General modal estimation for cross-bispectra

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 ℓ1 + ℓ2 + ℓ3 multipole domains and (3) both amplitude (fNL) 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.