Hyper Suprime-Cam Y3 results: photo-$z$ bias calibration with lensing shear ratios and cosmological constraints from cosmic shear

TL;DR

This paper demonstrates an independent calibration of source photometric redshift biases for the HSC-Y3 weak lensing data by using small-scale galaxy-galaxy lensing with lensing ratios across multiple source bins. The authors implement a blinding strategy on the source redshift distributions, compare the shear-ratio constraints to HSC-Y3 cosmic shear results, and show consistent photo-$z$ bias measurements within uncertainties. By combining shear-ratio data with BAO and cosmic shear, they obtain cosmological constraints $\Omega_{\rm m} \approx 0.304$ and $S_8 \approx 0.773$, consistent with cosmic shear alone, validating shear ratios as a geometry-dominated probe for photo-$z$ calibration. They also identify a mild tilt in the $\Delta z_3$–$\Delta z_4$ plane tied to heterogeneous lens-depth coverage, which diminishes with a more uniform lens sample (DESI-DR1), underscoring the importance of lens selection for robust photo-$z$ inferences. Overall, the work highlights the practical impact of small-scale lensing as an independent and complementary method for calibrating redshift biases in weak lensing cosmology and sets the stage for applying similar approaches to future surveys.

Abstract

We present an independent calibration of the photometric redshift (photo-$z$) distributions for source galaxies in the HSC-Y3 weak lensing survey using small-scale galaxy-galaxy lensing. By measuring the tangential shear around spectroscopic lens galaxies from GAMA, SDSS, and DESI, divided into fifteen narrow redshift bins, we compute shear ratios that are sensitive to the mean redshift of source galaxies. Using a blinded analysis, we derive constraints on the photo-$z$ bias parameters in source bins 2, 3 and 4, achieving signal-to-noise ratios of 59, 75, and 62, respectively. Our constraints for $Δz_2$, $Δz_3$ and $Δz_4$ are consistent with those from HSC-Y3 cosmic shear modeling. We observe a mild shift in the $Δz_3$-$Δz_4$ plane due to the heterogeneous depth of the lens sample, which disappears when using only DESI-DR1 lenses. Combining shear-ratio measurements with cosmic shear data, we obtain joint constraints on cosmological parameters: $Ω_{\rm m} = 0.304_{-0.029}^{+0.03}$ and $S_8 = 0.773_{-0.031}^{+0.031}$, consistent with cosmic shear-only results. This work demonstrates the utility of small-scale lensing as an independent probe for calibrating photometric redshift bias in weak lensing cosmology.

Figures (11)

• Figure 1: Lens redshift distribution: The figure shows the lens redshift distribution of our fiducial sample. The solid black line denotes the distribution for the full sample. The blue, orange, green, and red dashed lines represent the redshift distributions of the individual GAMA, DESI-BGS, BOSS, and SDSS-MGS samples, respectively.
• Figure 2: Tangential shear measurements: Shear signals with error bars estimated from 300 random rotations. Blue, orange, and green points correspond to source redshift bins two, three, and four, respectively. A small horizontal offset in $\theta$ facilitates comparison, and each panel indicates the lens redshift bin.
• Figure 3: Shear covariance: Normalized covariance matrices of the tangential shear measurements for each source redshift bin. The quantity $\gamma_{\rm t}^{z_i,\theta_j}$ represents the tangential shear measured in the $i$-th lens redshift bin (see Table \ref{['tab:lenses']}) at angular bin $\theta_j$, with correlation coefficient $r_{ij}$.
• Figure 4: Cumulative signal-to-noise ratio: Solid blue, orange, and green lines show the cumulative signal-to-noise ratio for the tangential shear profiles as a function of angular separation $\theta$ for source redshift $z_{\rm src}$ bins two, three, and four, respectively.
• Figure 5: Shear ratio measurements: Blue points with shape noise error bars show the measured shear ratios for each lens bin. The black line indicates the best fit prediction from the fiducial model. Indices $i$ and $j$ on the $y$-axis denote the source redshift bins used in the numerator and denominator of the shear ratio, respectively.