The asympiotic giant branch evolution of intermediate-mass stars as a function of mass and composition. II. Through the first major thermal pulse and the consequences of convective dredge-up.

The asymptotic giant branch evolution of intermediate-mass stars is further investigated following the end of the second dredge-up phase. The limiting mass for nondegenerate core carbon ignition is determined as a function of initial model mass and composition. A detailed description is given concerning the reignition of the hydrogen-burning shell through the appearance of the first major thermal pulse. Prior to the first major thermal pulse the luminosity of the helium-burning shell is found to undergo a number of small oscillations which ultimately grow to become the first major pulse. The behavior of the first major thermal pulse is discussed in detail. The results of our calculations and those of other authors are combined for further elucidation of the core mass-interflash period relation and the core mass-luminosity relation. We present more information to support the idea that the latter relationship does depend on both the initial model mass and the initial Y abundance. Model lifetimes for models on the asymptotic giant branch are discussed both for the prethermal pulse phase and for the later thermal pulse phase.

The abundance changes produced by the first and second dredge-up phases are summarized, and the possible role of meridional circulation is discussed. Finally, we consider the effect of the third dredge-up phase on the surface abundances. Analytic expressions concerning the abundance ratios of He/H, C/O, and N/O are given. It is found that for models ≲ 6 M_sun the third dredge-up phase results in a greater increase in He/H than that produced by all previous dredge-up phases. Comparisons are then made between theory and observations of planetary nebula abundances.