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

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 $ξ_\pm^{\mathrm{B}}(θ)$, 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.

Figures (8)

• Figure 1: Pure $E$/$B$-mode decomposition of the measured shear correlation functions for the fiducial catalog. Panels show $\xi_+$ (left) and $\xi_-$ (right) decomposed into total (black circles), $E$-mode (teal squares), $B$-mode (crimson $\times$), and ambiguous (purple triangles) components following schneider.etal22. The $E$ modes trace the lensing signal, while $B$ modes---which should vanish for pure gravitational lensing---diagnose systematic contamination. Ambiguous modes capture boundary effects from the finite angular range. Shaded regions indicate fiducial scale cuts. Error bars are derived from semi-analytical covariance propagation (\ref{['sec:covariance']}).
• Figure 2: COSEBI $B$-mode amplitudes for the fiducial catalog, normalized by uncertainty ($B_n/\sigma_n$). Orange squares: full angular range $1$--$250$ arcmin; blue circles: fiducial scale cuts $12.0$--$83.0$ arcmin. The shaded region highlights mode numbers $n \leq 6$, which capture nearly all cosmological information. On the full range, $n=1$ shows a $>4\,\sigma$ excess, with oscillatory structure through all twenty modes, consistent with repeating additive shear bias (\ref{['sec:discussion']}). Scale cuts suppress the first-mode excess to below 1.0 $\sigma$ and largely eliminate the oscillatory signature (see \ref{['tab:pte_results']}).
• Figure 3: Harmonic-space power spectra for the fiducial catalog, normalized by uncertainty. Top: $B$-mode auto-power $C_\ell^{BB}/\sigma$. Bottom: $E$-$B$ cross-power $C_\ell^{EB}/\sigma$. $C_\ell^{BB}$ is predominantly positive across the fiducial range. $C_\ell^{EB}$ scatters symmetrically around zero, suggesting that any $B$-mode contamination is not strongly correlated with the lensing signal.
• Figure 4: Pure $E$/$B$-mode correlation-function covariance matrix for the fiducial catalog from semi-analytical propagation of 2000 Monte Carlo realizations. The matrix is organized into six blocks: $\xi_+^{\mathrm{E}}$, $\xi_-^{\mathrm{E}}$, $\xi_+^{\mathrm{B}}$, $\xi_-^{\mathrm{B}}$, $\xi_+^{\mathrm{amb}}$, $\xi_-^{\mathrm{amb}}$, with 20 angular bins per block. Off-diagonal correlations arise from integral coupling in the pure-mode filters.
• 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 $\xi_\pm$ and $C_\ell$. Top: Pure $E$/$B$-mode correlation functions. Upper panels show $\xi_+$ and $\xi_-$ scaled by $\theta$; lower panels show $B$-mode components $\xi_\pm^{\mathrm{B}}/\sigma$. Middle: Harmonic-space power spectra $C_\ell^{BB}/\sigma$ and $C_\ell^{EB}/\sigma$. Bottom: COSEBI $B$-mode amplitudes $B_n/\sigma_n$ at full range (upper) and fiducial cuts (lower). Only the size-cut catalog passes all statistics at the fiducial scale cuts (\ref{['tab:pte_results']}).