Calibration of weak-lensing shear in the Kilo-Degree Survey

TL;DR

The paper develops and validates a comprehensive pipeline to measure weak-lensing shear in KiDS, combining self-calibration of noise bias, weight-bias corrections, and empirically calibrated residual biases using realistic GalSim-based image simulations. It demonstrates that, after calibration (including a robust 20x20-bin or resampling approach), multiplicative biases can be constrained to about 1% in KiDS tomographic bins, while additive biases are suppressed and PSF leakage is quantified. A key insight is the necessity to account for selection effects and calibration biases arising from using noisy observed properties; the work provides strategies to mitigate these through region- and tomographic-bin-aware calibration and resampling. The findings support KiDS cosmic shear analyses by delivering practical, testable bias corrections and clear guidance on uncertainty propagation, including a recommended prior on m and cross-bin correlation structure.

Abstract

We describe and test the pipeline used to measure the weak lensing shear signal from the Kilo Degree Survey (KiDS). It includes a novel method of `self-calibration' that partially corrects for the effect of noise bias. We also discuss the `weight bias' that may arise in optimally-weighted measurements, and present a scheme to mitigate that bias. To study the residual biases arising from both galaxy selection and shear measurement, and to derive an empirical correction to reduce the shear biases to $\lesssim 1\%$, we create a suite of simulated images whose properties are close to those of the KiDS survey observations. We find that the use of `self-calibration' reduces the additive and multiplicative shear biases significantly, although further correction via a calibration scheme is required, which also corrects for a dependence of the bias on galaxy properties. We find that the calibration relation itself is biased by the use of noisy, measured galaxy properties, which may limit the final accuracy that can be achieved. We assess the accuracy of the calibration in the tomographic bins used for the KiDS cosmic shear analysis, testing in particular the effect of possible variations in the uncertain distributions of galaxy size, magnitude and ellipticity, and conclude that the calibration procedure is accurate at the level of multiplicative bias $\lesssim 1\%$ required for the KiDS cosmic shear analysis.

Figures (19)

• Figure 1: $r$-band magnitude histograms of KiDS-450 data (black), GEMS survey data (blue) and UVUDF survey (cyan), with uncertainties given by the Poisson errors of each point. The red line is the best fit through KiDS-450 $20<m_r<23$ points, GEMS $25<m_r<26$ points and UVUDF $26<m_r<29$ datapoints and is used as the input magnitude distribution of the simulations.
• Figure 2: Distributions of PSF parameters in the simulations (red) and KiDS-450 (black) measured by lensfit using a 2.5 pixel weighting function. Shown are the distributions of measured pseudo-Strehl ratio, size and the two components of the ellipticity. The constant PSFs (for individual exposures) in the SCHOo l images give rise to very peaky distributions, but overall the range in properties in the data are matched by the image simulations.
• Figure 3: Comparison of KiDS-450 data (black) and SCHOo l simulations (red) for weighted normalised distributions of galaxy properties. From left to right, top to bottom: magnitude, size, SNR, modulus of the ellipticity $| \epsilon |$, lensfit weights, bulge fraction. The inset shows a zoom in of the ellipticity distributions for $\epsilon>0.8$.
• Figure 4: Ratio between the number of galaxies in the simulation and the data on a SNR and resolution grid defined using the real galaxies. The size of each data point is proportional to the total lensfit weight in each grid cell. The red stars indicate the grid points with a ratio of 0.
• Figure 5: Multiplicative (left panel) and additive (right panel) selection bias, $m$ and $c$, for the components aligned ($m_{\vert\vert},c_{\vert\vert}$) or cross-aligned ($m_{\times},c_{\times}$) with the PSF major axis orientation, as a function of galaxy magnitude, as discussed in §\ref{['sec:selectionbias']}. The grey band in the left panel indicates the requirement on the knowledge of the multiplicative bias set by KiDS450 in the context of a cosmic shear analysis.