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.     

An enlarged cosmic shear survey with the William Herschel Telescope

We report the results of a cosmic shear survey using the 4.2-m William Herschel Telescope on La Palma, to a depth of   R = 25.8 ( z ≈ 0.8)  , over 4 deg². The shear correlation functions are measured on scales from 1 to 15 arcmin, and are used to constrain cosmological parameters. We ensure that our measurements are free from instrumental systematic effects by performing a series of tests, including a decomposition of the signal into E - and B -modes. We also reanalyse the data independently, using the shear measurement pipeline developed for the COMBO-17 survey. This confirms our results and also highlights various effects introduced by different implementations of the basic 'Kaiser–Squires–Broadhurst' shear measurement method. We find that the normalization of the matter power spectrum on 8  h ⁻¹ Mpc scales is  σ₈= (1.02 ± 0.15)(0.3/Ω _m )^1/2  , where the 68 per cent confidence limit error includes noise, sample variance, covariance between angular scales, systematic effects, redshift uncertainty and marginalization over other parameters. We compare these results with other cosmic shear surveys and with recent constraints from the Wilkinson Microwave Anisotropy Probe experiment.     

Full-sky maps for gravitational lensing of the cosmic microwave background

We use the large cosmological Millennium Simulation (MS) to construct the first all-sky maps of the lensing potential and the angle, aiming at gravitational lensing of the cosmic microwave background (CMB), with the goal of properly including small-scale non-linearities and non-Gaussianity. Exploiting the Born approximation, we implement a map-making procedure based on direct ray tracing through the gravitational potential of the MS. We stack the simulation box in redshift shells up to z ∼ 11, producing continuous all-sky maps with arcmin angular resolution. A randomization scheme avoids the repetition of structures along the line of sight, and structures larger than the MS box size are added to supply the missing contribution of large-scale (LS) structures to the lensing signal. The angular power spectra of the projected lensing potential and the deflection-angle modulus agree quite well with semi-analytic estimates on scales down to a few arcmin, while we find a slight excess of power on small scales, which we interpret as being due to non-linear clustering in the MS. Our map-making procedure, combined with the LS adding technique, is ideally suited for studying lensing of CMB anisotropies, for analysing cross-correlations with foreground structures, or other secondary CMB anisotropies such as the Rees–Sciama effect.     

The three-dimensional power spectrum of dark and luminous matter from the VIRMOS-DESCART cosmic shear survey

We present the first optimal power spectrum estimation and three-dimensional deprojections for the dark and luminous matter and their cross-correlations. The results are obtained using a new optimal fast estimator, deprojected using minimum variance and Singular Value Decomposition (SVD) techniques. We show the resulting 3D power spectra for dark matter and galaxies, and their covariance for the VIRMOS-DESCART weak lensing shear and galaxy data. The survey is most sensitive to non-linear scales   k _NL∼ 1 h Mpc⁻¹  . On these scales, our 3D power spectrum of dark matter is in good agreement with the RCS 3D power spectrum found by Tegmark & Zaldarriaga. Our galaxy power is similar to that found by the 2MASS survey, and larger than that of SDSS, APM and RCS, consistent with the expected difference in galaxy population.
We find an average bias   b = 1.24 ± 0.18  for the I -selected galaxies, and a cross-correlation coefficient   r = 0.75 ± 0.23  . Together with the power spectra, these results optimally encode the entire two point information about dark matter and galaxies, including galaxy–galaxy lensing. We address some of the implications regarding galaxy haloes and mass-to-light ratios. The best-fitting 'halo' parameter   h ≡ r / b = 0.57 ± 0.16  , suggesting that dynamical masses estimated using galaxies systematically underestimate total mass.
Ongoing surveys, such as the Canada–France–Hawaii Telescope Legacy Survey, will significantly improve on the dynamic range, and future photometric redshift catalogues will allow tomography along the same principles.     

Direct observation of cosmic strings via their strong gravitational lensing effect – I. Predictions for high-resolution imaging surveys

We use present theoretical estimates for the density of long cosmic strings to predict the number of strong gravitational lensing events in astronomical imaging surveys as a function of the angular resolution and survey area. We show that angular resolution is the single most important factor, and that interesting limits on the dimensionless string tension   G μ/ c ²  can be obtained by existing and planned surveys. At the resolution of the Hubble Space Telescope ( HST ) (0.14 arcsec), it is sufficient to survey of the order of a few square degrees – well within reach of the current HST archive – to probe the regime   G μ/ c ²∼ 10⁻⁷  . If lensing by cosmic strings is not detected, such a survey would improve the limit on the string tension by a factor of two over that available from the cosmic microwave background. Future high resolution imaging surveys, covering a few hundred square degrees or more, either from space in the optical or from large-format radio telescopes on the ground, would be able to further lower this limit to   G μ/ c ²∼ 10⁻⁸  . These limits will not be improved significantly by increasing the solid angle of the survey.     

The effect of a binary source companion on the astrometric microlensing behaviour

If gravitational microlensing occurs in a binary source system, both source components are magnified, and the resulting light curve deviates from the standard one of a single source event. However, in most cases only one source component is highly magnified and the other component (the companion) can be treated as a simple blending source: this is a blending approximation. In this paper we show that, unlike the light curves, the astrometric curves, representing the trajectories of the source image centroid, of an important fraction of binary source events will not be sufficiently well-modelled by the blending effect alone. This is because the centroid shift induced by the source companion endures to considerable distances from the lens. Therefore, in determining the lens parameters from astrometric curves to be measured by future high-precision astrometric instruments, it will be important to take the full effect of the source companion into consideration.     

The effect of weak lensing on the angular correlation function of faint galaxies

The angular correlation function ο(θ) of faint galaxies is affected both by non-linear gravitational evolution and by magnification bias resulting from gravitational lensing. We compute the resulting ο(θ) for different cosmological models and show how its shape and redshift evolution depend on Ω and Λ. For galaxies at redshift greater than 1 ( R magnitude fainter than about 24), magnification bias can significantly enhance or suppress ο(θ), depending on the slope of the number–magnitude relation. We show, for example, how it changes the ratio of ο(θ) for two galaxy samples with different number count slopes.