A clustering-based self-calibration of the richness-to-mass relation of CAMIRA galaxy clusters out to z ≈ 1.1 in the Hyper Suprime-Cam survey

Abstract

ABSTRACT We perform a self-calibration of the richness-to-mass (N–M) relation of CAMIRA galaxy clusters with richness N ≥ 15 at redshift 0.2 ≤ z < 1.1 by modelling redshift-space two-point correlation functions. These correlation functions are the autocorrelation function ξcc of CAMIRA clusters, the autocorrelation function ξgg of the CMASS galaxies spectroscopically observed in the Baryon Oscillation Spectroscopic Survey, and the cross-correlation function ξcg between these two samples. We focus on constraining the normalization AN of the N–M relation with a forward-modelling approach, carefully accounting for the redshift-space distortion, the Finger-of-God effect, and the uncertainty in photometric redshifts of CAMIRA clusters. The modelling also takes into account the projection effect on the halo bias of CAMIRA clusters. The parameter constraints are shown to be unbiased according to validation tests using a large set of mock catalogues constructed from N-body simulations. At the pivotal mass $M_{500}=10^{14}\, h^{-1}\, \mathrm{M}_{\odot }$ and the pivotal redshift zpiv = 0.6, the resulting normalization AN is constrained as $13.8^{+5.8}_{-4.2}$, $13.2^{+3.4}_{-2.7}$, and $11.9^{+3.0}_{-1.9}$ by modelling ξcc, ξcc + ξcg, and ξcc + ξcg + ξgg, with average uncertainties at levels of 36, 23, and $21{{\ \rm per\ cent}}$, respectively. We find that the resulting AN is statistically consistent with those independently obtained from weak-lensing magnification and from a joint analysis of shear and cluster abundance, with a preference for a lower value at a level of ≲ 1.9σ. This implies that the absolute mass scale of CAMIRA clusters inferred from clustering is mildly higher than those from the independent methods. We discuss the impact of the selection bias introduced by the cluster finding algorithm, which is suggested to be a subdominant factor in this work.