Random Density Field Research Articles

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 non-linear 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.

Deep learning reconstruction of the large-scale structure of the Universe from luminosity distance

ABSTRACT Supernovae Ia (SNe) can provide a unique window on the large-scale structure (LSS) of the Universe at redshifts where few other observations are available, by solving the inversion problem (IP) consisting in reconstructing the LSS from its effects on the observed luminosity distance. So far the IP was solved assuming some restrictions about space–time, such as spherical symmetry for example, while we obtain for the first time solutions of the IP problem for arbitrary space–time geometries using deep learning. The method is based on the use of convolutional neural networks (CNN) trained on simulated data. The training data set is obtained by first generating random density and velocity fields, and then computing their effects on the luminosity distance. The CNN, based on an appropriately modified version of U-Net to account for the tridimensionality of the data, is then trained to reconstruct the density and velocity fields from the luminosity distance. We find that the velocity field inversion is more accurate than the density field, because the effects of the velocity on the luminosity distance only depend on the source velocity, while in the case of the density it is an integrated effect along the line of sight, giving rise to more degeneracy in the solution of the IP. Improved versions of these neural networks, modified to accommodate the non-uniform distribution of the SNe, can be applied to observational data to reconstruct the LSS of the Universe at redshifts at which few other observations are available.

Correlation function: biasing and fractal properties of the cosmic web

Aims. Our goal is to determine how the spatial correlation function of galaxies describes biasing and fractal properties of the cosmic web. Methods. We calculated spatial correlation functions of galaxies, ξ(r), structure functions, g(r) = 1 + ξ(r), gradient functions, γ(r) = d log g(r)/d log r, and fractal dimension functions, D(r) = 3 + γ(r), using dark matter particles of the biased Λ cold dark matter (CDM) simulation, observed galaxies of the Sloan Digital Sky Survey (SDSS), and simulated galaxies of the Millennium and EAGLE simulations. We analysed how these functions describe fractal and biasing properties of the cosmic web. Results. The correlation functions of the biased ΛCDM model samples at small distances (particle and galaxy separations), r ≤ 2.25 h−1 Mpc, describe the distribution of matter inside dark matter halos. In real and simulated galaxy samples, only the brightest galaxies in clusters are visible, and the transition from clusters to filaments occurs at a distance r ≈ 0.8−1.5 h−1 Mpc. At larger separations, the correlation functions describe the distribution of matter and galaxies in the whole cosmic web. The effective fractal dimension of the cosmic web is a continuous function of the distance (separation). Real and simulated galaxies of low luminosity, Mr ≥ −19, have almost identical correlation lengths and amplitudes, indicating that dwarf galaxies are satellites of brighter galaxies, and do not form a smooth population in voids. Conclusions. The combination of several physical processes (e.g. the formation of halos along the caustics of particle trajectories and the phase synchronisation of density perturbations on various scales) transforms the initial random density field to the current highly non-random density field. Galaxy formation is suppressed in voids, which increases the amplitudes of correlation functions and power spectra of galaxies, and increases the large-scale bias parameter. The combined evidence leads to the large-scale bias parameter of L⋆ galaxies the value b⋆ = 1.85 ± 0.15. We find r0(L⋆) = 7.20 ± 0.19 for the correlation length of L⋆ galaxies.

Kinetic field theory: exact free evolution of Gaussian phase-space correlations

In recent work we developed a description of cosmic large-scale structure formation in terms of non-equilibrium ensembles of classical particles, with time evolution obtained in the framework of a statistical field theory. In these works, the initial correlations between particles sampled from random Gaussian density and velocity fields have so far been treated perturbatively or restricted to pure momentum correlations. Here we treat the correlations between all phase-space coordinates exactly by adopting a diagrammatic language for the different forms of correlations, directly inspired by the Mayer cluster expansion. We will demonstrate that explicit expressions for phase-space density cumulants of arbitrary n-point order, which fully capture the non-linear coupling of free streaming kinematics due to initial correlations, can be obtained from a simple set of Feynman rules. These cumulants will be the foundation for future investigations of perturbation theory in particle interactions.

