Planck intermediate results. XXI. Comparison of polarized thermal
  emission from Galactic dust at 353 GHz with interstellar polarization in the
  visible
  The Planck survey provides unprecedented full-sky coverage of the
submillimetre polarized emission from Galactic dust, bringing new constraints
on the properties of dust. The dust grains that emit the radiation seen by
Planck in the submillimetre also extinguish and polarize starlight in the
visible. Comparison of the polarization of the emission and of the interstellar
polarization on selected lines of sight probed by stars provides unique new
diagnostics of the emission and light scattering properties of dust. Using
ancillary catalogues of interstellar polarization and extinction of starlight,
we obtain the degree of polarization, $p_V$ , and the optical depth in the V
band to the star, $\tau_V$. Toward these stars we measure the submillimetre
polarized intensity, $P_S$, and total intensity, $I_S$, in the Planck 353 GHz
channel. For those lines of sight through the diffuse interstellar medium with
comparable values of the estimated column density and polarization directions
close to orthogonal, we correlate properties in the submillimetre and visible
to find two ratios, $R_{S/V} = (P_S/I_S)/(p_V/\tau_V)$ and $R_{P/p} = P_S/p_V$
, the latter focusing directly on the polarization properties of the aligned
grain population alone. We find $R_{S/V}$ = 4.2, with statistical and
systematic uncertainties 0.2 and 0.3, respectively, and $R_{P/p}$ = 5.4 MJy
sr$^{-1}$, with uncertainties 0.2 and 0.3 MJy sr$^{-1}$, respectively. Our
estimate of $R_{S/V}$ is compatible with predictions based on a range of
polarizing dust models that have been developed for the diffuse interstellar
medium. However, our estimate of $R_{P/p}$ is not compatible with predictions,
which are too low by a factor of about 2.5. This more discriminating
diagnostic, $R_{P/p}$, indicates that changes to the optical properties in the
models of the aligned grain population are required.
