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REVIEW 4 major objections 5 minor 294 references

Lyman-break galaxies from UNIONS are reliable cosmological tracers via cross-correlations with CMB lensing and quasars, not via their own clustering.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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2026-08-02 07:27 UTC pith:XH23DCJO

load-bearing objection Honest feasibility study: UNIONS LBG cross-correlations are measurable and useful, but the unbiasedness claim outruns the tests since correlated systematics were never simulated. the 4 major comments →

arxiv 2607.09943 v2 pith:XH23DCJO submitted 2026-07-10 astro-ph.CO

Assessing the large-scale angular clustering of UNIONS Lyman Break Galaxies via cross-correlations

Constantin Payerne , Christophe Y\`eche , William d'Assignies Doumerg , Hendrik Hildebrandt , Martin Kilbinger , Calum Murray , Thomas de Boer , Kenneth C. Chambers
show 2 more authors
Scott Chapman Alan W. McConnachie
This is my paper
classification astro-ph.CO
keywords Lyman-break galaxiesUNIONSangular power spectrumcross-correlationCMB lensingimaging systematicsprimordial non-Gaussianityphotometric galaxy clustering
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.

The paper argues that UNIONS-selected Lyman-break galaxies at z~2.5 are viable cosmological tracers, but only when their angular clustering is measured in cross-correlation with external fields like CMB lensing and quasar samples. The auto-angular power spectrum of these galaxies is so contaminated by spatially varying depth, seeing, extinction, and stellar density that even state-of-the-art corrections leave it unusable on large scales. Using both data and mocks, the paper shows the LBG-CMB lensing cross-power spectrum survives contamination and matches theoretical amplitude predictions, with residual systematics inflating the covariance rather than biasing the mean. If right, this redirects high-redshift photometric clustering work toward cross-correlation analyses.

Core claim

For u-dropout LBGs drawn from the UNIONS GAaP ugri catalog (roughly 1,400 galaxies per square degree, effective area 2,400-2,800 square degrees), variations in PSF depth, seeing, Galactic extinction, and stellar density imprint large-scale fluctuations in the observed density that cannot be removed by linear or Random-Forest regression-based deprojection; the auto-spectrum remains orders of magnitude above the fiducial clustering model at ell < 300. The cross-power spectrum with Planck PR4 CMB lensing, however, is recovered robustly in mock contamination-decontamination tests, and in the real data shows a positive signal consistent with the fiducial model across ell ~ 30-300, with the caveat

What carries the argument

The pseudo-angular power spectrum (pseudo-C_ell) estimator with mode-coupling decoupling, plus template-based deprojection of imaging systematics: linear regression deprojection and Random-Forest systematic weights derived from imaging templates. The load-bearing mechanism is that cross-spectra between the LBG density field and external tracers are insensitive to systematics that are uncorrelated between the two maps; mock tests contaminated the LBG map only, confirming that cross-spectra survive strong linear and non-linear contamination while auto-spectra do not.

Load-bearing premise

The claim that residual systematics add variance but not bias rests on the untested premise that those systematics are statistically independent of the external tracer fields (CMB lensing and quasar maps).

What would settle it

Contaminate mock LBG maps with the same systematic weight pattern applied to the external CMB lensing or quasar maps (correlated contamination), then measure the recovered cross-spectrum amplitude; if it shifts by more than the Jackknife error bars, the 'no significant bias' claim fails. Alternatively, split the LBG sample by imaging depth and check whether the cross-spectrum amplitude varies across splits.

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

If this is right

  • LBG samples from wide photometric surveys at z~2.5 can deliver cosmological constraints through cross-correlations with CMB lensing and quasar samples, even when their auto-spectra are unusable.
  • Residual imaging systematics in faint, near-depth-limited samples must be budgeted as excess variance (via Jackknife) rather than assumed Gaussian, which strongly degrades constraints on local primordial non-Gaussianity.
  • The scale-dependent bias signature of local primordial non-Gaussianity is best pursued through cross-correlation rather than auto-clustering for these samples.
  • Mock contamination-decontamination validation with data-derived weights is a practicable way to test systematics robustness before cosmological interpretation.
  • Detection of the LBG-CMB lensing cross-power over roughly 6.6% of the sky is a first step toward competitive high-redshift PNG constraints for upcoming surveys.

