8 Discussion

   
8.1 Carrier

The models using MgS we present do very well in explaining the profile of the feature found in the C-stars and post-AGB objects. The model does not do as well in explaining the profile of the feature found in the PNe. However, the smooth relation found between the [25]-[60] colour and the $\lambda _{\rm c,30}$ shows a gradually changing profile with dust temperature. This suggests one carrier or closely related carriers. Also the similar P/C values for the different classes of objects is indicative of one carrier.

Recently Grishko et al. (2001) proposed HAC as the carrier of the mid-IR emission features in C-stars, post-AGBs and PNe. HAC is a very plausible dust component in those environments (e.g. Duley & Williams 1981; Goebel 1987; Borghesi et al. 1987; Henning & Schnaiter 1999). However, the mid and far-IR optical properties of HAC are dominated by a $\lambda^{-1}$continuum (Bussoletti et al. 1987). Grishko et al. (2001) identified some 13 weak spectral features in the range from 19-120 $\mu$m. The strongest of which occur at 21, 27 and 57 $\mu$m. We consider HAC a unlikely candidate for the circumstellar "30'' $\mu$m emission feature because the laboratory features are weak in contrast to the astronomical data and because the far-IR features of HAC are not observed in the astronomical spectra.

8.2 The effect of model simplifications

It is remarkable that our simple model works so well. We have applied various simplifications in order to be able to study the whole sample in a unified way. These simplifications necessarily lead to differences between the models and the observations. Instead of assuming a single temperature modified blackbody for the shape of the continuum one can certainly obtain a more detailed fit by taking into account the structure of the CS envelope and the opacities of the different molecular and dust constituents. Our method works well because the contributions of the other known other dust components around 30 $\mu$m are well behaved, smooth and thus indeed form a continuum. Moreover, the shape of our modelled continuum between 20-50 $\mu$m is not a strong function of the emissivity index (p) and varying the p-parameter or the temperature doesn't yield qualitatively different continuum shapes or levels. We already pointed out that in some cases our model fails at the longest wavelengths of the SWS observations, which may be related to our method to estimate the continuum.

We use a single temperature for the MgS to model its contribution. In the very extended envelope of a C-star or in the nebulous environments in the post-AGBs and PNe, the temperature of any dust component will not be constant but decreases as a function of the distance to the star. The fact that we still get good results using a single temperature is a clear indication that the emission is optically thin and that the density of the MgS falls off sharply with distance. In an optically thin environment we know that $T_{\rm dust}\propto\sqrt{R}$, where R is the distance to the star. If the density distribution drops with distance as R^-2 or steeper, the contributions are weighted to the highest temperature part of the envelope where $T_{\rm dust}$ and thus the source function is highest. If the density distribution is flatter there is relatively more dust far away than close by. In this case we will observe MgS with a range of temperatures. Also sources that are not optically thin will emit a feature broader than our single temperature MgS model (see also Sect. 6.2). We conclude that in the majority of the sources the "30'' $\mu$m emission is due to optically thin emission which is dominated by the highest temperature MgS closest to the star.

   
8.3 Shape

We find that a CDE shape distribution fits many observations well. A CDE shape distribution is used to model a collection of irregularly shaped grains. Irregularly shaped grains can for example result from grain growth by agglomeration (Blum et al. 2000).

We find evidence for differences in the shape distributions between sources. We have tested for correlations between the strength of the 26 $\mu$m excess (due to spherical MgS grain) and the CDE component and other parameters like the mass-loss rate, the P/C, the continuum temperature or the feature temperature. We find no clear correlations. We do however note that we find little evidence for the 26 $\mu$m excess in the hottest C-stars. Stars in our sample with a continuum temperature above 1000 K do not exhibit the excess. Below 1000 K we find both sources with and without the 26 $\mu$m excess. Note also that the occurrence rate of the 26 $\mu$m excess in the sample of post-AGB objects is high. Because the emission in the post-AGB phase may be dominated by the dust closest to the star and hence lost at the tip of the AGB during a phase of heavy mass loss (at a rate much higher than during the general AGB phase), this might suggest that the shape distribution of the grains changes to become more spherical towards the end of the AGB, possibly as a function of mass-loss rate.

