5 MgS

Figure 8: The effect of grain shape. We show the absorptivity of MgS as a function of grain shape. The numbers between brackets refer to the axis ratios of the elliptical grains. For comparison we show the derived emissivities of RAFGL 190 and NGC 7027.

Since, it has been demonstrated for a few sources that MgS is a viable candidate (Begemann et al. 1994; Jiang et al. 1999; Szczerba et al. 1999), we first test MgS as a possible candidate for the carrier of the feature. With the large sample of good quality spectra in this study we are able to test this possible identification systematically in a large population of evolved objects.

As explained above we cannot derive a priori information on the temperature of the "30'' $\mu$m carrier from the observations. Our knowledge is further limited by the fact that even for some of the candidate materials like MgS or FeS the optical properties are measured only in a limited wavelength range. We lack measurements in the UV, optical and near-IR range, which may well dominate the dust heating. We have decided to test the MgS identification, leaving the grain temperature as a free parameter. We adopt the method we describe below.

5.1 Material

We use the optical constants as published by Begemann et al. (1994). Of the materials they measured, Mg_0.9Fe_0.1S is closest to pure MgS. The real and imaginary part of the refractive index (n and k values) are given from 10-500 $\mu$m.

5.2 Shapes

From the n and k values we can calculate the absorption cross-sections for various grain shapes and shape distributions in the Rayleigh limit following Bohren & Huffman (1983, Chapters 5, 9 and 12). The absorption cross-section of MgS around 30 $\mu$m is very sensitive to the grain shape. In Fig. 8, we show the results of using different grain shapes on the absorption properties of MgS. We use a continuous distribution of ellipsoids (CDE) for the grain shapes. This shape distribution was used by Begemann et al. (1994) and gave a good fit to the "30'' $\mu$m feature observed in CW Leo. The same shape distribution was further used by Jiang et al. (1999) and Szczerba et al. (1999). They found reasonable fits for the two sources they study. As can be clearly seen in Fig. 8 when comparing the spheres with the CDE calculations, the feature broadens and the peak position shifts to longer wavelengths using the CDE shape distribution. The width of the feature calculated using CDE matches that of the observed "30'' $\mu$m feature well (e.g. RAFGL 190 in Fig. 8, see also Fig. .1).

5.3 Temperature

Figure 9: The effect of grain temperature on the MgS emission feature. We fold the $\kappa _{\rm abs}$ of MgS in a continuous distribution of ellipsoids (CDE) shape distribution with a Planck function of different temperatures. The shape and position of the feature are modified substantially.

To estimate the MgS temperature ( $T_{\rm MgS}$) we use the continuum subtracted spectra with the continuum as derived in Sect. 3. The emission from MgS grains is calculated using the $\kappa _{\rm abs}$ folded with a Planck function with the temperature of the grain. Due to the smooth and broad shape of the resonance the profile of the emission is very sensitive to $T_{\rm MgS}$. In particular the peak position changes strongly with $T_{\rm MgS}$. This allows us to estimate $T_{\rm MgS}$from the continuum subtracted profiles. This method is most sensitive for $T_{\rm MgS}$ < 300 K. Above 300 K, further changes in the profile are more subtle since the major part of the feature falls in the Rayleigh-Jeans domain of the Planck function.

We use this temperature estimate and the observed band strength in the continuum subtracted spectra to synthesise a MgS feature in order to compare with the astronomical spectra. In conclusion, we adopt MgS with a CDE shape distribution and allow both the strength and the temperature of the MgS grains to vary with respect to the underlying continuum.