标题： 探测CMB $B$-模极化统计性质的米氏泛函方法 显示英文标题

标题： Probing the statistical properties of CMB $B$-mode polarization through Minkowski Functionals

摘要： 未来宇宙微波背景（CMB）实验的主要目标是探测磁化类型$B$模式的偏振。在标准模型中，由于透镜效应的贡献，$B$模式的地图是一个强非高斯场。除了两点关联函数外，其他统计量对于挖掘偏振地图的信息同样非常重要。本文中，我们采用Minkowski泛函研究了透镜效应下的$B$模式地图的形态特性。我们发现，无论是全天空还是部分天空的调查，其非高斯性偏离都非常显著。作为分析的应用，我们研究了$B$模式地图中前景残差的形态印记。我们发现，即使是非常微小的前景残差，也可以通过Minkowski泛函分析被检测到。因此，这提供了一种互补的方法来研究CMB研究中的前景污染。 显示英文摘要

摘要： The detection of the magnetic type $B$-mode polarization is the main goal of future cosmic microwave background (CMB) experiments. In the standard model, the $B$-mode map is a strongly non-gaussian field due to the lensed component. Besides the two-point correlation function, the other statistics are also very important to dig the information of the polarization map. In this paper, we employ the Minkowski functionals to study the morphological properties of the lensed $B$-mode maps. We find that the deviations from Gaussianity are very significant for both full and partial-sky surveys. As an application of the analysis, we investigate the morphological imprints of the foreground residuals in the $B$-mode map. We find that even for very tiny foreground residuals, the effects on the map can be detected by the Minkowski functional analysis. Therefore, it provides a complementary way to investigate the foreground contaminations in the CMB studies.