AMICO galaxy clusters in KiDS-1000: cosmological constraints and mass calibration from counts and weak lensing

TL;DR

This paper presents a joint Bayesian analysis of stacked weak-lensing signals and cluster counts from the AMICO KiDS-1000 catalog to constrain cosmology and calibrate the cluster mass–richness relation. The authors model cluster abundances and lensing profiles with a truncated NFW (BMO) halo model, include a two-halo term, miscentring, projection, and SSC, and calibrate the background redshift distributions using self-organising maps. They find $\Omega_m=0.218^{+0.024}_{-0.021}$, $\sigma_8=0.86^{+0.03}_{-0.03}$, and $S_8=0.74^{+0.03}_{-0.03}$, with an average mass precision of $\sim8\%$ in the $\log\lambda^*-\log M_{200}$ relation, confirming $\lambda^*$ as a robust mass proxy. The results, halving the uncertainties relative to KiDS-DR3 and in agreement with recent cosmic-shear analyses, are nevertheless in tension with Planck CMB measurements, reinforcing the late-Universe vs early-Universe discrepancy in $S_8$. The work also demonstrates the value of comprehensive systematic treatment and SOM-based background calibration for robust cluster cosmology and sets the stage for future enhancements with KiDS-Legacy and additional data combinations.

Abstract

We present the joint modelling of weak-lensing and count measurements of the galaxy clusters detected with the AMICO code, in the fourth data release of the Kilo Degree Survey (KiDS-1000). The analysed sample comprises about 8000 clusters, covering an effective area of 839 deg$^{2}$ and extending up to a redshift of $z = 0.8$. Stacked cluster weak-lensing and count measurements have been derived in bins of redshift and intrinsic richness, $λ^*$. Based on self-organising maps, we reconstructed the true redshift distributions of the background galaxy samples. We accounted for the systematic uncertainties arising from impurities in the background and cluster samples, biases in the cluster $z$ and $λ^*$, projection effects, halo orientation and miscentring, truncation of cluster halo mass distributions, matter correlated with cluster haloes, multiplicative shear bias, baryonic matter, geometric distortions in the lensing profiles, uncertainties in the theoretical halo mass function, and super-sample covariance. We also employed a blinding strategy based on perturbing the cluster sample completeness. The improved statistics and photometry compared to the previous KiDS data release, KiDS-DR3, have led to a halving of the uncertainties on $Ω_{\rm m}$ and $σ_8$, as we obtained $Ω_{\rm m}=0.22\pm0.02$ and $σ_8=0.86\pm0.03$. The constraint on $S_8 \equiv σ_8(Ω_{\rm m}/0.3)^{0.5}$, $S_8=0.74\pm0.03$, is in excellent agreement with recent cluster count and KiDS-1000 cosmic shear analyses, while it shows a $2.8σ$ tension with Planck cosmic microwave background results. The constraints on the $\logλ^*-\log M_{200}$ relation imply a mass precision of 8%, on average. In addition, the result on the intrinsic scatter of the $\logλ^*-\log M_{200}$ relation, $σ_{\rm intr}=0.05\pm0.02$, confirms that $λ^*$ is an excellent mass proxy.

Figures (19)

• Figure 1: Redshift (top panel) and intrinsic richness (bottom panel) distributions of the AMICO galaxy clusters in KiDS-1000 (blue histograms), with ${\rm S/N}>3.5$ and $z\in[0.1,0.8]$, and in KiDS-DR3 (red hatched histograms), following the ${\rm S/N}$ and redshift selections employed in Bellagamba19. In both panels, no $\lambda^*$ selections have been applied.
• Figure 2: Purity of the cluster sample as a function of $\lambda^*_{\rm ob}$, in the redshift bins $z\in[0.1,0.3)$ (top panel), $z\in[0.3,0.45)$ (middle panel), and $z\in[0.45,0.8]$ (bottom panel). The pink histograms show the purity derived in the $\lambda^*_{\rm ob}$ bins used for cluster weak-lensing measurements, while the black hatched histograms display the purity in the bins used for cluster counts.
• Figure 3: Top panel: Mean of $P(x\,|\,\lambda^*_{\rm tr}, z_{\rm tr})$, namely $\mu_x$, as a function of $\lambda^*_{\rm tr}$ and in different bins of $z_{\rm tr}$ (see legend). Bottom panel: Grey band represents the 68% confidence level of the $\sigma_x$ model, while the dashed orange line shows the Poisson relative uncertainty on $\lambda^*_{\rm tr}$.
• Figure 4: Completeness of the cluster sample as a function of $\lambda^*_{\rm tr}$, for some values of $z_{\rm tr}$ (see the legend). Dashed lines display the completeness measurements, while solid lines show the completeness smoothed with Chebyshev polynomials.
• Figure 5: Number of galaxies that satisfy the photo-$z$ selection (red histograms) and the colour selection (blue hatched histograms) as a function of $z_{\rm g}$, in different cluster redshift bins, namely $z\in[0.1,0.3)$ (left panel), $z\in[0.3,0.45)$ (middle panel), and $z\in[0.45,0.8]$ (right panel). The grey histograms show the galaxies selected through the total selection criterion, defined in Eq. \ref{['eq:tot_selection']}.