The Probability Distribution Function of the Sunyaev-Zel’dovich Power Spectrum: An Analytical Approach
The Probability Distribution Function of the Sunyaev-Zel’dovich Power Spectrum: An Analytical Approach
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DOI：
10.1086/522913
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发表时间：
2007-01
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影响因子：
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通讯作者：
Pengjie Zhang;R. Sheth
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文献类型：
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作者：
Pengjie Zhang;R. Sheth
Sunyaev-Zel'dovich（SZ）信号是高度非高斯的，因此SZ功率谱（沿着平均y参数）不提供SZ效应的完整描述。因此，SZ为基础的宇宙学参数和集群gastrophysics假设高斯约束将是有偏见的。我们推导出SZ功率谱的n点联合PDF的解析表达式。我们的推导，这是基于晕模型，有几个优点：它是表示在一个积分的形式，允许快速计算;它适用于任何给定的调查和任何给定的角度尺度;它是简单的，将许多的复杂性时出现的SZ信号建模。为了说明，我们使用我们的表达式来估计p（C），SZ功率谱的一点PDF。对于小的天空覆盖（适用于比马/CBI和Sunyaev Zel'dovich阵列实验），我们的分析表明，在几个弧分尺度上的p（C）预计将强烈倾斜，峰值远低于平均值，并具有延伸到高C值的长尾。在大天空覆盖范围的限制下（适用于南极望远镜和普朗克望远镜），p（C）接近高斯形式。然而，即使在这个极限下，功率谱的方差也与基于朴素高斯的估计有很大的不同，因为不同的高斯模型是强相关的，使得SZ频带功率的宇宙方差比朴素估计大得多。我们的分析也应该是有用的建模的PDF的引力透镜引起的功率谱在大振幅。
The Sunyaev-Zel'dovich (SZ) signal is highly non-Gaussian, so the SZ power spectrum (along with the mean y-parameter) does not provide a complete description of the SZ effect. Therefore, SZ-based constraints on cosmological parameters and on cluster gastrophysics which assume Gaussianity will be biased. We derive an analytic expression for the n-point joint PDF of the SZ power spectrum. Our derivation, which is based on the halo model, has several advantages: it is expressed in an integral form which allows quick computation; it is applicable to any given survey and any given angular scale; and it is straightforward to incorporate many of the complexities which arise when modeling the SZ signal. To illustrate, we use our expression to estimate p(Cℓ), the one-point PDF of the SZ power spectrum. For small sky coverage (applicable to BIMA/CBI and the Sunyaev Zel'dovich Array experiments), our analysis shows that p(Cℓ) on the several arcminute scale is expected to be strongly skewed, peaking at a value well below the mean and with a long tail which extends to high Cℓ values. In the limit of large sky coverage (applicable to the South Pole Telescope and Planck), p(Cℓ) approaches a Gaussian form. However, even in this limit, the variance of the power spectrum is very different from the naive Gaussian-based estimate, because different ℓ models are strongly correlated, making the cosmic variance of the SZ bandpower much larger than the naive estimate. Our analysis should also be useful for modeling the PDF of the power spectrum induced by gravitational lensing at large ℓ.