Gas hydrate saturation from heterogeneous model constructed from well log in Krishna–Godavari Basin, Eastern Indian Offshore

The occurrence of gas hydrate in shallow marine sediments causes an increase of seismic velocity compared to that of water saturated host sediments. This increase of velocity depends on the spatial distribution of hydrates in pore spaces of sediments. Velocities derived from seismic data are low frequency effective values, which cannot be uniquely related to high frequency variation in the rock property. Characterisation of a gas hydrate reservoir from seismic data generally assumes homogeneous distribution of gas hydrates, which leads to overestimation of gas hydrate saturation. Contrary to this, we record higher resolution seismic velocities in well log that lead to characterisation of small scale heterogeneities due to fine scale distribution of gas hydrate in sediments. Here, we incorporate these small scale heterogeneities of gas hydrate reservoir by generating 2-D random stochastic heterogeneous velocity and density fields using well log data in the Krishna–Godavari (KG) basin, eastern Indian offshore. These simulated fields do not contain any information about phase distribution but include all heterogeneities of the reservoir in the well log scale. We demonstrate that the amount of gas hydrate estimated from seismic data is indeed higher (∼12.12 per cent of pore volume) than that obtained from simulated 2-D heterogeneous velocity and density models (∼9.60 per cent of pore volume) along the seismic line.

Matter power spectrum covariance matrix from the DEUS-PUR ΛCDM simulations: mass resolution and non-Gaussian errors

The upcoming generation of galaxy surveys will probe the distribution of matter in the universe with unprecedented accuracy. Measurements of the matter power spectrum at different scales and redshifts will provide stringent constraints on the cosmological parameters. However, on non-linear scales this will require an accurate evaluation of the covariance matrix. Here, we compute the covariance matrix of the 3D matter density power spectrum for the concordance $\Lambda$CDM cosmology from an ensemble of N-body simulations of the Dark Energy Universe Simulation - Parallel Universe Runs (DEUS-PUR). This consists of 12288 realisations of a $(656\,h^{-1}\,\textrm{Mpc})^3$ simulation box with $256^3$ particles. We combine this set with an auxiliary sample of 96 simulations of the same volume with $1024^3$ particles. We find N-body mass resolution effect to be an important source of systematic errors on the covariance at high redshift and small intermediate scales. We correct for this effect by introducing an empirical statistical method which provide an accurate determination of the covariance matrix over a wide range of scales including the Baryon Oscillations interval. Contrary to previous studies that used smaller N-body ensembles, we find the power spectrum distribution to significantly deviate from expectations of a Gaussian random density field at $k\gtrsim 0.25\,h\,\textrm{Mpc}^{-1}$ and $z<0.5$. This suggests that in the case of finite volume surveys an unbiased estimate of the ensemble averaged band power at these scales and redshifts may require a careful assessment of non-Gaussian errors more than previously considered.

Fixing a rigorous formalism for the accurate analytic derivation of halo properties

We establish a one-to-one correspondence between virialized haloes and their seeds, namely peaks with a given density contrast at appropriate Gaussian-filtering radii, in the initial Gaussian random density field. This fixes a rigorous formalism for the analytic derivation of halo properties from the linear power spectrum of density perturbations in any hierarchical cosmology. The typical spherically averaged density profile and mass function of haloes so obtained match those found in numerical simulations.

Excursion set theory for correlated random walks

We present a new method to compute the first crossing distribution in excursion set theory for the case of correlated random walks. We use a combination of the path integral formalism of Maggiore & Riotto, and the integral equation solution of Zhang & Hui, and Benson et al. to find a numerically robust and convenient algorithm to derive the first crossing distribution in terms of a perturbative expansion around the limit of an uncorrelated random walk. We apply this methodology to the specific case of a Gaussian random density field filtered with a Gaussian smoothing function. By comparing our solutions to results from Monte Carlo calculations of the first crossing distribution we demonstrate that our method accurate for power spectra $P(k)\propto k^n$ for $n=1$, becoming less accurate for smaller values of $n$. It is therefore complementary to the method of Musso & Sheth, which will therefore be more useful for standard $\Lambda$CDM power spectra. Our approach is quite general, and can be adapted to other smoothing functions, and also to non-Gaussian density fields.

