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

TL;DR

The paper develops a comprehensive methodology for a joint KiDS-1000 weak lensing and BOSS/2dFLenS galaxy clustering analysis, incorporating cross-correlations and a hybrid non-linear matter power spectrum model to exploit small- and intermediate-scale information.A band-power framework in Fourier space is used to minimize mask effects and to integrate diverse two-point statistics (cosmic shear, GGL, and clustering) with consistent covariance treatment validated by a large suite of lognormal mocks.Key advances include SOM-based photometric redshift calibration with explicit redshift-shift priors, a robust handling of multiplicative shear biases, and a principled reporting of constraints via MAP and PJ-HPD intervals to properly reflect high-dimensional posteriors.The analysis yields significantly tighter S_8 constraints, with a ~20% gain for cosmic shear and ~29% for the joint analysis, while finding no known systematic that biases S_8 by more than 0.1 sigma; GGL contributes modest additional information in this setup, and intrinsic alignments remain the dominant systematic.These results demonstrate readiness for future large surveys and highlight ongoing challenges in non-linear modelling, IA physics, and covariance accuracy as analyses scale to larger, deeper data sets.

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 BOSS and 2dFLenS surveys. Cross-correlations between galaxy positions and ellipticities have been incorporated into the analysis, necessitating a hybrid model of non-linear scales that blends perturbative and non-perturbative approaches, and an assessment of contributions by astrophysical effects. All weak lensing signals are 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 is propagated into the likelihood. A dedicated suite of more than 20000 mocks is 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 $χ^2$ goodness-of-fit statistic have been validated, with proposed changes to the number of degrees of freedom. Standard weak lensing point estimates on $S_8=σ_8\,(Ω_{\rm m}/0.3)^{1/2}$ derived from its marginal posterior are easily misinterpreted to be biased low, and an alternative estimator and associated credible interval have been proposed. Known systematic effects pertaining to weak lensing modelling and inference are shown to bias $S_8$ 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, $S_8$ constraints are expected to improve by 20% for weak lensing alone and by 29% for the joint analysis. [abridged]

Figures (34)

• Figure 1: Comparison of 3D power spectra, computed at $z=0.38$ and the parameters listed in Table$\,$\ref{['tab:fiducialpars']}. Top: Non-linear matter power spectra relative to the linear matter power spectrum, for the gRPT perturbative model, the mead15HMCode, the takahashi12 Halofit prescription, and the CosmicEmu emulated power spectrum heitmann14. Centre: Non-linear matter power spectra relative to the CosmicEmu model. The blue shaded region covers the power spectrum range within the prior range of our AGN feedback description. Bottom: Full galaxy-matter power spectrum $P_{\rm gm}$ relative to the mead15 power spectrum multiplied by the linear galaxy bias, shown for the gRPT perturbation theory model (orange) and the fit formula of Eq.$\,$(\ref{['eq:pgm']}), using gRPT (purple) or mead15 (grey) for the non-linear matter power spectrum term. The dotted grey curve includes an additional $r(k)$ term obtained from a semi-analytic model of a galaxy sample similar to the one used in our analysis. The vertical grey line indicates the smallest scales used in the galaxy clustering modelling.
• Figure 2: Bandpower Fourier-space filters for 8 bands logarithmically spaced $\ell \in [100,\,1500]$, as indicated by the vertical lines. The second to fourth panels from the top show the galaxy-galaxy lensing, cosmic shear, and EB-mode mixing kernels; see Eqs. (\ref{['eq:kernelshear']}), and (\ref{['eq:kernelggl']}). The top panel shows redshift $z$ as a function of $\ell$ for a selection of wavenumbers $k$ given in units of $h\,{\rm Mpc}^{-1}$. Red horizontal lines mark the mean redshifts of the source redshift bins, and the green band shows the redshift range of the two lens samples with a split at $z=0.5$. The apodisation width is chosen as $\Delta_x=0.5$.
• Figure 3: Bandpower real-space filters for different bands with the angular frequency range given in square brackets. For each case we show the lowest and highest band used in the fiducial analysis setup. The default correlation function binning has been assumed, with apodisation centred on the angular range boundaries of $0.5\,{\rm arcmin}$ and $300\,{\rm arcmin}$, using a log-width of $\Delta_x=0.5$. Top: filter for $\xi_+$; centre: filter for $\xi_-$; bottom: filter for $\gamma_{\rm t}$; cf. Eqs. (\ref{['eq:apodisation']}), (\ref{['eq:bp_kernel_cosmicshear']}), and (\ref{['eq:bp_kernel_ggl']}).
• Figure 4: Bandpowers for galaxy-galaxy lensing (top panels) and cosmic shear (bottom panels) for a selection of redshift bin combinations (indicated by ' L' and ' S' for lens and source galaxy samples, respectively; see Sect. \ref{['sec:data']} for details). Grey and black lines show the true underlying angular power spectrum; the associated dotted lines the average of these power spectra over the angular frequency band. The bottom panels show the relative deviations in the cases of maximum AGN feedback (blue/green) and using the takahashi12 Halofit version (orange/red) with respect to mead15 without AGN feedback. The grey shaded regions in the top panels show the conservative limits applied to the low- and high-redshift lens samples (excluding all and light/medium grey regions, respectively), as well as the more optimistic cut if galaxy biasing were well understood (only excluding the dark grey region).
• Figure 5: Bottom: Survey footprints of three data sets used in this analysis: BOSS (blue), 2dFLenS (green), and KiDS (orange). Overlapping regions of KiDS with either BOSS or 2dFLenS are shown in pink. Top: Cut-outs of the KiDS areas showing the variable depth patterns of our source samples as indicated by the $r$-band magnitude limit, $r_\mathrm{lim}$ (at $1\sigma$ for adaptive aperture size; see kuijken19 for details).