arXiv astro-ph/01034782001-03astro-ph

从峰值分布确定宇宙微波背景结构

Determining cosmic microwave background structure from its peak distribution

A. Kashlinsky, C. Hernández--Monteagudo, F. Atrio--Barandela

备注：: To be published in Ap.J. Letters. Minor changes to match the journal version
发表信息：: Ap.J. (Letters), 2001, 557, L1
DOI：: 10.1086/323172

摘要：

提出了一种基于高斯宇宙微波背景宇宙微波背景（CMB）谱峰谷特性的快速准确提取CMB谱的新方法。我们构造了一个统计描述他们的角集群-类似于星系，2点角相关函数，$ξ_ν(θ)$。我们发现，增加峰值阈值，$ν$，$ξ_ν(θ)$强烈放大，并成为可测量的$ν\geq$ 1上的角度尺度$\leq 10^\circ$。它在每个尺度上的幅度唯一地依赖于CMB温度相关函数$C(θ)$，因此测量的$ξ_ν$可以被唯一地反转以获得$C(θ)$及其勒让德变换，CMB场的功率谱。因为在该方法中，CMB功率谱是从CMB场的高峰值/谷值推导出的，所以该过程仅进行$[f(ν)]^2N^2$操作，其中$f(ν)$是在$N$像素的图中具有$|δT|\geqν$标准偏差的像素的分数，并且例如对于$ν$ = 2和2.5分别为0.045和0.01。我们开发的方法的理论形式主义，并显示与详细的模拟，使用MAP任务参数，该方法允许非常准确地确定CMB功率谱从即将到来的CMB地图中只有$\sim(10^{-4}-10^{-3})\times N^2$操作。

英文摘要：

We present a new method for time-efficient and accurate extraction of the power spectrum from future cosmic microwave background (CMB) maps based on properties of peaks and troughs of the Gaussian CMB sky. We construct a statistic describing their angular clustering - analogously to galaxies, the 2-point angular correlation function, $ξ_ν(θ)$. We show that for increasing peak threshold, $ν$, the $ξ_ν(θ)$ is strongly amplified and becomes measurable for $ν\geq$1 on angular scales $\leq 10^\circ$. Its amplitude at every scale depends uniquely on the CMB temperature correlation function, $C(θ)$, and thus the measured $ξ_ν$ can be uniquely inverted to obtain $C(θ)$ and its Legendre transform, the power spectrum of the CMB field. Because in this method the CMB power spectrum is deduced from high peaks/troughs of the CMB field, the procedure takes only $[f(ν)]^2N^2$ operations where $f(ν)$ is the fraction of pixels with $|δT|\geqν$ standard deviations in the map of $N$ pixels and is e.g. 0.045 and 0.01 for $ν$=2 and 2.5 respectively. We develop theoretical formalism for the method and show with detailed simulations, using MAP mission parameters, that this method allows to determine very accurately the CMB power spectrum from the upcoming CMB maps in only $\sim(10^{-4}-10^{-3})\times N^2$ operations.

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