EVN observations of 6.7-GHz methanol maser polarization in massive
  star-forming regions II. First statistical results
  Magnetic fields have only recently been included in theoretical simulations
of high-mass star formation. The simulations show that magnetic fields play an
important role in the formation and dynamics of molecular outflows. Masers, in
particular 6.7-GHz CH3OH masers, are the best probes of the magnetic field
morphologies around massive young stellar objects on the smallest scales of
10-100 AU. This paper focuses on 4 massive young stellar objects,
IRAS06058+2138-NIRS1, IRAS22272+6358A, S255-IR, and S231, which complement our
previous 2012 sample (the first EVN group). From all these sources, molecular
outflows have been detected in the past. Seven of the European VLBI Network
antennas were used to measure the linear polarization and Zeeman-splitting of
the 6.7-GHz CH3OH masers in the star-forming regions in this second EVN group.
We detected a total of 128 CH3OH masing cloudlets. Fractional linear
polarization (0.8%-11.3%) was detected towards 18% of the CH3OH masers in our
sample. The linear polarization vectors are well ordered in all the massive
young stellar objects. We measured significant Zeeman-splitting in
IRAS06058+2138-NIRS1 (DVz=3.8+/-0.6 m/s) and S255-IR (DVz=3.2+/-0.7 m/s). By
considering the 20 massive young stellar objects towards which the morphology
of magnetic fields was determined by observing 6.7-GHz CH3OH masers in both
hemispheres, we find no evident correlation between the linear distributions of
CH3OH masers and the outflows or the linear polarization vectors. On the other
hand, we present first statistical evidence that the magnetic field (on scales
10-100 AU) is primarily oriented along the large-scale outflow direction.
Moreover, we empirically find that the linear polarization fraction of
unsaturated CH3OH masers is P_l<4.5%.
