Source–lens clustering effects on the skewness of the lensing convergence

The correlation between source galaxies and lensing potentials causes a systematic effect on measurements of cosmic shear statistics, known as the source–lens clustering (SLC) effect. The SLC effect on the skewness of lensing convergence, S ₃, is examined using a non-linear semi-analytic approach and is checked against numerical simulations. The semi-analytic calculations have been performed in a wide variety of generic models for the redshift distribution of source galaxies and power-law models for the bias parameter between the galaxy and dark matter distributions. The semi-analytic predictions are tested successfully against numerical simulations. We find the relative amplitude of the SLC effect on S ₃ to be of the order of  5–40  per cent. It depends significantly on the redshift distribution of sources and on the way in which the bias parameter evolves. We discuss possible measurement strategies to minimize the SLC effects.     

The importance of Fourier phases for the morphology of gravitational clustering

The phases of the Fourier modes appearing in a plane-wave expansion of cosmological density fields play a vital role in determining the morphology of gravitationally developed clustering. We demonstrate this qualitatively and quantitatively using simulations. In particular, we use cross-correlation and rank-correlation techniques to quantify the agreement between a simulated distribution and phase-only reconstructions. The phase-only reconstructions exhibit a high degree of correlation with the original distributions, showing how meaningful spatial reconstruction of cosmological density fields depends more on phase accuracy than on amplitudes.     

Non-local scaling in two-dimensional gravitational clustering

Using an ensemble of high-resolution 2D numerical simulations, we explore the scaling properties of cosmological density fluctuations in the non-linear regime. We study the scaling behaviour of the usual N -point volume-averaged correlations, but also examine the scaling of the entire probability density function (PDF) of the fluctuations. We focus on two important issues: (i) whether the scaling behaviour of 2D clustering is consistent with what one infers from radial collapse arguments; and (ii) whether there is any evidence from these high-resolution simulations that a regime of stable clustering is ever entered. We find that the answers are (i) yes and (ii) no. We further find that the behaviour of the highly non-linear regime in these simulations suggests the existence of a regime in which the correlation function is independent of the initial power spectrum.     

The clustering of barred galaxies in the local Universe

We study the clustering properties of barred galaxies using data from the Sloan Digital Sky Survey. We compute projected redshift-space two-point cross-correlation functions   w _p( r _p)  for a sample of nearly 1000 galaxies for which we have performed detailed structural decompositions using the methods described in Gadotti. The sample includes 286 barred galaxies. The clustering of barred and unbarred galaxies of similar stellar mass is indistinguishable over all the scales probed (∼20 kpc–30 Mpc). This result also holds even if the sample is restricted to bars with bluer   g − i   colours (and hence younger ages). Our result also does not change if we split our sample of barred galaxies according to bar-to-total luminosity ratio, bar boxyness, effective surface brightness, length or the shape of the surface density profile within the bar. There is a hint that red, elliptical bars are more strongly clustered than red and less elliptical bars, on scales  ≳1 Mpc  , although the statistical significance is not high. We conclude that there is no significant evidence that bars are a product of mergers or interactions. We tentatively interpret the stronger clustering of the more elliptical bars as evidence that they are located in older galaxies, which reside in more massive haloes.     

Generalized inflation with a gravitational wave background

We propose a -inflation model that explains a significant part of the COBE signal by primordial cosmic gravitational waves. The primordial density perturbations fulfil both the constraints of large-scale microwave background and galaxy cluster normalization. The model is tested against the galaxy cluster power spectrum and the high-multipole angular cosmic microwave background anisotropy.     

