The Hyper Suprime-Cam Year 3 (HSC-Y3) cosmology analyses are based on a shear catalog covering 416 deg² of the sky with exquisite depth and seeing. The HSC-Y3 cosmology effort has been led by a group of primarily early-career scientists, who have prepared the shear catalog, developed redshift distribution inference methods, studied potential contamination from systematics, measured data vectors and carried out the cosmological analyses. This work is described in a set of 8 papers, each of which is described below.

All of the blinded cosmology analyses were carried out in a coordinated fashion to ensure an appropriate degree of consistency on common elements such as catalog-level systematics, and common decision criteria to define model choices. However, the actual results were produced independently, and consistency of the cosmological constraints assessed only after all analysis choices were complete. This approach to the scientific results lends robustness to the analysis results.

When referring to the HSC Y3 cosmic shear results in papers, please cite both Dalal et al. and Li et al., as these together are considered our primary cosmic shear results. When referring to the HSC Y3 3x2pt results in papers, please cite all 3 of More et al., Miyatake et al., and Sugiyama et al. The HSC-Y3 weak lensing products (including the galaxy shape catalog) will be released after the key cosmology papers are accepted. As further cosmological analyses with HSC-Y3 data are completed, we will add them to this webpage.

We held a webinar to present our latest results on April 3rd, 2023.  The recording and presentation slides are available below.

• The three-year shear catalog of the Subaru Hyper Suprime-Cam SSP Survey
• A General Framework for Removing Point Spread Function Additive Systematics in Cosmological Weak Lensing Analysis
• Weak Lensing Tomographic Redshift Distribution Inference for the Hyper Suprime-Cam Subaru Strategic Program three-year shape catalogue
• Hyper Suprime-Cam Year 3 Results: Cosmology from Cosmic Shear Two-Point Correlation Functions
  
• Hyper Suprime-Cam Year 3 Results: Cosmology from Cosmic Shear Power Spectra
  
• Hyper Suprime-Cam Year 3 Results: Measurements of the Clustering of SDSS-BOSS galaxies, galaxy-galaxy lensing and cosmic shear
  
• Hyper Suprime-Cam Year 3 Results: Cosmology from Galaxy Clustering and Weak Lensing with HSC and SDSS using the Minimal Bias Model
  
• Hyper Suprime-Cam Year 3 Results: Cosmology from Galaxy Clustering and Weak Lensing with HSC and SDSS using the Emulator Based Halo Model

Link to paper: arXiv, PASJ

The galaxy number density map of the HSC-Y3 shear catalog that is used in the Y3 cosmology analyses.

This paper presents the galaxy shear catalog that is used for the HSC-Y3 cosmological weak gravitational lensing analyses. The galaxy shapes are measured from the i-band imaging data in the Wide layer of the survey, acquired from 2014 to 2019. The shapes are calibrated with image simulations that resemble the observing conditions of the survey based on training galaxy images from the Hubble Space Telescope in the COSMOS region. The catalog covers an area of 433.48 sq. deg. of the northern sky, split into six subfields. The mean i-band seeing is 0.59 arcsec. With conservative galaxy selection criteria (e.g., i-band magnitude brighter than 24.5), the observed raw galaxy number density is 22.9 arcmin^-2, and the effective galaxy number density is 19.9 arcmin^-2. The calibration removes the galaxy property-dependent shear estimation bias to a level: δm < 9 x 10^-3. The bias residual δm shows no dependence on redshift in the range 0<z<3. We define the requirements for cosmological weak lensing science for this shear catalog, and quantify potential systematics in the catalog using a series of internal null tests for systematics related to point-spread function modeling and shear estimation. A majority of the null tests are statistically consistent with zero or within requirements. The shear catalogs for the HSC-Y3 cosmological analyses are subsets of this shear catalog.

Link to paper: arXiv, MNRAS

This figure describes the contamination on the cosmic shear two point correlation function by the PSF additive bias. We compare two models for the PSF systematics error, the red line includes both PSF second and fourth moments contribution, while the orange line only includes the former. We show that the contamination from the PSF fourth moment systematics is statistically significant compared to the statistical uncertainty of the shear-shear signal (shown in the dashed line.) Therefore, it is vital to model the PSF systematics using both PSF second and fourth moments in the HSC-Y3 cosmic shear analysis.

