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We establish new constraints on the intermediate-mass range of theinitial-final mass relation by studying white dwarfs in four young starclusters, and apply the results to study the evolution of stars on thethermally pulsing asymptotic giant branch (TP-AGB). We show that the stellarcore mass on the AGB grows rapidly from 10% to 30% for stars with $M_{\rminitial}$ = 1.6 to 2.0 $M_\odot$. At larger masses, the core-mass growthdecreases steadily to $\sim$10% at $M_{\rm initial}$ = 3.4 $M_\odot$. Theseobservations are in excellent agreement with predictions from the latest TP-AGBevolutionary models in Marigo et al. (2013). We also compare to models withvarying efficiencies of the third dredge-up and mass loss, and demonstrate thatthe process governing the growth of the core is largely the stellar wind, whilethe third dredge-up plays a secondary, but non-negligible role. Based on thenew white dwarf measurements, we perform an exploratory calibration of the mostpopular mass-loss prescriptions in the literature. Finally, we estimate thelifetime and the integrated luminosity of stars on the TP-AGB to peak at $t$$\sim$ 3 Myr and $E$ = 1.2 $\times$ 10$^{10}$ $L_\odot$ yr for $M_{\rminitial}$ $\sim$ 2 $M_\odot$ ($t$ $\sim$ 2 Myr for luminosities brighter thanthe RGB tip at $\log(L/L_{\odot})$ $>$ 3.4), decreasing to $t$ = 0.4 Myr and$E$ = 6.1 $\times$ 10$^{9}$ $L_\odot$ yr for stars with $M_{\rm initial}$$\sim$ 3.5 $M_\odot$. The implications of these results are discussed withrespect to general population synthesis studies that require correct modelingof the TP-AGB phase of stellar evolution.

The Core Mass Growth and Stellar Lifetime of Thermally Pulsing Asymptotic Giant Branch Stars