The Transition from a Lognormal to a Power-Law Column Density Distribution in Molecular Clouds: An Imprint of the Initial Magnetic Field and Turbulence

Abstract

We introduce a theory for the development of a transitional column density ${\Sigma }_{\mathrm{TP}}$ between the lognormal and the power-law forms of the probability distribution function (PDF) in a molecular cloud. Our turbulent magnetohydrodynamic simulations show that the value of ${\Sigma }_{\mathrm{TP}}$ increases as the strength of both the initial magnetic field and turbulence increases. We develop an analytic expression for ${\Sigma }_{\mathrm{TP}}$ based on the interplay of turbulence, a (strong) magnetic field, and gravity. The transition value ${\Sigma }_{\mathrm{TP}}$ scales with ${\mathcal{M}}_0^2$, the square of the initial sonic Mach number, and ${\beta }_0$, the initial ratio of gas pressure to magnetic pressure. We fit the variation of ${\Sigma }_{\mathrm{TP}}$ among different model clouds as a function of ${\mathcal{M}}_0^2{\beta }_0$, or equivalently the square of the initial Alfvénic Mach number ${\mathcal{M}}_{A0}^2$. This implies that the transition value ${\Sigma }_{\mathrm{TP}}$ is an imprint of cloud initial conditions and is set by turbulent compression of a magnetic cloud. Physically, the value of ${\Sigma }_{\mathrm{TP}}$ denotes the boundary above which the mass-to-flux ratio becomes supercritical and gravity drives the evolution.

7 pages, 2 figures, to appear in ApJL