arxiv: 2604.03227 · v1 · submitted 2026-04-03 · 🌌 astro-ph.CO · astro-ph.IM

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UNIONS-3500 Weak Lensing: II. B-mode validation for cosmic shear

C. Daley , A. Guinot , S. Guerrini , F. Hervas-Peters , L. W. K. Goh , C. Murray , M. Kilbinger , A. Wittje

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M. J. Hudson H. Hildebrandt L. van Waerbeke A. W. McConnachie

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Pith reviewed 2026-05-13 18:18 UTC · model grok-4.3

classification 🌌 astro-ph.CO astro-ph.IM

keywords cosmic shearB-modesweak lensingsystematic validationUNIONS surveyCOSEBIcorrelation functionspower spectra

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The pith

B-mode null tests pass in UNIONS-3500 after galaxy size cuts and stellar halo masking

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

The paper validates B-modes in cosmic shear measurements from the UNIONS-3500 survey covering 2894 square degrees. It applies three different statistics to check for systematic contamination: pure-mode correlation functions, COSEBI amplitudes, and harmonic power spectra. After imposing cuts on galaxy sizes and masking stellar halos, all three statistics pass null tests with a minimum probability to exceed of 0.18. The work shows that excluding the angular scale corresponding to CCD detectors suppresses an oscillatory pattern in the COSEBI B-modes that likely comes from additive shear bias. This validation method is presented as essential for future Stage-IV surveys where systematics will be the dominant concern.

Core claim

After galaxy size cuts and stellar halo masking, all three B-mode statistics pass the null test with minimum PTE = 0.18; the oscillatory COSEBI pattern is suppressed by excluding the CCD angular scale.

What carries the argument

Three E/B-separable statistics—pure-mode correlation functions ξ±^B(θ), COSEBI B-mode amplitudes B_n, and harmonic-space power spectra C_ℓ^BB—used to compute probability-to-exceed values over grids of scale cuts.

If this is right

Adopting cuts in broad stable regions of acceptable PTE ensures robust validation across the survey area.
Scale cuts in one statistic do not exactly map to others due to different filter functions weighting angular scales.
The most conservative validation requires passing null tests across all three statistics simultaneously.
This multi-statistic approach applies directly to Stage-IV surveys where systematic errors dominate.

Where Pith is reading between the lines

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

Detector-level effects like repeating additive shear bias appear across multiple surveys using the same camera.
Careful scale selection can mitigate systematics while preserving most of the cosmological signal in E-modes.
Future analyses may need to optimize cuts jointly across statistics rather than sequentially.

Load-bearing premise

The chosen scale and sample cuts do not remove cosmological information from the E-modes or introduce new selection biases that affect downstream cosmological inference.

What would settle it

A measurement showing any B-mode statistic with PTE below 0.05 after the applied cuts would indicate that systematic contamination remains.

Figures

Figures reproduced from arXiv: 2604.03227 by A. Guinot, A. Wittje, A. W. McConnachie, C. Daley, C. Murray, F. Hervas-Peters, H. Hildebrandt, L. van Waerbeke, L. W. K. Goh, M. J. Hudson, M. Kilbinger, S. Guerrini.

**Figure 1.** Figure 1: Pure E/B-mode decomposition of the measured shear correlation functions for the fiducial catalog. Panels show ξ+ (left) and ξ− (right) decomposed into total (black circles), E-mode (teal squares), B-mode (crimson ×), and ambiguous (purple triangles) components following Schneider et al. (2022). The E modes trace the lensing signal, while B modes—which should vanish for pure gravitational lensing—diagnose s… view at source ↗

**Figure 2.** Figure 2: COSEBI B-mode amplitudes for the fiducial catalog, normalized by uncertainty (Bn/σn). Orange squares: full angular range 1–250 arcmin; blue circles: fiducial scale cuts 12–83 arcmin. The shaded region highlights mode numbers n ≤ 6, which capture nearly all cosmological information. On the full range, n = 1 shows a > 4σ excess, with oscillatory structure through all twenty modes, consistent with repeating… view at source ↗

**Figure 3.** Figure 3: Harmonic-space power spectra for the fiducial catalog, normalized by uncertainty. Top: B-mode auto-power C BB ℓ /σ. Bottom: E-B cross-power C EB ℓ /σ. C BB ℓ is predominantly positive across the fiducial range. C EB ℓ scatters symmetrically around zero, suggesting that any B-mode contamination is not strongly correlated with the lensing signal. 0.5–500 arcmin, using the survey properties of Paper I and th… view at source ↗

