6.2.4 Evolutionary tracks

In Fig. 10 we compared the values of the effective temperature $ T_{\rm eff}$ and luminosity $ L_{\star}$ obtained from our two models listed in Table 6 to evolutionary tracks of hydrogen-burning and helium-burning models calculated by Blöcker (1995). We compared the post-AGB age of these different models with the dynamical age of the ring found in §3. The kinematic analysis indicates that the nebula was ejected about 23400-26300 yr ago. The post-AGB age of the hydrogen-burning model (left-hand panel in Fig. 10) is considerably shorter than the nebula's age, suggesting that the helium-burning model (VLTP; right-hand panel in Fig. 10) may be favoured to explain the age.

The physical parameters of the two A-type stars also yield a further constraint. The stellar evolutionary tracks of the rotating models for solar metallicity calculated by Ekström et al. (2012) imply that the A-type stars, both with masses close to $ 2.7{\rm M}_{\bigodot}$ and $ T_{\rm eff}\simeq9200$K, have ages of $ \sim500$ Myr. We see that they are in the evolutionary phase of the “blue hook”; a very short-lived phase just before the Hertzsprung gap. Interestingly, the initial mass of $ 3{\rm M}_{\bigodot}$ found for the ionizing source has the same age. As previously suggested by Exter et al. (2010), the PN progenitor with an initial mass slightly greater than $ 2.7{\rm M}_{\bigodot}$ can be coeval with the A-type stars, and it recently left the AGB phase. But, they adopted the system age of about 520 Myr according to the Y$ ^2$ evolutionary tracks (Yi et al., 2003; Demarque et al., 2004).

The effective temperature and stellar luminosity obtained for both models correspond to the progenitor mass of $ 3{\rm M}_{\bigodot}$. However, the strong nitrogen enrichment seen in the nebula is inconsistent with this initial mass, so another mixing process rather than the hot-bottom burning (HBB) occurs at substantially lower initial masses than the stellar evolutionary theory suggests for AGB-phase (Karakas et al., 2009; Herwig, 2005; Karakas & Lattanzio, 2007). The stellar models developed by Karakas & Lattanzio (2007) indicate that HBB occurs in intermediate-mass AGB stars with the initial mass of $ \geqslant5{\rm M}_{\bigodot}$ for the metallicity of $ Z=0.02$; and $ \geqslant4{\rm M}_{\bigodot}$ for $ Z=0.004$-$ 0.008$. However, they found that a low-metallicity AGB star ($ Z=0.0001$) with the progenitor mass of $ 3{\rm M}_{\bigodot}$ can also experience HBB. Our determination of the argon abundance in SuWt 2 (see Table6) indicates that it does not belong to the low-metallicity stellar population; thus, another non-canonical mixing process made the abundance pattern of this PN.

The stellar evolution also depends on the chemical composition of the progenitor, namely the helium content ($ Y$) and the metallicity ($ Z$), as well as the efficiency of convection (see e.g. Salaris & Cassisi, 2005). More helium increases the H-burning efficiency, and more metallicity makes the stellar structure fainter and cooler. Any change in the outer layer convection affects the effective temperature. There are other non-canonical physical processes such as rotation, magnetic field and mass-loss during Roche lobe overflow (RLOF) in a binary system, which significantly affect stellar evolution. Ekström et al. (2012) calculated a grid of stellar evolutionary tracks with rotation, and found that N/H at the surface in rotating models is higher than non-rotating models in the stellar evolutionary tracks until the end of the central hydrogen- and helium-burning phases prior to the AGB stage. The Modules for Experiments in Stellar Astrophysics (MESA) code developed by Paxton et al. (2013); Paxton et al. (2011) indicates that an increase in the rotation rate (or angular momentum) enhances the mass-loss rate. The rotationally induced and magnetically induced mixing processes certainly influence the evolution of intermediate-mass stars, which need further studies by MESA. The mass-loss in a binary or even triple system is much more complicated than a single rotating star, and many non-canonical physical parameters are involved (see e.g. BINSTAR code by Siess, 2006; Siess et al., 2013). Chen & Han (2002) used the Cambridge stellar evolution (STARS) code developed by Eggleton (1972); Eggleton (1971); Eggleton (1973) to study numerically evolution of Population I binaries, and produced a helium-rich outer layer. Similarly, Benvenuto & De Vito (2003); Benvenuto & De Vito (2005) developed a helium white dwarf from a low mass progenitor in a close binary system. A helium enrichment in the our layer can considerably influence other elements through the helium-burning mixing process.

Ashkbiz Danehkar