Hybrid estimation of cosmic microwave background polarization power spectra
Hybrid estimation of cosmic microwave background polarization power spectra
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DOI：
10.1111/j.1365-2966.2006.10486.x
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发表时间：
2006-07
影响因子：
4.8
通讯作者：
G. Efstathiou
中科院分区：
文献类型：
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作者：
G. Efstathiou
本文将前人提出的混合功率谱估计方法推广到宇宙微波背景辐射的极化功率谱估计中。混合功率谱估计是无偏的，我们表明，它是接近最佳的，在所有的多极，像素噪声满足一定的约束条件。此外，混合估计是计算速度快，可以很容易地被纳入到一个蒙特卡罗链普朗克规模的数据集，这可能是必不可少的考虑现实的噪声协方差和系统误差。简单的公式给出的协方差矩阵，包括不相关的非齐次仪器噪声，并对数值模拟进行了广泛的测试。我们比较的行为简单的伪C-1（PCL）估计与最大似然估计在低多极。对于真实的天空切割，最大似然估计非常显著地减少了E和B模式的混合。为了从具有真实天空切割的天空图中获得r << 0.1的标量-张量比的限制，最大似然方法或基于明确E和B模式的PCL估计器将是必不可少的。
This paper generalizes the hybrid power spectrum estimation method developed in a previous paper to the estimation of polarization power spectra of the cosmic microwave background radiation. The hybrid power spectrum estimator is unbiased and we show that it is close to optimal at all multipoles, provided the pixel noise satisfies certain constraints. Furthermore, the hybrid estimator is computationally fast and can easily be incorporated in a Monte Carlo chain for Planck-sized data sets, which may be essential to account for realistic noise covariance and systematic errors. Simple formulae are given for the covariance matrices, including uncorrelated inhomogeneous instrumental noise, and these are tested extensively against numerical simulations. We compare the behaviour of simple pseudo-C l (PCL) estimates with maximum-likelihood estimates at low multipoles. For realistic sky cuts, maximum-likelihood estimates reduce very significantly the mixing of E and B modes. To achieve limits on the scalar-tensor ratio of r << 0.1 from sky maps with realistic sky cuts, maximum-likelihood methods, or PCL estimators based on unambiguous E and B modes, will be essential.