Evolution and Nucleosynthesis in Low-Mass Asymptotic Giant Branch Stars. I. Formation of Population I Carbon Stars
New models of thermally pulsing asymptotic giant branch (TP-AGB) stars of low mass and solar chemical composition are presented, namely, 1 <= M/M☉ <= 3, Z = 0.02, and Y = 0.28. The influence of various parameters (such as the initial core mass, the envelope mass, the mass-loss rate, the opacity, and the mixing length) on the properties of the models is discussed in detail. Our main findings are the following:1. The third dredge-up (TDU) operates self-consistently (using the Schwarzschild criterion for convection and without invoking any extra-mixing) for masses as low as 1.5 M☉. The minimum core mass for which TDU is found is MH ~ 0.61 M☉. This value is attained after about 10 thermal pulses, almost independently of the initial mass. 2. During the early TP-AGB evolution, the relation between the pulse strength (i.e., the luminosity peak of the 3α burning during the pulse) and the core mass is in good agreement with previous findings. However, when TDU is settled on, the strength of the pulse increases more rapidly as the penetration of the convective envelope into the He intershell increases. No asymptotic limit is found. 3. Furthermore, the 3α luminosity peak is independent of the previous history: the strength of the pulse in a model with mass loss is the same as in a model without mass loss but having the same core and envelope masses. 4. Unless extreme mass-loss rates are assumed, carbon stars are obtained in all the sequences of models with initial mass M >= 1.5 M☉ after about 24-26 thermal pulses and 15-17 TDU episodes. At C-star formation, the core mass is less than 0.7 M☉, and the luminosity is of the order of 104 L☉. The dredged-up mass increases up to a maximum and then decreases as mass loss and/or the advancement of the H-burning shell consume the envelope. When the envelope mass is reduced below approximately 0.5 M☉, TDU eventually vanishes. 5. If some amount of protons is diffused below the base of the H-rich envelope during TDU, in the interpulse a 13C-pocket is formed and then burnt radiatively via the 13C(α, n)16O reaction, before the onset of a new pulse. Thus, s-process nucleosynthesis occurs in a radiative environment characterized by a fairly low neutron density. In advanced thermal pulses, when the temperature at the bottom of the convective shell approaches 3 × 108 K, a secondary source of neutrons comes from the marginal activation of the 22Ne(α, n)25Mg reaction.