Volume 664, August 2022
|Number of page(s)||23|
|Section||Cosmology (including clusters of galaxies)|
|Published online||05 August 2022|
Pure-mode correlation functions for cosmic shear and application to KiDS-1000
Argelander-Institut für Astronomie, Universität Bonn, Auf dem Hügel 71, 53121 Bonn, Germany
2 Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK
3 E. A. Milne Centre, University of Hull, Cottingham Road, Hull HU6 7RX, UK
4 Ruhr University Bochum, Faculty of Physics and Astronomy, Astronomical Institute (AIRUB), German Centre for Cosmological Lensing, 44780 Bochum, Germany
5 School of Mathematics, Statistics and Physics, Newcastle University, Herschel Building, NE1 7RU Newcastle-upon-Tyne, UK
6 Leiden Observatory, Leiden University, PO Box 9513 2300 RA Leiden, The Netherlands
7 Shanghai Astronomical Observatory (SHAO), Nandan Road 80, Shanghai 200030, PR China
8 University of Chinese Academy of Sciences, Beijing 100049, PR China
Accepted: 8 March 2022
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.
Key words: gravitational lensing: weak / methods: analytical / large-scale structure of Universe / cosmology: observations
© ESO 2022
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