Self-similarity and scaling behavior of scale-free gravitational clustering

We measure the scaling properties of the probability distribution of the smoothed density field in $N$-body simulations of expanding universes with scale-free initial power-spectra, with particular attention to the predictions of the stable clustering hypothesis. We concentrate our analysis on the ratios $S_Q(\ell)\equiv {\bar \xi}_Q/{\bar \xi}_2^{Q-1}$, $Q \leq 5$, where ${\bar \xi}_Q$ is the averaged $Q$-body correlation function over a cell of radius $\ell$. The behavior of the higher order correlations is studied through that of the void probability distribution function. As functions of ${\bar \xi}_2$, the quantities $S_Q$, $3 \leq Q \leq 5$, exhibit two plateaus separated by a smooth transition around ${\bar \xi}_2 \sim 1$. In the weakly nonlinear regime, {\bar \xi}_2 \la 1, the results are in reasonable agreement with the predictions of perturbation theory. In the nonlinear regime, ${\bar \xi}_2 > 1$, the function $S_Q({\bar \xi}_2)$ is larger than in the weakly nonlinear regime, and increasingly so with $-n$. It is well-fitted by the expression $S_Q= ({\bar \xi}_2/100)^{0.045(Q-2)}\ {\widetilde S}_Q$for all$n. This weak dependence on scale proves {\em a small, but significant departure from the stable clustering predictions} at least for n=0$and$n=+1$. The analysis of$P_0$confirms that the expected scale-invariance of the functions$S_Q$is not exactly attained in the part of the nonlinear regime we probe, except possibly for$n=-2$and marginally for$n=-1$. In these two cases, our measurements are not accurate enough to be discriminant.Comment: 31 pages, postscript file, figure 1 missing. Postscript file including figure 1 available at ftp://ftp-astro-theory.fnal.gov:/pub/Publications/Pub-95-256-

Observational Constraints on Higher Order Clustering up to $z\simeq 1

Constraints on the validity of the hierarchical gravitational instability theory and the evolution of biasing are presented based upon measurements of higher order clustering statistics in the Deeprange Survey, a catalog of $\sim710,000$ galaxies with $I_{AB} \le 24$ derived from a KPNO 4m CCD imaging survey of a contiguous $4^{\circ} \times 4^{\circ}$ region. We compute the 3-point and 4-point angular correlation functions using a direct estimation for the former and the counts-in-cells technique for both. The skewness $s_3$ decreases by a factor of $\simeq 3-4$ as galaxy magnitude increases over the range $17 \le I \le 22.5$ ($0.1 \lesssim z \lesssim 0.8$). This decrease is consistent with a small {\it increase} of the bias with increasing redshift, but not by more than a factor of 2 for the highest redshifts probed. Our results are strongly inconsistent, at about the $3.5-4 \sigma$ level, with typical cosmic string models in which the initial perturbations follow a non-Gaussian distribution - such models generally predict an opposite trend in the degree of bias as a function of redshift. We also find that the scaling relation between the 3-point and 4-point correlation functions remains approximately invariant over the above magnitude range. The simplest model that is consistent with these constraints is a universe in which an initially Gaussian perturbation spectrum evolves under the influence of gravity combined with a low level of bias between the matter and the galaxies that decreases slightly from $z \sim 0.8$ to the current epoch.Comment: 28 pages, 4 figures included, ApJ, accepted, minor change

