Practical Weak Lensing Shear Measurement with Metacalibration

TL;DR

This paper presents a practical, data-driven framework for weak-lensing shear calibration called metacalibration. By applying a small artificial shear to images and measuring the estimator’s response, it calibrates a wide range of shear estimators without heavy reliance on simulations, while addressing selection effects and correlated noise. The authors derive a formalism for mean and two-point shear statistics, implement robust corrections, and validate the approach with challenging parametric and real-galaxy simulations, achieving sub-per-mille accuracy under varied conditions. They also identify key practical challenges for real surveys, including blending, missing data, and PSF modeling, outlining concrete paths for future improvements.

Abstract

Metacalibration is a recently introduced method to accurately measure weak gravitational lensing shear using only the available imaging data, without need for prior information about galaxy properties or calibration from simulations. The method involves distorting the image with a small known shear, and calculating the response of a shear estimator to that applied shear. The method was shown to be accurate in moderate sized simulations with galaxy images that had relatively high signal-to-noise ratios, and without significant selection effects. In this work we introduce a formalism to correct for both shear response and selection biases. We also observe that, for images with relatively low signal-to-noise ratios, the correlated noise that arises during the metacalibration process results in significant bias, for which we develop a simple empirical correction. To test this formalism, we created large image simulations based on both parametric models and real galaxy images, including tests with realistic point-spread functions. We varied the point-spread function ellipticity at the five percent level. In each simulation we applied a small, few percent shear to the galaxy images. We introduced additional challenges that arise in real data, such as detection thresholds, stellar contamination, and missing data. We applied cuts on the measured galaxy properties to induce significant selection effects. Using our formalism, we recovered the input shear with an accuracy better than a part in a thousand in all cases.

Figures (10)

• Figure 1: Example of simulated galaxy images. Each image is a composite of a bulge and disk, plus knots of star formation. The half-light radius is the same for all components, while the fraction of light in each component varies. In the upper left and upper right we show pure bulge and pure disk models, respectively. In the lower left we show a disk with half the light in knots, and in the lower right we show a pure "irregular" galaxy composed entirely of knots. Each model was convolved by a Moffat PSF and pixelized. For demonstration purposes, we here show very large models to make the detailed structure visible; the galaxies used for our shear tests are typically much smaller than the PSF (see figure \ref{['fig:psimhlrcompare']}).
• Figure 2: Distribution of half-light-radius $r_{50}$ in the parametric simulations. The solid line represents the distribution of input $r_{50}$, drawn from fits to COSMOS data. The dashed line represents the $r_{50}$ for objects that passed the initial $S/N > 5$ pre-cut. The $r_{50}$ of the PSF is shown as the vertical dotted line.
• Figure 3: Distribution of S/N in the parametric simulations. The solid curve represents the true input distribution, the dashed curve represents the objects that passed the initial pre-cut on measured$S/N$$> 5$. The measured $S/N$ was biased and noisy, resulting in a smooth selection on true $S/N$. This pre-cut does not sharply cut on magnitude and results in a catalog that is limited at COSMOS i-band magnitude $\sim$25.
• Figure 4: Distribution of properties in the COSMOS real galaxy simulations. The left panel contains the distribution of measured S/N, while the right panel contains the distribution of half-light-radius from the cosmos catalog for the input galaxies. For comparison, the distributions for the Bulge+Disk+Knots BDK simulations are overplotted as dashed lines.
• Figure 5: Distribution of metacalibration responses for galaxies and stars in the BDK+Stars simulation. Stars have mean response close to zero, and thus do not bias the overall shear calibration.