E and B families of the Stokes parameters in the polarized synchrotron and thermal dust foregrounds

Abstract

Better understanding of Galactic foregrounds is one of the main obstacles to detection of primordial gravitational waves through measurement of the B mode in the polarized microwave sky. We generalize the method proposed in \cite{2011PhRvD..83h3003B} and decompose the polarization signals into the E and B families directly in the domain of the Stokes $Q$, $U$ parameters as $(Q,U)\equiv(Q_E, U_E)+(Q_B,U_B)$. This also enables an investigation of the morphology and the frequency dependence of these two families, which has been done in the WMAP K, Ka (tracing synchrotron emission) and Planck 2015 HFI maps (tracing thermal dust). The results reveal significant differences in spectra between the E and B families. The spectral index of the E family fluctuates less across the sky than that of the B family, and the same tendency occurs for the polarization angles of the dust and synchrotron channels. The new insight from WMAP and Planck data on the North Polar Spur and BICEP2 zones through our method clearly indicates that these zones are characterized by very low polarization intensity of the B family compared to the E family. We have detected global structure of the B family polarization angles at high Galactic latitudes which cannot be attributed to the cosmic microwave background or instrumental noise. However, we cannot exclude instrumental systematics as a partial contributor to these anomalies.