Statistics of the fractional polarisation of extragalactic dusty sources
  in Planck HFI maps
  We estimate the average fractional polarisation at 143, 217 and 353 GHz of a
sample of 4697 extragalactic dusty sources by applying stacking technique. The
sample is selected from the second version of the Planck Catalogue of Compact
Sources at 857 GHz, avoiding the region inside the Planck Galactic mask (fsky ~
60 per cent). We recover values for the mean fractional polarisation at 217 and
353 GHz of (3.10 \pm 0.75) per cent and (3.65 \pm 0.66) per cent, respectively,
whereas at 143 GHz we give a tentative value of (3.52 \pm 2.48) per cent. We
discuss the possible origin of the measured polarisation, comparing our new
estimates with those previously obtained from a sample of radio sources. We
test different distribution functions and we conclude that the fractional
polarisation of dusty sources is well described by a log-normal distribution,
as determined in the radio band studies. For this distribution we estimate
{\mu}_{217GHz} = 0.3 \pm 0.5 (that would correspond to a median fractional
polarisation of {\Pi}_{med} = (1.3 \pm 0.7) per cent) and {\mu}_{353GHz} = 0.7
\pm 0.4 ({\Pi}_{med} = (2.0 \pm 0.8) per cent), {\sigma}_{217GHz} = 1.3 \pm 0.2
and {\sigma}_{353GHz} = 1.1 \pm 0.2. With these values we estimate the source
number counts in polarisation and the contribution given by these sources to
the CMB B-mode angular power spectrum at 217, 353, 600 and 800 GHz. We conclude
that extragalactic dusty sources might be an important contaminant for the
primordial B-mode at frequencies > 217 GHz.