Reconstruction of primordial density fields

The Monge-Ampere-Kantorovich (MAK) reconstruction is tested against cosmological N-body simulations. Using only the present mass distribution sampled with particles, and the assumption of homogeneity of the primordial distribution, MAK recovers for each particle the non-linear displacement field between its present position and its Lagrangian position on a primordial uniform grid. To test the method, we examine a standard LCDM N-body simulation with Gaussian initial conditions and 6 models with non-Gaussian initial conditions: a chi-squared model, a model with primordial voids and four weakly non-Gaussian models. Our extensive analyses of the Gaussian simulation show that the level of accuracy of the reconstruction of the nonlinear displacement field achieved by MAK is unprecedented, at scales as small as about 3 Mpc. In particular, it captures in a nontrivial way the nonlinear contribution from gravitational instability, well beyond the Zel'dovich approximation. This is also confirmed by our analyses of the non-Gaussian samples. Applying the spherical collapse model to the probability distribution function of the divergence of the displacement field, we also show that from a well-reconstructed displacement field, such as that given by MAK, it is possible to accurately disentangle dynamical contributions induced by gravitational clustering from possible initial non-Gaussianities, allowing one to efficiently test the non-Gaussian nature of the primordial fluctuations. In addition, a simple application of MAK using the Zel'dovich approximation allows one to also recover accurately the present-day peculiar velocity field on scales of about 8 Mpc.Comment: Version to appear in MNRAS, 24 pages, 21 figures appearing (uses 35 figure files), 1 tabl

Extended Perturbation Theory for the Local Density Distribution Function

Perturbation theory makes it possible to calculate the probability distribution function (PDF) of the large scale density field in the small variance limit. For top hat smoothing and scale-free Gaussian initial fluctuations, the result depends only on the linear variance, sigma_linear, and its logarithmic derivative with respect to the filtering scale -(n_linear+3)=dlog sigma_linear^2/dlog L (Bernardeau 1994). In this paper, we measure the PDF and its low-order moments in scale-free simulations evolved well into the nonlinear regime and compare the results with the above predictions, assuming that the spectral index and the variance are adjustable parameters, n_eff and sigma_eff=sigma, where sigma is the true, nonlinear variance. With these additional degrees of freedom, results from perturbation theory provide a good fit of the PDFs, even in the highly nonlinear regime. The value of n_eff is of course equal to n_linear when sigma << 1, and it decreases with increasing sigma. A nearly flat plateau is reached when sigma >> 1. In this regime, the difference between n_eff and n_linear increases when n_linear decreases. For initial power-spectra with n_linear=-2,-1,0,+1, we find n_eff ~ -9,-3,-1,-0.5 when sigma^2 ~ 100.Comment: 13 pages, 6 figures, Latex (MN format), submitted to MNRA

Fluid-loaded metasurfaces

We consider wave propagation along fluid-loaded structures which take the form of an elastic plate augmented by an array of resonators forming a metasurface, that is, a surface structured with sub-wavelength resonators. Such surfaces have had considerable recent success for the control of wave propagation in electromagnetism and acoustics, by combining the vision of sub-wavelength wave manipulation, with the design, fabrication and size advantages associated with surface excitation. We explore one aspect of recent interest in this field: graded metasurfaces, but within the context of fluid-loaded structures. Graded metasurfaces allow for selective spatial frequency separation and are often referred to as exhibiting rainbow trapping. Experiments, and theory, have been developed for acoustic, electromagnetic, and even elastic, rainbow devices but this has not been approached for fluid-loaded structures that support surface waves coupled with the acoustic field in a bulk fluid. This surface wave, coupled with the fluid, can be used to create an additional effect by designing a metasurface to mode convert from surface to bulk waves. We demonstrate that sub-wavelength control is possible and that one can create both rainbow trapping and mode conversion phenomena for a fluid-loaded elastic plate model.Comment: 13 pages, 10 figure

A Count Probability Cookbook: Spurious Effects and the Scaling Model

We study the errors brought by finite volume effects and dilution effects on the practical determination of the count probability distribution function P_N(n,L), which is the probability of having N objects in a cell of volume L^3 for a set of average number density n. Dilution effects are particularly relevant to the so-called sparse sampling strategy. This work is mainly done in the framework of the scaling model (Balian \& Schaeffer 1989), which assumes that the Q-body correlation functions obey the scaling relation xi_Q(K r_1,..., K r_Q) = K^{-(Q-1) gamma} xi_N(r_1,..., r_Q). We use three synthetic samples as references to perform our analysis: a fractal generated by a Rayleigh-L\'evy random walk with 3.10^4 objects, a sample dominated by a spherical power-law cluster with 3.10^4 objects and a cold dark matter (CDM) universe involving 3.10^5 matter particles.Comment: 44 pages, uuencoded compressed postcript file, FERMILAB-Pub-94/229-A, accepted in ApJ

