THE STABILITY OF MOLECULAR CLOUDS

The stability of molecular clouds is examined using a local linear instability analysis of a self-gravitating, partially ionized, warm, magnetized gas. As long as the magnetic and thermal energy densities exceed the gravitational energy density, wave propagation is possible for wavelengths longer than the critical frictional damping scale in clouds. This damping scale depends upon the neutral-ion collision rate as well as the gravitational response frequency of the gas. When gravity dominates magnetic and thermal support on some scale, the cloud becomes gravitationally unstable. In the very long wavelength limit, the growth rate is just that for the Jeans instability in a warm, magnetized medium, but on smaller scales, this rate is modulated by friction effects. The analysis is extended to the case that a background spectrum of Alfvén waves supports the cloud against global collapse. For wave spectra of the form δυA(k) ∞ k-β, it is found that a band of growing modes with a fastest growing mode exists for sufficiently steep spectra (β>1.0). The wavelength and growth time of this dominant mode is calculated as a function of the cloud magnetization, temperature, and wave spectrum. The growth rates of the dominant modes are found to decrease as the spectral index β of the wave power spectrum increases. In particular, it is shown that the steepness of the wave spectrum is as important as the overall magnetization of the cloud in determining which modes go unstable. Thus, it is demonstrated that for wide range of wave spectra, the largest scales in a cloud can be supported against global collapse, while for a band of smaller wavelengths (about a decade), gravitational collapse can occur. Hydromagnetic wave spectra can simultaneously provide support against global collapse and still account for the formation of structure in clouds.