TERMINATION OF AGB-EVOLUTION BY HYDROGEN RECOMBINATION

The evolution of stars with mass between 0.8... 5M. along the Asymptot ic Giant B ranch has been calculated. We find that for the mass range of approximate to 1...4 M. there exists a critical luminosity above wh ich the stars experience a runaway expansion during the luminosity pea k of a thermal pulse. The physical reason for this lies in the recombi nation of hydrogen within a thermally and dynamically unstable envelop e. The calculations are supplemented by various stability tests. For t he first time this long-predicted instability has been found in comple te stellar evolution models. While our models indicate the complete an d fast ejection of the envelope, the assumptions of hydrostatic equili brium and instantaneous convective mixing limit the significance of th e results, although they confirm and complete earlier dynamical invest igations of static stellar envelopes. Our approach does not allow to d ecide conclusively whether the instability has any connection with the ejection of Planetary Nebulae from real stars; instead, we demonstrat e a definitive physical limit of standard hydrostatic AGB calculations .