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Modelling Galaxy Clustering and Tomographic Galaxy-Galaxy Lensing with HSC Y3 and SDSS using the Point-Mass Correction Model and Redshift Self-Calibration

T0 review · 2 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read A point-mass correction lets 2x2pt lensing-clustering fits use scales down to 2 h^-1 Mpc, yielding S8 = 0.804 ± 0.051 and self-calibrated redshift shifts for HSC Y3 source bins 3 and 4.

desk verdict A careful, well-blinded 2x2pt measurement whose central S8 result is credible, but the rigid-shift n(z) model and a data-driven scale cut keep it from being a clean final word. read the letter →

arxiv 2507.01377 v2 pith:IRPXFT7R submitted 2025-07-02 astro-ph.CO

Tianqing Zhang , Sunao Sugiyama , Surhud More , Rachel Mandelbaum , Xiangchong Li , Roohi Dalal , Hironao Miyatake , Arun Kannawadi
show 8 more authors
Atsushi J. Nishizawa Takahiro Nishimichi Masamune Oguri Ken Osato Markus M. Rau Masato Shirasaki Tomomi Sunayama Masahiro Takada
This is my paper
classification astro-ph.CO
keywords galaxy-galaxylensinggalaxyclustering2x2ptanalysispoint-masscorrectionredshiftself-calibrationphotometricHSCY3S8
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper tries to establish that a `minimal bias` model plus a single point-mass correction term adequately describes galaxy-galaxy lensing down to small scales, and that this enables unbiased cosmological constraints from a 2x2pt analysis (galaxy clustering plus galaxy-galaxy lensing). Using SDSS DR11 lenses and three tomographic source bins from HSC Y3, the fiducial flat LCDM analysis yields S8 = 0.804^+0.051_-0.051 and self-calibrated redshift shifts for the third and fourth source bins, Δz3 = -0.079^+0.074_-0.084 and Δz4 = -0.203^+0.167_-0.206. The paper also demonstrates that the galaxy-galaxy lensing signal alone can constrain the mean redshifts of bins that were previously only weakly calibrated by clustering cross-correlations, providing a foundation for a 3x2pt analysis.

What carries the argument

The key mechanism is the point-mass correction term, defined as ΔΣ_PM(Rp) = [ΔΣ_1halo(R0) - ΔΣ_gG(R0)] (R0/Rp)^2, with R0 fixed at 4 $h^{-1}$ Mpc. This term is constructed by inverting the Annular Differential Surface Density (ADSD) relation and introduces one free parameter per lens bin that marginalizes over the HaloFit model's missing 1-halo contribution, thereby allowing the usable scale range to extend down to 2 $h^{-1}$ Mpc.

What would settle it

A direct test would be to replace the single shift parameterization for the fourth source bin with a more flexible n(z) model (e.g., allowing a width change or an outlier fraction) and re-fit the 2x2pt data; if the inferred S8 moves by more than the statistical uncertainty, the rigid-shift assumption is falsified. Alternatively, comparing the model prediction of ΔΣ at Rp = 2 $h^{-1}$ Mpc with an independent small-scale measurement that does not rely on the point-mass term, such as a stacked halo profile from weak lensing at even smaller radii, would check the adequacy of the correction.

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Extended reading notes

Core claim

The central claim is that the sum of the minimal bias model ΔΣ_gG, a point-mass correction ΔΣ_PM, and a magnification term ΔΣ_mag accurately models the observed ΔΣ(Rp) down to Rp = 2 $h^{-1}$ Mpc, whereas the minimal bias model alone is only reliable above ~8 $h^{-1}$ Mpc. The point-mass term absorbs the mis-modeled 1-halo contribution to the projected correlation function. With this model, the 2x2pt likelihood yields S8 = 0.804^+0.051_-0.051 under flat LCDM, and the same data vector constrains the source redshift shifts Δz3 and Δz4, which remain in agreement with previous cosmic shear analyses while avoiding informative priors.

Load-bearing premise

The analysis assumes that the true source redshift distribution of each tomographic bin is exactly the fiducial n(z) shifted by a single rigid amount, so any photo-z error that is more complex than a mean shift (tails, wings, or bin-dependent width changes) can bias the fitted shifts and the S8 that is partly degenerate with them.

