EVN observations of 6.7 GHz methanol maser polarization in massive
  star-forming regions. V. Completion of the flux-limited sample
  Although the role of magnetic fields in launching molecular outflows in
massive YSOs has been convincingly demonstrated by theoretical arguments,
observationally, the alignment of the magnetic field lines with the molecular
outflows is still under debate. We aim to complete the measurements of the
direction of the magnetic fields at mas resolution around a sample of massive
star-forming regions (MSFRs) to determine whether the magnetic field and
outflows are aligned. In 2012, we started a large VLBI campaign with the EVN to
measure the magnetic field orientation and strength toward a sample of 31 MSFRs
(the flux-limited sample) by analyzing the polarized emission of 6.7GHz CH3OH
masers. In the previous papers of the series, we have presented 80% of the
sample. Here, we report the linearly and circularly polarized emission of
6.7GHz CH3OH masers toward the last five MSFRs of the flux-limited sample. The
sources are G30.70-0.07, G30.76-0.05, G31.28+0.06, G32.03+0.06, and
G69.52-0.97. We detected a total of 209 masers, 15% of which show linearly
polarized emission (0.07%-16.7%), and 2% of which show circularly polarized
emission (0.2%-4.2%). Zeeman splitting was measured toward G30.70-0.07,
G32.03+0.06, and G69.52-0.97. The statistical analysis of the entire
flux-limited sample shows that the observations are consistent with a bimodal
distribution in the difference between the 3D magnetic field direction and the
outflow axis, with half the magnetic field directions being perpendicular and
the other half being parallel to the outflow. In addition, we determined that
typical values of the linear and circular polarization fractions for 6.7 GHz
CH3OH masers are Pl=1.0%-2.5% and Pv=0.5%-0.75%, respectively. We found that a
typical Zeeman splitting is in the range between 0.5 m/s and 2.0 m/s. This
would correspond to 9 mG<$|B_{||}|$<40 mG if F=3->4 is the most favored
hyperfine transition.
