The non-Gaussianity of the cosmic shear likelihood - or: How odd is the Chandra Deep Field South?

(abridged) We study the validity of the approximation of a Gaussian cosmic shear likelihood. We estimate the true likelihood for a fiducial cosmological model from a large set of ray-tracing simulations and investigate the impact of non-Gaussianity on cosmological parameter estimation. We investigate how odd the recently reported very low value of $\sigma_8$ really is as derived from the \textit{Chandra} Deep Field South (CDFS) using cosmic shear by taking the non-Gaussianity of the likelihood into account as well as the possibility of biases coming from the way the CDFS was selected. We find that the cosmic shear likelihood is significantly non-Gaussian. This leads to both a shift of the maximum of the posterior distribution and a significantly smaller credible region compared to the Gaussian case. We re-analyse the CDFS cosmic shear data using the non-Gaussian likelihood. Assuming that the CDFS is a random pointing, we find $\sigma_8=0.68_{-0.16}^{+0.09}$ for fixed $\Omega_{\rm m}=0.25$. In a WMAP5-like cosmology, a value equal to or lower than this would be expected in $\approx 5$ of the times. Taking biases into account arising from the way the CDFS was selected, which we model as being dependent on the number of haloes in the CDFS, we obtain $\sigma_8 = 0.71^{+0.10}_{-0.15}$. Combining the CDFS data with the parameter constraints from WMAP5 yields $\Omega_{\rm m} = 0.26^{+0.03}_{-0.02}$ and $\sigma_8 = 0.79^{+0.04}_{-0.03}$ for a flat universe.Comment: 18 pages, 16 figures, accepted for publication in A&A; New Bayesian treatment of field selection bia

Probing Galaxy Dark Matter Haloes in COSMOS with Weak Lensing Flexion

Current theories of structure formation predict specific density profiles of galaxy dark matter haloes, and with weak gravitational lensing we can probe these profiles on several scales. On small scales, higher-order shape distortions known as flexion add significant detail to the weak lensing measurements. We present here the first detection of a galaxy-galaxy flexion signal in space-based data, obtained using a new Shapelets pipeline introduced here. We combine this higher-order lensing signal with shear to constrain the average density profile of the galaxy lenses in the Hubble Space Telescope COSMOS survey. We also show that light from nearby bright objects can significantly affect flexion measurements. After correcting for the influence of lens light, we show that the inclusion of flexion provides tighter constraints on density profiles than does shear alone. Finally we find an average density profile consistent with an isothermal sphere.Comment: 14 pages, 14 figures. Accepted for publication in MNRA

The mass distribution in an assembling super galaxy group at z=0.37z=0.37

We present a weak gravitational lensing analysis of supergroup SG1120$-$1202, consisting of four distinct X-ray-luminous groups, that will merge to form a cluster comparable in mass to Coma at $z=0$. These groups lie within a projected separation of 1 to 4 Mpc and within $\Delta v=550$ km s$^{-1}$ and form a unique protocluster to study the matter distribution in a coalescing system. Using high-resolution {\em HST}/ACS imaging, combined with an extensive spectroscopic and imaging data set, we study the weak gravitational distortion of background galaxy images by the matter distribution in the supergroup. We compare the reconstructed projected density field with the distribution of galaxies and hot X-ray emitting gas in the system and derive halo parameters for the individual density peaks. We show that the projected mass distribution closely follows the locations of the X-ray peaks and associated brightest group galaxies. One of the groups that lies at slightly lower redshift ($z\approx 0.35$) than the other three groups ($z\approx 0.37$) is X-ray luminous, but is barely detected in the gravitational lensing signal. The other three groups show a significant detection (up to $5 \sigma$ in mass), with velocity dispersions between $355^{+55}_{-70}$ and $530^{+45}_{-55}$ km s$^{-1}$ and masses between $0.8^{+0.4}_{-0.3} \times 10^{14}$ and $1.6^{+0.5}_{-0.4}\times 10^{14} h^{-1} M_{\odot}$, consistent with independent measurements. These groups are associated with peaks in the galaxy and gas density in a relatively straightforward manner. Since the groups show no visible signs of interaction, this supports the picture that we are catching the groups before they merge into a cluster.Comment: 10 pages, 10 figures, accepted for publication by Astronomy & Astrophysic

