The Magnetic Field versus Density relation in Star-Forming Molecular
  Clouds
  We study the magnetic field to density ($B-\rho$) relation in turbulent
molecular clouds with dynamically important magnetic fields using nonideal
three-dimensional magnetohydrodynamic simulations. Our simulations show that
there is a distinguishable break density $\rho_{\rm T}$ between the relatively
flat low density regime and a power-law regime at higher densities. We present
an analytic theory for $\rho_{\rm T}$ based on the interplay of the magnetic
field, turbulence, and gravity. The break density $\rho_{\rm T}$ scales with
the strength of the initial Alfv\'en Mach number $\mathcal{M}_{\rm A0}$ for
sub-Alfv\'enic ( $\mathcal{M}_{\rm A0}<1$) and trans-Alfv\'enic
($\mathcal{M}_{\rm A0} \sim 1$) clouds. We fit the variation of $\rho_{\rm T}$
for model clouds as a function of $\mathcal{M}_{\rm A0}$, set by different
values of initial sonic Mach number $\mathcal{M_{\rm 0}}$ and the initial ratio
of gas pressure to magnetic pressure $\beta_{\rm 0}$. This implies that
$\rho_{\rm T}$, which denotes the transition in mass-to-flux ratio from the
subcritical to supercritical regime, is set by the initial turbulent
compression of the molecular cloud.
