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

We introduce a theory for the development of a transitional column density Σ TP between the lognormal and the power-law forms of the probability distribution function in a molecular cloud. Our turbulent magnetohydrodynamic simulations show that the value of Σ TP increases as the strength of both the initial magnetic field and turbulence increases. We develop an analytic expression for Σ TP based on the interplay of turbulence, a (strong) magnetic field, and gravity. The transition value Σ TP scales with , the square of the initial sonic Mach number, and β 0 , the initial ratio of gas pressure to magnetic pressure. We fit the variation of Σ TP among different model clouds as a function of or, equivalently, the square of the initial Alfvénic Mach number . This implies that the transition value Σ TP is an imprint of cloud initial conditions and is set by turbulent compression of a magnetic cloud. Physically, the value of Σ TP denotes the boundary above which the mass-to-flux ratio becomes supercritical and gravity drives the evolution.