Ludovic Van Waerbeke

CFHTLenS: the Canada–France–Hawaii Telescope Lensing Survey

We present the Canada–France–Hawaii Telescope Lensing Survey (CFHTLenS) that accurately determines a weak gravitational lensing signal from the full 154 deg^2 of deep multicolour data obtained by the CFHT Legacy Survey. Weak gravitational lensing by large-scale structure is widely recognized as one of the most powerful but technically challenging probes of cosmology. We outline the CFHTLenS analysis pipeline, describing how and why every step of the chain from the raw pixel data to the lensing shear and photometric redshift measurement has been revised and improved compared to previous analyses of a subset of the same data. We present a novel method to identify data which contributes a non-negligible contamination to our sample and quantify the required level of calibration for the survey. Through a series of cosmology-insensitive tests we demonstrate the robustness of the resulting cosmic shear signal, presenting a science-ready shear and photometric redshift catalogue for future exploitation.

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.

CFHTLenS tomographic weak lensing cosmological parameter constraints: Mitigating the impact of intrinsic galaxy alignments

We present a finely-binned tomographic weak lensing analysis of the Canada-FranceHawaii Telescope Lensing Survey, CFHTLenS, mitigating contamination to the signal from the presence of intrinsic galaxy alignments via the simultaneous fit of a cosmological model and an intrinsic alignment model. CFHTLenS spans 154 square degrees in five optical bands, with accurate shear and photometric redshifts for a galaxy sample with a median redshift of zm = 0:70. We estimate the 21 sets of cosmic shear correlation functions associated with six redshift bins, each spanning the angular range of 1:5 < < 35 arcmin. We combine this CFHTLenS data with auxiliary cosmological probes: the cosmic microwave background with data from WMAP7, baryon acoustic oscillations with data from BOSS, and a prior on the Hubble constant from the HST distance ladder. This leads to constraints on the normalisation of the matter power spectrum 8 = 0:799 0:015 and the matter density parameter m = 0:271 0:010 for a flat CDM cosmology. For a flat wCDM cosmology we constrain the dark energy equation of state parameter w = 1:02 0:09. We also provide constraints for curved CDM and wCDM cosmologies. We find the intrinsic alignment contamination to be galaxy-type dependent with a significant intrinsic alignment signal found for early-type galaxies, in contrast to the late-type galaxy sample for which the intrinsic alignment signal is found to be consistent with zero.

The shear testing programme 2 : factors affecting high-precision weak-lensing analyses.

The Shear Testing Programme (STEP) is a collaborative project to improve the accuracy and reliability of weak-lensing measurement, in preparation for the next generation of wide-field surveys. We review 16 current and emerging shear-measurement methods in a common language, and assess their performance by running them (blindly) on simulated images that contain a known shear signal. We determine the common features of algorithms that most successfully recover the input parameters. A desirable goal would be the combination of their best elements into one ultimate shear-measurement method. In this analysis, we achieve previously unattained discriminatory precision via a combination of more extensive simulations and pairs of galaxy images that have been rotated with respect to each other. That removes the otherwise overwhelming noise from their intrinsic ellipticities. Finally, the robustness of our simulation approach is confirmed by testing the relative calibration of methods on real data. Weak-lensing measurements have improved since the first STEP paper. Several methods now consistently achieve better than 2 per cent precision, and are still being developed. However, we can now distinguish all methods from perfect performance. Our main concern continues to be the potential for a multiplicative shear calibration bias: not least because this cannot be internally calibrated with real data. We determine which galaxy populations are responsible for bias and, by adjusting the simulated observing conditions, we also investigate the effects of instrumental and atmospheric parameters. The simulated point spread functions are not allowed to vary spatially, to avoid additional confusion from interpolation errors. We have isolated several previously unrecognized aspects of galaxy shape measurement, in which focused development could provide further progress towards the sub-per cent level of precision desired for future surveys. These areas include the suitable treatment of image pixellization and galaxy morphology evolution. Ignoring the former effect affects the measurement of shear in different directions, leading to an overall underestimation of shear and hence the amplitude of the matter power spectrum. Ignoring the second effect could affect the calibration of shear estimators as a function of galaxy redshift, and the evolution of the lensing signal, which will be vital to measure parameters including the dark energy equation of state.

