TP-AGB STARS WITH ENVELOPE BURNING

In this paper we focus on the TP-AGB evolution of intermediate-mass st ars experiencing envelope burning (M = 4 divided by 5 M.). Our model o f the TP-AGB phase is suitably designed to follow the peculiar behavio ur of these stars, to which the simple analytical treatment valid in t he low-mass range can no longer be applied. The approach we have adopt ed is a semi-analytical one as it combines analytical relationships de rived from complete models of TP-AGB stars with sole envelope models i n which the physical structure is calculated from the photosphere down to the core. The solution for the envelope models stands on an origin al numerical method which allows to treat major aspects of envelope bu rning. The method secures that, during the quiescent inter-pulse perio ds, fundamental quantities such as the effective temperature, the surf ace luminosity, the physical structure of the deepest and hottest laye rs of the envelope, and the related energy generation from nuclear bur ning, are not input parameters but the consequence of envelope model c alculations. This minimizes the use of analytical relations, thus givi ng our results greater homogeneity and accuracy. Moreover, we would li ke to draw the attention on the general validity of our algorithm whic h can be applied also to the case of low-mass stars, in which envelope burning does not occur. Our efforts are directed to analyse the effec ts produced by envelope burning, such as: i) the energy contribution w hich may drive significant deviations from the standard core mass-lumi nosity relationship; and ii) the changes in the surface chemical compo sition due to nuclear burning via the CNO cycle. Evolutionary models f or stars with initial mass of 4.0, 4.5, 5.0 M. and two choices of the initial chemical composition ([Y = 0.28, Z = 0.02] and [Y = 0.25, Z = 0.008]) are calculated from the first thermal pulse till the complete ejection of the envelope. We find that massive TP-AGB stars can rapidl y reach high luminosities (-6 > M-bol > -7), without exceeding, howeve r, the classical limit to the AGE luminosity of M-bol similar or equal to -7.1 corresponding to the Chandrasekhar value of the core mass. No carbon stars brighter than M-bol similar to -6.5 are predicted to for m (the alternative of a possible transition from M-star to C-star duri ng the final pulses is also explored), in agreement with observations which indicate that most of the very luminous AGE stars are oxygen-ric h. Finally, new chemical yields from stars in the mass range 4 divided by 5 M. are presented, so as to extend the sets of stellar yields fro m low-mass stars already calculated by Marigo et al. (1996). For each CNO element we give both the secondary and the primary components.