Pure pseudo-Cℓ estimators for CMB B-modes

Fast heuristically weighted, or pseudo-Cℓ, estimators are a frequently used method for estimating power spectra in CMB surveys with large numbers of pixels. Recently, Challinor and Chon showed that the E-B mixing in these estimators can become a dominant contaminant at low noise levels, ultimately limiting the gravity wave signal which can be detected on a finite patch of sky. We define a modified version of the estimators which eliminates E-B mixing and is near-optimal at all noise levels.