CFHTLenS: Combined probe cosmological model comparison using 2D weak gravitational lensing

We present cosmological constraints from 2D weak gravitational lensing by the large-scale structure in the Canada–France–Hawaii Telescope Lensing Survey (CFHTLenS) which spans 154 deg^2 in five optical bands. Using accurate photometric redshifts and measured shapes for 4.2 million galaxies between redshifts of 0.2 and 1.3, we compute the 2D cosmic shear correlation function over angular scales ranging between 0.8 and 350 arcmin. Using non-linear models of the dark-matter power spectrum, we constrain cosmological parameters by exploring the parameter space with Population Monte Carlo sampling. The best constraints from lensing alone are obtained for the small-scale density-fluctuations amplitude σ_8 scaled with the total matter density Ωm. For a flat Λcold dark matter (ΛCDM) model we obtain σ_8(Ω_m/0.27)0.6 = 0.79 ± 0.03. We combine the CFHTLenS data with 7-year Wilkinson Microwave Anisotropy Probe (WMAP7), baryonic acoustic oscillations (BAO): SDSS-III (BOSS) and a Hubble Space Telescope distance-ladder prior on the Hubble constant to get joint constraints. For a flat ΛCDM model, we find Ω_m = 0.283 ± 0.010 and σ_8 = 0.813 ± 0.014. In the case of a curved wCDM universe, we obtain Ω_m = 0.27 ± 0.03, σ_8 = 0.83 ± 0.04, w0 = −1.10 ± 0.15 and Ω_K = 0.006^(+0.006)_(− 0.004). We calculate the Bayesian evidence to compare flat and curved ΛCDM and dark-energy CDM models. From the combination of all four probes, we find models with curvature to be at moderately disfavoured with respect to the flat case. A simple dark-energy model is indistinguishable from ΛCDM. Our results therefore do not necessitate any deviations from the standard cosmological model.

A weak lensing study of X-ray groups in the cosmos survey: form and evolution of the mass-luminosity relation

Measurements of X-ray scaling laws are critical for improving cosmological constraints derived with the halo mass function and for understanding the physical processes that govern the heating and cooling of the intracluster medium. In this paper, we use a sample of 206 X-ray-selected galaxy groups to investigate the scaling relation between X-ray luminosity (L_X) and halo mass (M_(200)) where M_(200) is derived via stacked weak gravitational lensing. This work draws upon a broad array of multi-wavelength COSMOS observations including 1.64 degrees^2 of contiguous imaging with the Advanced Camera for Surveys to a limiting magnitude of I_(F814W) = 26.5 and deep XMM-Newton/Chandra imaging to a limiting flux of 1.0 × 10^(–15) erg cm6(–2) s^(–1) in the 0.5-2 keV band. The combined depth of these two data sets allows us to probe the lensing signals of X-ray-detected structures at both higher redshifts and lower masses than previously explored. Weak lensing profiles and halo masses are derived for nine sub-samples, narrowly binned in luminosity and redshift. The COSMOS data alone are well fit by a power law, M_(200) (L_X)^α, with a slope of α = 0.66 ± 0.14. These results significantly extend the dynamic range for which the halo masses of X-ray-selected structures have been measured with weak gravitational lensing. As a result, tight constraints are obtained for the slope of the M-L_X relation. The combination of our group data with previously published cluster data demonstrates that the M-L_X relation is well described by a single power law, α = 0.64 ± 0.03, over two decades in mass, M_(200) ~ 10^(13.5)-10^(15.5) h^(–1)_72 M_☉. These results are inconsistent at the 3.7σ level with the self-similar prediction of α = 0.75. We examine the redshift dependence of the M-L_X relation and find little evidence for evolution beyond the rate predicted by self-similarity from z ~ 0.25 to z ~ 0.

Cosmology with weak lensing surveys

Weak gravitational lensing is responsible for the shearing and magnification of the images of high-redshift sources due to the presence of intervening mass. Since the lensing effects arise from deflections of the light rays due to fluctuations of the gravitational potential, they can be directly related to the underlying density field of the large-scale structures. Weak gravitational surveys are complementary to both galaxy surveys and cosmic microwave background observations as they probe unbiased nonlinear matter power spectra at medium redshift. Ongoing CMBR experiments such as WMAP and a future Planck satellite mission will measure the standard cosmological parameters with unprecedented accuracy. The focus of attention will then shift to understanding the nature of dark matter and vacuum energy: several recent studies suggest that lensing is the best method for constraining the dark energy equation of state. During the next 5 year period, ongoing and future weak lensing surveys such as the Joint Dark Energy Mission (JDEM; e.g. SNAP) or the Large-aperture Synoptic Survey Telescope will play a major role in advancing our understanding of the universe in this direction. In this review article, we describe various aspects of probing the matter power spectrum and the bi-spectrum and other related statistics with weak lensing surveys. This can be used to probe the background dynamics of the universe as well as the nature of dark matter and dark energy.

