The integrated angular bispectrum

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 $f_{\mathrm{N}\mathrm{L}}$ estimation, analyses of non-Gaussianity from secondary anisotropies (ISW-lensing and ISW-tSZ-tSZ bispectra) and studies of non-Gaussian signatures from foreground contamination.