Automated detection of galaxy-scale gravitational lenses in high resolution imaging data

Lens modeling is the key to successful and meaningful automated strong galaxy-scale gravitational lens detection. We have implemented a lens-modeling "robot" that treats every bright red galaxy (BRG) in a large imaging survey as a potential gravitational lens system. Using a simple model optimized for "typical" galaxy-scale lenses, we generate four assessments of model quality that are used in an automated classification. The robot infers the lens classification parameter H that a human would have assigned; the inference is performed using a probability distribution generated from a human-classified training set, including realistic simulated lenses and known false positives drawn from the HST/EGS survey. We compute the expected purity, completeness and rejection rate, and find that these can be optimized for a particular application by changing the prior probability distribution for H, equivalent to defining the robot's "character." Adopting a realistic prior based on the known abundance of lenses, we find that a lens sample may be generated that is ~100% pure, but only ~20% complete. This shortfall is due primarily to the over-simplicity of the lens model. With a more optimistic robot, ~90% completeness can be achieved while rejecting ~90% of the candidate objects. The remaining candidates must be classified by human inspectors. We are able to classify lens candidates by eye at a rate of a few seconds per system, suggesting that a future 1000 square degree imaging survey containing 10^7 BRGs, and some 10^4 lenses, could be successfully, and reproducibly, searched in a modest amount of time. [Abridged]Comment: 17 pages, 11 figures, submitted to Ap

Measuring cosmological weak lensing using the Advanced Camera for Surveys on board the Hubble Space Telescope

Following from the theory of General Relativity, light-bundles are deflected and differentially distorted while passing through the gravitational potential of matter inhomogeneities. The gravitational lensing effect caused by the large-scale matter distribution in the Universe is termed cosmological weak lensing, and provides a powerful probe of cosmology. By studying the distortions which are imprinted onto the observed shapes of distant galaxies, the statistical properties of the foreground density field can be constrained free of assumptions on the relation between luminous and dark matter. Due to the weakness of the effect, it is challenging to measure and can only be detected statistically from large ensembles of coherently lensed galaxies. In addition, careful correction for systematic effects is required, first of all for the image point-spread-function (PSF). In this PhD thesis we present a detailed cosmological weak lensing analysis using deep high-resolution images from the Advanced Camera for Surveys (ACS) on board the Hubble Space Telescope (HST). Including data from the ACS Parallel Cosmic Shear Survey, the HST/GEMS Survey, and the HST/COSMOS Survey, this data set constitutes the largest survey used to measure cosmological weak lensing from space today. In order to achieve the high accuracy required for weak lensing studies, we developed several upgrades for the data reduction pipeline including careful image registration, improved bad pixel masks, and an optimised weighting scheme. We also perform a thorough investigation of the ACS PSF and develop a new correction scheme for its spatial and temporal variations, which are caused by thermal breathing of the telescope. We present numerous tests of our shear measurement pipeline using simulated images from the STEP Programme, and demonstrate that it achieves a relative shear-measurement accuracy better than 2% for ACS-like images. We perform the analysis of the ACS data in two steps, starting with a pilot study, in which we test the capabilities of ACS for cosmological weak lensing measurements with early parallel observations and the combined GEMS and GOODS ACS mosaic of the Chandra Deep Field South (CDFS, 0.22 deg2). We perform a number of diagnostic tests indicating that the remaining level of systematics is consistent with zero for the GEMS and GOODS data confirming the success of our PSF correction scheme. For the parallel data we detect a low level of remaining systematics which we interpret to be caused by a lack of sufficient dithering of the data. Combining our shear estimate of the GEMS and GOODS observations using 96 galaxies arcmin-2 with the photometric redshift catalogue of the GOODS-MUSIC sample, we determine a local single field estimate for the mass power spectrum normalisation σ8=0.59+0.13-0.17(stat)±0.07(sys) (68% confidence assuming Gaussian sampling variance) at a fixed matter density Ωm=0.24 for a ΛCDM cosmology, where we marginalise over the uncertainty of the Hubble constant and the redshift distribution. This estimate agrees only marginally with the WMAP-3 result of σ8=0.761+0.049-0.048 (Spergel et al. 2007) and is significantly below values found by recent ground-based surveys. From this discrepancy we conclude that the CDFS is subject to strong sampling variance with a significant under-density of compact foreground structures. This is consistent with a recent study by Phleps et al. (2007), who find a strong deficiency of red galaxies in this field. In a second step we perform a preliminary cosmological weak lensing analysis of the HST/COSMOS Survey (1.64 deg2). The significantly increased statistical accuracy reveals previously undetectable residual systematic errors indicated by a significant B-mode signal. So far we have not been able to unambiguously identify their origin, but note that similar indications for remaining systematics have been found in an independent analysis of the same data by Massey et al. (2007). Using only B-mode-free scales (>1' in the shear two-point correlation function), we find σ8 = 0.71±0.09 (68% confidence) from COSMOS for a flat ΛCDM cosmology and fixed Ωm=0.24, where the error includes the uncertainties in the redshift distribution, the Hubble constant, and the shear calibration, as well as a Gaussian estimate for sampling variance. This result is in excellent agreement with the WMAP-3 constraints, but is significantly below the estimates found by Massey et al. (2007). In addition to the cosmological weak lensing analysis we present a reconstruction of the projected mass in the COSMOS field, as well as first results from a weak lensing analysis of the HST/STAGES Survey targeting the galaxy super-cluster Abell 901/902. Furthermore, we briefly summarise ACS studies of galaxy clusters, which make use of the developed data reduction and weak lensing pipeline

