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

Abstract

We use the full-sky ray-tracing weak lensing simulations to generate 2268 mock catalogues for the Subaru Hyper Suprime-Cam (HSC) survey first-year shear catalogue. Our mock catalogues 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, and the statistical noise in galaxy shape measurements including both intrinsic shapes and the measurement errors. We then utilize our mock catalogues to evaluate statistical uncertainties expected in measurements of cosmic shear twopoint correlations ξ ± with tomographic redshift information for the HSC survey. 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. We also show that different photo-z catalogues or the six disconnected fields, rather than a consecutive geometry, cause variations in the covariance by ∼ 5%. The mock catalogues enable us to study the chi-square distribution for ξ ± . We 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 nonzero multiplicative bias in mock shape catalogue and show the non-zero multiplicative bias can change the effective shape noise 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.

E/B mode decomposition of HSC-Y1 cosmic shear using COSEBIs: cosmological constraints and comparison with other two-point statistics

“…In addition to the HSC-Y1 data set, we have used HSC-Y1 mock shape catalogs constructed from full-sky gravitational lensing simulations (Takahashi et al 2017) that fully take account of the survey geometry and measurement noise (Shirasaki et al 2019). Using 2268 mock realizations, we have derived the E/B-mode covariance matrices adopted in our cosmological analysis.…”

“…Following the methodology of the HSC-Y1 cosmic shear TPCF analysis by H20, we derive covariance matrices of the COSEBIs measurement using 2268 realizations of mock HSC-Y1 shape catalogs (see Shirasaki et al (2019) for a detailed description of the mock catalogs). Since the HSC mock catalogs are constructed based on full-sky lensing simulation data with galaxy positions, intrinsic shape noise, and measurement noise taken from the real HSC-Y1 shape catalog, the mock data naturally have the same survey geometry and the same noise properties as the real catalog, and include super-survey cosmic shear signals from 1 We measured E/B-mode COSEBIs from each of 2268 HSC-Y1 mock catalogs but ignoring shape-noise (Shirasaki et al 2019), and took the average and root-mean-square (RMS) of them. We found that the averaged En signals agree with the theoretical predictions well within the RMSs which represent an expected sample variance of HSC-Y1 field, and that averaged Bn signals are consistent with zero.…”

“…In that figure, for rough comparison, approximate theoretical predictions of the covariance matrices are shown. To calculate them, we follow the prescription described in Appendix A of Asgari et al (2020), and we take only major components into accounts; the Gaussian and shape noise terms for E-mode, and only the shape noise term for B-mode (see Barreira et al 2018;Shirasaki et al 2019, for contributions from non-Gaussian term and super sample covariance). Overall, reasonably good agreements between measurements and theoretical predictions can be seen in Figure 4.…”

“…We note that these effects are properly taken into account in the mock covariance, which will be used in our cosmological analysis throughout the paper. Shirasaki et al (2019) studied in detail the accuracy of the covariance matrix of cosmic shear TPCFs from the HSC-Y1 mocks, and investigated the impact of various systematic effects in the cosmic shear analysis, including photo-z errors and the uncertainty in the multiplicative bias, on the covariance estimation. Based on their results, H20 concluded that the covariance matrix of TPCFs estimated from the mocks is calibrated with < 10% accuracy against various systematic effects in the cosmic shear analysis (see section 4.4 of H20).…”

“…We use the same data set as that used in H19 and H20 along with the same tomographic redshift binning (four bins with 0.3 < z < 0.6, 0.6 < z < 0.9, 0.9 < z < 1.2 and 1.2 < z < 1.5). We also use realistic HSC-Y1 mock catalogs constructed from full-sky gravitational lensing simulations (Takahashi et al 2017) with fully taking account of the survey geometry and measurement noise (Shirasaki et al 2019), from which we derive E/B-mode covariance matrices.…”