Self-calibrating optical galaxy cluster selection bias using cluster, galaxy, and shear cross-correlations

The clustering signals of galaxy clusters are known to be powerful tools for self-calibrating the mass-observable relation and complementary cluster abundance lensing. In this work, we explore possibility combining three correlation functions -- lensing, cluster-galaxy cross-correlation function, auto-correlation function self-calibrate optical selection bias, boosted lensing in a richness-selected sample mainly caused by projection effects. We develop mock catalogues redMaGiC-like galaxies redMaPPer-like applying Halo Occupation Distribution (HOD) models N-body simulations using counts-in-cylinders around massive haloes as richness proxy. addition previously small-scale boost projected functions, find that effects also significantly 3D out scales 100 $h^{-1} \mathrm{Mpc}$. perform likelihood analysis assuming survey conditions similar Dark Energy Survey (DES) show bias can self-consistently constrained at 10% level. discuss strategies approach real data. expect expanding smaller deeper data would further improve constraints on bias.