SYNTHETIC AGB EVOLUTION .1. A NEW MODEL

We have constructed a model to calculate in a synthetic way the evolution of stars on the asymptotic giant branch (AGB). The evolution is started at the first thermal pulse (TP) and is terminated when the envelope mass has been lost due to mass loss or when the core mass reaches the Chandrasekhar mass.Our model is more realistic than previous synthetic evolution models in that more physics has been included. The variation of the luminosity during the interpulse period is taken into account as well as the fact that, initially, the first few pulses are not yet at full amplitude and that the luminosity is lower than given by the standard core-mass-luminosity relations. Most of the relations used are metallicity dependent to be able to make a realistic comparison with stars of different metallicity. The effects of first, second and third dredge-up are taken into account. The effect of hot bottom burning (HBB) is included in an approximate way. Mass loss on the AGB is included through a Reimers Law. We also included mass loss prior to the AGB.The free parameters in our calculations are the minimum core mass for dredge-up (M(c)min), the third dredge-up efficiency (lambda) and three mass loss scaling parameters (eta(RGB), eta(EAGB), eta(AGB).The model has been applied to the LMC using a recent determination of the age-metallicity and star formation rate (SFR) for the LMC. The observed carbon star luminosity function and the observed ratio of oxygen-rich to carbon-rich AGB stars in the LMC acted as constraints to the model.Several models are calculated to demonstrate the effects of the various parameters. A model with M(c)min = 0.58M., lambda = 0.75, eta(RGB) = 0-86, eta(AGB) = eta(EAGB) = 5, including HBB reproduces the observations quite well. It is possible that the amount of carbon formed after a TP is higher than the standard value of X12 = 0.22. As long as lambdaX12=0.165 the model fits the observations. It is difficult to discriminate between a higher X12 and a higher lambda. Third dredge-up needs to be more efficient and must start at lower core masses than commonly predicted to account for the observed carbon star LF. It is suggested that evolutionary calculations have been performed with mixing-length parameters which are too small.The adopted mass loss rate coefficients correspond to a pre-AGB mass loss of 0.20M. for a 1M. and 1.8M. for a 5M. star. The low mass stars lose this on the RGB, the high mass stars in the core helium burning phase when they reach high luminosities before the TP-AGB. The Reimers coefficient on the AGB (eta(AGB) = 5) corresponds to a mass loss rate of 1.0 10(-6) M. yr-1 at the first TP for an initially 1 M. star with LMC abundances.These high mass loss rates are necessary to fit the initial-final mass relation and the high luminosity tail of the carbon star LF. The lifetime of the massive stars with these high mass loss rates are in good agreement with the observed number of massive AGB stars and their progenitors, the Cepheid variables. We suggest that the core mass at the first TP for massive stars has previously been overestimated because their evolution was calculated neglecting pre-AGB mass loss.Observationally the distribution of C-13 enriched carbon stars in the LMC is bimodal. There is a small number (approximately 0.1%) of high-luminosity (M(bol) - 4.75) J-type stars. The difference in relative numbers as well as the gap in luminosity between the two distributions suggst a different evolutionary origin. The low-luminosity J-type stars may be related to the R-stars in the Galactic bulge which have luminosities between 0 less than or similar to M(bol) less than or similar to - 3 indicating an origin at luminosities below the AGB.The small number of high-luminosity J-type carbon stars can be explained by HBB. Given the uncertainty in the observed LF and our approximate treatment of HBB the agreement is good. We predict that about 1 % of M and S stars are enriched in C-13 (and N-14).We considered the effect of ''obscuration'', when stars lose so much mass that they become optically invisible. Based on V-band, I-band and IRAS data of Reid et al. (1990) and a radiative transfer model we find that at most 3% of all carbon stars brighter than M(bol) = - 6 could have been missed in optical surveys. Using our model we derive that the overall effect of obscuration of carbon stars is negligible (approximately 0.1%).The predicted average final mass (M(f) = 0.59M.) is in good agreement with the observed value (0.60 +/- 0.02M.). We predict for our LMC model that stars with initial masses larger than 1.2-1.4M. turn into carbon stars directly and that stars initially more massive than about 1.5M. pass through an intermediate S-star phase before becoming carbon stars. This is consistent with the observation of carbon stars and S-stars in LMC clusters.The predicted birth rate of AGB stars is found to be in agreement with the death rate of Cepheids and the clump stars. The birth rate of planetary nebulae (PN) is a factor of 2 lower than the death rate of AGB stars suggesting that low mass stars (M less than or similar 1.1 M.) may not become PN.