Astron. Astrophys. 322, 924-932 (1997)

5. Discussion

In order to account for the difficulties we found in modelling the O-rich envelopes of subclass "S" and "Sil+", several possibilities can be considered: deviation from spherical symmetry, mixing between O-rich and C-rich dust and necessity of new opacities for silicates producing LRS other than "Sil" subclass.

Evidences for non-spherical symmetry of AGB CSEs arise from radio mapping, speckle interferometry, polarization studies and spectroscopic observations as well as from the shapes of planetary nebulae (Balick 1993). Departures from spherical symmetry should then be expected also for our sources (see e.g. Silvestro et al. 1996 for a photopolarimetric study of 5 sources in our sample), and may affect even the thermal IR emission, as shown in Paper I by the elongated shape of CW Leo. Axisymmetric models of AGB circumstellar envelopes have been recently developed by Collison & Fix (1991) and Lopez et al. (1995); here basically the optical depth depends on the orientation with respect to the line of sight. These models thus introduce a new free parameter that allows one to fit the dust feature strength; we notice however that the band intensity remains unchanged with the slope of the continuum, preventing the correct fitting of LRS spectra in our "S" and "Sil+" sources. Furthermore, it is not clear why deviations from spherical symmetry should be important only for these subclasses of envelopes. We conclude that, if a correct two-dimensional treatment of the system geometry is essential for the spatial description of the IR emissions, it does not significantly affect the spectra modelling.

In IE95 the IRAS colors of sources in the class are reproduced admitting mixtures of silicates (plus 20% cristalline olivine) and amourphous carbon (in the ratio 1:4). The possibility of such a mixing is controversial (dust formation in chemical equilibrium models predicts the depletion of the less abundant element between O and C, locked in CO molecules, see e.g. Salpeter 1974), but cannot be completely ruled out, since numerous C-rich stars display the silicate feature (see e.g. Willems & de Jong, 1986 and Le Van et al., 1992). Even though this hypothesis is unattractive, requiring the presence of mixtures only for sources of small optical depth, the others being well fitted by ordinary silicate opacities, we tested this prescription with our "S" and "Sil+" sources.

We have not obtained a real improvement in our "Sil+" model with mixed dust, because the introduction of a new fitting parameter (the silicate/carbon ratio) allowed only to reproduce the shape of the 9.8 µm feature, but not the slope of the continuum, even in the LRS region. On the other hand, in the case of the "S" source, the injection of a large quantity of amorphous carbon dust in the envelope (80% of the total) reduced the strenght of the silicate feature making possible to fit the continuum in a large wavelengths range (even thought the result of the fitting for the continuum is not as good as in the case of silicates only). To understand this result, one should consider that the S-stars like W And are considered objects in transition between the O-rich and the C-rich class, and thus a contamination of silicate dust in a C-rich circumstellar envelope is not at all surprising.

A third possibility to have weak silicate bands in O-rich envelopes, as required in "S" and "Sil+" LRS, without the introduction of carbonaceous dust, is to assume annealing and aging of dust grains, as proposed by Nuth & Hecht (1990). Their grain condensation scheme starts with oxydation of SiO, AlO and OH in O-rich stellar winds, producing grains characterized by weaker features and secondary bands at 11-13 µm; fully grown silicates with strong features condensate only later, and are thus present only in more evolved O-rich envelopes. This view is in agreement with the classification schemes of LML90, assuming that LRS subclasses are associated with dust of different ages. If the Nuth & Hecht (1990) sequence is correct, our O-rich sources with LRS subclass other than "Sil" should be associated with envelopes with less evolved dust.

A simple semi-analytic dust shell models taking into account the presence of oxides has been developed by Onaka et al. (1989a, b). They considered a double component dust shell of silicates and aluminium oxide (Al₂ O₃) with different condensation radii to fit a large sample of optically thin M Mira variables with known LRS. Choosing a larger condensation radius for the silicates, corresponding to a lower ( 500 K) dust temperature, they were able to reproduce LRS spectra with depressed 9.8 µm feature, and thus correctly fit class "Sil+" sources. Two sources in Onaka et al. (1989b) sample are present in our list. One of them is U Her, for which they obtained a more resonable distance determination than ours; the other is S CrB, for which the fitting results are similar. We have not tested Onaka et al. (1989a, b) prescriptions, because our model only describes single-component dust shell models. We postpone this test for a future new radiative-transfer model able to deal with multi component shells; in fact full radiative transfer modelling is necessary even to model optically thin envelopes, as shown by IE95.

© European Southern Observatory (ESO) 1997

Online publication: June 5, 1998

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