On the stability of thermonuclear shell sources in stars

We present a quantitative criterion for the thermal stability of thermonuclear shell sources. We find the thermal stability of shell sources to depend on exactly three factors: they are more stable when they are geometrically thicker, less degenerate and hotter. This confirms and unifies previously obtained results in terms of the geometry, temperature and density of the shell source, by a simplified but quantitative approach to the physics of shell nuclear burning. We present instability diagrams in the temperature-density plane for hydrogen and helium shell burning, which allow a simple evaluation of the stability conditions of such shell sources in stellar models. The performance of our stability criterion is demonstrated in various numerical models: in a 3 Msun AGB star, in helium accreting CO white dwarfs, in a helium white dwarf which is covered by a thin hydrogen envelope, and in a 1.0 Msun giant.