Dust polarization and ISM turbulence
  Perhaps the most intriguing result of Planck's dust-polarization measurements
is the observation that the power in the E-mode polarization is twice that in
the B mode, as opposed to pre-Planck expectations of roughly equal dust powers
in E and B modes. Here we show how the E- and B-mode powers depend on the
detailed properties of the fluctuations in the magnetized interstellar medium.
These fluctuations are classified into the slow, fast, and Alfv\'en
magnetohydrodynamic (MHD) waves, which are determined once the ratio of gas to
magnetic-field pressures is specified. We also parametrize models in terms of
the power amplitudes and power anisotropies for the three types of waves. We
find that the observed EE/BB ratio (and its scale invariance) and positive TE
correlation cannot be easily explained in terms of favored models for MHD
turbulence. The observed power-law index for temperature/polarization
fluctuations also disfavors MHD turbulence. We thus speculate that the 0.1--30
pc length scales probed by these dust-polarization measurements are not
described by MHD turbulence but, rather, probe the large-scale physics that
drives ISM turbulence. We develop a simple phenomenological model, based on
random displacements of the magnetized fluid, that produces EE/BB $\simeq2$ and
a positive TE cross-correlation. According to this model, the EE/BB and TE
signals are due to longitudinal, rather than transverse, modes in the
random-displacement field, providing, perhaps, some clue to the mechanism that
stirs the ISM. Future investigations involving the spatial dependence of the
EE/BB ratio, TE correlation, and local departures from statistical isotropy in
dust-polarization maps, as well as further tests of some of the assumptions in
this analysis, are outlined. This work may also aid in the improvement of
foreground-separation techniques for studies of CMB polarization.
