10807 spectra from the SDSS-DR7 (987 in voids, 6463 in filaments and walls, and 3357 in clusters) and derived their central mass-weighted average stellar metallicity ($\rm [M/H]_M$). We find that galaxies in voids have slightly lower stellar metallicities on average than galaxies in filaments and walls (by~$\sim~0.1$~dex), and they are much lower than those of galaxies in clusters (by~$\sim~0.4$~dex). These differences are more significant for low-mass ($ \sim~10^{9.25}~{\rm M_\odot}$) than for high-mass galaxies, for long-timescale SFH (extended along time) galaxies than for short-timescale SFHs (concentrated at early times) galaxies, for spiral than for elliptical galaxies, and for blue than for red galaxies.

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arXiv2023

Statistics of tidal and deformation eigenvalue fields in the primordial Gaussian matter distribution: the two-dimensional case

We study the statistical properties of the eigenvalues of the primordial tidal and deformation tensor for random Gaussian cosmic density fields. With the tidal and deformation tensors, Hessians of the gravitational and velocity potential, being Gaussian, the corresponding eigenvalue fields are distinctly non-Gaussian. Following the extension of the Doroshkevich formula for the joined distribution of eigenvalues to two-dimensional fields, we evaluate the two- and three-point correlation functions of the eigenvalue fields. In addition, we assess the number densities of singular points of the eigenvalue fields and find their corresponding two- and three-point correlation functions. The role of tidal forces and the resulting mass element deformation in shaping the prominent anisotropic wall-like and filamentary components of the cosmic web has since long been recognized based on the Zel'dovich approximation. Less well-known is that the weblike spatial pattern is already recognizable in the primordial tidal and deformation eigenvalue field, even while the corresponding Gaussian density and the potential field appear merely as a spatially incoherent and unstructured random field. Furthermore, against the background of a full phase-space assessment of structure formation in the Universe, the caustic skeleton theory entails a fully analytical framework for the nonlinear evolution of the cosmic web. It describes the folding of the dark matter sheet and the emerging caustic singularities, fully specified by the deformation eigenvalues and eigenvectors. Finally, tidal tensor eigenvalues are of central importance, and understanding their distribution is critical in predicting the resulting rotation and orientation. The current study applies to two-dimensional Gaussian random fields and will be generalized to a three-dimensional analysis in an upcoming study.

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arXiv2022

Cosmic Web & Caustic Skeleton: non-linear Constrained Realizations -- 2D case studies

The cosmic web consists of a complex configuration of voids, walls, filaments, and clusters, which formed under the gravitational collapse of Gaussian fluctuations. Understanding under what conditions these different structures emerge from simple initial conditions, and how different cosmological models influence their evolution, is central to the study of the large-scale structure. Here, we present a general formalism for setting up initial random density and velocity fields satisfying non-linear constraints for specialized N-body simulations. These allow us to link the non-linear conditions on the eigenvalue and eigenvector fields of the deformation tensor, as specified by caustic skeleton theory, to the current-day cosmic web. By extending constrained Gaussian random field theory, and the corresponding Hoffman-Ribak algorithm, to non-linear constraints, we probe the statistical properties of the progenitors of the walls, filaments, and clusters of the cosmic web. Applied to cosmological N-body simulations, the proposed techniques pave the way towards a systematic investigation of the evolution of the progenitors of the present-day walls, filaments, and clusters, and the embedded galaxies, putting flesh on the bones of the caustic skeleton. The developed nonlinear constrained random field theory is valid for generic cosmological conditions. For ease of visualization, the case study presented here probes the two-dimensional caustic skeleton.

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arXiv2021

Persistent homology of the cosmic web. I: Hierarchical topology in $Λ$CDM cosmologies

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 epoch reflects the changing network connections between these structural features. The persistence diagrams quantify the longevity and stability of topological features. In this study we establish, for the first time, the link between persistence diagrams, the features they show, and the gravitationally driven cosmic structure formation process. By following the diagrams' development over cosmic time, the link between the multiscale topology of the cosmic web and the hierarchical buildup of cosmic structure is established. The sharp apexes in the diagrams are intimately related to key transitions in the structure formation process. The apex in the matter concentration diagrams coincides with the density level at which, typically, they detach from the Hubble expansion and begin to collapse. At that level many individual islands merge to form the network of the cosmic web and a large number of filaments and tunnels emerge to establish its connecting bridges. The location trends of the apex possess a self-similar character that can be related to the cosmic web's hierarchical buildup. We find that persistence diagrams provide a significantly higher and more profound level of information on the structure formation process than more global summary statistics like Euler characteristic or Betti numbers.

