Nonlinear hydromagnetic wave support of a stratified molecular cloud. II. A parameter study

We use numerical simulations to study the effect of nonlinear MHD waves in a stratified, self-gravitating molecular cloud. In a previous paper, we had shown the details of a standard model and studied the effect of varying the dimensionless amplitude (a) over tilde (d) of sinusoidal driving. In this paper, we present the results of varying two other important free parameters: beta(0), the initial ratio of gas to magnetic pressure at the cloud midplane, and (nu) over tilde (0), the dimensionless frequency of driving. Furthermore, we present the case of a temporally random driving force. Our results demonstrate that a very important consideration for the actual level of turbulent support against gravity is the ratio of the driving wavelength lambda(0) to the size of the initial nonturbulent cloud; maximum cloud expansion is achieved when this ratio is close to unity. All of our models yield the following basic results: ( 1) the cloud is lifted up by the pressure of nonlinear MHD waves and reaches a steady state characterized by oscillations about a new time-averaged equilibrium state; ( 2) after turbulent driving is discontinued, the turbulent energy dissipates within a few sound crossing times of the expanded cloud; ( 3) the line-width-size relation is obtained by an ensemble of clouds with different free parameters. The best consistency with the observational correlation of magnetic field strength, turbulent line width, and density is achieved by cloud models with beta(0) approximate to 1. We also calculate the spatial power spectra of the turbulent clouds and show that significant power is developed on scales larger than the scale length H-0 of the initial cloud, even if the input wavelength of turbulence lambda(0) approximate to H-0. This explains why the relevant timescale for turbulent dissipation is the crossing time over the cloud scale rather than the crossing time over the driving scale.