arXiv 1109.09442011-09-05astro-ph.COastro-ph.IM

超越高斯性的双谱协方差：对数正态方法

The bispectrum covariance beyond Gaussianity: A log-normal approach

Sandra Martin, Peter Schneider, Patrick Simon

备注：: 8 pages, 12 figures, submitted to Astronomy and Astrophysics
DOI：: 10.1051/0004-6361/201118020

摘要：

为了研究和确定宇宙场的统计特性，特别是可能的非高斯特征，需要精确的双谱和双谱协方差公式。双谱是提供分布的非高斯性的估计的最低阶统计量，并且双谱协方差描述了双谱测量的误差及其在不同尺度上的相关性。目前，确实存在双谱的拟合公式和双谱协方差的解析表达式，但前者不是很准确，后者包含几个复杂的条款，只有一个可以很容易地从所研究的领域的功率谱评估。忽略所有高阶项会导致双谱协方差的高斯近似。我们研究了二维非高斯随机场的高斯近似的有效范围。为此，我们模拟高斯和非高斯随机场，后者表示为对数正态场，并直接从前者通过一个简单的变换。从模拟的场，我们计算功率谱，双谱，和双谱的样本方差的协方差，对于不同程度的非高斯性α，这相当于在给定的角度尺度θg的偏斜。我们发现高斯近似在α<0.6时提供了一个很好的近似，在α< 1时提供了一个相当精确的近似，两者都是在>8θg的尺度上。利用宇宙剪切模拟的结果，我们估计在θg~4”处宇宙剪切辐合场可用α<0.7来描述。因此，我们的结论是高斯近似的双谱协方差可能适用于正在进行的和未来的宇宙剪切研究。

英文摘要：

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 α, which is equivalent to the skewness on a given angular scale θg. We find that the Gaussian approximation provides a good approximation for α<0.6 and a reasonably accurate approximation for α< 1, both on scales >8θg. Using results from cosmic shear simulations, we estimate that the cosmic shear convergence fields are described by α<0.7 at θg~4". We therefore conclude that the Gaussian approximation for the bispectrum covariance is likely to be applicable in ongoing and future cosmic shear studies.

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