LINEAR GRAVITATIONAL-INSTABILITY OF FILAMENTARY AND SHEET-LIKE MOLECULAR CLOUDS WITH MAGNETIC-FIELDS

We study the linear evolution of small perturbations in self-gravitati ng fluid systems with magnetic fields. We consider wavelike perturbati ons to nonuniform filamentary and sheetlike hydrostatic equilibria in the presence of a uniform parallel magnetic field. Motivated by observ ations of molecular clouds that suggest substantial nonthermal (turbul ent) pressure, we adopt equations of state that are softer than isothe rmal. We numerically determine the dispersion relation and the form of the perturbations in the regime of instability. The form of the dispe rsion relation is the same for all equations of state considered, for all magnetic held strengths, and for both geometries examined. We demo nstrate the existence of a fastest growing mode for the system and stu dy how its characteristics depend on the amount of turbulence and the strength of the magnetic held. Generally, turbulence tends to increase the rate and the length scale of fragmentation. While tending to slow the fragmentation, the magnetic held has little effect on the fragmen tation length scale until reaching some threshold, above which the len gth scale decreases significantly. Finally, we discuss the implication s of these results for star formation in molecular clouds.