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Astron. Astrophys. 354, 125-134 (2000)
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 star has a
lifetime of yr (Marigo et al. 1999),
and there have been already
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
of that of the ISM in the Solar
neighbourhood (van Genderen 1970; Koornneef 1982; Clayton & Martin
1985), and in the SMC it is 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
( 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
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 for obscured AGB
stars in the SMC, in the LMC,
in the Solar neighbourhood, and
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
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 ) and the
dependence of the dust-to-gas ratio on z, assuming that
and
. It then follows that the slope for
equals
, and the slope for
equals
. 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
and , whilst I find for the obscured
carbon stars that and
. This yields for the dependences of
the mass-loss rate and dust-to-gas ratio on initial metallicity for
obscured AGB stars:
![[TABLE]](img142.gif)
![[FIGURE]](img140.gif) |
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.
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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
and
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 and
depend on the dust-type through the
wavelength dependent opacity and the
flux-weighted opacity ,
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
. The fact that this offset is not
seen must mean that, by mere coincidence, the differences in
are counteracted upon by the
differences in : 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
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
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 dredge-up has
enhanced the carbon abundance in the photosphere from
to
. 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
dredge-up to raise 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 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.
© European Southern Observatory (ESO) 2000
Online publication: January 31, 2000
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