Numerical simulations of weak lensing measurements

Weak gravitational lensing induces distortions on the images of background galaxies, and thus provides a direct measure of mass fluctuations in the Un iverse. The distortion signature from large-scale structure has recently be en detected by several groups for the first time, opening promising prospec ts for the near future. Since the distortions induced by lensing on the ima ges of background galaxies are only of the order of a few per cent, a relia ble measurement demands very accurate galaxy shape estimation and a careful treatment of systematic effects. Here, we present a study of a shear measu rement method using detailed simulations of artificial images. The images a re produced using realizations of a galaxy ensemble drawn from the Hubble S pace Telescope Groth strip. We consider realistic observational effects inc luding atmospheric seeing, point spread function (PSF) anisotropy and pixel ization, incorporated in such a manner as 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 (KSB). Overall, we find the KSB method to be reliable with the following provisos. First, although the recovered shear is linear ly related to the input shear, we find a coefficient of proportionality of about 0.8. In addition, we find a residual anti-correlation between the PSF ellipticity and the corrected ellipticities of faint galaxies. To guide fu ture weak lensing surveys, we study the ways in which seeing size, exposure time and pixelization affect the sensitivity to shear. We find that worsen ed seeing linearly increases the noise in the shear estimate, while the sen sitivity depends only weakly on exposure time. The noise is dramatically in creased if the pixel scale is larger than that of the seeing. In addition, we study the impact both of overlapping isophotes between neighbouring gala xies, and of PSF correction residuals: together these are found to 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 wea k lensing surveys.