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.