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Astron. Astrophys. 355, 176-180 (2000)

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3. Predicted 19F yields from individual WR stars

As discussed by Arnould et al. (1999) on grounds of the NACRE rates, [FORMULA] could be overproduced (with respect to solar) by the CNO cycle only at temperatures around [FORMULA] K, the exact level of this overproduction remaining poorly predictable, however, in view of remaining rate uncertainties. This conclusion contradicts the one derived from the use of the rates recommended by Caughlan & Fowler (1988), in which case fluorine can never emerge in significant amounts from the CNO burning. As the latter rates are adopted in our calculations, the CNO zones of the computed model stars are depleted in [FORMULA]. This translates directly into a decrease of the [FORMULA] mass fraction [FORMULA] at the stellar surfaces when the [FORMULA]-depleted CNO ashes are uncovered by mass loss (with the choice of the ordinate scales, the changes of fluorine abundance at the center and at the surface during the H-burning phase are not visible on Fig. 1). With the NACRE rates, it is expected that more [FORMULA] would be present at the surface. However, it is also likely that this change is not able to affect drastically the predicted final yields, as these are dominated by the [FORMULA] made during the He-burning phase.

[FIGURE] Fig. 1. Evolution of the total mass [FORMULA], of the mass of the convective core [FORMULA], and of the central ([FORMULA]) and surface ([FORMULA]) [FORMULA] mass fractions for the 60 [FORMULA] model stars with metallicities [FORMULA], 0.020 and 0.040 during the end of the H-burning stage and the whole He-burning phase. The initial [FORMULA] mass fraction is assumed to relate to the solar value [FORMULA] by [FORMULA]. The spectroscopic types encountered during the evolution are indicated on the right of the figure: OV for O-type main sequence stars, LBV for Luminous Blue Variables, WNL, WNE and WC for the different classes of WR stars. Note the different ordinate scales on the left and on the right of the figure.

In fact, as seen in Fig. 1, fluorine builds up through [FORMULA] during the early phase of core He-burning. However, at the end of He-burning, [FORMULA] is responsible for a significant [FORMULA] destruction. Thus, material experiencing the whole He-burning episode cannot be [FORMULA]-enriched. In contrast, in massive stars going through the WR stage (initial mass [FORMULA] for [FORMULA], [FORMULA] for [FORMULA]; see Maeder & Meynet 1994), some [FORMULA] synthesized early during the core He-burning phase is ejected into the interstellar medium by stellar winds before its destruction . Indeed, Fig. 1 exhibits an increase of [FORMULA] when the He-burning products appear at the surface during the WC phase. As a result, the ratio [FORMULA] of the average [FORMULA] surface mass fraction during the whole WC phase to the solar system [FORMULA] mass fraction takes values as high as about 55, 95 and 60 in the case of the [FORMULA] model stars with [FORMULA], 0.02 and 0.04, respectively.

Fig. 2 shows the [FORMULA] "wind" yields for the computed stars ([FORMULA], Z) with initial mass [FORMULA] and metallicity Z. These yields, noted [FORMULA], are equal to

[EQUATION]

where [FORMULA] is the total lifetime of the star ([FORMULA], Z), [FORMULA] its mass loss rate at age t, [FORMULA] its [FORMULA] surface mass fraction at age t, and [FORMULA] its initial [FORMULA] mass fraction, assumed to relate to [FORMULA] by [FORMULA]. These yields may be negative if most of the ejected material has been depleted in fluorine.

[FIGURE] Fig. 2. Mass of [FORMULA] ejected by the stellar winds ([FORMULA] in Eq. (1)) as a function of the initial mass and metallicity.

Fig. 2 demonstrates that the highest yields are obtained for stars with [FORMULA] and [FORMULA]. At lower metallicities, the winds are indeed weaker, and thus uncover the He-burning core only for the most massive stars and when the 19F has already been burnt. On the other hand, at higher metallicities and for [FORMULA], the H-burning core mass decreases so rapidly during the main sequence as a consequence of very strong stellar winds that the He-burning core becomes too small for being uncovered by the stellar winds.

The above discussion shows that the most important physical ingredient influencing the WR [FORMULA] yields is the metallicity-dependent mass loss rates, quantities like convective core masses being less crucial in this respect. As a numerical example, the value for [FORMULA] rises from about 18 in the 60 [FORMULA] low mass loss rate model of Meynet & Arnould (1993) to about 95 in the same model star computed in this paper with an increased [FORMULA] value. This high sensitivity to [FORMULA] might cast doubts on the reliability of the predicted [FORMULA] yields. In fact, some confidence in the results presented in this paper may be gained by noting that our present choice of the mass loss rates allows to account for the variation with metallicity of the number ratio of WR to O-type stars in regions of constant star formation rate (Maeder & Meynet 1994).

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© European Southern Observatory (ESO) 2000

Online publication: March 17, 2000
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