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

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1. Introduction

Since Burbridge et al. (1957) and Cameron (1957) published their pioneering studies, the nucleosynthesis theory has been developed in deep degree. In particular, TP-AGB stars are very important to study element nucleosynthesis and the Galactic chemical evolution because they synthesize significant parts of slow process (hereafter s-process) neutron capture elements and 12C. The products are taken out from the stellar interior, He-intershell, to the surface by the third dredge-up (hereafter TDU) process, and then are ejected into interstellar medium with the progressive stellar wind mass loss.

Our understanding of the AGB nucleosynthesis has undergone major revisions in these years. The earlier studies (Iben 1975; Truran & Iben 1977) illustrated that intermediate mass TP-AGB stars with 22Ne[FORMULA]Mg neutron source (the typical neutron density is least of a order of [FORMULA] cm-3) are the suitable nucleosynthesis sites of s-process elements. But new observations shed doubts on the above idea (Busso et al. 1995, 1999 and references therein). Busso et al. (1995) and Lambert et al. (1995) demonstrated that the measured abundances of Rb/Sr, the products of the branch in the s-process path at 85Kr, imply a definitely lower neutron density (typical of the order of [FORMULA] cm-3), which can be provided via the reaction 13C[FORMULA]O at low temperature in the He-intershell of low mass AGB stars.

Iben & Renzini (1982a,b) indicated that a suitable mechanism operated in low mass stars of low metallicity to allow the formation of a semiconvective layer, hence the 13C pocket. The pocket is engulfed by the next convective pulse where 13C nuclei easily capture [FORMULA] nuclei, release neutrons. Hollowell & Iben (1988) confirmed the possibility of formation of a consistent 13C pocket through a local time-dependent treatment of semiconvection. However, the semiconvection mixing mechanism was not found to work for the 12C-enriched Population I red giants, like the peculiar stars of MS, S and C stars, showing overabundances of s-process elements in their spectra.

Straniero et al. (1995) investigated the effect of a possible mixing of protons into a thin zone at the top of the carbon-rich region during each dredge-up episode, hence the formation of 13C pocket. They suggested that the 13C was completely burnt in the radiative condition, and the resulting s-process nucleosynthesis occurs during the quiescent interpulse period, instead of the convective thermal pulse. 22Ne[FORMULA]Mg was still active for a very short period during the convective pulse with minor influence on the whole nucleosynthesis. Herwig et al. (1997) and Herwig et al. (1998) supported the formation of 13C pocket via hydrodynamical calculations.

Straniero et al. (1997) adopted the above new s-process nucleosynthesis scenario to calculate the s-process nucleosynthesis of solar metallicity low mass AGB stars with 1[FORMULA][FORMULA][FORMULA]3, and gave the detailed results.

Recently, Gallino et al. (1998) explained further and developed the aforesaid new scenario. They divided the 13C pocket, q layer, into three zones in the light of the distribution in the mass of hydrogen introduced in the 12C-rich intershell. The characteristic neutron exposures in the three layers are different. Moreover, when the nucleosynthesis occurs in a radiative layer, only the nucleosynthesis products are ingested into the convective thermal pulse, which makes the classical concept of mean neutron exposure ([FORMULA]) become meaningless and the simple assumption of an exponential distribution of the neutron exposure fail to account for the complexity of the phenomenon (Arlandini et al. 1995; Gallino et al. 1998). Busso et al. (1999) reviewed this new s-process nucleosynthesis scenario in details.

The spectral and luminosity studies of AGB stars (including MS, S and N-type C stars) have shown that the M[FORMULA]S[FORMULA]C sequence is the result that the low-mass AGB stars have undergone carbon synthesis, s-process nucleosynthesis and the third dredge-ups (Lambert 1991). These stars are in the course of experiencing thermal pulse stage, and the original chemical abundances of their atmospheric envelope have been modified by two mixing mechanisms, namely, the first dredge-up when they became red giants and the third dredge-up when they became TP-AGB stars (Boothroyd & Sackmann 1988a, b, c and d).

The predicted evolutionary sequence of M[FORMULA]S[FORMULA]C in the heavier-lighter s-element abundances relationship (here and hereafter, `heavier' refers to the second metal peak elements: Ba, La, Ce, Nd and Sm etc.; `lighter' refers to the first metal peak elements: Y, Zr etc.) and the heavy-element abundances-C/O relationship (12C, together with the s-process elements, is dredged up from stellar interior during the third dredge-up process) are important to understand the nucleosynthesis and evolution of AGB stars. Because (1) they will provide theoretical basis for the observed evolution of the sequence, (2) they can check the available theories on the evolutions of AGB stars (e.g., the beginning of the third dredge-up process, the mass and the chemical abundance of the dredge-up material, the theory of s-process nucleosynthesis, the stellar wind mass loss, and the formation of carbon stars etc.).

Busso et al. (1992) discussed the heavy-element abundances of M, MS and S stars using the thermal pulse AGB model. Busso et al. (1995) analyzed the heavy-element overabundances of carbon stars under the assumption that the dredge-up started after reaching the asymptotic distribution (about the 20th pulse). It is difficult to calculate the AGB stars evolution and s-process nucleosynthesis. So there are few theoretical results to explain the M[FORMULA]S[FORMULA]C evolutionary sequence based on the combination of the heavier-lighter s-element abundances ratio and the C/O ratio, though the observational abundances exhibit a certain regularity. Zhang et al. (1998a) calculated the evolution of the surface heavy element abundances and C/O ratio for a 3[FORMULA] TP-AGB star with initial metallicity 0.015, and gave interesting results. But they adopted mean neutron exposure [FORMULA] and unbranch s-process path, which have been revised in these years.

