4. Modelling of the 10-µ m silicate emission band
The observed spectrum shown in Fig. 1 exhibits the 10 µ m silicate band in emission. The relatively large scatter of the data points makes it impossible to discern any structure if present in the band.
Observations of the silicate feature in the spectra of T Tauri stars and Herbig Ae/Be stars have been reported by Cohen (1980), Cohen & Witteborn (1985), and Hanner et al. (1995). The silicate band is seen as an emission feature in several objects, but also as an absorption band in others. Our profile of UX Ori matches the shape of the mean emission feature derived by Cohen (1980) from 5 T Tauri stars quite well. Contrary to this, the profile of Elias 1 derived by Hanner et al. (1994) is very different from our profile. It is much broader and the flat profile has its maximum beyond 10.5 µ m.
Determining the spectral emissivity of the silicates from observations requires the knowledge of the optical depths and the temperatures of the dust components contributing to the observed fluxes in the 10 µ m region. The lack of such knowledge led to the construction of simple models in the past (Gillett et al. 1975, Cohen & Witteborn 1985). The basic result of this procedure is that the observed profiles can be reproduced if the silicates are assumed to emit like the silicates in the Orion Trapezium region. The validity of the model parameters is limited by the fact that the spectral region used in the fitting procedure is small compared with the whole wavelength region dominated by the dust emission.
Our observational data for UX Ori can be easily explained in the frame of the mentioned simple models. For instance, using the isothermal model by Cohen & Witteborn (1985) and adopting a power law for the source function instead of a Planck function, (see i.e. Hanner et al. 1995)
where is the emissivity of the Orion Trapezium dust, we find as parameters , , . The general slope of the dust emission in the 10 µ m region is, however, characterized rather by (see Fig. 2). This discrepancy shows that a fitting based on a small portion of the spectrum may lead to physically unrealistic results.
Consequently it seems appropriate to use the temperature and density distributions from the modelling of the overall SED (see Sect. 3.2.) as a starting point to calculate the emission of the silicate feature. Assuming again the emissivity of the Orion Trapezium silicate dust, the model predicts a strong excess on the long-wavelength side of the 10 µ m band. (It is just this excess that is avoided by a source function in the model fitting procedure above!) We have to conclude that the silicate dust around UX Ori (and probably around other T Tauri stars, too) emits less strongly on the long-wavelength side of the 10 µ m peak than the Orion Trapezium dust.
Another approach may consist of using laboratory data of astrophysically plausible silicates for the explanation of the observed 10 µ m emission band. Cosmic abundances, conditions of grain formation in circumstellar envelopes, and interstellar elemental depletions all point to Mg-Fe silicates as the dominant interstellar silicate component and silicate glasses may be likely laboratory analogues of them (Dorschner & Henning 1986). Dorschner et al. (1995) published a thorough study of the optical constants of glassy olivines and pyroxenes of various Mg-Fe content. We used their data in our attempt to reproduce the UX Ori spectrum. In order to limit the parameters in the fitting procedure, we adopted their laboratory data for the silicates with an Mg/Fe ratio of 1. Additionally to the silicate emission, we assumed in the modelling that there is an underlying continuous emission from graphite as our spherically symmetric model predicts.
Because the observed profile peaks below 10 µ m pyroxenes seem to be better suited than olivines. Figure. 3b shows the result of our calculations. The overall representation of the profile is acceptable but not fully satisfying. An acceptable fit of the long-wavelength part of the profile could be reached only by assuming rather large particle sizes (typical radii 1 µ m).
The experience with the silicates in our Solar System shows that both pyroxenes and olivines exist. This notion led Pollack et al. (1994) to suggest a dust model in which - among other components - the silicate comes in a mixture of pyroxene and olivine in the ratio of 23:67. Several authors have successfully modelled the 10 µ m band of a number of comets by a mixture of different silicates (Bregman et al. 1987; Colangeli et al. 1995, 1996). This motivated us to include mixtures of pyroxene and olivine in our considerations. Figure. 3a shows the result of our calculations. A somewhat better representation of the observed profile could be reached. This seems not very surprising as more free parameters were available. On the other hand, the discrepancy between 8.8 and 9.3 µ m remains. The parameters of the fit are: pyroxene/olivine ratio (by grain number) 1:1, grain radius m.
We wish to emphasize that our both fits of the 10 µ m band with the laboratory data for glassy silicates requires grain radii significantly larger than those assumed in interstellar space. There is already some evidence that the circumstellar grains have larger sizes than interstellar ones (see, e. g., Chini et al. 1991; Mannings & Emerson 1994). Thus, the very broad 10 µ m feature observed by us provides an additional argument for grain growth in the circumstellar environment.
© European Southern Observatory (ESO) 1997
Online publication: April 20, 1998