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Astron. Astrophys. 332, 849-856 (1998)

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4. Towards a self-consistent model of Cha IRN

In this section, we will discuss the results of a radiative transfer model which was used to construct a self consistent model of the Cha IRN star/disk system. Before we present the results, we will summarize the observational constraints and give a short outline of the radiative transfer model.

4.1. Constraints on the model

By modelling the radiative transfer through the disk, it is also possible to determine the geometry of the star/disk system. To achieve this goal, it is necessary to fit the model spectrum to a wavelength range as wide as possible. Additionally, it is necessary to introduce as many observational constraints to the model as possible. From the IR spectra, we learn that there is mainly water, CO, and CO2 ice on the grains. The optical depth of the 3.1µm ice feature of [FORMULA] points to a visual extinction of [FORMULA] mag (Tanaka et al. 1990). According to Mathis (1990), this implies a K-extinction of [FORMULA] mag. Together with the distance modulus of 6.4 mag, we get a total extinction in K of around 12.7 mag. As we cannot detect the central object with our limiting magnitude of K=15 mag, this means it must at least have an absolute magnitude of [FORMULA] =2.3 mag. If this was to be attributed to a single main-sequence object, it would have to be of a spectral type later than F. However, such stars do not posses sufficient luminosity to explain the observed radiation from the whole object, which in turn would point to another source of radiation, e.g. active accretion from the disk. Alternatively, if the source is "beaming out" its radiation into the outflow lobes, as suggested by the polarized source model of Gledhill et al. (1996), the central object might well be considerably brighter. This would imply that the visual extinction towards the central object can be much higher than the above estimate (see the discussion of the radiative transfer model in the next section). Also, considering a binary system might change this estimate altogether.

A further hint towards the structure of Cha IRN is the point-like appearance at 10 µm (see Fig. 6) which means that the warm dust is concentrated close to the central object. This is a fact, against which the result of a radiation transfer calculation has to be checked.

[FIGURE] Fig. 6. The profiles of Cha IRN at 10µm compared to a point source. Only in Declination the Cha IRN appears to be slightly resolved, i.e. larger than the beam size of 1"

As stated in Sect. 3.1, we estimate the disk's radius to be of the order of 2000 AU. The fact that we do not detect any silicate feature in the spectrum might have two consequences for the model: Either the silicate abundance is unusually low or some kind of geometrical effect provides a cancelling mechanism for the expected 10 µm feature.

4.2. The radiative transfer code

The code used for fitting the spectral energy distribution and constraining the geometry of the dust configuration was developed by Manske et al. (1997) and is based on a method given by and described at length in Men'shchikov & Henning (1997). The main approximation used in this code is that, in spite of the flared disk geometry, the density distribution depends on the radial coordinate only. In addition, mean intensities and temperatures are self-consistently calculated for points in the disk's mid-plane and at its upper and lower conical surfaces only. The disk itself is part of a sphere with removed polar cones. Extensive explanations of the code and its strategy for solving the radiative transfer problem can be found in the two papers mentioned above.

4.3. The resulting model

In Fig. 7, we show the result of our model calculations compared to the spectral energy distribution of Cha IRN. The parameters used for the model are given in Table 3.

[FIGURE] Fig. 7. The spectral energy distribution of Cha IRN (symbols) and the model fit to it. The solid line gives the total flux from the object as calculated from the model. Beam size effects do not apply except at 3.5 µm, where the beam-corrected model flux is 0.2 Jy below the total flux.


Table 3. Parameters used in the model fit to the SED

The fit confirms the basic assumptions on the geometry of the system: A large-scale disk with a radius of 2000 AU, viewed at an inclination of [FORMULA], i.e. [FORMULA] out of the plane of sight very well reproduces the spectral energy distribution. The most striking features of the model are:

  • The unusually low silicate fraction in the dust composition. This is of course a result from the fact that no silicate feature is observed. As we could not completely reproduce a spectrum without a silicate feature by varying the geometry, we had to reduce the silicate-to-carbon ratio to 1:4. However, our model is not able to take all possible geometric effects into account: The density is independent from the distance from the disk's mid-plane. In reality however, the parts further from the mid-plane might exhibit lower density and thus lower optical depth. As we are looking at the central object almost along the disk's surface, silicate emission from the optically thin surface layers might "fill" the absorption feature. We should note that a similar spectral behaviour (no silicate feature) was found by Koresko et al. (1997) in case of Haro 6-10.
  • The high luminosity of the central object(s), that by far exceeds the observed luminosity of 14.4 [FORMULA] from Cohen & Schwartz (1984). Of course the highly non-spherically symmetric nature of the object easily explains the difference, yet this might be another hint that more than one central star contributes to the energy supply.
  • In the near-infrared region, we only considered the light from the inner [FORMULA]. In order to reproduce this part of the SED, we had to exclude scattering at the conical surfaces of the disk. Otherwise, the near-infrared brightness of the model would be orders of magnitude larger. This could mean that the disk surface is protected from direct starlight. Another possibility is the blocking of scattered NIR light by a slab of foreground extinction (see Ageorges et al. 1996).

Additionally, the model predicts an intensity distribution at 10 µm with a FWHM of only [FORMULA] in right ascension and [FORMULA] in declination. When observed with a [FORMULA] beam, the result in declination should have a FWHM [FORMULA] larger than the beam. This of course cannot be seen with a pixel size of [FORMULA]. However we do see a slight elongation by one pixel in declination in Fig. 6. Fig. 6 shows the measured intensity distribution of Cha IRN at 10 µm. In this figure, the source appears unresolved. This means that we can set an upper limit of [FORMULA] for the size, which is in good agreement with the model prediction.

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© European Southern Observatory (ESO) 1998

Online publication: March 30, 1998