Fast Estimator of Primordial Non-Gaussianity from Temperatureand Polarization Anisotropies in the Cosmic Microwave Background II: Partial Sky Coverage and Inhomogeneous Noise

In the recent paper by Yadav and coworkers we described a fast cubic (bispectrum) estimator of the amplitude of primordial non-Gaussianity of local type, fNL, from a combined analysis of the cosmic microwave background (CMB) temperature and E-polarization observations. In this paper we generalize the estimator to deal with a partial sky coverage as well as inhomogeneous noise. Our generalized estimator is still computationally efficient, scaling as O(N3/2pix) compared to the O(N5/2pix) scaling of the brute-force bispectrum calculation for sky maps with Npix pixels. Upcoming CMB experiments are expected to yield high-sensitivity temperature and E-polarization data. Our generalized estimator will allow us to optimally utilize the combined CMB temperature and E-polarization information from these realistic experiments and to constrain primordial non-Gaussianity.