1995A&A...293..381G

Based on a comparison of observations with new synthetic AGB evolution calculations we propose a revised evolutionary scenario for carbon stars in the solar neighbourhood. From observations we derive that the lowest initial mass from which carbon stars form is about 1.5M_☉. This constraint combined with four other constraints (the observed initial-final mass relation, the birth rate of carbon stars, the observed abundance ratios in planetary nebulae (PNe) and the number ratios C/M and S/C of AGB stars) are used to derive the following parameters for the synthetic AGB evolution model. Third dredge-up occurs for core masses above 0.58M_☉ and the dredge-up efficiency is λ=0.75. We consider a Reimers mass loss law (with a scaling factor η_AGB) and the mass loss rate law recently proposed by Bloecker & Schoenberner (1993IAUS..155..479B; with a scaling factor η_BS). We find η_AGB=4 and η_BS=0.08. Both models fit the observations equally well. The model predicts that stars in the range 1.5M_☉≲M≲1.6M_☉ become carbon stars at their last thermal pulse (TP) on the AGB and live only a few 10⁴yr as carbon stars. More massive stars experience additional TPs as carbon stars (up to about 25 for a 3M_☉ star) and live up to 10⁶yr. For M>4M_☉ hot-bottom burning prevents the formation of carbon stars. For M≲2M_☉, M-stars skip the S-star phase when they become carbon stars. The average lifetime of the carbon star phase is ∼3x10⁵yr. The carbon stars for which C/O ratios have been derived in the literature (with values ≲1.5) are predominantly optical carbon stars with a 60µm excess. Yet, disk PNe are known with C/O ratios up to about 4. We predict that carbon stars with C/O ratios >1.5 are to be found among the infrared carbon stars. The model predicts that the probability that a carbon star has C/O>1.5 is about 30%, in reasonable agreement with the observed ratio of the surface density in the galactic plane of infrared carbon stars to all carbon stars. The infrared carbon stars are predicted to be (on average) more massive than the optical carbon stars. The fact that carbon stars with C/O>1.5 apparently never reach the optical carbon star phase (with a detached shell) is probably due to differences in evolution. If indeed infrared carbon stars are on average more massive (i.e. have larger core masses) than optical carbon stars, the interpulse period is shorter, and the increase in luminosity during the TP is smaller (due to the larger envelope mass). Both effects will decrease the likelihood of a detached shell to occur. We predict that two-thirds of all detached shells around optical carbon stars are oxygen-rich.