The 3D skeleton: tracing the filamentary structure of the Universe

The skeleton formalism, which aims at extracting and quantifying the filamentary structure of our Universe, is generalized to 3D density fields. A numerical method for computing a local approximation of the skeleton is presented and validated here on Gaussian random fields. It involves solving equation     , where  ∇ρ  and     are the gradient and Hessian matrix of the field. This method traces well the filamentary structure in 3D fields such as those produced by numerical simulations of the dark matter distribution on large scales, and is insensitive to monotonic biasing.
Two of its characteristics, namely its length and differential length, are analysed for Gaussian random fields. Its differential length per unit normalized density contrast scales like the probability distribution function of the underlying density contrast times the total length times a quadratic Edgeworth correction involving the square of the spectral parameter. The total length-scales like the inverse square smoothing length, with a scaling factor given by  0.21 (5.28 + n )  where n is the power index of the underlying field. This dependency implies that the total length can be used to constrain the shape of the underlying power spectrum, hence the cosmology.
Possible applications of the skeleton to galaxy formation and cosmology are discussed. As an illustration, the orientation of the spin of dark haloes and the orientation of the flow near the skeleton is computed for cosmological dark matter simulations. The flow is laminar along the filaments, while spins of dark haloes within 500 kpc of the skeleton are preferentially orthogonal to the direction of the flow at a level of 25 per cent.     

Interpreting the clustering of radio sources

We develop the formalism required to interpret, within a CDM framework, the angular clustering of sources in a deep radio survey. The effect of non-linear evolution of density perturbations is discussed, as is the effect of the assumed redshift distribution of sources. We also investigate what redshift ranges contribute to the clustering signal at different angular scales. Application of the formalism is focused on the clustering detected in the FIRST survey, but measurements made for other radio surveys are also investigated. We comment on the implications for the evolution of clustering.     

Lensing magnification effects on the cosmic shear statistics

Gravitational lensing causes a correlation between a population of foreground large-scale structures and the observed number density of the background distant galaxies as a consequence of the flux magnification and the lensing area distortion. This correlation has not been taken into account in calculations of the theoretical predictions of the cosmic shear statistics but may cause a systematic error in a cosmic shear measurement. We examine its impact on the cosmic shear statistics using the semi-analytic approach. We find that the lensing magnification has no practical influence on the cosmic shear variance. Exploring the possible shapes of the redshift distribution of source galaxies, we find that the relative amplitude of the effect on the convergence skewness is 3 per cent at most.     

The Ω dependence in equations of motion

The equations of motion governing the evolution of a collisionless gravitating system of particles in an expanding universe can be cast in a form which is almost independent of the cosmological density parameter, Ω, and the cosmological constant, Λ. The new equations are expressed in terms of a time variable τ=ln D , where D is the linear rate of growth of density fluctuations. The dependence on the density parameter is proportional to ε=Ω^−0.2−1 times the difference between the peculiar velocity (with respect to τ) of particles and the gravity field (minus the gradient of the potential); or, before shell-crossing, times the sum of the density contrast and the velocity divergence. In a one-dimensional collapse or expansion, the equations are fully independent of Ω and Λ before shell crossing. In the general case, the effect of this weak Ω dependence is to enhance the rate of evolution of density perturbations in dense regions. In a flat universe with Λ7ne;0, this enhancement is less pronounced than in an open universe with Λ=0 and the same Ω. Using the spherical collapse model, we find that the increase of the rms density fluctuations in a low-Ω universe relative to that in a flat universe with the same linear normalization is ∼0.01ε(Ω)〈δ³〉, where δ is the density field in the flat universe. The equations predict that the smooth average velocity field scales like Ω^0.6, while the local velocity dispersion (rms value) scales, approximately, like Ω^0.5. High-resolution N -body simulations confirm these results and show that density fields, when smoothed on scales slightly larger than clusters, are insensitive to the cosmological model. Haloes in an open model simulation are more concentrated than haloes of the same M /Ω in a flat model simulation.     

Excursion set approach to the clustering of dark matter haloes in Lagrangian space

We present a stochastic approach to the spatial clustering of dark matter haloes in Lagrangian space. Our formalism is based on a local formulation of the 'excursion set' approach by Bond et al., which automatically accounts for the 'cloud-in-cloud' problem in the identification of bound systems. Our method allows us to calculate correlation functions of haloes in Lagrangian space using either a multidimensional Fokker–Planck equation with suitable boundary conditions, or an array of Langevin equations with spatially correlated random forces. We compare the results of our method with theoretical predictions for the halo autocorrelation function considered in the literature, and find good agreement with the results recently obtained within a treatment of halo clustering in terms of 'counting fields' by Catelan et al. Finally, the possible effect of spatial correlations on numerical simulations of halo merger trees is discussed.