We study the position-dependent power spectrum and the integrated bispectrum statistic for 2D cosmological fields on the sphere (integrated angular bispectrum). First, we derive a useful, $m$-independent, formula for the full-sky integrated angular bispectrum, based on the construction of azimuthally symmetric patches. We then implement a pipeline for integrated angular bispectrum estimation, including a mean-field correction to account for spurious isotropy-breaking effects in realistic conditions (e.g., inhomogenous noise, sky masking). Finally, we show examples of applications of this estimator to CMB analysis, both using simulations and actual Planck data. Such examples include $f_\mathrm{NL}$ estimation, analyses of non-Gaussianity from secondary anisotropies (ISW-lensing and ISW-tSZ-tSZ bispectra) and studies of non-Gaussian signatures from foreground contamination.

中文翻译：

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综合角双谱

我们研究了球体上二维宇宙学场的位置相关功率谱和积分双谱统计量（积分角双谱）。首先，我们基于方位角对称贴片的构建，推导出一个有用的、与 $m$ 无关的全天空积分角双谱公式。然后，我们实现了用于集成角双谱估计的管道，包括平均场校正，以解决现实条件下的虚假各向同性破坏效应（例如，非均匀噪声、天空掩蔽）。最后，我们展示了使用模拟和实际普朗克数据将此估计器应用于 CMB 分析的示例。这样的例子包括 $f_\mathrm{NL}$ 估计，