HSC Weak Lensing Catalog Overview

• HSC Weak Lensing Catalog is a high-precision dataset derived from Subaru HSC imaging that uses weak gravitational lensing to identify cluster and galaxy populations nearly independent of baryonic tracers.
• It employs rigorous photometric redshift filtering and simulation-calibrated shear corrections to mitigate systematics, achieving high purity with optical and X-ray cross-matching.
• The catalog underpins cosmological analyses by providing detailed cluster properties, mass–observable relations, and extensive data products for multi-wavelength studies.

The Hyper Suprime-Cam (HSC) Weak Lensing Catalog comprises a series of high-precision cluster and galaxy catalogs exploiting weak gravitational lensing measurements from the HSC Subaru Strategic Program, aimed at constructing shear-selected cluster samples and supporting cosmological inference. The methodology is rooted in rigorous shear measurement, selection of background source galaxies using photometric redshift filtering, sophisticated mass-map construction and peak identification, thorough calibration of shear and photo-z systematics, and extensive cross-matching to optical, X-ray and spectroscopic datasets. These catalogs offer unique samples of clusters selected almost independently of baryonic tracers, essential for unbiased cluster astrophysics and cosmology.

1. Survey Strategy, Shear Catalog Construction, and Shear Calibration

The HSC-SSP utilizes the 8.2 m Subaru telescope equipped with a wide-field optical imager, acquiring multi-band (grizy) data over up to 510 deg² with median i-band seeing of 0.58–0.59″ and 5σ point-source depth i ≈ 24.5–26 mag (Li et al., 2021). Galaxy shapes are measured using the re-Gaussianization algorithm (Hirata & Seljak 2003), with PSF modeling performed per exposure via PSFEx and coaddition in the HSC pipeline (Oguri et al., 2021, Mandelbaum et al., 2017). Each galaxy entry contains weighted ellipticities, weights, per-object multiplicative and additive shear calibration biases (typically |m| ≲ 0.01, |c| ≲ 10⁻³), and photometric redshift probability distributions.

Shear calibration is performed with end-to-end image simulations incorporating realistic HSC PSFs, noise properties, and ground-based representations of Hubble/COSMOS galaxy morphologies, including the effects of unrecognized blends (Mandelbaum et al., 2017, Li et al., 2021). Residual multiplicative calibration errors across tomographic bins are controlled to |δm| < 9 × 10⁻³ (Li et al., 2021), with additional corrections for selection, weight, and R₂-edge biases derived from the simulations. Star-galaxy cross-correlation and B-mode null tests demonstrate that residual systematics are well below cluster-scale noise thresholds (Oguri et al., 2021).

2. Background Source Selection and Photometric Redshift Calibration

Photometric redshift (“photo-z”) estimation combines machine-learning and SED-fitting codes, with current catalogs favoring DNNz, DEmP, MLZ, and mizuki approaches depending on catalog generation (Oguri et al., 2021, Rau et al., 2022, Janvry et al., 22 Nov 2025). Probability distributions P(z) are provided for each galaxy. Background selection for cluster lensing employs a “P-cut” criterion:

$\int_{z_{\min}}^{z_{\max}} P(z)\,dz > P_{\rm th}$

with $P_{\rm th} = 0.95$ (0.98 for individual lens fits), and $z_{\min} = z_l + 0.2$ for a lens at $z_l$, or, for map construction, fixed $z_{\min}$ in {0.2, 0.3, 0.5, 0.7}, $z_{\max} = 7$ (Oguri et al., 2021). This procedure enforces robust suppression of cluster-member and foreground contamination, achieving typical post-cut source densities of $n_{\rm gal}\sim20\,{\rm arcmin}^{-2}$ and mean source redshift $z \sim 0.8$–1.

