Cosmic Shears Should Not Be Measured In Conventional Ways

TL;DR

The paper argues that conventional methods for measuring cosmic shear from galaxy images are flawed and proposes a new ratio-based estimator in Fourier space that provides unbiased shear measurements, improving weak lensing analysis.

Contribution

It introduces a novel ratio-based shear estimator in Fourier space that remains unbiased, addressing limitations of traditional averaging methods in weak lensing.

Findings

Conventional shear estimators are nonlinear and unreliable.

The proposed ratio estimator yields unbiased shear measurements.

Shear correlation functions should be computed as ratios of correlations.

Abstract

A long standing problem in weak lensing is about how to construct cosmic shear estimators from galaxy images. Conventional methods average over a single quantity per galaxy to estimate each shear component. We show that any such shear estimators must reduce to a highly nonlinear form when the galaxy image is described by three parameters (pure ellipse), even in the absence of the point spread function (PSF). In the presence of the PSF, we argue that this class of shear estimators do not likely exist. Alternatively, we propose a new way of measuring the cosmic shear: instead of averaging over a single value from each galaxy, we average over two numbers, and then take the ratio to estimate the shear component. In particular, the two numbers correspond to the numerator and denominators which generate the quadrupole moments of the galaxy image in Fourier space, as proposed in Zhang (2008). This yields a statistically unbiased estimate of the shear component. Consequently, measurements of the n-point spatial correlations of the shear fields should also be modified: one needs to take the ratio of two correlation functions to get the desired, unbiased shear correlation.