2026/07/31 by Taisei Terawaki, Masahiro Takada
Physics and Astronomy · #astro-ph.CO
13 pages, 8 figures
arxiv created 2026/07/31 · arxiv published 2026/07/31 · arxiv updated 2026/08/03
The pseudo-C_ℓ estimator recovers the true cosmic shear power spectrum by correcting for the survey window convolution while employing inverse-variance weighting based on intrinsic shape noise of source galaxies. However, this weighting scheme is optimal only on small angular scales where shape noise dominates. In this paper, we derive a quadratic estimator for the unwindowed cosmic shear power spectrum by maximizing the Gaussian likelihood of the pixelized galaxy-shape field using the full covariance matrix, which accounts for both sample variance and shape noise. By combining FFTs in the flat-sky approximation, the conjugate-gradient method, and Monte Carlo realizations of Gaussian ancillary fields, we substantially reduce the computational cost of estimating the Fisher matrix, a key ingredient of the estimator that requires repeated inverse-covariance matrix operations. Using Gaussian simulations of shape fields, we validate the method and demonstrate that it can recover the input E-mode power spectrum with statistically optimal precision across all angular scales. We then apply the method to shape fields generated from ray-tracing simulations for a ΛCDM cosmology and show that, compared with the pseudo-C_ℓ method, it reduces the statistical uncertainties in the E-mode power spectrum by 5--15% at multipoles of ℓ \lesssim 500. We further demonstrate that the method significantly suppresses E- to B-mode leakage across the full multipole range. Our estimator therefore provides a statistically optimal approach for measuring cosmic shear power spectra from wide-area galaxy survey data.