Calibration of colour gradient bias in shear measurement using HST/CANDELS data

Accurate shape measurements are essential to infer cosmological parameters from large area weak gravitational lensing studies. The compact diffraction-limited point-spread function (PSF) in space-based observations is greatly beneficial, but its chromaticity for a broad band observation can lead to new subtle effects that could hitherto be ignored: the PSF of a galaxy is no longer uniquely defined and spatial variations in the colours of galaxies result in biases in the inferred lensing signal. Taking Euclid as a reference, we show that this colourgradient bias (CG bias) can be quantified with high accuracy using available multi-colour Hubble Space Telescope (HST) data. In particular we study how noise in the HST observations might impact such measurements and find this to be negligible. We determine the CG bias using HST observations in the F606W and F814W filters and observe a correlation with the colour, in line with expectations, whereas the dependence with redshift is weak. The biases for individual galaxies are generally well below 1%, which may be reduced further using morphological information from the Euclid data. Our results demonstrate that CG bias should not be ignored, but it is possible to determine its amplitude with sufficient precision, so that it will not significantly bias the weak lensing measurements using Euclid data

Calibration biases in measurements of weak lensing

As recently shown by Viola et al., the common (KSB) method for measuring weak gravitational shear creates a non-linear relation between the measured and the true shear of objects. We investigate here what effect such a non-linear calibration relation may have on cosmological parameter estimates from weak lensing if a simpler, linear calibration relation is assumed. We show that the non-linear relation introduces a bias in the shear-correlation amplitude and thus a bias in the cosmological parameters Omega_matter and sigma_8. Its direction and magnitude depends on whether the point-spread function is narrow or wide compared to the galaxy images from which the shear is measured. Substantial over- or underestimates of the cosmological parameters are equally possible, depending also on the variant of the KSB method. Our results show that for trustable cosmological-parameter estimates from measurements of weak lensing, one must verify that the method employed is free from ellipticity-dependent biases or monitor that the calibration relation inferred from simulations is applicable to the survey at hand.Comment: 5 pages, 3 figures, submitted to A&

