BICEP2/Keck Array. VII. Matrix Based E/B Separation Applied to Bicep2 and the Keck Array
Ade, P. A. R.; Bock, J. J.; Crill, B. P.; Hildebrandt, S. R.; Netterfield, C. B.; Halpern, M.; Nguyen, H. T.; Leitch, E. M.; Lueker, M.; Pryke, C.; Tucker, C.; Hilton, G. C.; Richter, S.; Barkats, D.; Alexander, K. D.; Schwarz, R.; Bowens-Rubin, R.; Aikin, R. W.; Benton, S. J.; Bischoff, C. A.; Brevik, J. A.; Buder, I.; Bullock, E.; Duband, L.; Filippini, J. P.; Fliescher, S.; Irwin, K. D.; Karkare, K. S.; Kaufman, J. P.; Keating, B. G.; Kernasovskiy, S. A.; Kovac, J. M.; Kuo, C. L.; O'Brient, R.; Ogburn, R. W., IV; Orlando, A.; Sheehy, C. D.; Staniszewski, Z. K.; Sudiwala, R. V.; Teply, G. P.; Tolan, J. E.; Turner, A. D.; Vieregg, A. G.; Wong, C. L.; Yoon, K. W.; Ahmed, Z.; Buza, V.; Connors, J.; Dvorkin, C.; Hui, H.; Kefeli, S.; Megerian, K. G.; Thompson, K. L.; Weber, A. C.; Willmert, J.; BICEP2 Collaboration; Keck Array Collaboration; Grayson, J.; Harrison, S.; Kang, J.; Karpel, E.; Namikawa, T.; Steinbach, B.; Wiebe, D. V.; Wu, W. L. K.
United Kingdom, United States, Canada, France
Abstract
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\lt 1× {10}-4.