互双谱的广义模态估计
General modal estimation for cross-bispectra
摘要：
我们描述了一个快速，最佳的估计测量角双谱之间的两个相关的弱非高斯字段（$Y$和$Z$）从观测数据集，基于一个可分离的模态双谱展开。我们的方法适用于（1）任何形状的输入理论双谱模板（可因式分解或不可因式分解），（2）偶数和奇数$\ell_1 + \ell_2 + \ell_3$多极域，以及（3）振幅（$f_{\rm NL})$双谱估计和全双谱重建，考虑（$YYY$、$ZZZ$、$YYZ$和$ZZY$）形状的联合估计，或者独立估计自双谱（$YYY$或$ZZZ$）和交叉双谱（$YYZ$或$ZZY$）;因此，它具有相当高的通用性。本文所述方法已得到实施，并用于对$Planck$卫星的温度和极化宇宙微波背景图进行正式分析。
英文摘要：
We describe a fast, optimal estimator for measuring angular bispectra between two correlated weakly non-Gaussian fields ($Y$ and $Z$) from observational datasets, based on a separable modal bispectrum expansion. Our methodology is applicable to (1) any shape of the input theoretical bispectrum templates (factorizable or not), (2) both even and odd $\ell_1 + \ell_2 + \ell_3$ multipole domains and (3) both amplitude ($f_{\rm NL})$ bispectrum estimation and full bispectrum reconstruction, considering either joint estimation of ($YYY$, $ZZZ$, $YYZ$ and $ZZY$) shapes, or independent estimation of auto-bispectra ($YYY$ or $ZZZ$) and cross-bispectra ($YYZ$ or $ZZY$); hence, it has quite high versatility. The methodology described here was implemented and used for the official analysis of temperature and polarization cosmic microwave background maps from the $Planck$ satellite.
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