Deep Dredge-up in Intermediate-Mass TP-AGB Stars
  We present results of the evolution of AGB stars of 3M_sol and 5M_sol 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 5M_sol star, we evolve through 25 thermal pulses and their associated third dredge-up events. We obtain a maximum helium luminosity of 1.7x10^9 L_sol and significantly deep dredge-up after the second pulse. Strong hot-bottom burning is observed after the 5th pulse. The 3M_sol model is evolved through 20 thermal pulse events and we find third dredge-up after the 7th 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 (0.584M_sol and 0.608M_sol, respectively) than in previous calculations for 3M_sol. 
R.J. Stancliffe (IoA, Cambridge), C.A. Tout (IoA, Cambridge), O.R.   Pols (Sterrekundig Instituut Utrecht)