Radiative transfer calculations show that the near-infrared visibility strongly constrains dust shell models since it is, e.g., a sensitive indicator of the grain size. Accordingly, high-resolution interferometry results provide essential ingredients for models of circumstellar dust-shells. Assuming spherical symmetry we carried out radiative transfer calculations for the hypergiant IRC +10 420 to model both its SED and m visibility. Since we failed to find good SED fits for single-component models, we improved our density distribution introducing a second component with enhanced values at a certain distance. For different scaled distances and density enhancements A of this cool component we considered different grain-size distributions , density distributions within the shells, and temperatures at the inner boundary of the hot shell.
An MRN grain size distribution with was found to be well suited for IRC +10 420. Larger negative exponents, i.e. a narrower distribution, can be accounted for by increasing the maximum grain size. For instance, requires m. However, the range of appropriate exponents seemed to be quite small and steeper declining distributions led to significantly worse fits.
Assuming a density distribution for both shells and K gives the best fit for and (Fig. 6). This model can be improved by introducing a somewhat flatter density distribution, viz. , for the outer shell leading to a better match with the observed SED for m. The quality of the visibility fit remains almost unchanged (Fig. 10). Both models show a somewhat larger curvature of the visibility at low spatial frequencies. However, the deviations are within the observational uncertainties. The various flux contributions at 2.11 µm are 62.2% stellar light, 26.1% scattered radiation and 10.7% dust emission.
Alternatively one may increase the temperature at the inner boundary of the hot shell to K which gives somewhat better matches to the near-infrared flux and lowers the low-frequency visibility curvature. To counteract the concomitant loss of flux in the far-infrared one has to assume a density distribution (Fig. 13). The fit to the silicate features is, however, somewhat worse than in the case of the K model.
The intensity distribution was found to be ring-like. This appears to be typical for optically thin shells (here , ; see also Ivezi & Elitzur 1996) showing limb-brightened dust-condensation zones. Accordingly, the interpretation of the observational data by FWHM Gauß diameters may give misleading results.
The two components can be interpreted as if IRC +10 420 has suffered from much higher mass-loss rates in its recent past than today. For instance, the K model gives and . The kinematic age of the outer component gives a corresponding timescale of yr (for kpc). If K both shells are located closer to the central star by approximately 30% leading to a correspondingly smaller timescale. The failure of constant mass-loss wind models to fit the SED agrees with the findings of Oudmaijer et al. (1996) and Humphreys et al. (1997). A previous high mass-loss episode is in line with the suspected post-RSG stage of IRC +10 420.
Although, the present observations give only marginal evidence for deviation from spherical symmetry (if elliptical, position angle of the long axis , axis ratio to 1.1), the hot shell may also be interpreted as a disk with a typical diameter of approximately 50 mas. The presence of a rotating equatorial disk has been proposed by Jones et al. (1993), and Oudmaijer et al. (1996) interpreted their hot dust-shell as a disk as well. Provided the disk is not viewed pole-on, the corresponding two-dimensional power spectra should be clearly elongated. It should be noted, however, that disks with an extension of typically 50 mas can only be detected in the power spectra if they provide at least, say, 10% of the total flux. Oudmaijer (1995) discussed several models for the circumstellar shell of IRC +10 420 and found neither a bipolar nor a disk-like wind to be consistent with optical and infrared high-resolution spectroscopy. This seems to be supported by the present observations. In order to be in line with optical blue-shifted emission lines and red-shifted absorption lines Oudmaijer suggested the scenario of infall of circumstellar material onto the stellar photosphere. However, according to Klochkova et al. (1997) the concept of accretion does not appear to be unproblematic either.
Thus, the question which scenario is best suited still appears to be a matter of debate. Bispectrum speckle interferometry gives important information on the spatial extension of the circumstellar shell. It will be in particular the combination of different observations - photometry, spectroscopy and high-resolution imaging - and their simultaneous modelling, which will shed more light on the nature of IRC +10 420 that is probably being witnessed in its transition to the Wolf-Rayet phase.
© European Southern Observatory (ESO) 1999
Online publication: August 13, 199