基于目录的伪$C_\ell$的解析协方差
Analytical covariances for catalogue-based pseudo-$C_\ell$s
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中文总结 AI 辅助
研究基于目录的宇宙学可观测量角功率谱非连通协方差，提出基于窄核近似的方法，考虑多种微妙效应，通过与暴力方法比较及模拟验证，证明其在多种现实场景中准确且已实现于公开代码NaMaster。
中文摘要 AI 辅助
多个宇宙学可观测量，如星系过密度或宇宙切变，由天体物理源离散位置处采样的场组成。近期工作提出了估计此类场角功率谱的方法，避免构建像素化天图及其相关的有限分辨率效应。本文提出一种估计这些角功率谱非连通（即“高斯”）协方差的方法，解决了不同基于目录的场之间有效面积重叠以及目录离散性质产生的额外泊松类方差等微妙效应。该方法依赖窄核近似来考虑不同源对估计器的贡献，同时精确包含自对的类噪声贡献。我们将此方法与能为稀疏样本产生精确协方差的暴力方法明确比较，并通过模拟验证。结果表明该方法在现实场景中准确，涵盖密集和噪声主导数据集（如宇宙切变）以及稀疏、噪声主导的可观测量（如快速射电暴）。该方法已在公开代码NaMaster中实现。
英文摘要
Multiple cosmological observables, such as the galaxy overdensity or cosmic shear, consist of fields sampled at the discrete positions of astrophysical sources. Recent work has presented methods to estimate the angular power spectra of such fields, avoiding the construction of pixelated sky maps and the finite-resolution effects associated with them. In this work, we present a method to estimate the disconnected (also known as "Gaussian") covariance of these angular power spectra, addressing subtle effects such as the effective area overlap between different catalogue-based fields and the additional Poisson-like variance arising from the discrete nature of the catalogues. The method relies on the so-called Narrow-Kernel Approximation to account for the contribution of distinct source pairs to the estimator, while including the noise-like contributions from self-pairs exactly. We explicitly compare this approach with a brute-force method that can produce the exact covariance for sparse samples, and validate it against simulations. We show that the method is accurate in realistic scenarios, spanning both dense and noise-dominated datasets (e.g., cosmic shear) and sparse, noise-dominated observables (e.g., fast radio bursts). The method is implemented in the public code NaMaster.
