Nonlinear criterion for the stability of molecular clouds

Dynamically significant magnetic fields are routinely observed in molecular clouds, with mass-to-flux ratio λ ≡ (2π√G)∑/B ∼1 (here ∑ is the total column and B the field strength). It is widely believed that "subcritical" clouds with λ < 1 cannot collapse, based on virial arguments by Mestel and Spitzer and a linear stability analysis by Nakano and Nakamura. Here we confirm, using high-resolution numerical models that begin with a strongly supersonic velocity dispersion, that this criterion is a fully nonlinear stability condition. All the high-resolution models with λ ≤ 0.95 form "Spitzer sheets" but collapse no further. All models with λ ≥ 1.02 collapse to the maximum numerically resolvable density. We also investigate other factors determining the collapse time for supercritical models. We show that there is a strong stochastic element in the collapse time: models that differ only in details of their initial conditions can have collapse times that vary by as much as a factor of 3. The collapse time cannot be determined from just the velocity dispersion; it depends also on its distribution. Finally, we discuss the astrophysical implications of our results.