Galaxy–point spread function correlations as a probe of weak-lensing systematics with UNIONS data

¹ Université Paris Cité, Université Paris-Saclay, CEA, CNRS, AIM, F-91191 Gif-sur-Yvette, France
² Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM, 91191 Gif-sur-Yvette, France
³ Université Caen Normandie, ENSICAEN, CNRS, Normandie Univ, GREYC UMR 6072, F-14000 Caen, France
⁴ Department of Physics, McWilliams Center for Cosmology, Carnegie Mellon University, Pittsburgh, PA 15213, USA
⁵ Sorbonne Université, CNRS, UMR 7095, Institut d’Astrophysique de Paris (IAP), 98 bis boulevard Arago, 75014 Paris, France
⁶ École Nationale Supérieure des Mines de Paris, 60 boulevard Saint-Michel, 75272 Paris Cedex 06, France
⁷ Department of Physics and Astronomy, University of Waterloo, Waterloo, ON N2L 3G1, Canada
⁸ Waterloo Centre for Astrophysics, Waterloo, ON N2L 3G1, Canada
⁹ Perimeter Institute for Theoretical Physics, 31 Caroline St. N., Waterloo, ON N2L 2Y5, Canada
¹⁰ NRC Herzberg Astronomy and Astrophysics Research Centre, 5071 West Saanich Road, Victoria, B.C. V9E 2E7, Canada
¹¹ Ruhr University Bochum, Faculty of Physics and Astronomy, Astronomical Institute (AIRUB), German Centre for Cosmological Lensing, 44780 Bochum, Germany

^⋆ Corresponding authors: sacha.guerrini@cea.fr; martin.kilbinger@cea.fr

Received: 19 December 2024
Accepted: 26 June 2025

Abstract

Context. Weak gravitational lensing requires precise measurements of galaxy shapes and therefore accurate knowledge of the point spread function (PSF) model. The latter can be a source of systematics that affect the shear two-point correlation function. A key aspect of weak-lensing analysis is the forecasting of the systematics due to the PSF.

Aims. Correlation functions of galaxies and the PSF, the so-called ρ and τ statistics, are used to evaluate the level of systematics coming from the PSF model and PSF corrections and contributing to the two-point correlation function used to perform cosmological inference. Our goal is to introduce a fast and simple method to estimate this level of systematics and to assess its agreement with state-of-the-art approaches.

Methods. We introduce a new way to estimate the covariance matrix of τ statistics using analytical expressions. The covariance allows us to estimate parameters directly related to the level of systematics associated with the PSF and provides us with a tool to validate the PSF model used in a weak-lensing analysis. We applied these methods to data from the Ultraviolet Near-Infrared Optical Northern Survey (UNIONS).

Results. We show that semi-analytical covariance yields results comparable to those obtained by using covariances obtained from simulations or jackknife resampling. The approach requires less computation time and is therefore well suited to rapid comparison of the systematic level obtained from different catalogues. We also show how one can break degeneracies between parameters with a redefinition of the τ statistics.

Conclusions. The methods developed in this work will be useful tools in the analysis of current weak-lensing data but also of Stage IV surveys such as Euclid, LSST, and Roman. They provide fast and accurate diagnostics on PSF systematics that are crucial in the context of cosmic shear studies.