AKRA 2.0: Accurate Kappa Reconstruction Algorithm for masked shear catalog
Yuan Shi, Pengjie Zhang, Furen Deng, Shuren Zhou, Hongbo Cai, Ji Yao, Zeyang Sun · Journal of Cosmology and Astroparticle Physics · 2025
Abstract Cosmic shear surveys serve as a powerful tool for mapping the underlying matter density field, including non-visible dark matter. A key challenge in cosmic shear surveys is the accurate reconstruction of lensing convergence ( κ ) maps from shear catalogs impacted by survey boundaries and masks, which seminal Kaiser-Squires (KS) method are not designed to handle. To overcome these limitations, we previously proposed the Accurate Kappa Reconstruction Algorithm (AKRA), a prior-free maximum likelihood map-making method. Initially designed for flat sky scenarios with periodic boundary conditions, AKRA has proven successful in recovering high-precision κ maps from masked shear catalogs. In this work, we upgrade AKRA to AKRA 2.0 by integrating the tools designed for spherical geometry. This upgrade employs spin-weighted spherical harmonic transforms to reconstruct the convergence field over the full sky. To optimize computational efficiency, we implement a scale-splitting strategy that segregates the analysis into two parts: large-scale analysis on the sphere (referred to as AKRA-sphere) and small-scale analysis on the flat sky (referred to as AKRA-flat); the results from both analyses are then combined to produce final reconstructed κ map. We tested AKRA 2.0 using simulated shear catalogs with various masks, demonstrating that the reconstructed κ map by AKRA 2.0 maintains high accuracy. For the reconstructed κ map in unmasked regions, the reconstructed convergence power spectrum C κ rec and the correlation coefficient with the true κ map r ℓ achieve accuracies of (1- C ℓ rec / C ℓ true ) ≲ 1% and (1- r ℓ ) ≲ 1%, respectively. Our algorithm is capable of straightforwardly handling further issues such as inhomogeneous shape measurement noise, which we will address in subsequent analysis.