A&a Manuscript No. the Brightest Carbon Stars

It is currently accepted that Hot-Bottom-Burning (HBB) in intermediate-mass asymptotic giant branch (AGB) stars prevents the formation of C stars. Nevertheless, we present in this paper the results of some detailed evolutionary calculations which show that even with HBB we obtain C stars at the highest luminosities reached on the AGB. This is due to mass-loss reducing the envelope mass so that HBB ceases but dredge-up continues. The high mass-loss rate produces an optically thick wind before the star reaches C/O> 1. This is consistent with the recent results of van Loon et al. (1997a,b) who nd obscured C stars in the Magellanic Clouds at lumi-nosities up to M bol = ?6:8. AGB stars present a signiicant challenge to theorists because they combine many physical processes which are not well understood, such as mass-loss and third dredge-up. Both are rmly established theoretically and observationally , but reliable calculations are still impossible at present (Vassiliadis & Wood 1993, hereafter VW93; Frost & Lattanzio 1996a). Nevertheless, we do have a qualitative understanding of these fascinating stars and the main physical processes which govern their evolution (for recent reviews see Frost & Lattanzio 1996b, Lattanzio et al. 1996) as well as their extensive nucleosynthesis (for exam-In the absence of Hot-Bottom Burning (HBB), that is for AGB stars initially less massive than about 4 to 5 M (depending on metallicity Z), the question of whether a star actually becomes a C star or not depends primarily on two things: { the extent and time-variation of mass-loss on the AGB; { the eeciency (i.e. the depth) of dredge-up. Mass-loss is usually included by ts chosen to simulate observed rates. For reliable models we require a self-consistent scheme for determining the mass-loss rate and its variation along the AGB and beyond. There are observational indications that toward the end of their evolution, some AGB stars experience a short phase of extremely rapid mass-loss, often called a \super-wind" (Justtanont et al. 1996, Delfosse et al. 1997). These stars are often surrounded by a dense circumstellar envelope and are no longer visible in optical studies. Some show at present rather low mass-loss rates (Jura et al. 1988), suggesting a complex time dependence. The eeciency of dredge-up is usually described by the \dredge-up parameter" which is deened as the ratio of the mass dredged to the stellar surface following a ash to the mass processed by the hydrogen burning …