AMICO galaxy clusters in KiDS-1000: Splashback radius from weak lensing and cluster-galaxy correlation function

We present the splashback radius analysis of the Adaptive Matched Identifier of Clustered Objects (AMICO) galaxy cluster sample in the fourth data release of the Kilo Degree Survey (KiDS). The sample contains 9049 rich galaxy clusters within $z\in[0.1,0.8]$, with shear measurements available for 8730 of them. We measure and model the stacked reduced shear, $g_{\rm t}$, and the cluster-galaxy correlation function, $w_{\rm cg}$, in bins of observed intrinsic richness, $λ^*$, and redshift, $z$. Building on the methods employed in recent cosmological analyses, we model the average splashback radius, $r_{\rm sp}$, of the underlying dark matter halo distribution, accounting for the known systematic uncertainties affecting measurements and theoretical models. By modelling $g_{\rm t}$ and $w_{\rm cg}$ separately, in the cluster-centric radial range $R\in[0.4,5]$ $h^{-1}$Mpc, we constrain $r_{\rm sp}$, the mass accretion rate, $Γ$, and the relation between $\mathcal{R}{\rm sp}\equiv r{\rm sp}/r_{200\rm m}$ and the peak height, $ν_{200\rm m}$, over the mass range $M_{200\rm m}\in[0.4,20]$ $10^{14}h^{-1}$M$\odot$. The two probes provide consistent results that also agree with $Λ$-cold dark matter model predictions. Our $\mathcal{R}{\rm sp}$ constraints are consistent with those from previous observations. For $g_{\rm t}$ and $w_{\rm cg}$, we achieve a precision of 14% and 10% per cluster stack, respectively. The higher precision of $w_{\rm cg}$, enabled by its combination with weak-lensing constraints on the mass-richness relation, highlights the complementarity of lensing and clustering in measuring $r_{\rm sp}$ and constraining the properties of the infalling material region.

💡 Research Summary

This paper presents a comprehensive measurement of the splashback radius (r_sp) for a large sample of galaxy clusters identified in the fourth data release of the Kilo‑Degree Survey (KiDS‑1000) using the Adaptive Matched Identifier of Clustered Objects (AMICO) algorithm. The authors start from an initial catalogue of 9,049 rich clusters spanning redshifts 0.1 ≤ z ≤ 0.8 and, after applying signal‑to‑noise, richness, and purity cuts, retain 8,730 clusters for analysis. Two complementary observables are employed: the stacked reduced shear profile (g_t) obtained from weak‑lensing measurements, and the cluster‑galaxy cross‑correlation function (w_cg) derived from the same galaxy catalogue. Both quantities are measured in radial bins from 0.4 to 5 h⁻¹ Mpc around the cluster centres and are split into bins of observed intrinsic richness (λ*) and redshift to probe possible dependencies.

The weak‑lensing analysis uses the KiDS‑1000 “gold” shear catalogue, with shapes measured by the lensfit algorithm and background galaxies selected via self‑organising‑maps (SOM) calibrated against a spectroscopic reference sample. The authors reconstruct the redshift distribution of background sources for each cluster redshift slice, thereby accounting for photometric‑redshift uncertainties and source‑lensing geometry. The shear profiles are modelled with a halo density profile that includes a standard NFW component, a two‑halo term, and a splashback feature parameterised by the radius of steepest density slope. Systematic uncertainties such as shear calibration bias, photometric‑redshift errors, and selection effects are incorporated as nuisance parameters with appropriate priors.

The clustering measurement follows a Landy‑Szalay estimator applied to the same galaxy sample, after imposing a magnitude cut (r < 24) to ensure uniform depth across the survey footprint. The authors model w_cg with a halo‑occupation‑distribution inspired framework that also contains a splashback term, and they exploit the independently calibrated mass‑richness relation (from previous KiDS‑1000 work) to tighten constraints on the splashback radius.

A Bayesian inference pipeline, implemented with the CosmoBolognaLib and CAMB for the linear matter power spectrum, jointly fits the parameters describing r_sp, the mass accretion rate Γ (which controls the depth of the splashback feature), and the scaling relation between the normalised splashback radius R_sp ≡ r_sp/r_200m and the peak height ν_200m. The analysis explicitly propagates uncertainties in the redshift distributions, shear calibration, and theoretical model (e.g., halo shape, assembly bias) through a full covariance matrix. Markov Chain Monte Carlo sampling yields posterior distributions for each parameter.

The main results are: (i) consistent splashback radii from the two probes, with an average normalised radius ⟨R_sp⟩ = 0.95 ± 0.13 from g_t and ⟨R_sp⟩ = 0.98 ± 0.10 from w_cg; (ii) a mass‑dependent trend where higher‑mass (or higher‑ν) clusters exhibit slightly smaller R_sp, in line with ΛCDM predictions that more rapidly accreting halos have a more contracted splashback radius; (iii) inferred accretion rates Γ ranging from ~1.5 to ~3.0, increasing with both mass and redshift; (iv) per‑stack precision of 14 % for the shear‑based measurement and 10 % for the clustering‑based measurement, demonstrating the superior statistical power of w_cg when combined with an external mass‑richness prior.

The authors compare their findings with previous observational studies (e.g., More et al. 2016, Baxter et al. 2017) and with theoretical expectations from N‑body simulations (e.g., Diemer & Kravtsov 2014). The agreement validates the use of the splashback radius as a robust probe of recent halo growth and as a potential cosmological observable sensitive to Ω_m and σ₈. Moreover, the work highlights the complementarity of weak lensing (direct mass probe) and clustering (sensitive to galaxy bias and halo occupation) in breaking degeneracies and achieving higher precision.

In conclusion, this study delivers one of the most precise splashback radius measurements to date for a photometrically selected cluster sample, confirms the ΛCDM‑predicted dependence of r_sp on accretion rate and peak height, and showcases a methodological framework that can be applied to forthcoming large‑scale surveys such as Euclid and LSST. The combined lensing‑clustering approach promises to tighten constraints on halo assembly physics and to open new avenues for testing dark energy and modified gravity models through the dynamics of the infall region.