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

TL;DR

This paper measures the splashback radius of a large optically selected cluster sample from the AMICO KiDS-1000 catalogue by combining stacked weak-lensing profiles $g_t$ and cluster-galaxy correlations $w_{cg}$. Using a Diemer14-based halo model with a flexible transition and infall component, the authors constrain the splashback radius $r_{sp}$, the normalised radius $R_{sp}$, and the mass accretion rate $\Gamma$ across redshift and richness bins, linking them to the peak height $\nu_{200m}$. The two probes yield consistent $R_{sp}$ constraints that agree with $\Lambda$CDM predictions, with $14\%$ precision for $g_t$ and $10\%$ for $w_{cg}$ per stack, the latter benefiting from joint constraints on the mass-richness relation. They find a slight systematic offset where $w_{cg}$ implies smaller $r_{sp}$ than $g_t$, which they attribute to dynamical friction acting on cluster member galaxies, and they demonstrate the complementary power of lensing and clustering for probing the infalling material and boundary region of galaxy clusters. The results strengthen the empirical understanding of halo boundaries and set the stage for future Stage IV surveys to sharpen tests of gravity and dark matter physics at large radii.

Abstract

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.

Figures (9)

• Figure 1: Left panel: Cluster photo-$z$ distributions as measured by AMICO (hatched red) and unbiased using a reference spectroscopic sample (blue). Middle panel: Observed photo-$z$ (hatched grey) and SOM-reconstructed (purple) redshift distributions of the full galaxy sample. Right panel: examples of SOM-reconstructed background galaxy redshift distributions, given a cluster redshift of $z=0.125$ (cyan), $z=0.425$ (hatched black), $z=0.725$ (orange), derived by using the background selections by Lesci25.
• Figure 2: Measurements of $g_{\rm t}$ (blue dots) and $w_{\rm cg}$ (orange diamonds) profiles of the AMICO KiDS-1000 galaxy clusters, in bins of $z$ (increasing from top to bottom) and $\lambda^*$ (increasing from left to right). The error bars are the sum of statistical errors and residual uncertainties coming from systematic errors (see Sect. \ref{['sec:modelling:likelihood']}). The bands superimposed to the measurements represent the 68% confidence levels of the $g_{\rm t}$ (blue) and $w_{\rm cg}$ (orange) models. The vertical bands show the 68% confidence of the splashback radius, derived from the modelling of $g_{\rm t}$ (blue) and $w_{\rm cg}$ (orange). The dashed lines represent median values.
• Figure 3: Left panels: Constraints on the ratio of $r_{\rm sp}$ to $r_{200\rm m}$ as a function of $\nu_{200\rm m}$ (top panel), obtained from the modelling of $g_{\rm t}$ (blue band) and $w_{\rm cg}$ (orange band) presented in this work, and by Giocoli24 in KiDS-DR3 (grey band). The median theoretical models by More15 (black dashed line) and Diemer20_2 (magenta dashed line) are shown. Both models are computed at $z=0.45$. Squares represent the results from X-ray-selected clusters by Umetsu17, Contigiani19, Bianconi21, Rana23, Joshi25. Triangles display results from SZ-selected cluster catalogues by Zurcher19, Shin19, Shin21. Crosses show the results from optically-selected clusters by More16Baxter17, Chang18, Murata20. The probes used in these analyses, namely weak lensing (WL), strong lensing (SL), luminosity distribution (LD), and galaxy distribution (GD), are reported in the legend. Mass accretion rates from $g_{\rm t}$ and $w_{\rm cg}$ measurements are shown in the middle and bottom panels, respectively. Here, the model by Diemer20_2 is shown, computed at $z=0.2$ (solid lines), $z=0.37$ (dotted lines), and $z=0.62$ (dash-dotted lines). Right panels: $r_{\rm sp}$ derived from the modelling of $g_{\rm t}$ (blue dots) and $w_{\rm cg}$ (orange diamonds), as a function of $M_{200\rm m}$ and for $z_{\rm ob}\in[0.1,0.3)$ (top panel), $z_{\rm ob}\in[0.3,0.45)$ (middle panel), $z_{\rm ob}\in[0.45,0.8]$ (bottom panel).
• Figure 4: Precision of the $\mathcal{R}_{\rm sp}$ (top panels), $r_{\rm sp}$ (middle panels), and $M_{200\rm m}$ (bottom panels) constraints, obtained from the modelling of $g_{\rm t}$ (blue dots) and $w_{\rm cg}$ (orange diamonds), for $z_{\rm ob}\in[0.1,0.3)$ (left panels), $z_{\rm ob}\in[0.3,0.45)$ (central panels), and $z_{\rm ob}\in[0.45,0.8]$ (right panels).
• Figure 5: Comparison between $M_{200}^{\rm BMO}$, derived by Lesci25, and the mass estimates obtained from the $g_{\rm t}$ modelling presented in this work, $M_{200}^{\rm DK14}$, for $z_{\rm ob}\in[0.1,0.3)$ (top), $z_{\rm ob}\in[0.3,0.45)$ (middle), and $z_{\rm ob}\in[0.45,0.8]$ (bottom), applying the $\lambda^*$ cuts listed in Table \ref{['tab:sample']} to the AMICO KiDS-1000 cluster sample. The mean and error bars are derived by marginalising the mass estimates over all the free model parameter posteriors. The dashed red lines represent the 1:1 relation.