The Stability of a Self-Gravitating Nonrotating Gas Layer with Stellar, Magnetic, and Cosmic-Ray Components. I.
A time-independent linear stability analysis is performed on a self-gravitating, plane-parallel, isothermal layer of nonrotating gas with magnetic and cosmic-ray components. The gas layer is immersed in a plane-stratified isothermal layer of stars which supply a self-consistent gravitational field; however, only the gaseous component is perturbed. The stability of the gas layer is considered wim respect to waves with motions perpendicular to the (B,, g,) lane (longitudinal compressions perpendicular to B,), where B, and g, are the equilibrium magnetic and gravitational field vectors The equation governing the size of the perturbations in the midplane is found to be analogous to the one-dimensional time-independent equation for a particle bound by a potential well, and with similar boundary conditions. The radius of the neutral or marginally unstable state is computed numerically and compared with the Jeans and Ledoux radii. The principal result to emerge from this study is that the magnetic field and cosmi&ray gas hinder gravitational instability,increasing the minimum length necessary to produce instability by the factor (1 + a + ) 1/2, where a is the ratio of magnetic pressure to gas pressure and P is the ratio of cosmic-ray pressure to gas pressure. The possibility is discussed that gravitational instability of the gaseous component in the outer regions of galaxies excites density waves of the type described by Lin