Fast Estimator Of Primordial Non-Gaussianity From Temperature And 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, f(NL), 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(N-pix(3/2)) compared to the O(N-pix(5/2)) 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.