We determine the magnetic field strength in the OMC 1 region of the Orion A filament via a new implementation of the Chandrasekhar-Fermi method using observations performed as part of the James Clerk Maxwell Telescope (JCMT) B-Fields In Star-Forming Region Observations (BISTRO) survey with the POL-2 instrument. We combine BISTRO data with archival SCUBA-2 and HARP observations to find a plane-of-sky magnetic field strength in OMC 1 of $B_{rm pos}=6.6pm4.7$ mG, where $delta B_{rm pos}=4.7$ mG represents a predominantly systematic uncertainty. We develop a new method for measuring angular dispersion, analogous to unsharp masking. We find a magnetic energy density of $sim1.7times 10^{-7}$ Jm$^{-3}$ in OMC 1, comparable both to the gravitational potential energy density of OMC 1 ($sim 10^{-7}$ Jm$^{-3}$), and to the energy density in the Orion BN/KL outflow ($sim 10^{-7}$ Jm$^{-3}$). We find that neither the Alfv{e}n velocity in OMC 1 nor the velocity of the super-Alfv{e}nic outflow ejecta is sufficiently large for the BN/KL outflow to have caused large-scale distortion of the local magnetic field in the $sim$500-year lifetime of the outflow. Hence, we propose that the hour-glass field morphology in OMC 1 is caused by the distortion of a primordial cylindrically-symmetric magnetic field by the gravitational fragmentation of the filament and/or the gravitational interaction of the BN/KL and S clumps. We find that OMC 1 is currently in or near magnetically-supported equilibrium, and that the current large-scale morphology of the BN/KL outflow is regulated by the geometry of the magnetic field in OMC 1, and not vice versa.
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