利用双谱相位探测宇宙结构。I.数学基础
Detection of Cosmic Structures using the Bispectrum Phase. I. Mathematical Foundations
摘要：
许多低频射电干涉仪的目标是从宇宙学红移的结构中探测非常微弱的光谱特征，特别是使用其特征21 cm谱线的中性氢。由于需要非常高的动态范围来将这些微弱的光谱波动与非常明亮的前景隔离开来，因此来自仪器或分析的光谱系统学，而不是热噪声，目前限制了它们的灵敏度。如果不能用分数不准确度$\lesssim 10^{-5}$实现光谱校准，就不可能探测到临界宇宙信号。来自干涉测量的双谱相位在很大程度上不受该校准问题的影响。我们提出了一个基础，探讨的性质，双谱相位的小光谱波动的限制。我们确定，他们测量的内在差异的横向结构的宇宙信号相对于前景，表示为旋转的基本相位角。它们的大小与宇宙信号相对于前景的强度有关。使用一系列的天空模型，我们详细的行为，双谱相位波动使用标准傅立叶域技术，并发现它与现有的方法相比，有一些关键的差异。模式混合的前景污染比现有的方法更明显，因为双谱相位是三个单独的干涉相位的产物。双谱相位波动中前景的乘法耦合导致前景签名与宇宙信号的混合。我们简要概述了这种方法的变化，以避免广泛的模式混合。尽管其局限性，使用双谱相位的结果的解释是可能的，与前向建模。重要的是，它是现有方法的独立和可行的替代方案。
英文摘要：
Many low-frequency radio interferometers are aiming to detect very faint spectral signatures from structures at cosmological redshifts, particularly of neutral Hydrogen using its characteristic 21 cm spectral line. Due to the very high dynamic range needed to isolate these faint spectral fluctuations from the very bright foregrounds, spectral systematics from the instrument or the analysis, rather than thermal noise, are currently limiting their sensitivity. Failure to achieve a spectral calibration with fractional inaccuracy $\lesssim 10^{-5}$ will make the detection of the critical cosmic signal unlikely. The bispectrum phase from interferometric measurements is largely immune to this calibration issue. We present a basis to explore the nature of bispectrum phase in the limit of small spectral fluctuations. We establish that they measure the intrinsic dissimilarity in the transverse structure of the cosmic signal relative to the foregrounds, expressed as rotations in the underlying phase angle. Their magnitude is related to the strength of the cosmic signal relative to the foregrounds. Using a range of sky models, we detail the behavior of bispectrum phase fluctuations using standard Fourier-domain techniques and find it comparable to existing approaches, with a few key differences. Mode-mixed foreground contamination is more pronounced than in existing approaches because the bispectrum phase is a product of three individual interferometric phases. The multiplicative coupling of foregrounds in the bispectrum phase fluctuations results in the mixing of foreground signatures with that of the cosmic signal. We briefly outline a variation of this approach to avoid extensive mode-mixing. Despite its limitations, the interpretation of results using bispectrum phase is possible with forward-modeling. Importantly, it is an independent and a viable alternative to existing approaches.
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