Abstract
The magnetohydrodynamic (MHD) stability of a self-gravitating fluid cylinder embedded into a self-gravitating bounded medium has been developed. The problem is formulated and solved and, upon appropriate boundary conditions, the eigenvalue relation is derived. The latter is discussed in order to determine the stable and unstable domains and their characteristics. Some reported and previously published work is recovered as limiting cases. The self-gravitating force is destabilizing only for axisymmetric modes while it is stabilizing for the rest. The axial magnetic field has a strong stabilizing influence; but the transverse magnetic field is stabilizing or not according to restrictions. The fluid-tenuous media radii ratio plays an important role in stabilizing the model. An added feature of the present work is that we have considered all mathematical solutions of the differential equations because singular solutions are not present at all in this case.