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Astron. Astrophys. 354, 125-134 (2000)

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5. Discussion

5.1. Metallicities of obscured AGB stars in the Magellanic Clouds and in the Milky Way

What are the initial metallicities of the obscured AGB stars in the samples under study? First I discuss the dust-to-gas ratios in the ISM, before discussing metallicities of relatively young stellar populations. These considerations lead to estimates of the typical initial metallicities of the obscured AGB stars under study. These will then be used to correlate the mass-loss rates and dust-to-gas ratios with initial metallicity.

Most of the mass of stars that eventually evolve into AGB stars is returned to the ISM, enriched with dust. These intermediate-mass stars are sufficiently numerous and short-lived that the ISM has been recycled by them at least several times over the history of their parent galaxy. A 5 [FORMULA] star has a lifetime of [FORMULA] yr (Marigo et al. 1999), and there have been already [FORMULA] generations of these massive AGB stars at work in mixing dust with the ISM. Dust-to-gas ratios in the ISM of the LMC are found to be [FORMULA] of that of the ISM in the Solar neighbourhood (van Genderen 1970; Koornneef 1982; Clayton & Martin 1985), and in the SMC it is [FORMULA] of that in the Solar neighbourhood (van den Bergh 1968; van Genderen 1970; Lequeux et al. 1982; Bouchet et al. 1985). Dust is being destroyed in the ISM by shocks and gas accretion, especially in Star Formation Regions. Hence the dust-to-gas ratios in the ISM may only pose a lower limit to the dust-to-gas ratios in the CSEs of obscured AGB stars.

Initial metallicities for relatively young ([FORMULA] yr) field stars are found to be about 2 and 5 times lower in the LMC and SMC, respectively, compared to Solar metallicity (Spite et al. 1989a,b; Russell & Bessell 1989; Meliani et al. 1995; Luck et al. 1998). When depicting the chemical evolution of the MCs, however, it is clear that the initial metallicity with which stars were born a few Gyr ago was considerably lower - roughly twice - than what is measured in massive stars today (de Freitas Pacheco et al. 1998; Da Costa & Hatzidimitriou 1998; Bica et al. 1998). Obscured AGB stars, with a characteristic age of [FORMULA] yr, are thus expected to have initial metallicities somewhat lower than those measured in young field stars. Stars in the central regions of the Milky Way galaxy are found to cover a range in metallicity from sub- to super-solar, with the most easily observed obscured AGB population likely to comprise relatively massive stars of slightly super-solar initial metallicity (Rich 1988; Wood et al. 1998).

These considerations lead us to adopt a typical initial metallicity (logarithmic) of [FORMULA] for obscured AGB stars in the SMC, [FORMULA] in the LMC, [FORMULA] in the Solar neighbourhood, and [FORMULA] in the Galactic Centre. The margins are rough estimates for the typical range in initial metallicities, meaning that the typical metallicity for the sample is not expected to lie outside of these margins.

5.2. Mass-loss rates and dust-to-gas ratios

The values for the combination of mass-loss rates and dust-to-gas ratios as derived from using Eqs. (4) & (5) and listed in Tables 1 & 2 are plotted in Fig. 7. First order polynomials are drawn through the points. For the obscured M-type stars with [FORMULA] d the polynomial was forced to cross the LMC data point, while the average was taken of the slopes obtained by either omitting the "Solar neighbourhood" data point or the Galactic Centre data point. The slopes of the polynomials can be used to constrain the dependence of the mass-loss rate on initial metallicity z (with [FORMULA]) and the dependence of the dust-to-gas ratio on z, assuming that [FORMULA] and [FORMULA]. It then follows that the slope for [FORMULA] equals [FORMULA], and the slope for [FORMULA] equals [FORMULA]. The sub-samples that had been selected according to the pulsation periods have, in fact, very similar slopes, and hence their averages are taken. Thus I find for the obscured M-type AGB stars that [FORMULA] and [FORMULA], whilst I find for the obscured carbon stars that [FORMULA] and [FORMULA]. This yields for the dependences of the mass-loss rate and dust-to-gas ratio on initial metallicity for obscured AGB stars:

[TABLE]

[FIGURE] Fig. 7. Mass-loss rates and dust-to-gas ratios for the obscured AGB stars in the SMC, LMC, "Solar neighbourhood" and Galactic Centre, as a function of their initial metallicities.

