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 (Chen et al. 2022), for which a correction factor ${\beta}_{ml}$ = $B_{ml}$/$B_{DCF}$ 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 ${\beta}_{ml}\approx$ 0.7 when $B_{DCF} \propto {{\sigma}_{\theta}}^{-1}$ due to turbulent excitation of Afv\'enic MHD waves, and ${\beta}_{ml}\approx$ 0.9 when $B_{DCF} \propto {{\sigma}_{\theta}}^{-1/2}$ due to non-Alfv\'enic 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.Comment: Accepted for publication in The Astrophysical Journa

Can Protostellar Outflows Set Stellar Masses?

The opening angles of some protostellar outflows appear too narrow to match the expected core-star mass efficiency SFE = 0.3-0.5 if outflow cavity volume traces outflow mass, with a conical shape and a maximum opening angle near 90 deg. However, outflow cavities with paraboloidal shape and wider angles are more consistent with observed estimates of the SFE. This paper presents a model of infall and outflow evolution based on these properties. The initial state is a truncated singular isothermal sphere which has mass $\approx$1 $M_\odot$, free fall time $\approx$80 kyr, and small fractions of magnetic, rotational, and turbulent energy. The core collapses pressure-free as its protostar and disk launch a paraboloidal wide-angle wind. The cavity walls expand radially and entrain envelope gas into the outflow. The model matches SFE values when the outflow mass increases faster than the protostar mass by a factor 1 - 2, yielding protostar masses typical of the IMF. It matches observed outflow angles if the outflow mass increases at nearly the same rate as the cavity volume. The predicted outflow angles are then typically $\sim$50 deg as they increase rapidly through the stage 0 duration of $\sim$40 kyr. They increase more slowly up to $\sim$110 deg during their stage I duration of $\sim$70 kyr. With these outflow rates and shapes, model predictions appear consistent with observational estimates of typical stellar masses, SFEs, stage durations, and outflow angles, with no need for external mechanisms of core dispersal.Comment: Accepted for publication by The Astrophysical Journal; 47 pages, 10 figure