Can Nonlinear Hydromagnetic Waves Support a Self-gravitating Cloud?

Using self-consistent magnetohydrodynamic (MHD) simulations, we explore the hypothesis that nonlinear MHD waves dominate the internal dynamics of galactic molecular clouds. Our models employ an isothermal equation of state and allow for self-gravity. We adopt "slab symmetry," which permits motions V⊥ and fields B⊥ perpendicular to the mean field, but permits gradients only parallel to the mean field. This is the simplest possible geometry that relies on waves to inhibit gravitational collapse along the mean field. In our simulations, the Alfvén speed VA exceeds the sound speed Cs by a factor 3-30, which is realistic for molecular clouds. We simulate the free decay of a spectrum of Alfvén waves, both with and without self-gravity. We also perform simulations with and without self-gravity that include small-scale stochastic forcing, meant to model the mechanical energy input from stellar outflows. Our major results are as follows: (1) We confirm that the pressure associated with fluctuating transverse fields can inhibit the mean field collapse of clouds that are unstable by Jeans's criterion. Cloud support requires the energy in Alfvén-like disturbances to remain comparable to the cloud's gravitational binding energy. (2) We characterize the turbulent energy spectrum and density structure in magnetically dominated clouds. The perturbed magnetic and transverse kinetic energies are nearly in equipartition and far exceed the longitudinal kinetic energy. The turbulent spectrum evolves to a power-law , , approximately V2⊥,k ≈ B2,K/4πρ ∝ k-s with s ∼2, i.e., approximately consistent with a "line width-size relation σv(R) ∝ R½. The simulations show large density contrasts, with high-density regions confined in part by the pressure of the fluctuating magnetic field. (3) We evaluate the input power required to offset dissipation through shocks, as a function of cs/vA, the velocity dispersion σ, and the characteristic scale λ of the forcing. In equilibrium, the volume dissipation rate is ≈5.5(cs/vA)½(λ/L)-½ × ρσ3v/L, for a cloud of linear size L and density ρ. (4) Somewhat speculatively, we apply our results to a "typical" molecular cloud. The mechanical power input required for equilibrium (tens of Lsun), and the implied star formation efficiency (∼1%), are in rough agreement with observations. Because this study is limited to slab symmetry and excludes ion-neutral friction, the dissipation rate we calculate probably provides a lower limit on the true value.