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Non-Ideal Magnetohydrodynamic Simulations of the Two-Stage Fragmentation Model for Cluster Formation

We model molecular cloud fragmentation with thin disk non-ideal magnetohydrodynamic simulations that include ambipolar diffusion and partial ionization that transitions from primarily ultraviolet dominated to cosmic ray dominated regimes. These simulations are used to determine the conditions required for star clusters to form through a two-stage fragmentation scenario. Recent linear analyses have shown that the fragmentation length and time scales can undergo a dramatic drop across the column density boundary that separates the ultraviolet and cosmic ray dominated ionization regimes. As found in earlier studies, the absence of an ionization drop and regular perturbations leads to a single-stage fragmentation on parsec scales in transcritical clouds, so that the nonlinear evolution yields the same fragment sizes as predicted by linear theory. However, we find that a combination of initial transcritical mass-to-flux ratio, evolution through a column density regime in which the ionization drop takes place, and regular small perturbations to the mass-to-flux ratio are sufficient to cause a second stage of fragmentation during the nonlinear evolution. Cores of size ~0.1 pc are formed within an initial fragment of ~ pc size. Regular perturbations to the mass-to-flux ratio also accelerate the onset of runaway collapse.