HSC-Y3: Subaru Cosmology Survey

• Hyper Suprime-Cam (HSC) Y3 is a wide-field imaging survey that provides high-precision weak lensing and clustering measurements using multi-probe analyses.
• It employs advanced methodologies including two-point correlation functions, pseudo-Cℓ power spectra, and third-order shear statistics to robustly constrain cosmological parameters.
• Rigorous photo-z calibration, extensive mock simulations, and stringent systematic error controls underpin its benchmark performance in ground-based cosmology.

The Hyper Suprime-Cam Year 3 (HSC-Y3) program refers to the third annual cosmological analysis of wide-field imaging data from the Subaru Telescope’s Hyper Suprime-Cam (HSC). HSC-Y3 delivers high-precision weak lensing and clustering measurements across 416 deg² to an i-band depth of 24.5 mag, exploiting a source density of up to 20 arcmin⁻² in four tomographic redshift bins. The survey underlies a suite of joint and single-probe cosmological constraints, including cosmic shear two-point correlation functions (2PCFs), power spectrum analyses, 3×2pt methods combining clustering and lensing, and—for the first time—incorporates third-order statistics such as aperture-mass skewness. HSC-Y3 is notable for its control of systematic errors and rigorous blinding procedures, setting a benchmark for contemporary ground-based cosmology.

1. Survey Design and Data Products

HSC-Y3 uses data from the Subaru Strategic Program S19A release (2014–2019), covering six disjoint fields after masking regions affected by PSF or B-mode systematics (More et al., 2023). Imaging is conducted across five bands (g, r, i, z, y), with the i-band seeing at ∼0.6″ and 5σ point-source depth approaching i≃26 mag (More et al., 2023).

The main HSC-Y3 shape catalog contains approximately 25 million galaxies with reliable shape measurements, yielding an effective number density of n_eff ≈ 15–20 arcmin⁻² depending on redshift bin (Li et al., 2023, Terasawa et al., 29 Mar 2024). Shape measurements utilize re-Gaussianization corrections and are calibrated via extensive image simulations, achieving multiplicative shear bias |m|≲0.01 (More et al., 2023, Sugiyama et al., 19 Aug 2025).

Photometric redshifts are inferred via three independent codes (DNNz, DEmPZ, Mizuki), each producing per-galaxy posteriors (Rau et al., 2022). Calibration is accomplished using cross-correlations with CAMIRA luminous red galaxies (LRGs) and hierarchical Bayesian inference, establishing Gaussian priors on the mean redshift shift (Δz) for bins 1-2 and broad flat priors for bins 3-4 (Rau et al., 2022). The tomographic bin edges are 0.3<z≤0.6, 0.6<z≤0.9, 0.9<z≤1.2, 1.2<z≤1.5 (Terasawa et al., 29 Mar 2024, Dalal et al., 2023).

2. Cosmological Measurement Methodologies

HSC-Y3 supports two principal frameworks for cosmic shear analysis: real-space two-point correlation functions (2PCFs) ξ±(θ) (Li et al., 2023, Terasawa et al., 29 Mar 2024) and pseudo-Cℓ power spectra (Dalal et al., 2023). Measurements are performed on angular scales from θ=0.28′ up to 333′ in 24 log-spaced bins (Terasawa et al., 29 Mar 2024, Sugiyama et al., 19 Aug 2025). Shear components (γt, γ×) are weighted and corrected for PSF effects, with systematic error mitigation extending to B-mode decompositions and star–galaxy cross-correlation null tests (Dalal et al., 2023, Sugiyama et al., 19 Aug 2025).

For joint analyses, HSC-Y3 provides 3×2pt frameworks combining projected clustering w_p(R), galaxy–galaxy lensing ΔΣ(R), and cosmic shear ξ_±(θ) (Miyatake et al., 2023, Sugiyama et al., 2023). Theoretical modeling employs the Dark Emulator for the halo model down to quasi-nonlinear scales (Miyatake et al., 2023), and a minimal-bias model restricted to linear scales for w_p and ΔΣ (Sugiyama et al., 2023). Assembly bias, baryonic effects, and intrinsic galaxy alignments are modeled and marginalized across analysis pipelines (Miyatake et al., 2023, Dalal et al., 2023).

Mock catalogs are central for covariance estimation, exploiting 1404 full-sky ray-tracing N-body simulations adapted to the HSC-Y3 footprint and source-lens geometry (Li et al., 2023, Dalal et al., 2023, Sugiyama et al., 19 Aug 2025).

3. Photometric Redshift Calibration and Error Marginalization

Redshift uncertainty constitutes a primary systematic in weak lensing analyses. HSC-Y3’s redshift inference leverages a Bayesian hierarchical mixture of photometric posteriors and clustering-redshift cross-correlations (Rau et al., 2022). Ensemble redshift distributions n_i(z) for each tomographic bin are robustly inferred and prior-constrained:

Bin	Mean z (Joint Inference)	Prior Width (σ_Δz)
1	0.452 ± 0.004	±0.024
2	0.766 ± 0.003	±0.022
3	1.081 ± 0.004	±0.031
4	... (no WX)	±0.034

These Gaussian priors are implemented as n_i(z) → n_i(z−Δz_i) in all cosmology likelihoods, propagating photo-z uncertainty into joint inference (Rau et al., 2022).

