The Dynamical State of the Interstellar Gas and Fields. II. Non-Liner Growth of Clouds and Forces in Three Dimensions

Abstract

The growth of the two-dimensional instability of a gas in a gravitational field g confining a horizontal magnetic field B is followed into the non-linear regime to provide an illustration of the formation of discrete gas clouds from a more uniform medium. A shock forms as the gas falls together, dissipating the energy and making the process irreversible. The effective force field of an element of gas (suspended on the lines of force of a horizontal magnetic field) is calculated in three dimensions. The force field is made up of an attractive force of the same form as gravity but stronger by the factor g 2 /GB 2 , and a force which extends undiminished along the lines of force passing near the element of gas. The latter dominates the former at large distances and is attractive on the lines of force through, and above and below, the element of gas, and repulsive along the lines of force passing beside the element of gas. The overall effect is a strong attraction, accompanied by vigorous streaming of gas both toward and away from an established cloud. Clouds are expected to accumulate gas in such a way as to increase their vertical dimension relative to the transverse dimension g X B. I. INTRODUCTION It was demonstrated earlier (Parker 1966, hereafter referred to as "Paper 1"; Lerche 1967a) that the pressure of the galactic magnetic field and cosmic rays both produce an instability in the interstellar gas. The process is basically a Rayleigh-Taylor instability, with the interstellar gas draining into the low places along the magnetic lines of force. It was suggested that this effect is largely responsible for the observed clumping of inter-stellar gas into clouds. The effect is stronger than self-gravitation by the factor g^/GB 2 ^ 5-10, where g is the acceleration of gravity perpendicular to the disk of the galaxy and B is the galactic field density. It follows that the dynamical behavior of the general interstellar gas is determined largely by g 1 B, and the cosmic-ray pressure P, rather than by self-gravitation. Hence, in order to understand the dynamical behavior of the inter-stellar gas and its evolution into stars, etc., it is necessary to understand the nature of the g, P, P forces. In Paper I a linear perturbation analysis in two dimensions (0, B) was employed to demonstrate the instability of a number of equilibrium configurations, illustrating the tendency for the gas to depress the lines of force and accumulate in the newly created low places. But, of course, a linear analysis can show only the beginning of the departure from equilibrium. The next step is to examine the dynamics of the system when the departure is large. In this connection it was shown in Paper I that in two dimensions any two small condensed elements of gas supported in a large-scale field B slide along the lines of force under the influence of a force which has the same form as the two-dimensional gravitational attraction between the elements, but is larger by the factor g 2 /GB 2. It follows that in two dimensions the non-linear dynamical behavior of a tenuous gas threaded by a large-scale field B is the same as one would expect from self-gravitation but more vigorous. Hence, in two dimensions, the formation and contraction of gas *