Magnetized Interstellar Molecular Clouds. I. Comparison Between
  Simulations and Zeeman Observations
  The most accurate measurements of magnetic fields in star-forming gas are
based on the Zeeman observations analyzed by Crutcher et al. (2010). We show
that their finding that the 3D magnetic field scales approximately as
density$^{0.65}$ can also be obtained from analysis of the observed
line-of-sight fields. We present two large-scale AMR MHD simulations of several
thousand $M_\odot$ of turbulent, isothermal, self-gravitating gas, one with a
strong initial magnetic field (Alfven Mach number $M_{A,0}= 1$) and one with a
weak initial field ($M_{A,0}=10$). We construct samples of the 100 most massive
clumps in each simulation and show that they exhibit a power-law relation
between field strength and density in excellent agreement with the observed
one. Our results imply that the average field in molecular clumps in the
interstellar medium is $<B_{tot}> \sim 42 n_{H,4}^{0.65} \mu$G. Furthermore,
the median value of the ratio of the line-of-sight field to density$^{0.65}$ in
the simulations is within a factor of about (1.3, 1.7) of the observed value
for the strong and weak field cases, respectively. The median value of the
mass-to-flux ratio, normalized to the critical value, is 70% of the
line-of-sight value. This is larger than the 50% usually cited for spherical
clouds because the actual mass-to-flux ratio depends on the volume-weighted
field, whereas the observed one depends on the mass-weighted field. Our results
indicate that the typical molecular clump in the ISM is significantly
supercritical (~ factor of 3). The results of our strong-field model are in
very good quantitative agreement with the observations of Li et al. (2009),
which show a strong correlation in field orientation between small and large
scales. Because there is a negligible correlation in the weak-field model, we
conclude that molecular clouds form from strongly magnetized (although
magnetically supercritical) gas.
