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Clustering redshifts with spectroscopic tracers beyond z~1.2 calibrate all four HSC tomographic bins and find smaller photo-z shifts than the cosmic shear analyses assumed.

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2026-08-03 20:48 UTC pith:43DN3C3J

load-bearing objection DESI clustering redshifts finally cover HSC Y3's high-z bins, and the measured shifts are smaller than shear's — the result is worth refereeing, though the r_xy assumption and mildly circular spline prior need scrutiny. the 3 major comments →

arxiv 2511.18133 v2 pith:43DN3C3J submitted 2025-11-22 astro-ph.CO

Full calibration of the tomographic redshift distribution from the HSC PDR3 Shape Catalog with DESI

J. Choppin de Janvry , S. Gontcho A Gontcho , U. Seljak , A. Baleato Lizancos , E. Chaussidon , W. d'Assignies , J. DeRose , S. Heydenreich
show 48 more authors
E. Paillas D. Valcin T. Zhang J. Aguilar S. Ahlen D. Bianchi D. Brooks F.J. Castander T. Claybaugh A. Cuceu A. de la Macorra P. Doel S. Ferraro A. Font-Ribera J.E. Forero-Romero E. Gazta\~naga G. Gutierrez H.K. Herrera-Alcantar K. Honscheid M. Ishak R. Joyce S. Juneau R. Kehoe D. Kirkby T. Kisner A. Kremin O. Lahav C. Lamman M. Landriau L. Le Guillou M. Manera A. Meisner R. Miquel S. Nadathur N. Palanque-Delabrouille W.J. Percival C. Poppett F. Prada I. P\'erez-R\`afols G. Rossi E. Sanchez D. Schlegel M. Schubnell J. Silber D. Sprayberry G. Tarl\'e B.A. Weaver R. Zhou
This is my paper
classification astro-ph.CO
keywords clustering redshiftstomographic redshift distributionsweak lensingphotometric redshiftsgalaxy biasmagnificationDESIHSC
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper tries to establish that the true redshift distributions of the four HSC weak-lensing tomographic bins can be fully recovered from galaxy clustering, without relying on photometric redshift estimates. It uses a spectroscopic sample extending beyond z~1.2 with emission-line galaxies and quasars, so the two highest bins are calibrated for the first time. The result is that the first bin shifts slightly toward lower redshift, the second agrees with photometry, and bins 3 and 4 shift toward higher redshift by about -0.039 and -0.048 in mean redshift. Those shifts are considerably smaller than the values HSC's own cosmic shear analyses had marginalized over, so if correct, the shear analyses were over-correcting for photo-z uncertainty. The paper also finds the high-redshift tail of bin 3 is stronger than the photometric calibration expected.

Core claim

The clustering-redshift estimator, applied with a spectroscopic sample reaching beyond z~1.2, recovers the complete redshift distribution of all four HSC tomographic bins. After correcting for spectroscopic and photometric galaxy bias evolution and for magnification, the measured mean redshifts differ from the previous photometry-based calibration by +0.029, -0.003, -0.039 and -0.048 for bins 1 through 4 (fiducial 0.3-3 h^-1 Mpc scales, with magnification corrections). Bin 3's tail at z~1.3-1.8 is stronger than the photometric distribution suggested, which explains part of the high-bin shifts. These shifts are smaller than the posterior modes from the HSC Year 3 cosmic shear analyses, which

What carries the argument

The key identity is the clustering-redshift estimator: inside a narrow spectroscopic redshift slice, the scale-averaged cross-correlation between a spectroscopic tracer and the photometric sample, divided by the square root of the product of their auto-correlations, is proportional to the photometric sample's redshift density at that slice. The paper relaxes linear bias to a weaker assumption — no redshift evolution of the cross-correlation coefficient between tracer and sample — and sets that coefficient to 1 after renormalization. The measured densities are then smoothed with B-splines under a Dirichlet prior that pushes coefficients toward zero where the signal is consistent with zero. Ma

Load-bearing premise

The recovered n(z) shape assumes the cross-correlation coefficient between each spectroscopic tracer and the HSC galaxies is constant across each tomographic bin and equal to 1 after renormalization; if that coefficient evolves with redshift inside a bin, the reconstructed distribution is distorted and no renormalization can remove the error.