Redshift distribution calibration is performed hierarchically by combining photometric P(z) stacking, cross-correlations with well-calibrated tracer populations (e.g. CAMIRA LRGs, DESI LRG/ELG/QSO) up to $z \sim 1.5$, and explicit modeling of galaxy and magnification bias evolution (Rau et al., 2022, Janvry et al., 22 Nov 2025). Uncertainties from cosmic variance and photo-z model error are propagated via Gaussian-process priors or spline-based expansions, yielding recommended Gaussian priors $\Delta z^i$ on the mean redshift in each tomographic bin that can be directly propagated into cosmological likelihoods (Janvry et al., 22 Nov 2025). The most recent calibrations using DESI now cover all four HSC tomographic bins, with residual shifts smaller than those preferred by self-calibrating cosmic shear analyses.

3. Mass Map Construction, Filtering, and Shear-Selected Cluster Detection

Aperture mass maps $M_{\mathrm{ap}}$, constructed from filtered galaxy shears, are central to weak lensing cluster searches:

$$M_{\mathrm{ap}}(\boldsymbol\theta) = \int \gamma_+(\boldsymbol\theta'; \boldsymbol\theta) Q(|\boldsymbol\theta' - \boldsymbol\theta|) \, d^2\theta'$$

with $Q(\theta)$ a compensated filter related to the filter $U(\theta)$. Several filter choices are used: truncated Gaussian (TG15; $\theta_0=1.5'$, $\theta_{\rm out}=13'$), truncated isothermal (TI05/20; parameterized by $\nu_1\theta_R$ and inner boundaries) (Oguri et al., 2021, Chen et al., 17 Jun 2024), with the latter providing direct suppression of cluster-member dilution for $\theta_{\rm in} \gtrsim 2'$.

Shape noise per map pixel is estimated via 500 random rotations of the catalog, and the S/N ratio at each grid point is $\nu = M_{\mathrm{ap}}/\sigma_{\mathrm{Map}}$, with $$\sigma_{\mathrm{Map}} = \sigma_e \sqrt{\pi \int \theta Q^2(\theta) d\theta / n_{\mathrm{gal}}}$$ $\sigma_e \approx 0.4$. Mass maps are built on a $0.25'$ grid, with peaks identified as local maxima exceeding a detection threshold $\nu_{\rm th}$. Maps are constructed and peaks detected independently for different filter and background selection recipes.

A conservative threshold $\nu \ge 4.7$ is adopted, producing catalogs ranging from 129–418 shear-selected clusters over $510\,\mathrm{deg}^2$ (for Year 3; (Chen et al., 17 Jun 2024)), depending on filtering and background selection. Multi-filter recipes (e.g., TG15, TI05, TI20) allow robustness tests and balance between completeness and purity.

4. Purity Estimation, Optical/X-ray Cross-Matching, and Cluster Property Measurement

Clusters are validated by cross-matching shear-selected peaks within 1–1.5 $h^{-1}$ Mpc to optical catalogs (CAMIRA/HSC, redMaPPer/SDSS, WHL/SDSS, CODEX/RASS+redMaPPer). Optical matches at the highest S/N approach 97% for TG15 and TI20 filters; after correcting for random matches and sample incompleteness, purities of $\geq95\%$ (TG15, TI20) and $\geq91\%$ (TI05) are established (Oguri et al., 2021, Chen et al., 17 Jun 2024). Random matches are estimated from spatially shuffled peaks, with false-positive corrections typically at a few percent.

Stacked weak-lensing profiles (using $\Delta\Sigma(R)$) are fitted with NFW profiles to estimate cluster masses $M_{500c}$ and concentrations $c_{500c}$. The mass–observable relation, critical for cosmological inference, is calibrated using injection simulations of synthetic halos into real data, yielding a mapping $P(\nu|M,z)$ and completeness function $\mathcal{C}(M,z)$ that account for non-uniform depth, mask geometry, large-scale structure projections, and intrinsic alignments (Chen et al., 17 Jun 2024). The resulting mass–observable relations can be reparameterized in terms of observable lensing quantities to reduce cosmological dependence.