Small-scale galaxy–galaxy lensing shear ratios provide an independent geometric constraint on photo-z bias shifts, particularly for bins 3 and 4 where traditional calibration is weakest (Rana et al., 29 Aug 2025). The blinded shear-ratio results yield Δz_3=–0.002^{+0.085}_{–0.217}, Δz_4=–0.292^{+0.229}_{–0.324}, in good agreement with standard cosmic shear calibrations (Rana et al., 29 Aug 2025).

4. Cosmological Results and S₈ Tension

The leading HSC-Y3 weak lensing analyses converge on percent-level constraints for the amplitude parameter S₈≡σ₈(Ω_m/0.3)^0.5, with substantial internal and external consistency:

• 2PCF analysis: S₈=0.769^{+0.031}_{–0.034}, Ωm=0.256^{+0.056}{–0.044} (Li et al., 2023)
• Pseudo-C_ℓ: S₈=0.776^{+0.032}_{–0.033}, Ωm=0.219^{+0.075}{–0.052} (Dalal et al., 2023)
• 3×2pt halo-model: S₈=0.763^{+0.040}_{–0.036}, Ωm=0.382^{+0.031}{–0.047} (Miyatake et al., 2023)
• Minimal-bias large-scale: S₈=0.775^{+0.043}_{–0.038} (Sugiyama et al., 2023)
• Cosmic shear + shear ratios: S₈=0.760^{+0.044}_{–0.145}, Ωm=0.286{–0.074}^{+0.038} (Rana et al., 29 Aug 2025)
• Joint 2+3pt (skewness): S₈=0.736±0.020, Ω_m=0.277±0.040 (Sugiyama et al., 19 Aug 2025)

These constraints are internally robust to a wide range of scale cuts, IA models, sampler choices, and baryonic feedback prescriptions (systematic shifts in S₈ <0.5σ) (Dalal et al., 2023, Terasawa et al., 29 Mar 2024). Third-order shear statistics (aperture-mass skewness) improve the Ω_m–S₈ figure of merit by ∼80%, enhancing degeneracy breaking and increasing tension with Planck to >3σ (Sugiyama et al., 19 Aug 2025).

No significant baryonic suppression or feedback signature is observed down to θ_min=0.28′ (k≈20 h Mpc⁻¹), and the measured ∼5% suppression in P_m(k=1 h Mpc⁻¹) is insufficient to reconcile the S₈ tension with Planck, which would require ∼25% suppression at these scales (Terasawa et al., 29 Mar 2024). All analyses consistently report a 2–3σ downward tension in S₈ relative to the Planck CMB result (S₈≈0.83), reinforcing the mild “low-z/Planck tension” (Dalal et al., 2023, Sugiyama et al., 19 Aug 2025).

5. Systematic Controls and Validation Strategies

HSC-Y3 achieves its systematics robustness via multi-tiered validation:

• Blinding: Analysis-level blinding of shear catalogues and cosmology chains to avoid confirmation bias (Dalal et al., 2023, Li et al., 2023).
• PSF Modeling: Residual leakage and modeling errors are parameterized and marginalized, with dedicated star–galaxy null tests, achieving additive bias well below statistical errors (Dalal et al., 2023, Sugiyama et al., 19 Aug 2025).
• Shear Calibration: Multiplicative bias controlled and validated via image simulations; parameter priors Δm∼N(0,0.01) (More et al., 2023, Dalal et al., 2023).
• Photo-z Validation: Hierarchical Bayesian inference, clustering-z cross-correlation, and shear-ratio calibration (Rau et al., 2022, Rana et al., 29 Aug 2025).
• Intrinsic Alignments: Marginalized via nonlinear models (NLA, TATT), with flat broad priors; found to shift S₈ <0.25σ (Dalal et al., 2023).
• Covariance: Calculation from thousands of full-fidelity mock catalogs, including shape noise, sample variance, and super-sample covariance (Li et al., 2023, Dalal et al., 2023).
• Null Tests: Internal splits (field, bin, scale), B-mode decomposition, jackknife removals all yield subdominant shifts in S₈ and Ω_m (Dalal et al., 2023, Sugiyama et al., 19 Aug 2025).

6. Methodological Innovations and Impact

Several methodological milestones distinguish HSC-Y3:

• Implementation of compressed third-order shear statistics (M_ap³) for cosmology, demonstrating 80% improvement in joint Ω_m–S₈ constraints (Sugiyama et al., 19 Aug 2025).
• Use of small-scale shear-ratio tests as a bias-free geometric probe for photo-z calibration (Rana et al., 29 Aug 2025).
• Emulator-based halo modeling and minimal-bias linear modeling provide cross-validation between small- and large-scale analyses (Miyatake et al., 2023, Sugiyama et al., 2023).
• Extensive pipeline-level blinding and systematics marginalization establish a best-practices template for Stage-IV experiments (LSST, Euclid, Roman) (Dalal et al., 2023, Sugiyama et al., 19 Aug 2025).

7. Implications and Future Prospects

HSC-Y3 delivers high-precision, systematics-controlled constraints on Ω_m and S₈, verifying the mild tension with Planck CMB cosmology and demonstrating that baryonic feedback is unlikely to be the sole cause (Terasawa et al., 29 Mar 2024). Third-order and shear-ratio–calibrated statistics represent maturing tools for future surveys. For HSC Y5, the anticipated expansion to ∼1 100 deg² and improved redshift calibration are projected to reduce S₈ uncertainty to <0.025, substantially improving cosmological leverage (Li et al., 2023). Integration with spectroscopic samples (DESI, PFS) and multi-band imaging will further strengthen redshift systematics control, bolstering cosmological inference in the forthcoming Stage IV era.