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The Davis-Chandrasekhar-Fermi (DCF) method is widely used to indirectlyestimate the magnetic field strength from the plane-of-sky field orientation.In this work, we present a set of 3D MHD simulations and synthetic polarizationimages using radiative transfer of clustered massive star-forming regions. Weapply the DCF method on the synthetic polarization maps to investigate itsreliability in high-density molecular clumps and dense cores where self-gravityis significant. We investigate the validity of the assumptions of the DCFmethod step by step and compare the model and estimated field strength toderive the correction factors for the estimated uniform and total (rms)magnetic field strength at clump and core scales. The correction factors indifferent situations are catalogued. We find the DCF method works well instrong field cases. However, the magnetic field strength in weak field casescould be significantly overestimated by the DCF method when the turbulentmagnetic energy is smaller than the turbulent kinetic energy. We investigatethe accuracy of the angular dispersion function (ADF, a modified DCF method)method on the effects that may affect the measured angular dispersion and findthat the ADF method correctly accounts for the ordered field structure, thebeam-smoothing, and the interferometric filtering, but may not be applicable toaccount for the signal integration along the line of sight in most cases. Ourresults suggest that the DCF methods should be avoided to be applied below$\sim$0.1 pc scales if the effect of line-of-sight signal integration is notproperly addressed.

astrophysical journal/the astrophysical journal

Calibrating the Davis-Chandrasekhar-Fermi method with numerical  simulations: uncertainties in estimating the magnetic field strength from  statistics of field orientations