Editorial extensions

If this is right

  • If the fiducial model is correct, future 2x2pt analyses can routinely include galaxy-galaxy lensing data at scales below 4 h^-1 Mpc without needing full small-scale halo models, improving statistical power.
  • The self-calibration mechanism demonstrated here—using the shear-ratio information implicit in the lensing data—can be used to constrain the mean redshifts of source bins in surveys where clustering-based redshift calibration is unavailable.
  • The validated scale cuts (Rp,min = 2, R0 = 4 h^-1 Mpc) and the point-mass model provide a template for 3x2pt analyses combining cosmic shear with galaxy-galaxy lensing and clustering, which is expected to yield tighter constraints on S8.
  • The consistency of the inferred Δz3 and Δz4 with the previous cosmic shear results suggests that the photometric redshift bias in the HSC Y3 source catalog is well captured by the shift parameterization and can be marginalized over in future analyses.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the point-mass term is absorbing not just the 1-halo term but also contributions from baryonic feedback or off-centering, then the scale cuts or the physical interpretation of the fitted ΔΣ_PM could change; the paper shows that fixing these effects in mock tests leaves S8 unbiased, but this relies on the mocks covering the same physical scenarios as the data.
  • The stronger constraint on Δz4 (−0.203) compared to Δz3 (−0.079) suggests that the highest source bin, which is completely uncalibrated by clustering cross-correlation, is now being pinned by the shear-ratio information; but this also means that a non-shift photo-z error (e.g., tail contamination) in bin 4 could directly propagate into S8, so a dedicated test with a more flexible n(z) would be a u
  • Given the McAdam-style argument that the shrinkage of the covariance matrix Hartlap factor is substantial for 1404 mocks and a 182-point data vector, future 3x2pt analyses using the same mocks may need data compression or more mocks to keep the covariance noise below the statistical error; the paper mentions MOPED as a possible solution.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. This paper presents a tomographic 2x2pt cosmological analysis combining SDSS DR11 BOSS galaxy clustering measurements with galaxy-galaxy lensing from the HSC Y3 shear catalog. The lens sample is split into LOWZ, CMASS1, and CMASS2 redshift bins, and the source sample into four tomographic bins. The galaxy-galaxy lensing model augments the minimal linear-bias model with a point-mass correction term (Eq. 31), allowing the projected lensing scale cut to be lowered from 8 to 2 h^-1 Mpc. Source redshift uncertainties are modeled as per-bin rigid shifts (Eq. 36), with flat priors on the shifts of the third and fourth bins. The fiducial flat-Lambda-CDM analysis reports S8 = 0.804 +/- 0.051, Delta-z3 = -0.079^{+0.074}_{-0.084}, and Delta-z4 = -0.203^{+0.167}_{-0.206}. The analysis is supported by catalog-level blinding, extensive null tests, mock validation with injected systematics, and many internal consistency tests.

Significance. If the modeling assumptions hold, this paper demonstrates a useful and transferable way to include galaxy-galaxy lensing down to 2 h^-1 Mpc through a point-mass nuisance term, and it shows that a tomographic 2x2pt analysis can self-calibrate source redshift shifts in the bins that were previously assigned uninformative priors. The paper has notable strengths: the lensing measurements are analyzed under catalog-level blinding on three parallel catalogs; the null-test suite is extensive; the mock validation covers baryonic feedback, off-centering, assembly bias, and other systematics; and the internal consistency tests span photo-z choices, individual-field splits, and tomographic bin removals. The headline S8 and Delta-z constraints are therefore likely defensible under the analysis assumptions. However, the central redshift-shift assumption and one data-informed scale-cut choice require additional scrutiny before the constraints can be taken at face value.