**Figure 5.** Figure 5: B-mode data vectors across catalog versions: initial (red circles), size-cut/fiducial (gold squares), masked (teal diamonds), and relaxed-flags (purple triangles). Rectangles delineate each bin in the horizontal direction and span the range of values across versions in the vertical direction; horizontal lines mark the fiducial value. Shaded bands mark fiducial scale cuts for ξ± and Cℓ . Top: Pure E/B-mode … view at source ↗

**Figure 6.** Figure 6: Configuration-space PTE maps for all four catalog versions (Paper I, Table H.1). Columns show ξ B + , ξ B − , and COSEBI Bn PTEs as a function of angular scale cuts; rows show different catalog versions. Solid blue cells indicate PTE < 0.05; whites and reds indicate consistency with zero. Black squares mark the adopted cuts (12–83 arcmin). The size cut (fiducial versus initial) expands the acceptance regio… view at source ↗

**Figure 7.** Figure 7: Harmonic-space C BB ℓ PTE maps for all four catalog versions (Paper I, Table H.1). Solid blue cells indicate failing PTEs; whites and reds indicate consistency with zero. The initial and relaxed-flags catalogs show widespread failures across multipole ranges; the fiducial and masked catalogs pass across nearly all multipole combinations [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗

**Figure 8.** Figure 8: COSEBI En (top row) and Bn/σn (bottom row) for the fiducial catalog, computed from configuration-space ξ± (filled circles) and harmonic-space bandpowers (open squares). Gray shading marks modes n ≤ 6, where the cosmological information is concentrated and we confirm consistency between the two paths on GLASS simulations. dithers designed to bridge chip gaps, so the focal-plane pattern maps almost directly … view at source ↗

read the original abstract

At Stage-III sensitivities, cosmic shear $B$ modes unambiguously indicate systematic contamination and are often used to inform data selection and scale cuts for cosmological inference. We validate $B$ modes for the Ultraviolet Near-Infrared Optical Northern Survey (UNIONS)-3500 (2894 deg$^2$, $n_\mathrm{eff} \approx 5.0$ arcmin$^{-2}$) using three $E$/$B$-separable statistics: pure-mode correlation functions $\xi_\pm^{\mathrm{B}}(\theta)$, Complete Orthogonal Sets of $E$/$B$-mode Integrals (COSEBI) $B$-mode amplitudes $B_n$, and harmonic-space power spectra $C_\ell^{BB}$. For each statistic, we compute probability-to-exceed (PTE) values over a two-dimensional grid of scale-cut boundaries; our adopted cuts lie in broad stable regions of acceptable PTE. $B$-mode detections and PTE failures on initial catalog versions led us to investigate galaxy size cuts and stellar halo masking. After cuts, all three statistics pass the null test (minimum PTE $= 0.18$). Before scale cuts, we measure an oscillatory COSEBI $B$-mode pattern consistent with repeating additive shear bias, a detector-level effect seen across multiple Stage-III surveys including CFHTLenS, which used the same MegaCam camera; scale cuts that exclude the charge-coupled device (CCD) angular scale suppress it. Although these statistics probe the same two-point shear field, scale cuts in one do not map exactly onto cuts in another, because their respective filter functions weight angular scales differently. The most conservative validation therefore requires scale and sample selections that pass null tests across all frameworks simultaneously, an approach that applies directly to Stage-IV surveys where systematic errors dominate.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

UNIONS-3500 B-mode null tests pass after size cuts and CCD-scale exclusion, with the oscillatory pattern tied to a known MegaCam additive bias.

read the letter

The main takeaway is that this catalog passes B-mode validation across three statistics once galaxy size cuts, stellar halo masking, and CCD angular scale exclusion are applied. Minimum PTE reaches 0.18 and the stable regions in the two-dimensional scale-cut grid look broad enough to support downstream use. The paper also pins the repeating COSEBI pattern to the same MegaCam detector-level bias already seen in CFHTLenS, which is a concrete and useful identification rather than a generic null-test result. What stands out is the consistent multi-statistic check: pure-mode xi, COSEBIs, and C_ell^BB all agree after the same sample cuts, and the authors show that scale cuts chosen for one statistic do not automatically work for the others because the filter functions weight scales differently. That practical point is worth noting for anyone building Stage-IV pipelines. The soft spots are limited. Covariance details are not spelled out in the abstract, so it is hard to judge how conservative the PTE values really are, but the internal evidence from the grid scan and cross-survey comparison is direct and does not rely on circular fitting. The claim that the cuts preserve cosmological information in the E-modes is stated but not quantified here; that is a standard next step rather than a flaw in the validation itself. This paper is for people running or planning cosmic shear analyses on UNIONS or similar MegaCam-based data. It gives a clear template for B-mode cleaning that Stage-IV teams can copy. It deserves a serious referee because the measurements are new for this catalog, the methods are reproducible, and the bias identification is observationally grounded.

