We present the first high-angular resolution ( up to 0 \farcs 7 , \sim 5000 AU ) polarization and thermal dust continuum images toward the massive star-forming region W51 North .
The observations were carried out with the Submillimeter Array ( SMA ) in both the subcompact ( SMA-SubC ) and extended ( SMA-Ext ) configurations at a wavelength of 870 \mu m. W51 North is resolved into four cores ( SMA1 to SMA4 ) in the 870 \mu m continuum image .
The associated dust polarization exhibits more complex structures than seen at lower angular resolution .
We analyze the inferred morphologies of the plane-of-sky magnetic field ( B _ { \bot } ) in the SMA1 to SMA4 cores and in the envelope using the SMA-Ext and SMA-SubC data .
These results are compared with the B _ { \bot } archive images obtained from the CSO and JCMT .
The polarization percentage is about 1 % to 4 % , and it is found to decrease with higher intensity in our SMA images , which is a similar trend as previously reported in the CSO and JCMT data .
A correlation between dust intensity gradient position angles ( \phi _ { \nabla I } ) and magnetic field position angles ( \phi _ { B } ) is found in the CSO , JCMT and both SMA data sets .
This correlation is further analyzed quantitatively .
A systematically tighter correlation between \phi _ { \nabla I } and \phi _ { B } is found in the cores , whereas the correlation decreases in outside-core regions .
Magnetic field-to-gravity force ratio ( \Sigma _ { B } ) maps are derived using the newly developed polarization - intensity gradient method by .
We find that the force ratios tend to be small ( \Sigma _ { B } \lower 2.15 pt \hbox { $ \buildrel < \over { \sim } $ } 0.5 ) in the cores in all 4 data sets .
In regions outside of the cores , the ratios increase or the field is even dominating gravity ( \Sigma _ { B } > 1 ) .
This possibly provides a physical explanation of the tightening correlation between \phi _ { \nabla I } and \phi _ { B } in the cores : the more the B field lines are dragged and aligned by gravity , the tighter the correlation is .
Finally , we propose a schematic scenario for the magnetic field in W51 North to interpret the four polarization observations at different physical scales .