A likelihood-based method for measuring weak gravitational lensing shear in deep galaxy surveys is described and applied to the Canada-France-Hawaii Telescope (CFHT) Lensing Survey (CFHTLenS). ...CFHTLenS comprises 154 deg2 of multi-colour optical data from the CFHT Legacy Survey, with lensing measurements being made in the i
′ band to a depth i′AB < 24.7, for galaxies with signal-to-noise ratio νSN 10. The method is based on the lensfit algorithm described in earlier papers, but here we describe a full analysis pipeline that takes into account the properties of real surveys. The method creates pixel-based models of the varying point spread function (PSF) in individual image exposures. It fits PSF-convolved two-component (disc plus bulge) models to measure the ellipticity of each galaxy, with Bayesian marginalization over model nuisance parameters of galaxy position, size, brightness and bulge fraction. The method allows optimal joint measurement of multiple, dithered image exposures, taking into account imaging distortion and the alignment of the multiple measurements. We discuss the effects of noise bias on the likelihood distribution of galaxy ellipticity. Two sets of image simulations that mirror the observed properties of CFHTLenS have been created to establish the method's accuracy and to derive an empirical correction for the effects of noise bias.
Higher order, non-Gaussian aspects of the large-scale structure carry valuable information on structure formation and cosmology, which is complementary to second-order statistics. In this work, we ...measure second- and third-order weak-lensing aperture-mass moments from the Canada–France–Hawaii Lensing Survey (CFHTLenS) and combine those with cosmic microwave background (CMB) anisotropy probes. The third moment is measured with a significance of 2σ. The combined constraint on Σ8 = σ8(Ωm/0.27)α is improved by 10 per cent, in comparison to the second-order only, and the allowed ranges for Ωm and σ8 are substantially reduced. Including general triangles of the lensing bispectrum yields tighter constraints compared to probing mainly equilateral triangles. Second- and third-order CFHTLenS lensing measurements improve Planck CMB constraints on Ωm and σ8 by 26 per cent for flat Λ cold dark matter. For a model with free curvature, the joint CFHTLenS–Planck result is Ωm = 0.28 ± 0.02 (68 per cent confidence), which is an improvement of 43 per cent compared to Planck alone. We test how our results are potentially subject to three astrophysical sources of contamination: source-lens clustering, the intrinsic alignment of galaxy shapes, and baryonic effects. We explore future limitations of the cosmological use of third-order weak lensing, such as the non-linear model and the Gaussianity of the likelihood function.
We present weak lensing and X-ray analysis of 12 low-mass clusters from the Canada–France–Hawaii Telescope Lensing Survey and XMM-CFHTLS surveys. We combine these systems with high-mass systems from ...Canadian Cluster Comparison Project and low-mass systems from Cosmic Evolution Survey to obtain a sample of 70 systems, spanning over two orders of magnitude in mass. We measure core-excised L
X–T
X, M–L
X and M–T
X scaling relations and include corrections for observational biases. By providing fully bias-corrected relations, we give the current limitations for L
X and T
X as cluster mass proxies. We demonstrate that T
X benefits from a significantly lower intrinsic scatter at fixed mass than L
X. By studying the residuals of the bias-corrected relations, we show for the first time using weak lensing masses that galaxy groups seem more luminous and warmer for their mass than clusters. This implies a steepening of the M–L
X and M–T
X relations at low masses. We verify the inferred steepening using a different high-mass sample from the literature and show that variance between samples is the dominant effect leading to discrepant scaling relations. We divide our sample into subsamples of merging and relaxed systems, and find that mergers may have enhanced scatter in lensing measurements, most likely due to stronger triaxiality and more substructure. For the L
X–T
X relation, which is unaffected by lensing measurements, we find the opposite trend in scatter. We also explore the effects of X-ray cross-calibration and find that Chandra calibration leads to flatter L
X–T
X and M–T
X relations than XMM–Newton.
