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Astron. Astrophys. 360, 213-226 (2000)

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3. Results

In this section we present the results for the composition and abundance study of the grain population in AB Aur and HD 163296. We have split this presentation in a discussion of the near IR properties on the one hand, and of the far IR properties on the other hand. However, we start out with a discussion of those properties that we found to be similar for both stars.

In Fig. 1 we present the SWS & LWS spectra together with ground-based and IRAS photometry (see Paper I). Overplotted in these figures are the current best model fits. The parameters of these model fits are listed in Table 3. The most striking feature in these spectra appear to be the presence of two distinct dust components, a relatively hot dust component with a mass averaged temperature of [FORMULA]1000 K and a relatively cold dust component with a mass averaged temperature of [FORMULA]100 K. This bi-modal temperature structure in the circumstellar dust surrounding both Herbig Ae stars is best seen in the spectrum of HD 163296, where for wavelengths shorter than 40 µm the hot dust component dominates the spectrum, while for longer wavelengths the Wien tail of the cold dust component starts to dominate the SED. In a similar way the cold dust in AB Aur starts to dominate the spectrum longward of 30 µm. The total dust mass derived from the model fits in the cold dust component is [FORMULA] and [FORMULA] [FORMULA] for AB Aur and HD 163296 respectively. The mass ratio of the hot over the cold dust component is [FORMULA]-[FORMULA], so by far most of the mass is contained in the cold component. In view of the uncertainties in the modelling discussed in the next sections the derived masses are uncertain by a factor of two to three. A blow-up covering the ISO SWS and LWS wavelength region for both stars is shown in Fig. 2. Again we include the best model fits but now we have indicated the relative contribution of all individual dust species.

[FIGURE] Fig. 1. Model fit to the spectral energy distribution (SED) of AB Aur (top) and HD 163296 (bottom). The solid dots indicate ground-based and IRAS photometry corrected for extinction. Also plotted are the ISO-SWS spectra, and for AB Aur the ISO-LWS spectrum. The dashed lines represent Kurucz models for the stellar photospheres. The dotted lines show the contribution from the hot dust component and the dot-dashed lines the contribution from the cold dust component. Indicated in the figure are the effective temperature of the adopted Kurucz model and the line-of-sight visual extinction at maximum brightness.

[FIGURE] Fig. 2. Model fit to the ISO spectra of AB Aur and HD 163296. The solid dots indicate ground based and IRAS photometry. The dotted lines represent the contributions to the continuum flux of the individual dust components. The curves are offset for clarity. The squares indicate the zero flux level for each component.


Table 3. Model fit parameters of AB Aur and HD 163296. Listed are the parameters defining the density and grain size distribution, the chemical composition and the mass fraction [FORMULA] of the individual dust species in both the hot as well as the cold dust component. Note that the given value for [FORMULA], i.e. the density at the inner radius of the shell, assumes that all dust species exist at [FORMULA] irrespective of the condensation temperature. In reality, we only have a dust species present if its temperature is below [FORMULA] (see Table 2). This implies that for the hot component, the density at the inner radius is slightly modified, i.e. it is somewhat lower.

The features in the observed spectra of AB Aur and HD 163296 have been described in detail in Paper I. Therefore we only briefly discuss the most prominent ones relevant for the model fitting. Both stars show a rather flat continuum up to [FORMULA] 8 µm, similar to the observed near-IR fluxes of other HAEBE stars. A prominent broad amorphous silicate band is present around [FORMULA] µm due to the Si-O stretching mode. HD 163296 clearly shows the presence of a broad emission complex between [FORMULA] µm in which olivine bending modes have an important contribution. In AB Aur this complex does not appear as pronounced, because the cool component already starts to dominate the spectrum longwards of [FORMULA] µm. The main difference in spectral signature between the stars is that AB Aur shows emission bands at 6,2, 7.7, 8.6 and 11.2 µm, usually ascribed to polycyclic aromatic hydrocarbons (PAH) while HD 163296 does not show these bands. Conversely, the spectrum of HD 163296 reveals crystalline silicates at 11.3, 16.3, 17.8, 23.5, 31.3 and 33.5 µm, while AB Aur does not appear to have any crystalline material.

