Nonlinear Hydromagnetic Wave Support of a Stratified Molecular Cloud. II. A Parameter Study

Abstract

We use numerical simulations to study the effect of nonlinear MHD waves in a stratified, self-gravitating molecular cloud that is bounded by a hot and tenuous external medium. In a previous paper, we had shown the details of a standard model and studied the effect of varying the dimensionless amplitude. 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 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 driving wavelength lambda_0 to the the size of the initial non-turbulent cloud; maximum cloud expansion is achieved when this ratio is close to unity. The best consistency with the observational correlation of magnetic field strength, turbulent line width, and density is achieved by cloud models with beta_0 approx 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 approx H_0. The cloud stratification and resulting increase of Alfven speed toward the cloud edge allows for a transfer of energy to wavelengths significantly larger than lambda_0. This explains why the relevant time scale for turbulent dissipation is the crossing time over the cloud scale rather than the crossing time over the driving scale.