EQUIPARTITION OF ENERGY FOR TURBULENT ASTROPHYSICAL FLUIDS - ACCOUNTING FOR THE UNSEEN ENERGY IN MOLECULAR CLOUDS

Molecular clouds are observed to be partially supported by turbulent p ressure. The kinetic energy of the turbulence is directly measurable, but the potential energy, which consists of magnetic, thermal, and gra vitational potential energy, is largely unseen. We have extended previ ous results on equipartition between kinetic and potential energy to s how that it is likely to be a very good approximation in molecular clo uds. We have used two separate approaches to demonstrate this result: For small-amplitude perturbations of a static equilibrium, we have use d the energy principle analysis of Bernstein et al. (1958); this deriv ation applies to perturbations of arbitrary wavelength. To treat pertu rbations of a nonstatic equilibrium, we have used the Lagrangian analy sis of Dewar (1970); this analysis applies only to short-wavelength pe rturbations. Both analyses assume conservation of energy. Wave damping has only a small effect on equipartition if the wave frequency is sma ll compared to the neutral-ion collision frequency; for the particular case we considered, radiative losses have no effect on equipartition. These results are then incorporated in a simple way into analyses of cloud equilibrium and global stability. We discuss the effect of Alfve nic turbulence on the Jeans mass and show that it has little effect on the magnetic critical mass.