THE CORE MASS GROWTH AND STELLAR LIFETIME OF THERMALLY PULSING ASYMPTOTIC GIANT BRANCH STARS

We establish new constraints on the intermediate-mass range of the initial-final mass relation, and apply the results to study the evolution of stars on the thermally pulsing asymptotic giant branch (TP-AGB). These constraints derive from newly discovered (bright) white dwarfs in the nearby Hyades and Praesepe star clusters, including a total of 18 high signal-to-noise ratio measurements with progenitor masses of M initial = 2.8-3.8 M ?. We also include a new analysis of existing white dwarfs in the older NGC?6819 and NGC?7789 star clusters, M initial = 1.6 and 2.0 M ?. Over this range of initial masses, stellar evolutionary models for metallicity Z initial = 0.02 predict the maximum growth of the core of TP-AGB stars. By comparing the newly measured remnant masses to the robust prediction of the core mass at the first thermal pulse on the AGB (i.e., from stellar interior models), we establish several findings. First, 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 ?. At larger masses, the core-mass growth decreases steadily to ~10% at M initial = 3.4 M ?, after which there is a small hint of a upturn out to M initial = 3.8 M ?. These observations are in excellent agreement with predictions from the latest TP-AGB evolutionary models in Marigo et al. 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, as well as of the third dredge-up efficiency as a function of the stellar mass. Finally, we estimate the lifetime and the integrated luminosity of stars on the TP-AGB to peak at t ~ 3?Myr and E = 1.2 ? 1010 L ? yr for M initial ~ 2 M ? (t ~ 2?Myr for luminosities brighter than the red giant branch tip at log (L/L ?) > 3.4), decreasing to t = 0.4?Myr and E = 6.1 ? 109 L ? yr for stars with M initial ~ 3.5 M ?. The implications of these results are discussed, especially with respect to general studies aimed at characterizing the integrated light output of TP-AGB stars in population synthesis models.