WAVE MOTIONS IN MOLECULAR CLOUDS - RESULTS IN 2 DIMENSIONS

We study the linear evolution of small perturbations in self-gravitati ng fluid systems in two spatial dimensions; we consider both cylindric al and Cartesian (i.e., slab) geometries. The treatment is general but the application is to molecular clouds. We consider a class of equati ons of state that heuristically take into account the presence of turb ulence; in particular, we consider equations of state that are softer than isothermal. We take the unperturbed cloud configuration to be in hydrostatic equilibrium. We find a class of wave solutions that propag ate along a pressure-supported cylinder (or slab) and have finite (tra pped) spatial distributions in the direction perpendicular to the dire ction of propagation. Our results indicate that the dispersion relatio ns for these two dimensional waves have similar forms for the two geom etries considered here. Both cases possess a regime of instability and a fastest growing mode. We also find the (perpendicular) form of the perturbations for a wide range of wavelengths. Finally, we discuss the implications of our results for star formation and molecular clouds. The mass scales set by instabilities in both molecular cloud filaments and sheets are generally much larger than the masses of stars. Howeve r, these instabilities can determine the length scales for the initial conditions for protostelar collapse.