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

TL;DR

This paper investigates the relationship between magnetic field strength and density in turbulent molecular clouds, identifying a critical density where the magnetic behavior transitions, influenced by initial turbulence and magnetic conditions.

Contribution

The study provides a new analytic theory for the break density in the magnetic field-density relation, linking it to initial turbulence and magnetic parameters in molecular clouds.

Findings

Identifies a distinguishable break density in the magnetic field-density relation.

Develops an analytic model for the break density based on initial conditions.

Shows the break density depends on initial Alfvén Mach number and turbulence parameters.

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 $\rho_{\rm T}$ between the relatively flat low density regime and a power-law regime at higher densities. We present an analytic theory for $\rho_{\rm T}$ based on the interplay of the magnetic field, turbulence, and gravity. The break density $\rho_{\rm T}$ scales with the strength of the initial Alfv\'en Mach number $\mathcal{M}_{\rm A0}$ for sub-Alfv\'enic ( $\mathcal{M}_{\rm A0}<1$) and trans-Alfv\'enic ($\mathcal{M}_{\rm A0} \sim 1$) clouds. We fit the variation of $\rho_{\rm T}$ for model clouds as a function of $\mathcal{M}_{\rm A0}$, set by different values of initial sonic Mach number $\mathcal{M_{\rm 0}}$ and the initial ratio of gas pressure to magnetic pressure $\beta_{\rm 0}$. This implies that $\rho_{\rm T}$, 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.