KAI-FENG CHENet. al.2025-08-052025-08-052025-01-06https://scholars.lib.ntu.edu.tw/handle/123456789/731001We present the first step toward deriving cosmological constraints through the abundances of galaxy clusters selected in a 510 deg2 weak-lensing aperture mass map, constructed with the Year-Three shear catalog from the Hyper Suprime-Cam Subaru Strategic Program. We adopt a conservative source galaxy selection to construct a sample of 129 weak-lensing peaks with a signal-to-noise ratio above 4.7. We use semi-analytical injection simulations to derive the selection function and the mass-observable relation of our sample. These results take into account complicated uncertainties associated with weak-lensing measurements, such as the non-uniform survey depth and the complex survey geometry, projection effects from uncorrelated large-scale structures, and the intrinsic alignment of source galaxies. We also propose a novel modeling framework to make parts of the mass-observable relation insensitive to assumed cosmological parameters. Such a framework not only offers a great computational advantage to cosmological studies, but can also benefit future astrophysical studies using shear-selected clusters. Our results are an important step toward utilizing these cluster samples that are constructed nearly independent of any baryonic assumptions in upcoming deep-and-wide lensing surveys from the Vera Rubin Observatory, Euclid, and the Nancy Grace Roman Space Telescope.journal article10.33232/001c.128019