Astron. Astrophys. 326, 271-276 (1997)

3. Modelling of the circumstellar dust shell

3.1. Available optical and infrared data

For UX Orionis many photometric data exist. They show irregular light variations in the optical wavelength region. Algol-like minima with amplitudes up to  mag are the most prominent among these variations and indicate that the star is obscured from time to time by circumstellar dust clouds. The presence of circumstellar dust is convincingly revealed by the infrared data. Measurements in the K band show some degree of variability (see, e. g., Kolotilov et al. 1977). The observed amplitude is, however, compatible with a constant envelope contribution. Our modelling (see below) predicts that 30-40 per cent of the total light at K comes from the star. Therefore, the obscuration of the star by a circumstellar cloud must have observational consequences at K. However, some fraction of the variability may also arise from star spots since Evans et al. (1989) gave evidence for variations of the effective temperature of the star. The IRAS data are compatible with the notion of a constant shell luminosity. The probability of variable IRAS fluxes is 20 per cent.

The spectral type of UX Ori is A3e III after Herbig & Bell (1988), while Tjin A Djie et al. (1984) classified it as A2 III. Therefore, we adopt a luminosity of 53  and an effective temperature of 8600 K in our model calculations.

The interstellar extinction in the direction to UX Ori is only poorly known because it is situated at the high galactic latitude of and only few photometric data of early-type field stars are available. Fitzgerald (1968) gives mag for distances pc. Walker (1969) determined as the foreground extinction of the Orion Complex. Observational data obtained for UX Ori by different authors (Zaytseva 1973; Herbst et al. 1983; Tjin A Djie et al. 1984) give colour indices  0.28-0.38 outside Algol-like minima. We consider as a typical value. Adopting an intrinsic colour index of (Schmidt-Kaler 1982), we find a colour excess of . If UX Ori has the same foreground extinction as the Orion Complex, the circumstellar shell produces a reddening of outside the Algol-like minima. Therefore, the circumstellar shell must consist of a diffuse more or less smoothly distributed component and a second that is formed by a larger number of clouds responsible for the stellar occultations we observe as Algol-like minima.

3.2. A spherically symmetric circumstellar shell

In order to get some information about mass and extent of the circumstellar dust distribution, we adopt a simple spherically symmetric model. In our modelling we will assume that the obscuring of the star by the dust clouds does not strongly influence the temperature structure, and consequently the emission of the shell is invariable. We use the brightness measurements of the star during maximum light as representative for the irradiation of the circumstellar dust. The effect of the clumpiness on the emission of the shell should be small since the observed infrared radiation comes from the whole shell and the clumps are optically thin at IR wavelengths.

The calculations were done using a code which is discussed in some detail by Chini et al. (1986). Input parameters of the computer program are the radius of the inner dust free zone, the outer radius of the envelope, and the radial dust density distribution (approximated by a power law). The star as the central heating source is characterized by its luminosity and effective temperature. For the optical properties of the dust grains we used the data published by Draine & Lee (1984). The relative proportions of the silicate and carbon is set by the condition that there are per H atom 3 C atoms in graphite and 3.1 Si atoms in silicate.

In Fig. 2 we compare the result of our model calculations with the observed spectral energy distribution (SED). The parameters of the fit are listed in Table 1. Keeping in mind the simplifying assumtions on witch our modelling is based, we did not attempt to select our final model by a -test but only by a visual judgement of the quality of the fit. In the fitting procedure we attempted to reproduce the SED defined by maximum brightness since the obscuration of the star should not effect the heating of the envelope. The general trend of the SED is well represented. However, there is a discrepancy in the 3-8 µ m region. All our attempts to get a better fit in this spectral range failed. We conclude from this fact that for this shape of the SED the simple model of a smooth density distribution is not fully appropriate. Bibo & Thé (1990) reproduced the SED by assuming two distinct isothermal shells, which is certainly an oversimplification.

Fig. 2. The observed spectral energy distribution of UX Ori and the prediction of our spherically symmetric model. The observations are from Herbst et al. (1983) , Cohen (1973) , IRAS , and Hillenbrand et al. (1992) . The vertical bars indicate observational errors. Our observed 10 µ m spectrum is shown too.

Table 1. Model parameters for a spherically symmetric circumstellar dust shell around UX Ori

It is noteworthy that the dip in the spectrum of UX Ori at 4.8 µ m in the SED is not unique among Herbig Ae/Be stars but can be seen in the spectra of a relatively large number of objects (see Hartmann et al. 1993, Hillenbrand et al. 1992). It seems unlikely that it due to the observational uncertainties alone although it cannot excluded that the time-dependent influence of some constituents of the earth's atmosphere (O₃, CO₂, H₂ O) could not be removed completely. The modelling of the dip at 4.8 µ m lies beyond the scope of this paper. Since our model calculations reproduce the general trend of the SED, we feel that the results for the density and temperature distributions of the circumstellar dust grains are a realistic basis for the modelling of the observed profile of the 10 µ m emission band (see Sect. 4.).

Our model predicts a far too low 100 µ m flux if compared with the IRAS observations. However, this value is probably contaminated by cirrus emission and therefore uncertain.

The assumption of spherical symmetry is certainly a great simplification. There is much evidence for disk-like structures around young stars. The orbital motion of the clouds causing the Algol-like minima may point to a proto-planetary system. Our modelling of the infrared radiation shows that the envelope is much more extended than the region where the occulting clouds move (see Friedemann et al. 1995). It seems plausible that the outer parts of the circumstellar shell kept their spherical symmetry. Moreover, the small optical depth of the circumstellar dust shell secure that all circumstellar dust grains contribute to the observed infrared radiation. Therefore, the estimate of the total dust mass is not sensitive to the exact geometry of the shell. Actual deviations from the spherical symmetry would influence the shape of the density distribution.

It seems remarkable that the density distribution in the circumstellar shells of the Herbig Ae/Be stars UX Ori, SV Cep, WW Vul modelled by us (this paper, Friedemann et al. 1992, 1993) deviates significantly from a law . Recently Miroshnichenko et al. (1977) reached a comparable result for 9 additional stars.

© European Southern Observatory (ESO) 1997

Online publication: April 20, 1998
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