Disconnected covariance of 2-point functions in large-scale structure
Disconnected covariance of 2-point functions in large-scale structure
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DOI：
10.1088/1475-7516/2019/01/016
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发表时间：
2018-11
影响因子：
6.4
通讯作者：
Yin Li;Sukhdeep Singh;Byeonghee Yu;Yu Feng;U. Seljak
中科院分区：
文献类型：
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作者：
Yin Li;Sukhdeep Singh;Byeonghee Yu;Yu Feng;U. Seljak
使用大规模结构探针的2点函数的优化分析需要精确的协方差矩阵。2点函数的协方差矩阵包括不连通部分和连通部分。虽然连接协方差仅在小尺度上变得重要，但断开协方差在大尺度上占主导地位，其中调查窗口具有显着影响。在这项工作中，我们开发了一种分析方法来计算断开的协方差，占窗口效应。在平天近似下导出的，我们的形式主义是适用于广泛的调查交换在弯曲的天空窗口函数。我们的方法适用于功率谱和相关函数，并适用于各种探针的协方差，包括多极和3D聚类的楔形，聚类和剪切的角度和投影统计，以及不同探针之间的交叉协方差。我们验证了分析协方差对样本协方差从星系模拟在两个测试情况下：（1）功率谱多极协方差，（2）联合协方差的投影相关函数和相关函数多极。我们的方法取得了很好的协议与模拟，而在一个可以忽略不计的计算成本。与模拟不同，我们的分析协方差没有采样噪声，这通常会导致数值问题和需要夸大误差。此外，我们的方法可以使用最佳拟合的功率谱作为输入，与使用基准模型的标准程序相比，基准模型可能会显着偏离真相。我们还表明，一个天真的对角功率谱协方差低估了我们的分析协方差相比，信噪比。本文附带的代码可以在https://github.com/eelregit/covdisc上找到。
Optimal analyses using the 2-point functions of large-scale structure probes require accurate covariance matrices. A covariance matrix of the 2-point function comprises the disconnected part and the connected part. While the connected covariance only becomes important on small scales, the disconnected covariance is dominant on large scales, where the survey window has a significant impact. In this work, we develop an analytical method to compute the disconnected covariance, accounting for the window effect. Derived under the flat-sky approximation, our formalism is applicable to wide surveys by swapping in the curved-sky window functions. Our method works for both the power spectrum and the correlation function, and applies to the covariances of various probes including the multipoles and the wedges of 3D clustering, the angular and the projected statistics of clustering and shear, as well as the cross covariances between different probes. We verify the analytic covariance against the sample covariance from the galaxy mock simulations in two test cases: (1) the power spectrum multipole covariance, and (2) the joint covariance of the projected correlation function and the correlation function multipoles. Our method achieve good agreement with the mocks, while at a negligible computational cost. Unlike mocks, our analytic covariance is free of sampling noise, which often leads to numerical problems and the need to inflate the errors. In addition, our method can use the best-fit power spectrum as input, in contrast to the standard procedure of using a fiducial model that may deviate significantly from the truth. We also show that a naive diagonal power spectrum covariance underestimates the signal-to-noise ratio compared to our analytic covariance. The code that accompanies this paper is available at https://github.com/eelregit/covdisc.