The link between E-B polarization modes and gas column density from
  interstellar dust emission
  The analysis of the Planck polarization E and B mode power spectra of
interstellar dust emission at 353 GHz recently raised new questions on the
impact of Galactic foregrounds to the detection of the polarization of the
Cosmic Microwave Background (CMB) and on the physical properties of the
interstellar medium (ISM). In the diffuse ISM a clear E-B asymmetry is
observed, with twice as much power in E modes than in B modes; as well as a
positive correlation between the total power, T, and both E and B modes,
presently interpreted in terms of the link between the structure of
interstellar matter and that of the Galactic magnetic field. In this paper we
aim at extending the Planck analysis of the high-latitude sky to low Galactic
latitude, investigating the correlation between the TEB power spectra with the
gas column density from the diffuse ISM to molecular clouds. We divide the sky
between Galactic latitude |b|>5 deg and |b|<60 deg in 552 circular patches and
we study the cross-correlations between the TEB power spectra and the column
density of each patch using the latest release of the Planck polarization data.
We find that the B-to-E power ratio (BB/EE) and the TE correlation ratio (rTE)
depend on column density. While the former increases going from the diffuse ISM
to molecular clouds in the Gould Belt, the latter decreases. This systematic
variation must be related to actual changes in ISM properties. The data show
significant scatter about this mean trend. The variations of BB/EE and rTE are
observed to be anti-correlated for all column densities. In the diffuse ISM,
the variance of these two ratios is consistent with a stochastic non-Gaussian
model in which the values of BB/EE and rTE are fixed. We finally discuss the
dependencies of TB and EB with column density, which are however hampered by
instrumental noise.
