---
title: 'KiDS-1000: Cosmological Data Release'
url: https://www.emergentmind.com/topics/kids-1000
type: topic
---

# KiDS-1000: Cosmological Data Release

Searching arXiv for recent KiDS-1000 papers to ground the article.
KiDS-1000 is the fourth data release of the Kilo-Degree Survey, covering 1006 deg\(^2\) in nine optical-to-near-infrared bands, \(ugriZYJHK_s\), from VST/OmegaCAM and VIKING/VISTA, and optimized for weak lensing. For weak-lensing analyses, the release is typically described through an effective unmasked area of \(777.4\) deg\(^2\), a “gold sample” of 21 million galaxies with calibrated redshift distributions, and five tomographic source bins spanning \(0.1<z_B\le1.2\) [2007.01845, 2007.15635]. KiDS-1000 has been used for cosmic shear, galaxy-galaxy lensing, spectroscopic clustering, higher-order shear statistics, density split statistics, peak counts, cluster abundance and weak lensing, CMB-lensing cross-correlation, and simulation-based inference, with repeated emphasis on the structure-growth parameter \(S_8\equiv \sigma_8\sqrt{\Omega_{\rm m}/0.3}\) and on the control of shear, redshift, intrinsic-alignment, and baryonic systematics [2007.15632, 2309.08602, 2404.15402].

## 1. Survey definition and catalogue construction

KiDS-1000 combines deep \(r\)-band imaging for shape measurement with matched nine-band photometry for photometric redshifts. The \(r\)-band weak-lensing data were observed under the requirement that the PSF full-width at half maximum is \(<0.8''\), yielding a mean seeing of \(0.7''\) and a median \(5\sigma\) point-source depth of \(r=25.02\pm0.13\) mag in a \(2''\) aperture [2007.01845]. Shape estimation is based on the model-fitting algorithm lensfit, applied to the set of unstacked \(r\)-band exposures, with each galaxy assigned an ellipticity \(\epsilon=\epsilon_1+i\epsilon_2\) and a weight \(w\) [2007.01845].

The release is often summarized through a small set of survey-level quantities.

| Quantity | Value | Source |
|---|---:|---|
| Total imaging footprint | \(1006\) deg\(^2\) | [2007.01845] |
| Effective unmasked weak-lensing area | \(777.4\) deg\(^2\) | [2007.01845] |
| Gold-sample size | 21 million galaxies | [2007.01845] |
| Gold-sample \(n_{\rm eff}\) | \(6.17\) arcmin\(^{-2}\) | [2007.01845] |
| Pre-redshift-selection \(n_{\rm eff}\) | \(8.43\) arcmin\(^{-2}\) | [2007.01845] |
| Tomographic binning | five bins, \(0.1<z_B\le1.2\) | [2007.15635] |

PSF modelling was constructed on a \(32\times32\) pixel grid per exposure, with each pixel represented by a 2D polynomial of order \(n=4\) across the focal plane and of order \(n_c=1\) per CCD chip, so as to capture discontinuities at chip boundaries [2007.01845]. The shear catalogue paper states that the PSF model meets the requirement to induce less than a \(0.1\sigma\) change in the inferred cosmic-shear constraints on \(S_8\), and the catalogue-level validation found no evidence for significant non-lensing B-mode distortions in the data [2007.01845].

Later reanalyses refined the basic catalogue products rather than replacing the survey definition. The “v2” cosmic-shear analysis updated lensfit from v309c to v321, applied an empirical PSF-leakage correction, and reported that the overall additive bias \(c_2\) was halved relative to the v1 catalogue, now at \(c_2\sim3\times10^{-4}\) [2306.11124]. A still later reanalysis implemented MetaCalibration, obtained \(n_{\rm eff}=7.77\) arcmin\(^{-2}\) versus \(6.69\) arcmin\(^{-2}\) for lensfit in the cosmology sample, and found multiplicative biases \(|m|<0.017\) in all five cosmology bins [2510.01122].

