Stability of thermal structures with an internal heating source
  We study the thermal equilibrium and stability of isobaric, spherical structures having a radiation source located at its center. The thermal conduction coefficient, external heating and cooling rates are represented as power laws of the temperature. The internal heating decreases with distance from the source r approximately as exp(-tau)/(r**2), being tau the optical depth. We find that the influence of the radiation source is important only in the central region, but its effect is enough to make the system thermally unstable above a certain threshold central temperature. This threshold temperature decreases as the internal heating efficiency increases, but, otherwise, it does not depend on the structure size. Our results suggest that a solar-like star migrating into a diffuse interstellar region may destabilize the surrounding medium. 
Nestor Sanchez, Eugenio Lopez