Shear-flexion cross-talk in weak-lensing measurements

Abstract

Gravitational flexion, caused by derivatives of the gravitational tidal field, is potentially important for the analysis of the dark-matter distribution in gravitational lenses, such as galaxy clusters or the dark-matter haloes of galaxies. Flexion estimates rely on measurements of galaxy-shape distortions with spin-1 and spin-3 symmetry. We show in this paper that and how such distortions are generally caused not only by the flexion itself, but also by coupling terms of the form (shear $\times$ flexion), which have hitherto been neglected. Similar coupling terms occur between intrinsic galaxy ellipticities and the flexion. We show, by means of numerical tests, that neglecting these terms can introduce biases of up to 85% on the $F$ flexion and 150% on the $G$ flexion for galaxies with an intrinsic ellipticity dispersion of ${\sigma }_{\epsilon }=0.3$. In general, this bias depends on the strength of the lensing fields, the ellipticity dispersion, and the concentration of the lensed galaxies. We derive a new set of equations relating the measured spin-1 and spin-3 distortions to the lensing fields up to first order in the shear, the flexion, the product of shear and flexion, and the morphological properties of the galaxy sample. We show that this new description is accurate with a bias $\le 7$ (spin-1 distortion) and $\le 3$ (spin-3 distortion) even close to points where the flexion approach breaks down due to merging of multiple images. We propose an explanation why a spin-3 signal could not be measured yet and comment on the difficulties in using a model-fitting approach to measure the flexion signal.

11 pages, MNRAS accepted

References in corpus (6)

• Weak lensing goes bananas: What flexion really measures
• A Method for Weak Lensing Flexion Analysis by the HOLICs Moment Approach
• Probing Galaxy Dark Matter Haloes in COSMOS with Weak Lensing Flexion
• A New Method for measuring Weak Gravitational Lensing Shear using Higher Order Spin-2 HOLICs
• Lensing signals in the Hubble Ultra-Deep Field using all 2nd order shape deformations
• New Constraints on the Complex Mass Substructure in Abell 1689 from Gravitational Flexion

Cited by in corpus (17)

• Image Analysis for Cosmology: Results from the GREAT10 Galaxy Challenge
• Cluster-galaxy weak lensing
• High Resolution Weak Lensing Mass-Mapping Combining Shear and Flexion
• Galaxy imaging surveys as spin-sensitive detector for cosmological colliders
• Flexion measurement in simulations of Hubble Space Telescope data
• Dark Matter Astrometry: Accuracy of sub-halo positions for the measurement of self-interaction cross sections
• Weak lensing distortions beyond shear
• Raytracing simulations of coupled dark energy models
• Analytical shear and flexion of Einasto dark matter haloes
• Internal Cluster Structure
• Reconstruction of small-scale galaxy cluster substructure with lensing flexion
• Constraining primordial non-Gaussianity with cosmological weak lensing: shear and flexion
• Measurement of halo properties with weak lensing shear and flexion
• Estimation of halo ellipticity using spin-3 flexion
• Improving lensing cluster mass estimate with flexion
• Measurement of differential magnification
• A short review on joint weak and strong cluster lens-mass reconstruction