What would settle it

Measure r_xy(z) directly in narrow redshift slices from mock catalogs with known n(z), or from a deep spectroscopic sample that fully covers one tomographic bin; if r_xy varies by more than a few percent within a bin, the recovered mean redshifts will shift by amounts comparable to the quoted uncertainties.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • If the claim holds, the HSC Year 3 cosmic shear shift marginalization overestimated the photo-z correction needed for bins 3 and 4; the true distributions sit closer to photometry.
  • Bin 3's high-redshift tail is stronger than photometry predicted, changing the effective source distribution and thus the lensing-weighted interpretation.
  • Bin 4 is calibrated for the first time, removing the previous reliance on extrapolated photometric distributions.
  • The agreement between 0.3-3 and 1-5 h^-1 Mpc scale cuts indicates small-scale bias modeling and fiber-assignment effects are not dominating the measurement.
  • The calibrated n(z) distributions will feed the companion cosmic shear analysis, so cosmological constraints from HSC Y3 can be updated.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • A direct test of the constant cross-correlation coefficient assumption, using mocks with known n(z) or a fully spectroscopic bin, would settle whether the recovered shapes are distorted; the paper's defense is scale-cut consistency rather than a measurement of r_xy(z).
  • If the smaller high-bin shifts persist, Stage IV surveys may not need as aggressive photo-z shift priors, which would tighten S8 constraints.
  • The stronger bin-3 tail implies source-lens magnification and overlap corrections will matter more for high-redshift tomographic bins in future surveys.
  • The spline-plus-Dirichlet parametrization is portable to other surveys, but its knot density and prior strength should be validated against simulated n(z) shapes before adoption.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper calibrates the redshift distributions n(z) of the four HSC PDR3/Y3 tomographic bins using the clustering-redshift technique against DESI DR1/DR2 spectroscopic tracers (BGS, LRG, ELG, QSO). The new ingredients relative to the previous HSC calibration (Rau et al. 2022) are the inclusion of DESI ELGs and QSOs at z > 1.2, allowing coverage of bins 3 and 4, and a B-spline posterior model. The central results are the measured shifts relative to the Rau+2022 Y3 Total calibration: Δz1 = +0.029, Δz2 = -0.003, Δz3 = -0.039, Δz4 = -0.048 (fiducial 0.3-3 h^-1 Mpc scale cut, with photometric and spectroscopic bias corrections and magnification). The authors argue that the HSC Y3 cosmic-shear analyses' large negative shifts in bins 3 and 4 are overestimated, and that the high-redshift tail of bin 3 is stronger than the photometric-only calibration predicted.

Significance. If the results are correct, this is an important measurement for HSC Y3 cosmology and for clustering-redshift methodology more generally: it is the first complete clustering calibration of all four HSC tomographic bins, and it provides a direct, spectroscopic-tracer-based anchor for the photo-z shift parameters that weak-lensing analyses have so far marginalized over. The paper's strengths include the release of code and data products, the explicit treatment of photometric sample bias and magnification, and the demonstration that two scale cuts (0.3-3 and 1-5 h^-1 Mpc) give consistent shifts in bins 3 and 4 at the ~0.01 level. Appendix A also provides a useful, albeit idealized, test of the Δzp = 0.1 photometric-bias-bin approximation. The main limitations are systematic in nature: the recovered n(z) depends on an assumption about the cross-correlation coefficient r_xy(z), and the B-spline prior is constructed from the same measurements that are being modeled. Both issues can affect the quoted central values and error bars, so the manuscript requires revisions before the central claim can be accepted.