   
8.4 Planetary nebulae

The profile of the "30'' $\mu$m feature we find in most PNe is narrower than in our model. The largest discrepancy occurs around 26 $\mu$m. Our model fits are able to explain the shift in centroid position observed in the PNe; however, the models that explain the band-shift best, over-predict the flux at 26 and 40 $\mu$m.

There are several observational properties that are important when considering explanations for the observed discrepancies. First, there is the similar values of P/C in the sample of post-AGBs and PNe (Fig. 15b). This indicates that the carriers are related and similar in abundance. Second, the smooth trend we find in the centroid position of the "30'' $\mu$m feature with the [25]-[60] colour (Fig. 6). The PNe profiles follow the general trend. This indicates that the main effect for the peak shift also in the PNe is due to temperature. We also note that there are three non-PNe sources in our sample with cold MgS (R Scl, IRAS 19454 and IRAS 23321). These sources are well fitted by our model. This indicates that the narrow profiles are particular to the PN environment.

We have explored possible MgS based heterogeneous grains and variations in MgS grain shape. The heterogeneous grains we have explored do not compare satisfactorily with the observed profile in the PNe. MgS grains coated with a layer of amorphous carbon provide a somewhat better match in terms of the band shape however the contrast of the feature with respect to the continuum is strongly reduced. The reduced band strength is in contradiction with the observed peak over continuum ratios.

We find that the emission from plate-like MgS grains appears similar to the feature found in the PNe. In Sect. 6.1 we consider an extra contribution of spherical MgS grain to the "30'' $\mu$m feature at 26 $\mu$m. The varying strength of this contribution demonstrates that there are variations in the grains shape distribution between sources. The question is: "Is it possible that the narrow "30'' $\mu$m feature in the PNe is carried by flattened MgS grains?'' This would either imply that the MgS grain shape distribution in the PNe is heavily skewed to the plate-like grains or that the oblate grains emit more efficiently.

The origin of these variations in the shape distribution are unclear. They may reflect variations in the formation and destruction of grains. We do not know of a mechanism that drives towards oblate grains shapes during the PN-phase or a mechanism that selectively destroys spherical and prolate grains. Note, that the peak over continuum value in the PNe is similar to those found in the post-AGB objects arguing against a destruction of a part of the MgS grains. It is important to remark that in the CDE distribution only $\sim$20 per cent of the grains is oblate with an axis ratio of 1: ${1}\over{5}$ or more extreme, i.e. with axes ratios of 1:X:Y, where Y is smaller than ${1}\over{5}$ and X can vary between $\sqrt{X}$ and 1. Such axes ratios are required in order to shift the peak position to the wavelength where the "30'' $\mu$m feature in the PNe peaks and to suppress the emission at 26 $\mu$m.

Alternatively, these inferred shape variations may result from a shape dependent heating of grains. In the C-stars, likely, heating and cooling occurs at IR wavelengths. Because the grains are small compared to these wavelengths the temperature will be shape independent. However, in the PNe heating occurs through absorption of visible and UV radiation, which scales with the cross-section. Hence in that case dust temperatures will be shape dependent. Indeed flattened grains have on average a larger geometric cross-section compared to their volume that spherical or prolate grains.

As noted before, the PNe in the sample with the warmest dust continuum are well fitted by our model. The model fails in the PNe sample at MgS temperatures below $\sim$90 K. Perhaps, the observed discrepancies are due to changes in the optical properties of pure MgS at low temperatures. No laboratory measurements of MgS at these temperatures are published. FeO has the same lattice structure as MgS and measurements of FeO at different temperatures (10 K, 100 K, 200 K and 300 K) are available (Henning & Mutschke 1997). We have used FeO as an analogue to examine the effect of temperature. The trend with lower temperature is for the FeO resonance at 20 $\mu$m to become narrower and stronger with respect to the continuum. There is a small shift in the peak position. Comparing the 300 K measurement to 10 K the latter resonance peaks $\sim$0.1 $\mu$m more to the blue for spherical grains. Like MgS, FeO is also very sensitive to the shape of the grains. Using a CDE shape distribution the resonance of the 10 K sample lies $\sim$1 $\mu$m on the blue side of the 300 K resonance. If we translate this behaviour to the MgS data and the "30'' $\mu$m feature in the PNe it worsens the situation since we would expect a stronger contribution at shorter wavelengths exactly where our model already over-predicts. As an alternative, one might speculate that a change in lattice structure at low temperatures may occur resulting in different optical properties. It is interesting to note that Berthold (1964) reports that MgS can condense in two lattice structures: cubic and hexagonal. This author finds that hexagonal MgS exhibits a narrower mid-IR resonance than cubic and amorphous MgS.

