Weak Lensing Tomographic Redshift Distribution Inference for the Hyper Suprime-Cam Subaru Strategic Program three-year shape catalogue

We present posterior sample redshift distributions for the Hyper Suprime-Cam Subaru Strategic Program Weak Lensing three-year (HSC Y3) analysis. Using the galaxies' photometry and spatial cross-correlations, we conduct a combined Bayesian Hierarchical Inference of the sample redshift distributions. The spatial cross-correlations are derived using a subsample of Luminous Red Galaxies (LRGs) with accurate redshift information available up to a photometric redshift of $z < 1.2$. We derive the photometry-based constraints using a combination of two empirical techniques calibrated on spectroscopic- and multiband photometric data that covers a spatial subset of the shear catalog. The limited spatial coverage induces a cosmic variance error budget that we include in the inference. Our cross-correlation analysis models the photometric redshift error of the LRGs to correct for systematic biases and statistical uncertainties. We demonstrate consistency between the sample redshift distributions derived using the spatial cross-correlations, the photometry, and the posterior of the combined analysis. Based on this assessment, we recommend conservative priors for sample redshift distributions of tomographic bins used in the three-year cosmological Weak Lensing analyses.