Self-gravitating instability of a gas-core fluid cylinder pervaded by magnetic fields

Abstract

The self-gravitating instability of gas-core fluid cylinder pervaded by magnetic fields has been investigated. The eigenvalue relation is derived, discussed analytically, and the results are confirmed numerically. The gravitational instability is decreasing with increasing S (0< S<1), neutral stability occurs when S=1, and a surprising result is that the model is unstable not only for perturbation with long wavelengths, but also for those of short wavelengths as 1< S<∞, where S=s 2/ s 1 ( s 1 is the gas density and s 2 is the fluid density). This is physically interpreted with correlation of spiral arms of galaxies instabilities and also of destruction of interstellar clouds. The inclusion of the electromagnetic force influence leads to the modification of the eigenvalue relation, and improves the gravitational instability, in several cases it suppressed it completely. The magnetic field always has a stabilizing influence for all wavelengths in all symmetric and asymmetric modes of disturbances. As the model is acting upon the combined effect of the self-gravitating and the electromagnetic forces, the densities gas-fluid ratio S is strongly stabilizing as 0< S<1, but it is still destabilizing as 1< S<∞, as for the case in which the model is acting upon the self-gravitating only, where the field intensity H o=0. Several results for the cases ( S=0, H o≠0), ( S=0, H o=0) and ( S≠0, H=0) are well documented in the literature and are reviewed here.