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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.