Where Pith is reading between the lines

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

  • The robustness argument assumes systematics in the LBG map are statistically independent of the external tracer maps; a natural extension is to inject correlated contamination into both maps in mocks to see at what amplitude bias appears.
  • The excess Jackknife variance at large scales implies that survey-systematics mitigation should target the covariance, not just the mean; estimators that model or downweight contaminated modes may recover fNL sensitivity.
  • The technique transfers directly to LSST-scale surveys; UNIONS acts as a pathfinder for u-dropout LBG samples at scale.
  • Cross-correlation with spectroscopic quasar samples can serve as an independent systematic audit for CMB-lensing cross-spectra, since the two external tracers have separate selection functions.

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

4 major / 5 minor

Summary. Using the UNIONS GAaP ugri catalogue, the authors build a u-dropout LBG sample (~1,400 deg^-2) and measure angular auto- and cross-power spectra. They show that the LBG auto-spectrum remains contaminated by PSF-depth, seeing, extinction, and stellar-density systematics after NaMaster deprojection and regressis corrections, and therefore focus on cross-correlations with Planck PR4 lensing, DESI DR1 QSOs, and Quaia. Controlled mocks with linear and non-linear contamination are used to argue that the cross-spectrum is recovered even when linear auto-spectrum mitigation fails. In the data, the LBG-lensing and LBG-QSO cross-spectra are positive and broadly match a fiducial model, while the jackknife covariance exceeds the Gaussian-only variance by factors of ~3-15. A simplified f_NL analysis shows that this excess variance substantially weakens constraints. The paper concludes that UNIONS LBGs are reliable tracers for cross-correlation cosmology at z~2.5.

Significance. If the conclusion holds, the paper is a valuable proof of concept for using faint, depth-limited photometric samples in cross-correlation cosmology: the failure of the auto-spectrum is honestly demonstrated, and the cross-spectrum route is subjected to a non-linear contamination stress test. Strengths include the controlled mock pipeline (Section 4.3), the alpha=3 test where only Random-Forest mitigation recovers the input auto-spectrum, and the explicit jackknife-versus-Gaussian covariance comparison. The first large-area LBG-lensing cross-correlation measurement at this redshift is interesting in its own right. However, two load-bearing assumptions are not independently established: the decorrelation between residual LBG systematics and external tracer fields, and the amplitude normalization of the theoretical prediction. These issues affect the strength of the abstract's 'no significant bias' claim, so the paper needs revision rather than acceptance in its current form.

