Deep dredge-up in intermediate-mass thermally pulsing asymptotic giant branch stars

We present results of the evolution of asymptotic giant branch (AGB) stars of 3 and 5 M. with solar metallicity calculated with the Eggleton stellar evolution code (STARS), which has a fully implicit and simultaneous method for solving for the stellar structure, convective mixing and nuclear burning. We introduce the concept of a viscous mesh in order to improve the numerical stability of the calculations. For the 5-M. star, we evolve through 25 thermal pulses and their associated third dredge-up events. We obtain a maximum helium luminosity of 1.7 x 10(9) L. and significantly deep dredge-up after the second pulse. Strong hot-bottom burning is observed after the fifth pulse. The 3-M. model is evolved through 20 thermal pulse events, and we find third dredge-up after the seventh pulse. During the 14th pulse, sufficient carbon has been brought to the surface to produce a carbon star. We find that dredge-up and the transformation into a carbon star occur at significantly smaller core masses (0.584 and 0.608 M., respectively) than in previous calculations for 3 M..