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Astron. Astrophys. 345, 181-186 (1999)

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4. Radiative transfer modelling

It is clear from the diversity of spectral features in the near- and far-IR that the dust consists of two spatially divided components. To model this geometry, we have used the dust radiative transfer program MODUST (Bouwman & Waters 1998; de Koter et al. in preparation). Currently, MODUST solves the radiative transfer equations subject to radiative equilibrium in spherical geometry. A 2D version is presently being developed. The density distribution of one or multiple (physically separated) shells may be freely specified. To take into account the effect of grain size on the extinction properties of the dust a powerlaw grain-size distribution is assumed. In the presented calculations, grains are assumed to be spherical, compact and to consist of a single grain material. A nice feature of the program is a library of optical constants - derived in laboratory measurements - containing about fifty dust species that may contribute to the predicted spectrum. This allows for detailed modelling of ISO spectra. As optical depths in the shells are well below unity, we run the program in the optical thin limit.

This spherical geometry is not correct for our scientific purpose, though because of the optically thin fingerprints of the dust, except for geometrical parameters, the overall results should be consistent.

4.1. The hot dust

The first of the two distinct dust populations is located close to the object, and has a dust temperature ranging from 500 to 1500 K.

The dust is mainly composed of silicates. The presence of both olivines (island silicates consisting of [FORMULA] tetrahedra linked to each other by divalent cations) and pyroxenes (chain silicates, of which each [FORMULA] tetrahedron shares two of its oxygen atoms with its neighbours, resulting in the symbolic formula [FORMULA], see Henning 1998) is evident from the broadness of the 10 µm band, from which the shortest (8-10 µm) and longer (9-11 µm) wavelength part can be attributed to respectively pyroxenes and olivines (see Fig. 2). In addition to the amorphous silicate component, crystalline olivine and pyroxene dust has been used in the fit as well. Mg-rich crystalline olivines cause the 11.2 µm emission and can explain the rather noisy shape of the spectrum at 16 µm as well.

[FIGURE] Fig. 2. Short wavelength part of the SWS spectrum of HD 142527. The silicate bump dominates this wavelength range, but also the 3.3 and 6.2 µm PAH bands can be identified. Overplotted are the absorption efficiencies (arbitrary units) for an amorphous pyroxene ([FORMULA], dashed line) and an amorphous olivine ([FORMULA], dot-dashed line) (Dorschner et al. 1995). The different noise levels ([FORMULA] 4 µm vs. [FORMULA] 4 µm) are caused by the use of different detector materials (de Graauw et al. 1996).

[FORMULA] has, next to a feature at 20 µm which can partially explain the shape and flux of the spectrum, a strongly rising emissivity at short wavelengths (2-6 µm) and can account for most of the near-IR continuum flux. A graphite component with a small abundance completes the inner part.

4.2. The cold dust

In order to model the second dust population, which is located further out, a first attempt to derive the cold dust temperature has been made using an optically thin dust disk model (Waters et al. 1988; Malfait et al. 1998a). Using an emissivity law [FORMULA], a best fit was found for a dust surface density law dropping as [FORMULA] and for inner and outer disk temperatures of 90 [FORMULA] 3 and 30 [FORMULA] 1 K, respectively (see Fig. 3). In the residuals, we can distinguish a broad feature at 100 µm, in addition to the features mentioned above. The 100 µm band might be present as well in the spectrum of HD 100546, but is much less prominent than in HD 142527 (Waters & Waelkens, 1998). Barlow (1998) also found a band at [FORMULA] [FORMULA] 95 µm in the spectrum of several evolved objects, such as the planetary nebula NGC 6302, which also shows prominent crystalline [FORMULA]-bands. It is then probable that the 100 µm band is related to [FORMULA]. However, laboratory experiments (Bertie et al. 1969; Moore & Hudson 1994) clearly show that [FORMULA]-ice is not the carrier of the 100 µm band. It is even likely that the bands seen in the diverse spectra are not caused by one single kind of dust, but rather by a family of dust species, resulting in spectral fingerprints at somewhat different wavelengths (NGC 6302 [FORMULA] HD 142527).

[FIGURE] Fig. 3. Far-IR continuum fit of HD 142527, using an optically thin dust model with [FORMULA], [FORMULA], an inner and outer disk temperatures of 90 K and 30 K, respectively.

