Cosmological inference from an emulator based halo model. II. Joint analysis of galaxy-galaxy weak lensing and galaxy clustering from HSC-Y1 and SDSS

We present high-fidelity cosmology results from a blinded joint analysis of galaxy-galaxy weak lensing ($\mathrm{\ensuremath{\Delta}}\mathrm{\ensuremath{\Sigma}}$) and projected galaxy clustering (${w}_{\mathrm{p}}$) measured from the Hyper Suprime-Cam Year-1 (HSC-Y1) data and spectroscopic Sloan Digital Sky Survey (SDSS) galaxy catalogs in the redshift range $0.15<z<0.7$. We define luminosity-limited samples of SDSS galaxies to serve as the tracers of ${w}_{\mathrm{p}}$ in three spectroscopic redshift bins, and as the lens samples for $\mathrm{\ensuremath{\Delta}}\mathrm{\ensuremath{\Sigma}}$. For the $\mathrm{\ensuremath{\Delta}}\mathrm{\ensuremath{\Sigma}}$ measurements, we select a single sample of $4\ifmmode\times\else\texttimes\fi{}{10}^{6}$ source galaxies over $140\text{ }\text{ }{\mathrm{deg}}^{2}$ from HSC-Y1 with photometric redshifts (photo $z$) greater than 0.75, enabling a better handle of photo-$z$ errors by comparing the $\mathrm{\ensuremath{\Delta}}\mathrm{\ensuremath{\Sigma}}$ amplitudes for the three lens redshift bins. The deep, high-quality HSC-Y1 data enable significant detections of the $\mathrm{\ensuremath{\Delta}}\mathrm{\ensuremath{\Sigma}}$ signals, with integrated signal-to-noise ratio $S/N\ensuremath{\sim}15$ in the range $3\ensuremath{\le}R/[{h}^{\ensuremath{-}1}\text{ }\mathrm{Mpc}]\ensuremath{\le}30$ for the three lens samples, despite the small area coverage. For cosmological parameter inference, we use an input galaxy-halo connection model built on the dark emulator package (which uses an ensemble set of high-resolution $N$-body simulations and enables fast, accurate computation of the clustering observables) with a halo occupation distribution that includes nuisance parameters to marginalize over modeling uncertainties. We model the $\mathrm{\ensuremath{\Delta}}\mathrm{\ensuremath{\Sigma}}$ and ${w}_{\mathrm{p}}$ measurements on scales from $R\ensuremath{\simeq}3$ and $2\text{ }\text{ }{h}^{\ensuremath{-}1}\text{ }\mathrm{Mpc}$, respectively, up to $30\text{ }\text{ }{h}^{\ensuremath{-}1}\text{ }\mathrm{Mpc}$ (therefore excluding the baryon acoustic oscillations information) assuming a flat $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ cosmology, marginalizing over about 20 nuisance parameters and demonstrating the robustness of our results to them. With various tests using mock catalogs described in Miyatake et al. [preceding paper, Phys. Rev. D 106, 083519 (2022)], we show that any bias in the clustering amplitude ${S}_{8}\ensuremath{\equiv}{\ensuremath{\sigma}}_{8}({\mathrm{\ensuremath{\Omega}}}_{\mathrm{m}}/0.3{)}^{0.5}$ due to uncertainties in the galaxy-halo connection is less than $\ensuremath{\sim}50%$ of the statistical uncertainty of ${S}_{8}$, unless the assembly biaseffect is unexpectedly large. Our best-fit models have ${S}_{8}=0.79{5}_{\ensuremath{-}0.042}^{+0.049}$ (mode and 68% credible interval) for the flat $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model; we find tighter constraints on the quantity ${S}_{8}(\ensuremath{\alpha}=0.17)\ensuremath{\equiv}{\ensuremath{\sigma}}_{8}({\mathrm{\ensuremath{\Omega}}}_{\mathrm{m}}/0.3{)}^{0.17}=0.74{5}_{\ensuremath{-}0.031}^{+0.039}$.

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