Pure-mode correlation functions for cosmic shear and application to KiDS-1000

TL;DR

This paper develops a method to decompose cosmic shear correlation functions into pure E-, B-, and ambiguous modes, enabling better systematics diagnostics and applying it to KiDS-1000 data with consistent results.

Contribution

It introduces explicit equations for pure-mode shear correlation functions and their ambiguous components, improving the analysis of cosmic shear data.

Findings

Pure-mode functions can be derived from measured correlations on finite intervals.

The new statistics fit the cosmological model as well as previous analyses.

Ambiguous modes include shear fields from point masses and random ensembles.

Abstract

One probe for systematic effects in gravitational lensing surveys is the presence of so-called B-modes in the cosmic shear two-point correlation functions \xi_\pm(\vt), since lensing is expected to produce only E-mode shear. Furthermore, there exist ambiguous modes which can not uniquely be assigned to either E- or B-mode shear. We derive explicit equations for the pure-mode shear correlation functions \xi_\pm^E/B(\vt) and their ambiguous components \xi_\pm^amb(\vt), that can be derived from the measured \xi_\pm(\vt) on a finite angular interval \tmin\le\vt\le\tmax, such that the latter can be decomposed uniquely into pure-mode functions as \xi_+=\xi_+^E+\xi_+^B+\xi_+^amb and \xi_-=\xi_-^E-\xi_-^B+\xi_-^amb. The derivation is obtained by defining a new set of COSEBIs, for which explicit relations are obtained, and which yields a smaller covariance between COSEBI modes. We derive the relation between \xi_\pm^E/B/amb and the underlying E-/B-mode power spectra. The pure-mode correlation functions can provide a diagnostics of systematics in configuration space. We then apply our results to SLICS simulations and the KiDS-1000 cosmic shear data, calculate the new COSEBIs and the pure-mode correlation functions, as well as the corresponding covariances, and show that the new statistics fit equally well to the best-fitting cosmological model as the previous KiDS-1000 analysis and recovers the same level of (insignificant) B-modes. We also consider in some detail the ambiguous modes at first- and second-order level, finding some surprising results; for example, the shear field of a point mass, when cut along a line through the center, can not be ascribed uniquely to an E-mode shear and is thus ambiguous, and the shear correlation functions resulting from a random ensemble of point masses, when measured over a finite angular range, correspond to an ambiguous mode.