Astron. Astrophys. 350, 163-180 (1999)

6. Discussion

6.1. The distance and luminosity

In the literature distances ranging from 0.67-3.3 kpc (García-Lario et al. 1994) are given. However one should note that AFGL 4106 is located in the direction of Carina, so we are looking along a spiral arm, which makes it hard to relate column density and distance. Fortunately, we have spatial information from the N-band image. The inner radius of the dust shell is about , and together with the expansion velocity found in CO (Josselin et al. 1998) and [NII]-line (van Loon et al., in prep.) of 30 to 40 km/s and the present-day shape of the SED, one can put a lower limit to its distance. Assuming that the outflow is spherical, which seems plausible according to our modelling results and the [N II]-line velocity distribution by van Loon et al. (in prep.), and that the velocity has not changed significantly in time, one can derive a kinematical age for the dust shell of 135 years times the distance in kpc. Due to the expansion of the dust shell it is expected that the circumstellar dust extinction becomes smaller, leading to an increase in the brightness at short wavelengths. AFGL 4106 has already been identified in the Cape Observatory Photographic Durchmusterung from 1895 to 1900 (Gill and Kapteyn 1900) with a photographic magnitude mag. In the Cordoba Durchmusterung (Thome 1914) a visual magnitude of 9.4 has been estimated for AFGL 4106. In the extended Henry Draper Catalogue, with observations taken between 1922 and 1937 (Cannon and Mayall 1949), its photographic magnitude was . On 18 March 1988 Hrivnak et al. (1989) measured a B magnitude of () and a V magnitude of . From these observations one can derive that mag. over the last 90 years and mag. over the last 75 years, assuming an error of 0.5 magnitude in both Durchmusterungen. So the visual and photographic band trends contradict each other, although the errorbars are significant. Since the hot star is the dominant component at these two wavelengths it is possible that the star lowered its temperature, from a temperature with its peak luminosity at the photographic band to a temperature with its peak luminosity at the visual band. However, this is in contradiction with the present temperature, which peaks around the photographic band and is also not expected from evolutionary considerations.

In any case, the stability of the optical brightness of AFGL 4106 over a timescale of years can be used to constrain its distance and luminosity. Using our dust model fit we can calculate the expected SED of the system and the visual and photographic brightness in the past, assuming that the dust composition, the outflow velocity, the temperature and the radii of the stars did not change. For the photographic magnitude, it is safe to assume that the star has not brightened more than 0.3 magnitude over the last 90 years. This puts the star at a distance of at least 3.15 kpc and probably further away. On the other hand the brightning in the V-band over the last 75 years of puts the star at a distance of kpc. There is only a very small overlap region between these two trends, suggesting a distance of 3.3 kpc, just at the upper limit quoted by García-Lario et al. (1994). The size of this overlap region is mainly based on the estimated errors of the Cape Observatory Photographic Durchmusterung and the Cordoba Durchmusterung.

This distance of 3.3 kpc implies that the luminosity is and for the hot and cool star respectively, again pointing to a massive binary system. Their luminosities point to stars with a main sequence mass between 15 and 20 , using evolutionary tracks by Maeder & Meynet (1988). Other properties of AFGL 4106 also support the high masses of both stars. The expansion velocity of 30 to 40 km/sec is unusually high for AGB stars, and the relative large grains are typically found in the outflows massive supergiants (Jura 1996).

It is likely that the warm star is responsible for the expelled dust shell, and is now in the very rare evolutionary phase of the post-Red-Supergiants, which makes it a blue supergiant or WR star progenitor. Only a few other stars are in the same evolutionary status, e.g. IRC+10420 (Jones et al. 1993), and the central star of the radio nebula G79.29+0.46 (Trams et al. 1999).

6.2. The dust shell

At a distance of 3.3 kpc the mass loss episode took about years and stopped 450 years ago. During this period the star expelled 3.9 , assuming a gas to dust ratio of 100. This implies that the average mass loss rate is roughly  /yr.