This work demonstrates a general framework for detecting and modeling the impact of PSF systematics on the cosmic shear two-point correlation function (2PCF), and mitigating their impact on cosmological analyses. Our framework can detect PSF leakage and modeling error from all spin-2 quantities contributed by the PSF second and higher moments, rather than just the second moments, using the cross-correlation of galaxy shape and PSF moments. We interpret null tests using the HSC-Y3 catalogs with this formalism, and find that leakage from the spin-2 combination of PSF fourth moments is the leading contributor to additive shear systematics, with a total contamination that is an order of magnitude higher than that contributed by PSF second moments alone. We conduct a mock cosmic shear analysis for HSC-Y3, and find that, if uncorrected, PSF systematics can bias the cosmological parameters Ω_m and S₈ by ~0.3σ. The traditional second moment-based model can only correct for a 0.1σ bias, leaving the contamination largely uncorrected. We conclude that it is necessary to model both PSF second and fourth moment contamination for HSC-Y3 cosmic shear analysis. We also reanalyze the HSC-Y1 cosmic shear analysis with our updated systematics model, and identify a 0.07σ bias on Ω_m when using the more restricted second moment model from the original analysis. We demonstrate how to self-consistently use the method in both real space and Fourier space, assess shear systematics in tomographic bins, and test for PSF model overfitting.

Link to paper: arXiv, MNRAS

Sample redshift distribution (p_samp(z)) posteriors for the four tomographic redshift bins of the HSC-Y3 source sample derived to include information from the photometry (`PhotZ (DNNz)’, gray area), spatial clustering (`WX (0.1 – 1.0 Mpc)’, black dots) and the combination of spatial information and photometry (`PhotZ & WX’, red area). The blue dots denote the standard deviation on the mean of WX (i.e., clustering redshift) measurements. The CAMIRA LRG sample has a limited redshift coverage to z < 1.2, due to which the high redshift tomographic bin does not include a cross-correlation data vector. The inference includes the lensing weights consistently in all likelihood terms. The piecewise intervals denote the ±1σ errors.

This work presents posterior sample redshift distributions for the HSC-Y3 cosmology analyses. Using the galaxies’ photometry and spatial cross-correlations, we conduct a combined Bayesian Hierarchical Inference of the sample redshift distributions. The spatial cross-correlations are derived using a subsample of Luminous Red Galaxies (LRGs) with accurate redshift information available up to a photometric redshift of z < 1.2. We derive the photometry-based constraints using a combination of two empirical techniques calibrated on spectroscopic- and multiband photometric data that cover a spatial subset of the shear catalog. The limited spatial coverage induces a cosmic variance error budget that we include in the inference. Our cross-correlation analysis models the photometric redshift error of the LRGs to correct for systematic biases and statistical uncertainties. We demonstrate consistency between the sample redshift distributions derived using the spatial cross-correlations, the photometry, and the posterior of the combined analysis. Based on this assessment, we recommend conservative priors for residual errors in the sample redshift distributions of tomographic bins used in the HSC-Y3 cosmological weak lensing analyses.

Link to paper: arXiv, PRD

The HSC-Y3 cosmological constraints from cosmic shear 2PCFs (blue, solid), compared to the results from Planck-2018 (orange, dashed), as well as DES-Y3 (green, dotted) and KiDS-1000 (red, dash-dotted).

This work presents the HSC-Y3 cosmological constraints using cosmic shear two-point correlation functions (2PCFs). The analysis is coordinated with the cosmology analysis using power spectra (Dalal et. al 2023). We measure 2PCFs measured from galaxies in the HSC-Y3 shear catalog in four tomographic redshift bins ranging from 0.3 to 1.5 and in the angular range: 7.1 < θ /arcmin < 56.6 for ξ₊ and 31.2 < θ / arcmin < 248 for ξ_–, with a total signal-to-noise ratio 26.6. By fitting a flat LambdaCDM model prediction to the 2PCFs after marginalizing over astrophysical and systematic uncertainties, we find Ω_m=0.256^+0.056_-0.044 (68% CI) and S₈ = σ₈ (Ω_m/0.3)^0.5=0.769^+0.031_-0.034 (68% CI).

