Most-likely DCF Estimates of Magnetic Field Strength

The Davis-Chandrasekhar-Fermi (DCF) method is widely used to evaluate magnetic fields in star-forming regions. Yet it remains unclear how well DCF equations estimate the mean plane-of-the-sky field strength in a map region. To address this question, five DCF equations are applied to an idealized cloud map. Its polarization angles have a normal distribution with dispersion sigma(theta), and its density and velocity dispersion have negligible variation. Each DCF equation specifies a global field strength B-DCF and a distribution of local DCF estimates. The "most-likely" DCF field strength B-ml is the distribution mode, for which a correction factor beta(ml) equivalent to B-ml/B-DCF is calculated analytically. For each equation, beta(ml) < 1, indicating that B-DCF is a biased estimator of B-ml. The values of beta(ml) are beta(ml) approximate to 0.7 when B-DCF proportional to sigma(-1)(theta) due to turbulent excitation of Alfv & eacute;nic MHD waves, and beta(ml) approximate to 0.9 when B-DCF proportional to sigma(-1/2)(theta) due to non-Alfv & eacute;nic MHD waves. These statistical correction factors beta(ml) have partial agreement with correction factors beta sim obtained from MHD simulations. The relative importance of the statistical correction is estimated by assuming that each simulation correction has both a statistical and a physical component. Then the standard, structure function, and original DCF equations appear most accurate because they require the least physical correction. Their relative physical correction factors are 0.1, 0.3, and 0.4 on a scale from 0 to 1. In contrast, the large-angle and parallel-delta B equations have physical correction factors 0.6 and 0.7. These results may be useful in selecting DCF equations, within model limitations.