## 2. Redshift calibration and tomographic binning

KiDS-1000 tomography is defined from BPZ photometric-redshift point estimates \(z_B\), with bins \((0.1,0.3], (0.3,0.5], (0.5,0.7], (0.7,0.9], (0.9,1.2]\) [2007.15635]. The baseline calibration of the source redshift distributions used deep spectroscopic reference catalogues re-weighted with a self-organising map (SOM) in nine-dimensional magnitude space. If \(N_p(c)\) and \(N_s(c)\) denote the photometric and spectroscopic occupancies of SOM cell \(c\), the cell weight is
\[
w(c)=\frac{N_p(c)}{N_s(c)},
\]
and the reweighted redshift distribution is
\[
n_{\rm SOM}(z)=\sum_{c=1}^{N_{\rm cells}} w(c)\,n_{{\rm spec},c}(z).
\]
A “gold” selection removes cells without spectroscopic support or with a large spectroscopic-photometric discrepancy [2007.15635].

Validation on 100 independent KiDS-like MICE realizations found \(|\Delta\langle z\rangle_j^{\rm SOM}|\lesssim0.01\) in all five bins, with \(\sigma(\Delta\langle z\rangle^{\rm SOM})\approx0.01\) [2007.15635]. An independent clustering-redshift approach fitted
\[
n_{\rm CZ}(z)\approx A\cdot n_{\rm SOM}(z+\delta z^{\rm CZ}),
\]
and found offsets consistent with zero, with combined uncertainties of order \(0.01\)–\(0.02\) across the five bins [2007.15635]. This dual calibration is central to the claim that redshift errors remain a subdominant part of the KiDS-1000 weak-lensing error budget [2007.15635].

The redshift calibration was later expanded in a dedicated cosmic-shear reanalysis. That work compiled 17 spectroscopic campaigns across six \(1\) deg\(^2\) “KiDZ” fields, enlarging the spectroscopic sample from \(\sim25{,}000\) to \(52{,}900\), then to \(61{,}200\) with PAUS and to \(112{,}400\) with COSMOS2015 photo-\(z\)s [2204.02396]. The fraction of KiDS-1000 source galaxies with reliable calibration rose from \(\sim80\%\) to \(\sim89\%\) with the “spec-z fiducial” sample and to \(\sim95\%\) when PAUS and COSMOS2015 were included, with shifts in \(S_8\) of at most \(0.5\sigma\) across the tested calibration subsets [2204.02396].

A more recent development replaced summary redshift calibration with full posterior inference of galaxy properties. The pop-cosmos analysis performed SED fitting for 4 million KiDS-1000 galaxies, validated photometric redshifts against \(\sim185{,}000\) DESI DR1 spectroscopic matches, and argued that physically selected source samples can mitigate intrinsic-alignment systematics while preserving statistical power [2602.03930]. This suggests a transition from tomographic samples defined only by \(z_B\) to source samples defined by posterior physical properties.

## 3. Shear estimation and summary statistics

The basic KiDS-1000 shear observables are the tomographic two-point correlation functions
\[
\xi_\pm^{(ij)}(\theta)=\langle \gamma_t\gamma_t\rangle_{ij}(\theta)\pm \langle \gamma_\times\gamma_\times\rangle_{ij}(\theta),
\]
estimated from weighted galaxy pairs [2007.01845]. Multiple compressed representations of these two-point functions were developed for KiDS-1000. In the COSEBI basis, the pure-E mode on a finite angular interval is
\[
E_n^{(ij)}=\frac12\int_{\theta_{\min}}^{\theta_{\max}} d\theta\,\theta
\left[T_{+n}(\theta)\,\xi_+^{(ij)}(\theta)+T_{-n}(\theta)\,\xi_-^{(ij)}(\theta)\right],
\]
with \(T_{\pm n}\) chosen so that only pure E-modes contribute [2309.08602]. KiDS-1000 COSEBI analyses used \(\theta_{\min}=0.5'\), \(\theta_{\max}=300'\) in earlier work and \(\theta_{\min}=2'\), \(\theta_{\max}=300'\) in the improved cosmic-shear analysis [2204.02396, 2306.11124].

