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Consistent cosmic shear in the face of systematics: a B-mode analysis of KiDS-450, DES-SV and CFHTLenS

Marika Asgari, Catherine Heymans, Hendrik Hildebrandt, Lance Miller, Peter Schneider, Alexandra Amon, Ami Choi, Thomas Erben, Christos Georgiou, Joachim Harnois-Deraps, Konrad Kuijken

TL;DR

COSEBIs enable clean $E$-/$B$-separation over finite angular ranges to diagnose non-lensing $B$-modes in KiDS-450, DES-SV, and CFHTLenS. The authors model a suite of systematics, including PSF leakage, repeating additive biases, random PSF residuals, and a novel photometric redshift selection bias, using mock SLICS/KiDS-like data to interpret $B$-mode signatures and their impact on cosmological inferences. They find strong $B$-modes in DES-SV (up to $5.5\sigma$ tomographic), weaker or absent $B$-modes in KiDS-450 and CFHTLenS in many analyses, and show that systematic-induced biases can push $\Sigma_8=\sigma_8(\Omega_m/0.3)^\alpha$ high, underscoring the need for robust $B$-mode diagnostics in future surveys. The study advocates using COSEBIs and compressed COSEBIs for $B$-mode null tests and cosmology-relevant data compression, while highlighting a newly identified photometric-redshift selection bias as a key systematic to mitigate. Together, these results advance practical guidelines for detecting and mitigating systematics in weak lensing cosmic shear analyses.

Abstract

We analyse three public cosmic shear surveys; the Kilo-Degree Survey (KiDS-450), the Dark Energy Survey (DES-SV) and the Canada France Hawaii Telescope Lensing Survey (CFHTLenS). Adopting the COSEBIs statistic to cleanly and completely separate the lensing E-modes from the non-lensing B-modes, we detect B-modes in KiDS-450 and CFHTLenS at the level of about 2.7 $σ$. For DES- SV we detect B-modes at the level of 2.8 $σ$ in a non-tomographic analysis, increasing to a 5.5 $σ$ B-mode detection in a tomographic analysis. In order to understand the origin of these detected B-modes we measure the B-mode signature of a range of different simulated systematics including PSF leakage, random but correlated PSF modelling errors, camera-based additive shear bias and photometric redshift selection bias. We show that any correlation between photometric-noise and the relative orientation of the galaxy to the point-spread-function leads to an ellipticity selection bias in tomographic analyses. This work therefore introduces a new systematic for future lensing surveys to consider. We find that the B-modes in DES-SV appear similar to a superposition of the B-mode signatures from all of the systematics simulated. The KiDS-450 and CFHTLenS B-mode measurements show features that are consistent with a repeating additive shear bias.

Consistent cosmic shear in the face of systematics: a B-mode analysis of KiDS-450, DES-SV and CFHTLenS

TL;DR

COSEBIs enable clean -/-separation over finite angular ranges to diagnose non-lensing -modes in KiDS-450, DES-SV, and CFHTLenS. The authors model a suite of systematics, including PSF leakage, repeating additive biases, random PSF residuals, and a novel photometric redshift selection bias, using mock SLICS/KiDS-like data to interpret -mode signatures and their impact on cosmological inferences. They find strong -modes in DES-SV (up to tomographic), weaker or absent -modes in KiDS-450 and CFHTLenS in many analyses, and show that systematic-induced biases can push high, underscoring the need for robust -mode diagnostics in future surveys. The study advocates using COSEBIs and compressed COSEBIs for -mode null tests and cosmology-relevant data compression, while highlighting a newly identified photometric-redshift selection bias as a key systematic to mitigate. Together, these results advance practical guidelines for detecting and mitigating systematics in weak lensing cosmic shear analyses.