major comments (2)
  1. [Sec. IVB1, Eq. (36); Sec. IIB; Sec. VIC3, Table III] The rigid-shift model n_i(z) -> n_i(z + Delta-z_i) is the most load-bearing assumption in the paper, and it is not adequately stress-tested. The fourth source bin is explicitly uncalibrated by clustering redshifts (Sec. IIB), and Fig. 3 shows that the shear-ratio geometric signal is nearly flat for sources well behind the lenses, so the lensing data constrain the mean inverse critical density much more strongly than the shape of n(z). A low-redshift tail or a width error in bin 4 (or bin 3) would dilute the lensing amplitude in a way that mimics a lower S8 and simultaneously biases Delta-z4, yet it would not be flagged by the current internal consistency tests. The mock validation in Sec. VIC3 and Table III injects only rigid shifts (Delta-z3,4 = -0.2), so it validates shift recovery, not shape robustness. I request a concrete test in which mock Delta-Sigma data are generated from n(z) with a tail contamination or width change and then analyzed with the shift-only model to quantify the resulting bias in S8 and Delta-z4; alternatively, the model should be extended with a shape parameter and shown to be constrained by the data.
  2. [Sec. IIIC and Sec. IVC2] The maximum scale cut for Delta-Sigma is determined after inspecting the null-test p-values: the paper states that the last data points in all tomographic bin pairs are removed because including them 'would significantly worsen the chi-square of the fit' and drop the LOWZ-HSC3 p-value to 0.002. Because this decision is informed by the measured data itself and the selection rule is not specified a priori, it risks overfitting noise and can make the quoted p-values and error budget optimistic. Even though the procedure was performed on blinded catalogs, the criterion is not a fixed rule. I request either a pre-defined, data-independent maximum-scale selection or a robustness check showing that the fiducial S8 and Delta-z constraints are stable when the maximum scale is varied over a range that does or does not include the disputed points.
minor comments (5)
  1. [Fig. 8] The figure panel title says CMASS2 while the caption says the comparison is for the mock measurement of CMASS1; these should be reconciled.
  2. [Sec. VIB] The text refers to a 'no photo-z bias' test, whereas Table IV names the same configuration 'no photo-z uncertainty'; the naming should be unified.
  3. [References] Reference [77], the companion 3x2pt paper, is listed only as 'arXiv e-prints (2025)' without an arXiv identifier; it should be completed if the paper is available.
  4. [Sec. IVA] The sentence about excluding baryonic feedback effects appears twice in consecutive sentences and should be reduced to one statement.
  5. [Fig. 6 caption] The phrase 'and all three terms measured using DNNz' is unclear; it should say 'all three panels' or otherwise identify which quantities are shown.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the headline S8 and redshift-shift constraints are genuine posterior fits, and the point-mass and self-calibration parameters are explicit nuisance parameters validated against external N-body mocks.

full rationale

Walking the derivation chain, no claimed result reduces to its own inputs by construction. The point-mass correction term (Eq. 31) is a free nuisance parameter per lens bin, marginalized in the fit; the paper's claim that this model extends the usable scale to 2 h^-1 Mpc is validated against mock data vectors from N-body simulations (Fig. 8, Section VA), not derived from the S8 result. The redshift-shift parameters Delta z3 and Delta z4 are fitted parameters with flat priors (Table II), and the paper explicitly calls this 'self-calibration'—ordinary joint parameter estimation rather than a prediction from the same data. The rigid-shift n(z) parameterization (Eq. 36) is an explicit modeling assumption, and the paper itself notes that bin 4 is uncalibrated and calls for DESI spectroscopic calibration, so the limitation is disclosed rather than hidden. The paper does cite prior work by overlapping authors for the minimal bias model, photo-z calibration, and mock validation, but these citations are not used as a uniqueness theorem or as the sole justification for the headline numbers; the validation tests compare inferred parameters against true simulation inputs, and the final constraints are consistency-checked against external cosmic shear results. No equation is found to be equivalent to a fitted input by definition, and no 'prediction' is merely a renamed fitted parameter. Therefore the analysis is self-contained in the sense relevant to circularity.

Assumptions & free parameters 22 free parameters · 8 assumptions · 0 invented entities

The analysis fits 22 parameters (5 cosmological, 3 galaxy biases, 3 point-mass amplitudes, 3 magnification slopes, 4 shear biases, 4 redshift shifts). No new physical entities are introduced. The main external assumptions are flat LCDM, minimal bias, shift-only redshift errors, and mock covariance fidelity.

