4. Application to IRC+10420. OH-FIR lines
The supergiant star IRC+10420 has a large FIR excess which is attributed to the presence of a cold circumstellar dust shell. In addition to strong OH main line masers and satellite masers, several OH-FIR rotational lines have been detected with the ISO spectrometers by Sylvester et al. (1997) (Table 1). The mass loss rate is still uncertain but from recent observations of Oudmaijer et al. (1996) it must be at least equal to . The distance to this star is also uncertain ranging from 3 - 5 kpc; we adopt the value of 3.4 kpc determined by Mutel et al. (1979).
Table 1. OH-FIR line fluxes from observations and models
4.1. Infrared continuum emission
IRC+10420 is known to vary irregularly. We adopted the spectrum as synthesized by Hrivnak et al. (1989). In Fig. 2, the dots represent the ground-based data and the triangles, the IRAS data as color-corrected by these authors. Using an existing model of radiative transfer through a spherical circumstellar dust shell (Le Bertre et al. 1984), we have attempted to fit this spectrum. The dust is taken to be of the "dirty silicate" type (Jones & Merrill 1976). The central star has been assumed to radiate as a blackbody at 6100 K on the basis of its spectral type: "F8Ia, or perhaps Iab" (Giguere et al. 1976).
One of our best fits is displayed in Fig. 2. together with the near and FIR photometric data. The temperature of the hottest grains has been set to 650 K and the optical depth at , , to 1.0. The dust density distribution has been taken to vary as 1/r2. The quality of the fit is comparable to that of the fits already obtained by Hrivnak et al. (1989) or Oudmaijer et al. (1996). In general, it is difficult to adjust the optical and near-infrared parts of the spectrum. In fact, the shape of the energy distribution is similar to those of bipolar objects such as AFGL 2688 or the Red Rectangle. As shown by Lopez et al. (1997), their spectra can be better modeled with an axisymmetrical dust shell. There are evidences (e.g. Diamond et al. 1983) that IRC +10420 is a bipolar source and that the line of sight is near its equatorial plane as for the objects discussed by Lopez et al. (1997).
On the basis of such fit and the adopted distance of 3.4 kpc, the bolometric luminosity is estimated to be 3.7 105 . This is slightly superior to the luminosity of F8 hypergiants (Lang 1991). However, our estimation may be biased by the assumption of spherical symmetry. Using the relation (2b) of Le Sidaner & Le Bertre (1993), the dust mass loss rate is found to be 3 10-6 yr-1. For a gas-to-dust mass ratio in the range 100-200, this translates to a total mass loss rate of 3-6 10-4 yr-1. In the following, we will adopt 5 10-4 yr-1 in good agreement with the estimation of Oudmaijer et al. (1996).
The fit in the far-infrared ( m), is not of a
sufficient quality for the modeling of the OH lines. Therefore, we
have interpolated the IRAS data by using the optically thin model
presented in Sect. 3. In this model, the dependence of dust absorption
efficiency on frequency is assumed to be a power law similar to that
used in Volk & Kwok (1988):
The variation of temperature of dust grains with radius which fits IRAS observations for 20 m is:
where is the inner boundary of the dust shell: = 8.5 cm and = 475 K. The outer radius of the dust envelope is defined as the radius beyond which the dust FIR flux in our computation does not change. In our model is found to be cm ( at this radius is about 70 K).
The output continuum spectrum is displayed in Fig. 2.
4.2. Radiative excitation in an optically thin envelope
We have applied the radiative pumping model described in Sect. 2 to the FIR rotational lines of OH recently observed by ISO. All line fluxes are derived from the fluxes of the pumping absorption lines at 34.6 µm and 53.3 µm. The 34.6 µm line was detected in IRC+10420 by ISO but not the 53.3 µm line. We take the upper limit of the 53.3 µm line flux from the ISO observations as the flux of the 53.3 µm absorption line. The results given in Table 1 show that the FIR line intensities predicted by the optically thin radiative model tend to be systematically weaker than the observed intensities. Radiative pumping alone seems insufficient to account for the OH-FIR lines in the envelope of IRC+10420. Both the collisional excitation and the radiative trapping must play an important role in the excitation of OH molecules.
4.3. Collisional and radiative excitation of OH
We use the model described in Sect. 3 which includes both the collisional and the radiative excitation. The mass loss rate and the terminal velocity are taken to be and 35 kms-1 respectively.
The limits of the OH shell are estimated from the VLA observations
of Nedoluha & Bower (1992):
is taken to be 100 K at = 2 1016 cm.
OH molecules are produced in the outer part of the circumstellar envelope due to photodissociation of by the interstellar UV photons. The contribution of the stellar UV photons is negligible except for the regions very close to the central star. The model of Netzer & Knapp (1987) shows that for a star with a mass loss rate comparable to that of IRC+10420, OH molecules are formed at a radial distance of about 1017 cm. This prediction is in rough agreement with VLA observations of Nedoluha & Bower (1992). Because the radial distribution of OH molecules depends on several factors such as the UV field, dust shielding etc, we simply assume that OH abundance is constant throughout the OH envelope. The value of OH abundance which fits the ISO observations towards IRC+10420 is 1.2 10-5.
Our model provides a satisfactory fit to the intensities of OH-FIR rotational lines except for the 79.2 line which is underestimated by 60 % (Table 1). Our model predicts that the 53.3 µm line which turns out to be also in absorption can be a pumping line. A sample of the calculated rotational line profiles is shown in Fig. 3-6. We present only one of the two -doubling profiles since they have about the same profile. Because the spectrometers on board of the ISO satellite have spectral elements much larger than the OH-FIR linewidth determined by the expansion velocity of the envelope, the observed line profiles are averaged out. As a result, the FIR observed amplitudes appear weaker than the calculated amplitudes.
In our model, there is an absorption by OH at zero and positive velocities in the lines at 34.6 m and 53.3 m (Fig. 3). This is an indication of the presence of warm dust ( 70 - 180 K) outside the OH shell. Therefore, this spectral feature could be used to infer the relative location of the warm dust with respect to the OH envelope. But considering the small amplitude of the absorption and the required high velocity resolution of the observed spectra, this test is probably not feasible with current instruments (i.e ISO).
© European Southern Observatory (ESO) 1998
Online publication: February 4, 1998