David J. Bacon

The Shear Testing Programme ¿ I. Weak lensing analysis of simulated ground-based observations

The Shear Testing Programme (STEP) is a collaborative project to improve the accuracy and reliability of all weak lensing measurements in preparation for the next generation of wide-field surveys. In this first STEP paper, we present the results of a blind analysis of simulated ground-based observations of relatively simple galaxy morphologies. The most successful methods are shown to achieve percent level accuracy. From the cosmic shear pipelines that have been used to constrain cosmology, we find weak lensing shear measured to an accuracy that is within the statistical errors of current weak lensing analyses, with shear measurements accurate to better than 7 per cent. The dominant source of measurement error is shown to arise from calibration uncertainties where the measured shear is over or underestimated by a constant multiplicative factor. This is of concern as calibration errors cannot be detected through standard diagnostic tests. The measured calibration errors appear to result from stellar contamination, false object detection, the shear measurement method itself, selection bias and/or the use of biased weights. Additive systematics (false detections of shear) resulting from residual point-spread function anisotropy are, in most cases, reduced to below an equivalent shear of 0.001, an order of magnitude below cosmic shear distortions on the scales probed by current surveys. Our results provide a snapshot view of the accuracy of current ground-based weak lensing methods and a benchmark upon which we can improve. To this end we provide descriptions of each method tested and include details of the eight different implementations of the commonly used Kaiser, Squires & Broadhurst method (KSB+) to aid the improvement of future KSB+ analyses.

Dark matter maps reveal cosmic scaffolding

Ordinary baryonic particles (such as protons and neutrons) account for only one-sixth of the total matter in the Universe. The remainder is a mysterious ‘dark matter’ component, which does not interact via electromagnetism and thus neither emits nor reflects light. As dark matter cannot be seen directly using traditional observations, very little is currently known about its properties. It does interact via gravity, and is most effectively probed through gravitational lensing: the deflection of light from distant galaxies by the gravitational attraction of foreground mass concentrations. This is a purely geometrical effect that is free of astrophysical assumptions and sensitive to all matter—whether baryonic or dark. Here we show high-fidelity maps of the large-scale distribution of dark matter, resolved in both angle and depth. We find a loose network of filaments, growing over time, which intersect in massive structures at the locations of clusters of galaxies. Our results are consistent with predictions of gravitationally induced structure formation, in which the initial, smooth distribution of dark matter collapses into filaments then into clusters, forming a gravitational scaffold into which gas can accumulate, and stars can be built.

Joint cosmic shear measurements with the Keck and William Herschel Telescopes

The recent measurements of weak lensing by large-scale structure present significant new opportunities for studies of the matter distribution in the Universe. Here, we present a new cosmic shear survey carried out with the Echelle Spectrograph and Imager on the Keck II telescope. This covers a total of 0.6 square degrees in 173 fields probing independent lines of sight, hence minimizing the impact of sample variance. We also extend our measurements of cosmic shear with the William Herschel Telescope (Bacon, Refregier & Ellis 2000) to a survey area of I square degree. The joint measurements with two independent telescopes allow us to assess the impact of instrument-specific systematics, one of the major difficulties in cosmic shear measurements. For both surveys, we account for effects such as smearing by the point spread function and shearing due to telescope optics carefully. We find negligible residuals in both cases and recover mutually consistent cosmic shear signals, significant at the 5.1σ level. We present a simple method to compute the statistical error in the shear correlation function, including non-Gaussian sample variance and the covariance between different angular bins. We measure shear correlation functions for all fields and use these to ascertain the amplitude of the matter power spectrum, finding σ 8 (Ω m /0.3) 0 . 6 8 = 0.97 ′ 0.13 with 0.14 < Ω m < 0.65 in a A cold dark matter (ACDM) model with r = 0.21. These 68 per cent confidence level uncertainties include sample variance, statistical noise, redshift uncertainty and the error in the shear measurement method. The results from our two independent surveys are both consistent with measurements of cosmic shear from other groups. We discuss how our results compare with current normalization from cluster abundance.