We study the effect that various modeling choices and systematic errors could have on this value, and find that they can shift the best-fit values of S₈ by no more than ~0.5σ, indicating that our result is robust to such systematics. The constraint on S₈ is ~2σ lower than the constraint from Planck-2018.

Link to paper: arXiv, PRD

The HSC-Y3 cosmological constraints from cosmic shear power spectra (blue, solid), compared to the results from Planck 2018 (orange, dashed), as well as DES-Y3 (green, dotted) and KiDS-1000 (red, dash-dotted), 2 other Stage III cosmic shear experiments.

This work presents the HSC-Y3 cosmological constraints using cosmic shear power spectra. The analysis in this paper is conducted in coordination with Li et al. (2023), which uses cosmic shear two point correlation functions. We use the Pseudo-Cl method to obtain an unbiased and high-significance measurement of the cosmic shear power spectrum, with a signal-to-noise ratio of approximately 26.4 in the multipole range 300<ℓ<1800. We then fit a cosmological model to the spectra while marginalizing over uncertainties in astrophysical models, such as baryonic feedback and intrinsic alignments, as well as systematics in our data, including, most significantly, uncertainties in our source redshift distribution inference. For a flat LambdaCDM model, we find S₈= 0.776^+0.032_-0.033 (68% CI), which is in excellent agreement with the constraints from the other HSC Year 3 cosmology analyses, as well as those from a number of other cosmic shear experiments. This result is in ~2σ tension with the constraint from Planck 2018. We study the effect that various systematic errors and modeling choices could have on this value, and find that they can shift the best-fit values of S₈ by no more than ~0.5σ, indicating that our result is robust to such systematics.

Link to paper: arXiv, PRD

The high signal-to-noise ratio measurements of the projected correlation functions of the three different subsamples of SDSS galaxies (top panels), their weak lensing signal (middle panels), and the cosmic shear correlations (bottom panels).

This work presents the measurements of the three two-point correlations that form the basis of the cosmological analyses performed in the companion papers, Miyatake et al. and Sugiyama et al. We use three approximately volume limited subsamples of spectroscopic lens galaxies selected by their i-band magnitude from SDSS-BOSS: LOWZ (0.1<z<0.35), CMASS1 (0.43<z<0.55) and CMASS2 (0.55<z<0.7). We present high signal-to-noise ratio measurements of the projected correlation functions of these galaxies. In order to break the degeneracy between the amplitude of the matter correlation and the bias of these spectroscopic galaxies, we measure the galaxy-galaxy lensing signal using background galaxies from the Subaru HSC survey, which probes the projected galaxy-matter cross-correlation function of the SDSS-BOSS galaxies. Finally, we also measure the cosmic shear correlation functions from HSC galaxies which is related to the projected matter correlation function. We demonstrate the robustness of our measurements by subjecting each of these measurements to a variety of systematic tests and present results of null tests. We also describe the construction of a suite of mocks: i) spectroscopic galaxy catalogs which obey the clustering and abundance of each of the three SDSS-BOSS subsamples, and ii) galaxy shape catalogs which obey the footprint of the HSC survey and have been appropriately sheared by the large scale structure expected in a flat LambdaCDM model. These mock catalogs are used to compute the covariance of each of our observables.

Link to paper: arXiv, PRD

The HSC-Y3 cosmological constraints from the 3x2pt analyses: the joint analyses of cosmic shear, galaxy-galaxy leasing and galaxy clustering, compared to the Planck 2018 CMB result and the external weak lensing surveys’ results, DES Y3 and KiDS 1000.

