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

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4. Discussion

An important result of the presented study is that the circumstellar material around both AB Aur and HD 163296 is characterized by a bi-modal mass over temperature distribution. This dichotomy is presented in Fig. 7. The left panels show the distribution for AB Aur; the right panels that for HD 163296. Upper panels show the hot component; lower panels the cool component. The choice of the vertical axis unit ensures that the integral of each shaded region (representing different species) reflects the total mass per component. Note the large difference in scaling of the vertical axis for the hot, respectively cold dust. The inset panel shows the warmest dust in the cold component in the same scaling as the hot component.

[FIGURE] Fig. 7. Cumulative dust mass over temperature distribution. The left panels show the distribution for AB Aur, and the right panels that for HD 163296. The top panels show the hot dust component and the bottom panels the cold dust distribution. Indicated in the figures are the relative contributions of the individual dust species. The inset figures in the bottom panels show the warmest dust of the cold dust component, being dominated by the iron oxide grains. Note that the scale of the y-axis differs for the bottom panels, which is in units of [FORMULA] for both panels.

The presented mass over temperature distribution reflects the dust properties responsible for the observed SED and holds irrespective of the assumed model geometry and/or associated optical depth. In our optically thin model, the dichotomy in the temperature distribution can only be explained if we assume a physical gap of [FORMULA] 20 AU between the hot and cold component. These two separate dust shells are really necessary, as even a bi-modal grain size distribution, consisting of small hot grains and larger cooler grains cannot solve this problem.

As discussed in Sect. 1, imaging shows a disk like structure around AB Aur and HD 163296. The bi-modal temperature distribution may therefore perhaps be naturally explained with the cold dust distributed in an optically thick disk and the hot dust in an optically thin surface layer or extended atmosphere on top of this disk. In this model, a discontinuity in the spatial dust distribution may not be needed. Fig. 8 shows a schematic outline of such a disk geometry. The dense, optically thick inner regions of the disk shield material located somewhat farther out from direct illumination by stellar radiation. In a dust distribution which is optically thick both to locally and non-locally emitted radiation, the temperature as a function of radial distance will drop as T[FORMULA]. In an optically thin medium the temperature is expected to drop as T[FORMULA] (assuming the dust opacity is proportional to [FORMULA]). This means that in the optically thick case, a given temperature is reached closer to the star. Fig. 8 also shows the schematic run of temperature for two radial paths through the proto-planetary disk: path A represents a beam for which the optical depth [FORMULA] is less than unity, therefore T is relatively high; while path B represents a beam for which [FORMULA], therefore the temperature is relatively low. The difference in optical depth between the hot and cold component seems consistent with the difference in mass in both these components, i.e. the hot dust contains of the order of [FORMULA]-[FORMULA] less mass than does the cold dust.

[FIGURE] Fig. 8. Schematic representation of a proto-planetary disk. The dark area represent the part of the disk where optical depths in excess of one are reached. Area I is optically thin for all paths emanating from the central star and can be directly illuminated. Area II is shielded from direct illumination by the inner part of the disk. The inset figure gives a schematic temperature profile for two beams one through the disk along path B and missing the disk along path A.

The above model could in principle reproduce the mass over temperature distribution of the cold dust closer to the star compared to our optically thin model and thus could bridge the gap between the hot and cold component, resulting in a more continuous dust distribution. Indeed, more detailed modeling of proto-planetary disks (e.g. Chiang & Goldreich 1997; Men'shchikov & Henning 1997) shows that the required bi-modal temperature distribution can occur in an optically thick disk.

Still, the possibility that a hot and cold dust component are physically separated can not be excluded. The presence of a large mass, such as a proto-planet, clearing a part of the disk could be an explanation for such a distribution. This is also suggested by a previous study of the shape of the energy distribution of a sample of HEABE stars (Malfait et al. 1998a). Evidence for larger bodies around Herbig Ae stars is suggested by observations of infalling circumstellar material. The observed velocities of the infalling gas seem consistent with infalling and evaporating larger bodies (Grady et al. 1999).

The chemical composition of the dust closest to the central star is determined by the dust destruction temperatures of the individual dust species. As can be seen from Fig. 7, the mass at the highest temperatures is dominated by metallic iron. At lower temperatures the iron is not in the form of metallic iron but is incorporated in iron oxide and silicates. This is suggestive of chemical processing of the dust. The dust, being slowly accreted, is heated up thereby transforming iron oxide to metallic iron and releasing the iron by solid state reduction from the olivine. Several models for the chemical evolution of proto-planetary disks predict the presence of trolite (FeS) (e.g. Gail 1998; Pollack et al. 1994). This component is also found in meteorites and interplanetary dust particles (IDPs). However, using the optical constants measured by Henning & Stognienko (1996), which show a clear spectral signatures between 30 and 40 µm, no evidence could be found for the presence of this species.

The requirement of having dust grains at temperatures up to their destruction or condensation temperatures poses an interesting problem for the silicates. Silicate grains with a temperature in excess of [FORMULA] 800 K, (much lower than the condensation temperature), can crystallize at time scales shorter than the age of the Herbig Ae stars (Gail 1998). The relatively small fraction of forsterite compared to that of amorphous olivine in HD 163296, and the complete absence of crystalline silicates in AB Aur seems in contradiction with these crystallization time scales.

A solution to this apparent problem is that we are not looking at a static mass distribution, but have a situation where the hot dust component is removed (by infall) and replenished with unprocessed material. The difference in spectral signature between AB Aur, where no crystalline silicates are detected and HD 163296 where a mass fraction of [FORMULA] in the hot dust component is in crystalline form, could be explained in terms of different rates of removal of the high temperature silicate grains.

The amount of forsterite that could be added to the hot dust component of AB Aur without causing a spectral signature is [FORMULA] [FORMULA]. To comply with observations, this amount is [FORMULA] [FORMULA] for HD 163296. The total mass of silicate grains with a temperature above the crystallisation temperature is [FORMULA] [FORMULA] for both AB Aur and HD 163296. From a comparison of these masses with observed accretion rates of [FORMULA] and [FORMULA] [FORMULA] (assuming a dust to gass ratio of 0.01) for AB Aur and HD 163296 respectively (Skinner et al. 1993), one can conclude that it is possible to accrete the hot amorphous silicate grains at a short enough time scale before they give a significant spectral signature.

The presence of crystalline silicates in the cold dust around HD 163296 could be explained by vertical mixing in a disk between the hot, optically thin surface layer and the optically thick inner part, though non-thermal annealing of amorphous silicates is also a possibility (Molster et al. 1999).

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© European Southern Observatory (ESO) 2000

Online publication: July 27, 2000