3.1. The 2-8 µm spectral region

We first concentrate on modelling the flat near-IR continuum from 2-8 µm. The presented results are essentially equally valid for both AB Aur and HD 163296. We identified several dust species that can reproduce the observed continuum flux. These are metallic iron, iron oxide and a carbonaceous dust component, either graphite or a more "amorphous" form of carbon dust. Due to the lack of clear spectral signatures in this wavelength region, the possibility of confusion of the relative contribution of individual dust species exists.

As an example Fig. 3 shows three different models for the near-IR flux of AB Aur which are spectroscopically indistinguishable from one another. The chemical composition of the three solutions is given in the figure caption. It is clear, one has to introduce secondary arguments to distinguish between these models. The highest grain temperature required to reproduce the observed flux at the shortest wavelengths is [FORMULA]1500 K, which exceeds the grain evaporation temperature of iron oxide, but is at the condensation temperature of metallic iron and carbonaceous grains (e.g. Gail 1998). However, at about [FORMULA]1000 K, carbon grains become subject to chemical sputtering (oxidation) and will be destroyed before reaching the condensation temperature (Duschl et al. 1996; Finocchi et al. 1997). This also applies to amorphous carbon grains (AMC), which cannot reproduce the observed flux between 2 and 4 µm even when heated up to 1500 K. The only dust species that can reproduce the observed flux at these short wavelengths with an acquired grain temperature up to 1500 K is metallic iron. A satisfactory fit to this part of the spectrum could only be achieved when the temperature distribution of the iron grains ranged between [FORMULA] 700-1500 K. When more grains at lower temperature where included, we were not able to reproduce the flat near-IR spectrum. The continuum longwards of 4 µm can be reproduced by thermal emission of iron oxide and carbonaceous grains heated to their grain destruction temperatures. Iron oxide however does not easily reach temperatures close to its condensation temperature as above [FORMULA] 400 K it is slowly converted into solid iron (H.-P. Gail priv. comm.). In Fig. 2 we have indicated the contribution of each individual dust species to the total flux. This clearly shows that metallic iron is the chemical species responsible for the 2-4 µm fluxes. For the dust at [FORMULA] K we have used amorphous carbon in our model fits, however graphite cannot be ruled out on spectroscopic grounds.

[FIGURE] Fig. 3. Continuum dust emission from dust species contributing to the NIR between 2 and 8 µm for three different models. The solid line indicates a model consisting of amorphous carbon, metallic iron and iron oxide, with mass fractions of 0.55, 0.2 and 0.25 respectively. The dashed line indicates a model with only amorphous carbon and metallic iron with mass fractions of 0.53 and 0.47 respectively. The dotted line indicates a model where the entire NIR emission is due to graphite.

For the model fit to AB Aur, additional constraints on the dust properties near the inner boundary can be obtained using recent interferometric observations (Millan-Gabet et al. 1999). Fig. 4 shows the visibility curves of three models to the NIR spectrum of the star. These visibilities essentially probe the innermost region of the disk, where the emission is dominated by the metallic iron grains. The solid line gives the best fit model, in which Fe grains in sizes from 0.01 to 0.1 µm are used. Note that this model does not reproduce the observed visibilities in the K- and H-band. Also shown in the figure are the resulting visibility curves using models containing only single sized Fe grains of 0.1 and 0.32 µm, respectively. Note that both these models yield identical fits to the observed spectrum as does the best fit model. The 0.32 µm grain model fits the visibility best. The associated inner radius of the iron dust at 0.35 AU is consistent with that found by Millan-Gabet et al. (1999). This result is therefore suggestive that grain evaporation plays an important rôle in the inner part of the proto-planetary disk, where only the largest grains, having the lowest temperature, survive to a distance of [FORMULA] 0.3 AU of the central star. However, the latter model would lead to a discontinuity in the spatial distribution with respect to the other dust species. This is because our current models do not consistently incorporate the destruction of dust grains.

