thesis - IRS, The Infrared Spectrograph

88 CHAPTER 5: Probing AGB nucleosynthesis via accurate Planetary Nebula abundancesFigure 5.6–. Carbon abundances and C/O ratios in PNe with low helium abundances (He/H≤ 0.13).Open symbols denote predictions of synthetic TP-AGB calculations for various choices of model parameters– specified in the legenda – corresponding to a stellar progenitor with (M i = 2.0M ⊙, Z i =0.019). See text and cases B-C-D-E of Table 5.4 for more details.Reproducing the extent of carbon enrichmentTo tackle the problem of carbon we consider a stellar model with 2 M ⊙ initial mass, a typicalmass of carbon stars in the Galactic disk (Groenewegen et al. 1995). Figure 5.6 shows a fewmodels of the predicted carbon abundance and corresponding PN values.As starting model we consider the one with the κ fix assumption. It is clearly located wellabove the observed points (diamond in left panel of Fig. 5.6).A first significant improvement is obtained acting on the opacity, that is adopting variablemolecular opacities during the TP-AGB calculations. We replace κ fix with κ var , whilekeeping the other model parameters fixed. In this model (starred symbol) the predicted C/His lowered because of a shorter C-star phase, hence a decrease in the number of dredge-upepisodes (see Marigo 2002, 2003).Additional cases are explored. The usual assumption of constant dredge-up efficiency λis replaced with the recent recipe by Karakas et al. (2002), who provide analytic relations– fitting the results of full AGB calculations – that express the evolution of λ as a functionof metallicity Z, stellar mass M, and progressive pulse number. For a given M and Z, λ isfound to increase from initially zero up to nearly constant maximum value, λ max . This latteralso varies depending on mass loss. Adopting λ max = 0.457 as suggested by Karakas et al.(2002) for the (M = 2 M ⊙ , Z = 0.02) combination, we end up with a somewhat lower C/H(triangle), compared to the case with (κ var , λ = 0.5). This reflects the smaller amount ofcarbon globally dredged-up with the λ var assumption.