A parallel line of work used Fourier-space statistics. The pseudo-\(C_\ell\) analysis divided 21,262,011 galaxies into five tomographic bins and measured eight logarithmic bandpowers in the multipole range \(76<\ell<1500\) for all auto- and cross-spectra [2110.06947]. The method forward-modelled the survey mask through a mixing matrix \(M_{\ell\ell'}\), and the B-mode bandpowers were reported to be consistent with zero signal, with no significant residual contamination from E/B-mode leakage [2110.06947]. The joint weak-lensing and clustering methodology paper similarly emphasized band powers and related Fourier-space statistics because they are insensitive to the survey mask and display low levels of mode mixing [2007.01844].

KiDS-1000 also supported genuinely non-Gaussian lensing statistics. The third-order aperture-mass statistic is defined from the compensated filter \(U\) and shear-space partner \(Q\), with
\[
M(\theta;\theta_{\rm ap})=\int d^2\theta' \,U_{\theta_{\rm ap}}(|\theta'|)\,\kappa(\theta+\theta')
=\int d^2\theta' \,Q_{\theta_{\rm ap}}(|\theta'|)\,\gamma_t(\theta+\theta'),
\]
and third moments \(\langle M^3\rangle^{(ijk)}(\theta_{{\rm ap},1},\theta_{{\rm ap},2},\theta_{{\rm ap},3})\) probe the bispectrum of the convergence field [2309.08602]. These higher-order quantities were later combined with COSEBIs in a tomographic cosmology analysis.

## 4. Modelling, covariance, and inference pipeline

The standard KiDS-1000 cosmology pipeline couples weak-lensing projection kernels, calibrated source redshift distributions, non-linear matter modelling, nuisance-parameter marginalization, and validated covariance models. In the joint weak-lensing and clustering methodology, linear power spectra were computed with CAMB, non-perturbative non-linear matter power with HMCode, and galaxy clustering with a hybrid model that blends one-loop renormalised perturbation theory with halo-model ingredients [2007.01844]. In the later cosmic-shear and higher-order analyses, the non-linear matter power spectrum was modelled with HMcode2020, while third-order statistics used BiHalofit for the bispectrum [2306.11124, 2309.08602].

Intrinsic alignments are generally treated with the non-linear alignment model. In the higher-order shear analysis,
\[
\delta_I=f_{\rm IA}(z)\,\delta,\qquad
f_{\rm IA}(z)= -A_{\rm IA}\,C_1\,\bar\rho(z)/D_+(z),
\]
which induces the familiar \(P_{\delta I}\), \(P_{II}\), and bispectrum analogues [2309.08602]. Baryonic feedback is incorporated either through HMCode nuisance parameters such as \(A_{\rm bary}\) or \(T_{\rm AGN}\), or through multiplicative responses measured from hydrodynamical simulations such as Magneticum [2007.15632, 2306.11124, 2309.08602]. Across these analyses, photo-\(z\) shifts \(\delta z_i\) and shear-calibration uncertainties \(m_i\) are propagated as nuisance parameters or additive covariance contributions [2007.01844, 2306.11124].

Covariance construction was a major methodological component of KiDS-1000. The joint weak-lensing and clustering methodology used a dedicated suite of more than 20,000 mocks to assess covariance performance and to quantify the impact of survey geometry and spatial variations of survey depth on signals and errors [2007.01844]. The same work found that standard point estimates of \(S_8\) from a marginal posterior can under-cover the true value and introduced the projected joint highest-posterior-density (PJ-HPD) interval around the multivariate MAP point to improve calibration [2007.01844]. This inference convention recurs in later KiDS-1000 analyses.

The simulation-based inference analysis replaced an analytic likelihood by a learned likelihood. KiDS-SBI used 18,000 forward realizations, score compression from 120 data points down to 7 summaries, non-Limber projection via Levin’s method, and log-normal random matter fields on the curved sky [2404.15402]. The forward model included variable depth, PSF anisotropy, shear calibration, and redshift calibration. A key methodological result was that neglecting variable depth and PSF anisotropies can cause \(S_8\) to be overestimated by \(\sim5\%\), and that fixing the covariance at a fiducial cosmology underestimates uncertainties on \(S_8\) by \(\sim10\%\) [2404.15402].

