Planck intermediate results. L. Evidence for spatial variation of the
  polarized thermal dust spectral energy distribution and implications for CMB
  $B$-mode analysis
  The characterization of the Galactic foregrounds has been shown to be the
main obstacle in the challenging quest to detect primordial B-modes in the
polarized microwave sky. We make use of the Planck-HFI 2015 data release at
high frequencies to place new constraints on the properties of the polarized
thermal dust emission at high Galactic latitudes. Here, we specifically study
the spatial variability of the dust polarized spectral energy distribution, and
its potential impact on the determination of the tensor-to-scalar ratio. We use
the correlation ratio of the $C_\ell^{BB}$ angular power spectra between the
217- and 353-GHz channels as a tracer of these potential variations, computed
on different high Galactic latitude regions, ranging from 80% to 20% of the
sky. The new insight from Planck data is a departure of the correlation ratio
from unity that cannot be attributed to a spurious decorrelation due to the
cosmic microwave background, instrumental noise, or instrumental systematics.
The effect is marginally detected on each region, but the statistical
combination of all the regions gives more than 99% confidence for this
variation in polarized dust properties. In addition, we show that the
decorrelation increases when there is a decrease in the mean column density of
the region of the sky being considered, and we propose a simple power-law
empirical model for this dependence, which matches what is seen in the Planck
data. We explore the effect that this measured decorrelation has on simulations
of the BICEP2-Keck Array/Planck analysis and show that the 2015 constraints
from those data still allow a decorrelation between the dust at 150 and 353GHz
of the order of the one we measure. Finally we show that either spatial
variation of the dust SED or of the dust polarization angle could produce
decorrelations between 217- and 353-GHz data similar to those we observe in the
data.
