We establish new constraints on the intermediate-mass range of the initial-final mass relation by studying white dwarfs in four young star clusters , and apply the results to study the evolution of stars on the thermally pulsing asymptotic giant branch ( TP-AGB ) .
We show that the stellar core mass on the AGB grows rapidly from 10 % to 30 % for stars with M _ { initial } = 1.6 to 2.0 M _ { \odot } .
At larger masses , the core-mass growth decreases steadily to \sim 10 % at M _ { initial } = 3.4 M _ { \odot } .
These observations are in excellent agreement with predictions from the latest TP-AGB evolutionary models in ( 54 ) .
We also compare to models with varying efficiencies of the third dredge-up and mass loss , and demonstrate that the process governing the growth of the core is largely the stellar wind , while the third dredge-up plays a secondary , but non-negligible role .
Based on the new white dwarf measurements , we perform an exploratory calibration of the most popular mass-loss prescriptions in the literature .
Finally , we estimate the lifetime and the integrated luminosity of stars on the TP-AGB to peak at t \sim 3 Myr and E = 1.2 \times 10 ^ { 10 } L _ { \odot } yr for M _ { initial } \sim 2 M _ { \odot } ( t \sim 2 Myr for luminosities brighter than the RGB tip at \log ( L / L _ { \odot } ) > 3.4 ) , decreasing to t = 0.4 Myr and E = 6.1 \times 10 ^ { 9 } L _ { \odot } yr for stars with M _ { initial } \sim 3.5 M _ { \odot } .
The implications of these results are discussed with respect to general population synthesis studies that require correct modeling of the TP-AGB phase of stellar evolution .