Cosmological constraints from the 100-deg2 weak-lensing survey★

We present a cosmic shear analysis of the 100-deg 2 weak-lensing survey, combining data from the CFHTLS-Wide, RCS, VIRMOS-DESCART and GaBoDS surveys. Spanning ∼100 deg 2 , with a median source redshift ∼0.78, this combined survey allows us to place tight joint constraints on the matter density parameter Ω m , and the amplitude of the matter power spectrum σ 8 , finding σ 8 (Ω m /0.24) 0.59 = 0.84 ±0.05. Tables of the measured shear correlation function and the calculated covariance matrix for each survey are included as supplementary material to the online version of this article. The accuracy of our results is a marked improvement on previous work owing to three important differences in our analysis; we correctly account for sample variance errors by including a non-Gaussian contribution estimated from numerical simulations; we correct the measured shear for a calibration bias as estimated from simulated data; we model the redshift distribution, n(z), of each survey from the largest deep photometric redshift catalogue currently available from the CFHTLS-Deep. This catalogue is randomly sampled to reproduce the magnitude distribution of each survey with the resulting survey-dependent n(z) parametrized using two different models. While our results are consistent for the n(z) models tested, we find that our cosmological parameter constraints depend weakly (at the 5 per cent level) on the inclusion or exclusion of galaxies with low-confidence photometric redshift estimates (z > 1.5). These high-redshift galaxies are relatively few in number but contribute a significant weak-lensing signal. It will therefore be important for future weak-lensing surveys to obtain near-infrared data to reliably determine the number of high-redshift galaxies in cosmic shear analyses.

Results of the GREAT08 Challenge: an image analysis competition for cosmological lensing

We present the results of the Gravitational LEnsing Accuracy Testing 2008 (GREAT08) Challenge, a blind analysis challenge to infer weak gravitational lensing shear distortions from images. The primary goal was to stimulate new ideas by presenting the problem to researchers outside the shear measurement community. Six GREAT08 Team methods were presented at the launch of the Challenge and five additional groups submitted results during the 6-month competition. Participants analyzed 30 million simulated galaxies with a range in signal-to-noise ratio, point spread function ellipticity, galaxy size and galaxy type. The large quantity of simulations allowed shear measurement methods to be assessed at a level of accuracy suitable for currently planned future cosmic shear observations for the first time. Different methods perform well in different parts of simulation parameter space and come close to the target level of accuracy in several of these. A number of fresh ideas have emerged as a result of the Challenge including a re-examination of the process of combining information from different galaxies, which reduces the dependence on realistic galaxy modelling. The image simulations will become increasingly sophisticated in future GREAT Challenges, meanwhile the GREAT08 simulations remain as a benchmark for additional developments in shear measurement algorithms.

Potential sources of contamination to weak lensing measurements: constraints from N-body simulations

We investigate the expected correlation between the weak gravitational shear of distant galaxies and the orientation of foreground galaxies, throu gh the use of numerical simulations. This shear-ellipticity correlation can mimic a cosmological weak lensing signal, and is potentially the limiting physical systematic effect for cosmolo gy with future high-precision weak lensing surveys. We find that, if uncorrected, the shear-ell ipticity correlation could contribute up to 10% of the weak lensing signal on scales up to 20 arcminutes, for lensing surveys with a median depth zm = 1. The most massive foreground galaxies are expected to cause the largest correlations, a result also seen in the Sloan Digital Sky Sur vey. We find that the redshift dependence of the effect is proportional to the lensing efficie ncy of the foreground, and this offers prospects for removal to high precision, although with some model dependence. The contamination is characterised by a weakly negative B-mode, which can be used as a diagnostic of systematic errors. We also provide more accurate predictions for a second potential source of error, the intrinsic alignment of nearby galaxies . This source of contamination is less important, however, as it can be easily removed with distance information.