major comments (4)
  1. [Sec. 4.3, Step 3; Figs. 11-13] The mock validation contaminates only the LBG map: 'no contamination is applied to the external map.' This demonstrates robustness against systematics that are uncorrelated with the external tracer, but the central claim that residual systematics 'manifest as excess variance... without introducing a significant bias' requires the stronger assumption that any remaining systematics are also uncorrelated with the external fields. Section 4.1 shows that the LBG density depends on E(B-V) and Gaia stellar density; the same Galactic fields can modulate Quaia selection and leave residuals in DESI QSO corrections and in Planck lensing maps. If a common template component is present, the cross-spectrum acquires a term <delta_sys delta_ext> != 0 and is biased, not merely noisier. A mock test with correlated contamination injected into both maps, or a null test against the shared E(B-V)/stellar-dens
  2. [Sec. 5.1] The statement that the LBG-lensing cross-spectrum amplitude is 'consistent with theoretical predictions' is partly built in by construction. The theory curve is normalized by b0=0.65, chosen because it 'was found to provide a good description of the LBG bias inferred from clustering measurements for the same LBG selection' in Payerne et al. (2025a) - the same team and the same selection. The f_NL+b0 fit in Table 1 then returns b0 ~ 0.6-0.8. Thus the data-theory agreement is not an independent validation of the bias model or of the cross-spectrum amplitude calibration. Please separate the predicted amplitude (with b0 fixed from external clustering constraints) from the fitted amplitude, or explicitly frame the consistency check as shape-only, not amplitude-calibration.
  3. [Sec. 5.2, Table 1] The abstract's 'without introducing a significant bias' is in tension with Table 1. With Gaussian-only covariance, the inferred f_NL changes from +158 +/- 56 (no correction) to -166 +/- 49 (NaMaster), which is a several-sigma shift; the values become mutually consistent only after adopting the jackknife covariance, whose diagonal is inflated by a factor of 6-7. Thus the conclusion that residual systematics produce only excess variance depends critically on which covariance estimator is adopted. The paper should quantify the per-bin effect of the correction on the cross-spectrum itself (e.g., Delta C / sigma_JK for the ell < 100 bins) and explicitly discuss whether the suppression seen in Fig. 6 at low ell is consistent with zero within the final error bars.
  4. [Eq. (1)] As typeset, Eq. (1) defines the pseudo-spectrum as (2l+1)^-1 sum |a_X^* a_Y|^2. For X != Y this is not a cross-power spectrum; it reduces to a product of auto-spectra. The standard estimator is (2l+1)^-1 sum Re(a_X^* a_Y). If this is only a typographical error, it should be corrected because Eq. (6) and all subsequent uses rely on the usual cross-spectrum definition. If the code actually implements Eq. (1) as written, the cross-spectrum measurements are not what the paper claims them to be. Please fix this and confirm that the analysis pipeline uses the standard estimator.
minor comments (5)
  1. [Sec. 3.1] The survey area is quoted as 3,580 deg^2 initially, then 2,800 deg^2 effective after masking, then 2,400 deg^2 after systematics-based cleaning. Please make explicit which area is used for the number density, the masks, and the power-spectrum normalization.
  2. [Fig. 4 caption] Typo: 'mutliply' should be 'multiply'. Also, the caption says the fiducial model is multiplied by 5 to fit in the frame; this should be stated clearly in the main text so the reader does not misread the amplitude ratio.
  3. [Sec. 5.1] The text refers to 'the fifth l-bin' showing a significant deviation, but the bin edges are not specified. Please identify the l range explicitly and state whether this bin is included or excluded in the f_NL fit.
  4. [Appendix C, Fig. 13] The main text says the original C^gg is 10 times larger and C^kappag is 'resp. 5 times' larger, while the figure caption only states C^gg. Align the text and caption for reproducibility.
  5. [Sec. 2 / Eq. (6)] The noise term N^XY_b is introduced as delta_XY^K N^X_b. For clarity, state explicitly that this means the shot-noise/reconstruction-noise term appears only in auto-spectra and is zero for cross-spectra between different fields.

Circularity Check

0 steps flagged

No significant circularity: cross-spectrum claims are calibrated against independent observables and the mock tests are self-consistency checks, not input=output reductions.

full rationale

The paper's central claims are data measurements with explicit estimator validation, not derivations from self-defined inputs. The angular power spectrum formalism (Eqs. 1-7) is standard projection theory; the mock pipeline in Sec. 4.3 generates an input C^gg, contaminates it, and tests recovery with NaMaster/regressis. That is a self-consistency test of the estimator, not a circular derivation of the cosmological signal. The known limitation is stated in Sec. 4.3 Step 3: 'no contamination is applied to the external map', so the mocks only validate robustness against LBG-only systematics. This is an untested-correlation caveat (a correctness risk), not a circular step. The theory curves in Sec. 5.1 use b0=0.65 from Payerne et al. (2025a), the same team's clustering analysis of the same LBG selection. However, this is a calibration from a different statistic, explicitly framed as 'a consistency check', and the paper also reports a fitted b0 from the cross-spectrum (Table 1: b0 ~ 0.6-0.8) and compares the amplitude to DESI QSO-CMB lensing, which is an external benchmark. The amplitude agreement is therefore a cross-check between related but distinct observables, not an identity forced by construction. The fNL results are explicitly presented as a proof of concept, and the large Jackknife-vs-Gaussian covariance ratio is reported rather than hidden, so no fitted parameter is renamed as a prediction. No equation is shown to reduce to its own input, and no load-bearing result depends on an unverified self-citation chain.

