A Method for Weak Lensing Observations

Abstract

We develop and test a method for measuring the gravitational lensing induced distortion of faint background galaxies. We first describe how we locate the galaxies and measure a 2-component `polarisation' or ellipticity statistic $e_\alpha$ whose expectation value should be proportional to the gravitational shear $\gamma_\alpha$. We then show that an anisotropic instrumental psf perturbs the polarisation by $\delta e_\alpha = P^s_{\alpha\beta} p_\beta$, where $p_\alpha$ is a measure of the psf anisotropy and $P^s_{\alpha\beta}$ is the `linearised smear polarisability tensor'. By estimating $P^s_{\alpha\beta}$ for each object we can determine $p_\alpha$ from the foreground stars and apply a correction $-P^s_{\alpha\beta}p_\beta$ to the galaxies. We test this procedure using deep high-resolution images from HST which are smeared with an anisotropic psf and then have noise added to simulate ground-based observations. We find that the procedure works very well. A similar analysis yields a linear shear polarisability tensor $P^\gamma_{\alpha\beta}$ which describes the response to a gravitational shear. This calibrates the polarisation-shear relation, but only for galaxies which are well resolved. To empirically calibrate the effect of seeing on the smaller galaxies we artificially stretch HST images to simulate lensing and then degrade them as before. These experiments provide a rigorous and exacting test of the method under realistic conditions. They show that it is possible to remove the effect of instrumental psf anisotropy, and that the method provides an efficient and quantitative measurement of the gravitational shear.Comment: 39 pages, no figures, Latex, available by anonymous ftp inc figs from ftp://ftp.cita.utoronto.ca/cita/nick/methods.p

Observational probes of cosmic acceleration

“…The prototype moments-based method was that of Kaiser, Squires, and Broadhurst (KSB;Kaiser et al 1995; improved by Luppino and Kaiser 1997;Hoekstra et al 1998). Many improvements of these methods have been made -e.g., in computing better conversion factors from shear to quadrupole moments 50 (Semboloni et al, 2006b).…”

Evidence of the accelerated expansion of the Universe from weak lensing tomography with COSMOS

“…For the latter, we use the KSB+ formalism (Kaiser et al 1995;Luppino & Kaiser 1997;Hoekstra et al 1998), see Erben et al (2001), Schrabback et al (2007) and Appendix B.1 for details on our implementation. As found with simulations of ground-based weak lensing data, KSB+ can significantly underestimate gravitational shear (Erben et al 2001;Bacon et al 2001;Heymans et al 2006a;Massey et al 2007a), where the calibration bias m and possible PSF anisotropy residuals c, defined via…”

Cosmological constraints from weak lensing peak statistics with Canada-France-Hawaii Telescope Stripe 82 Survey

“…Another approach for weak lensing peak studies is to reconstruct the convergence field from ǫ taking into account the nonlinear relation between g and γ (e.g., Kaiser & Squires 1993;Kaiser et al 1995;Seitz & Schneider 1995;Bartelmann 1995;Squire & Kaiser 1996;Seitz & Schneider 1997;Jauzac et al 2012;Jullo et al 2014). In this approach, to avoid unphysical results, it is important to filter ǫ first and then to proceed with convergence reconstruction using the filtered ǫ .…”