The Energy Dissipation Rate of Supersonic, Magnetohydrodynamic Turbulence in Molecular Clouds

Molecular clouds have broad linewidths suggesting turbulent supersonic motions in the clouds. These motions are usually invoked to explain why molecular clouds take much longer than a free-fall time to form stars. It has classically been thought that supersonic hydrodynamical turbulence would dissipate its energy quickly, but that the introduction of strong magnetic elds could maintain these motions. In a previous paper it has been shown, however, that isothermal, compressible, MHD and hydrodynamical turbulence decay at virtually the same rate, requiring that constant driving occur to maintain the observed turbulence. In this paper direct numerical computations of uniformly driven turbulence with the ZEUS astrophysical MHD code are used to derive the absolute value of energy dissipation, which is found to be _ Ekin ' vm~ kv rms; with v = 0:21= , where vrms is the root-mean-square velocity in the region, Ekin is the total kinetic energy in the region, m is the mass of the region, and ~ k is the driving wavenumber. The ratio of the formal decay time Ekin= _ Ekin of turbulence to the free-fall time of the gas can then be shown to be