AI 中文总结
本研究针对伪$C_\ell$估计量仅在小角尺度最优的问题，提出一种结合FFT、共轭梯度法与蒙特卡洛模拟的无窗宇宙剪切功率谱二次估计量，可提升全尺度测量精度并抑制模泄漏。
AI 中文摘要
伪$C_\ell$估计量通过修正巡天窗卷积，同时采用基于源星系内禀形状噪声的逆方差加权，来恢复真实的宇宙剪切功率谱。然而，这种加权方案仅在形状噪声占主导的小角尺度上是最优的。\n本文中，我们通过利用包含样本方差和形状噪声的完整协方差矩阵，最大化像素化星系形状场的高斯似然，推导了一种用于无窗宇宙剪切功率谱的二次估计量。通过结合平天近似下的快速傅里叶变换（FFT）、共轭梯度法以及高斯辅助场的蒙特卡洛实现，我们大幅降低了估计费希尔矩阵的计算成本——费希尔矩阵是该估计量的关键组成部分，需要重复进行协方差矩阵求逆运算。\n我们利用形状场的高斯模拟验证了该方法，并证明它能在所有角尺度上以统计最优精度恢复输入的$E$模功率谱。随后我们将该方法应用于$\Lambda$CDM宇宙学的射线追踪模拟生成的形状场，结果表明，与伪$C_\ell$方法相比，该方法在多极矩$\ell \lesssim 500$时将$E$模功率谱的统计不确定度降低了5%–15%。我们进一步证明，该方法在整个多极矩范围内显著抑制了$E$模到$B$模的泄漏。因此，我们的估计量为从大天区星系巡天数据测量宇宙剪切功率谱提供了一种统计最优的方法。
英文摘要
The pseudo-$C_\ell$ 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 $Λ$CDM cosmology and show that, compared with the pseudo-$C_\ell$ method, it reduces the statistical uncertainties in the $E$-mode power spectrum by 5--15\% at multipoles of $\ell \lesssim 500$. 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.
Comments13 pages, 8 figures
