The Initial-Final Mass Relation of White Dwarfs: A Tool to Calibrate the Third Dredge-up

The initial mass-final mass relationship (IFMR) of white dwarfs (WD) represents a crucial benchmark for stellar evolution models, especially for the efficiency of mixing episodes and mass loss during the asymptotic giant branch (AGB) phase. In this study, we argue that such relation offers the opportunity of constraining the third dredge-up (3DU), with important consequences for chemical yields. The results are discussed in light of recent studies that have identified a kink in the IFMR for initial masses close to $2\,M_{\odot}$. Adopting a physically-sound approach in which the efficiency $\lambda$ of the 3DU varies as a function of core and envelope masses, we calibrate $\lambda$ in solar-metallicity TP-AGB models in order to reproduce the final masses of their WD progeny, over a the range of initial masses $0.9 \le M_{\rm i}/M_{\odot} \le 6$. In particular, we find that in low-mass stars with $1.4 \le M_{\rm i}/M_{\odot} \le 2.0$ the efficiency is small, $\lambda \le 0.3$, it steeply rises to about $\lambda \simeq 0.65$ in intermediate-mass stars with $2.0 \le M_{\rm i}/M_{\odot} \le 4.0$, and then it drops in massive TP-AGB stars with $4.0 \le M_{\rm i}/M_{\odot} \le 6.0$. Our study also suggests that a second kink may show up in the IFMR at the transition between the most massive carbon stars and those that are dominated by hot-bottom burning.