## 5. Principal cosmological constraints and the \(S_8\) issue

Published KiDS-1000 cosmic-shear analyses report closely related but not identical \(S_8\) constraints. The pseudo-\(C_\ell\) analysis found
\[
S_8=0.754_{-0.029}^{+0.027},
\]
and, when combined with SDSS BAO, RSD, and Ly\(\alpha\), obtained \(S_8=0.771^{+0.006}_{-0.032}\) [2110.06947]. The enhanced redshift-calibration COSEBIs analysis reported
\[
S_8=0.748_{-0.025}^{+0.021},
\]
while the improved cosmic-shear measurements paper reported
\[
S_8=0.776_{-0.027-0.003}^{+0.029+0.002},
\]
where the second uncertainty quantifies systematic shear-calibration uncertainty [2204.02396, 2306.11124]. The MetaCalibration reanalysis found
\[
S_8=0.789_{-0.024}^{+0.020},
\]
with about \(28\%\) improved constraining power relative to the lensfit analysis, while concluding that the difference with Planck remains at a similar level and is not caused by the shear measurements [2510.01122].

The flagship multi-probe KiDS-1000 \(3\times2\)pt analysis combined cosmic shear, spectroscopic galaxy clustering from BOSS, and galaxy-galaxy lensing from the KiDS-BOSS and KiDS-2dFLenS overlaps. Its fiducial MAP+PJ-HPD result was
\[
S_8=0.766^{+0.020}_{-0.014},\qquad
\sigma_8=0.760^{+0.021}_{-0.023},\qquad
\Omega_{\rm m}=0.305^{+0.010}_{-0.015},
\]
with \(S_8\) lower than Planck by \(8.3\pm2.6\%\) [2007.15632]. In the companion beyond-flat-\(\Lambda\)CDM study, the same \(3\times2\)pt data were found to be fully consistent with \(\Omega_K=0.011^{+0.054}_{-0.057}\), \(\sum m_\nu<1.76\) eV at \(95\%\) CL, and \(w=-0.99^{+0.11}_{-0.13}\), with no clear preference for the fiducial flat \(\Lambda\)CDM model or the tested extensions [2010.16416].

A recurrent theme of the KiDS-1000 literature is the “\(S_8\) tension” with Planck. The quoted significance depends on probe combination, modelling choices, and the tension metric. The improved cosmic-shear measurements paper reported \(\sim2.3\sigma\) [2306.11124], the enhanced redshift-calibration analysis reported \(\sim3.4\sigma\) [2204.02396], the pseudo-\(C_\ell\) analysis reported \(\sim3\sigma\) [2110.06947], and the \(3\times2\)pt analysis found \(\sim3\sigma\) for one-dimensional \(S_8\) comparisons but \(\sim2\sigma\) in the full multidimensional parameter space [2007.15632]. The beyond-\(\Lambda\)CDM analysis further showed that one-dimensional \(S_8\) tension can disappear in \(w\)CDM while persisting in the joint \((S_8,w)\) space [2010.16416].

## 6. Non-Gaussian, multi-probe, and methodological extensions

KiDS-1000 has been a testbed for moving beyond Gaussian two-point statistics. The combined second- and third-order shear analysis performed the first cosmological parameter analysis of KiDS-1000 with COSEBIs and \(\langle M_{\rm ap}^3\rangle\), using HMcode2020 for the power spectrum, BiHalofit for the bispectrum, an analytic intrinsic-alignment model, and hydrodynamical simulations for baryonic feedback [2309.08602]. A key technical step was the equal-filter-radii ansatz, with \(\theta_{\rm ap}=\{4',8',14',32'\}\), which reduced the data-vector dimension from \(\sim775\) to 215 while losing only \(\simeq8\%\) of the joint \(\Omega_{\rm m}\)–\(S_8\) figure of merit [2309.08602]. The resulting combined constraint was
\[
\Omega_{\rm m}=0.248^{+0.062}_{-0.055},\qquad
S_8=0.772\pm0.022,
\]
with negligible validation bias and smaller errors than the second-order-only case [2309.08602].

