  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.
