On the formation of carbon stars

We present an integrated model of asymptotic giant branch (AGB) evolution, using empirical formulae to allow for nuclear shell burning in the core, the dredge-up of heavy elements to the envelope, and mass loss from the surface. We emphasize the role of mass loss in the formation of carbon stars. The formation rate of carbon stars, for an assumed constant dredge-up every thermal pulse, is critically dependent on the mass-loss formula. The observed luminosity distribution of AGB stars, the initial-final mass relationship, the oxygen-rich-to-carbon-rich star ratio, and the total population of carbon stars can be reproduced by a new proposed mass-loss formula based upon the Reimers formula but with an initial mass- [M *(0)] dependent η value (η = 0.2875[M *(0) 2-10.6M *(0) + 10.2]). For initial masses between 1.25 and 8 M ⊙, our best fit is obtained with a carbon dredge-up of ∼6% by mass each thermal pulse. The observed data are, however, not consistent with any of the "superwind" mass-loss formulae where most of the envelope mass is removed near the end of the AGB. We also find that carbon stars primarily descended from a low-mass (