The Magnetic Field versus Density relation in Star-Forming Molecular Clouds

Abstract

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 ${\rho }_{\mathrm{T}}$ between the relatively flat low density regime and a power-law regime at higher densities. We present an analytic theory for ${\rho }_{\mathrm{T}}$ based on the interplay of the magnetic field, turbulence, and gravity. The break density ${\rho }_{\mathrm{T}}$ scales with the strength of the initial Alfvén Mach number ${\mathcal{M}}_{A0}$ for sub-Alfvénic ( ${\mathcal{M}}_{A0}<1$) and trans-Alfvénic (${\mathcal{M}}_{A0}\sim 1$) clouds. We fit the variation of ${\rho }_{\mathrm{T}}$ for model clouds as a function of ${\mathcal{M}}_{A0}$, set by different values of initial sonic Mach number ${\mathcal{M}}_0$ and the initial ratio of gas pressure to magnetic pressure ${\beta }_0$. This implies that ${\rho }_{\mathrm{T}}$, 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.

6 pages, 3 Figures, 1 online animation, accepted in ApJL

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