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Register a new userWeak Lensing Measurements: A Revisited Method and Application to HST Images
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Jason Rhodes
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The weak distortions produced by gravitational lensing in the images of background galaxies provide a method to measure directly the distribution of mass in the universe. However this technique requires high precision measurements of the lensing shear and cautious corrections for systematic effects. Kaiser, Squires, & Broadhurst (1995) proposed a method to calibrate the ellipticity-shear relation in the presence of Point Spread Function (PSF) anisotropies and camera distortions. We revisit the KSB method and show that both the PSF and the camera distortions can be corrected for using source moments, as opposed to ellipticities. We clarify the applicability of some of the approximations made in this method. We derive expressions for the corrections which only involve the galaxy moments. We derive an explicit relation between the shear and the average ellipticity. We discuss the shortcomings of the method, and test its validity using numerical simulations. As an application of the method, we repeat the analysis of the HST WFPC2 camera performed by Hoekstra et al. (1998). We confirm the presence of sizable (10%) PSF ellipticities at the edge of the WFPC2 chips. We also show that the PSF ellipticity varies by as much as 2% over time. We use these measurements to correct the shape of galaxies in the HST Survey Strip (``Groth Strip). By considering the dependence of the ellipticities on object size, we show that, after corrections, the residual systematic uncertainty for galaxies with radii greater than 0.15 arcsec, is about 0.4%, when averaged over each chip. We discuss how these results provide good prospects for measuring weak lensing by large-scale structure with deep HST surveys.
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We present a study of weak lensing shear measurements for simulated galaxy images at radio wavelengths. We construct a simulation pipeline into which we can input galaxy images of known ellipticity, and with which we then simulate observations with eMERLIN and the international LOFAR array. The simulations include the effects of the CLEAN algorithm, uv sampling, observing angle, and visibility noise, and produce realistic restored images of the galaxies. We apply a shapelet-based shear measurement method to these images and test our ability to recover the true source ellipticities. We model and deconvolve the effective PSF, and find suitable parameters for CLEAN and shapelet decomposition of galaxies. We demonstrate that ellipticities can be measured faithfully in these radio simulations, with no evidence of an additive bias and a modest (10%) multiplicative bias on the ellipticity measurements. Our simulation pipeline can be used to test shear measurement procedures and systematics for the next generation of radio telescopes.
Mass measurements of astronomical objects are most wanted but still elusive. We need them to trace the formation and evolution of cosmic structure but we can get direct measurements only for a minority. This lack can be circumvented with a proxy and a scaling relation. The twofold goal of estimating the unbiased relation and finding the right proxy value to plug in can be hampered by systematics, selection effects, Eddington/Malmquist biases and time evolution. We present a Bayesian hierarchical method which deals with these issues. Masses to be predicted are treated as missing data in the regression and are estimated together with the scaling parameters. The calibration subsample with measured masses does not need to be representative of the full sample as far as it follows the same scaling relation. We apply the method to forecast weak lensing calibrated masses of the Planck, redMaPPer and MCXC clusters. Planck masses are biased low with respect to weak lensing calibrated masses, with a bias more pronounced for high redshift clusters. MCXC masses are under-estimated by ~20 per cent, which may be ascribed to hydrostatic bias. Packages and catalogs are made available with the paper.
Weak lensing is emerging as a powerful observational tool to constrain cosmological models, but is at present limited by an incomplete understanding of many sources of systematic error. Many of these errors are multiplicative and depend on the population of background galaxies. We show how the commonly cited geometric test, which is rather insensitive to cosmology, can be used as a ratio test of systematics in the lensing signal at the 1 per cent level. We apply this test to the galaxy-galaxy lensing analysis of the Sloan Digital Sky Survey (SDSS), which at present is the sample with the highest weak lensing signal to noise and has the additional advantage of spectroscopic redshifts for lenses. This allows one to perform meaningful geometric tests of systematics for different subsamples of galaxies at different mean redshifts, such as brighter galaxies, fainter galaxies and high-redshift luminous red galaxies, both with and without photometric redshift estimates. We use overlapping objects between SDSS and the DEEP2 and 2SLAQ spectroscopic surveys to establish accurate calibration of photometric redshifts and to determine the redshift distributions for SDSS. We use these redshift results to compute the projected surface density contrast DeltaSigma around 259 609 spectroscopic galaxies in the SDSS; by measuring DeltaSigma with different source samples we establish consistency of the results at the 10 per cent level (1-sigma). We also use the ratio test to constrain shear calibration biases and other systematics in the SDSS survey data to determine the overall galaxy-galaxy weak lensing signal calibration uncertainty. We find no evidence of any inconsistency among many subsamples of the data.
We present our cosmic shear analysis of GEMS, one of the largest wide-field surveys ever undertaken by the Hubble Space Telescope. Imaged with the Advanced Camera for Surveys (ACS), GEMS spans 795 square arcmin in the Chandra Deep Field South. We detect weak lensing by large-scale structure in high resolution F606W GEMS data from ~60 resolved galaxies per square arcminute. We measure the two-point shear correlation function, the top-hat shear variance and the shear power spectrum, performing an E/B mode decomposition for each statistic. We show that we are not limited by systematic errors and use our results to place joint constraints on the matter density parameter Omega_m and the amplitude of the matter power spectrum sigma_8. We find sigma_8(Omega_m/0.3)^{0.65}=0.68 +/- 0.13 where the 1sigma error includes both our uncertainty on the median redshift of the survey and sampling variance. Removing image and point spread function (PSF) distortions are crucial to all weak lensing analyses. We therefore include a thorough discussion on the degree of ACS PSF distortion and anisotropy which we characterise directly from GEMS data. Consecutively imaged over 20 days, GEMS data also allows us to investigate PSF instability over time. We find that, even in the relatively short GEMS observing period, the ACS PSF ellipticity varies at the level of a few percent which we account for with a semi-time dependent PSF model. Our correction for the temporal and spatial variability of the PSF is shown to be successful through a series of diagnostic tests.
(Abridged) Weak gravitational lensing induces distortions on the images of background galaxies, and thus provides a direct measure of mass fluctuations in the universe. Since the distortions induced by lensing on the images of background galaxies are only of a few percent, a reliable measurement demands very accurate galaxy shape estimation and a careful treatment of systematic effects. Here, we present a study of a shear measurement method using detailed simulations of artificial images. The images are produced using realisations of a galaxy ensemble drawn from the HST Groth strip. We consider realistic observational effects including atmospheric seeing, PSF anisotropy and pixelisation, incorporated in a manner to reproduce actual observations with the William Herschel Telescope. By applying an artificial shear to the simulated images, we test the shear measurement method proposed by Kaiser, Squires & Broadhurst (1995, KSB). Overall, we find the KSB method to be reliable with several provisos. To guide future weak lensing surveys, we study how seeing size, exposure time and pixelisation affect the sensitivity to shear. In addition, we study the impact of overlapping isophotes of neighboring galaxies, and find that this effect can produce spurious lensing signals on small scales. We discuss the prospects of using the KSB method for future, more sensitive, surveys. Numerical simulations of this kind are a required component of present and future analyses of weak lensing surveys.
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