Efficient optimal non-Gaussian CMB estimators with polarization

In this paper we demonstrate an efficient method for including both CMB temperature and polarization data in optimal non-Gaussian estimators. The method relies on orthogonalizing the multipoles of the temperature and polarization maps and results in a reduction by a factor of over 3 the terms required to calculate the estimator. The method is illustrated with the modal method applied to bispectrum estimation via the CMB with the trispectrum included as an appendix. However, the method is quite general and can be applied to any optimal bispectrum or trispectrum estimator including the Komatsu-Spergel-Wandelt, binned and wavelet approaches. It would also be applicable to any situation where multiple data sets with known correlations are being considered.