The Effects of Calibration on the Bias of Shear Measurements

TL;DR

This paper analyzes how calibration procedures affect biases in galaxy shear measurements, showing that calibration reduces additive bias but leaves residual multiplicative bias, and discussing when higher-order corrections are beneficial.

Contribution

It provides a theoretical understanding of calibration effects on shear measurement biases, highlighting the conditions under which different bias correction strategies are effective.

Findings

Calibration removes residual additive bias on average.

Residual multiplicative bias remains after calibration.

First-order bias correction is generally beneficial, higher-order correction is case-dependent.

Abstract

Forthcoming large-scale surveys will soon attempt to measure cosmic shear to an unprecedented level of accuracy, requiring a similarly high level of accuracy in the shear measurements of galaxies. Factors such as pixelisation, imperfect point-spread function (PSF) correction, and pixel noise can all directly or indirectly lead to biases in shear measurements, and so it can be necessary for shear measurement methods to be calibrated against internal, external, or simulated data to minimize bias. It is thus important to understand the nature of this calibration. In this paper, we show that a typical calibration procedure will on average leave no residual additive bias, but will leave a residual multiplicative bias. Additionally, the errors on the post-calibration bias parameters will be changed, and on average increased, from the errors on the pre-calibration measurements of these parameters, but that this is generally worth the benefit in decreasing the expected value of the multiplicative bias. We find that in most typical cases, it is worthwhile to apply a first-order bias correction, while a higher-order bias correction is only worthwhile for methods with intrinsically high multiplicative bias ($>10$ per cent) or when the simulation size is very small ($<10^6$ simulated galaxies).