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Astron. Astrophys. 326, 318-328 (1997)

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3. Circumstellar gas and dust

3.1. The mass of the circumstellar shell

The mass of circumstellar gas is now derived by modeling the CO observations. We assume a distance of 380 pc and a [FORMULA] ratio of [FORMULA]. The radius of the circumstellar shell was taken as [FORMULA] cm, as given by the observations described in the previous section. As described above, the line profiles show that there are several kinematic components, and these were modeled separately - no attempt was made to construct a single model of the whole circumstellar shell. The line profiles for the 15 [FORMULA] component have a roughly parabolic shape (see especially Fig. 5a) and this component was modeled using the code described by Morris (1980) which assumes outflow at a constant speed and at constant mass loss rate, giving n(r) [FORMULA]. The 45 [FORMULA] and 200 [FORMULA] components do not have parabolic profiles, and were modeled using a constant-density LVG code based on that described by Goldsmith et al. (1983). Excitation both by collisions and by radiation at the 4.6 [FORMULA] v = 0 [FORMULA] 1 transition of CO was included. The results are listed in Table 3, which gives for each component the total mass of gas within [FORMULA] cm, the corresponding steady-state mass loss rate (the mass divided by the envelope crossing time), and the model main-beam brightness temperature at line center in the CO(2-1) and CO(3-2) lines as observed by a 10 meter telescope. We find, in agreement with KABM, that the 45 [FORMULA] component dominates the shell mass. The 200 [FORMULA] wind, however, dominates the shell energy and momentum. For all of these components, the radius of the CO emitting region were the shell to be truncated by photodestruction of CO (Mamon et al. 1988) is [FORMULA] cm, larger than the value of [FORMULA] cm inferred from the CO mapping observations. Finally, Table 3 gives the ratios of the momentum and energy fluxes in each component relative to the corresponding quantities in the starlight. The momentum ratio in all cases is a lower limit, since the outflows are not isotropic.


Table 3. Circumstellar envelope properties of V Hya

The masses and in particular the mass loss rates in Table 3 are significantly higher than those derived by KABM, who find a total envelope mass of [FORMULA] and a total mass loss rate of [FORMULA]. Ignoring the 200 [FORMULA] outflow which was not detected by KABM, our corresponding values are [FORMULA] and [FORMULA] (where we have used KABM's distance of 340 pc). The derived envelope masses agree to a factor of 2, and the large difference in the derived mass loss rate can be attributed to the smaller linear size for the V Hya envelope assumed in our calculations.

3.2. The circumstellar dust shell

The broad-band spectrum of V Hya, found using the data summarized in Table 4, is shown in Fig. 9. We used the data of Bergeat et al. (1976) & Noguchi et al. (1981) between 0.44 [FORMULA] and 20 [FORMULA] because both of these papers give data covering a broad wavelength range, and used the calibrations given in these papers to calculate the flux densities. The two papers have observations at J (1.25 [FORMULA]) and H (1.65 [FORMULA]) in common and the flux densities agree well (cf. Table 3) so it is reasonable to combine them. Other near infrared broad-band photometry for the star is given by Fouqué et al. (1992) and Kerschbaum & Hron (1994).


Table 4. Broad-band spectrum of V Hya

[FIGURE] Fig. 9. Observed and model broad-band spectrum of V Hya. The open triangle is an upper limit. Dashed line: model black-body spectrum of star. Solid line: emission from star surrounded by dusty envelope (see text).

The ultraviolet flux densities at 0.26 [FORMULA] and 0.32 [FORMULA] were measured from IUE archival data. The flux densities at 12 [FORMULA], 25 [FORMULA], 60 [FORMULA] and 100 [FORMULA] were obtained by co-adding the IRAS data and are in good agreement with the values in the IRAS Point Source Catalogue (1988). Finally, we list three observations at radio wavelengths from Sahai et al. 1989), Luttermoser & Brown (1992) and van der Veen et al. (1995).

