标题： 非高斯性下的双谱协方差：对数正态方法 显示英文标题

标题： The bispectrum covariance beyond Gaussianity: A log-normal approach

摘要： 为了研究并明确宇宙学场的统计特性，特别是可能的非高斯特征，需要准确的双谱和双谱协方差公式。 双谱是提供分布非高斯性的估计的最低阶统计量，而双谱协方差描述了双谱测量在不同尺度上的误差及其相关性。 目前，存在双谱的拟合公式和双谱协方差的解析表达式，但前者不够准确，后者包含多个复杂项，其中仅有一个可以从所研究场的功率谱中直接计算。 忽略所有高阶项会导致双谱协方差的高斯近似。 我们研究了这种高斯近似在二维非高斯随机场中的适用范围。 为此，我们模拟了高斯和非高斯随机场，后者由对数正态场表示，并通过简单的变换直接从前者获得。 从模拟场中，我们计算了不同非高斯度 \alpha 的功率谱、双谱以及从双谱样本方差得到的协方差，这相当于给定角度尺度 \theta g 上的偏度。我们发现，当 \alpha <0.6 时，高斯近似提供了良好的近似，当 \alpha < 1 时，提供了合理准确的近似，且在大于 8\theta g 的尺度上均如此。利用宇宙剪切模拟的结果，我们估计宇宙剪切会聚场在 \theta g~4" 时由 \alpha <0.7 描述。 因此，我们得出结论，双谱协方差的高斯近似很可能适用于当前和未来的宇宙剪切研究。 显示英文摘要

摘要： To investigate and specify the statistical properties of cosmological fields with particular attention to possible non-Gaussian features, accurate formulae for the bispectrum and the bispectrum covariance are required. The bispectrum is the lowest-order statistic providing an estimate for non-Gaussianities of a distribution, and the bispectrum covariance depicts the errors of the bispectrum measurement and their correlation on different scales. Currently, there do exist fitting formulae for the bispectrum and an analytical expression for the bispectrum covariance, but the former is not very accurate and the latter contains several intricate terms and only one of them can be readily evaluated from the power spectrum of the studied field. Neglecting all higher-order terms results in the Gaussian approximation of the bispectrum covariance. We study the range of validity of this Gaussian approximation for two-dimensional non-Gaussian random fields. For this purpose, we simulate Gaussian and non-Gaussian random fields, the latter represented by log-normal fields and obtained directly from the former by a simple transformation. From the simulated fields, we calculate the power spectra, the bispectra, and the covariance from the sample variance of the bispectra, for different degrees of non-Gaussianity \alpha, which is equivalent to the skewness on a given angular scale \theta g. We find that the Gaussian approximation provides a good approximation for \alpha<0.6 and a reasonably accurate approximation for \alpha< 1, both on scales >8\theta g. Using results from cosmic shear simulations, we estimate that the cosmic shear convergence fields are described by \alpha<0.7 at \theta g~4". We therefore conclude that the Gaussian approximation for the bispectrum covariance is likely to be applicable in ongoing and future cosmic shear studies.