Low-Mass Stars. III. Low-Mass Stars with Steady Mass Loss: Up to the Asymptotic Giant Branch and through the Final Thermal Pulses

Detailed stellar evolutionary calculations were carried out for a metal-poor case (Z = 0.001) for stars of initial masses 1.0 Msun, 1.2 Msun, 2.0 Msun, and 3.0 Msun, and for a metal-rich case (Z = 0.02) for stars of initial masses 1.2 Msun and 3.0 Msun. Ongoing mass loss via a Reimers-type wind was included. The latest nuclear reaction rates were used, as well as the latest Los Alamos opacities, including low-temperature carbon opacities and some molecular opacities. The stars were evolved from the main sequence through the red giant branch (RGB), including the helium core flash that occurs in stars of Mi < 2 Msun, through core helium burning on the horizontal branch, and finally through a number of helium shell flashes (thermal pulses) on the asymptotic giant branch. A reasonable wind mass loss rate severely limits the total number of flashes experienced on the AGB, particularly for stars of initial masses Mi 1.2 Msun. Also, it was found that for stars of Z = 0.001, only stars of Mi < 2 Msun experience flashes at a low enough core mass to become carbon stars while still satisfying the observational initial-final mass relation discovered by Weidemann and Koester; it was found that a Reimers wind mass loss is sufficient to account for the total mass loss required by the Weidemann-Koester relation in stars of Mi < 1.5 Msun, but that additional mass loss is required for higher initial masses. It should be noted that the correct choice of Reimers wind parameter η depends sensitively on the choice of mixing length (i.e., η ∝ 1/α), composition, and opacities; for low-mass stars of Z = 0.001, a value of η = 0.4 is appropriate only for #8alpha; ≈ 2. The onset of shell flashes was found to occur considerably earlier in luminosity than indicated by the IbenRenzini relation, allowing flashes to build up in strength before reaching the luminosity domain where carbon stars are observed to exist. This flash onset turned out to occur much lower in luminosity for high-Z stars than for low-Z stars; it was a much steeper function of the star's initial mass for the low-Z case than for the high-Z case. The flash strength L maxHe was not found to level out for the later flashes, but rather to grow linearly, growing faster (and reaching considerably greater strengths) for low-Z stars than for high-Z stars. No evidence was found for the existence of any universal curve giving L maxHe as a function of core mass Mc = MH. This implies that misleading results may be obtained from the commonly used computational shortcut or arbitrarily manipulating envelope mass or core mass in the hopes of simulating the behavior of a star of different initial mass. Other general relations that do exist, including the Mc - Tb and Mc - τi f relations, turn out to depend appreciably on the composition. The new, increased ¹²C(α, γ)¹⁶O reaction rate resulted in carbon-poor, oxygen-rich cores (C ∼ 20%, O ∼ 80%), but had little effect on flash-produced "carbon pocket" abundances (C ∼ 20%, ¹⁶O ∼ 2%), nor did any significant ²⁰Ne-production via ¹⁶O(α, γ) ²⁰Ne result from the increased ¹⁶O production. One run (Mi = 3.0 Msun, Z = 0.02) was performed with a new, increased ¹⁴N(p, γ)¹⁵ O reaction rate; this proved to have little effect.