In the first part of this paper, we adopt the new s-process nucleosynthesis scenario (Straniero et al. 1995; Straniero et al. 1997; Gallino et al. 1998; Busso et al. 1999 etc.), and the branch s-process nucleosynthesis path to calculate the s-process nucleosynthesis of solar metallicity 3[FORMULA] AGB stars. And then, we discuss the M[FORMULA]S[FORMULA]C sequence based on the heavy-element abundances and C/O ratio.

The importance of AGB stars nucleosynthesis is not only to explain the observational M[FORMULA]S[FORMULA]C sequence but also to be responsible for the origin of some other classes of stars with overabundances of heavy-elements.

Observations revealed that some stars with overabundances of heavy-elements were not luminous to up to the stage of AGB. Following Lambert (1991), the stars showing heavy-element overabundances are divided into two classes: (1) intrinsic TP-AGB stars-they include MS, S and C (N-type) stars exhibiting the unstable nucleus [FORMULA]Tc ([FORMULA]yr) as evidence that they are presently undergoing nucleosynthesis activity and the third dredge-up, and (2) extrinsic AGB stars-they include the various classes of G-, K-type barium stars and the cooler S, C stars where [FORMULA]Tc is not observed. It is generally believed that the extrinsic AGB stars belong to binary systems and their heavy-element overabundances come from accretion of the matter ejected by the companions (the former AGB stars, now evolved into white dwarfs) (McClure et al. 1980; Boffin & Jorissen 1988; Jorissen et al. 1998; Jorissen & Van Eck 2000; Jorissen 1999). The mass exchange took place about [FORMULA] years ago, so the 99Tc produced in the original TP-AGB stars have decayed. The accretion may either be disk accretion (Iben & Tutukov 1985) or common envelope ejection (Paczynski 1976). Han et al. (1995) investigated in detail the evolutionary channels for the formation of barium stars. In this paper we will only discuss the stellar wind accretion scenario because it is very important to explain the formation of barium stars (Boffin & Jorissen 1988; Jorissen et al. 1998).

Boffin & Jorissen (1988) calculated qualitatively the variation of orbital elements caused by wind accretion in binary systems. They also estimated the heavy-element overabundances of barium stars. Subsequently, Boffin & Zacs (1994) used similar methods to calculate the overabundances, and interpreted the relationship between the heavy-element abundances and the orbital periods of barium stars.

Some important conclusions have been drawn in the theory of wind accretion, but the previous calculations on orbital elements were not very reliable because of the neglect of the [FORMULA] term (r represents the distance between the two components of the binary system), and using the tangential momentum conservation (Chang et al. 1997 and references therein). For the rotating binary system with wind mass loss, the total angular momentum conservation is more reasonable than tangential momentum conservation. Also, the previous calculations of heavy-element overabundances used the `step-process' (Boffin & Jorissen 1988; Boffin & Zacs 1994), which means that the overabundance factor changes at one single instant from 1 to f (f is the relative ratio of the heavy-elements to the solar abundances, and differs for different elements. Earlier calculations used the mean f value of carbon stars), and then keeps the value until the end of the AGB phase. However, after the start of the TDU, the overabundance factor f of the intrinsic AGB stars changes during successive dredge-ups. It is after a number of dredge-ups that the C/O ratio in the outer envelope of the intrinsic AGB star reaches 1, which means that the AGB star becomes a carbon star. The heavy-element overabundances of the barium star should be caused by the successive pulsed accretions and mixing.

According to the analysis to the orbital elements of barium and S stars, Jorissen & Mayor (1992) presented the evolutionary pathways of binaries leading to barium and S systems. They concluded that the binary systems with longer orbital period formed through wind accretion and those with shorter orbital period formed via Roche lobe overflow. But the specific range of orbital period was not presented. Jorissen et al. (1998) analyzed the orbital elements of a large sample of binary systems to give insight into the formations of barium and Tc-poor S stars. They suggested that barium stars with orbital period P[FORMULA]1500 d formed through wind accretion scenario. Zhang et al. (1999) suggested that the barium stars with P[FORMULA]1600 d formed via wind accretion according to their model. Liu et al. (2000) suggested that the barium stars with orbital period P[FORMULA]1600 d evolved from normal G, K giants through wind accretion scenario.

Besides the orbital elements, the heavy-element abundances of barium stars have been discussed in some literatures. Busso et al. (1995) discussed the observational heavy-element abundances of barium stars. And a more detailed analysis of the abundance distributions for five stars has been performed using the method of mixing the accretion mass with the envelope mass. But the effect of mass accretion and the changes of orbital elements were not considered. Chang et al. (1997) and Liang et al. (1999) attempted to explore the relationships between the heavy-element overabundances and orbital elements of bariums stars using the binary accretion scenario, but with the shortcomings: or using the tangential momentum conservation, or adopting the old nucleosynthesis scenario of TP-AGB stars.

In the second part of this paper, we firstly calculate the variation equations of orbital elements based on the angular momentum conservation model of wind accretion, then we calculate the heavy-element overabundances of barium stars via successive pulsed accreting matter enriched heavy-elements from the intrinsic AGB stars, and mixing the matter with their envelopes.

This paper is organized as follows. The observational data of MS, S, C (N-type) stars and barium stars are given in Sect. 2. In Sect. 3, we present the model and the main parameters of AGB stars nucleosynthesis and the angular momentum conservation model of wind accretion scenario for barium stars. Sect. 4 illustrates and analyzes our results. We conclude and discuss in Sect. 5.

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© European Southern Observatory (ESO) 2000

Online publication: December 11, 2000