Weak-lensing Shear-Selected Galaxy Clusters from the Hyper Suprime-Cam Subaru Strategic Program: III. A precision cosmological sample enabled by optical confirmation

We develop fCAMIRA (forced-mode CAMIRA), a tool for optical cluster confirmation, and apply it to a sample of 129 weak-lensing (WL) shear-selected galaxy clusters identified in aperture-mass maps obtained from the Hyper Suprime-Cam Subaru Strategic Program Three-Year (HSC-SSP Y3) weak-lensing data. fCAMIRA is built upon the CAMIRA cluster-finding algorithm and relies on a red-sequence (RS) galaxy model that is calibrated in a data-driven way. The RS model adopts the metallicity-luminosity relation measured in this work using X-ray-selected clusters up to redshift \(z\approx1.3\), followed by the calibration of color offsets using large spectroscopic samples. With the RS model, we build two types of galaxy richness maps, one obtained with a spatial filter matched to a typical cluster size of \(R=0.8\,h^{-1}\,\mathrm{Mpc}\) and the other obtained with a fixed angular-size filter identical to that used in constructing the WL aperture-mass maps. The fCAMIRA algorithm utilizes these two richness maps, identifies all optical counterpart candidates along the line of sight of each shear-selected cluster, and measures the cluster photometric redshift from the highest-ranked counterpart. The ranking is determined by the fractional lensing contribution \(f_{\mathrm{lens}}\) of each candidate. Using available spectroscopic cluster redshifts, we quantify the mean bias and scatter in the cluster photometric redshifts at levels of approximately 0.005 and 0.008, respectively, demonstrating excellent photometric-redshift performance. We compare the fCAMIRA photometric redshifts with estimates from direct positional cross-matching and find that approximately 8% of the total sample exhibits redshift discrepancies greater than 0.15. This outlier fraction is primarily attributed to projection effects, leading to the mis-identification of the optical counterparts. We quantify the systematics of the resulting cluster redshifts and find that they have a negligible impact on the cosmological constraints from HSC-Y3 like samples.