2026A&A...705A.208A

This paper, the third in a series, investigates the scaling relations between optical richness, weak-lensing mass, and Compton Y for a sample of galaxy clusters selected purely by their gravitational effect on the shapes of background galaxies. This selection method is uncommon, as most cluster samples in the literature are selected based on signals originating from cluster baryons. We analyze a complete sample of 13 gravity-selected clusters at intermediate redshifts (with 0.12 ≤ z_phot ≤ 0.40) with weak-lensing signal-to-noise ratios exceeding 7. We measured cluster richness by counting red-sequence galaxies, identifying two cases of line-of-sight projections in the process, later confirmed by spectroscopic data. Both clusters are sufficiently separated in redshift that richness contamination can be easily mitigated, since the two red sequences do not blend with each other. We find an exceptionally tight richness-mass relation using our red-sequence-based richness estimator, with a scatter of ∼0.05 dex, smaller than the intrinsic scatter of Compton Y with mass for the same sample. The lower scatter highlights the effectiveness of richness compared to Compton Y. No outliers are found in the richness-mass scaling, even when the cluster with a mass likely affected by projection effects is included in the sample. In the Compton Y-richness plane, the data do not delineate a clear trend. The limited sample size is not the sole reason for the unclear relation between Compton Y and richness, since the same sample, with identical richness values, exhibits a highly significant and tight mass-richness correlation.