Nonlinear Weak Lensing reconstruction for Galaxy Clusters

TL;DR

This work addresses nonlinear weak-lensing mass reconstruction in galaxy clusters where the convergence $\kappa$ is non-negligible and the common $g\approx\gamma$ approximation breaks down. It introduces two key modifications to traditional KS/AKRA frameworks: (i) initializing the convergence with a model-based estimate via a Singular Isothermal Sphere and (ii) replacing binary masks with smooth transition masks to reduce numerical instabilities and spectral leakage. Through tests on two mock clusters (a toy two-$NFW$-halo model and a realistic Abell 2744-like B23 model), the authors demonstrate that AKRA-based reconstructions with a smooth mask and model-informed initialization (A3) achieve residuals as low as $\sim 0.003$ in unmasked regions and substantially suppress biases relative to KS methods. The approach improves mass-map fidelity in the nonlinear regime, provides practical guidance on masking and iteration stopping, and sets the stage for application to real cluster data with publicly available code.

Abstract

We present a numerical investigation of nonlinear cluster lens reconstruction using weak lensing mass mapping. Recent advances in imaging and shear estimation have pushed reliable reduced shear measurements closer to cluster cores, making mass reconstruction accessible in the nonlinear regime. However, the Kaiser-Squires based algorithm becomes unstable in cluster cores, where convergence $κ$ significantly deviates from zero and the linear approximation breaks down. To address this limitation, we develop a reconstruction framework with two key modifications: applying smooth masks to these regions and using a model-derived analytical solution as the initial guess, rather than assuming $κ= 0$. We validate our framework using simulated cluster lensing data with known mass distributions, incorporating realistic masks that arise from limitations in reduced shear measurements. We show that in the absence of shape noise, our framework yields high-fidelity mass reconstruction in regions of large reduced shear, with the best-performing method achieving residuals below $0.02 σ$ in the unmasked regions. This pushes mass reconstruction to higher accuracy in the nonlinear regime.

Figures (6)

• Figure 1: Iterative cluster mass reconstruction procedure.
• Figure 2: Comparison of reconstructed convergence maps for the toy model. Top panels: True convergence $\kappa_{\rm true}$, the binary mask with $g_{\rm th} = 0.4$ and masked reduced shear $g^{\rm m}$. Middle panels: Normalized residual $\sigma$ (Eq. \ref{['eq:sigma']}) for KS-based methods K1 and K2 at first and fifth iterations. Lower panels: Same as middle panels but for AKRA-based methods A1 and A2. The blue dashed box indicates the region where the mean $\sigma$ is computed. The mean $\sigma$ values are shown in each panel. The inner blue dashed contour outlines the masked region.
• Figure 3: Reconstructed convergence maps for the B23 model. Top panels: True convergence map, binary mask with $g_{\rm th} = 0.5$, and the masked reduced shear $g^{\rm m}$. Middle and lower panels: Normalized residuals for KS-based and AKRA-based methods, respectively.
• Figure 4: Iterative reconstruction results under different masking schemes. Top panels: A3 with smooth mask ($g_{\rm th} = 0.5$, $g_* = 0.3$) and normalized residuals. Middle panels: A2 with binary mask ($g_{\rm th} = 0.8$) and normalized residuals. Bottom panels: A3 with smooth mask ($g_{\rm th} = 0.8$, $g_* = 0.6$) and normalized residuals.
• Figure 5: Normalized residual maps at iterations 1--5 and 10 for the toy model. Rows from top to bottom correspond to methods K1, K2, A1, and A2. Mean $\sigma$ values within the evaluation region are indicated in each panel.