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 (PDF) 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

more »

... Σ_ TP scales with M^2_ 0, 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 M^2_ 0β_0, or equivalently the square of the initial Alfvénic Mach number M^2_ A0. 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.