Fig. 9 shows the results of two model curves fit to the data; the stellar flux, and the emergent flux from the model circumstellar dust shell (see below). The stellar emission was approximated as a black body with a luminosity of 7850 [FORMULA], but the ultraviolet, optical and near-infrared flux densities suggest that the effective temperature of 2650 K derived by Lambert et al. (1986) may be a little high, and the model in Fig. 9 assumes [FORMULA] = 2300 K. The IUE flux densities are consistent with this effective temperature and no extinction. This is in disagreement with the spectra measured by Lloyd-Evans (1991), who finds that V Hya has an excess of blue emission with respect to other cool variables and carbon stars, and shows Balmer absorption in the blue, suggestive of the presence of a blue companion. However, the radial velocity monitoring by Barnbaum et al. (1995) shows no evidence that V Hya is a spectroscopic binary, and the existence of a binary companion remains in question.

The radio frequency observations of V Hya are of considerable interest. The 20 GHz upper limit measured by Sahai et al. (1989) turns out to be too high to be useful, but the star is detected at 3.6 cm by Luttermoser & Brown (1992) in observations made in May-June 1989 and at 1.1 mm by van der Veen et al. (1995) in observations made about a year later. V Hya is the only star in the sample of carbon stars measured by Luttermoser & Brown from which radio continuum emission was detected, and its strength is well in excess of that expected from the stellar photosphere (cf. Fig. 9). The spectral index between 3.6 cm and 1.1 mm is 1.8 [FORMULA] 0.05, shallower than the black body value and almost certainly showing that the 3.6 cm emission is due to partly ionized gas near the star.

The broad-band spectrum of V Hya at wavelengths longer than about 3 [FORMULA] was modeled by emission from circumstellar dust. We assumed a dust shell with [FORMULA] consisting of spherical particles of amorphous carbon with radius 2000 Å and material density 1.85 [FORMULA]. Lorenz-Martins & Lefèvre (1994) show that such a model provides a reasonable fit to the spectrum of V Hya and derive a relative abundance of SiC to amorphous carbon of 3% from the strength of the 11.3 [FORMULA] feature. Our model ignores this small amount of SiC and uses the optical constants for amorphous carbon calculated by Rouleau & Martin (1991). The longest wavelength (lowest frequency) for which these authors give data is 300 [FORMULA] ([FORMULA] GHz). The long wavelength emissivity [FORMULA] has a power-law dependence on frequency with index [FORMULA] = 1, and we estimated [FORMULA] at frequencies lower than 1000 GHz by extrapolation using this index.

The inner shell radius was set at the location where amorphous carbon evaporates or condenses, assumed to happen at 1500 K. The outer radius was the same as that used in modeling the CO emission. The resulting mass of dust and the corresponding dust loss rate (assuming an outflow speed of 15 [FORMULA]) are given in Table 3. The gas to dust ratio in the envelope is 360 by mass.

The model broad-band spectrum is compared with the data in Fig. 9, and fits the observations between 5 [FORMULA] and 200 [FORMULA] well. The model predicts far less flux at wavelengths shorter than 5 [FORMULA] than is observed, showing that V Hya is not heavily obscured by circumstellar extinction, in agreement with the flattened geometry suggested by the CO data. Indeed, the broad-band spectrum in Fig. 9 could best be fit by the sum of the photospheric and dust shell emission. Many evolved stars with extensive circumstellar shells have similar broad-band spectra, and as Fig. 9 shows, their total fluxes may be overestimated by integrating the broad-band spectrum; the lack of spherical symmetry in the circumstellar envelope means that flux is contributed both by the relatively unobscured star and by the radiation from warm circumstellar dust when the structure is viewed close to pole-on. Derivation of the stellar bolometric flux in these cases needs a model of the circumstellar dust shell.

The other disagreement between the data and the model is at submillimeter and radio wavelengths. Both the observed 1.1 mm and, especially, the 3.6 cm flux density are well in excess of the predicted model flux density from both the stellar photosphere and the circumstellar dust. The models of van der Veen et al. (1995) show that the excess 1.1 mm emission cannot readily be explained by a second extended cold dust shell. Neither can the 3.6 cm flux; not only is the discrepancy much larger but the radio emission arises from a very small region; it is unresolved by the [FORMULA] beam of the VLA, and so must arise from a region within [FORMULA] cm of the star. Its likely source is ionized gas close to the star. Luttermoser & Brown (1992) suggest that the ionization is produced by shock propagation in the stellar chromosphere. Radio observations of several other cool evolved stars show similar excesses (Reid & Menten 1996; Knapp 1996; Reid & Menten 1997).

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© European Southern Observatory (ESO) 1997

Online publication: April 20, 1998