The Magnetic Field versus Density Relation in Star-forming Molecular Clouds

We study the magnetic field to density (B–ρ) 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 ρT between the relatively flat low-density regime and a power-law regime at higher densities. We present an analytic theory for ρT based on the interplay of the magnetic field, turbulence, and gravity. The break density ρT scales with the strength of the initial Alfvén Mach number ${{ \mathcal M }}_{{\rm{A}}0}$ for sub-Alfvénic (${{ \mathcal M }}_{{\rm{A}}0}\lt 1$) and trans-Alfvénic (${{ \mathcal M }}_{{\rm{A}}0}\sim 1$) clouds. We fit the variation of ρT for model clouds as a function of ${{ \mathcal M }}_{{\rm{A}}0}$, set by different values of initial sonic Mach number ${{ \mathcal M }}_{0}$ and the initial ratio of gas pressure to magnetic pressure β0. This implies that ρT, which denotes the transition in mass-to-flux ratio from the subcritical to the supercritical regime, is set by the initial turbulent compression of the molecular cloud.