Theoretical dark matter halo kinematics and triaxial shape

In a recent paper, Salvador-Sol\'e et al. (2012) have derived the typical inner structure of dark matter haloes from that of peaks in the initial random Gaussian density field, determined by the power-spectrum of density perturbations characterising the hierarchical cosmology under consideration. In the present paper, we extend this formalism to the typical kinematics and triaxial shape of haloes. Specifically, we establish the link between such halo properties and the power-spectrum of density perturbations through the typical shape of peaks. The trends of the predicted typical halo shape, pseudo phase-space density and anisotropy profiles are in good agreement with the results of numerical simulations. Our model sheds light on the origin of the power-law-like pseudo phase-space density profile for virialised haloes.

Analytical linear theory for the interaction of a planar shock wave with a two- or three-dimensional random isotropic density field

We present an analytical linear model describing the interaction of a planar shock wave with an isotropic random pattern of density nonuniformities. This kind of interaction is important in inertial confinement fusion where shocks travel into weakly inhomogeneous cryogenic deuterium-wicked foams, and also in astrophysics, where shocks interact with interstellar density clumps. The model presented here is based on the exact theory of space and time evolution of the perturbed quantities generated by a corrugated shock wave traveling into a small-amplitude single-mode density field. Corresponding averages in both two and three dimensions are obtained as closed analytical expressions for the turbulent kinetic energy, acoustic energy flux, density amplification, and vorticity generation downstream. They are given as explicit functions of the two parameters (adiabatic exponent γ and shock strength M(1)) that govern the dynamics of the problem. In addition, these explicit formulas are simplified in the important asymptotic limits of weak and strong shocks and highly compressible fluids.

Halo Assembly Bias in Hierarchical Structure Formation

We investigate the origin of halo assembly bias, the dependence of halo clustering on assembly history. We relate halo assembly to peak properties measured in the Lagrangian space of the initial linear Gaussian random density field, and show how these same Lagrangian properties determine large-scale bias. We focus on the two regimes where assembly bias has been observed to be significant: at masses very large and very small compared to the nonlinear mass scale. At high masses, we show that assembly bias is expected from the statistics of the peaks of Gaussian random fluctuations, and we show that the extent of assembly bias found in N-body simulations of rare halos is in excellent agreement with our theoretical prediction. At low masses, we argue that assembly bias largely arises from a sub-population of low mass halos whose mass accretion has ceased. Due to their arrested development, these halos naturally become unbiased, in contrast to their anti-biased peers. We show that a simple toy model incorporating these effects can roughly reproduce the bias trends found in N-body simulations.

Topology of large-scale structure in the 2dF Galaxy Redshift Survey

We investigate the topology of the completed 2dF Galaxy Redshift Survey (2dFGRS), drawing two flux-limited samples of the local Universe from the 2dFGRS catalogue, which contains over 220000 galaxies at a median redshift of z = 0.11. The samples are cut at z = 0.2 and corrected for selection effects. We then use the three-dimensional genus statistic to probe the connectedness of the galaxy distribution on scales ranging from 8 to 20 Mpc, and compare these measurements with the analytical result for a Gaussian random density field, a generic prediction of inflationary models. We demonstrate consistency with inflation on the range of scales considered. We then introduce a parametrization of the analytic genus curve formula that is sensitive to asymmetries in genus number as a function of density and use it to demonstrate that such phenomena are ruled out with 95 per cent confidence between 8 and 16 Mpc.

