The impact of higher-order distortions on the precise measurement of weak gravitational lensing shear and flexion

TL;DR

This work formalizes a generalized framework for weak-lensing distortions by introducing $L^{N}_{M}$ and their reduced forms ${\cal L}^{N}_{M}$, and develops the Generalized Distortions Measurement method (GEM) to estimate them from galaxy images. By deriving analytic expressions for five lens models (Point Mass, SIS, Power Law, SIC, NFW) up to fifth order, the authors quantify how neglecting higher-order terms biases traditional shear and flexion measurements. Simulations show that including up to 4th and 5th order distortions can reduce systematic errors from a few percent to well below 1% in many scenarios, with error magnitude depending on lens strength and source size. The results highlight the practical importance of higher-order corrections for exploiting high-resolution data (e.g., JWST/Euclid) and for potential disentanglement of intrinsic shapes from lensing signals, ultimately enabling more precise cosmological inferences.

Abstract

In this paper, we investigate the impact of higher-order distortions on the precise measurement of weak gravitational lensing shear and flexion. We begin by defining generalized higher-order distortions and outlining methods for measuring them. Then, using several lens models, we examine how these distortions affect shear and flexion measurements. Our results show that neglecting higher-order distortions can introduce systematic errors of a few percent in both shear and flexion measurements, indicating that these effects cannot be ignored. Although the strength of these errors depends on factors such as lensing strength and the size of background sources, we demonstrate that simultaneous measurement of higher-order distortions can reduce the systematic errors to below 1% in most cases.

Figures (14)

• Figure 1: Measurement error ratio in the reduced shear for a background object with $r_g=r_s/16$. The horizontal axis shows the absolute value of lensing reduced shear. The vertical axis shows the absolute error ratio in the measured reduced shear, calculated as the difference between the theoretical value from the lens model and the measured value. The colors indicate the order of the shape measurement method.
• Figure 2: Comparison of the error ratios of reduced shear measured with GEM-2nd and GEM-4th. The horizontal axis shows the error ratio of the reduced shear measured with GEM-2nd, and the vertical axis shows that measured with GEM-4th.
• Figure 3: Same as Figure \ref{['fig:Error_Shr_NFW_4']}, but showing the error ratio in the reduced first flexion.
• Figure 4: Same as Figure \ref{['fig:Error_Shr_NFW_4']}, but showing the error ratio in the reduced second flexion.
• Figure 5: Same as Figure \ref{['fig:Error_Shr_ALL']}, but showing the error ratio in the reduced first flexion measured GEM-3rd and GEM-5th.