[FIGURE] Fig. 4. Visibility curves of three model fits of the metallic iron component to the NIR spectrum of AB Aur as a function of baseline length. The black squares indicate the observational data with the error bars indicating the rms error. The top panel shows the visibility in the K-band, and the bottom panel the H-band. The solid line indicates the current best fit, while the dashed and dot-dashed line indicate models with a single grain size of 0.1 and 0.32 µm respectively.

3.2. The 8-30 µm region

Substantial contribution to the flux around 10 µm in both Herbig Ae stars comes from disordered (amorphous) silicates (see Fig. 2). The width of the silicate feature is such that it cannot be fitted with a single-size dust distribution, which would yield an emission feature which is too narrow. A size distribution is required in which the smallest grains contribute most to the short wavelength side of the 10 µm silicate feature, while the largest grains contribute to the long wavelength tail. Though a clear spectral signature for the silicates exists and confusion with emission from other species is not a problem, a different type of degeneracy exists in the modelling. For a fixed grain composition the shape and strength of the SEDs is determined by the mass over temperature distribution and the emissivity of the dust. Fig. 5a shows three model fits for the silicate emission around AB Aur for different grain size distributions all having the same mass over temperature distribution. The value given in Table 3 (and represented by the solid line in Fig. 5a) for the power of the grain size distribution is the mean value between the limiting cases (dashed and dashed-dotted lines) for which a model fit could be made. Though an uncertainty in the exact grain size distribution remains, one can however conclude that the required distributions deviate substantially from the ISM size distribution (m=3.5, [FORMULA] and [FORMULA]m). Substantial grain growth/coagulation must have taken place to produce the required grain size distributions. The maximum grain size required to fit the 10 µm silicate feature (5 µm in our best fit model) depends, to a lesser extent, also on the strength of the underlying continuum at the long wavelength tail of this feature. Assuming the carbonaceous grains to be graphitic results in a slightly higher continuum contribution at these wavelengths, resulting in a smaller maximum size for the silicate dust by a factor of two, compared to the assumption of an amorphous carbonaceous dust component.

[FIGURE] Fig. 5a and b. Degeneracies in the model fits. Panel a shows three model fits to the 10 µm silicate feature of AB Aur for different grain size distributions. Indicated in the figure are the minimum and maximum grain size and power m (see Eq. 2). Panel b shows the degeneracies in the dust density distribution. The density at the inner edge is [FORMULA] (solid line) and [FORMULA] gr cm-3 (dashed line) respectively for the two models. Indicated in the figure are the inner and outer radii (in stellar radii) between which the dust shells are confined and the power of the density distribution p (see Eq. 1). The solid lines in both panels represent the best model fit to the silicate component in AB Aur (see also Table 3).

Between 14 and 20 µm the spectra are characterized by a strong rise in flux. This rise can be attributed to O-Si-O bending modes in the amorphous silicates around 18 µm. However, between 20 µm and the wavelengths where the cold dust starts to dominate the spectra, an additional solid-state emission component, apart from the silicate, is required to explain the observed fluxes. This broad emission complex is most clearly seen in HD 163296. Apart from the broad resonances in the near-IR, which may contribute to the observed flux in this region, iron oxide has a strong spectral feature between 21 and 25 µm, depending on grain shape (Begemann et al. 1995). Only by including non-spherical FeO grains a satisfactory model fit could be obtained. Because we calculated the optical properties of FeO entirely in the Rayleigh limit, no information about grain sizes could be obtained for this species (see also Sect. 2).