X-ray cross-matching using MCXC (RASS) and XXL clusters reveals that shear-selected clusters often display X-ray underluminosity at fixed weak-lensing mass, highlighting the selection of cluster populations not captured in X-ray or optical richness-limited samples (Miyazaki et al., 2018). This enables studies of baryon-independent cluster properties.

5. Mitigation of Dilution, Masking, and Systematic Uncertainties

Foreground and cluster-member galaxy dilution is mitigated by rigorous P-cut selection of source galaxies and adoption of filters with large inner radii (e.g., TI20 with $\theta_{\rm in}\approx 2'$), as these suppress contaminated sources and obscure masking at cluster centers (Oguri et al., 2021, Hamana et al., 2020). Empirical stacks of source density around X-ray/optical cluster centers confirm the efficacy of this mitigation: with no z-cut, source densities rise strongly at $\theta<2'$; with optimized P-cut, masking dominates at small scales, and the weak-lensing signal avoids significant dilution.

Catalog-level systematics—PSF model error, star-galaxy ellipticity cross-correlation, additive/multiplicative shear bias—are controlled to below cluster-scale statistical noise via simulation-based calibration and null tests (Li et al., 2021, Mandelbaum et al., 2017).

6. Catalog Schema, Data Products, and Applications

Each HSC shear-selected cluster catalog entry minimally contains:

• Unique ID
• RA, Dec (J2000)
• Signal-to-noise $\nu$
• Photometric redshift $z_{\rm cl}$
• Optical counterpart ID and projected separation
• Weak-lensing mass $M_{500c}$, concentration $c_{500c}$
• Goodness of fit ($\chi^2$, dof for profile fits)
• Filter name and field/patch label

All data products (catalogs, mass maps, noise maps, calibration tables, completeness/sensitivity grids) are provided through the HSC-SSP public data release site. Injection-based completeness and mass–observable calibration files are included for direct incorporation into cosmological analyses (Chen et al., 17 Jun 2024).

These catalogs are appropriate for cluster abundance cosmology, calibration of optical or SZ cluster mass–observable relations, tests of mass/X-ray/richness scaling, and lensing cross-correlations. Selection functions derived from injection tests must be used, not simple analytic approximations. Systematic modeling of survey depth, mask, and projection effects is intrinsic to the catalog.

7. Recent Advances and Future Directions

The current HSC weak lensing cluster catalogs achieve high sample purity, robust shear and redshift calibration, and sophisticated control of astrophysical selection effects. Recent implementations, such as the cosmology-insensitive parameterization of the observable–mass relation and clustering-redshift calibration with DESI to $z>1.5$ (Janvry et al., 22 Nov 2025), advance weak-lensing selection as the least-biased route to defining cluster samples. Releases now include cosmological selection functions, machine-readable injection calibration files, and support codes.

Future directions involve expansion to deeper and wider surveys (Rubin/LSST, Euclid, Roman), further mitigating systematics at high redshift and for high-mass, X-ray-faint systems, and direct integration of these catalog-level products into large-scale structure and cosmic shear likelihoods for the next generation of cosmological inference (Chen et al., 17 Jun 2024, Rau et al., 2022).

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References:

• Oguri et al. "Hundreds of weak lensing shear-selected clusters from the Hyper Suprime-Cam Subaru Strategic Program S19A data" (Oguri et al., 2021)
• Chen et al. "Weak-Lensing Shear-Selected Galaxy Clusters from the Hyper Suprime-Cam Subaru Strategic Program: I. Cluster Catalog, Selection Function and Mass--Observable Relation" (Chen et al., 17 Jun 2024)
• Rau et al. "Weak Lensing Tomographic Redshift Distribution Inference for the Hyper Suprime-Cam Subaru Strategic Program three-year shape catalogue" (Rau et al., 2022)
• Mandelbaum et al. "Weak lensing shear calibration with simulations of the HSC survey" (Mandelbaum et al., 2017)
• Full list as detailed in the source block above.