The effect of baryons on the variance and the skewness of the mass distribution in the Universe at small scales

We study the dissipative effects of baryon physics on cosmic statistics at small scales using a cosmological simulation of a (50 Mpc h−1)3 volume of universe. The MareNostrum simulation was performed using the adaptive mesh refinement (AMR) code ramses, and includes most of the physical ingredients which are part of the current theory of galaxy formation, such as metal-dependent cooling and UV heating, subgrid modelling of the interstellar medium, star formation and supernova feedback. We reran the same initial conditions for a dark matter only universe, as a reference point for baryon-free cosmic statistics. In this paper, we present the measured small-scale amplification of σ2 and S3 due to baryonic physics and their interpretation in the framework of the halo model. As shown in recent studies, the effect of baryons on the matter power spectrum can be accounted for at scales k≲ 10 h Mpc−1 by modifying the halo concentration parameter. We propose to extend this result by using a composite halo profile, which is a linear combination of a Navarro, Frenk and White profile for the dark matter component and an exponential disc profile mimicking the baryonic component at the heart of the halo. This halo profile form is physically motivated and depends on two parameters, the mass fraction f d of baryons in the disc and the ratio λd of the disc's characteristic scale to the halo's virial radius. We find this composite profile to reproduce both the small-scale variance and skewness boosts measured in the simulation up to k∼ 102 h Mpc−1 for physically meaningful values of the parameters f d and λd. Although simulations like the one presented here usually suffer from various problems when compared to observations, our modified halo model could be used as a fitting model to improve the determination of cosmological parameters from weak lensing convergence spectra and skewness measurement

The redshift evolution of bias and baryonic matter distribution

We study the distribution of baryonic and luminous matter within the framework of a hierarchical scenario. Using an analytical model for structure formation which has already been checked against observations for galaxies, Lyman-$\alpha$ clouds, clusters and reionization processes, we present its predictions for the bias of these objects. We describe its dependence on the luminosity (for galaxies or quasars) or the column density (for Lyman-$\alpha$ absorbers) of the considered objects. We also study its redshift evolution, which can exhibit an intricate behaviour. These astrophysical objects do not trace the dark matter density field, the Lyman-$\alpha$ forest clouds being undercorrelated and the bright galaxies overcorrelated, while the intermediate class of Lyman-limit systems is seen to sample the matter field quite well. We also present the distribution of baryonic matter over these various objects. We show that light does not trace baryonic mass, since bright galaxies which contain most of the stars only form a small fraction of the mass associated with virialized and cooled halos. We consider two cosmologies: a critical density universe and an open universe. In both cases, our results agree with observations and show that hierarchical scenarios provide a good model for structure formation and can describe a wide range of objects which spans at least the seven orders of magnitude in mass for which data exist. More detailed observations, in particular of the clustering evolution of galaxies, will constrain the astrophysical models involved.Comment: 13 pages, final version published in A&

Large-Scale Structure of the Universe and Cosmological Perturbation Theory

We review the formalism and applications of non-linear perturbation theory (PT) to understanding the large-scale structure of the Universe. We first discuss the dynamics of gravitational instability, from the linear to the non-linear regime. This includes Eulerian and Lagrangian PT, non-linear approximations, and a brief description of numerical simulation techniques. We then cover the basic statistical tools used in cosmology to describe cosmic fields, such as correlations functions in real and Fourier space, probability distribution functions, cumulants and generating functions. In subsequent sections we review the use of PT to make quantitative predictions about these statistics according to initial conditions, including effects of possible non Gaussianity of the primordial fields. Results are illustrated by detailed comparisons of PT predictions with numerical simulations. The last sections deal with applications to observations. First we review in detail practical estimators of statistics in galaxy catalogs and related errors, including traditional approaches and more recent developments. Then, we consider the effects of the bias between the galaxy distribution and the matter distribution, the treatment of redshift distortions in three-dimensional surveys and of projection effects in angular catalogs, and some applications to weak gravitational lensing. We finally review the current observational situation regarding statistics in galaxy catalogs and what the future generation of galaxy surveys promises to deliver