The reader should realise that these exponents are indicative, but not very accurate. The errors (excluding those resulting from uncertainties in the adopted initial metallicities) mainly result from the small number of spectroscopically confirmed carbon and M-type stars in the SMC. If the initial metallicity dependence of the mass-loss rate and dust-to-gas ratio is really as similar as suggested here, then the obscured AGB stars in the SMC and LMC may be compared without distinction by chemical type, and the resulting errors on the exponents will become much smaller without significantly changing the values of the exponents themselves. Clearly, it is shown that the method employed here has the prospect of constraining the initial metallicity dependences of the mass-loss rate and dust-to-gas ratio for obscured AGB stars. Suitable data have only recently become available, and more such data are needed to improve on the preliminary results.

5.3. Obscured M-type AGB stars and carbon stars

Obscured M-type AGB stars and obscured carbon stars have been treated separately for two reasons: (i) the optical properties of their circumstellar dust are different, possibly leading to differences in the constants of proportionality [FORMULA] and [FORMULA] in Eqs. (1) and (2), respectively, and (ii) their dust-to-gas ratios and/or mass-loss rates may depend differently on initial metallicity. I here discuss these two issues in more detail.

Both [FORMULA] and [FORMULA] depend on the dust-type through the wavelength dependent opacity [FORMULA] and the flux-weighted opacity [FORMULA], respectively. Using Eq. (4) in the LMC yields indistinguishable distributions of the obscured M-type AGB stars and of the obscured carbon stars. However, in the LMC, obscured carbon stars are bolometrically fainter and exhibit lower mass-loss rates than obscured M-type AGB stars (van Loon et al. 1999b), which is expected to result in an offset between the distributions over [FORMULA]. The fact that this offset is not seen must mean that, by mere coincidence, the differences in [FORMULA] are counteracted upon by the differences in [FORMULA]: at a given luminosity, dust-to-gas ratio and mass-loss rate, obscured carbon stars are redder than obscured M-type AGB stars. Also the coincidence between the distributions of obscured M-type AGB stars and obscured carbon stars using Eq. (5) in the LMC for [FORMULA] d must be coincidental and/or due to low number statistics (only two obscured carbon stars), as the constant in Eq. (5) is proportional to [FORMULA] and differences in optical properties between the different dust species are likely to become apparent. This may explain at least partly the differences in distributions between the obscured M-type AGB stars and obscured carbon stars in the "Solar neighbourhood".

Obscured M-type AGB stars and obscured carbon stars seem to show very similar dependencies of their dust-to-gas ratios and especially their mass-loss rates on initial metallicity. There is no a-priori reason why the mass-loss mechanism should have a different dependency on initial metallicity for stars with different chemical types of circumstellar dust, other than due to a different dependency of their dust-to-gas ratios on initial metallicity. The similarity between the dependencies of the dust-to-gas ratio on initial metallicity is surprising. For obscured M-type AGB stars one may expect that the fraction of metals that are available for the formation of dust particles scales directly with the oxygen abundance in the photosphere, which scales at least approximately directly with the initial metallicity of the star. Hence a direct proportionality between dust-to-gas ratio and initial metallicity may not come as a surprise for obscured M-type AGB stars. For obscured carbon stars, however, the situation is very different: carbon stars only become carbon stars after [FORMULA] dredge-up has enhanced the carbon abundance in the photosphere from [FORMULA] to [FORMULA]. For obscured carbon stars it is crucial to know the photospheric abundances of both carbon and oxygen, because the carbon is locked into CO molecules until oxygen exhaustion and hence only the carbon excess is available for dust formation. It was thought that at lower initial metallicity, the lower oxygen abundance would make it easier for [FORMULA] dredge-up to raise [FORMULA] above unity, but the fact that no optically bright luminous carbon stars were found in the MCs meant that it is not that simple (Iben 1981). Not only is it poorly understood how [FORMULA] dredge-up depends on initial metallicity (but see Marigo et al. 1999), there is also a second important phenomenon active: carbon star formation is avoided as long as the stellar mantle is massive enough to yield pressures and temperatures at the bottom of the convective layer sufficiently high for processing of carbon into oxygen and nitrogen to occur (Hot Bottom Burning; Iben & Renzini 1983; Wood et al. 1983). Thus it remains to be seen how the carbon excess for obscured carbon stars depends on initial metallicity (see also van Loon et al. 1999a). The data and analysis presented here suggest that the carbon excess for obscured carbon stars may be directly proportional to the initial metallicity.

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Online publication: January 31, 2000
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