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Astron. Astrophys. 363, 555-567 (2000)

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5. Conclusion and discussion

5.1. The intrinsic AGB stars

Adopting the latest AGB stars evolutionary theory and nucleosynthesis scenario, the heavy-element abundances of solar metallicity 3[FORMULA] AGB stars are calculated. It is shown that, adopting reasonable parameters, the calculated results of the heavier/lighter s-elements ratio- overabundance relationships and the C/O ratio-overabundance relationships can fit the observations. The evolution of AGB stars along the M[FORMULA]S[FORMULA]C sequence is thus further explained from the evolutionary theories and heavy-elements nucleosynthesis of AGB stars. A 3[FORMULA] AGB star will undergo about 27 pulses before it becomes carbon star.

The results showed that the overabundances of s-process elements depend significantly on the neutron exposure: for the lower neutron exposures (a[FORMULA]1.5), the lighter s-process elements are more abundant than the heavier ([hs/ls][FORMULA]0.0); for the higher neutron exposures (a[FORMULA]1.5), the latter can increase strongly with the increase of neutron exposures, and the lighter s-process elements change slightly ([hs/ls][FORMULA]0.0); while the results with a=1.5 can explain the solar heavy-element abundance distribution, which confirm the results of Gallino et al. (1998). Moreover, 12C abundance correlates to the s-process element abundances. Both C/O ratio and s-element abundances increase with the occurrence of TDU. After some dredge-ups, C/O ratio reaches 1, from which the AGB stars become carbon stars. The observed MS, S and C (N-type) stars lie in a range of neutron exposure: a=0.5-2.5. The over low neutron exposure can not produce carbon stars (e.g. a=0.5). Our calculation thus provides a further theoretical basis for the evolution of AGB stars along the M[FORMULA]S[FORMULA]C sequence based on the heavy-element abundances and C/O ratio. The general agreements between our calculations and the observations indicate that we adopt reasonable parameters and theories of evolution and nucleosynthesis of AGB stars in calculation.

The stars with initial main sequence mass 1.5-4[FORMULA] can form carbon stars (Groenewegen et al. 1995). We consider only a 3[FORMULA] star model in our calculation. So the comparison between the calculated results and the observations is somewhat rough. With further studies of the evolutionary theory of AGB stars and increasing observational data, we can expect a deeper understanding on the nucleosynthesis of AGB stars.

5.2. The barium stars

Taking the conservation of angular momentum in place of the conservation of tangential momentum for wind accretion scenario, considering the change of [FORMULA] term, and not neglecting the square and higher power terms of eccentricity, the change equations of orbital elements are recalculated. We combine wind accretion with the nucleosynthesis of intrinsic AGB stars, to calculate, in a self-consistent manner, the heavy-element overabundances of barium stars through mass accretion during successive pulsed ejection, followed by mixing.

The calculated relationships of heavy-element abundances - orbital period P can fit the observations within the error ranges. Moreover, the predictions of the detailed abundances of different atomic charge Z can match well the observations of 11 program barium stars with longer orbital period (P[FORMULA]1600 d). The corresponding neutron exposures are in the range of 0.8[FORMULA]a[FORMULA]2.5. The higher neutron exposure (e.g. a=2.0) will produce the more abundant the heavier s-elements than the lighter (see Fig. 4c); on the contrary, the abundances of the lighter s-elements are higher than the heavier with low neutron exposure (e.g. a=1.0, see Fig. 4a); while a=1.5 will produce the almost equal abundances of the heavier to the lighter s-elements (see Fig. 4h). These neutron exposures can fit the corresponding results of intrinsic AGB stars. Naturally, we can understand the observations of no-Tc MS and S stars, which are commonly believed to be the descendants of barium stars. These results of the extrinsic AGB stars confirm the reliability of the nucleosynthesis and evolution of intrinsic AGB stars. Simultaneously, the results confirm that our wind accretion model and parameters adopted are suitable.

Analyzing our results, we understand that the barium stars with longer orbital period (P[FORMULA]1600 d) form through wind accretion. Those with shorter orbital period (P[FORMULA]600 d) form through other scenarios, such as dynamically stable late case C mass transfer or common envelope ejection. Moreover, the change range of mass accretion rate should be 0.1 to 0.5 times as much as the Bondi-Hoyle's accretion rate. The corresponding range of orbital periods and mass accretion rate to the formation of barium stars still need to be tested by more observations.

At present, the orbital elements of a large sample barium stars, Tc-poor S stars have been published (Udry et al. 1998a, 1998b; Carquillat et al. 1998). But the corresponding heavy-element abundances have not been obtained. So we need the high resolution, high signal-to-noise spectral observations of these stars, which are combined with the observations of orbital elements, to research their characters and formation.

In addition, we should note that metallicity is an important factor to the AGB stars nucleosynthesis and the formation of chemical peculiar stars. Actually, 13C neutron source is related to the metallicity (Busso et al. 1995, 1999 and references therein; Gallino et al. 1999). Gallino et al. (1998) calculated the s-element nucleosynthesis of 2[FORMULA] AGB stars with low metallicity Z=0.01, and obtained similar abundance distribution to the 3[FORMULA] with solar metallicity AGB stars model. Busso et al. (1999) and Zhang et al. (1998b) have discussed the inverse correlation between the heavy-element abundances and the metallicity [Fe/H] of intrinsic and extrinsic AGB stars. Also, the nucleosynthesis results of low metallicity AGB stars are more suitable to study the Galactic chemical evolution in the early stage of the Galaxy. For extrinsic AGB stars, Jorissen et al. (1998) suggested that the s-process operation was more efficient in a low-metallicity population, so the Pop. II CH stars may has accreted the material much enriched in heavy elements from the former AGB companion. In this paper, our main aims are (1) calculating the AGB stars nucleosynthesis, so that we can explain the observed heavy-element abundances of MS, S and C (N-type) stars, which are near solar metallicity, and supply evidence to the M[FORMULA]S[FORMULA]C evolutionary sequence; (2) discussing the wind accretion scenario of Ba stars, which are near solar metallicity too (Zacs 1994; Smith et al. 1993). So we only calculate the solar metallicity case. We will extend to study the low metallicity case in the forthcoming paper.

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© European Southern Observatory (ESO) 2000

Online publication: December 11, 2000