KiDS-Legacy: Joint analysis of second- and third-order cosmic shear

Abstract

Weak lensing by large-scale structure is a powerful cosmological probe. While most analyses rely on second-order correlations, these are primarily sensitive to the parameter combination $S_8=\ddot{I}{ƒ}_8(\hat{I}{\text{c◯}}_m/0.3{)}^{0.5}$, limiting their ability to constrain $\hat{I}{\text{c◯}}_m$ and other cosmological parameters independently. Higher-order statistics capture non-Gaussian features of the density field and can therefore break parameter degeneracies and extract more cosmological information from weak lensing surveys. We present a joint analysis of second- and third-order cosmic shear in the final data release of the Kilo-Degree Survey (KiDS-Legacy). We combine COSEBIs (Complete Orthogonal Sets of E-/B-mode Integrals) at scales between 2' and 300' with third-order aperture mass moments at scales between 4' and 32' to perform a joint analysis of second- and third-order statistics. Compared to previous KiDS analyses, we implement several methodological advances: an intrinsic alignment model with redshift and mass dependence, a baryon correction model validated on multiple hydrodynamical simulations, and corrections for reduced shear and source clustering. Combining COSEBIs with third-order aperture mass statistics in KiDS-Legacy yields $\hat{I}{\text{c◯}}_m=0.297_{-0.040}^{+0.056}$ and $S_8=0.806_{-0.023}^{+0.025}$, significantly tightening the $\hat{I}{\text{c◯}}_m$ constraints and more than doubling the figure of merit in the $\hat{I}{\text{c◯}}_m$--$S_8$ plane compared to the two-point analysis alone. The third-order measurements pass stringent internal consistency tests, are fully compatible with the KiDS-Legacy 2-point constraints, other 2+3-point lensing results and with Planck CMB measurements within $1\ddot{I}ƒ$, providing no evidence for an $S_8$ tension and demonstrating the maturity of 3-point cosmic shear as a key probe for forthcoming surveys.

14 pages plus appendix, 15 figures, submitted to A&A