Shear fields due to weak gravitational lensing have characteristic coherent patterns. We describe the topological defects in shear fields in terms of the curvature of the surface described by the lensing potential. A simple interpretation of the characteristic defects is given in terms of the the umbilical points of the potential surface produced by ellipsoidal halos. We show simulated lensing shear maps and point out the typical defect configurations. Finally, we show how statistical properties such as the abundance of defects can be expressed in terms of the correlation function of the lensing potential.
We present the optimal convergence and shear estimators for lensing reconstruction from the cosmic microwave background temperature field. This generalizes the deflection estimator, is sensitive to non-lensing modes, provides internal consistency checks, and is always at least as optimal. Previously, these estimators were only known in the squeezed limit. This paper decomposes convergence and shear fields into cosine and sine waves and the lensed correlation function is then Taylor expanded in the wave amplitudes. Maximizing the likelihood function gives the optimal estimators for the converge…
We present a combined cosmic shear analysis of the modeling of line-of-sight distortions on strongly lensed extended arcs and galaxy shape measurements in the COSMOS field. We develop a framework to predict the covariance of strong lensing and galaxy shape measurements of cosmic shear on the basis of the small scale matter power-spectrum. The weak lensing measurement is performed using data from the COSMOS survey calibrated with a cloning scheme using the Ultra Fast Image Generator UFig (Berge 2013). The strong lensing analysis is performed by forward modeling the lensing arcs with a main lens…
The magnification of galaxies in modern galaxy surveys induces additional correlations in the cosmic shear, galaxy-galaxy lensing and clustering observables used in modern lensing "3x2pt" analyses, due to sample selection. In this paper, we emulate the magnification contribution to all three observables utilising the SLICS simulations suite, and test the sensitivity of the cosmological model, galaxy bias and redshift distribution calibration to un-modelled magnification in a Stage-IV-like survey using Monte-Carlo sampling. We find that magnification cannot be ignored in any single or combined …
An excess up-scattering mass bias on a weak lensing cluster mass estimate is a statistical bias that an observed weak lensing mass ($M_{\rm obs}$) of a cluster of galaxies is, in a statistical sense, larger than its true mass ($M_{\rm true}$) because of a higher chance of up-scattering than that of down-scattering due to random noises in a weak lensing cluster shear profile. This non-symmetric scattering probability is caused by a monotonically decreasing cluster mass function with increasing mass. We examine this bias (defined by $b=M_{\rm obs}/M_{\rm true}$) in weak lensing shear-selected cl…
We quantify the cosmological constraining power of the `lensing PDF' - the one-point probability density of weak lensing convergence maps - by modelling this statistic numerically with an emulator trained on $w$CDM cosmic shear simulations. After validating our methods on Gaussian and lognormal fields, we show that `multi-scale' PDFs - measured from maps with multiple levels of smoothing - offer considerable gains over two-point statistics, owing to their ability to extract non-Gaussian information: for a mock Stage-III survey, lensing PDFs yield 33\% tighter constraints on the clustering para…
A systematic study of projection biases in the Weak Lensing analysis of cosmic shear and the combination of galaxy clustering and galaxy-galaxy lensing
We derive a new relation between cosological distances, valid in any (statistically) isotropic space-time and independent of cosmological parameters or even the validity of the field equation of General Relativity. In particular, this relation yields an equation between those distance ratios which are the geometrical factors determining the strength of the gravitational lensing effect of mass concentrations. Considering a combination of weak lensing shear ratios, based on lenses at two different redshifts, and sources at three different redshifts, we derive a relation between shear-ratio tests…
Hyper Suprime-Cam Y3 results: photo-$z$ bias calibration with lensing shear ratios and cosmological constraints from cosmic shear
Leiden Observatory, Leiden University（莱顿天文台，莱顿大学）；Inter University Centre for Astronomy and Astrophysics（大学天文学与天体物理中心）；Kavli Institute for the Physics and Mathematics of the Universe (WPI), University of Tokyo（东京大学 Kavli宇宙物理学与数学研究所（WPI））；Kobayashi-Maskawa Institute for the Origin of Particles and the Universe (KMI), Nagoya University（名古屋大学 Kobayashi-Maskawa粒子宇宙起源研究所（KMI））；Institute for Advanced Research, Nagoya University（名古屋大学高等研究院）；Department of Physics and Astronomy, University of Pennsylvania（宾夕法尼亚大学物理与天文学系）；Department of Physics and Astronomy and PITT PACC, University of Pittsburgh（匹兹堡大学物理与天文学系及PITT PACC）；National Astronomical Observatory of Japan (NAOJ), National Institutes of Natural Science（日本国立天文台（NAOJ），国立自然科学研究院）；The Institute of Statistical Mathematics（统计科学研究所）
In this paper we show how response function corrections to shear measurements (e.g. as required by Metacalibration) propagate into cosmic shear power spectra. We investigate a 2-sphere pixel (also known as HEALpixel') correction and a forward-modelling approach using simple Gaussian simulations. In the 2-sphere pixel-correction approach we find a free parameter that is the tolerated condition number of the local response matrices: if this is too large then this can cause an amplification of the shot noise power spectrum, if too small it can lead to a loss of area (and a possible selection bias…
The Shear-to-Cosmology Paradigm I. Hybrid Field-Level and Simulation-Based Framework for Weak Lensing Surveys
Shanghai Astronomical Observatory, Chinese Academy of Sciences（中国科学院上海天文台）；School of Physics and Astronomy, Sun Yat-Sen University（中山大学物理学院）；CSST Science Center for the Guangdong–Hong Kong–Macau Greater Bay Area, SYSU（中山大学嫦娥四号科学中心粤港澳大湾区分中心）
Weak gravitational lensing flexions are a kind of weak lensing distortion which are defined as the spin 1 and spin 3 combinations of the third order derivatives of gravitational lensing potential. Since the shear has spin 2 combination of the second order derivative, the flexion signal gives a partly independent information from shear signal and is more sensitive to the local mass distribution than shear signal. Thus its measurement is expected to play important roles in observational cosmology. However, since the weakness of the flexion signal as well as the complicatedness of its intrinsic n…
Metacalibration is a state-of-the-art technique for measuring weak gravitational lensing shear from well-sampled galaxy images. We investigate the accuracy of shear measured with metacalibration from fitting elliptical Gaussians to undersampled galaxy images. In this case, metacalibration introduces aliasing effects leading to an ensemble multiplicative shear bias about 0.01 for Euclid, and even larger for the Roman Space Telescope, well exceeding the missions' requirements. We find that this aliasing bias can be mitigated by computing shapes from weighted moments with wider Gaussians as weigh…
Weak-Lensing Shear Response for Photometric Redshift-Based Tomographic Binning
Brookhaven National Laboratory（布鲁海文国家实验室）；University of Pittsburgh（匹兹堡大学）；SLAC National Accelerator Laboratory（SLAC国家加速器实验室）；Carnegie Mellon University（卡内基梅隆大学）
We study the gravitational lensing influence of a massive object in a dark matter halo, using a simple model of a point mass embedded in a spherical Navarro--Frenk--White halo. Building on the analysis of critical curves and caustics presented in the first part of this work, we proceed to explore the geometry of images formed by the lens. First, we analyze several lensing quantities including shear, phase, and their weak-lensing approximations, illustrating the results with image-plane maps. We derive formulae and present a geometric interpretation for the shear and phase of a combination of t…
