2014MNRAS.438..739K

We study the linear thermal instability of a self-gravitating cloud, including the Hall effect and ambipolar diffusion, when the unperturbed state is subject to global cooling and expansion. We derive the eighth-order characteristic equation, which, in the absence of the self-gravity, expansion and other added effects, leads to the prior characteristic equations. The new criteria for thermal instability show that the background expansion (but not self-gravity) stabilizes the medium, but each of these diffusion mechanisms can destabilize the system for some of the angles. We find that self-gravity has a destabilizing effect on the isobaric thermal mode. When non-ideal effects are neglected, the stabilizing effect of the magnetic field might be reduced by the self-gravity for the wave vectors normal to the magnetic field vector. The effect of diffusion mechanisms on an expanding medium with self-gravity is similar to that on a medium without expansion and self-gravity. We can conclude that structures can form along the direction of the magnetic field lines.