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

Abstract

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  A 0 for sub-Alfvénic (  A 0 < 1 ) and trans-Alfvénic (  A 0 ∼ 1 ) clouds. We fit the variation of ρ T for model clouds as a function of  A 0 , set by different values of initial sonic Mach number  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.