This work, together with Miyatake & Sugiyama et al. (2023), presents the cosmological parameter constraints from the joint analyses of cosmic shear, galaxy clustering, and galaxy-galaxy lensing, the so-called 3x2pt analyses. We analyze the measurements of these observables from More & Sugiyama et al. (2023), especially focusing on the large-scale signal of the galaxy clustering and the galaxy-galaxy lensing signal above R=8 h^-1 Mpc and 12 h^-1 Mpc respectively, using the minimal bias model. We perform the various model validations with mock data vectors and test analysis choices, which are all conducted in the blind fashion. After fixing the analysis choice and unblinding, we find a ~5% fractional precision estimate of the clustering amplitude, S₈ = 0.775^+0.043_-0.038 (68% C.I.). We assess the tension between our result and Planck 2018 CMB result, and find no significant tension.

Link to paper: arXiv, PRD

The HSC-Y3 cosmological constraints from the small-scale 3x2pt analysis: the joint analysis of cosmic shear, galaxy-galaxy leasing, and galaxy clustering, compared to the constraints from the Planck 2018 primary CMB. Red lines show the posterior for the HSC-Y3 3x2pt results when the prior of σ(Ω_m)=N(0.3,0.01) is added. The parameter Δz_ph is a parameter to model residual systematic error of the HSC source galaxies. Our result indicate a non-zero Δz_ph.

This work presents the cosmological parameter constraints from the joint analysis of cosmic shear, galaxy-galaxy lensing, and galaxy-galaxy clustering signals measured by More, Sugiyama et al. (2023). While Sugiyama et al. focus on large scales (8 Mpc/h for galaxy-galaxy clustering and 12 Mpc/h for galaxy-galaxy lensing) where the linear bias approximation holds, this analysis uses small scales down to 2 Mpc/h for galaxy-galaxy clustering and 3 Mpc/h for galaxy-galaxy lensing to obtain more signal-to-noise ratio. To robustly model the non-linear regime, we combine Dark Emulator (Nishimichi et al., 2019), the cosmic emulator that computes halo-matter and halo-halo correlation function to a few percent accuracy, and the halo occupation distribution prescription to model the relation between galaxy and halo distributions. We perform a blind analysis while testing the robustness of the model with various analysis choices. After unblinding, we find the constraints on the matter clustering S₈=0.763^+0.040_-0.036 (68% C.I.), which exhibits about 2.5-sigma tension with the Planck constraint for a flat LambdaCDM cosmology. We emphasize that we use an uninformative prior for the photo-z residual systematics and fully make use of the self-calibration scheme proposed by Oguri & Takada (2011). Hence this analysis is robust against photo-z uncertainties, which are considered one of the most important systematics in weak lensing analysis.

Link to paper 1: arXiv, OJAP

Link to paper 2: arXiv, OJAP

This plot shows the cosmological constraints obtained from the abundance modelling of the 129 weak-lensing shear-selected clusters in the HSC-Y3 data (blue) in comparison with other probes (other colors). The constraints in the parameter space of Ω_m and S₈ are displayed in the left panel, while the fully marginalized posteriors of S₈ are shown in the right panel. The parameter of S₈ is defined as S₈ = σ₈ (Ω₈ /0.3)^0.25. As seen, our results based on 129 clusters are in good agreement with others and suggest no statistically significant tension with Planck.

Cluster cosmology has achieved great success over the past two decades, as one of the most powerful probes based on structure formation at late times. However, galaxy clusters are typically selected based on their baryonic observables, which makes their selection function challenging to model and subject to selection biases.

Taking full advantage of the HSC-Y3 weak-lensing data, we construct the aperture-mass maps over ~500 deg² with high angular resolution and select galaxy clusters directly on these maps based solely on their weak-lensing signals, resulting in a gravity-based and baryon-independent selection function. In total, we have 129 weak-lensing shear-selected clusters with signal-to-noise ratios of ν > 4.7 across the HSC-Y3 footprint.

Validated against the optical counterparts from optically selected cluster samples, our cluster catalog achieves a purity exceeding ~99%. We model the abundance of these 129 weak-lensing shear-selected clusters and derive the cosmological constraints, particularly on the parameter of S₈ = σ₈ (Ω₈ /0.3)^0.25. We obtain good consistency with other probes and find no statistically significant tensions with Planck.

Link to paper: arXiv, PRD

Comparison of the 68% and 95% confidence regions for cosmological parameters of interest from our fiducial analysis (blue) with results from other HSC-Y3 cosmological probes. All analyses show mutual consistency within the $1\sigma$ level, demonstrating robust agreement among independent large-scale structure measurements based on the HSC-Y3 dataset.

