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

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4. Analysis of the spectral energy distribution

In Fig. 4 we have plotted available observational data for IRAS 22272 [FORMULA] 5435.

[FIGURE] Fig. 4. Fit to the spectral energy distribution of IRAS 22272 obtained with dust properties described in Sect. 3, taking into account quantum heating effects (heavy solid line). Thin long-dashed line shows the input energy distribution of the central star, taken to radiate according to a model atmosphere calculations for log(g) = 0.5 and [FORMULA] = 5300 K. The inset shows MIR part of the spectrum in more detail. The solid line represents our best fit, the dotted line shows the fit which was obtained assuming thermal equilibrium for all dust particles, while heavy dashed line shows the fit where, in addition, hotter dust has been neglected (see text for details). Presented photometry (filled symbols from B to M band) is corrected for interstellar extinction assuming the total extinction at V of 1.0 or 2.0 magnitudes and plotted as open symbols. The dashed line with arrow indicate the beam effect of the IRAM observations at 1.3 mm. For more details concerning observational data shown in the figure see text.

Spectroscopic data plotted (shown by thin continuous lines) include the KAO spectrum in the range 16-49 µm (Omont et al. 1995b); averaged IRAS LRS spectrum (7.5-23 µm) obtained from the University of Calgary IRAS Data Analysis Facility (see details of the processing procedure in Volk et al. 1991); UKIRT spectrum from 32-channel Cooled Grating Spectrometer 3 (CGS3) kindly provided by K. Justtanont (from Justtanont et al. 1996) in the ranges from 7.6 to 13 and from 17.2 to 23.6 µm; MIR spectrum (4.8 - 13.1 µm) from Buss et al. (1990); near-infrared (NIR) spectra (2.82 - 3.72 µm) from Buss et al. (1990) and another NIR spectrum (3.15 - 3.66 µm) from Geballe et al. (1992). Photometric data shown in this figure include: two sets of photometric data at UV and visual wavelengths (filled circles or filled squares) together with estimated errors from Hrivnak & Kwok (1991) - these data are connected by thin solid lines to show more clearly the possible variations in the central star fluxes; three sets of the NIR photometry at J, H, K, L and M bands (also with estimated errors) from Manchado et al. 1989 (triangles), van der Veen et al. 1989 (squares) and from Hrivnak & Kwok 1991 (circles); IRAS Point Source Catalogue (PSC) fluxes (filled circles) together with errors at 12, 25, 60 and 100 µm (the colour corrected fluxes are represented by open symbols - see Kwok et al. 1986, for details concerning the colour-correction procedure applied); in addition, a flux measured by Walmsley et al. (1991) at 1.3 mm together with their estimated error is plotted as a filled circle.

In Fig. 4 we also present two sets of photometry (from B to M bands) corrected for interstellar extinction according to the average extinction law of Cardelli et al. (1989), assuming the total extinction at V of 1.0 or 2.0 magnitudes and plotting only the smallest and largest values of the corrected fluxes for a given band. This estimate of the total extinction was inferred from Fig. 6o (304) of Neckel & Klare (1980). The total extinction in the direction of this object shows some scatter but is almost independent of distance for [FORMULA] 1 kpc. During modelling we tried to arrange that our model energy distribution, when normalized to the NIR data, fell in between the two sets of corrected fluxes. In this way we have taken into account the effect of the interstellar extinction. This is important for the determination of the star luminosity, or more exactly for [FORMULA]. Without taking into account the interstellar extinction, the derived [FORMULA] value would be lower.

