In the recent years, the internal-linear-combination (ILC) method was investigated extensively in the context of reconstruction of Cosmic Microwave Background (CMB) temperature anisotropy signal using observations obtained by WMAP and Planck satellite missions. In this article, we, for the first time, apply the ILC method to reconstruct the large scale CMB E mode polarization signal, which serves as the unique probe of ionization history of the Universe, using simulated observations of 15 frequency CMB polarization maps of future generation COrE satellite mission. We find that usual ILC cleaned E mode map is highly erroneous due to presence of a chance-correlation between CMB and astrophysical foreground components in the empirical covariance matrix which is used to estimate the weight factors. The cleaned angular power spectrum for E mode is strongly biased and erroneous due to these chance correlation factors. In order to address the issues of bias and errors we extend and improve the usual ILC method for CMB E mode reconstruction by incorporating prior information of theoretical E mode angular power spectrum while estimating the weights for linear combination of input maps. Using the E mode covariance matrix effectively suppresses the CMB-foreground chance correlation power leading to an accurate reconstruction of cleaned CMB E mode map and its angular power spectrum. We provide a comparative study of the performance of the usual ILC and the new method over large angular scales of the sky and show that the later produces significantly statistically improved results than the former. The new E mode CMB angular power spectrum contains neither any significant negative bias at the low multipoles nor any positive foreground bias at relatively higher mutlipoles. The error estimates of the cleaned spectrum agree very well with the cosmic variance induced error.

中文翻译：

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在ILC算法中使用CMB协方差矩阵的先验信息在大角尺度上精确重建CMB E模式信号

近年来，在使用 WMAP 和普朗克卫星任务获得的观测值重建宇宙微波背景 (CMB) 温度各向异性信号的背景下，内部线性组合 (ILC) 方法得到了广泛研究。在本文中，我们首次应用 ILC 方法重建大尺度 CMB E 模式偏振信号，该信号作为宇宙电离历史的独特探测器，使用未来 15 个频率的 CMB 偏振图的模拟观测。一代核心卫星任务。我们发现，由于在用于估计权重因子的经验协方差矩阵中 CMB 和天体物理前景分量之间存在机会相关性，通常 ILC 清洁的 E 模式图是高度错误的。由于这些机会相关因素，E 模式的清洁角功率谱有很大的偏差和错误。为了解决偏差和误差问题，我们通过结合理论 E 模式角功率谱的先验信息，同时估计输入映射线性组合的权重，扩展和改进了用于 CMB E 模式重建的常用 ILC 方法。使用 E 模式协方差矩阵有效地抑制了 CMB-前景机会相关功率，从而准确重建清洁的 CMB E 模式图及其角功率谱。我们对通常的 ILC 和新方法在天空的大角尺度上的性能进行了比较研究，并表明后者在统计上比前者产生了显着改善的结果。新的 E 模式 CMB 角功率谱在低多极点处既不包含任何显着的负偏置，也不在相对较高的多极点处包含任何正前景偏置。清洁光谱的误差估计与宇宙方差引起的误差非常吻合。