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