The bispectrum covariance beyond Gaussianity - A log-normal approach
The bispectrum covariance beyond Gaussianity - A log-normal approach
复制标题
超越高斯性的双谱协方差 - 对数正态方法
DOI：
10.1051/0004-6361/201118020
复制
发表时间：
2012
影响因子：
6.5
通讯作者：
Schneider
中科院分区：
文献类型：
--
作者：
Martin;Schneider
为了研究和确定宇宙场的统计特性，特别注意可能的非高斯特征，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。忽略所有高阶项的结果在高斯近似的双谱协方差的aims我们研究的有效范围的高斯近似的二维非高斯随机场的为此目的，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。在这样做时，我们通过选择相同的“相位”的高斯和非Gaussian field.ResultsWe发现，高斯近似的双谱协方差提供了一个很好的近似度的非高斯α≤ 0.5和一个相当准确的近似α≤ 1，无论是在尺度<$8 θg。对于较大的α值，高斯近似显然失效。利用宇宙剪切模拟的结果，我们估计在θg~ 4′′处宇宙剪切会聚场的描述为α = 0.7.结论我们认为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.
ContextTo 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 theGaussian approximationof the bispectrum covariance.AimsWe study the range of validity of this Gaussian approximation for two-dimensional non-Gaussian random fields.MethodsFor 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-Gaussianityα, which is equivalent to the skewness on a given angular scaleθg. In doing so, we minimize sample variance by selecting the same “phases” of the Gaussian and non-Gaussian fields.ResultsWe find that the Gaussian approximation of the bispectrum covariance provides a good approximation for degrees of non-Gaussianityα≤ 0.5 and a reasonably accurate approximation forα≤ 1, both on scales ≳ 8θg. For larger values ofα, the Gaussian approximation clearly breaks down. Using results from cosmic shear simulations, we estimate that the cosmic shear convergence fields are described byα≲ 0.7 atθg~ 4′′.ConclusionsWe therefore conclude that the Gaussian approximation for the bispectrum covariance is likely to be applicable in ongoing and future cosmic shear studies.
登录
查看更多内容
平坦天空极限下的双谱协方差
影响因子：
6.5
作者：
B. Joachimi;X. Shi;P. S. A. F. Astronomie;Universitat Bonn University College London
通讯作者：
Universitat Bonn University College London
DOI：
10.1111/j.1365-2966.2010.17430.x
发表时间：
2010-05
影响因子：
4.8
作者：
E. Semboloni;T. Schrabback;L. Waerbeke;S. Vafaei;J. Hartlap;S. Hilbert
通讯作者：
E. Semboloni;T. Schrabback;L. Waerbeke;S. Vafaei;J. Hartlap;S. Hilbert
DOI：
10.1046/j.1365-8711.2001.04281.x
发表时间：
2000-09
影响因子：
4.8
作者：
R. Scoccimarro;H. Couchman
通讯作者：
R. Scoccimarro;H. Couchman
弱透镜场的对数正态性质
DOI：
--
发表时间：
2002
期刊：
影响因子：
--
作者：
A. Taruya;M. Takada;T. Hamana;I. Kayo;T. Futamase
通讯作者：
T. Futamase
高斯初始条件下宇宙密度涨落的概率分布函数：单点和两点对数正态模型预测与 N 体模拟的比较
DOI：
10.1086/323227
发表时间：
2001
期刊：
The Astrophysical Journal
影响因子：
--
作者：
I. Kayo;A. Taruya;Y. Suto
通讯作者：
Y. Suto