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(T) between the relatively flat low-density regime and a power-law regime at higher densities. We present an analytic theory for rho(T) based on the interplay of the magnetic field, turbulence, and gravity. The break density rho(T) scales with the strength of the initial Alfven Mach number M-A0 for sub-Alfvenic (M-A0 < 1) and trans-Alfvenic (M-A0 similar to 1 <i ) clouds. We fit the variation of rho(T) for model clouds as a function of M-A0, set by different values of initial sonic Mach number beta(0). This implies that rho(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.