Solar acoustic oscillations in a random density field

Solar acoustic oscillations in a random density field

Solar acoustic oscillations in a random density field

The influence of a space-dependent random mass density field on the development of solar p -modes is investigated using analytical and numerical means. Using a perturbative approach, which is valid for a weak random field and small amplitude waves, we derive a linear dispersion relation whose solutions correspond to attenuated oscillations. The real part of the frequency of these oscillations exceeds the one of waves propagating in a medium without random density. We give an interpretation of the unphysical nature of the frequency shift and of the amplitude attenuation which is similar to Landau damping. The analytical findings are compared with the results of the numerical solution of a model wave equation. We find that, for weak random fields and for wavelengths which are a few times the correlation length of the random density fluctuations, numerical results agree with the analytical theory. Two practical formulas for deriving the correlation spectrum of the random density field from observations are also given.

On the Initial Mass Function of Population III Stars

The collapse and fragmentation of filamentary primordial gas clouds are explored using one- and two-dimensional hydrodynamical simulations coupled with the nonequilibrium processes of hydrogen molecule formation. The cloud evolution is computed from the initial central density nc = 10-106 cm-3. The simulations show that depending on the initial density, there are two occasions for the fragmentation of primordial filaments. If a filament has relatively low initial density such as nc 105 cm-3, the radial contraction is slow as a result of less effective H2 cooling and appreciably decelerates at densities higher than a critical density, where LTE populations are achieved for the rotational levels of H2 molecules and the cooling timescale becomes accordingly longer than the free-fall timescale. This filament tends to fragment into dense clumps before the central density reaches 108-109 cm-3, where H2 cooling by three-body reactions is effective and the fragment mass is more massive than some tens of M?. In contrast, if a filament is initially as dense as nc 105 cm-3, the more effective H2 cooling with the help of three-body reactions allows the filament to contract up to n ~ 1012 cm-3. After the density reaches n ~ 1012 cm-3, the filament becomes optically thick to H2 lines and the radial contraction subsequently almost stops. At this final hydrostatic stage, the fragment mass is lowered down to ?1 M? because of the high density of the filament. The dependence of the fragment mass upon the initial density could be translated into the dependence on the local amplitude of random Gaussian density fields or the epoch of the collapse of a parent cloud. Hence, it is predicted that the initial mass function of Population III stars is likely to be bimodal with peaks of ?102 and ?1 M?, where the relative heights could be a function of the collapse epoch. Implications for the metal enrichment by Population III stars at high redshifts and baryonic dark matter are briefly discussed.

Peak and gravity constraints in Gaussian primordial density fields: an application of the Hoffman-Ribak method

We develop an algorithm for setting up initial Gaussian random density and velocity fields containing one or more peaks or dips, in an arbitrary cosmological scenario. The intention is to generate appropriate initial conditions for cosmological N-body simulations that focus on the evolution of the progenitors of the present-day galaxies and clusters. The procedure is an application of the direct and accurate prescription of Hoffman & Ribak (1991) for generating constrained random fields. For each peak a total of 21 physical characteristics can be specified, including its scale, position, density Hessian, velocity, and velocity gradient. The velocity (or, equivalently, gravity) field constrants are based on a generalization of the formalism developed by Bardeen et al. (1986). The resulting density field is sculpted such that it induces the desired amount of net gravitational and tidal forces. We provide a detailed mathematical presentation of the formalism. Afterwards we provide analytical estimates of the likelihood of the imposed constraints. Amongst others, it is shown that the tidal field has a strong tendency to align itself along the principal axes of the mass tensor. The method is illustrated by means of some concrete examples. In addition to the illustration of constraint-field correlation functions and how they add up to the mean fields, followed by illustrations of the variance characteristics of field realizations, we concentrate in particular on the consequences of imposing gravitational field constraints (or, equivalent in the linear regime for growing mode fluctuations, peculiar velocity field constraints).