Other non-Gaussian statistics were also applied to KiDS-1000. Density split statistics yielded
\[
\Omega_{\rm m}=0.27\pm0.02,\qquad
S_8=0.731^{+0.030}_{-0.018},
\]
and were described as competitive with two-point cosmic shear while additionally constraining galaxy bias and shot-noise deviations [2208.02171]. Peak count statistics obtained
\[
\Sigma_8\equiv \sigma_8\left[\Omega_{\rm m}/0.3\right]^{0.60}=0.765^{+0.030}_{-0.030},
\]
in the KiDS-only analysis and \(\Sigma_8^{\rm joint}=0.759^{+0.020}_{-0.017}\) in the combined KiDS-1000 and DES-Y1 analysis [2405.10312]. A halo-model joint analysis of the stellar mass function, projected clustering, and galaxy-galaxy lensing found
\[
S_8=0.773^{+0.028}_{-0.030},\qquad
\Omega_{\rm m}=0.290^{+0.021}_{-0.017},
\]
demonstrating that small-scale clustering and galaxy-galaxy lensing can deliver constraints comparable to \(3\times2\)pt analyses without including cosmic shear [2210.03110]. A cluster-count and stacked weak-lensing analysis of about 8000 AMICO clusters reported
\[
\Omega_{\rm m}=0.218^{+0.024}_{-0.021},\qquad
\sigma_8=0.86^{+0.03}_{-0.03},\qquad
S_8=0.74^{+0.03}_{-0.03},
\]
together with an average mass precision of \(\simeq8\%\) for the \(\log\lambda^*-\log M_{200}\) relation [2507.14285].

| Analysis | Parameter | Representative result |
|---|---|---|
| Improved cosmic shear measurements | \(S_8\) | \(0.776_{-0.027-0.003}^{+0.029+0.002}\) |
| Multi-probe \(3\times2\)pt | \(S_8\) | \(0.766^{+0.020}_{-0.014}\) |
| COSEBIs \(+\langle M_{\rm ap}^3\rangle\) | \(S_8\) | \(0.772\pm0.022\) |
| Density split statistics | \(S_8\) | \(0.731^{+0.030}_{-0.018}\) |
| Peak counts | \(\Sigma_8\) | \(0.765^{+0.030}_{-0.030}\) |
| AMICO clusters: counts + weak lensing | \(S_8\) | \(0.74^{+0.03}_{-0.03}\) |

KiDS-1000 has also supported cross-correlation and model-building studies. The Planck CMB-lensing cross-correlation analysis used an intrinsic-alignment self-calibration method and obtained \(A_{\rm lens}=0.84^{+0.22}_{-0.22}\) and \(A_{\rm IA}=0.60^{+1.03}_{-1.03}\), while stressing the importance of boost-factor, cosmic-magnification, and photometric-redshift modelling [2301.13437]. A model-agnostic reconstruction of the three-dimensional power spectrum found that a Planck-consistent reference spectrum requires \(20\%\)–\(30\%\) suppression on non-linear scales to match KiDS-1000, whereas a lower-\(S_8\) reference avoids suppression; the authors explicitly noted that this could indicate spurious systematic errors, inaccuracies in the intrinsic-alignment model, or potentially a non-standard cosmological model with delayed structure growth [2502.04449]. At the methodological level, KiDS-1000 has further been used for map-level emulation with conditional generative adversarial networks [2112.12741] and for accelerated constraints on Dark Scattering with ReACT and CosmoPower emulators [2402.18562].

Taken together, these analyses show that KiDS-1000 is not a single cosmological measurement but a survey framework in which the same imaging and calibrated source sample support multiple estimators of late-time structure growth. A consistent pattern across the literature is that the dominant limitations are no longer purely statistical. Intrinsic alignments, baryonic feedback, redshift calibration, and forward-modelled observational anisotropies recur as the leading modelling issues, and several KiDS-1000 papers present specific methodological responses: improved SOM calibration, physical SED-based source characterization, MetaCalibration, equal-filter-radii compression for third-order statistics, and SBI with catalogue-level systematics [2204.02396, 2602.03930, 2510.01122, 2309.08602, 2404.15402].

Source: https://www.emergentmind.com/topics/kids-1000