free parameters (22)
  • Omega_m = 0.332^+0.074_-0.069
    Matter density; flat prior U[0.0906,0.5406], fitted in the likelihood (Sec. VI, Eq. 47).
  • omega_c = Omega_c h^2 = posterior mode in Fig. 14, not quoted separately
    CDM density; flat prior U[0.0998,0.1398] in Table II.
  • omega_b = Omega_b h^2 = tight around BBN prior 0.02268 ± 0.00038
    Baryon density; Gaussian prior from BBN, Table II.
  • n_s = tight around 0.9646 ± 0.0126
    Scalar spectral index; Gaussian prior from Planck, Table II.
  • log(10^10 A_s) = posterior mode in Fig. 14
    Primordial amplitude; flat prior U[1.0,5.0], one of the most sensitive parameters for lensing amplitude.
  • b1 (LOWZ linear galaxy bias) = posterior mode approximately 1.6 to 3.2 from Fig. 14
    Linear galaxy bias for the LOWZ lens bin; flat prior U[0.1,5].
  • b2 (CMASS1 linear galaxy bias) = posterior mode approximately 2 to 4 from Fig. 14
    Linear galaxy bias for the CMASS1 lens bin; flat prior U[0.1,5].
  • b3 (CMASS2 linear galaxy bias) = posterior mode approximately 2 to 4 from Fig. 14
    Linear galaxy bias for the CMASS2 lens bin; flat prior U[0.1,5].
  • DeltaSigma_PM,1 at R0 = 4 Mpc/h = posterior mode approximately 1.6 to 2.5 in 10^6 M_sun/pc^2
    Point-mass correction amplitude for the LOWZ lens bin; flat prior U[0,10].
  • DeltaSigma_PM,2 at R0 = 4 Mpc/h = posterior mode approximately 1.6 to 2.4 from Fig. 14
    Point-mass correction amplitude for the CMASS1 lens bin; flat prior U[0,10].
  • DeltaSigma_PM,3 at R0 = 4 Mpc/h = posterior mode approximately 1.5 to 2.5 from Fig. 14
    Point-mass correction amplitude for the CMASS2 lens bin; flat prior U[0,10].
  • alpha_mag,1 = prior N(2.258,0.5)
    Magnification bias slope for LOWZ; Gaussian prior with sigma = 0.5, Table II.
  • alpha_mag,2 = prior N(3.563,0.5)
    Magnification bias slope for CMASS1; Gaussian prior with sigma = 0.5, Table II.
  • alpha_mag,3 = prior N(3.729,0.5)
    Magnification bias slope for CMASS2; Gaussian prior with sigma = 0.5, Table II.
  • m1 (multiplicative shear bias, source bin 1) = prior N(0,0.01)
    Residual shear calibration for source bin 1; Gaussian prior, Table II.
  • m2 (multiplicative shear bias, source bin 2) = prior N(0,0.01)
    Residual shear calibration for source bin 2; Gaussian prior, Table II.
  • m3 (multiplicative shear bias, source bin 3) = prior N(0,0.01)
    Residual shear calibration for source bin 3; Gaussian prior, Table II.
  • m4 (multiplicative shear bias, source bin 4) = prior N(0,0.01)
    Residual shear calibration for source bin 4; Gaussian prior, Table II.
  • Delta z1 = prior N(0,0.024)
    Redshift shift for source bin 1; Gaussian prior from [24].
  • Delta z2 = prior N(0,0.022)
    Redshift shift for source bin 2; Gaussian prior from [24].
  • Delta z3 = -0.079^+0.074_-0.084
    Self-calibrated redshift shift for source bin 3; flat prior U[-1,1].
  • Delta z4 = -0.203^+0.167_-0.206
    Self-calibrated redshift shift for source bin 4; flat prior U[-1,1].
assumptions (8)
  • domain assumption Flat LCDM with fixed tau = 0.0561, Omega_nu = 0.06, Omega_k = 0, w = -1, wa = 0.
    All cosmological inference assumes this model (Sec. IVC1, Table II); deviations would shift S8 and Delta-z constraints.
  • domain assumption Linear (minimal) bias model with one scale-independent bias per lens bin.
    Used for w_p at Rp > 8 Mpc/h and for Delta-Sigma with point-mass correction at Rp > 2 Mpc/h (Sec. IVA).
  • ad hoc to paper HaloFit nonlinear matter power spectrum plus point-mass correction models Delta-Sigma down to 2 Mpc/h.
    The point-mass correction parameter is introduced ad hoc to absorb the small-scale difference between HaloFit plus linear bias and the true signal (Eqs. 29-31); validated only on mocks.
  • domain assumption Source n(z) shape is correct and uncertainty is a rigid shift n_i(z) -> n_i(z + Delta z_i).
    Entered at Eq. 36; bin 4 is uncalibrated by clustering cross-correlation (Sec. IIB), so the shape assumption is load-bearing.
  • domain assumption No covariance between w_p and Delta-Sigma data vectors.
    Assumed in Sec. IIIB because HSC-SDSS overlap is small; if wrong, reported error bars and contours are underestimated.
  • domain assumption Tangential shear of source galaxies physically associated with lenses is zero (no intrinsic alignment).
    The boost factor correction (Eq. 22) assumes this; the paper notes IA breaks it and defers treatment (Sec. IIIB).
  • domain assumption Baryonic feedback and intrinsic alignment are negligible at the scales used.
    Excluded from the model (Secs. IVA and IVB); argued subdominant and tested with mocks.
  • domain assumption Covariance from 1404 HOD-populated N-body mocks correctly represents the real data covariance.
    Used for all error bars and the Hartlap correction (Secs. IID and IVC2); if the mocks are not representative, the quoted uncertainties fail.