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arXiv2021

Caught in the cosmic web: Environmental effect on halo concentrations, shape, and spin

Using a set of high-resolution simulations we study the statistical correlation of dark matter halo properties with the large-scale environment. We consider halo populations split into four Cosmic Web (CW) elements: voids, walls, filaments, and nodes. For the first time we present a study of CW effects for halos covering six decades in mass: $10^{8}-10^{14}{h^{-1}{\rm M}_{\odot}}$. We find that the fraction of halos living in various web components is a strong function of mass, with the majority of $M>10^{12}{h^{-1}{\rm M}_{\odot}}$ halos living in filaments and nodes. Low mass halos are more equitably distributed in filaments, walls, and voids. For halo density profiles and formation times we find a universal mass threshold of $M_{th}\sim6\times10^{10}{h^{-1}{\rm M}_{\odot}}$ below which these properties vary with environment. Here, filament halos have the steepest concentration-mass relation, walls are close to the overall mean, and void halos have the flattest relation. This amounts to $c_{200}$ for filament and void halos that are respectively $14\%$ higher and $7\%$ lower than the mean at $M=2\times10^8{h^{-1}{\rm M}_{\odot}}$, with low-mass node halos being most likely splashed-back. We find double power-law fits that very well describe $c(M)$ for the four environments in the whole probed mass range. A complementary picture is found for the average formation times, with the mass-formation time relations following trends shown for the concentrations: the nodes halos being the oldest and void halo the youngest. The CW environmental effect is much weaker when studying the halo spin and shapes. The trends with halo mass is reversed: the small halos with $M<10^{10}{h^{-1}{\rm M}_{\odot}}$ seem to be unaffected by the CW environment. Some weak trends are visible for more massive void and walls halos, which, on average, are characterized by lower spin and higher triaxiality parameters.

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arXiv2021

Cosmic Ballet III: halo spin evolution in the cosmic web

We explore the evolution of halo spins in the cosmic web using a very large sample of dark matter haloes in the $Λ$CDM Planck-Millennium N-body simulation. We use the NEXUS+ multiscale formalism to identify the hierarchy of filaments and sheets of the cosmic web at several redshifts. We find that at all times the magnitude of halo spins correlates with the web environment, being largest in filaments, and, for the first time, we show that it also correlates with filament thickness as well as the angle between spin-orientation and the spine of the host filament. For example, massive haloes in thick filaments spin faster than their counterparts in thin filaments, while for low-mass haloes the reverse is true. We also have studied the evolution of alignment between halo spin orientations and the preferential axes of filaments and sheets. The alignment varies with halo mass, with the spins of low-mass haloes being predominantly along the filament spine, while those of high-mass haloes being predominantly perpendicular to the filament spine. On average, for all halo masses, halo spins become more perpendicular to the filament spine at later times. At all redshifts, the spin alignment shows a considerable variation with filament thickness, with the halo mass corresponding to the transition from parallel to perpendicular alignment varying by more than one order of magnitude. The environmental dependence of halo spin magnitude shows little evolution for $z\leq2$ and is likely a consequence of the correlations in the initial conditions or high redshift effects

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arXiv2021

Deviations from tidal torque theory: evolution of the halo spin-filament alignment

The alignment between halo spins and the cosmic web is still poorly understood despite being a widely studied topic. Here, we study this alignment within the context of tidal torque theory (TTT) and deviations from it. To this end, we analyze the evolution of the shape and spin direction of proto-haloes, i.e. of all the volume elements associated to a $z=0$ halo, with respect to the present-day filaments. We find that the major axis of proto-haloes undergoes a major change, from being strongly perpendicular to the filament spine in the initial conditions, to being preferentially aligned at the present time. In comparison, the spin orientation shows only a mild evolution: it starts slightly parallel to the filament spine, but the subsequent evolution, up to $z{\sim}1$, gradually changes its orientation to preferentially perpendicular. In order to analyze these signals in the TTT framework, we split the haloes according to their net spin growth with respect to the median TTT expectation, finding a clear correlation with the spin--filament alignment. At the present time, haloes whose spin grew the most are the ones most perpendicular to the filament spine, while haloes whose spin grew below the median TTT expectation are typically more aligned. The dependence of spin directions on net spin growth is already present in the initial conditions, and gets further modified by late-time, $z<2$, evolution. Also, spin directions mildly deviate from the TTT predictions even at high redshift, indicating the need for extensions to the model.

