KiDS-1000 cosmology: Combined second- and third-order shear statistics

Aims: In this work, we perform the first cosmological parameter analysis of the fourth release of Kilo Degree Survey (KiDS-1000) data with second- and third-order shear statistics. This paper builds on a series of studies aimed at describing the roadmap to third-order shear statistics.
Methods: We derived and tested a combined model of the second-order shear statistic, namely, the COSEBIs and the third-order aperture mass statistics «ℳ_ap³» in a tomographic set-up. We validated our pipeline with N-body mock simulations of the KiDS-1000 data release. To model the second- and third-order statistics, we used the latest version of HMCODE2020 for the power spectrum and BIHALOFIT for the bispectrum. Furthermore, we used an analytic description to model intrinsic alignments and hydro-dynamical simulations to model the effect of baryonic feedback processes. Lastly, we decreased the dimension of the data vector significantly by considering only equal smoothing radii for the «ℳ_ap³» part of the data vector. This makes it possible to carry out a data analysis of the KiDS-1000 data release using a combined analysis of COSEBIs and third-order shear statistics.
Results: We first validated the accuracy of our modelling by analysing a noise-free mock data vector, assuming the KiDS-1000 error budget, finding a shift in the maximum of the posterior distribution of the matter density parameter, ΔΩ_m < 0.02 σ_Ωm, and of the structure growth parameter, ΔS₈ < 0.05 σ_S8. Lastly, we performed the first KiDS-1000 cosmological analysis using a combined analysis of second- and third-order shear statistics, where we constrained Ω_m = 0.248_−0.055^+0.062 and S₈ = σ₈√(Ω_m/0.3 )= 0.772 ± 0.022. The geometric average on the errors of Ω_m and S₈ of the combined statistics decreases, compared to the second-order statistic, by a factor of 2.2.