2019ApJ...881L..15A

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 M₀², the square of the initial sonic Mach number, and β₀, the initial ratio of gas pressure to magnetic pressure. We fit the variation of Σ_TP among different model clouds as a function of M₀²β₀ or, equivalently, the square of the initial Alfvenic Mach number M_A0². 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.