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, $\lambda^*$, 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, $\Gamma$, and the relation between $\mathcal{R}_{\rm sp}\equiv r_{\rm sp}/r_{200\rm m}$ and the peak height, $\nu_{200\rm m}$, 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 $\Lambda$-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.