In spite of the possible variability of the source in the visible and UV (Hrivnak & Kwok 1991), all photometric measurements in the NIR seem to be in agreement with each other (within the estimated observational errors) and agree with the available NIR and MIR spectroscopy. This is in agreement with the variability index (only 3 % over a 6 month interval) assigned to the IRAS data. There is also an excellent agreement between the KAO observations and the IRAS fluxes: integrating the KAO spectrum over the profile of the 25 µm IRAS band yields a flux of 295 Jy to be compared to the 25 µm PSC flux of 302 Jy. A similar good agreement is found between the KAO and LRS spectra in the region where the data overlap. However, the integration of the LRS spectrum over the instrumental profile of the 12 µm IRAS band gave only 64 Jy, while PSC flux at this wavelength is about 16 % larger (74 Jy). This discrepancy seems to be produced by too low values of the fluxes in the short-wavelength part of the LRS spectrum. Two other spectroscopic measurements in the MIR region are in excellent agreement and show higher flux levels than LRS. Replacing, short-wavelength part of the LRS spectrum by data from Buss et al. (1990) results in a flux of 70 Jy - very close to the PSC flux at 12 µm. As far as long-wavelength band of CGS3 data is concerned, we can see that these values are about 10 % higher than the KAO and LRS spectra, both of which agree very well with the PSC flux at 25 µm.

Adopting a dust mixture made of PAHs, AC grains and including the empirical opacity function which was discussed in Sect. 3, we derived the fit to the spectral energy distribution of IRAS 22272 shown in Fig. 4 by the heavy solid line (as one can see our model is able to explain quite well almost all important aspects of the observed SED). The dashed line with arrow indicates the beam effect of the IRAM observations at 1.3 mm (HPBW of the telescope was [FORMULA] - see Walmsley et al. 1991). Our model predicts a flux density (21.5 mJy) which is consistent with the flux density observed by Walmsley et al. (16.5 [FORMULA] 4.3 mJy). The small difference could be easily explained by slightly different slope of dust optical properties at sub-millimeter wavelengths. The thin long-dashed line represents the input energy distribution of the central star for log(g) = 0.5 and [FORMULA] = 5300 K according to model atmosphere calculations by Kurucz (private communication). The inset in this figure shows MIR part of the spectrum in some more details. The solid line represents our best fit which takes also into account quantum heating effects. The dotted line plotted from 4 to 11 µm shows the fit which was obtained when no quantum treatment of small grain heating was included. As we can see the quantum heating effects are necessary to explain the presence of the emission features at 6.2, 7.7 and 8.6 µm. But otherwise the quantum effects appear to have only a relatively moderate role in producing the spectrum of IRAS 22272. We note that in other sources displaying the 21 and/or 30 µm features this is not the case and that quantum effects are much more important (a detailed analysis of these sources will appear elsewhere - Szczerba et al. 1996a, see also Szczerba et al. 1996b). The short-dashed line presents the effect of neglecting the quantum treatment for the dust temperature and supposing that there is no hot dust present between the star and the main detached shell. The parameters of the model fit shown in Fig. 4 are listed in Table 1.


[TABLE]

Table 1. Model parameters for IRAS 22272 [FORMULA] 5435.


As we can see from Fig. 4 a small amount of hot dust seems to be necessary (about 6.75 10-7 [FORMULA] which corresponds to gas mass of 1.35 10-4 [FORMULA] if [FORMULA] = 0.005 is adopted) to obtain a good fit to the observed SED in the NIR. It can be interpreted as an indication that the mass loss on the AGB diminished gradually rather than stopping abruptly. Of course, another explanation is that a process of new mass loss has just started. However, in our model the inner radius of hot dust is [FORMULA]  pc and the average dust temperature at this radius is only about 660 K so it is rather difficult to understand why and how dust could condense at such large distance (about 300 stellar radii) where the gas density is rather low, probably too low to start process of the new dust condensation. Any attempt to include much hotter dust ([FORMULA] above 1000 K) in our model resulted in too much emission predicted in the NIR. Therefore, we favor a scenario in which the mass loss process, which is inseparably connected to dust formation, stopped about 50-100 years ago after a quite long period of decline.