We conducted a cosmological analysis based on galaxy cluster abundance, cluster projected clustering, and cluster lensing signals. We utilize observational data from the Sloan Digital Sky Survey (SDSS) redMaPPer cluster catalog in combination with the Hyper Suprime-Cam (HSC) Year 3 shape catalog. A full forward-modeling framework is developed for predicting the cluster observables, incorporating empirical models for anisotropic boosts affecting both the lensing and clustering signals of optically selected clusters. To ensure the robustness of our methodology, we validate the analysis using realistic mock cluster catalogs that include key observational systematics such as line-of-sight projection effects and baryonic feedback. Our validation tests confirm that the proposed framework can reliably constrain cosmological parameters without relying on informative priors. Applying this model within the flat ΛCDM cosmological paradigm, we obtain tight constraints on the parameter S₈ = σ₈ (Ω₈ /0.3)^0.5 = 0.816^+0.041_-0.039. This result is consistent with previous S₈ estimates from both cosmic microwave background observations and large-scale structure analyses, including the Planck 2018 primary CMB results.

Link to paper: arXiv, PRD

The dark and light red-color shaded regions are the 68% and 95% credible intervals of the model predictions in each k bin, which are computed from the posterior distribution of the parameter inference using the 6-parameter HMCode20 model. The left and right panels show the results at z=0.0 and 0.5, respectively. For comparison, we show the results for the cosmological hydrodynamical simulations. The error bar in the plot of z=0.0 denotes a lower limit of the suppression indicated by the baryon mass fraction of cluster-scale halos, based on the observations such as the X-ray data. The gray shaded regions are the similar results, which are computed from the posterior distribution of the parameter inference adopting the Gaussian priors around Planck cosmology.

The baryonic feedback effect is considered as a possible solution to the so-called S8 tension indicated in cosmic shear cosmology. The baryonic effect is more significant on smaller scales, and affects the cosmic shear two-point correlation functions (2PCFs) with different scale- and redshift-dependencies from those of the cosmological parameters. In this paper, we use the Hyper Suprime-Cam Year 3 (HSC-Y3) data to measure the cosmic shear 2PCFs χ_± down to 0.28~arcminutes, taking full advantage of the high number density of source galaxies in the deep HSC data, to explore a possible signature of the baryonic effect. While the published HSC analysis used the cosmic shear 2PCFs on the angular scales that are sensitive to the matter power spectrum at k<~ 1 hMpc^-1, the smaller scale HSC cosmic shear signal allows us to probe the signature of matter power spectrum up to k ~ 20 hMpc^-1. Using the accurate emulator of the nonlinear matter power spectrum, DarkEmulator2, we show that the dark matter-only model can provide an acceptable fit to the HSC-Y3 2PCFs down to the smallest scales. In other words, we do not find any clear signature of the baryonic effects or do not find a systematic shift in the S₈ value with the inclusion of the smaller-scale information as would be expected if the baryonic effect is significant. Alternatively, we use a flexible 6-parameter model of the baryonic effects, which can lead to both enhancement and suppression in the matter power spectrum compared to the dark matter-only model, to perform the parameter inference of the HSC-Y3 2PCFs. We find that the small-scale HSC data allow only a fractional suppression of up to 5 percent in the matter power spectrum at k ~ 1 hMpc^-1, which is not sufficient to reconcile the S₈ tension. Finally, we discuss that χ_– on scales smaller than a few arcminutes can be used to monitor characteristic features caused by the baryonic effect if present, while χ_± with appropriate scale cuts can be used to constrain the cosmological parameters, simultaneously.

Link to paper: arXiv

This figure compares the best-fitting “linear bias only” model versus the “point-mass correction” model on the mock measurement of R_pΔ𝚺 of CMASS2. The “linear bias only” can only accurately describe the signal for physical scales above R_p = 12 h^-1Mpc (right dashed line), while the point-mass correction model can describe the data down to scales around 2 h^-1Mpc, showing its capability to model the small-scale galaxy-galaxy lensing signal. The error bars reflect the uncertainties of the real data vector, so it is important to model the noiseless mock within 1σ of the errorbar.