Probing dark energy with the shear-ratio geometric test

We adapt the Jain-Taylor (2003) shear-ratio geometric lensing method to measure the dark energy equation of state, w = pv /ρv and its time derivative from dark matter haloes in cosmologies with arbitrary spatial curvature. The full shear-ratio covariance matrix is calculated for lensed sources, including the intervening large-scale structure and photometric redshift errors as additional sources of noise, and a maximum likelihood method for applying the test is presented. Decomposing the lensing matter distribution into dark matter haloes we calculate the parameter covariance matrix for an arbitrary experiment. Combining with the expected results from the cosmic microwave background (CMB) we design an optimal survey for probing dark energy. This shows that a targeted survey imaging 60 of the largest clusters in a hemisphere with five-band optical photometric redshifts to a median galaxy depth of Z m = 0.9 could measure ω 0 = ω(z = 0) to a marginal 1σ error of Δω 0 = 0.5. We marginalize over all other parameters including ω a , where the equation of state is parametrized in terms of scalefactor a as w(a) = ω 0 + ω a (1- a). For higher accuracy a large-scale photometric redshift survey is required, where the largest gain in signal arises from the numerous ≈0 14 M ⊙ haloes corresponding to medium-sized galaxy clusters. Combined with the expected Planck Surveyor results, such a near-future five-band survey covering 10000 deg 2 to Z m = 0.7 could measure ω 0 to Δω 0 = 0.075 and Δωa = 0.33. A stronger combined constraint is put on w measured at the pivot redshift z p = 0.27 of Aw(zp) = 0.0298. We compare and combine the geometric test with the cosmological and dark energy parameters measured from planned baryon acoustic oscillation (BAO) and supernova Type Ia experiments, and find that the geometric test results combine with a significant reduction in errors due to different degeneracies. A combination of geometric lensing, CMB and BAO experiments could achieve Δω 0 = 0.047 and Δωa = 0.111 with a pivot redshift constraint of Δω(Z p ) = 0.020 at z p = 0.62. Simple relations are presented that show how our lensing results can be scaled to other telescope classes and survey parameters.

Cosmological constraints from COMBO‐17 using 3D weak lensing

We present the first application of the {3D} cosmic shear method developed in Heavens, Kitching \& Taylor and the geometric shear-ratio analysis developed in Taylor et al., to the {COMBO-17} data set. {3D} cosmic shear has been used to analyse galaxies with redshift estimates from two random {COMBO-17} fields covering 0.52 deg2 in total, providing a conditional constraint in the (??8, ??m) plane as well as a conditional constraint on the equation of state of dark energy, parametrized by a constant w ??? pde/??dec2. The (??8, ??m) plane analysis constrained the relation between ??8 and ??m to be ??8(??m/0.3)0.57+/-0.19 = 1.06+0.17-0.16, in agreement with a {2D} cosmic shear analysis of {COMBO-17.} The {3D} cosmic shear conditional constraint on w using the two random fields is w = -1.27+0.64-0.70. The geometric shear-ratio analysis has been applied to the A901/2 field, which contains three small galaxy clusters. Combining the analysis from the A901/2 field, using the geometric shear-ratio analysis, and the two random fields, using {3D} cosmic shear, w is conditionally constrained to w = -1.08+0.63-0.58. The errors presented in this paper are shown to agree with Fisher matrix predictions made in Heavens, Kitching \& Taylor and Taylor et al. When these methods are applied to large data sets, as expected soon from surveys such as {Pan-STARRS} and {VST-KIDS}, the dark energy equation of state could be constrained to an unprecedented degree of accuracy.

