Magnetic Field Structure in Spheroidal Star-Forming Clouds. II. Estimating Field Structure from Observed Maps

This paper presents models to estimate the structure of density and magnetic field strength in spheroidal condensations, from maps of their column density and their polarization of magnetically aligned dust grains. The density model is obtained by fitting a column density map with an embedded p = 2 Plummer spheroid of any aspect ratio and inclination. The magnetic properties are based on the density model, on the Davis-Chandrasekhar-Fermi (DCF) model of Alfv\'enic fluctuations, and on the Spheroid Flux Freezing (SFF) model of mass and flux conservation in Paper I. The field strength model has the resolution of the column density map, which is finer than the resolution of the DCF estimate of field strength. The models are applied to ALMA observations of the envelope of the protostar BHR71 IRS1. Column density fits give the density model, from (2.0 +- 0.4) x 10^5 cm^-3 to (7 +- 1) x 10^7 cm^-3 . The density model predicts the field directions map, which fits the polarization map best within 1100 au, with standard deviation of angle differences 17{\deg}. In this region the DCF mean field strength is 0.7 +- 0.2 mG and the envelope mass is supercritical, with ratio of mass to magnetic critical mass 1.5 +- 0.4. The SFF field strength profile scales with the DCF field strength, from 60 x 10{\mu}G to 4+-1 mG. The spatial resolution of the SFF field strength estimate is finer than the DCF resolution by a factor ~7, and the peak SFF field strength exceeds the DCF field strength by a factor ~5.