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

Schneider, Peter; Asgari, Marika; Jozani, Yasaman Najafi; Dvornik, Andrej; Giblin, Benjamin; Harnois-Déraps, Joachim; Heymans, Catherine; Hildebrandt, Hendrik; Hoekstra, Henk; Kuijken, Konrad; Shan, Huanyuan; Tröster, Tilman; Wright, Angus H

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, ϑ min ≤ ϑ ≤ ϑ max , 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.

Citation

Schneider, P., Asgari, M., Jozani, Y. N., Dvornik, A., Giblin, B., Harnois-Déraps, J., …Wright, A. H. (in press). Pure-mode correlation functions for cosmic shear and application to KiDS-1000. Astronomy and Astrophysics, https://doi.org/10.1051/0004-6361/202142479

• Journal Article Type: Article
• Acceptance Date: Mar 8, 2022
• Online Publication Date: May 16, 2022
• Deposit Date: Jun 14, 2022
• Publicly Available Date: Jun 20, 2022
• Journal: Astronomy and Astrophysics
• Print ISSN: 0004-6361
• Publisher: EDP Sciences
• Peer Reviewed: Peer Reviewed
• DOI: https://doi.org/10.1051/0004-6361/202142479
• Keywords: Cosmology; Gravitational lensing; Large-scale structure of the Universe
• Public URL: https://hull-repository.worktribe.com/output/4014227