KiDS-1000 methodology: Modelling and inference for joint weak gravitational lensing and spectroscopic galaxy clustering analysis

¹ Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK
e-mail: b.joachimi@ucl.ac.uk
² Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK
e-mail: calin@roe.ac.uk
³ Ruhr-Universität Bochum, Astronomisches Institut, German Centre for Cosmological Lensing (GCCL), Universitätsstr. 150, 44801 Bochum, Germany
⁴ Max-Planck-Institut für Extraterrestrische Physik, Postfach 1312, Gießenbachstr., 85741 Garching, Germany
⁵ Center for Theoretical Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland
⁶ Centre for Astrophysics & Supercomputing, Swinburne University of Technology, PO Box 218, Hawthorn, VIC 3122, Australia
⁷ Institute of Space Sciences (ICE, CSIC), Campus UAB, Carrer de Can Magrans, s/n, 08193 Barcelona, Spain
⁸ Institut d‘Estudis Espacials de Catalunya (IEEC), 08034 Barcelona, Spain
⁹ Argelander-Institut für Astronomie, Universität Bonn, Auf dem Hügel 71, 53121 Bonn, Germany
¹⁰ INAF – Astronomical Observatory of Capodimonte, Via Moiariello 16, 80131 Napoli, Italy
¹¹ Leiden Observatory, Leiden University, PO Box 9513, 2300 RA Leiden, The Netherlands
¹² Department of Astrophysical Sciences, Princeton University, 4 Ivy Lane, Princeton, NJ 08544, USA
¹³ School of Physics and Astronomy, Sun Yat-sen University, Zhuhai Campus, Guangzhou 519082, PR China
¹⁴ Center for Cosmology and Particle Physics, Department of Physics, New York University, New York, NY 10003, USA
¹⁵ Shanghai Astronomical Observatory (SHAO), Nandan Road 80, Shanghai 200030, PR China
¹⁶ University of Chinese Academy of Sciences, Beijing 100049, PR China

Received: 3 July 2020
Accepted: 17 December 2020

Abstract

We present the methodology for a joint cosmological analysis of weak gravitational lensing from the fourth data release of the ESO Kilo-Degree Survey (KiDS-1000) and galaxy clustering from the partially overlapping Baryon Oscillation Spectroscopic Survey (BOSS) and the 2-degree Field Lensing Survey (2dFLenS). Cross-correlations between BOSS and 2dFLenS galaxy positions and source galaxy ellipticities have been incorporated into the analysis, necessitating the development of a hybrid model of non-linear scales that blends perturbative and non-perturbative approaches, and an assessment of signal contributions by astrophysical effects. All weak lensing signals were measured consistently via Fourier-space statistics that are insensitive to the survey mask and display low levels of mode mixing. The calibration of photometric redshift distributions and multiplicative gravitational shear bias has been updated, and a more complete tally of residual calibration uncertainties was propagated into the likelihood. A dedicated suite of more than 20 000 mocks was used to assess the performance of covariance models and to quantify the impact of survey geometry and spatial variations of survey depth on signals and their errors. The sampling distributions for the likelihood and the χ² goodness-of-fit statistic have been validated, with proposed changes for calculating the effective number of degrees of freedom. The prior volume was explicitly mapped, and a more conservative, wide top-hat prior on the key structure growth parameter S₈ = σ₈ (Ω_m/0.3)^1/2 was introduced. The prevalent custom of reporting S₈ weak lensing constraints via point estimates derived from its marginal posterior is highlighted to be easily misinterpreted as yielding systematically low values of S₈, and an alternative estimator and associated credible interval are proposed. Known systematic effects pertaining to weak lensing modelling and inference are shown to bias S₈ by no more than 0.1 standard deviations, with the caveat that no conclusive validation data exist for models of intrinsic galaxy alignments. Compared to the previous KiDS analyses, S₈ constraints are expected to improve by 20% for weak lensing alone and by 29% for the joint analysis.