On the validity of the core-mass luminosity relation for TP-AGB stars with efficient dredge-up

We investigate the validity of the core mass - luminosity relation (CMLR), originally described by Paczynski (1970), for asymptotic giant branch stars under the presence of third dredge-up events. We find, that models with efficient third dredge-up with less massive cores than those associated with hot bottom burning (Bloecker and Schoenberner 1991) do not obey the linear CMLR. Complete evolutionary calculations of thermal pulse stellar models which consider overshoot according to an exponential diffusive algorithm show systematically larger third dredge-up for lower core masses (0.55 Msol < M_H < 0.8 Msol) than any other existing models. We present and discuss the luminosity evolution of these models.