major comments (3)
  1. [§3.3, Eq. (3.7)] Equation (3.7) recovers n_p(z_j) ∝ ω̄_sj p / sqrt(ω̄_sj sj ω̄_pj pj). After renormalization, the recovered distribution is n_p(z) r_sp(z) / ∫ n_p(z') r_sp(z') dz', where r_sp(z) is the cross-correlation coefficient. The paper assumes r_sp is constant across each tomographic bin and equal to 1, but this is not tested. The consistency between the 0.3-3 and 1-5 h^-1 Mpc scale cuts does not bound a redshift-dependent r_sp, since r_sp can be scale-independent while still evolving with z. The claimed multi-tracer consistency is asserted in §5.1 but per-tracer n(z) curves are not shown; different tracers can have different r_sp(z) evolution. For bins 3 and 4, the crucial high-z tail is probed mainly by ELGs and QSOs, whose stochasticity relative to HSC galaxies may well evolve across the bin. A few-percent monotonic r_sp(z) trend across the tail would shift the first moment by an amount compara
  2. [§5.3, Eq. (5.5)] The Dirichlet prior on the B-spline coefficients is set to α_i = a0 + b c_i^NNLS, where c^NNLS is the Non-Negative Least Squares solution fit to the same n(z) measurements that the spline model subsequently fits. This is a double use of the data: the measurements shape both the likelihood and the prior, which can artificially shrink the reported posterior uncertainties and may also bias the posterior location. The chosen values a0 = 0.05 and b = 3 are not motivated by a sensitivity study. The central shifts in Table 5 should be shown to be robust to the prior choice, for example by comparing with a flat Dirichlet prior (b = 0) or by treating the NNLS coefficients as part of a proper hierarchical model. Without such a test, the quoted error bars on Δz cannot be regarded as fully data-driven.
  3. [§3.4, Eqs. (3.8)-(3.9) and Appendix A] The photometric sample bias correction itself relies on Eq. (3.8), which assumes r_sp = 1 and no redshift evolution of r_sp within each Δzp = 0.1 bin. Appendix A tests the bin-width approximation using the §3.4 n_pk(z) measurements as the 'true' distributions. If those measured n_pk(z) are already distorted by redshift-dependent r_sp, the Appendix's conclusion of <1.7% bias error does not include this contamination. Since the same r_sp assumption enters both the bias correction and the final n(z) recovery, the distortion is not removed by renormalization. Please quantify the impact of a redshift-dependent r_sp on the recovered b_p(z) power law and, in turn, on the final n(z) and Δz values. This can be done with a two-parameter r_sp(z) model or with galaxy mocks with known stochasticity.
minor comments (5)
  1. [§3.3, footnote 5] The interval notation appears to have a typo: '[zj + Δz/2, zj + Δz/2)' should presumably be '[zj − Δz/2, zj + Δz/2)'.
  2. [§3.5, Eq. (3.14)] The quantity M(z_j) is used before the matrix M is introduced in Eq. (3.16); consider reordering or clarifying the notation for readability.
  3. [§4, Eq. (4.1)] The jackknife covariance formula includes the prefactor (NJK −1)/NJK; please verify that this is the intended form and clarify whether the usual jackknife correction (NJK −1) is applied separately.
  4. [§5.1, Eq. (5.1)] The inverse-variance combination of tracers ignores cross-covariances between tracers on overlapping redshift ranges. The paper acknowledges this, but it would be helpful to state how much the final error bars would grow if a cross-tracer covariance were included.
  5. [Table 5] The acronyms WX and Y3 Total are used without definition in the table caption; please define them in the caption for the non-specialist reader.

Circularity Check

0 steps flagged

No load-bearing circularity: the central n(z) is a clustering-redshift inversion from independent DESI/HSC correlations; only minor, non-load-bearing self-citations and a data-informed regularization prior are present.

full rationale

The derivation chain is not circular. The central estimator, Eq. (3.7), n_p(z_j) = w_sj,p / sqrt(w_sj,sj w_pj,pj), is a standard clustering-redshift inversion: the DESI auto-correlation removes the spectroscopic tracer bias, and the HSC auto-correlation (with the Sec. 3.4 photo-z spread correction) removes the photometric bias, with the cross-correlation coefficient r_xy assumed constant and set to 1 after renormalization. This is an explicit modeling assumption, not a quantity fitted to the target result. The Sec. 3.4 correction does use auxiliary clustering-redshift estimates n_pk(z) (Eq. 3.8) to correct the photometric auto-correlation used in the denominator; this reuses the same technique, but it does not insert the target bin's n_p(z) into itself. The corrected auto-correlation is a nuisance factor, and any redshift evolution of r_xy would be a systematic effect, not a by-construction identity. The Sec. 5.3 Dirichlet prior is data-informed: alpha_i = a0 + b c_i^NNLS, where c_i^NNLS is an NNLS fit to the same n(z) measurements used as the likelihood. This is an empirical-Bayes/regularization double-counting concern that can flatter error bars, but it does not make the posterior equal to the prior or reduce the reported shifts to a fitted parameter. Citations to Rau et al. (2022) and the companion paper [100] are used as comparison benchmarks and forward references, not as load-bearing justifications of the method. The measured shifts dz3 and dz4 are therefore not forced by construction; they are measurements from cross-correlation data with explicit, testable assumptions.

