Sources of contamination to weak lensing three-point statistics: constraints from N-body simulations

We investigate the impact of the observed correlation between a galaxy's shape and its surrounding density field on the measurement of third-order weak lensing shear statistics. Using numerical simulations, we estimate the systematic error contribution to a measurement of the third-order moment of the aperture mass statistic (GGG) from three-point intrinsic ellipticity correlations (III), and the three-point coupling between the weak lensing shear experienced by distant galaxies and the shape of foreground galaxies (GGI and GII). We find that third-order weak lensing statistics are typically more strongly contaminated by these physical systematics compared to second-order shear measurements, contaminating the measured three-point signal for moderately deep surveys with a median redshift   z _m∼ 0.7  by ∼15 per cent. It has been shown that accurate photometric redshifts will be crucial to correct for this effect, once a model and the redshift dependence of the effect can be accurately constrained. To this end we provide redshift-dependent fitting functions to our results and propose a new tool for the observational study of intrinsic galaxy alignments. For a shallow survey with   z _m∼ 0.4  we find III to be an order of magnitude larger than the expected cosmological GGG shear signal. Compared to the two-point intrinsic ellipticity correlation which is similar in amplitude to the two-point shear signal at these survey depths, third-order statistics therefore offer a promising new way to constrain models of intrinsic galaxy alignments. Early shallow data from the next generation of very wide weak lensing surveys will be optimal for this type of study.     

Evolution of the dark matter distribution with three-dimensional weak lensing

We present a direct detection of the growth of large-scale structure, using weak gravitational lensing and photometric redshift data from the COMBO-17 survey. We use deep R -band imaging of two  0.5 × 0.5 deg²  fields, affording shear estimates for over 52 000 galaxies; we combine these with photometric redshift estimates from our 17-band survey, in order to obtain a 3D shear field. We find theoretical models for evolving matter power spectra and correlation functions, and fit the corresponding shear correlation functions to the data as a function of redshift. We detect the evolution of the power at the 4.7σ level given reasonable priors, and measure the rate of evolution for  0 < z < 1  . We also fit correlation functions to our 3D data as a function of cosmological parameters σ₈ and  Ω_Λ  . We find joint constraints on  Ω_Λ  and σ₈, demonstrating an improvement in accuracy by ≃40 per cent over that available from 2D weak lensing for the same area.     

Galaxy–QSO correlation induced by weak gravitational lensing arising from large-scale structure

Observational evidence shows that gravitational lensing induces an angular correlation between the distribution of galaxies and much more distant QSOs. We use weak gravitational lensing theory to calculate this angular correlation, updating previous calculations and presenting new results exploring the dependence of the correlation on the large-scale structure. We study the dependence of the predictions on a variety of cosmological models, such as cold dark matter models, mixed dark matter models and models based on quintessence. We also study the dependence on the assumptions made about the nature of the primordial fluctuation spectrum: adiabatic, isocurvature and power spectra motivated by the cosmic string scenario are investigated. Special attention is paid to the issue of galaxy biasing, which is fully incorporated. We show that different mass power spectra imply distinct predictions for the angular correlation, and therefore the angular correlation provides an extra source of information about cosmological parameters and mechanisms of structure formation. We compare our results with observational data and discuss their potential uses. In particular, it is suggested that the observational determination of the galaxy–QSO correlation may be used to give an independent measurement of the mass power spectrum.     

Probing the gravity-induced bias with weak lensing: test of analytical results against simulations

Future weak lensing surveys will directly probe the density fluctuation in the Universe. Recent studies have shown how the statistics of the weak lensing convergence field is related to the statistics of collapsed objects. Extending earlier analytical results on the probability distribution function of the convergence field, we show that the bias associated with the convergence field can be directly related to the bias associated with the statistics of underlying overdense objects. This will provide us with a direct method to study the gravity-induced bias in galaxy clustering. Based on our analytical results, which use the hierarchical Ansatz for non-linear clustering, we study how such a bias depends on the smoothing angle and the source redshift. We compare our analytical results with ray-tracing experiments through N -body simulations of four different realistic cosmological scenarios, and find a very good match. Our study shows that the bias in the convergence map strongly depends on the background geometry and hence can help us in distinguishing different cosmological models in addition to improving our understanding of the gravity-induced bias in galaxy clustering.     

Theory and statistics of weak lensing from large-scale mass inhomogeneities

Weak lensing by large-scale mass inhomogeneities in the Universe induces correlations in the observed ellipticities of distant sources. We first review the harmonic analysis and statistics required of these correlations and discuss calculations for the predicted signal. We consider the ellipticity correlation function, the mean-square ellipticity, the ellipticity power spectrum and a global maximum-likelihood analysis to isolate a weak-lensing signal from the data. Estimates for the sensitivity of a survey of a given area, surface density, and mean intrinsic source ellipticity are presented. We then apply our results to the FIRST radio-source survey. We predict an rms ellipticity of roughly 0.011 in 1 × 1 deg² pixels and 0.018 in 20 × 20 arcmin² pixels if the power spectrum is normalized to σ₈ Ω^0.53 = 0.6, as indicated by the cluster abundance. The signal is significantly larger in some models if the power spectrum is normalized instead to the COBE anisotropy. The uncertainty in the predictions from imprecise knowledge of the FIRST redshift distribution is about 25 per cent in the rms ellipticity. We show that FIRST should be able to make a statistically significant detection of a weak-lensing signal for cluster-abundance-normalized power spectra.     

Weak lensing predictions at intermediate scales

As pointed out in previous studies, the measurement of the skewness of the convergence field κ will be useful in breaking the degeneracy among the cosmological parameters constrained from weak lensing observations. The combination of shot noise and finite survey volume implies that such a measurement is likely to be performed in a range of intermediate scales (0.5 to 20 arcmin) where neither perturbation theory nor the hierarchical ansatz applies. Here we explore the behaviour of the skewness of κ at these intermediate scales, based on results for the non-linear evolution of the mass bispectrum. We combined different ray-tracing simulations to test our predictions, and we find that our calculations describe accurately the transition from the weakly non-linear to the strongly non-linear regime. We show that the single lens-plane approximation remains accurate even in the non-linear regime, and we explicitly calculate the corrections to this approximation. We also discuss the prospects of measuring the skewness in upcoming weak lensing surveys.     

Investigating cosmological weak lensing with the ray-bundle method

Using the ray-bundle method for calculating gravitational lens magnifications, we outline a method by which the magnification probability may be determined specifically in the weak lensing limit for cosmological models obtained from N -body simulations.
16 different models are investigated, which are variations on three broad classes of cold dark matter model: the standard model with  (Ω₀, λ ₀)=(1.0,0.0)  , the open model with  (Ω₀, λ ₀)=(0.3,0.0)  and the lambda model, which is a flat model with a cosmological constant  (Ω₀, λ ₀)=(0.3,0.7)  .
The effects of varying the Hubble parameter, H ₀, the power spectrum shape parameter, Γ, and the cluster mass normalization, σ ₈, are studied. It is shown that there is no signature of these parameters in the weak lensing magnification distributions. The magnification probability distributions are also shown to be independent of the numerical parameters such as the lens mass and simulation box size in the N -body simulations.