The effect of magnetic fields and ambipolar diffusion on the column density probability distribution function in molecular clouds

Simulations generally show that non-self-gravitating clouds have a lognormal column density (Σ) probability distribution function (PDF), while self-gravitating clouds with active star formation develop a distinct power-law tail at high column density. Although the growth of the power-law can be attributed to gravitational contraction leading to the formation of condensed cores, it is often debated if an observed lognormal shape is a direct consequence of supersonic turbulence alone, or even if it is really observed in molecular clouds. In this paper we run three-dimensional magnetohydrodynamic simulations including ambipolar diffusion with different initial conditions to see the effect of strong magnetic fields and non-linear initial velocity perturbations on the evolution of the column density PDFs. Our simulations show that column density PDFs of clouds with supercritical mass-to-flux ratio, with either linear perturbations or non-linear turbulence, quickly develop a power-law tail such that dN/dlog Σ ∝ Σ−α with index α ≃ 2. Interestingly, clouds with subcritical mass-to-flux ratio also proceed directly to a power-law PDF, but with a much steeper index α ≃ 4. This is a result of gravitationally driven ambipolar diffusion. However, for non-linear perturbations with a turbulent spectrum (⁠|vₖ² ∝ k⁻⁴|⁠), the column density PDFs of subcritical clouds do retain a lognormal shape for a major part of the cloud evolution, and only develop a distinct power-law tail with index α ≃ 2 at greater column density when supercritical pockets are formed.