BICEP2 / Keck Array VII: Matrix based E/B Separation applied to BICEP2 and the Keck Array
A linear polarization field on the sphere can be uniquely decomposed into an E-mode and a B-mode component. These two components are analytically defined in terms of spin-2 spherical harmonics. Maps that contain filtered modes on a partial sky can also be decomposed into E-mode and B-mode components. However, the lack of full sky information prevents orthogonally separating these components using spherical harmonics. In this paper, we present a technique for decomposing an incomplete map into E and B-mode components using E and B eigenmodes of the pixel covariance in the observed map. This method is found to orthogonally define E and B in the presence of both partial sky coverage and spatial filtering. This method has been applied to the Bicep2 and the Keck Array maps and results in reducing E to B leakage from ΛCDM E-modes to a level corresponding to a tensor-to-scalar ratio of r < 1 x 10^(-4).
© 2016 American Astronomical Society. Received 2016 March 18; revised 2016 May 15; accepted 2016 May 17; published 2016 June 29. Bicep2 was supported by the US National Science Foundation under grants ANT-0742818 and ANT-1044978 (Caltech/Harvard) and ANT-0742592 and ANT-1110087 (Chicago/Minnesota). The computations in this paper were run on the Odyssey cluster supported by the FAS Science Division Research Computing Group at Harvard University. The analysis effort at Stanford/SLAC is partially supported by the US Department of Energy Office of Science. Tireless administrative support was provided by Irene Coyle and Kathy Deniston. We thank the staff of the US Antarctic Program and in particular the South Pole Station without whose help this research would not have been possible. We thank all those who have contributed efforts to the Bicep/Keck Array series of experiments, including the Bicep1 and Bicep3 teams.
Submitted - 1603.05976v2.pdf
Published - apj_825_1_66.pdf