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Calibrating the Davis–Chandrasekhar–Fermi Method with Numerical Simulations: Uncertainties in Estimating the Magnetic Field Strength from Statistics of Field Orientations

The Davis–Chandrasekhar–Fermi (DCF) method is widely used to indirectly estimate the magnetic field strength from the plane-of-sky field orientation. In this work, we present a set of 3D MHD simulations and synthetic polarization images using radiative transfer of clustered massive star-forming regions. We apply the DCF method to the synthetic polarization maps to investigate its reliability in high-density molecular clumps and dense cores where self-gravity is significant. We investigate the validity of the assumptions of the DCF method step by step and compare the model and estimated field strength to derive the correction factors for the estimated uniform and total (rms) magnetic field strength at clump and core scales. The correction factors in different situations are cataloged. We find the DCF method works well in strong-field cases. However, the magnetic field strength in weak-field cases could be significantly overestimated by the DCF method when the turbulent magnetic energy is smaller than the turbulent kinetic energy. We investigate the accuracy of the angular dispersion function (ADF; a modified DCF method) method on the effects that may affect the measured angular dispersion and find that the ADF method correctly accounts for the ordered field structure, the beam smoothing, and the interferometric filtering, but may not be applicable to account for the signal integration along the line of sight in most cases. Our results suggest that the DCF methods should be avoided to be applied below ∼0.1 pc scales if the effect of line-of-sight signal integration is not properly addressed.