Axiom & Free-Parameter Ledger

5 free parameters · 7 axioms · 0 invented entities

The claim that LBGs can serve as cross-correlation tracers rests on standard tracer physics (linear bias, Wilson & White prescription, universality for p_Phi) plus two assumptions specific to this analysis: statistical decorrelation of residual systematics with external fields and representativeness of the XMM-LSS n(z). The only free parameters that enter the 'prediction' being validated are b0=0.65 (from the authors' prior clustering work) and the mock-calibrated first-bin transfer function; the contamination amplitudes A_t are validation-mock parameters, not data-analysis parameters. No new physical entities are postulated; 'excess variance' and the transfer function are statistical constructs without falsifiable handles outside the paper.

free parameters (5)
  • b0 (bias rescaling factor) = 0.65
    Rescales the Wilson & White (2019) bias prescription; taken from Payerne et al. (2025a) clustering measurements of the exact same u-dropout selection. It normalizes the 'theoretical prediction' against which the measured cross-spectrum amplitude is declared consistent (Section 5.1).
  • b0 (in f_NL fit) = 0.6-0.8 +/- 0.1-0.2
    Bias amplitude fitted jointly with f_NL from the LBG x CMB-lensing cross-spectrum (Table 1); the point estimate shifts with covariance choice, roughly doubling sigma(b0) between Gaussian and jackknife cases.
  • Mock contamination amplitudes A_t = Gaussian random variables matched to data-template correlations
    Appear in Eq. (14): 'A_t are correlation amplitudes... Gaussian random variables to mimic, on average, the overall correlation amplitude measured between the data and the templates'. They govern the mock validation only, not the data analysis.
  • First-ell-bin transfer function = 0.8
    Ratio of corrected to uncorrected mock cross-spectra, applied to the data's first bin before f_NL fitting (Section 5.2, footnote 4); a mock-calibrated correction that shapes the reported constraint.
  • LBG selection and footprint cleaning thresholds = 23.5<r<24.2; 23<u10sigma<24.5; 0.5<PSFsize<1.2; etc.
    Hand-set in Sections 3.2-4.1 to balance sample size, purity and systematics; the r-band faint limit places the sample in a regime where density is hypersensitive to depth variations, which drives the paper's main negative result.
axioms (7)
  • standard math Flat LCDM and linear perturbation theory with a standard matter power spectrum at ell<300 (k<~0.05-0.075 h/Mpc)
    Underlies Eqs. (6)-(7) and A.7 used for every theoretical prediction; stated in Appendix A.1.
  • domain assumption LBG bias is linear, approximately scale-independent in the absence of PNG, and its amplitude follows Wilson & White (2019) times b0
    Invoked in Section 5.1 and Appendix A.1 (Eq. A1); the amplitude-consistency check and the f_NL analysis both depend on this prescription.
  • domain assumption Residual imaging systematics of the LBG field are statistically independent of the Planck lensing and QSO fields
    Central premise of Sections 4.3-5 ('these systematics are largely uncorrelated between independent probes'). Mock validation only contaminates the LBG side, so this is asserted, not tested in the correlated case.
  • domain assumption The LePhare photo-z n(z) measured in the 2 sq-deg XMM-LSS overlap is representative of the full 2,800 sq-deg sample
    Used as 'the truth' for the fiducial cross-spectrum prediction (Section 5.1); the selection function visibly varies across the footprint (Figs. 1, 3), so the kernel may be unrepresentative.
  • domain assumption Magnification bias and RSD contributions follow Payerne et al. (2025a) with no propagated uncertainty
    Eqs. A3-A4 enter all model curves; their amplitudes enter the consistency statement but carry no error bars in Fig. 6.
  • domain assumption Universality relation p_Phi=1 in the PNG scale-dependent bias
    Used in Eq. (15)/A.2; an approximation in the cited literature (Slosar et al. 2008; Barreira et al. 2020), not validated for this LBG selection.
  • domain assumption Jackknife covariance over N_JK=110 patches captures the true estimator variance including systematics
    Validated on uncontaminated mocks (Appendix E) where it matches Gaussian theory and simulation scatter; on data it is adopted as the empirical covariance and its excess over Gaussian is attributed to residual systematics (Section 5.1, Fig. 7).

