AKRA 2.0: Accurate Kappa Reconstruction Algorithm for masked shear catalog

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 $C_κ^{\rm{rec}}$ and the correlation coefficient with the true $κ$ map $r_\ell$ achieve accuracies of $(1-C_\ell^{\rm{rec}}/C_\ell^{\rm{true}}) \lesssim 1\%$ and $(1-r_\ell) \lesssim 1\%$, respectively. Our algorithm is capable of straightforwardly handling further issues such as inhomogeneous shape measurement noise, which we will address in subsequent analysis.

Figures (17)

• Figure 1: Algorithm flow chart of the AKRA 2.0 algorithm. The process initiates with the yellow hexagon, representing the generation of the observed shear catalog, which includes essential data for each galaxy indexed by $i$: shear components $\gamma_{1,2}^{i}$, weight $w^{i}$, and celestial coordinates ($\theta_{\rm RA}^{i}$, $\theta_{\rm Dec}^{i}$). Subsequently, the workflow is divided into two main analysis steps: Step 1 (red panels) applies the AKRA-sphere algorithm for large-scale analysis, and Step 2 (blue panels) employs the AKRA-flat algorithm for small-scale analysis. The results from both scales are integrated to produce the final convergence map (step 3).
• Figure 2: Input data applying DESI imaging surveys DR8 mask. From left to right, the panels show the masked shear field $\gamma_{1}^{m}(\hat{\boldsymbol{n}})$, $\gamma_{2}^{m}(\hat{\boldsymbol{n}})$, and the mask $m(\hat{\boldsymbol{n}})$ (referred to as A1), respectively.
• Figure 3: Results for the DESI imaging surveys DR8 mask using AKRA 2.0 (top row) and the KS direct inversion method (bottom row). (a) Comparison of the results is made with the reconstructed map $\kappa^{\rm{rec}}$ and residual maps normalized by the root mean square (r.m.s.) of the true signal $| \kappa^{\text{true}} - \kappa^{\text{rec}}/\kappa^{\text{true}}_{\text{RMS}}|$. (b) The $\kappa^{\rm rec}$-$\kappa^{\rm true}$ scatter plot for unmasked pixels. The data points are displayed as gray dots, with the x-axis and y-axis denoting the pixel values for the input $\kappa$ map and the reconstructed $\kappa$ map, respectively. The blue dashed line represents the result obtained from fitting a regression model to the pixels from the data points, while the black solid line indicates the ideal result. The slope $s$ of the blue dashed line, PCC $\rho$, and localization measure $L$ are also shown in the panels.
• Figure 4: Results for 100 realizations. Power spectrum ratio (left panel) and cross-correlation coefficient (right panel) using the DESI imaging surveys DR8 mask. The blue and red regions represent the 1$\sigma$ confidence interval. The deviations from $1$ are also illustrated in the bottom panels.
• Figure 5: An illustration of the CSST-like mask used in the CSST forcast simulation. This mask combines the CSST mask derived from cosmic shear forecasts, with a random mask having a 20% mask fraction. The mask will be employed to evaluate the performance of both the AKRA 2.0 and KS methods.