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 upsilon(perpendicular to) and fields B-perpendicular to 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 Alfven speed upsilon(A) exceeds the sound speed c(s) by a factor 3-30, which is realistic for molecular clouds. We simulate the free decay of a spectrum of Alfven 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 held collapse of clouds that are unstable by Jeans's criterion. Cloud support requires the energy in Alfven-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 shape, approximately upsilon(perpendicular to,k)(2) approximate to B-perpendicular to,B-k/4 pi rho proportional to k(-s) with s similar to 2, i.e., approximately consistent with a ''line width-size'' relation sigma(upsilon)(R) proportional to R(1/2). The simulations show large density contrasts, with high-density regions confined in part by the pressure of the huctuating magnetic field. (3) We evaluate the input power required to offset dissipation through shocks, as a function of c(s)/upsilon(A), the velocity dispersion sigma(upsilon), and the characteristic scale lambda of the forcing. In equilibrium, the volume dissipation rate is approximate to 5.5(c(s)/upsilon(A))(1/2)(lambda/L)(-1/2) x rho sigma(upsilon)(3)/L, for a cloud of linear size L and density rho. (4) Somewhat speculatively, we apply our results to a ''typical'' molecular cloud. The mechanical power input required for equilibrium (tens of L.), and the implied star formation efficiency (similar to 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.