We present data products from the Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS). CFHTLenS is based on the Wide component of the Canada-France-Hawaii Telescope Legacy Survey (CFHTLS). It ...encompasses 154 deg2 of deep, optical, high-quality, sub-arcsecond imaging data in the five optical filters u*g
′
r
′
i
′
z
′. The scientific aims of the CFHTLenS team are weak gravitational lensing studies supported by photometric redshift estimates for the galaxies. This paper presents our data processing of the complete CFHTLenS data set. We were able to obtain a data set with very good image quality and high-quality astrometric and photometric calibration. Our external astrometric accuracy is between 60 and 70 mas with respect to Sloan Digital Sky Survey (SDSS) data, and the internal alignment in all filters is around 30 mas. Our average photometric calibration shows a dispersion of the order of 0.01-0.03 mag for g
′
r
′
i
′
z
′ and about 0.04 mag for u* with respect to SDSS sources down to i
SDSS ≤ 21. We demonstrate in accompanying papers that our data meet necessary requirements to fully exploit the survey for weak gravitational lensing analyses in connection with photometric redshift studies. In the spirit of the CFHTLS, all our data products are released to the astronomical community via the Canadian Astronomy Data Centre at http://www.cadc-ccda.hia-iha.nrc-cnrc.gc.ca/community/CFHTLens/query.html. We give a description and how-to manuals of the public products which include image pixel data, source catalogues with photometric redshift estimates and all relevant quantities to perform weak lensing studies.
Here we present the results of various approaches to measure accurate colours and photometric redshifts (photo-z) from wide-field imaging data. We use data from the Canada-France-Hawaii Telescope ...Legacy Survey which have been re-processed by the Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS) team in order to carry out a number of weak gravitational lensing studies. An emphasis is put on the correction of systematic effects in the photo-z arising from the different point spread functions (PSFs) in the five optical bands. Different ways of correcting these effects are discussed and the resulting photo-z accuracies are quantified by comparing the photo-z to large spectroscopic redshift (spec-z) data sets. Careful homogenization of the PSF between bands leads to increased overall accuracy of photo-z. The gain is particularly pronounced at fainter magnitudes where galaxies are smaller and flux measurements are affected more by PSF effects. We discuss ways of defining more secure subsamples of galaxies as well as a shape- and colour-based star-galaxy separation method, and we present redshift distributions for different magnitude limits. We also study possible re-calibrations of the photometric zero-points (ZPs) with the help of galaxies with known spec-z. We find that if PSF effects are properly taken into account, a re-calibration of the ZPs becomes much less important suggesting that previous such re-calibrations described in the literature could in fact be mostly corrections for PSF effects rather than corrections for real inaccuracies in the ZPs. The implications of this finding for future surveys like the Kilo Degree Survey (KiDS), Dark Energy Survey (DES), Large Synoptic Survey Telescope or Euclid are mixed. On the one hand, ZP re-calibrations with spec-z values might not be as accurate as previously thought. On the other hand, careful PSF homogenization might provide a way out and yield accurate, homogeneous photometry without the need for full spectroscopic coverage. This is the first paper in a series describing the technical aspects of CFHTLenS.