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Cite this review

Pith. "Pith review of Modelling Galaxy Clustering and Tomographic Galaxy-Galaxy Lensing with HSC Y3 and SDSS using the Point-Mass Correction Model and Redshift Self-Calibration." pith.science (2026). https://pith.science/paper/IRPXFT7R

@misc{pith2026250701377,
  author       = {Pith},
  title        = {Pith review of: Modelling Galaxy Clustering and Tomographic Galaxy-Galaxy Lensing with HSC Y3 and SDSS using the Point-Mass Correction Model and Redshift Self-Calibration},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IRPXFT7R}},
  note         = {Machine review of arXiv:2507.01377}
}
abstract

The combination of galaxy-galaxy weak lensing and galaxy clustering is a powerful probe of the cosmological model, and exploration of how to best model and extract this information from the signals is essential. 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 $\Delta \Sigma (R_p)$ 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 $\Delta \Sigma (R_p)$ ($2\times2$pt) data vectors and perform likelihood inference with a flat $\Lambda$CDM model. For $\Delta \Sigma (R_p)$, we extend the lower limit of the scale cut compared to previous HSC Y3 analyses to $2 h^{-1}$Mpc 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 $\Lambda$CDM context, our fiducial model yields $S_8 = 0.804^{+0.051}_{-0.051}$. The $2\times2$pt data vector provides redshift parameter constraints for the third and fourth redshift bins $\Delta z_3 = -0.079^{+0.074}_{-0.084}$, and $\Delta z_4 = -0.203^{+0.167}_{-0.206}$, which is consistent with results from the previous tomographic cosmic shear studies, and serves as the foundation for a future $3\times 2$pt analysis.

Figures

Figures reproduced from arXiv: 2507.01377 by the authors.

Figure 1
Figure 1. FIG. 1. The redshift distributions of the HSC Y3 source galaxies [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. The top row shows the measurement of the [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. A demonstration of [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (12 more)
Figure 4
Figure 4. Figure 4: FIG. 4. The correlation matrix [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 4
Figure 4. Figure 4: C. Null Testing The clustering signal measurement in this work is identical to that in More et al. [21]. Therefore, we do not repeat the null tests or systematics tests for the 𝑤𝑝 data vector and refer the reader to More et al. [21] for details. For the galaxy-galaxy l…
Figure 5
Figure 5. Figure 5: FIG. 5. The boost factor [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. The cross component of the weak lensing signal. The blue points are the cross-component around the lens catalog, [PITH_FULL_IMAGE:figures/full_fig_p011_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. The cumulative signal-to-noise ratio (SNR) of the galaxy-galaxy lensing using tomographic source samples. The colored lines show [PITH_FULL_IMAGE:figures/full_fig_p012_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. This figures compares the best-fitting “linear bias only” [PITH_FULL_IMAGE:figures/full_fig_p013_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9. Posterior constraints from the fiducial [PITH_FULL_IMAGE:figures/full_fig_p018_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10. The purple distribution shows the MAP value of 100 noisy [PITH_FULL_IMAGE:figures/full_fig_p019_10.png]
Figure 11
Figure 11. Figure 11: FIG. 11. One-dimensional marginalized posterior constraints on five key parameters—- [PITH_FULL_IMAGE:figures/full_fig_p020_11.png]
Figure 12
Figure 12. Figure 12: FIG. 12. One-dimensional marginalized posterior constraints on five key parameters— [PITH_FULL_IMAGE:figures/full_fig_p022_12.png]
Figure 13
Figure 13. Figure 13: FIG. 13. The Median Absolute Deviation (MAD) of [PITH_FULL_IMAGE:figures/full_fig_p023_13.png]
Figure 14
Figure 14. Figure 14: FIG. 14. The posterior distribution of the fiducial [PITH_FULL_IMAGE:figures/full_fig_p025_14.png]

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Forward citations

Cited by 1 Pith paper

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  1. Cosmic Shear constraints from HSC Year 3 with clustering calibration of the tomographic redshift distributions from DESI

    astro-ph.CO 2025-11 unverdicted novelty 6.0 of 10

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Reference graph

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    The cosmological parameter space consists of five flatΛCDM pa- rameters:[Ω 𝑚,Ω𝑐ℎ2,Ω𝑏ℎ2,𝑛𝑠,log(10 10𝐴𝑠)]

    Parameter Space and Prior AsdescribedinSectionsIVAandIVB,weconstructafor- wardmodeltogeneratetheoreticaldatavectorsfor𝑤 𝑝 andΔΣ based on a set of cosmological and nuisance parameters. The cosmological parameter space consists of five flatΛCDM pa- rameters:[Ω 𝑚,Ω𝑐ℎ2,Ω𝑏ℎ2,𝑛𝑠,log(10 10𝐴𝑠)]. Among these, Ω𝑚 andlog(10 10𝐴𝑠)are the parameters to which weak lens...

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