A literature search for optical constants of [FORMULA]-related dust components resulted in identifying a possible carrier for the far-IR feature at 100 µm. Koike el al. (1982) and Koike & Hiroshi (1990) studied hydrous silicates and found that the far-IR spectrum of montmorillonite measured at room temperature is characterized by sharp peaks, the longest wavelength one of them located at 49 µm, and a broad band centered at about 100 µm. The chemical composition of montmorillonite (Koike et al. 1982) is:

[EQUATION]

It has a very definite structure consisting of silicate tetrahedra (arranged in parallel planes and connected at their mutual corners) separated by layers of cations such as [FORMULA], [FORMULA], [FORMULA] etc., and layers of what is known as interstitial water. In addition, some of the non-bridging oxygens can be [FORMULA] rather than [FORMULA].

We were able to fit the far-IR excess with a mixture composed of 60 [FORMULA] [FORMULA]-ice (of which 90 [FORMULA] is crystalline), 25 [FORMULA] cold amorphous silicates and 15 [FORMULA] montmorillonite.

We independently inserted the three dust components in the model, changing the inner and outer radii of their population, assuming each population to behave independently of the others. The best fit was obtained when the dust temperatures of the three mineral populations agreed very well. This confirms that the dust is mixed and in thermal equilibrium. The dust temperatures (30-60 K) estimated from this radiative transfer modelling are in disagreement with the temperature estimated from black-body modelling (30-90 K), the optical properties of realistic particles being drastically different from [FORMULA].

The dust mass of this cold component is [FORMULA] 5 [FORMULA] 10-4 [FORMULA], i.e. [FORMULA] 106 times more massive than what we estimated from our fit for the warm dust component, using MODUST . If we assume a dust to gas ratio of [FORMULA], the circumstellar disk has a mass of the order of a few percent of a solar mass.

4.3. Shortcomings of the modelfit

In Fig. 4, we show the fit we have obtained. Although it matches rather well, we still see some significant discrepancies. The model fails to reproduce the flux level at wavelengths between 12 and 30 µm. Adding a minor fraction of [FORMULA] ([FORMULA] 1 [FORMULA]) to the cold dust component can solve the lack of flux at 20 µm, but does not explain the total mismatch. Some other explanations could solve the problem. First of all, the model uses a dust density law, which, for each component, starts at a given distance [FORMULA] from the star and ends at an outer radius [FORMULA]. In between these two radii, a particle density law [FORMULA] is used, while at the two edges, a smoother density gradient should be used. A second effect is related to the shape of the dust particles. In our fit, we only used spherical particles (Mie-theory, see e.g. Bohren & Huffman 1983), though CDE-effects (continuous distribution of ellipsoids) have a major influence on the optical properties of [FORMULA] (but only a minor influence on e.g. silicates), resulting in a much broader feature at 20 µm (Henning et al. 1995). Our assumption to use two spatially separated dust populations might be questionable as well. At 10-25 µm, the predicted flux cannot account for the observed flux, which is up to 5 Jy brighter. This can be caused by the presence of an intermediary dust component with a temperature between 120 and 300 K.

[FIGURE] Fig. 4. Modelfit (using MODUST ), for details: see text.

In the far-IR, our model does not reproduce the sharp peaks at 47 and 50 µm. When Koike & Hiroshi (1990) measured the absorption efficiency of montmorillonite, they derived optical constants (n, k) by fitting the experimental results with Lorentz oscillators. Since the peak at 49 µm could not be reproduced this way, it has been neglected and therefore, it is not incorporated in the optical constant set we used. In addition to this, from a comparison of the mass extinction coefficients of montmorillonite at room temperature and at 2 K (Koike et al. 1982), it looks like the 49 µm feature breaks up in two peaks, one at slightly shorter and one at slightly longer wavelength. Although the resolution of these published old measurements is poor, it is tempting to conclude that the 47 µm and 50 µm features present in the spectrum of HD 142527 are again due to montmorillonite. Future laboratory measurements should clarify this matter.

The observations longwards of 180 µm should not be trusted, since in our observing mode, this part of the spectrum is observed with a much lower S/N.

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© European Southern Observatory (ESO) 1999

Online publication: April 12, 1999
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