Axiom & Free-Parameter Ledger

6 free parameters · 8 axioms · 0 invented entities

No new physical entities are introduced. The free parameters are empirical fits (bias amplitudes, slopes, magnification slopes) and modeling choices (knot spacing, prior hyperparameters); all are disclosed and propagated (or, for hyperparameters, stated). The mildest self-referential chain is the data-informed Dirichlet prior and the clustering-derived bias proxy feeding its own correction.

free parameters (6)
  • Photometric bias power-law amplitude alpha = 0.416 ± 0.004
    Fit to corrected sqrt(bar-omega_pp) measurements (Eq 3.10); used in magnification matrix (Eq 3.18) and bias correction.
  • Photometric bias power-law slope beta = 0.430 ± 0.0145
    Same fit as alpha; controls redshift evolution of the bias proxy.
  • Tracer galaxy bias coefficients (c_s, d_s) = BGS 0.606/0.524; LRG 0.236/1.346; ELG 0.155/0.595; QSO 0.252/0.710
    Fit to DESI auto-correlations at 30-65 h^-1 Mpc (Table 2); enter magnification corrections.
  • HSC magnification slopes s_mu per bin = 0.002, 0.065, 0.142, 0.206
    Measured from i-band number count slope, constant per bin (Table 3); redshift evolution neglected.
  • Dirichlet prior hyperparameters (a0, b) = a0=0.05, b=3
    Hand-chosen to make spline coefficients sparse (Eq 5.5); prior concentrations are data-informed via NNLS.
  • Spline knot placement = one knot per two data points
    Uniform internal knots; modeling choice affecting smoothness (section 5.3).
axioms (8)
  • standard math Limber approximation valid for dz_s=0.05 spectroscopic slices
    Invoked in Eqs 3.4, 3.13; McQuinn and White [39] found it reasonable for such widths.
  • domain assumption Cross-correlation coefficient r_xy constant within a tomographic bin and set to 1 after renormalization
    Eqs 3.4/3.7 — if r_xy evolves with z, the recovered n(z) shape is distorted; not directly measured.
  • domain assumption Spectroscopic bin n_s(z) is an indicator function; b_s, b_p and bar-omega_mm evolution neglected within dz_s
    Dirac approximation leading to Eq 3.6 (section 3.3); edge-of-catalog deviations acknowledged.
  • domain assumption b_p(z) * sqrt(bar-omega_mm(z)) constant over dz_p=0.1 photo-z bins
    Bias-recovery correction (section 3.4, Eqs 3.8-3.9); tested in App A with <1.7% deviations.
  • domain assumption Redshift-space distortions negligible for wide projections and small scales
    Stated in section 3 with ref [65].
  • domain assumption Fiducial cosmology fixed to HSC Y3 values (Omega_m, h, n_s, sigma_8)
    Sets scale cuts and bar-omega_mm in magnification corrections; cosmology dependence discussed in section 6.
  • domain assumption Magnification slopes of DESI tracers taken from literature and interpolated; ELG-VLO assumed same as ELG-LOP
    Table 4 (section 3.5); interpolation error assumed negligible relative to g x g term.
  • domain assumption HSC magnification slope described by i-band magnitude selection only, constant per bin
    Assumption kept from HSC Y1 [70] (section 3.5, Table 3); calibration-cut selection effects neglected.

pith-pipeline@v1.3.0-alltime-deepseek · 32321 in / 19676 out tokens · 182455 ms · 2026-08-03T20:48:46.949205+00:00 · methodology

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read the original abstract

The calibration of tomographic redshift distributions is essential for cosmological analysis of weak lensing data. In this work, we calibrate all four tomographic bins of the Hyper Suprime Camera (HSC) weak lensing catalog with the Dark Energy Spectroscopic Instrument (DESI) Data Release 1 and 2 using the clustering redshifts technique. We include z > 1.2 redshift sources such as emission line galaxies (ELG) and quasars (QSO) sources in our calibration, which were not available in the previous HSC calibration (Rau et al. 2022), allowing a complete calibration of all the redshift bins. We find the first tomographic bin exhibits a small shift towards low redshifts. The second bin is in good agreement with the photometric calibration, while third and fourth bin exhibit a shift towards higher redshifts. However, these shifts are considerably smaller than the shifts obtained in the HSC Year 3 cosmic shear analyses. We evaluate the impact of galaxy bias and magnification effects from all the samples on the measurements, finding them to be small, and we propose corrections to reduce them further. Specifically, we relax the assumption of linear bias and only assume no redshift evolution of the cross-correlation coefficient, allowing us to leverage smaller clustering scales. We model the redshift distributions with splines and compare our results to previous analyses as well as to other parameterizations found in literature. For the two high-redshift tomographic bins, we find the shifts to higher redshifts with respect to the measurements performed in Rau+2022 to be $\Delta z_3=-0.039^{+0.020}_{-0.021}$ and $\Delta z_4=-0.048^{+0.012}_{-0.012}$.

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