Intrinsic Mass–Richness Relation of Clusters from THE THREE HUNDRED Hydrodynamic Simulations

Abstract

Abstract The main systematics in cluster cosmology is the uncertainty in the mass–observable relation. In this paper, we focus on the most direct cluster observable in optical surveys, i.e., richness, and constrain the intrinsic mass–richness (MR) relation of clusters in THE THREE HUNDRED hydrodynamic simulations with two runs: GIZMO-SIMBA and GADGET-X. We find that modeling the richness at a fixed halo mass with a skewed Gaussian distribution yields a simpler and smaller scatter compared to the commonly used lognormal distribution. Additionally, we observe that baryon models have a significant impact on the scatter while exhibiting no influence on the mass dependence and a slight effect on the amplitude in the MR relation. We select member galaxies based on both stellar mass M ⋆ and absolute magnitude M . We demonstrate that the MR relations obtained from these two selections can be converted to each other by using the M ⋆ – M relation. Finally, we provide a seven-parameter fitting result comprehensively capturing the dependence of the MR relation on both stellar mass cutoff and redshift.