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Astron. Astrophys. 317, 859-870 (1997)

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5. Discussion

In the following we will discuss the implications of the parameters derived from the model fit to the energy distribution of IRAS 22272 (Fig. 4) which are listed in Table 1. Our attempt to find a fit to the energy distribution which lies in between the observed fluxes as corrected for different amounts of interstellar extinction (see Fig. 4 for details) showed that it is possible if we assume a [FORMULA] of about 5300 K for the star which radiates according to the model atmosphere calculations (the assumption of the black-body emission gave too much emission in UV part of the spectrum). If we assume a stellar temperature higher than [FORMULA] 5500 K or lower than about 5000 K then we can obtain equally good fits in the IR range but the resulting models predict too much or too little energy emitted in the UV wavelengths respectively. At the same time a small adjustment (about 10 %) in distance (assuming constant stellar luminosity) is necessary. If we increased the assumed stellar temperature we had to adjust the fit by decreasing the assumed distance to the source slightly and vice versa if the assumed stellar temperature was decreased. This behaviour is a result of changes in wavelengths where maximum stellar flux is emitted for different effective temperatures. Our estimated effective temperature of about 5300 K agrees with a rough spectral classification of the source (Gp Ia - see Hrivnak & Kwok 1991), however it is slightly in disagreement with the more precise spectral class (G5 Ia) attributed to the source by Hrivnak (1995) which implies a central stellar temperature of about 4850 K (see Schmidt-Kaler 1982). With so low a central source temperature we were able to obtain a reasonable fit only to the short-wavelength observational data which were not corrected for interstellar extinction. Note, that Zas et al. (1995) got from the excitation analysis of their spectroscopic data for IRAS 22272 [FORMULA] = 5600 [FORMULA] 250 K in a good agreement with our estimate. It is possible that the effective temperature value for this star differs from that of a "real" G5 Ia star because IRAS 22272 presumably has an extremely low mass stellar envelope.

For modeling purposes, we adopted a stellar luminosity of 8318 [FORMULA]. For the distance derived from our fit ([FORMULA] = 1.67 kpc) we find that the total bolometric flux normalized to a distance of 1 kpc is 2982 [FORMULA] (in a good agreement with results of van der Veen et al. 1989), while the IR flux (also normalized to 1 kpc) of 1470 [FORMULA] agrees very well with the estimate of the total flux radiated in the IRAS wavelength range (1410 [FORMULA]) obtained from formula (1) of Loup et al. (1993).

Our assumed luminosity corresponds to a core mass of 0.64 [FORMULA] on the basis of the core mass-luminosity relation (Wood & Zarro 1981). Comparison of the model parameters with the transition times presented in Table 1 of Górny et al. (1994) and based on the models of Schönberner (1979, 1983) and Blöcker & Schönberner (1990), suggests that the mass (and thus the luminosity) assumed for the central star of IRAS 22272 is rather too high. A strong argument against such a high mass comes from that the periods of radial pulsation for post-AGB objects are rather smaller than 100 days (Saselov 1984; Alcolea & Bujarrabal 1991) while for an assumed core mass of 0.64 [FORMULA] the temperature of the star which would produce a fundamental pulsational period of 100 days is about 5250 K. The [FORMULA] value from our model is very close to this value which could suggest, if we assume that the AGB stellar wind ceased when the stellar pulsation period was near 100 days, that during the last few hundred years ([FORMULA] = [FORMULA] (main shell)/ [FORMULA] = 750 yr) the star has not had any change its temperature. However, this is in contradiction with the one-to-one relation between mass of the stellar envelope and star temperature for H-burning models during post-AGB phase of evolution (Schönberner, 1989). Nuclear burning itself, by reducing the mass of the envelope, is able to evolve the star to a temperature of about 5400 K from 5250 K during the estimated 750 yr period since the end of the AGB, but as we have shown we need some amount of hotter dust to obtain a good fit (if the estimated 1.35 10-4 [FORMULA] of gas in the hot dust component is removed from the stellar H-rich envelope the effective temperature is predicted to increase to about 6000 K from the post-AGB evolution models).