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arXiv2019

The DTFE public software: The Delaunay Tessellation Field Estimator code

We present the DTFE public software, a code for reconstructing fields from a discrete set of samples/measurements using the maximum of information contained in the point distribution. The code is written in C++ using the CGAL library and is parallelized using OpenMP. The software was designed for the analysis of cosmological data but can be used in other fields where one must interpolate quantities given at a discrete point set. The software comes with a wide suite of options to facilitate the analysis of 2- and 3-dimensional data and of both numerical simulations and galaxy redshift surveys. For comparison purposes, the code also implements the TSC and SPH grid interpolation methods. The code comes with an extensive user guide detailing the program options, examples and the inner workings of the code. The DTFE public software and further information can be found at http://www.astro.rug.nl/~voronoi/DTFE/dtfe.html .

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arXiv2019

Stochastic Homology of Gaussian vs. non-Gaussian Random Fields: Graphs towards Betti Numbers and Persistence Diagrams

The topology and geometry of random fields - in terms of the Euler characteristic and the Minkowski functionals - has received a lot of attention in the context of the Cosmic Microwave Background (CMB), as the detection of primordial non-Gaussianities would form a valuable clue on the physics of the early Universe. The virtue of both the Euler characteristic and the Minkowski functionals in general, lies in the fact that there exist closed form expressions for their expectation values for Gaussian random fields. However, the Euler characteristic and Minkowski functionals are summarizing characteristics of topology and geometry. Considerably more topological information is contained in the homology of the random field, as it completely describes the creation, merging and disappearance of topological features in superlevel set filtrations. In the present study we extend the topological analysis of the superlevel set filtrations of two-dimensional Gaussian random fields by analysing the statistical properties of the Betti numbers - counting the number of connected components and loops - and the persistence diagrams - describing the creation and mergers of homological features. Using the link between homology and the critical points of a function - as illustrated by the Morse-Smale complex - we derive a one-parameter fitting formula for the expectation value of the Betti numbers and forward this formalism to the persistent diagrams. We, moreover, numerically demonstrate the sensitivity of the Betti numbers and persistence diagrams to the presence of non-Gaussianities.

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arXiv2019

Bayesian cosmic density field inference from redshift space dark matter maps

We present a self-consistent Bayesian formalism to sample the primordial density fields compatible with a set of dark matter density tracers after cosmic evolution observed in redshift space. Previous works on density reconstruction did not self-consistently consider redshift space distortions or included an additional iterative distortion correction step. We present here the analytic solution of coherent flows within a Hamiltonian Monte Carlo posterior sampling of the primordial density field. We test our method within the Zel'dovich approximation, presenting also an analytic solution including tidal fields and spherical collapse on small scales using augmented Lagrangian perturbation theory. Our resulting reconstructed fields are isotropic and their power spectra are unbiased compared to the true one defined by our mock observations. Novel algorithmic implementations are introduced regarding the mass assignment kernels when defining the dark matter density field and optimization of the time step in the Hamiltonian equations of motions. Our algorithm, dubbed barcode, promises to be specially suited for analysis of the dark matter cosmic web down to scales of a few Megaparsecs. This large scale structure is implied by the observed spatial distribution of galaxy clusters --- such as obtained from X-ray, SZ or weak lensing surveys --- as well as that of the intergalactic medium sampled by the Lyman alpha forest or perhaps even by deep hydrogen intensity mapping. In these cases, virialized motions are negligible, and the tracers cannot be modeled as point-like objects. It could be used in all of these contexts as a baryon acoustic oscillation reconstruction algorithm.

