General modal estimation for cross-bispectra

Abstract

We describe a fast, optimal estimator for measuring angular bispectra between two correlated weakly non-Gaussian fields ($Y$ and $Z$) from observational datasets, based on a separable modal bispectrum expansion. Our methodology is applicable to (1) any shape of the input theoretical bispectrum templates (factorizable or not), (2) both even and odd ${\ell }_1+{\ell }_2+{\ell }_3$ multipole domains and (3) both amplitude ($f_{\mathrm{NL}})$ bispectrum estimation and full bispectrum reconstruction, considering either joint estimation of ($YYY$, $ZZZ$, $YYZ$ and $ZZY$) shapes, or independent estimation of auto-bispectra ($YYY$ or $ZZZ$) and cross-bispectra ($YYZ$ or $ZZY$); hence, it has quite high versatility. The methodology described here was implemented and used for the official analysis of temperature and polarization cosmic microwave background maps from the $Planck$ satellite.

21 pages, 2 tables; version matching publication in JCAP

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Cited by in corpus (4)

• Tensor Non-Gaussianity Search: Current Status and Future Prospects
• Cosmic Birefringence: Cross-Spectra and Cross-Bispectra with CMB Anisotropies
• Stochastic gravitational waves from long cosmic strings
• Constraining graviton non-Gaussianity through the CMB bispectra