The first AKRA mass map reconstruction from HSC Y1 data

TL;DR

The paper presents AKRA, a prior-free, maximum-likelihood method for reconstructing unbiased convergence maps from weak-lensing shear in the presence of masks and spatially varying noise. By solving the linear system $\boldsymbol{\gamma} = \mathbf{A}\boldsymbol{\kappa} + \boldsymbol{n}$ with a regularized inverse $\hat{\boldsymbol{\kappa}} = ( \mathbf{A}^T \mathbf{N}^{-1} \mathbf{A} + \mathbf{R} )^{-1} \mathbf{A}^T \mathbf{N}^{-1} \boldsymbol{\gamma}$ and a noise-covariance-aware $\mathbf{N}$, AKRA directly incorporates survey geometry into the reconstruction. Applied to the HSC Y1 data, AKRA yields convergences maps and power spectra across six fields, with unbiased recovery of two-point and non-Gaussian statistics validated against Kun mocks. The validation shows AKRA outperforms the traditional KS method, particularly near masks, and preserves higher-order information such as skewness and the one-point PDF, enabling robust non-Gaussian cosmological analyses. The work releases a complete κ-map product set and demonstrates AKRA's readiness for upcoming wide-field surveys and tomographic extensions.

Abstract

Weak lensing mass-mapping from shear catalogs faces systematic challenges from survey masks and spatially varying noise. To overcome these issues and reconstruct unbiased convergence $κ$ maps, we have constructed the AKRA (Accurate Kappa Reconstruction Algorithm), a prior-free and maximum-likelihood based analytical method. It has been validated for mock shear catalogs with a variety of survey masks. In this work, we present the first real-data application of the AKRA on the Subaru Hyper Suprime-Cam Year 1 (HSC Y1) data. We first validate AKRA using mock shear catalogs from the \texttt{Kun} simulation suite, with masks corresponding to the six HSC Y1 regions (\texttt{GAMA09H}, \texttt{GAMA15H}, \texttt{HECTOMAP}, \texttt{VVDS}, \texttt{WIDE12H}, and \texttt{XMMLSS}). The investigated statistics, including the lensing power spectrum, $\langle κ^2\rangle$, $\langle κ^3\rangle$, and the one-point probability distribution function of $κ$, are all unbiased. We then apply AKRA to the HSC Y1 shear catalog and provide reconstructed $κ$ maps ready for subsequent scientific analyses.

Figures (7)

• Figure 1: Overview of the mass map reconstruction pipeline. The left side shows the processing of HSC Y1 galaxy catalogs into shear maps and masked fields, while the right side shows parallel validation using mock simulations. The central AKRA module performs prior-free reconstruction of the convergence field.
• Figure 2: Weak lensing mass mapping results for the XMMLSS field with source galaxies in $z_{\text{best}}\in(0.3,1.5]$. Panels show (from left to right, top to bottom): (1) the effective source number density $n_\mathrm{eff}$; (2) the binary mask derived from $n_\mathrm{eff}$ (pixels with $n_\mathrm{eff}<10$ galaxies are excluded); (3) the AKRA reconstructed convergence $\kappa^{\rm AKRA}$; (4) the KS convergence $\kappa^{\rm KS}$; (5) the SNR map of $\kappa^{\rm AKRA}$; (6) the SNR map of $\kappa^{\rm KS}$. The convergence, and SNR maps are smoothed with a Gaussian window of $\sigma = 5$ arcmin for better demonstration.
• Figure 3: Overview of mass mapping results in the five representative HSC-Y1 fields: GAMA15H, GAMA09H, WIDE12H, HECTOMAP, and VVDS. For each field, panels (from left to right) show the effective source density $n_\mathrm{eff}$, the binary mask, and the AKRA reconstructed convergence maps $\kappa^{\rm AKRA}$. The convergence maps are smoothed with a Gaussian window of $\sigma = 5$ arcmin for demonstration.
• Figure 4: Power spectrum of the reconstructed convergence maps from HSC Y1 data in the redshift range $0.3<z_s\leq1.5$. From left to right, we show results for three large fields: XMMLSS, GAMA15H and GAMA09H. The error bars are estimated from 300 noise realizations per field. The black dashed curves indicate the theoretical power spectrum for a fiducial $\Lambda$CDM cosmology, shown for reference rather than as a best-fit model.
• Figure 5: Validation of reconstructed convergence power spectra from mock simulations. Panel (a) shows the ratio of noise-subtracted auto-spectra $C_\ell^{\rm rec}/C_\ell^{\rm true}$, and panel (b) shows the ratio of cross-spectra $C_\ell^{\rm rec\!-\!true}/C_\ell^{\rm true}$ between reconstructed and true fields. Results are averaged over 200 realizations per field, with error bars indicating the standard deviation. AKRA (in red) follows the true input spectrum across a broad multipole range, demonstrating that its treatment of masks and spatially varying noise preserves both large- and small-scale modes. KS (in blue), in contrast, underestimates power on all scales, especially on large scales. This difference illustrates that explicitly modeling the mask, as done in AKRA, is essential for an unbiased recovery of the convergence field.