We conclude that, although it is possible to find MgS based candidate materials that provide a better spectral match to the observed "30'' $\mu$m feature in the PNe no explanation for the "30'' $\mu$m profiles in the PNe is completely satisfactory at this time.

   
8.5 MgS temperature

We have found that the "30'' $\mu$m feature is very well explained with MgS provided that the continuum temperature and the MgS can be substantially different from each other (see also Fig. 17). Moreover, the temperature difference changes between classes of sources. In the C-stars we find that MgS is colder than the continuum while in the post-AGB sample the MgS grains are warmer. The temperature difference and the fact that the continuum temperature varies relative to the MgS temperature implies that the MgS grain are not in thermal contact with the amorphous carbons grains that carry the continuum. Thus, MgS is condensed in these environments into separate grains.

The relatively warm hot MgS that we observe in the post-AGB sample is certainly a phenomenon that deserves further study. As pointed out above, this must be due to a difference in the heating properties of MgS relative to the other dust constituents. We suggest that due to the strong resonance in the mid-IR MgS is (partially) heated by IR radiation. This may cause a temperature difference as observed. It requires measured optical constants for MgS over a much wider wavelength range than now available and radiative transfer modelling to understand the detailed temperature behaviour of the MgS grains.

We have shown in Fig. 17 that the warmest C-stars that exhibit the "30'' $\mu$m feature have cold MgS. We consider two possible explanations for this behaviour. First, MgS can be cold because it is unable to absorb the radiation from the central source efficiently. This would require that the MgS grains are very transparent in the visible and near-IR where these warm C-stars emit most of their radiation. In this case a cooler star will emit more radiation at wavelengths where MgS can absorb and as a result the MgS grains will be warmer. This explanation is consistent with our notion that MgS is (partially) heated by IR radiation.

A second intriguing possibility is that the MgS around these sources is located far away from the star. R Scl, U Cam and W Ori are known to have a detached dust shell (Zuckerman 1993). These shells are formed during an earlier phase when the mass-loss rate was higher than the current mass-loss rate (Willems & de Jong 1988). If during this phase the AGB star was already a C-star, MgS could have condensed in the outflow and be present in the detached shell. We have sketched in Fig. 1 the evolution of a star which suffers a brief period of enhanced mass loss. First, the star becomes redder during the phase of high mass loss. When the shell becomes detached the 12 $\mu$m flux quickly drops while the inner edge of the dust shell moves away from the star and the warmest dust is rapidly lost. The star moves back to the locus of the warmest C-stars but with an excess of cold dust. The excess of cold dust is observable as a 60 $\mu$m excess. The sources mentioned above indeed show the 60 $\mu$m excess. We note that some stars with 60 $\mu$m excess do not show the "30'' $\mu$m feature.

To distinguish between these two possibilities requires radiative transfer modelling and a more detailed investigation of these particular sources which is beyond the scope of this paper. The location and temperature of the MgS in the warmest C-stars will be further discussed in a forthcoming paper (Hony et al., in prep.).

   
8.6 MgS in the ISM

The behaviour of the MgS we find in this study has implications for our understanding of the fate of MgS that is produced during the C-star phase. Previously, the existence of MgS in the ISM has been excluded because of the lack of spectral signature at 26 $\mu$m. We have shown that at low dust temperatures no emission signature is expected at 26 $\mu$m. For the dust temperatures in the ISM we would expect a smooth feature at wavelengths longer than 35 $\mu$m. In this respect it is interesting to note that the peak to continuum (P/C) values in the post-AGB and PNe sample are similar. We find no evidence for a rapid destruction by the UV radiation field in the PN. This shows that the MgS will indeed be injected into the ISM. Of course, in the ISM the contrast will be much less because the injected material will be diluted with other star-dust and general ISM material. Nevertheless a search for the "30'' $\mu$m feature in the ISM may be very worthwhile. In this respect it is important to note that Chan et al. (1997) have discussed a broad emission feature they observed along several lines of sight towards the galactic centre. The feature they observed is similar to the "30'' $\mu$m feature observed in the C-rich post-AGB objects.