pith-pipeline@v1.3.0-alltime-deepseek · 21207 in / 27414 out tokens · 276086 ms · 2026-08-02T07:27:24.301173+00:00 · methodology

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read the original abstract

Lyman-break galaxies (LBGs), selected via the strong spectral break blueward of the Lyman limit, are powerful tracers of large-scale structure at redshifts $z>2$. In this work, we assess the feasibility of using LBGs selected from the Ultraviolet Near Infrared Optical Northern Survey (UNIONS) multi-band photometric catalog as cosmological probes of the high-redshift Universe using two-point statistics. We demonstrate that spatially varying imaging systematics, driven by variations in PSF depth, seeing across the UNIONS footprint, limit robust measurements of the LBG auto-angular power spectrum on large scales, even after correcting the LBG field with linear or non-linear mitigation techniques. This study shows that clustering analyses of faint galaxy samples close to survey depth are challenging. We therefore turn to cross-correlation measurements with external tracers, in particular the \textit{Planck} CMB lensing convergence and quasars from DESI DR1 and \textit{Quaia}, which are less sensitive to the angular imaging systematics. Using both data and mock catalogues, we demonstrate that the LBG--CMB lensing cross-power spectrum can be measured more robustly than the auto-spectrum, with an amplitude consistent with theoretical predictions. Residual systematics primarily manifest as excess variance at large angular scales, without introducing a significant bias in the recovered signal. Taken together, these results establish UNIONS-selected LBGs as reliable tracers for cross-correlation cosmology at $z\sim 2.5$, and highlight cross-correlation techniques as a powerful and robust avenue for extracting cosmological information from photometric high-redshift galaxy samples in the presence of complex imaging systematics.

Figures

Figures reproduced from arXiv: 2607.09943 by Alan W. McConnachie, Calum Murray, Christophe Y\`eche, Constantin Payerne, Hendrik Hildebrandt, Kenneth C. Chambers, Martin Kilbinger, Scott Chapman, Thomas de Boer, William d'Assignies Doumerg.

