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 on 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 catalogued. 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
$\sim$0.1 pc scales if the effect of line-of-sight signal integration is not
properly addressed.
