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

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, ξ±(ϑ), since lensing is expected to produce only E-mode shear. Furthermore, there exist ambiguous modes that cannot uniquely be assigned to either E- or B-mode shear. In this paper we derive explicit equations for the pure-mode shear correlation functions, ξ±E/B(ϑ), and their ambiguous components, ξ±amb(ϑ), that can be derived from the measured ξ±(ϑ) on a finite angular interval, ϑmin ≤ ϑ ≤ ϑmax, such that ξ±(ϑ) can be decomposed uniquely into pure-mode functions as ξ+ = ξ+E+ξ+B+ξ+amb and ξ− = ξ−E−ξ−B+ξ−amb. The derivation is obtained by defining a new set of Complete Orthogonal Sets of E and B mode-separating Integrals (COSEBIs), for which explicit relations are obtained and which yields a smaller covariance between COSEBI modes. We derive the relation between ξ±E/B/amb and the underlying E- and B-mode power spectra. The pure-mode correlation functions can provide a diagnostic of systematics in configuration space. We then apply our results to Scinet LIght Cone Simulations (SLICS) and the Kilo-Degree Survey (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 recover the same level of (insignificant) B modes. We also consider in some detail the ambiguous modes at the 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, cannot be ascribed uniquely to an E-mode shear and is thus ambiguous; additionally, the shear correlation functions resulting from a random ensemble of point masses, when measured over a finite angular range, correspond to an ambiguous mode.