Figure 1
Figure 1. Figure 1: Left: HEALPix pixel coverage for the GAaP footprint. Right: Local density of selected u-dropout galaxies (in deg−2 ), corrected from surface coverage. left panel of [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Left: color-color diagram of UNIONS galaxies, with u-dropout selected objects shown in blue. Red points correspond to stars (specified with the flag OBJ TYPE hsc==1 in the CLAUDS+HSC catalogs). Right: Photometric redshift distribution of the u-dropout galaxies, compared to the redshift distribution of all galaxies before applying the u-dropout selection. rPSFsize < 1. We also remove by hand some ”bad” pho￾… view at source ↗
Figure 3
Figure 3. Figure 3: Upper panels: LBG overdensity as a function of UNIONS survey characteristics (left: 5σ PSF depth, right: PSF size in arcsec). Lower panels: Overdensity as a function of external templates (left: Galactic extinction E(B − V ), right: stellar density). Solid lines correspond to the uncorrected LBG field, while dashed lines show the results after deprojection with namaster. different telescopes, varying depth… view at source ↗
Figure 4
Figure 4. Figure 4: Left: Angular power spectrum of the LBG density field before and after mitigation with namaster (note that neither angular mode removal nor deprojection noise bias has been applied). Dots refer to the catalog-based approach in namaster, when full lines denote for the HEALPix-based namaster method. The curve at the bottom of the plot corresponds to a fiducial model for the LBG angular clustering amplitude, … view at source ↗
Figure 5
Figure 5. Figure 5: Left: Angular power spectrum of a mock LBG density map, shown before and after contamination using the UNIONS LBG regressis Random Forest (RF) weight map, and before and after mitigation with namaster and regressis. Right: Same as left, but for the cross-correlation spectrum between the mock LBG density maps and CMB lensing maps. The CMB photons are gravitationally lensed by the in￾tervening large-scale st… view at source ↗
Figure 6
Figure 6. Figure 6: Left: Angular power spectrum between UNIONS LBGs (or DESI DR1 QSOs) and the Planck PR4 CMB lensing map. Right: Angular power spectrum between the UNIONS LBGs and the DESI DR1 QSO sample, as well as the Quaia sample. ing Surveys and two infrared bands (W1, W2) from the Wide-field Infrared Survey Explorer (WISE) and was ex￾tensively validated during the DESI Survey Validation campaign. The final quasar targe… view at source ↗
Figure 7
Figure 7. Figure 7: Left: Ratio of the diagonal elements of the Jackknife covariance matrix to those of the Gaussian-only covariance matrix. Right: Two-dimensional posterior distribution of f loc NL and b0 inferred from the C κg ℓ measurements, using either the theoretical or Jackknife covariance. further methodological developments or more stringent control of large-scale survey systematics. In contrast, cross-correlation me… view at source ↗
Figure 8
Figure 8. Figure 8: UNIONS PSF depth [PITH_FULL_IMAGE:figures/full_fig_p015_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: UNIONS image quality [PITH_FULL_IMAGE:figures/full_fig_p015_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Summary of UNIONS PSF depth and UNIONS image quality [PITH_FULL_IMAGE:figures/full_fig_p016_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Left: Angular power spectrum of mock LBG density maps, contaminated and decontaminated using a linear contamination model (Awan et al. 2025) (i.e., α = 1 in Eq. (14)), with the same C gg ℓ used for both the original contaminated map and the mocks. Right: Same as left, but for the cross-correlation between the mock LBG density maps and the CMB lensing maps [PITH_FULL_IMAGE:figures/full_fig_p017_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Same as [PITH_FULL_IMAGE:figures/full_fig_p017_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Same as [PITH_FULL_IMAGE:figures/full_fig_p017_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Left: Jackknife binning scheme of the default UNIONS LBG footprint. Right: Ratio between (i) the variance of diverse estimated cross-correlation angular power spectra between mock LBGs and mock CMB lensing maps, where the LBG maps were either contaminated or corrected and (ii) the un-contaminated variance [PITH_FULL_IMAGE:figures/full_fig_p018_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Random Forest regressis systematic weights [PITH_FULL_IMAGE:figures/full_fig_p018_15.png] view at source ↗
Figure 15
Figure 15. Figure 15: Random Forest regressis systematic weights [PITH_FULL_IMAGE:figures/full_fig_p020_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: regressis systematic weights versus UNIONS imaging features (left: 5σ PSF depth, right= PSF size) [PITH_FULL_IMAGE:figures/full_fig_p018_16.png] view at source ↗
Figure 16
Figure 16. Figure 16: regressis systematic weights versus UNIONS imaging features (left: 5σ PSF depth, right= PSF size) [PITH_FULL_IMAGE:figures/full_fig_p020_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Same as [PITH_FULL_IMAGE:figures/full_fig_p019_17.png] view at source ↗
Figure 17
Figure 17. Figure 17: Same as [PITH_FULL_IMAGE:figures/full_fig_p021_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Same as [PITH_FULL_IMAGE:figures/full_fig_p019_18.png] view at source ↗
Figure 18
Figure 18. Figure 18: Same as [PITH_FULL_IMAGE:figures/full_fig_p021_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: Variance of the auto and cross-spectrum (theory, standard deviation over 100 simulations, Jackknife) [PITH_FULL_IMAGE:figures/full_fig_p020_19.png] view at source ↗
Figure 19
Figure 19. Figure 19: Variance of the auto and cross-spectrum (theory, standard deviation over 100 simulations, Jackknife) [PITH_FULL_IMAGE:figures/full_fig_p022_19.png] view at source ↗

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