Puremode correlation functions for cosmic shear and application to KiDS1000
Abstract
One probe for systematic effects in gravitational lensing surveys is the presence of socalled B modes in the cosmic shear twopoint correlation functions, ξ_{±}(ϑ), since lensing is expected to produce only Emode shear. Furthermore, there exist ambiguous modes that cannot uniquely be assigned to either E or Bmode shear. In this paper we derive explicit equations for the puremode 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 puremode 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 modeseparating 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 Bmode power spectra. The puremode correlation functions can provide a diagnostic of systematics in configuration space. We then apply our results to Scinet LIght Cone Simulations (SLICS) and the KiloDegree Survey (KiDS1000) cosmic shear data, calculate the new COSEBIs and the puremode 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 KiDS1000 analysis and recover the same level of (insignificant) B modes. We also consider in some detail the ambiguous modes at the first and secondorder 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 Emode 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.
 Publication:

Astronomy and Astrophysics
 Pub Date:
 August 2022
 DOI:
 10.1051/00046361/202142479
 arXiv:
 arXiv:2110.09774
 Bibcode:
 2022A&A...664A..77S
 Keywords:

 gravitational lensing: weak;
 methods: analytical;
 largescale structure of Universe;
 cosmology: observations;
 Astrophysics  Cosmology and Nongalactic Astrophysics
 EPrint:
 24 pages, A&