5 Conclusions

The results of this study can be summarized as follows:

1.

The observed 10 $\mu$m silicate bands in the ISO spectra of the studied HAEBE systems can be ordered from a profile peaking at 9.8 $\mu$m - resembling the ISM silicate band - towards a profile similar to cometary spectra, peaking at 11.3 $\mu$m. We find a relation between the 11.3 $\mu$m flux and the occurrence of a broad shoulder at
$\sim$8.6 $\mu$m.

2.

We can model the different 10 $\mu$m silicate profiles using three components:

-

silica (SiO₂), responsible for the 8-9 $\mu$m blue shoulder in the silicate band;

-

forsterite, contributing at 11.3 $\mu$m; and

-

amorphous olivine with two typical grain sizes of 0.1 and 2.0 $\mu$m.

3.

We identify two main causes for the observed shift in peak position of the silicate band:

-

a change in average grain size from small (0.1 $\mu$m) to large (2 $\mu$m). This is the result of the depletion of small grains in the inner region of the disk, due to coagulation or other effects that preferentially remove small grains;

-

a change in composition from amorphous silicate to a mixture of amorphous and Mg-rich crystalline silicate (forsterite). This may be the result of thermal annealing in the inner regions of the disk. Laboratory experiments indicate that thermal annealing produces both crystalline silicates and SiO₂.

4.

The change in shape of the 10 $\mu$m silicate band in HAEBE stars is mainly due to an increase in average grain size of the dust.

5.

The HAEBE stars, $\beta$ Pic and the solar system comet Halley form a sequence of increasing silicate crystallinity. As the degree of crystallinity increases, the abundance of SiO₂ also tends to increase. This is consistent with the expected changes in composition resulting from thermal annealing of amorphous silicates in the inner regions of the proto-planetary disk.

6.

The observed relation between silica (SiO₂) and forsterite abundance implies that the composition of the amorphous silicate from which these materials are formed can not be chemically homogeneous. A combination of smectite (4% by mass) and serpentine (96%) gave a good fit result.

7.

The mineralogy of HD 100546 and comet Hale-Bopp is remarkable, with very high forsterite abundance and no evidence for SiO₂(cf. Crovisier et al. 1997; Malfait et al. 1998). This composition, which deviates from that of the other objects, suggests a different origin for the forsterite, possibly from the destruction of highly differentiated large parent bodies. Two other objects, HD 150193 and HD 179218 show very high SiO₂ and enstatite abundances, respectively. The origin of these deviating mineralogies is not well understood.

8.

Crystallisation timescales appear to be longer than coagulation timescales.

9.

No correlation between dust composition and disk geometry can be observed.

Acknowledgements

The authors would like to thank the referee J. Mathis, for helpful comments that have improved this paper, and F. J. M Rietmeijer for constructive discussions. The authors would like to acknowledge the financial support from NWO Pionier grant 600-78-333. AdK also gratefully acknowledges support from NWO Spinoza grant 08-0 to E. P. J. van den Heuvel.