How well constrained are the results listed in Table 3 for the hot dust component? Apart from degeneracies in the model fits due to a lack of clear spectral signatures and the uncertainties in the grain size distribution, both discussed above, another degeneracy may be identified (Bouwman et al. 1999). As an example for this degeneracy, Fig. 5b shows two model fits to the silicate component in AB Aur, both having the same mass averaged temperature, but with different density distributions, resulting in identical spectra. This example is equally valid for the other dust species around AB Aur as well as around HD 163296. As discussed in the previous subsection, to explain the observed NIR fluxes the dust grains have to be heated to their destruction temperatures, which determines the inner radius of the dust distribution of the individual dust species. With the assumption that all dust species are well mixed and that, therefore, the only spatial separation between species is caused by differences in grain destruction temperatures, resulting in different inner radii, the density distributions listed in Table 3 are the most likely ones.

3.3. The cold dust component

Fig. 1 and Fig. 2 also show the ISO-LWS spectrum of AB Aur, the one star for which we also have LWS observations. For wavelengths exceeding the LWS wavelength range for AB Aur and for wavelengths exceeding the ISO-SWS wavelengths for HD 163296, we only have photometric points. This means that far less information about the chemical composition can be derived at these wavelengths than from the ISO-SWS spectra, also because the LWS spectrum does not show any discrete spectral signatures. To get around this problem we have taken the chemical composition of the hot dust component, derived from the SWS spectra, and used the same material to model the cold dust component. The main difference is the inclusion of water ice as component of the cold dust. We further assume that all iron is locked up in amorphous silicate grains and, as a minor constituent, in iron oxide. This is suggested by the temperature distribution of the metallic iron in the hot dust component which, having a minimum temperature of [FORMULA] 700 K, suggests a presence of metallic iron only at the inner edge of the hot dust component. Also the sharp rise in flux levels between 40 and 60 µm points to the absence of metallic iron in the cold dust, as including this dust species would tend to flatten out the SED in this region, in contradiction with the observations. Evidence for crystalline H2O ice was found in the Herbig star HD 142527 (Malfait et al. 1999), and is expected to be present in the outer parts of proto-planetary disks. The inclusion of H2O ice significantly improves the quality of the fit in the 40-80 µm wavelength range. Only by adding H2O ice as a dust constituent the correct slope could be reproduced as a result of the strong 60 µm feature of water ice. Tabel 3 lists the model parameters of the best fit to the cold dust component. The listed relative abundances are, due to confusion of the relative contribution of the individual dust species, uncertain by a factor of two.

In the current model a gap of [FORMULA] 20 AU is required between the hot and the cold dust component in order to create the required bi-model temperature structure. We will come back to this point in the next section.

The spectral energy distribution at sub-mm to radio wavelengths is determined by the temperature and density distribution of the cold grains, as well as by their (average) grain size. (Sub)-mm and radio imaging constrain the location of these cold grains to distances less than several 100 AU. Using these constraints, a population of large ([FORMULA] 1 and [FORMULA] 0.1 mm for HD 163296 and AB Aur respectively) grains is required to reproduce the observed shape of the SED from sub-mm to radio wavelengths. Large grains ([FORMULA] 1 mm) radiate as black bodies at mm wavelengths, and the Rayleigh-Jeans part of the SED of HD 163296 can naturaly be explained by such grains emitting at temperatures [FORMULA] 20 K. The spectral shape of AB Aur at these long wavelengths is significantly steeper than that of a Rayleigh-Jeans tail (of a black body), hence smaller grains dominate the SED.