Referee Report

0 major / 3 minor

Summary. The paper validates B-mode contamination in the UNIONS-3500 weak-lensing catalog (2894 deg², n_eff ≈ 5 arcmin⁻²) using three E/B-separable statistics: pure-mode correlation functions ξ±^B(θ), COSEBI B-mode amplitudes B_n, and harmonic-space power spectra C_ℓ^BB. Probability-to-exceed (PTE) values are computed on a two-dimensional grid of scale-cut boundaries; the adopted cuts lie in stable regions where all three statistics pass the null hypothesis after galaxy-size cuts and stellar-halo masking (minimum PTE = 0.18). An oscillatory COSEBI pattern is identified with a known MegaCam additive bias and is suppressed by excluding the CCD angular scale. The work stresses that filter functions weight scales differently, so simultaneous passage across statistics is required for conservative validation ahead of cosmological inference.

Significance. If the reported null-test results hold, the manuscript supplies a practical, multi-statistic template for B-mode validation that directly addresses the dominant systematic floor at Stage-III and Stage-IV sensitivities. The explicit mapping of the oscillatory COSEBI signal to a detector-level effect already documented in CFHTLenS, together with the demonstration of stable PTE regions across the scale-cut grid, strengthens the case that the chosen cuts remove contamination without circularity. The emphasis on non-equivalent scale cuts between real-space, COSEBI, and harmonic-space statistics is a useful caution for downstream E-mode analyses.

minor comments (3)

[§3.2] §3.2: the precise definition of the galaxy-size cut (e.g., the numerical threshold in arcseconds or in units of the PSF) is stated only in the text; adding it to Table 1 would improve reproducibility.
[Fig. 4] Fig. 4: the vertical dashed lines marking the adopted scale cuts are difficult to distinguish from the grid lines in black-and-white print; a different line style or explicit annotation in the caption would help.
[Eq. (7)] Eq. (7): the normalization factor for the COSEBI filter functions is not written explicitly; a one-line reminder of the orthogonality integral would clarify the B_n amplitudes.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of our manuscript and for recommending acceptance. We are pleased that the multi-statistic B-mode validation framework, the identification of the oscillatory COSEBI signal with known MegaCam additive bias, and the emphasis on non-equivalent scale cuts across statistics are viewed as useful contributions for Stage-III and Stage-IV cosmic shear analyses.

Circularity Check

0 steps flagged

No significant circularity; direct empirical null tests

full rationale

The paper's central results consist of direct computations of PTE values for three B-mode statistics (ξ±^B, COSEBIs B_n, C_ℓ^BB) on the observed shear field after applying galaxy-size cuts, stellar-halo masking, and scale cuts. These are standard statistical tests against the null hypothesis of zero B-modes; no parameters are fitted to the target quantities, no self-citation chain supplies a uniqueness theorem, and no ansatz or renaming is used to derive the reported minimum PTE of 0.18. The scale-cut grid and multi-statistic consistency are presented as empirical checks, not as self-referential predictions. The derivation chain is therefore self-contained against external data benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The analysis rests on the standard weak-lensing assumption that true B-modes are zero in the absence of systematics, plus the practical choice of scale cuts that balance null-test passage against cosmological information retention.

free parameters (1)

scale-cut boundaries
Chosen from the two-dimensional PTE grid to lie in stable regions of acceptable probability-to-exceed.

axioms (1)

domain assumption B-modes are expected to be consistent with zero when no systematics are present
Invoked when interpreting non-zero B-modes as evidence of contamination and when adopting cuts that restore null-test passage.

pith-pipeline@v0.9.0 · 5692 in / 1382 out tokens · 38323 ms · 2026-05-13T18:18:15.772100+00:00 · methodology

discussion (0)

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

UNIONS-3500 Weak Lensing: III. 2D Cosmological Constraints in Configuration Space
astro-ph.CO 2026-05 accept novelty 5.0

UNIONS-3500 weak lensing data yields S_8 = 0.831^{+0.067}_{-0.078} in flat LCDM from 2D cosmic shear, consistent with Planck within 1 sigma.

Reference graph

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