The combination of galaxy clustering and weak lensing is a powerful probe of the cosmological model. We present the measurement of the galaxy-galaxy weak lensing signals using the SDSS DR11 spectroscopic galaxies as lens galaxies, and the HSC Y3 shear catalog as source galaxies, binned into four tomographic bins by their photometric redshift. The SDSS DR11 galaxies, with a redshift range 0.15<z<0.7, are binned into three redshift bins, each as a probe for measuring the projected correlation function, w_p(R_p). We measure the galaxy-galaxy lensing signal Δ𝚺(R_p) in 12 lens-source bin pairs and show that there is no evidence for significant systematic biases in the measurement with null testing. We combine our w_p(R_p) and Δ𝚺(R_p) (2x2pt) data vectors and perform likelihood inference with a flat 𝚲CDM model. For Δ𝚺(R_p), we extend the lower limit of the scale cut compared to previous HSC Y3 analyses to 2 h^-1Mpc by including a point-mass correction term in addition to the minimal bias model. We present various tests to validate our model and provide extended consistency tests. In the 𝚲CDM context, our fiducial model yields S₈ = 0.804^+0.051_-0.051. The 2x2pt data vector provides redshift parameter constraints for the third and fourth redshift bins Δz₃ = -0.079^+0.074_-0.084, and Δz₄ = -0.203^+0.167_-0.206, which is consistent with results from the previous tomographic cosmic shear studies, and serves as the foundation for a future 3x2p analysis.

Link to paper: arXiv

Comparison of the 3x2pt analysis results from this work (black contours) to previous HSC Y3 results: the 3x2pt analysis using a single source bin at large scales (Sugiyama et al. 2023), the 3x2pt analysis using a single source bin including small scales (Miyatake et al. 2023), and the cosmic shear analysis (Li et al. 2023). Relative to previous 3x2pt results, our analysis yields slightly lower 𝛀_m and higher σ₈ values, while the S₈ constraints remain statistically consistent across all analyses.

We present a joint analysis of galaxy clustering and weak lensing cosmology using SDSS data as the tracer of dark matter (lens sample) and the HSC Y3 dataset as source galaxies. The analysis divides HSC Y3 galaxies into four tomographic bins for both galaxy-galaxy lensing and cosmic shear measurements, and employs a point-mass correction model to utilize galaxy-galaxy lensing signals down to 2h^-1Mpc, extending up to 70h^-1Mpc. These strategies enhance the signal-to-noise ratio of the galaxy-galaxy lensing data vector. Using a flat 𝚲CDM model, we find S₈ = 0.780^+0.029_-0.030, and using a wCDM model, we obtain S₈ = 0.756^+0.038_-0.036 with w = -1.176^+0.310_-0.346. We apply uninformative priors on the redshift mean-shift parameters for the third and fourth tomographic bins. Leveraging the self-calibration power of tomographic weak lensing, we measure Δz₃ = -0.112^+0.046_-0.049 and Δz₄ = -0.185^+0.071_-0.081, in agreement with previous HSC Y3 results. This demonstrates that weak lensing self-calibration can achieve redshift constraints comparable to other methods such as photometric and clustering redshift calibration.

Link to paper: arXiv

Comparison of the cosmological parameter S₈​ and photo-z bias Δz constraints for source redshift bins 2, 3, and 4 from the combined analysis of HSC-Y3 cosmic shear and shear-ratio measurements. The blue contours show the results from combining fiducial shear-ratio data with cosmic shear, while the orange contours represent constraints from cosmic shear alone. The contours correspond to the 68% and 95% confidence intervals, demonstrating consistency between the cosmic shear–only analysis (orange) and the combined analysis including fiducial shear-ratio data (blue).

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 ∆z₂, ∆z₃ and ∆z₄ are consistent with those from HSC-Y3 cosmic shear modeling. We observe a mild shift in the ∆z₃–∆z₄ 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_m = 0.286^+0.038 _−0.074 and S₈ = 0.760^+0.044 _−0.145, 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.