Analytical weak-lensing shear response of galaxy model fitting

TL;DR

This paper introduces a novel algebraic system called quintuple numbers to analytically determine how galaxy model fitting outputs respond to weak-lensing shear distortions, improving shear estimation accuracy.

Contribution

The paper develops quintuple numbers for propagating shear response through galaxy model fitting, enhancing understanding of shear biases in weak lensing analyses.

Findings

Multiplicative bias below 0.003 for ground-based images

Quintuple numbers effectively propagate shear response in model fitting

Validated approach with realistic blending simulations

Abstract

Galaxy model fitting is widely employed to estimate properties such as galaxy shape, size, and color. Understanding how the outputs of galaxy model fitting respond to weak-lensing shear distortions is crucial for accurate shear estimation and mitigating shear-related systematics in weak lensing image analyses. In this paper, we investigate how the fitted parameters - specifically flux, size, and shape - respond to weak-lensing shear distortions within the AnaCal framework. To achieve this, we introduce quintuple numbers, a novel algebraic system inspired by dual numbers from automatic differentiation. Quintuple numbers enable the propagation of shear response information throughout the entire model-fitting process by linking analytical pixel shear responses to those of the fitted parameters. We integrate quintuple numbers into the AnaCal framework to derive the shear responses of shapes estimated with model fitting and validate the pipeline using image simulations that include realistic blending. Our results demonstrate that the multiplicative bias remains below 0.003 for ground-based, oversampled images.