Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Reconstructing spatially-varying multiplicative bias for Stage IV weak lensing galaxy surveys with a quadratic estimator

Konstantinos Tanidis, David Alonso, Lance Miller, Joachim Harnois-Déraps

TL;DR

The paper addresses spatially varying multiplicative shear bias $m(oldsymbol{\theta})$ in weak lensing by introducing a quadratic estimator that exploits EB-mode coupling to reconstruct $m$ to first order. Building on the CMB lensing analogy, it derives the off-diagonal $E$-$B$ correlations induced by $m$ and formulates an optimal estimator $\hat{m}(\boldsymbol{L})$ with inverse-variance weighting and a normalization ensuring unbiased, minimum-variance recovery. The method is tested with Gaussian and non-Gaussian simulations (including cosmo-SLICS N-body maps) across large and small field patches, showing that 5% rms $m$-bias patterns are detectable after stacking of a few hundred to thousand patches, while 1% rms patterns require substantially more data but remain within near-future survey capabilities. Robustness tests indicate insensitivity to moderate cosmology mis-specification, negligible impact from additive bias, and resilience to intrinsic alignments and baryonic effects, making the approach practical for Euclid/LSST-era systematics control and mitigation.

Abstract

We present a quadratic estimator that detects and reconstructs spatially-varying multiplicative ($m-$) bias in weak lensing shear measurements, by exploiting the $EB$ mode coupling that it generates. The method combines $E$ and $B$ modes with inverse-variance weights, to yield an unbiased reconstruction of $m(\boldsymbolθ)$ to first order. We study the ability of future Stage IV surveys to obtain an unbiased reconstruction of the $m$-bias in differing scenarios, considering differing bias morphologies, and characteristic scales, as well as differing metrics to quantify the signal-to-noise ratio of the reconstructed map. Considering an $m$ pattern repeating on $\sim 1^\circ\times1^\circ$ sky patches, as might be the case for an $m$ field caused by focal-plane systematics. With a Euclid-like redshift distribution, we find that $\sim5\%$ rms variations in $m$-bias may be detected at the 20$σ$ level, after stacking between $\sim400$ and $\sim1000$ patches (rising to between $\sim2800$ and $\sim7600$ for $1\%$ rms variations, data volumes that are becoming available with upcoming surveys), depending on the morphology of the $m$ pattern. We show that these results are robust against the cosmological model assumed in the reconstruction, as well as the presence of intrinsic alignments or baryonic effects, and that the method shows no spurious response to additive ($c-$) bias. These results demonstrate that percent-level, spatially-varying $m-$bias can be detected at high significance, enabling diagnosis and mitigation in the Stage IV weak lensing era.

Reconstructing spatially-varying multiplicative bias for Stage IV weak lensing galaxy surveys with a quadratic estimator

TL;DR

The paper addresses spatially varying multiplicative shear bias in weak lensing by introducing a quadratic estimator that exploits EB-mode coupling to reconstruct to first order. Building on the CMB lensing analogy, it derives the off-diagonal - correlations induced by and formulates an optimal estimator with inverse-variance weighting and a normalization ensuring unbiased, minimum-variance recovery. The method is tested with Gaussian and non-Gaussian simulations (including cosmo-SLICS N-body maps) across large and small field patches, showing that 5% rms -bias patterns are detectable after stacking of a few hundred to thousand patches, while 1% rms patterns require substantially more data but remain within near-future survey capabilities. Robustness tests indicate insensitivity to moderate cosmology mis-specification, negligible impact from additive bias, and resilience to intrinsic alignments and baryonic effects, making the approach practical for Euclid/LSST-era systematics control and mitigation.

Abstract

We present a quadratic estimator that detects and reconstructs spatially-varying multiplicative () bias in weak lensing shear measurements, by exploiting the mode coupling that it generates. The method combines and modes with inverse-variance weights, to yield an unbiased reconstruction of to first order. We study the ability of future Stage IV surveys to obtain an unbiased reconstruction of the -bias in differing scenarios, considering differing bias morphologies, and characteristic scales, as well as differing metrics to quantify the signal-to-noise ratio of the reconstructed map. Considering an pattern repeating on sky patches, as might be the case for an field caused by focal-plane systematics. With a Euclid-like redshift distribution, we find that rms variations in -bias may be detected at the 20 level, after stacking between and patches (rising to between and for rms variations, data volumes that are becoming available with upcoming surveys), depending on the morphology of the pattern. We show that these results are robust against the cosmological model assumed in the reconstruction, as well as the presence of intrinsic alignments or baryonic effects, and that the method shows no spurious response to additive () bias. These results demonstrate that percent-level, spatially-varying bias can be detected at high significance, enabling diagnosis and mitigation in the Stage IV weak lensing era.

Paper Structure

This paper contains 19 sections, 27 equations, 6 figures.

Table of Contents

  1. Introduction
  2. Method
  3. Introduction to the method
  4. Spatially-varying shear bias and mode-coupling
  5. Quadratic estimator for the $m-$bias field
  6. Survey simulations and $m-$bias realisations
  7. The testing methodology
  8. Galaxy survey sample
  9. $m-$bias patterns
  10. Gaussian realisations
  11. N-body simulations
  12. Results
  13. Evaluation of results
  14. Signal-to-noise estimates
  15. $m-$bias reconstruction on large scales
  16. ...and 4 more sections

Figures (6)

  • Figure 1: Left: Galaxy redshift distribution $p(z)$ for a Euclid-like photometric sample (see Eq.\ref{['eq:n_of_z']}). Middle: A blob-like $m-$bias given by Eq.\ref{['eq:blob_mbias']}. Right: A strip-like $m-$bias model given by Eq.\ref{['eq:strip_mbias']}. Both $m-$bias patterns have an rms of 5% and are $20\times20$ pixel grids.
  • Figure 2: The angular power spectra from an N-body (green) and a Gaussian (red) simulation at an area of $1\deg^2$ with their $1\sigma$ uncertainties and the input theory prediction (dashed black). The high-$\ell$ suppression visible in the figure is due to finite-resolution effects.
  • Figure 3: The 'template', 'data' and 'peak' SNR definitions as a function of the number of patches. We consider patches of $10\times10\deg^2$ and a 5% rms blob-like $m-$bias.
  • Figure 4: Top left: One input $\gamma_1$ component of the cosmic shear from Gaussian realisations. Top middle: Reconstruction of the 5% rms blob-like $m-$bias field at $\rm SNR_{\rm temp}$=10 with 600 realisations. Top right: Reconstruction of the same $m-$bias field at $\rm SNR_{\rm temp}$=20 with 2800 realisations. The grid area is 100 $\deg^2$ with $20\times20$ pixels. Similarly, the bottom panels show the 5% rms strip-like $m-$bias model reconstructed with 2000 (bottom middle) and 6700 realisations (bottom right).
  • Figure 5: Top left: One input $\gamma_1$ component of the cosmic shear from N-body realisations. Top right: Reconstruction of the 20% rms $m-$bias field at $\rm SNR_{\rm temp}$=81 with 50 simulations. The grid area is 100 $\deg^2$, with $100\times100$ pixels. Bottom panels are for a 20% rms strip-like $m-$bias, reconstructed with $\rm SNR_{\rm temp}$=81, using also 50 simulations.
  • ...and 1 more figures