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arXiv 2308.03412astro-ph.CO
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用于CMB偏振数据的非参数极大似然成分分离

Non-parametric maximum likelihood component separation for CMB polarization data

Clément Leloup, Josquin Errard, Radek Stompor

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AI总结：

本文提出一种基于极大似然的“最小信息”非参数方法，用于在CMB偏振数据分析中分离前景与CMB信号，并证明其在恢复B模式偏振信号时性能与标准参数化方法相当。

摘要：

减轻前景贡献对宇宙微波背景（CMB）偏振测量的影响是现代CMB数据分析中的关键步骤，对于探测大尺度CMB B模式具有特别重要的意义。文献中已描述了大量基于不同假设的技术，旨在实现完整的成分分离或仅从CMB图中清理前景信号。在本工作中，我们在基于极大似然原理的统一框架内考虑这一问题，假设每个频率的信号可以表示为天空模板的线性混合。我们讨论了各种额外假设对程序最终结果的影响。我们发现成分分离问题可以在两种特定情况下完全解决：当我们知道所有成分的频率缩放，或者可以用有限数量的未知参数正确建模它们时，如参数化成分分离技术中的情况；或者当我们知道所有成分（前景和CMB）的统计特性，或者可以用有限数量的参数正确建模它们时，例如在类似SMICA的方法中。然而，我们也表明，如果我们仅旨在恢复清理后的CMB信号，则更宽松的假设就足够了。特别是，我们讨论了一种基于极大似然的“最小信息”非参数方法。该方法仅假设成分特性与天空方向无关，至少在天空的某些区域上如此，并且CMB协方差在有限数量的参数范围内是已知的。我们将该方法应用于即将到来的CMB实验背景下，以恢复CMB B模式偏振信号，并将其性能与标准参数化方法进行比较。

英文摘要：

Mitigation of the impact of foreground contributions to measurements of Cosmic Microwave Background (CMB) polarization is a crucial step in modern CMB data analysis and is of particular importance for a detection of large-scale CMB $B$ modes. A large variety of techniques, based on different assumptions and aiming at either a full component separation or merely cleaning the foreground signals from the CMB maps, have been described in the literature. In this work, we consider this problem within a unified framework based on the maximum likelihood principle, under the assumption that the signal at each frequency can be represented as a linear mixture of sky templates. We discuss the impact of various additional assumptions on the final outcome of the procedure. We find that the component separation problem can be fully solved in two specific situations: when we either know the frequency scaling of all the components or can correctly model them with a limited number of unknown parameters, as is the case in the parametric component separation techniques; or when we either know the statistical properties of all the components, the foregrounds and CMB, or can correctly model them with a limited number of parameters, as for instance in SMICA-like approaches. However, we also show that much less stringent assumptions are sufficient if we only aim at recovering the cleaned CMB signal. In particular, we discuss a ``minimally informed'' non-parametric method based on maximum likelihood. The method only assumes that the component properties are independent on the sky direction, at least over some region of the sky, and that the CMB covariance is known up to some limited number of parameters. We apply this method to recover the CMB $B$ modes polarization signal in the context of forthcoming CMB experiments and compare its performance with that of the standard parametric... (abridged)

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