Parameterising the third dredge-up in asymptotic giant branch stars

We present new evolutionary sequences for low and intermediate mass stars for three different metallicities, Z = 0.02,0.008 and 0.004. We evolve the models from the pre-main sequence to the thermally-pulsing asymptotic giant branch phase. We have two sequences of models for each mass, one which includes mass loss and one without mass loss. Typically 20 or more pulses have been followed for each model, allowing us to calculate the third dredge-up parameter for each case. Using the results from this large and homogeneous set of models, we present an approximate fit for the core mass at the first thermal pulse, as well as for the third dredge-up efficiency parameter, and the core mass at the first third dredge-up episode as a function of metallicity and total mass. We also examine the effect of a reduced envelope mass on the value of the third dredge-up efficiency parameter.