4 Profiles

Figure 7: Emissivities for different sources as deduced from the ISO spectra. There are large differences in the profile of the excess emission. Notice the shift in peak position and change in width of the circumstellar "30'' $\mu$m feature going from the C-stars to post-AGBs to PNe (top to bottom).

Using the continua defined in this way, we measure the following properties of the "30'' $\mu$m feature: the centroid wavelength ( $\lambda _{\rm c,30}$), i.e., the wavelength where the integrated flux in the feature at either side is equal; the full width at half maximum (fwhm); the flux in the "30'' $\mu$m feature and the height of the peak of the "30'' $\mu$m feature after continuum subtraction over the continuum ratio, i.e., the peak to continuum ratio (P/C). The measured values are listed in Table 2. We list upper limits for P/C and the flux for the sources without detection. In Fig. 6, we show the relation between the [25]-[60] colour and $\lambda _{\rm c,30}$. There is a clear reasonably smooth trend for the feature to move to longer wavelengths with redder IRAS colours. This indicates that the temperature of the dust is an important parameter in determining the profile of the "30'' $\mu$m feature since [25]-[60] is a direct measure of the dust temperature provided that the dust composition in the different sources is similar.

We first try to remove the effect of temperature by dividing by the continuum; a method that is commonly applied. Using the modelled continua as described in Sect. 3, we convert the observed features to relative excess emission by dividing by the continuum and subtracting 1.

If the feature emission is optically thin and the temperature of the carriers of the feature is equal to the continuum temperature the derived excess emissions are proportional to the absorptivity ( $\kappa _{\rm abs}$) of the carrier and if the carrier is the same in these sources then the derived band shape should be the same for all sources. However, we find large variations in the derived profiles. In Fig. 7, we show some examples of the derived profiles. Most notable are variations in peak position and the appearance around 26 $\mu$m. Such changes, albeit within a smaller range of feature peak positions have led other authors (Volk et al. 2000,2002) to conclude that the "30'' $\mu$m feature is composed of two features and the observed variations are due to varying relative contributions of these two components. One key question is: "What possible causes could there be for the observed large variations in band shape?''. We discuss three possibilities below. First, optical depth effects. Second, temperature effects. Finally, we discuss multiple band carriers.

The optically thin assumption most likely holds because the optical depth in the circumstellar shell strongly decreases towards longer wavelengths. Note, in this respect that the "30'' $\mu$m feature is never found in absorption (however, see also Sect. 6.2). Hence, optical depth effects are not responsible for the observed profile variations.

Whether the temperature of the amorphous carbon grains (defining the shape of the continuum) and the temperature of the "30'' $\mu$m carrier are equal is very uncertain. The temperature of a dust grain in a circumstellar envelope is determined by the distance to the star, the absorption properties in the wavelength range where the star or the dust shell emits light and the grain size. In case the temperature of the grains species responsible for the continuum and the "30'' $\mu$m emission feature are not the same, the resulting excess profiles will also not be the same from source to source even if the carrier of the band is the same. The differences will be very pronounced when the emission feature is broad. In this case systematic difference between sources are bound to occur in league with the strongly changing continuum temperature. Thus, the temperature of the carrier of the "30'' $\mu$m feature is an important parameter that determines the profile of the emission.

There may be multiple carriers involved as discussed before. In this case the feature near 26 $\mu$m dominates in the warmest objects while the cooler objects are more and more dominated by emission towards 35 $\mu$m. However, this scenario has its difficulties since it would require changes in the composition of the dust in the relatively dispersed and cold nebular surroundings of a post-AGB object or even during the PN phase. Such chemical changes can only occur extremely slowly, if at all.

Lastly, variations in grain shape or variations in shape distribution can influence the emission profiles. The optical properties of materials with a high value of the refractive index are sensitive to the grain shape. Variations in the shape distribution will lead to variations in the profiles.

In our analysis, we will focus on explaining the profile variations with temperature variations and the effects of variations in the shape distribution of the emitting dust grains.