Is the core mass-luminosity relation violated by the occurrence of the third dredge-up?

The core mass-luminosity (Mc-L) relation of thermally pulsing asymptotic giant branch (TP-AGB) stars is a key ingredient in synthetic calculations of their evolution. Recently, Herwig et al. (1998) have presented full calculations of TP-AGB models with strong dredge-up occurring already during early thermal pulses. The resulting luminosity evolution differs appreciably from the simple linear Mc-L relation. In this paper, we show that at least part of the luminosity evolution can be understood as being the result of two well-known effects: the gradual approach to the asymptotic behaviour that characterises the first thermal pulses, and the chemical composition changes of the envelope. Both effects are already implemented in the Mc-L relations used in synthetic models. Consequently, these models are able to reproduce the behaviour of full calculations. Whether additional effects, not yet taken into account, are present, can be decided only through additional calculations and data. We also comment on the validity of a linear Mc-L relation and its possible violation, as mentioned by Herwig et al.