Abstract

We analyse three public cosmic shear surveys; the Kilo-Degree Survey (KiDS-450), the Dark Energy Survey (DES-SV) and the Canada France Hawaii Telescope Lensing Survey (CFHTLenS). Adopting the COSEBIs statistic to cleanly and completely separate the lensing E-modes from the non-lensing B-modes, we detect B-modes in KiDS-450 and CFHTLenS at the level of about 2.7 . For DES- SV we detect B-modes at the level of 2.8 in a non-tomographic analysis, increasing to a 5.5 B-mode detection in a tomographic analysis. In order to understand the origin of these detected B-modes we measure the B-mode signature of a range of different simulated systematics including PSF leakage, random but correlated PSF modelling errors, camera-based additive shear bias and photometric redshift selection bias. We show that any correlation between photometric-noise and the relative orientation of the galaxy to the point-spread-function leads to an ellipticity selection bias in tomographic analyses. This work therefore introduces a new systematic for future lensing surveys to consider. We find that the B-modes in DES-SV appear similar to a superposition of the B-mode signatures from all of the systematics simulated. The KiDS-450 and CFHTLenS B-mode measurements show features that are consistent with a repeating additive shear bias.

Paper Structure

This paper contains 27 sections, 44 equations, 25 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Methods
  3. E/B-mode 2PCFs
  4. COSEBIs
  5. CCOSEBIs
  6. Covariance matrix
  7. Data
  8. Results: Survey E/B-modes
  9. Modelling systematics
  10. Shear measurement errors
  11. Point spread function (PSF) leakage: $\alpha \epsilon^*$
  12. Regular repeating additive pattern: $c(x,y)$
  13. Random but correlated noise: $\beta\, \delta \epsilon^*$
  14. Photometric redshift selection bias
  15. Results: Mock E/B-modes
  16. ...and 12 more sections

Figures (25)

  • Figure 1: Log-COSEBIs filter functions, $T_{\pm n}(\theta)$. These filter functions convert $\xi_\pm$ to COSEBIs E and B modes through equations \ref{['eq:EnReal']} and \ref{['eq:BnReal']}. We show four example $n$-modes for each filter for the angular separation range of $[0.5', 100']$. By definition $T_{\pm n}(\theta)$ are equal to zero outside of the range of their support.
  • Figure 2: Log-COSEBIs weight functions, $W_{n}(\ell)$, normalized to their maximum value. These weight functions convert E and B shear power spectra to COSEBIs modes through equation \ref{['eq:EnBnFourier']}. Four example $n$-modes are shown for the angular range of $[0.5',100']$.
  • Figure 3: COSEBIs E-modes (left) and B-modes (right) for a single broad redshift bin. Results for DES-SV are shown with blue squares, KiDS-450 with black stars and CFHTLenS with magenta triangles. The angular ranges are shown for each row in the upper right corner. In addition, the significance of the B-modes is shown as $p$-values for each survey and angular range. E-mode predictions are calculated using the best fitting cosmological parameter values given in Table\ref{['tab:CosmoParam']} for DES-SV (solid), KiDS-450 (dashed) and CFHTLenS (dotted). Note that COSEBIs modes are discrete and the theory values are connected to each other only as a visual aid. A zero-line is also shown for reference.
  • Figure 4: CCOSEBIs E and B-modes for non-tomographic (left) and tomographic (right) analyses. The E-modes are shown as empty symbols, with the B-modes shown as filled symbols, for DES-SV (blue squares), KiDS-450 (black stars) and CFHTLenS (magenta triangles). The analysis is conducted over three different angular ranges, denoted in the upper right corner of each panel. The CCOSEBIs mode is indicated on the horizontal-axis. E-mode predictions are calculated using the best fitting cosmological parameter values given in Table\ref{['tab:CosmoParam']} for DES-SV (solid), KiDS-450 (dashed) and CFHTLenS (dotted). A zero-line is also shown for reference.
  • Figure 5: $\xi_{\rm E}$ and $\xi_{\rm B}$ E/B-modes for a single broad redshift bin. The E-modes are shown as empty symbols, with the B-modes shown as filled symbols, for DES-SV (blue squares), KiDS-450 (black stars) and CFHTLenS (magenta triangles). The DES-SV and CFHTLenS results are horizontally offset relative to KiDS-450 to aid visualisation. E-mode predictions for $\xi_{\rm E}$ are calculated using the best fitting cosmological parameter values given in Table\ref{['tab:CosmoParam']} for DES-SV (solid), KiDS-450 (dashed) and CFHTLenS (dotted). A zero-line is also shown for reference. We detect significant B-modes in all cases as shown by the $p$-values, in the legend, which determine the probability of the data B-modes given a null B-mode model.
  • ...and 20 more figures