Our model fit gives a maximum grain size of [FORMULA] 0.1 mm, a factor of ten smaller compared to HD 163296. As stated above, these results are derived by constraining the dust distribution with the available image data. However, relating the predicted mass over temperature distribution to the exact spatial distribution imposed by the imaging depends on the correctness of the model assumptions, i.e. on whether the assumption that the medium is optically thin is correct. Shielding of direct stellar radiation by an optically thick dust distribution will modify the temperature-distance relation of the grains, and consequently will change the spatial distribution of the dust considerably compared to an optically thin model with the same mass over temperature distribution (see Sect. 6 for further discussion). The question therefore is: can one relate the current model directly to the image data? Adopting the same grain sizes as derived for the hot dust component, i.e. assuming a maximum grain size of a few micron, the cold dust of AB Aur can only be fitted with our optically thin model if the grains are about a factor of 10 further out than imposed by the image data. If considerable optical depth effects are present in the dust around AB Aur the dust could be moved inwards, having the same temperatures as in the optically thin model, thus complying with the observations without the need for large grains. However, in the case of HD 163296 we want to point out that it is not possible to fit the observed slope of the SED at mm wavelengths using our optically thin model and an identical size distribution as derived for the hot dust component. As optical depth effects primarily affect the location of the dust and not the slope of the far-IR spectrum, which in both an optically thin and thick medium is essentially transparent for locally emitted radiation, this result will also be valid for an optically thick model. Therefore, even if optical depth effects play a role in HD 163296, the grains needed to explain the sub-mm to radio wavelength part of the SED need to be of the same size ([FORMULA] 1 mm) as predicted in our optically thin model.

3.4. PAHs and crystalline silicates

Fig. 6 shows the residue of the ISO-SWS spectra subtracted by the best fit dust continuum for AB Aur and HD 163296. Clearly visible are the PAH bands in AB Aur and the forsterite bands in HD 163296, where we have over-plotted the model fit to this component. A forsterite component has to be present in both the hot and in the cold dust component to reproduce all observed features. The presence of this cold crystalline material poses some interesting problems. While in the hot dust component the temperatures are sufficient to have thermal annealing at sufficiently short time scales compared to the dynamic time scales of these systems to produce crystalline silicates (e.g. Gail 1998), this is not the case for the cold dust component. This would suggest that either extensive mixing between the cold and the hot regime has taken place, or that crystallization at low temperatures can take place by means of a non-thermal annealing process of the amorphous silicates (Molster et al. 1999). Another interesting problem is the difference in grain size between the forsterite and the amorphous olivine (see Table 3) for our best model fit. The requirement that the forsterite in the cold dust component has to reproduce the emission feature at 33.6 µm limits the maximum grain size to [FORMULA] 5 µm. This is much smaller than the average size of the amorphous grains ([FORMULA] 1 mm) in the cold component of HD 163296. Adopting similar large grain sizes for the crystalline silicates in the cold component would not produce any observational emission band at 33.6 µm due to the large grain size compared to the wavelength. This does not imply, however, that large crystalline grains can be excluded. Large ([FORMULA] 100 µm) crystalline grains effectively have the same spectroscopic behaviour as amorphous grains and are thus spectroscopically indistinguishable from amorphous grains. The above does however imply that there is no continuous grain size distribution from small ([FORMULA] 0.1 µm) to large ([FORMULA] 1 mm) grains for the forsterite. A bi-model grain size distribution remains a possibility, where the smaller grains (say up to 5 µm) could reproduce the flux between 40 and 100 µm and a population of large grains would be responsible for the (sub)millimetre fluxes.

[FIGURE] Fig. 6. Residual spectra of AB Aur (top) and HD 163296 ISO SWS spectra subtracted by the current best model fit. Indicated in top panel with the thick vertical lines are the positions of the main features attributed to polycyclic aromatic hydrocarbons (PAH) bands at 3.3, 6.2, 7.7 8.6 and 11.3 µm for AB Aur; and in the lower panel are indicated the main features of forsterite at 11.3, 16.3, 18.7, 23.4, 27.5 and 33.6 µm for HD 163296. The dotted line represent the best model fit for forsterite.

The modelling of the PAH bands observed in AB Aur is beyond the scope of this paper. The 6.2 µm band caused by the C-C strech of the bonds in a benzene ring (Schutte et al. 1993) is at 6.25 µm in AB Aur, while in most other objects it is close to 6.22 µm. Furthermore, the absence of the 3.3 µm PAH feature suggests processing of the PAH molecules (Peeters et al. in prep).

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© European Southern Observatory (ESO) 2000

Online publication: July 27, 2000