On the other hand, assuming that the mass of IRAS 22272 is equal to 0.60 [FORMULA] the estimated distance to this source would be 14 % smaller (i.e. 1.45 kpc) and the dynamical age of the object would be reduced by approximately the same percentage to about 650 yr. If the large-scale mass loss (forming the main shell in our model) ended when the radial pulsation period dropped to a value of 100 days (when the stellar temperature reaches about 5000 K) then the derived age of 650 yr agrees with the transition times presented in Table 1 of Górny et al. (1994). The mass of the H-rich envelope predicted for this star at the end of the AGB phase is 1.175 10-3 [FORMULA]. If we reduce this mass by our estimated mass of the hot dust shell (1.35 10-4 [FORMULA]) and in addition by the mass of H used for nuclear burning over the post-AGB time period (5.43 10-5 [FORMULA]) we estimate the mass of the remaining H-rich envelope to be 9.86 10-4 [FORMULA], which corresponds to a stellar effective temperature of 5370 K. This closely matches our estimate of 5300 K for the stellar effective temperature. Thus the parameters derived for IRAS 22272 are all consistent with a stellar mass of 0.60 [FORMULA]. We would like to mention that kinematic distance to the IRAS 22272 of 2.7 kpc (Woodsworth et al. 1990) seems to imply too high mass for the central star (about 0.89 [FORMULA] on the basis of the core mass-luminosity relation of Wood & Zarro 1981 and obtained [FORMULA] = 2982 [FORMULA]). According to theoretical calculations (e.g. Blöcker 1995) star with such a high mass should evolve so fast that its effective temperature cannot be still around 5000 K for the estimated dynamical time of post-AGB evolution of a few hundred years.

Of course, such an interpretation is only correct if central star of IRAS 22272 is generating its energy via hydrogen shell-burning. If the energy source is He shell-burning than the situation is more complicated as there is no unique relation between the mass of the envelope and the central star temperature according to the available models. IRAS 22272 has a C-rich envelope and if we take into account that all presently known Wolf-Rayet type stars (which are believed to be He-burners) among planetary nebula central stars are classified as C-type (they show carbon emission lines in their spectra, whereas the "regular" Wolf-Rayet stars which are thought to be much more massive are divided between C-type and N-type depending upon whether carbon or nitrogen emission lines are dominant in their spectra), there is a chance that at least some of the carbon-rich nebulae have central stars burning He rather than H at the base of their envelopes (but see Górny & Stasiska 1995 for a more detailed discussion). Unfortunately, we are not able to solve this problem with the present state of theory concerning H and He-burners.

We were not able to find a good fit to the IRAS 60 and 100 µm bands using amorphous carbon of AC type and a density distribution inversely proportional to the squared radius (which supposes a constant mass loss rate during AGB phase). Therefore we introduced a density distribution [FORMULA] for the fit. Of course, different slopes of the dust opacity in the FIR will change slightly our results. Such an inferred density distribution for IRAS 22272 suggests that the mass loss rate increased during the formation of the circumstellar shell, from [FORMULA] 4.70 10-6 up to [FORMULA] 5.76 10-5 [FORMULA] (if we assume a dust-to-gas ratio equal to 0.005). Note, that gas mass loss rate estimated by Omont et al. (1993) from the measured CO line intensities (about 7.0 10-6 [FORMULA] after scaling to the preferred by us distance to the IRAS 22272 of 1.45 kpc) is in agreement with our estimate as it is some type of mass-averaged value. From the best fit model we found that the required mass of dust necessary to explain the observed IR emission is about 2.3 10-3 [FORMULA].

While for AGB envelopes spherical symmetry seems to be typical, observations of post-AGB objects show that almost all of them are bipolar or have even more complicated structure. The reason for this and the moment when significant departure from the spherical symmetry inside ejected envelope took place is not clear. In principle, the easiest way to explain the shell asymmetry is to assume that most of the post-AGB objects evolve in binary systems (e.g. we can imagine that supergiant in IRAS 22272 has still undetected companion - maybe observations by International Ultroviolet Explorer could help test this possibility). On the other hand, an explanation which involves non-radial pulsations of late AGB star or its rotation are also plausible. In the context of aspherical shell structure, so typical for post-AGB evolution, it seems that for modeling of such sources anisotropic models could be more relevant. However, construction of such models is much more complicated and time consuming so their application to the larger group of objects is almost not possible at the moment. In the nearest future, we plan to apply some new method of the solution of the radiative transfer equation for axially-symmetric circumstellar dust disks (Men'shchikov & Henning 1996) to check how our conclusions in the case of IRAS 22272 depends on the possible anisotropies. Since degree of anisotropy in this object seems to be not so high (Trammell et al. 1994, Meixner at al. 1994) we can suspect that result should not be much different from that obtained by assumption of spherical symmetry. On the other hand, in the case of such objects as e.g. the Egg Nebula where anisotropy is really pronounced application of anisotropic models seems to be necessary.

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© European Southern Observatory (ESO) 1997

Online publication: July 8, 1998