We present the results of a study of weak gravitational lensing by galaxies using imaging data that were obtained as part of the second Red Sequence Cluster Survey (RCS2). In order to compare to the ...baryonic properties of the lenses we focus here on the ~300 square degrees that overlap with the data release 7 (DR7) of the Sloan Digital Sky Survey (SDSS). The depth and image quality of the RCS2 enables us to significantly improve upon earlier work for luminous galaxies at z ≥ 0.3. To model the lensing signal we employ a halo model which accounts for the clustering of the lenses and distinguishes between satellite and central galaxies. Comparison with dynamical masses from the SDSS shows a good correlation with the lensing mass for early-type galaxies. The correlation is less clear for late-type galaxies, possibly due to rotation. For low luminosity (stellar mass) early-type galaxies we find a satellite fraction of ~40% which rapidly decreases to <10% with increasing luminosity (stellar mass). The satellite fraction of the late-types has a value in the range 0–15%, independent of luminosity or stellar mass. At high masses the satellite fraction is not well constrained, which we partly attribute to the modelling assumptions. To infer virial masses we apply simple models based on an independent satellite kinematics analysis to account for intrinsic scatter in the scaling relations. We find that early-types in the range 1010 < Lr < 1011.5 L⊙ have virial masses that are about five times higher than those of late-type galaxies and that the mass scales as M200 ∝ L2.34-0.16+0.09. For an early-type galaxy with a fiducal luminosity of 1011 Lr, ⊙ , we obtain a mass M200 = (1.93-0.14+0.13)×1013 h-1 M⊙. We also measure the virial mass-to-light ratio, and find for L200 < 1011 L⊙ a value of M200/L200 = 42 ± 10 for early-types, which increases for higher luminosities to values that are consistent with those observed for groups and clusters of galaxies. For late-type galaxies we find a lower value of M200/L200 = 17 ± 9. Our measurements also show that early- and late-type galaxies have comparable halo masses for stellar masses M∗ < 1011 M⊙, whereas the virial masses of early-type galaxies are higher for higher stellar masses. To compare the efficiency with which baryons have been converted into stars, we determine the total stellar mass within r200. Our results for early-type galaxies suggest a variation in efficiency with a minimum of ~10% for a stellar mass M∗,200 = 1012 M⊙. The results for the late-type galaxies are not well constrained, but do suggest a larger value.
We present a comprehensive analysis of weak gravitational lensing by large-scale structure in the Hubble Space Telescope Cosmic Evolution Survey (COSMOS), in which we combine space-based galaxy shape ...measurements with ground-based photometric redshifts to study the redshift dependence of the lensing signal and constrain cosmological parameters. After applying our weak lensing-optimized data reduction, principal-component interpolation for the spatially, and temporally varying ACS point-spread function, and improved modelling of charge-transfer inefficiency, we measured a lensing signal that is consistent with pure gravitational modes and no significant shape systematics. We carefully estimated the statistical uncertainty from simulated COSMOS-like fields obtained from ray-tracing through the Millennium Simulation, including the full non-Gaussian sampling variance. We tested our lensing pipeline on simulated space-based data, recalibrated non-linear power spectrum corrections using the ray-tracing analysis, employed photometric redshift information to reduce potential contamination by intrinsic galaxy alignments, and marginalized over systematic uncertainties. We find that the weak lensing signal scales with redshift as expected from general relativity for a concordance ΛCDM cosmology, including the full cross-correlations between different redshift bins. Assuming a flat ΛCDM cosmology, we measure $\sigma_8$($\Omega_\mathrm{m}$/0.3$)^{0.51}$ = 0.75±0.08 from lensing, in perfect agreement with WMAP-5, yielding joint constraints $\Omega_\mathrm{m}$ = $0.266^{+0.025}_{-0.023}$, $\sigma_8$ = $0.802^{+0.028}_{-0.029}$ (all 68.3% conf.). Dropping the assumption of flatness and using priors from the HST Key Project and Big-Bang nucleosynthesis only, we find a negative deceleration parameter q0 at 94.3% confidence from the tomographic lensing analysis, providing independent evidence of the accelerated expansion of the Universe. For a flat wCDM cosmology and prior w ∈ -2,0, we obtain w <-0.41 (90% conf.). Our dark energy constraints are still relatively weak solely due to the limited area of COSMOS. However, they provide an important demonstration of the usefulness of tomographic weak lensing measurements from space.
