GRAIN FORMATION AROUND CARBON STARS .1. STATIONARY OUTFLOW MODELS

Asymptotic giant branch (AGB) stars are known to be sites of dust form ation and undergo significant mass loss. The outflow is believed to be driven by radiation pressure on grains and momentum coupling between the grains and gas. While the physics of shell dynamics and grain form ation are closely coupled, most previous models of circumstellar shell s have treated the problem separately. Studies of shell dynamics typic ally assume the existence of grains needed to drive the outflow, while most grain formation models assume a constant velocity wind in which grains form. Furthermore, models of grain formation have relied primar ily on classical nucleation theory instead of using a more realistic a pproach based on chemical kinetics. To model grain formation in carbon -rich AGE stars, we have coupled the kinetic equations governing small cluster growth to moment equations which determine the growth of larg e particles. Phenomenological models assuming stationary outflow are p resented to demonstrate the differences between the classical nucleati on approach and the kinetic equation method. It is found that classica l nucleation theory predicts nucleation at a lower supersaturation rat io than is predicted by the kinetic equations, resulting in significan t differences in grain properties. Coagulation of clusters larger than monomers is unimportant for grain formation in high mass-loss models but becomes more important to grain growth in low mass-loss situations . The properties of the dust grains are altered considerably if differ ential drift velocities are ignored in modeling grain formation. The e ffect of stellar temperature, stellar luminosity, and different outflo w velocities are investigated. The models indicate that changing the s tellar temperature while keeping the stellar luminosity constant has l ittle effect on the physical parameters of the dust shell formed. Incr easing the stellar luminosity while keeping the stellar temperature co nstant results in large differences in grain properties. For small out flow velocities, grains form at lower supersaturation ratios and close to the stellar photosphere, resulting in larger but fewer grains. The reverse is true when grains form under high outflow velocities, i.e., they form at higher supersaturation ratios, farther from the star, an d are much smaller but at larger quantities.