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

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4. Results and analysis

4.1. The intrinsic AGB stars

Using the recent evolutionary model and nucleosynthesis scenario of intrinsic TP-AGB stars (Straniero et al. 1995; Straniero et al. 1997; Gallino et al. 1998), we calculate the heavy-element abundances on the surface of solar metallicity 3[FORMULA] AGB star with wind mass loss. The TDU begins at the 8th pulse. The average heavy element abundances on the surface are given in Fig. 1.

[FIGURE] Fig. 1. Comparison of the theoretical predictions of surface heavy-element abundances for different neutron exposures (solid lines) with observations of intrinsic AGB stars. The numbers of `a' represent the times of the corresponding exposures in the 13C profile suggested by the Fig. 1 of Gallino et al. (1998).

In Fig. 1, the abscissa represents the average logarithmic ratio of the abundances of the heavier s-elements Ba, La, Nd, and Sm (`hs') to the lighter s-elements Y and Zr (`ls'), which depends on the neutron exposure. The ordinate is the logarithmic enhancement in `ls' with respect to iron in the envelope, which is closely related to the synthesis in the He-intershell and the dilution factor. The different curves represent the results of different neutron exposures.

Indeed, the neutron exposures of 22Ne in different thermal pulses have been showed in Sect. 3.1. In calculation, we adjust the neutron exposure of 13C source. Gallino et al (1998) suggested the 13C profile in 13C pocket by their Fig. 1, namely their `standard' case. Then they showed that the resulting heavy-elements abundances were nonsolar by their Fig. 14, while simply increasing the previously adopted abundance of 13C by a factor of 2 could reproduce the main component of solar system (see their Fig. 16). Here, instead of the abundance of 13C, we adjust the total neutron exposure caused by 13C source to calculate the nucleosynthesis of AGB stars. Thus, the different values of `a' in our Fig. 1 represent the different times of the actual total neutron exposures to the `standard' case suggested by Gallino et al. (1998). Our result of a=1.0 corresponds to the `standard' case of Gallino et al. (1998), and the a=1.5 case corresponds to their results of increasing the previously adopted abundance of 13C by a factor of 2. In reality, Gallino et al. (1998) have illustrated this times relationship (1.5 vs. 2) in the description and discussion about their Figs. 14, 15 and 16.

Our Fig. 1 shows that our results are very similar to those of Gallino et al. (1998). The curve with a=1.0 exhibits clearly that the abundances of the heavier nuclei are lower than those of the lighter nuclei in the 23rd interpulse phase like Gallino et al. (1998), namely [hs/ls][FORMULA]0.0 (the abscissa), which means that this case can not reproduce the solar abundance distribution due to a lower production for heavier nuclei. While the curve with a=1.5 produces [hs/ls][FORMULA]0.0 in the 23rd interpulse phase, which means that the abundances of the heavier and the lighter nuclei are solar like. So, our `average' heavy-element abundances on the surfaces of AGB stars can fit the detailed abundance distribution of nuclei obtained by Gallino et al. (1998). In addition, we should note that, because we neglect the effects of light neutron poisons on nucleosynthesis in calculation, our `a' values are slightly higher than the corresponding case of Gallino et al. (1998).

We calculate some other curves with different a values, which are given in Fig. 1 too. The results show that all of our available observational data are compatible with the range 0.5[FORMULA]a[FORMULA]2.0. The evolutionary curves for three cases (a=1.0, 1.5, 2.0) move upward as the dredge-ups proceed, and from the region of MS, S stars to reach the region of the carbon stars (symbol plus). And the larger neutron exposure, the higher [hs/ls] ratio will be, which means the large neutron exposure benefits the production of the heavier s-process elements.

12C isotope in the He-intershell of TP-AGB stars, together with the s-process elements, is dredged-up and mixed to the envelope by the TDU process, which causes that the C/O ratio on the surface increases gradually with the thermal pulses. The increase correlates to the overabundances of heavy-elements. Our Fig. 2 displays the relationship of heavy-element abundances to C/O ratio. The values of `a' are relevant to the values in Fig. 1. From the beginning of TDU, the values of C/O ratio and heavy-element abundances increase gradually. After some dredge-ups, C/O becomes greater than 1, that is, the star become carbon star (a=1.2, 1.5, 2.5). The different curves show that the higher neutron exposure, the more heavy elements are produced.

[FIGURE] Fig. 2. Comparison of theoretical predictions of the relationships between heavy-element abundances and C/O ratios for different neutron exposures (solid lines) with observations of intrinsic AGB stars. The numbers of `a'represent the same meanings as in Fig. 1.

The results of Fig. 1 and Fig. 2 illustrate that, adopting the new TP-AGB nucleosynthesis scenario, choosing the reasonable parameters, we can explain the observed heavy-element abundances and C/O ratio of MS, S and C (N-type) stars. Also, we can explain the M[FORMULA]S[FORMULA]C evolutionary sequence on the basis of the lighter-heavier s-element abundances relationship and the heavy-element abundances-C/O ratio relationship simultaneously.

