Linear Gravitational Instability of Filamentary and Sheetlike Molecular Clouds with Magnetic Fields

We study the linear evolution of small perturbations in self-gravitatingfluid systems with magnetic fields. We consider wave-like perturbations tononuniform filamentary and sheet-like hydrostatic equilibria in the presence ofa uniform parallel magnetic field. Motivated by observations of molecularclouds that suggest substantial nonthermal (turbulent) pressure, we adoptequations of state that are softer than isothermal. We numerically determinethe dispersion relation and the form of the perturbations in the regime ofinstability. The form of the dispersion relation is the same for all equationsof state considered, for all magnetic field strengths, and for both geometriesexamined. We demonstrate the existence of a fastest growing mode for the systemand study how its characteristics depend on the amount of turbulence and thestrength of the magnetic field. Generally, turbulence tends to increase therate and the length scale of fragmentation. While tending to slow thefragmentation, the magnetic field has little effect on the fragmentation lengthscale until reaching some threshold, above which the length scale decreasessignificantly. Finally, we discuss the implications of these results for starformation in molecular clouds.Comment: 22 pages AASTeX 4.0, 11 postscript figure