Fast Scalar Quadratic Maximum Likelihood Estimators for the CMB B-mode Power Spectrum

Constructing a fast and efficient estimator for the B-mode power spectrum of cosmic microwave background (CMB) is critical importance CMB science. For general survey, Quadratic Maximum Likelihood (QML) polarization has been proved to be optimal with minimal uncertainties, but it computationally very expensive. In this article, we propose two new QML methods estimation. We use Smith–Zaldarriaga approach prepare pure map E-mode recycling method obtain leakage free map. then scalar analyze B (QML-SZ) or (QML-TC). The QML-SZ QML-TC estimators have similar error bars as standard their computational cost nearly one order magnitude smaller. basic idea that can construct by using E–B separation proposed Smith & Zaldarriaga (SZ) considering template cleaning (TC) technique, apply these fields. By simulating potential observations space-based ground-based detectors, test reliability comparing them corresponding results traditional pseudo-C? estimator.