点源极化估计的贝叶斯方法
A Bayesian method for point source polarization estimation
摘要：
宇宙微波背景图像中河外致密源的极化$P$的估计是一项非常重要的任务，以便为宇宙学目的清理这些图像-例如，限制暴胀期间原始波动的张量与标量比-并获得关于致密源本身在频率范围$ν\sim 10$ - $200$ GHz，那里的观测数据最近才开始可用。在本文中，我们提出了一个贝叶斯最大后验概率（MAP）的方法估计方案，它结合了先验信息的1和100 GHz之间的河外致密源的极化分数的分布。我们将此贝叶斯方案的白噪声模拟和更现实的模拟，包括CMB强度，银河前景和仪器噪声的特点，在11 GHz的QUIJOTE实验宽调查。使用这些模拟，我们还比较了我们的贝叶斯方法与频率滤波融合方法，已被用于WMAP数据和\emph{Planck}任务。我们发现，贝叶斯方法允许我们将$P$的可行估计的阈值降低到低于$\sim 100$ mJy的水平（与频率滤波融合的等效阈值$\sim 500$ mJy相比）。我们比较了贝叶斯方法引入的偏差，发现它在绝对值上很小。最后，我们测试的鲁棒性的贝叶斯估计对不确定性的先验和通量密度的来源。我们发现，贝叶斯估计是强大的对温和的变化的参数的先验和几乎不敏感的现实误差估计测光的来源。
英文摘要：
The estimation of the polarization $P$ of extragalactic compact sources in Cosmic Microwave Background images is a very important task in order to clean these images for cosmological purposes -- as, for example, to constrain the tensor-to-scalar ratio of primordial fluctuations during inflation -- and also to obtain relevant astrophysical information about the compact sources themselves in a frequency range, $ν\sim 10$--$200$ GHz, where observations have only very recently started to be available. In this paper we propose a Bayesian maximum a posteriori (MAP) approach estimation scheme which incorporates prior information about the distribution of the polarization fraction of extragalactic compact sources between 1 and 100 GHz. We apply this Bayesian scheme to white noise simulations and to more realistic simulations that include CMB intensity, Galactic foregrounds and instrumental noise with the characteristics of the QUIJOTE experiment Wide Survey at 11 GHz. Using these simulations, we also compare our Bayesian method with the frequentist Filtered Fusion method that has been already used in WMAP data and in the \emph{Planck} mission. We find that the Bayesian method allows us to decrease the threshold for a feasible estimation of $P$ to levels below $\sim 100$ mJy (as compared to $\sim 500$ mJy that was the equivalent threshold for the frequentist Filtered Fusion). We compare the bias introduced by the Bayesian method and find it to be small in absolute terms. Finally, we test the robustness of the Bayesian estimator against uncertainties in the prior and in the flux density of the sources. We find that the Bayesian estimator is robust against moderate changes in the parameters of the prior and almost insensitive to realistic errors in the estimated photometry of the sources.
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