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

## TL;DR

This study measures the relation between cluster richness and halo mass using weak lensing and abundance data from Subaru HSC, providing insights into the mass-richness relation across redshifts and its implications for cosmology.

## Contribution

It presents the first detailed measurement of the richness-mass relation for optically-selected clusters over a wide redshift range using Subaru HSC data, including modeling of redshift-dependent scatter.

## Key findings

- Richness-mass relation is consistent with models when including redshift-dependent terms.
- Scatter in mass-richness relation varies with richness and differs between Planck and WMAP cosmologies.
- Constraints on the mean relation are consistent across cosmological models.

## 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 $0.1\leq z_{\rm cl}\leq 1.0$ with $N\geq 15$ using the HSC first-year shear catalog covering $\sim$$140$ ${\rm deg^2}$. The exquisite depth and image quality of the HSC survey allow us to measure lensing signals around the high-redshift clusters at $0.7\leq z_{\rm cl}\leq 1.0$ with a signal-to-noise ratio of 19 in the comoving radius range $0.5\lesssim R\lesssim 15 h^{-1}{\rm Mpc}$. We constrain richness-mass relations $P(\ln N|M,z)$ of the 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 which are proportional to $\ln (1+z)$ and $[\ln (1+z)]^{2}$ into 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 the redshift. We show that the constraints on the mean relation $\langle M|N \rangle$ are consistent between the Planck and WMAP models, whereas the scatter values $\sigma_{\ln M|N}$ 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.