Hybrid Estimation of CMB Polarization Power Spectra

This paper generalises the hybrid power spectrum estimator developed in Efstathiou (2004a) to the estimation of polarization power spectra of the cosmic microwave background radiation. The hybrid power spectrum estimator is unbiased and we show that it is close to optimal at all multipoles, provided the pixel noise satisfies certain reasonable constraints. Furthermore, the hybrid estimator is computationally fast and can easily be incorporated in a Monte-Carlo chain for Planck-sized data sets. Simple formulae are given for the covariance matrices, including instrumental noise, and these are tested extensively against numerical simulations. We compare the behaviour of simple pseudo-Cl estimates with maximum likelihood estimates at low multipoles. For realistic sky cuts, maximum likelihood estimates reduce very significantly the mixing of E and B modes. To achieve limits on the scalar-tensor ratio of r ≪ 0.1 from sky maps with realistic sky cuts, maximum likelihood methods, or pseudo-Cl estimators based on unambiguous E and B modes, will be essential.