arXiv 1010.26362010-10astro-ph.CO

如何使用适当的前景掩蔽在CMB E和B模式之间进行清晰的分离

How to make a clean separation between CMB E and B modes with proper foreground masking

Jaiseung Kim

备注：: v2: typos corrected, v3: matched with the published version (the clarity improved) v4: a typo corrected v5: a bibliography file error fixed
发表信息：: Astronomy & Astrophysics, 531, A32, 2011
DOI：: 10.1051/0004-6361/201116733

摘要：

本文研究了有遮蔽天空中CMB偏振的E/B分解。在实空间中，E和B模式分解的算子仅涉及CMB偏振的微分。因此，原则上，我们可以从不完整的天空数据中进行干净的E/B分解。由于对观测数据应用二阶导数是不切实际的，我们通常依靠球谐变换和逆变换，而不是使用实空间算子。在球谐表象中，除非球谐展开到无限高的多极子，否则切空中的跳跃间断会产生吉布斯现象。通过平滑前景掩模，我们可以以与在其他作品中讨论的前景掩模的切趾类似的方式有效地抑制吉布斯现象。然而，我们通过平滑前景掩模而招致前景污染，因为原始掩模中的零值像素可能通过平滑过程而呈现为非零。在这项工作中，我们研究了一个最佳的前景掩模，它确保适当的前景掩蔽和抑制吉布斯现象。我们将我们的方法应用到模拟地图的像素分辨率相媲美的普朗克卫星。模拟结果表明，泄漏功率低于张量标量比$r\sim 1\times10^{-7}$的无透镜CMB B模功率谱。我们将结果与原始掩模的结果进行了比较。我们发现，泄漏功率减少了$10^{6} \sim 10^{9}$的一个因素，在成本的天空分数$0.07$，并在最低的多极增强是最高的。我们确认原始掩码中的所有零值像素在我们的掩码中保持为零。将这种方法应用于普朗克数据，将提高原始张量扰动的可探测性。

英文摘要：

We investigate the E/B decomposition of CMB polarization on a masked sky. In real space, operators of E and B mode decomposition involve only differentials of CMB polarization. We may, therefore in principle, perform a clean E/B decomposition from incomplete sky data. Since it is impractical to apply second derivatives to observation data, we usually rely on spherical harmonic transformation and inverse transformation, instead of using real-space operators. In spherical harmonic representation, jump discontinuities in a cut sky produces Gibbs phenomenon, unless a spherical harmonic expansion is made up to an infinitely high multipole. By smoothing a foreground mask, we may suppress the Gibbs phenomenon effectively in a similar manner to apodization of a foreground mask discussed in other works. However, we incur foreground contamination by smoothing a foreground mask, because zero-value pixels in the original mask may be rendered non-zero by the smoothing process. In this work, we investigate an optimal foreground mask, which ensures proper foreground masking and suppresses Gibbs phenomenon. We apply our method to a simulated map of the pixel resolution comparable to the Planck satellite. The simulation shows that the leakage power is lower than unlensed CMB B mode power spectrum of tensor-to-scalar ratio $r\sim 1\times10^{-7}$. We compare the result with that of the original mask. We find that the leakage power is reduced by a factor of $10^{6} \sim 10^{9}$ at the cost of a sky fraction $0.07$, and that the enhancement is highest at lowest multipoles. We confirm that all the zero-value pixels in the original mask remain zero in our mask. The application of this method to the Planck data will improve the detectability of primordial tensor perturbation.

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