The mass–richness relation of optically selected clusters from weak gravitational lensing and abundance with Subaru HSC first-year data

Abstract

Abstract Constraining the relation between the richness N and the halo mass M over a wide redshift range for optically selected clusters is a key ingredient for cluster-related science in optical surveys, including the Subaru Hyper Suprime-Cam (HSC) survey. We measure stacked weak-lensing profiles around 1747 HSC CAMIRA clusters over a redshift range of 0.1 ≤ zcl ≤ 1.0 with N ≥ 15 using the HSC first-year shear catalog covering ∼140 deg2. The exquisite depth and image quality of the HSC survey allow us to measure lensing signals around high-redshift clusters at 0.7 ≤ zcl ≤ 1.0 with a signal-to-noise ratio of 19 within the comoving radius range $0.5\lesssim R\lesssim 15\, h^{-1}\:{\rm Mpc}$. We constrain the richness–mass relations P(ln N ∣ M, z) of HSC CAMIRA clusters assuming a log-normal distribution without informative priors on model parameters, by jointly fitting to the lensing profiles and abundance measurements under both Planck and WMAP cosmological models. We show that our model gives acceptable p-values when we add redshift-dependent terms proportional to ln (1 + z) and [ln (1 + z)]2 in the mean and scatter relations of P(ln N ∣ M, z). Such terms presumably originate from the variation of photometric redshift errors as a function of redshift. We show that constraints on the mean relation 〈M ∣ N〉 are consistent between the Planck and WMAP models, whereas the scatter values σln M ∣ N for the Planck model are systematically larger than those for the WMAP model. We also show that the scatter values for the Planck model increase toward lower richness values, whereas those for the WMAP model are consistent with constant values as a function of richness. This result highlights the importance of the scatter in the mass–richness relation for cluster cosmology.