Magnetic fields in star formation: a complete compilation of all the DCF
  estimations
  The Davis-Chandrasekhar-Fermi (DCF) method provides an indirect way to
estimate the magnetic field strength from statistics of magnetic field
orientations. We compile all the previous DCF estimations from polarized dust
emission observations and re-calculate the magnetic field strength of the
selected samples with the new DCF correction factors in Liu et al. (2021). We
find the magnetic field scales with the volume density as $B \propto n^{0.57}$.
However, the estimated power-law index of the observed $B-n$ relation has large
uncertainties and may not be comparable to the $B-n$ relation of theoretical
models. A clear trend of decreasing magnetic viral parameter (i.e., increasing
mass-to-flux ratio in units of critical value) with increasing column density
is found in the sample, which suggests the magnetic field dominates the gravity
at lower densities but cannot compete with the gravity at higher densities.
This finding also indicates that the magnetic flux is dissipated at higher
column densities due to ambipolar diffusion or magnetic recennection, and the
accumulation of mass at higher densities may be by mass flows along the
magnetic field lines. Both sub-Alfv\'{e}nic and super-Alfv\'{e}nic states are
found in the sample, with the average state being approximately
trans-Alfv\'{e}nic.
