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arXiv · 1904.02599

General modal estimation for cross-bispectra

Maresuke Shiraishi·Michele Liguori·James R. Fergusson·E. P. S. Shellard
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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 ($f_{\rm NL})$ 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.

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Maresuke Shiraishi, Michele Liguori, James R. Fergusson, E. P. S. Shellard. 2019-04-04. General modal estimation for cross-bispectra. https://doi.org/10.1088/1475-7516%2F2019%2F06%2F046

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