Improving the accuracy of mass reconstructions from weak lensing: from the shear map to the mass distribution

TL;DR

This paper analyzes and optimizes weak lensing mass reconstruction methods by studying two-point correlation functions, leading to improved accuracy and kernel selection for better mass distribution estimates.

Contribution

It provides a statistical framework for error assessment in non-local weak lensing mass reconstructions, highlighting the benefits of curl-free kernels.

Findings

Proper error estimation requires two-point correlation functions.

Curl-free kernels improve reconstruction accuracy.

Analytical results clarify previous numerical simulations.

Abstract

In this paper we provide a statistical analysis of the parameter-free method often used in weak lensing mass reconstructions. It is found that a proper assessment of the errors involved in such a non-local analysis requires the study of the relevant two-point correlation functions. After calculating the two-point correlation function for the reduced shear, we determine the expected error on the inferred mass distribution and on other related quantities, such as the total mass, and derive the error power spectrum. This allows us to optimize the reconstruction method, with respect to the kernel used in the inversion procedure. In particular, we find that curl-free kernels are bound to lead to more accurate mass reconstructions. Our analytical results clarify the arguments and the numerical simulations by Seitz & Schneider (1996).