Weak lensing mass bias and the alignment of center proxies

Galaxy cluster masses derived from observations of weak lensing suffer from a number of biases affecting the accuracy of mass-observable relations calibrated from such observations. In particular, the choice of the cluster center plays a prominent role in biasing inferred masses. In the past, empirical miscentring distributions have been used to address this issue. Using hydro-dynamical simulations, we aim to test the accuracy of weak lensing mass bias predictions based on such miscentring distributions by comparing the results to mass biases computed directly using intra-cluster medium (ICM)-based centers from the same simulation. We construct models for fitting masses to both centered and miscentered Navarro-Frenk-White profiles of reduced shear, and model the resulting distributions of mass bias with normal and log-normal distributions. We find that the standard approach of using miscentring distributions leads to an over-estimation of cluster masses at levels of between 2\% and 6\% when compared to the analysis in which actual simulated ICM centers are used, even when the underlying miscentring distributions match in terms of the miscentring amplitude. We find that neither log-normal nor normal distributions are generally reliable for approximating the shapes of the mass bias distributions, regardless of whether a centered or miscentered radial model is used.Comment: 15 pages, 9 figures, submitted to MNRA

Weak lensing from space: first cosmological constraints from three-point shear statistics

We use weak lensing data from the Hubble Space Telescope COSMOS survey to measure the second- and third-moments of the cosmic shear field, estimated from about 450,000 galaxies with average redshift ~ 1.3. We measure two- and three-point shear statistics using a tree-code, dividing the signal in E, B and mixed components. We present a detection of the third-order moment of the aperture mass statistic and verify that the measurement is robust against systematic errors caused by point spread function (PSF) residuals and by the intrinsic alignments between galaxies. The amplitude of the measured three-point cosmic shear signal is in very good agreement with the predictions for a WMAP7 best-fit model, whereas the amplitudes of potential systematics are consistent with zero. We make use of three sets of large Lambda CDM simulations to test the accuracy of the cosmological predictions and to estimate the influence of the cosmology-dependent covariance. We perform a likelihood analysis using the measurement and find that the Omega_m-sigma_8 degeneracy direction is well fitted by the relation: sigma_8 (Omega_m/0.30)^(0.49)=0.78+0.11/-0.26. We present the first measurement of a more generalised three-point shear statistic and find a very good agreement with the WMAP7 best-fit cosmology. The cosmological interpretation of this measurement gives sigma_8 (Omega_m/0.30)^(0.46)=0.69 +0.08/-0.14. Furthermore, the combined likelihood analysis of this measurement with the measurement of the second order moment of the aperture mass improves the accuracy of the cosmological constraints, showing the high potential of this combination of measurements to infer cosmological constraints.Comment: 17 pages, 11 figures. MNRAS submitte

Fitting formulae of the reduced-shear power spectrum for weak lensing

Context. Weak gravitational lensing is a powerful probe of large-scale structure and cosmology. Most commonly, second-order correlations of observed galaxy ellipticities are expressed as a projection of the matter power spectrum, corresponding to the lowest-order approximation between the projected and 3d power spectrum. Aims. The dominant lensing-only contribution beyond the zero-order approximation is the reduced shear, which takes into account not only lensing-induced distortions but also isotropic magnification of galaxy images. This involves an integral over the matter bispectrum. We provide a fast and general way to calculate this correction term. Methods. Using a model for the matter bispectrum, we fit elementary functions to the reduced-shear contribution and its derivatives with respect to cosmological parameters. The dependence on cosmology is encompassed in a Taylor-expansion around a fiducial model. Results. Within a region in parameter space comprising the WMAP7 68% error ellipsoid, the total reduced-shear power spectrum (shear plus fitted reduced-shear correction) is accurate to 1% (2%) for l<10^4 (l<2x10^5). This corresponds to a factor of four reduction of the bias compared to the case where no correction is used. This precision is necessary to match the accuracy of current non-linear power spectrum predictions from numerical simulations.Comment: 7 pages, 3 figures. A&A in press. Revised version with minor change