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 ρ _T between the relatively flat low-density regime and a power-law regime at higher densities. We present an analytic theory for ρ _T based on the interplay of the magnetic field, turbulence, and gravity. The break density ρ _T 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 ρ _T 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 β ₀. This implies that ρ _T, 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.