To estimate the infrared emission underlying the 21 and 30 µm features, we assumed that shell is optically thin in the wavelength range of interest, i.e. from 18 to 50 µm. Taking into account PAHs and pure AC grains only (no EOF) we used equilibrium temperatures or (in the cases where quantum effects are important) probabilities that the dust particles are at a given temperatures, as found from the solutions of detailed radiative transfer calculations for dust with EOF, to estimate the infrared flux outgoing from the shell.

Fig. 5 presents the model results (without the observational data and now for [FORMULA] less than about 200 µm) and shows the estimated IR continuum level underlying

[FIGURE] Fig. 5. Estimation of the IR continuum level below 21 and 30 µm bands (thin solid line: see text for more details) which is sum of three components: PAHs with radii from 5 to 10 Å (dotted line); mixture of PAH and pure AC grains (EOF has been neglected) for radii from 10 to 50 Å (dashed line); pure AC grains with radii from 50 Å to 0.25 µm (long-dashed line). Heavy solid line shows the best fit (the same as in Fig. 4), while thin solid line with features at 21 and 30 µm shows IR emission as estimated assuming that shell is optically thin.

the 21 and 30 µm bands (thin solid line) together with its decomposition into the contributions of the different types of dust grains: PAHs with radii from 5 to 10 Å (dotted line), mixture of PAH and pure AC grains for radii from 10 to 50 Å (short-dashed line) and pure AC grains with radii from 50 Å to 0.25 µm (long-dashed line). The thin solid line with features at 21 and 30 µm presents the results for dust with the EOF assuming also that dust shell is optically thin in the MIR and FIR, while the heavy solid line shows the same fit as in Fig. 4. As can be seen, the assumption that the shell is optically thin in the mid- and far-infrared is quite good (the thin solid line agrees quite well with the heavy one). The difference between the approximated flux and the flux of the best fit model is between 3.6 and 4.6 %. Taking into account the estimated continuum level (lowered by 4 % for the above reason) and assuming that 21 µm feature extends from 18 to 22 µm while the 30 µm feature extends from 22 up to 48 µm, we estimate that the energy emitted in the 21 µm band represents 2.3 % of the total infrared emission (1470 [FORMULA] in between 5 and 300 µm adopting a distance to the source of 1 kpc). The energy in the 30 µm band is estimated to account for as much as 24 % of the total IR emission.

As mentioned before, the available opacity data for MgS grains does not provide sufficient information to carry out detailed quantitative modeling. However, we can estimate the IR emission due to sulfides by assuming that the shell is optically thin and that quantum effects are not important near 30 µm (both assumptions are fulfilled quite well - see Figs. 4 and 5).

For sulfide dust grains with a size distribution given by [FORMULA] which are in thermal equilibrium inside an optically thin shell, we can write the contribution to infrared energy emitted per cubic centimeter as follows

[EQUATION]

where [FORMULA] means dust specific density. The mass absorption coefficient for sulfides in the far-infrared is not a function of dust size, so the only hidden dependence on a in the integral above is the dependence of the dust temperature on the size (in principle, dust particles of different sizes will have different temperatures because their UV and visual absorption properties could differ). We have no laboratory measurements of the optical properties of sulfides for wavelengths shorter than 10 µm so we cannot estimate their temperatures. Therefore, for simplicity, we assumed that at a given distance r from the central source grains of all sizes have the same temperature. Then the volume emissivity is simply given by:

[EQUATION]

where [FORMULA] is the density of sulfide grains at distance r. In the case of post-AGB objects maximum density of sulfides is determined by the abundance of sulphur ([FORMULA] - Aller & Czyzak 1983). Therefore, we can represent the density of sulfides by the density of gas and the amount of sulphur which is tied up in it:

[EQUATION]

where the factor 0.71 assumes a ratio [FORMULA] of 0.1 and [FORMULA] represents the fraction of MgS in the MgS-FeS mixture ([FORMULA] 0.9 was taken). Finally, with some simplifying assumptions, we obtain a formula for the volume emissivity of sulfides with the only one unknown, in fact the most important quantity, which is the dust temperature itself.

