AMICO galaxy clusters in KiDS-DR3: Measurement of the halo bias and power spectrum normalization from a stacked weak lensing analysis

Abstract

Galaxy clusters are biased tracers of the underlying matter density field. At very large radii beyond about 10 Mpc/\textit{h}, the shear profile shows evidence of a second-halo term. This is related to the correlated matter distribution around galaxy clusters and proportional to the so-called halo bias. We present an observational analysis of the halo bias-mass relation based on the AMICO galaxy cluster catalog, comprising around 7000 candidates detected in the third release of the KiDS survey. We split the cluster sample into 14 redshift-richness bins and derive the halo bias and the virial mass in each bin by means of a stacked weak lensing analysis. The observed halo bias-mass relation and the theoretical predictions based on the $\Lambda$CDM standard cosmological model show an agreement within $2\sigma$. The mean measurements of bias and mass over the full catalog give $M_{200c}=(4.9\pm 0.3)\times 10^{13}{M}_{\odot }/\text{h}$ and $b_h{\sigma }_8^2=1.2\pm 0.1$. With the additional prior of a bias-mass relation from numerical simulations, we constrain the normalization of the power spectrum with a fixed matter density ${\Omega }_m=0.3$, finding ${\sigma }_8=0.63\pm 0.10$.

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