Nonlinear Evolution of Genus in a Primordial Random Gaussian Density Field

The genus statistics is studied using large $N$-body simulations for several cosmological models. We consider the effects of nonlinear gravitational evolution, smoothing the particle data in fully nonlinear regime, and the redshift-space distortion on the genus curve. Detailed comparison between the theoretical prediction in weakly nonlinear theory and the appropriate simulation results shows that the analytic formula describes the behavior of genus in weakly nonlinear regime fairly accurately. We also find that the redshift-space distortion on genus statistics is small in linear and weakly nonlinear regimes. We conclude that if weakly nonlinear theory and direct numerical simulations are combined, the normalized genus curve $G(\nu)/G(0)$ is a powerful tool to directly check the random-Gaussian paradigm of the origin of the large-scale structure in the universe.

Similarity states of passive scalar transport in buoyancy-generated turbulence

The mixing of a passive scalar field by turbulence that is generated by buoyancy forces acting on an initial random density field is considered. Various asymptotic similarity states of the passive scalar field with and without a uniform mean passive scalar gradient are determined by dimensional arguments based on exact or near invariants of the density and passive scalar fields. The results of large-eddy numerical simulations are shown to support the derived scaling laws. The large-eddy simulations also demonstrate the different mixing properties of an active and passive scalar field.

The inverse problem for the refractometry diagnostics of electromagnetic turbulence in plasma

Turbulence is an important property of laboratory plasmas. A number of relevant diagnostics are based on the interaction of an electromagnetic beam with plasma. Here we discuss a reflectometry technique, where information on plasma properties is obtained by probing plasma with a plane polarized electromagnetic beam. It is shown that the problem of recovering statistical properties of plasma turbulence from the line integrated data can be solved uniquely using a realistic model of plasma. Analytical expressions relating statistics of both the random density and random magnetic fields to the measured statistics have been found. This information is of importance in studies of plasma turbulence,.

The nonlinear evolution of rare events

view Abstract Citations (159) References (28) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The Nonlinear Evolution of Rare Events Bernardeau, Francis Abstract In this paper I consider the nonlinear evolution of a rare density fluctuation in a random density field with Gaussian fluctuations, and I rigorously show that it follows the spherical collapse dynamics applied to its mean initial profile. This result is valid for any cosmological model and is independent of the shape of the power spectrum. In the early stages of the dynamics the density contrast of the fluctuation is seen to follow with a good accuracy the form δ = (1 - δ_L_/1.5)^-1.5^ - 1, where δ_L_ is the linearly extrapolated overdensity. I then investigate the validity domain of the rare event approximation in terms of the parameter V = δ_L_/σ giving the initial overdensity scaled by the rms fluctuation at the same mass scale, and find that it depends critically on the shape of the power spectrum. When the power-law index n is lower than - 1 the departure from the spherical collapse is expected to be small, at least in the early stages of the dynamics, and even for moderate values of ν (|ν| >= 2). However, for n >= - 1 and whatever the value of ν, the dynamics seems to be dominated by the small-scale fluctuations, and the subsequent evolution of the peak may not be necessarily correlated to its initial overdensity. I discuss the implications of these results for the nonlinear dynamics and the formation of the astrophysical objects. Publication: The Astrophysical Journal Pub Date: May 1994 DOI: 10.1086/174121 arXiv: arXiv:astro-ph/9311066 Bibcode: 1994ApJ...427...51B Keywords: Applications Of Mathematics; Big Bang Cosmology; Galactic Clusters; Galaxies; Lagrange Coordinates; Perturbation; Mass Distribution; Normal Density Functions; Poisson Equation; Power Spectra; Space; Astrophysics; COSMOLOGY: LARGE-SCALE STRUCTURE OF UNIVERSE; COSMOLOGY: THEORY; GALAXIES: FORMATION; INSTABILITIES; Astrophysics E-Print: 43 pages in Plain TeX, 8 postscript figures available upon request, CITA 93/14, Astrophysical Journal (in press) May 10th, 1994 issue full text sources arXiv | ADS |