In Fig. 6 we show the highest dust equilibrium temperature distribution

[FIGURE] Fig. 6. Distribution of equilibrium dust temperature inside shell model of IRAS 22272 for PAH grain with radius of 10 Å (solid line) and for AC with EOF grain of 0.01 µm size (dotted line).

as obtained from the modeling of IRAS 22272 for PAH molecules with size a = 10 Å (solid line) as well as the lowest one obtained for AC and EOF grain with size of 0.01 µm (dotted line). Spikes seen on these curves, at the radius where hot dust shell and main dust shell join each other, are results of different densities in the two regions (see Table 1 for details). Now, assuming that one of these temperature distributions applies to sulfides, we can estimate the total IR emission of the MgS-FeS grains, by integrating the emissivity estimated above over the volume of the shell.

To compute the total IR energy emitted by the shell we took into account the IR continuum level under the 30 µm feature (see thin solid line in Fig. 5) and added to it the contribution from the MgS-FeS mixture. Trying to find a reasonable fit we were able to estimate the amount of sulphur which is tied up in sulfides. In Figs. 7 and 8, we show the fits obtained for the highest dust temperature distribution found in our model assuming that the MgS and FeS grains are spherical or that their optical properties are such as computed from CDE approximation, respectively.

[FIGURE] Fig. 7. Fit (heavy solid line) to the spectral energy distribution of IRAS 22272 obtained by summation of IR emission by spherically symmetric sulfide grains with the highest temperature distribution found in our model (thin solid line) and the IR continuum level (dashed line). For details concerning observational data see Sect. 4.

[FIGURE] Fig. 8. The same as Fig. 7 but now for optical properties of sulfides obtained in CDE approximation.

Both fits require n(S)/n(H) = 4 10-6, well below the abundance of sulphur estimated for planetary nebulae. Comparison between Figs. 7 and 8 clearly shows that the shape of sulfide particles is critical and one can easily imagine that an appropriate distribution of shapes could account for the 30 µm emission band in IRAS 22272. On the other hand, unknown sulfide dust temperature prevents us from stating more definitely that they are responsible for the observed feature. Similar calculations performed assuming that the sulfide particles have the lowest possible dust temperature distribution predicted by our model gave fits of similar quality but required at the same time almost 4 times more sulphur (i.e. n(S)/n(H) = 1.6 10-5), much more than the available abundance of S in PNe. Therefore, further laboratory measurements are necessary to estimate the short-wavelength absorption properties of MgS and in consequence to check whether this material could be responsible for the observed 30 µm feature.

Finally, to verify consistency of our model (which has been constructed by modeling of the spectral energy distribution) we compare its prediction with more detailed information about spatial distribution of emission at MIR wavelength. For this purpose we selected an image of IRAS 22272 at 11.8 µm obtained by Meixner et al. (1994). IRAS 22272 is resolved at this wavelength and has slightly elliptical structure with dimensions [FORMULA] x [FORMULA] 8. To compare extension of emission at 11.8 µm with our 1D model we made a scan along the major axis of the image.

In Fig. 9 we present normalized scan by means of open circles together with a gaussian of FWHM = [FORMULA] representing the beam profile (dashed line). To get the model scan we convolved the model surface brightness at 11.8 µm with the appropriate circular gaussian beam. As can be seen in Fig. 9 the resulting spatial scan (solid line) matches reasonably well the extent of the emission at this wavelength.

[FIGURE] Fig. 9. Model fit (solid line) to the scan along major axis of IRAS 22272 (open circles) image at 11.8 µm. Dashed line represent gaussian beam profile with FWHM of [FORMULA].
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© European Southern Observatory (ESO) 1997

Online publication: July 8, 1998
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