TP-AGB stars with envelope burning

In this paper we focus on the TP-AGB evolution of intermediate-mass stars experiencing envelope burning (M = 4 divided by 5 M.). Our model of the TP-AGB phase is suitably designed to follow the peculiar behaviour of these stars, to which the simple analytical treatment valid in the low-mass range can no longer be applied. The approach we have adopted is a semi-analytical one as it combines analytical relationships derived from complete models of TP-AGB stars with sole envelope models in which the physical structure is calculated from the photosphere down to the core. The solution for the envelope models stands on an original numerical method which allows to treat major aspects of envelope burning. The method secures that, during the quiescent inter-pulse periods, fundamental quantities such as the effective temperature, the surface luminosity, the physical structure of the deepest and hottest layers of the envelope, and the related energy generation from nuclear burning, are not input parameters but the consequence of envelope model calculations. This minimizes the use of analytical relations, thus giving our results greater homogeneity and accuracy. Moreover, we would like to draw the attention on the general validity of our algorithm which 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 effects produced by envelope burning, such as: i) the energy contribution which may drive significant deviations from the standard core mass-luminosity relationship; and ii) the changes in the surface chemical composition due to nuclear burning via the CNO cycle. Evolutionary models for 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 rapidly reach high luminosities (-6 > M-bol > -7), without exceeding, however, 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 form (the alternative of a possible transition from M-star to C-star during the final pulses is also explored), in agreement with observations which indicate that most of the very luminous AGE stars are oxygen-rich. 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 from low-mass stars already calculated by Marigo et al. (1996). For each CNO element we give both the secondary and the primary components.