4.2. The barium stars

Our model assumes that the binary system remains always detached, so that the only interaction between the two components of the binary system occurs via the accretion by the less evolved component of some fraction of the mass lost through stellar wind by the carbon- and heavy elements-rich AGB component. In other words, the internal structure of each component remains unaffected by the presence of its companion, so that the usual structural properties of single stars remain valid. Based the above-mentioned model, the heavy-element abundances of intrinsic AGB stars are calculated firstly, then the heavy-element overabundances of barium stars are self-consistently calculated through the progressive pulsed wind accretion and mixing.

The change equations of orbital elements are obtained by adopting the angular momentum conservation of the total system (including the two companions and the ejected matter) (see Sect. 3.2.1 and Appendix).

The observed orbital periods of 14 barium stars are in the range of 80.53 to 6489 days. According to the discussions of Jorissen et al. (1998) and Zhang et al. (1999), the barium stars with orbital period P[FORMULA]1500 or P[FORMULA]1600 d formed through wind accretion, while those with P[FORMULA]600 d formed through other scenarios. So in calculation, we adopt 600-7000 d to be the orbital period range of wind accretion.

The actual mass accretion rate between the components of binary systems can be 0.1-1 times of B-H rate ( Boffin & Zacs 1994), while SPH simulation (Theuns et al. 1996) indicated that the actual rate was about 10 times smaller than B-H rate. We adopt 0.15 times of B-H rate as the standard case in our calculation.

The calculated relationships between the heavy-element overabundances [s/Fe] and orbital period P of barium stars are displayed in Fig. 3, which are based on the standard case of wind accretion. Here, again, the various curves correspond to different times of the neutron exposures of the intrinsic AGB stars, and `a' represents the same meanings as in Fig. 1 and Fig. 2. Every point of every curve refers to the different orbital period, within the range 600-7000 d. Since the shorter the orbital period, the greater the accretion, and hence the larger the heavy-element overabundances will be. For the curves in Fig. 3, the higher points correspond to the shorter periods. The theoretical results with 0.8[FORMULA]a[FORMULA]2.5 can fit the observations within the error range.

[FIGURE] Fig. 3. Comparison of the predicted to observed relationships of surface heavy-element abundances to the orbital periods of barium stars corresponding to different neutron exposures of intrinsic AGB stars (solid lines) in standard case of wind accretion. The numbers represent the same meanings as in Fig. 1.

To make further examination to the dependence of heavy-element abundances on the angular momentum conservation model of wind accretion, the mass accretion scenario of barium stars is analyzed carefully by comparing the predicted heavy-element overabundances of different atomic charge Z with the observations of 14 barium stars.

In calculation, we try to make the calculated eccentricity e and orbital period P match to the observations of the barium stars. The results are given in Fig. 4a-n. The corresponding neutron exposure of intrinsic AGB components, a, and the orbital period P of barium stars are exhibited in the every Figure.

[FIGURE] Fig. 4a-c. The fitting of the predicted to observed heavy-element abundances of 14 barium stars in standard case of wind accretion. But the curves in Fig. 4j and k represent the results of higher accretion rate: 0.5 times of the Bondi-Hoyle's rate. In every figure, the alphabet `a' represents the times of the corresponding neutron exposure in the 13C profile suggested by the Fig. 1 of Gallino et al. (1998), and `P' represents the orbital period of the barium star.

[FIGURE] Fig. 4d-f.

[FIGURE] Fig. 4g-i.

[FIGURE] Fig. 4j-l.

[FIGURE] Fig. 4m-n.

Because the same program barium stars are chosen in Fig. 4 as in Fig. 3, the reasonable result would be that the same observational sample should correspond to the same neutron exposure of intrinsic AGB stars in the two figures. The results are advantageous to the standpoint: for most of barium stars, the corresponding neutron exposures of `a' in Fig. 4a-n are consistent to the values of `a' in Fig. 3 within the error ranges. Namely, the comparisons between the predicted and the observed results are basically identical in the heavy-element abundances diagram and the heavy-element abundance-orbital period P diagram of barium stars.

These results show that, for the 9 long-period barium stars (P[FORMULA]1600 d), the calculated curves can fit well to the observed heavy-element abundances in the error range (see Fig. 4a-i) according to the standard case of our wind accretion scenario. For the two classical barium giant stars HD 204075 ([FORMULA] Cap) and HD 16458 (HR 774), the results will fit the observations better after the mass accretion rate is improved to 0.5 times as much as the B-H accretion rate (see Fig. 4j and k). For the three barium stars with shorter orbital periods, HD 199939, HD 46407 and HD 77247 (the orbital periods are 584.9, 457.4 and 80.53 days respectively), the calculations can not fit the observations (see Fig. 4l-n).

Comparisons between the predicted and the observed abundances of barium stars in Fig. 3 and Fig. 4 show that the barium stars with longer orbital period (P[FORMULA]1600 d) form through wind accretion, and 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 barium stars with shorter period (P[FORMULA]600 d) can form through other scenarios: stable case C disk accretion or common envelope ejection. Our results support quantitatively the conclusions of Jorissen et al. (1998) and Zhang et al. (1999).

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© European Southern Observatory (ESO) 2000

Online publication: December 11, 2000