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arXiv2019

The Cosmic Ballet II: Spin alignment of galaxies and haloes with large-scale filaments in the EAGLE simulation

We investigate the alignment of galaxies and haloes relative to cosmic web filaments using the EAGLE hydrodynamical simulation. We identify filaments by applying the NEXUS+ method to the mass distribution and the Bisous formalism to the galaxy distribution. Both web finders return similar filamentary structures that are well aligned and that contain comparable galaxy populations. EAGLE haloes have an identical spin alignment with filaments as their counterparts in dark matter only simulations: a complex mass dependent trend with low mass haloes spinning preferentially parallel to and high mass haloes spinning preferentially perpendicular to filaments. In contrast, galaxy spins do not show such a spin transition and have a propensity for perpendicular alignments at all masses, with the degree of alignment being largest for massive galaxies. This result is valid for both NEXUS+ and Bisous filaments. When splitting by morphology, we find that elliptical galaxies show a stronger orthogonal spin--filament alignment than spiral galaxies of similar mass. The same is true of their haloes, with the host haloes of elliptical galaxies having a larger degree of orthogonal alignment than the host haloes of spirals. Due to the misalignment between galaxy shape and spin, galaxy minor axes are oriented differently with filaments than galaxy spins. We find that the galaxies whose minor axis is perpendicular to a filament are much better aligned with their host haloes. This suggests that many of the same physical processes determine both the galaxy--filament and the galaxy--halo alignments.

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arXiv2019

Cosmic voids: a novel probe to shed light on our Universe

Cosmic voids, the less dense patches of the Universe, are promising laboratories to extract cosmological information. Thanks to their unique low density character, voids are extremely sensitive to diffuse components such as neutrinos and dark energy, and represent ideal environments to study modifications of gravity, where the effects of such modifications are expected to be more prominent. Robust void-related observables, including for example redshift-space distortions (RSD) and weak lensing around voids, are a promising way to chase and test new physics. Cosmological analysis of the large-scale structure of the Universe predominantly relies on the high density regions. Current and upcoming surveys are designed to optimize the extraction of cosmological information from these zones, but leave voids under-exploited. A dense, large area spectroscopic survey with imaging capabilities is ideal to exploit the power of voids fully. Besides helping illuminate the nature of dark energy, modified gravity, and neutrinos, this survey will give access to a detailed map of under-dense regions, providing an unprecedented opportunity to observe and study a so far under-explored galaxy population.

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arXiv2019

Topology and Geometry of Gaussian random fields I: on Betti Numbers, Euler characteristic and Minkowski functionals

This study presents a numerical analysis of the topology of a set of cosmologically interesting three-dimensional Gaussian random fields in terms of their Betti numbers $β_0$, $β_1$ and $β_2$. We show that Betti numbers entail a considerably richer characterization of the topology of the primordial density field. Of particular interest is that Betti numbers specify which topological features - islands, cavities or tunnels - define its spatial structure. A principal characteristic of Gaussian fields is that the three Betti numbers dominate the topology at different density ranges. At extreme density levels, the topology is dominated by a single class of features. At low levels this is a \emph{Swiss-cheeselike} topology, dominated by isolated cavities, at high levels a predominantly \emph{Meatball-like} topology of isolated objects. At moderate density levels, two Betti number define a more \emph{Sponge-like} topology. At mean density, the topology even needs three Betti numbers, quantifying a field consisting of several disconnected complexes, not of one connected and percolating overdensity. A {\it second} important aspect of Betti number statistics is that they are sensitive to the power spectrum. It reveals a monotonic trend in which at a moderate density range a lower spectral index corresponds to a considerably higher (relative) population of cavities and islands. We also assess the level of complementary information that Betti numbers represent, in addition to conventional measures such as Minkowski functionals. To this end, we include an extensive description of the Gaussian Kinematic Formula (GKF), which represents a major theoretical underpinning for this discussion.

