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We present the stability analysis of two regions, OMC-3 and OMC-4, in themassive and long molecular cloud complex of Orion A. We obtained $214~\mu$mHAWC+/SOFIA polarization data, and we make use of archival data for the columndensity and C$^{18}$O (1-0) emission line. We find clear depolarization in bothobserved regions and that the polarization fraction is anti-correlated with thecolumn density and the polarization-angle dispersion function. We find that thefilamentary cloud and dense clumps in OMC-3 are magnetically supercritical andstrongly subvirial. This region should be in the gravitational collapse phaseand is consistent with many young stellar objects (YSOs) forming in the region.Our histogram of relative orientations (HROs) analysis shows that the magneticfield is dynamically sub-dominant in the dense gas structures of OMC-3. Wepresent the first polarization map of OMC-4. We find that the observed regionis generally magnetically subcritical except for an elongated dense core, whichcould be a result of projection effect of a filamentary structure aligned closeto the line-of-sight. The relative large velocity dispersion and the unusualpositive shape parameters at high column densities in the HROs analysis suggestthat our viewing angle may be close to axes of filamentary substructures inOMC-4. The dominating strong magnetic field in OMC-4 is unfavorable for starformation and is consistent with much fewer YSOs than in OMC-3.

The Role of Magnetic Fields in the Stability and Fragmentation of Filamentary Molecular Clouds: Two Case Studies at OMC-3 and OMC-4