In our modelling we assumed spherical symmetry, but we do see substructure in our N-band images. This is also expected, since it is likely that the M-type supergiant will influence the spatial distribution of the dust and gas, expelled by the hot star, by transferring orbital momentum to the gas and dust. This effect can create a density enhancement in the plane of the binary. This possible enhancement can lead to an over- or under-estimate of the total mass, depending on the angle at which we observe this system. However, the shape of the [N II]-line derived from different rotation angles of the slit, suggest that the shape of the dust shell is close to a sphere (van Loon et al., in prep.). This implies that the orbital seperation between the two stars is probably relatively large and therefore the influence of the companion on the mass-loss not so important. So, although the spherical symmetry and other assumptions used in our model calculations might be somewhat simple, it is not expected that the mass-loss rate and the total mass found in our calculations would change more than a factor 2.

6.3. Formation of crystalline silicates

The formation of crystalline silicates is still largely unknown. Several researchers have tried to quantify the condensation sequence of oxygen rich dust (e.g. Tielens, 1990; Gail, 1998). However, these are mainly based on the different condensation temperatures, therefore assuming thermal equilibrium; it is not known if this assumption is valid. Condensation of dust species and chemical reactions will only occur if: (I) the density is high enough and (II) the temperature is suitable (low enough for condensation and high enough for chemical reactions). Since both the density and the temperature decrease with the distance from the star, it is likely that at a certain moment the dust structure freezes out. It is this stable dust configuration which we see at the moment. Taking the condensation sequences mentioned above, it is expected that the first silicate that will form is forsterite. When the temperature becomes lower and the density is still high enough this will transform into enstatite. Both species are expected to form above the glass temperature and are therefore thought to be crystalline. We see evidence in our spectrum for both forsterite and enstatite. This implies that the forsterite to enstatite transition is stopped before the forsterite was completely transformed. There might be 3 reasons for this: (I) The density became too low, (II) the temperature dropped too rapidly or (III) other chemical reactions took over. It is likely that it is a combination of these three. One chemical reaction that could take place at lower temperatures is the incorporation of Fe into the silicates. Since our spectra show that the crystalline silicates are very Mg- rich and the amorphous silicates contain a lot of Fe, it is likely that this incorporation of Fe results in a destruction of the crystal structure. The clear chemical separation between the amorphous and crystalline materials is intriguing. It appears that the inclusion of Fe in Mg-rich silicates is a kind of runaway process.

Tielens et al. (1998) proposed a scenario for such a chemical separation between amorphous and crystalline silicates. When the temperature becomes low enough Fe may react with the Mg-rich crystalline silicates. The opacity will increase, due to the incorporation of Fe, and therefore the temperature of the grain. This process will act as a thermostat, incorporating just sufficient Fe in the grains to keep the temperature near 800 K where Fe can just diffuse in. This temperature is below the glass temperature for Fe-bearing silicates and the lattice cannot attain its energetically most favorable structure, thus leading to an amorphous structure. Because of the increased opacity due to the incorporation of Fe, it is likely that the temperature of the other grains behind this Fe-reaction zone will decrease, leading to an even higher difference between the Fe-rich (amorphous) and Mg-rich (crystalline) silicates if thermal coupling between gas and dust can be neglected. Grains that already contain a small amount of Fe will be hotter and therefore the reaction rate for the adsorption of Fe will be higher then for grains without any Fe. This would lead to the required runaway process. If this scenario is correct, it would imply that the crystalline silicates are the primordial condensation products, and this will give us new insights in the dust nucleation. Although this would lead to the required chemical separation between the crystalline and amorphous materials, it is not clear why the amorphous olivines should contain more Fe than the amorphous pyroxenes, if present at all.

Besides the forsterite-enstatite condensation sequence, Tielens (1990) also presented a condensation sequence starting with corundum. The next condensation product would then be melilite, for which we find some evidence. According to the same scheme diopside would form. Since certain strong features of this material are not found in our ISO-spectrum, this may imply that the dust forming process along this condensation sequence line froze out around amorphous melilite.

Gail and Sedlmayr (submitted to A&A) applied non-equilibrium calculation for the dust formation in outflows of M stars. They do explain the formation of several dust species, such as the amorphous Fe-rich olivines, however they do not consider, based on laboratorium experiments, the formation of pyroxenes and are not capable to explain the co-existence of pure forserite particles and Fe-rich amorphous olivines.

© European Southern Observatory (ESO) 1999

Online publication: September 24, 1999
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