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arXiv2018

Unexpected Topology of the Temperature Fluctuations in the Cosmic Microwave Background

We study the topology generated by the temperature fluctuations of the Cosmic Microwave Background (CMB) radiation, as quantified by the number of components and holes, formally given by the Betti numbers, in the growing excursion sets. We compare CMB maps observed by the Planck satellite with a thousand simulated maps generated according to the LCDM paradigm with Gaussian distributed fluctuations. The survey of the CMB over $\mathbb{S}^2$ is incomplete due to obfuscation effects by bright point sources and other extended foreground objects like our own galaxy. To deal with such situations, where analysis in the presence of "masks" is of importance, we introduce the concept of relative homology. The parametric $χ^2$-test shows differences between observations and simulations, yielding $p$-values at per-cent to less than per-mil levels roughly between 2 to 7 degrees. The highest observed deviation for $b_0$ and $b_1$ is approximately between $3σ$-4$σ$ at scales of 3 to 7 degrees. There are reports of mildly unusual behaviour of the Euler characteristic at 3.66 degrees in the literature, computed from independent measurements of the CMB temperature fluctuations by Planck's predecessor WMAP satellite. The mildly anomalous behaviour of Euler characteristic is related to the strongly anomalous behaviour of components and holes. These are also the scales at which the observed maps exhibit low variance compared to the simulations. Non-parametric tests show even stronger differences at almost all scales. Regardless, beyond the trivial possibility that this may still be a manifestation of an extreme Gaussian case, these observations, along with the super-horizon scales involved, may motivate to look at primordial non-Gaussianity. Alternative scenarios worth exploring may be models with non-trivial topology.

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arXiv2018

Persistent topology of the reionisation bubble network. I: Formalism & Phenomenology

We present a new formalism for studying the topology of HII regions during the Epoch of Reionisation, based on persistent homology theory. With persistent homology, it is possible to follow the evolution of topological features over time. We introduce the notion of a persistence field as a statistical summary of persistence data and we show how these fields can be used to identify different stages of reionisation. We identify two new stages common to all bubble ionisation scenarios. Following an initial pre-overlap and subsequent overlap stage, the topology is first dominated by neutral filaments (filament stage) and then by enclosed patches of neutral hydrogen undergoing outside-in ionisation (patch stage). We study how these stages are affected by the degree of galaxy clustering. We also show how persistence fields can be used to study other properties of the ionisation topology, such as the bubble size distribution and the fractal-like topology of the largest ionised region.

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arXiv2018

The Cosmic Ballet: spin and shape alignments of haloes in the cosmic web

We investigate the alignment of haloes with the filaments of the cosmic web using an unprecedently large sample of dark matter haloes taken from the P-Millennium $Λ$CDM cosmological N-body simulation. We use the state-of-the-art NEXUS morphological formalism which, due to its multiscale nature, simultaneously identifies structures at all scales. We find strong and highly significant alignments, with both the major axis of haloes and their peculiar velocity tending to orient along the filament. However, the spin - filament alignment displays a more complex trend changing from preferentially parallel at low masses to preferentially perpendicular at high masses. This "spin flip" occurs at an average mass of $5\times10^{11}~h^{-1}M_\odot$. This mass increases with increasing filament diameter, varying by more than an order of magnitude between the thinnest and thickest filament samples. We also find that the inner parts of haloes have a spin flip mass that is several times smaller than that of the halo as a whole. These results confirm that recent accretion is responsible for the complex behaviour of the halo spin - filament alignment. Low-mass haloes mainly accrete mass along directions perpendicular to their host filament and thus their spins tend to be oriented along the filaments. In contrast, high-mass haloes mainly accrete along their host filaments and have their spins preferentially perpendicular to them. Furthermore, haloes located in thinner filaments are more likely to accrete along their host filaments than haloes of the same mass located in thicker filaments.

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arXiv2018

The cosmic spiderweb: equivalence of cosmic, architectural, and origami tessellations

For over twenty years, the term 'cosmic web' has guided our understanding of the large-scale arrangement of matter in the cosmos, accurately evoking the concept of a network of galaxies linked by filaments. But the physical correspondence between the cosmic web and structural-engineering or textile 'spiderwebs' is even deeper than previously known, and extends to origami tessellations as well. Here we explain that in a good structure-formation approximation known as the adhesion model, threads of the cosmic web form a spiderweb, i.e. can be strung up to be entirely in tension. The correspondence is exact if nodes sampling voids are included, and if structure is excluded within collapsed regions (walls, filaments and haloes), where dark-matter multistreaming and baryonic physics affect the structure. We also suggest how concepts arising from this link might be used to test cosmological models: for example, to test for large-scale anisotropy and rotational flows in the cosmos.

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