2. Condensation calculations
2.1. Element abundances
Condensation calculations are done for two non-standard element mixtures: For S-stars and for stars where heavy mass-loss has exposed layers which formerly have burnt hydrogen by the CNO cycle. The element abundances used in our model calculations are shown in Table 1 for some important elements. For all elements not shown in this table the standard cosmic abundances of Anders & Grevesse (1989) and Grevesse & Noels (1993) are used.
Table 1. Abundances of some elements used in the condensation calculations for S-stars and stars with CNO-cycle equilibrium abundances exposed by mass-loss. Last column shows solar system abundances for comparison.
For S-stars all photospheric element abundances up to the iron peak are not changed during stellar evolution up to the TP-AGB except for He, C, N, and O. For these we scaled the standard abundances according to the change in stellar surface abundances found in the evolutionary calculations of Schaller et al. (1992) for stars of small and intermediate masses. The result agrees with observationally determined mean abundances in AGB stars (Smith & Lambert 1990).
The second element mixture in Table 1 is relevant for very massive and luminous stars, like Car, which loose considerable amounts of mass during their life time by a hot stellar wind and start to expose layers of CNO-cycle processed material after a few million years. The model calculations of Maeder & Meynet (1987, 1988) show that after several million years of stellar evolution the abundances of C and O start to drop considerably below their initial abundances while the abundance of N increases. If we take their final abundance ratios after the sudden C, O depletion and N enrichment of the surface and scale the standard abundances of C, N, and O, we obtain the abundances given in Table 1.
2.2. Condensation sequences
We have calculated chemical equilibrium compositions of a solid-gas mixture which considers the 25 most abundant elements, their first two ionisation stages, their approx. 100 most stable molecules, and approx. 90 solid compounds. Data for equilibrium constants are taken from Sharp & Huebner (1990), Chase et al. (1985), Binnewies (1996), and Tsuji (1973).
Fig. 1 shows the stability limits for the stable condensates of the abundant refractory elements C, Si, Fe, Mg, and Al for a fixed pressure dyn cm-2 which is representative for the condensation zone in circumstellar dust shells. For M-stars () and C-stars () the results agree with the results of previous calculations (e.g. Grossman 1972; Sharp & Huebner 1990; Lodders & Fegley 1993). For S-stars () we find that FeSi is the most stable condensate formed from abundant elements (for C-stars carbon dust, not shown in Fig. 1, is the most stable condensate). The compounds FeSi, FeSi2, and Fe3Si7, considered in our calculation, have not been included in earlier chemical equilibrium calculations.
Fig. 2 shows the stability limits of the stable condensates for the abundant refractory elements Si, Fe, Mg, and Al for the peculiar element mixture (cf. Table 1) when the elements C, N, and O have obtained their equilibrium abundances if a star burns H to He via the CNO-cycle. The abundance of O and C is reduced, then, below the abundances of the refractory elements Mg, Si, and Fe. In our chemical equilibrium calculations we again find FeSi to be the first condensate of the abundant refractory elements in this case. These results indicate that solid FeSi may be formed as an abundant dust component in the outflows of highly evolved stars.
© European Southern Observatory (ESO) 2000
Online publication: May 3, 2000