Mock galaxy shape catalogs in the Subaru Hyper Suprime-Cam Survey

We use the full-sky ray-tracing weak lensing simulations to generate 2268 mock catalogs for the Subaru Hyper Suprime-Cam (HSC) survey first-year shear catalog in Mandelbaum et al. (2018). Our mock catalogs take into account various effects as in the real data: the survey footprints, inhomogeneous angular distribution of source galaxies, statistical uncertainties in photometric redshift (photo-z) estimate, variations in the lensing weight due to observational conditions and galaxy's properties, and the statistical noise in galaxy shape measurements due to both intrinsic shapes and the measurement errors. We then utilize our mock catalogs to evaluate statistical uncertainties expected in measurements of cosmic shear two-point correlations $\xi_{\pm}$ with tomographic redshift information for the HSC survey. First we develop a quasi-analytical formula for the Gaussian sample variance properly taking into account the number of source pairs in the survey footprints. The standard Gaussian formula significantly overestimates or underestimates the mock results by 50\% level. Secondly we show that different photo-z catalogs or the six disconnected fields, rather than a consecutive geometry for the same area, cause variations in the covariance by ~5\%. Thirdly, we study the chi-square distribution for $\xi_{\pm}$ among the mock catalogs and find the wider distribution than that naively expected for the distribution with the degrees-of-freedom of data vector used. Finally, we propose a method to include non-zero multiplicative bias in mock shape catalog and show the non-zero multiplicative bias can change the effective shape noise term in cosmic shear analyses. Our results suggest an importance of estimating an accurate form of the likelihood function (and therefore the covariance) for robust cosmological parameter inference from the precise measurements.