基于模式投影的无偏伪CI功率谱估计
Unbiased pseudo-Cl power spectrum estimation with mode projection
摘要：
随着当前和未来星系巡天所提供的灵敏度的稳步提高，两点关联函数测量值的稳健提取可能会越来越受到天体物理前景或观测系统的阻碍。模式投影的概念已被引入作为一种手段，以消除污染物，它是可能的，以构建一个空间映射反映预期的信号贡献。由于其计算效率相比，最小方差方法，次优伪CI（PCL）功率谱估计是一种流行的工具，用于分析高分辨率数据集。在这里，我们集成模式投影到PCL功率谱估计的框架。与最优估计得到的结果相比，我们表明，模板映射的未校正投影导致有偏功率谱。基于分析计算，我们找到了偏差的期望值的精确闭合形式表达式，并证明它们可以以允许数值有效评估的形式进行重新铸造，保持PCL估计算法的有利O（l_max^3）时间复杂度。使用模拟数据集，我们评估了各种分析参数的偏差的缩放，并证明它可以可靠地删除。我们的结论是，在模式投影相结合，PCL估计允许一个快速和强大的计算功率谱的存在系统的影响-属性的高需求的分析正在进行和未来的大尺度结构调查。
英文摘要：
With the steadily improving sensitivity afforded by current and future galaxy surveys, a robust extraction of two-point correlation function measurements may become increasingly hampered by the presence of astrophysical foregrounds or observational systematics. The concept of mode projection has been introduced as a means to remove contaminants for which it is possible to construct a spatial map reflecting the expected signal contribution. Owing to its computational efficiency compared to minimum-variance methods, the sub-optimal pseudo-Cl (PCL) power spectrum estimator is a popular tool for the analysis of high-resolution data sets. Here, we integrate mode projection into the framework of PCL power spectrum estimation. In contrast to results obtained with optimal estimators, we show that the uncorrected projection of template maps leads to biased power spectra. Based on analytical calculations, we find exact closed-form expressions for the expectation value of the bias and demonstrate that they can be recast in a form that allows a numerically efficient evaluation, preserving the favorable O(l_max^3) time complexity of PCL estimator algorithms. Using simulated data sets, we assess the scaling of the bias with various analysis parameters and demonstrate that it can be reliably removed. We conclude that in combination with mode projection, PCL estimators allow for a fast and robust computation of power spectra in the presence of systematic effects -- properties in high demand for the analysis of ongoing and future large scale structure surveys.
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