Mapping the 3D dark matter with weak lensing in COMBO‐17

We present a three-dimensional (3D) lensing analysis of the z = 0.16 supercluster A901/2, resulting in a 3D map of the dark matter distribution within a 3 x 10 5 [h -1 Mpc] 3 volume. This map is generated from a combined catalogue of 3D galaxy coordinates together with shear estimates, using R-band imaging and photometric redshifts from the COMBO-17 survey. We perform a X 2 fit of isothermal spheres to the tangential shear pattern around each cluster as a function of redshift to estimate the 3D positions and masses of the main clusters in the supercluster from lensing alone. Motivated by the appearance of a second cluster behind A902 in galaxy number density, we also fit a two-cluster model to A902. We then present the first 3D map of the dark-matter gravitational potential field, Φ, from weak lensing using the Kaiser-Squires and Taylor inversion methods. These maps clearly show the potential wells of the main supercluster components, including the new cluster behind A902, and demonstrate the applicability of 3D dark-matter mapping and projection-free, mass-selected cluster finding to current data. Finally, we develop the halo model of dark matter and galaxy clustering and compare this with the auto- and cross-correlation functions of the 3D gravitational potential, galaxy number densities and galaxy luminosity densities measured in the A901/2 field. We find significant anticorrelations between the gravitational potential field and the galaxy number density and luminosities, as expected due to baryonic infall into dark-matter concentrations. We find good agreement with the halo model for the number densities and luminosity correlation functions, but some disagreement with the shape of the gravitational potential correlation function, which we attribute to finite-field effects.

Weak Lensing from Space. III. Cosmological Parameters

Weak gravitational lensing provides a unique method to directly map the dark matter in the universe and measure cosmological parameters. Current weak-lensing surveys are limited by the atmospheric seeing from the ground and by the small fields of view of existing space telescopes. We study how a future wide-field space telescope can measure the lensing power spectrum and skewness and thus set constraints on cosmological parameters. The lensing sensitivity was calculated using detailed image simulations and instrumental specifications studied in earlier papers in this series. For instance, the planned SuperNova/Acceleration Probe (SNAP) mission will be able to measure the matter density parameter Ωm and the dark energy equation-of-state parameter w with precisions comparable and nearly orthogonal to those derived with SNAP from supernovae. The constraints degrade by a factor of about 2 if redshift tomography is not used but are little affected if only the skewness is dropped. We also study how the constraints on these parameters depend on the survey geometry and define an optimal observing strategy.

Mapping the 3D dark matter potential with weak shear

We investigate the practical implementation of Taylors three-dimensional gravitational potential reconstruction method using weak gravitational lensing, together with the requisite reconstruction of the lensing potential. This methodology calculates the 3D gravitational potential given a knowledge of shear estimates and redshifts for a set of galaxies. We analytically estimate the noise expected in the reconstructed gravitational field taking into account the uncertainties associated with a finite survey, photometric redshift uncertainty, redshift-space distortions and multiple scattering events. In order to implement this approach for future data analysis, we simulate the lensing distortion fields due to various mass distributions. We create catalogues of galaxies sampling this distortion in three dimensions, with realistic spatial distribution and intrinsic ellipticity for both ground-based and space-based surveys. Using the resulting catalogues of galaxy position and shear, we demonstrate that it is possible to reconstruct the lensing and gravitational potentials with our method. For example, we demonstrate that a typical ground-based shear survey with redshift limit z = 1 and photometric redshifts with error Δz = 0.05 is directly able to measure the 3D gravitational potential for mass concentrations ≥10 1 4 M O . between 0.1 ≤ z ≤ 0.5. and can statistically measure the potential at much lower mass limits. The intrinsic ellipticity of objects is found to be a serious source of noise for the gravitational potential, which can be overcome by Wiener filtering or examining the potential statistically over many fields. We examine the use of the 3D lensing potential to measure mass and position of clusters in 3D, and to detect clusters behind clusters.

Evolution of the Dark Matter Distribution with 3-D 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. Deep R-band imaging of two 0.5??0.5 square degree fields is used to provide shear estimates for over 52000 galaxies; these are combined with photometric redshift estimates from our 17 band survey, in order to obtain a 3-D shear field. We discuss how theoretical models for evolving matter power spectra and correlation functions cab be used to find a best fit to this 3-D shear field. We present the detection of the evolution of the power, and measurements of the rate of evolution for 0{\textless}1. We discuss future refinements which will improve the accuracy with which the effect can be measured.