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The analysis of the Planck polarization E and B mode power spectra ofinterstellar dust emission at 353 GHz recently raised new questions on theimpact of Galactic foregrounds to the detection of the polarization of theCosmic Microwave Background (CMB) and on the physical properties of theinterstellar medium (ISM). In the diffuse ISM a clear E-B asymmetry isobserved, with twice as much power in E modes than in B modes; as well as apositive correlation between the total power, T, and both E and B modes,presently interpreted in terms of the link between the structure ofinterstellar matter and that of the Galactic magnetic field. In this paper weaim at extending the Planck analysis of the high-latitude sky to low Galacticlatitude, investigating the correlation between the TEB power spectra with thegas column density from the diffuse ISM to molecular clouds. We divide the skybetween Galactic latitude |b|>5 deg and |b|<60 deg in 552 circular patches andwe study the cross-correlations between the TEB power spectra and the columndensity 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 ISMto molecular clouds in the Gould Belt, the latter decreases. This systematicvariation must be related to actual changes in ISM properties. The data showsignificant scatter about this mean trend. The variations of BB/EE and rTE areobserved to be anti-correlated for all column densities. In the diffuse ISM,the variance of these two ratios is consistent with a stochastic non-Gaussianmodel in which the values of BB/EE and rTE are fixed. We finally discuss thedependencies of TB and EB with column density, which are however hampered byinstrumental noise.

The link between E-B polarization modes and gas column density from interstellar dust emission