We present a quantitative analysis of the largest contiguous maps of projected mass density obtained from gravitational lensing shear. We use data from the 154 deg2 covered by the ...Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS). Our study is the first attempt to quantitatively characterize the scientific value of lensing maps, which could serve in the future as a complementary approach to the study of the dark universe with gravitational lensing. We show that mass maps contain unique cosmological information beyond that of traditional two-point statistical analysis techniques.
Using a series of numerical simulations, we first show how, reproducing the CFHTLenS observing conditions, gravitational lensing inversion provides a reliable estimate of the projected matter distribution of large-scale structure. We validate our analysis by quantifying the robustness of the maps with various statistical estimators. We then apply the same process to the CFHTLenS data. We find that the two-point correlation function of the projected mass is consistent with the cosmological analysis performed on the shear correlation function discussed in the CFHTLenS companion papers. The maps also lead to a significant measurement of the third-order moment of the projected mass, which is in agreement with analytic predictions, and to a marginal detection of the fourth-order moment. Tests for residual systematics are found to be consistent with zero for the statistical estimators we used. A new approach for the comparison of the reconstructed mass map to that predicted from the galaxy distribution reveals the existence of giant voids in the dark matter maps as large as 3° on the sky. Our analysis shows that lensing mass maps are not only consistent with the results obtained by the traditional shear approach, but they also appear promising for new techniques such as peak statistics and the morphological analysis of the projected dark matter distribution.
The spatial variation of the colour of a galaxy may introduce a bias in the measurement of its shape if the point spread function (PSF) profile depends on wavelength. We study how this bias depends ...on the properties of the PSF and the galaxies themselves. The bias depends on the scales used to estimate the shape, which may be used to optimize methods to reduce the bias. Here, we develop a general approach to quantify the bias. Although applicable to any weak lensing survey, we focus on the implications for the ESA Euclid mission.
Based on our study of synthetic galaxies, we find that the bias is a few times 10−3 for a typical galaxy observed by Euclid. Consequently, it cannot be neglected and needs to be accounted for. We demonstrate how one can do so using spatially resolved observations of galaxies in two filters. We show that Hubble Space Telescope (HST) observations in the F606W and F814W filters allow us to model and reduce the bias by an order of magnitude, sufficient to meet Euclid's scientific requirements. The precision of the correction is ultimately determined by the number of galaxies for which spatially resolved observations in at least two filters are available. We use results from the Millennium simulation to demonstrate that archival HST data will be sufficient for the tomographic cosmic shear analysis with the Euclid data set.
We present the first direct measurement of the galaxy-matter bispectrum as a function of galaxy luminosity, stellar mass and type of spectral energy distribution (SED). Our analysis uses a ...galaxy-galaxy-galaxy lensing technique (G3L), on angular scales between 9 arcsec and 50 arcmin, to quantify (i) the excess surface mass density around galaxy pairs (excess mass hereafter) and (ii) the excess shear-shear correlations around single galaxies, both of which yield a measure of two types of galaxy-matter bispectra. We apply our method to the state-of-the-art Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS), spanning 154 square degrees. This survey allows us to detect a significant change of the bispectra with lens properties. Measurements for lens populations with distinct redshift distributions become comparable by a newly devised normalization technique. That will also aid future comparisons to other surveys or simulations. A significant dependence of the normalized G3L statistics on luminosity within −23 ≤ M
r
≤ −18 and stellar mass within 5 × 109 M ≤ M
* ≤ 2 × 1011 M is found (h = 0.73). Both bispectra exhibit a stronger signal for more luminous lenses or those with higher stellar mass (up to a factor of 2-3). This is accompanied by a steeper equilateral bispectrum for more luminous or higher stellar mass lenses for the excess mass. Importantly, we find the excess mass to be very sensitive to galaxy type as recently predicted with semi-analytic galaxy models: luminous (M
r
< −21) late-type galaxies show no detectable signal, while all excess mass detected for luminous galaxies seems to be associated with early-type galaxies. We also present the first observational constraints on third-order stochastic galaxy biasing parameters.
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