4 Discussion

The present observations of Z Cyg clearly show a large variation in the infrared spectrum: the circumstellar emission increases at visual maximum and the variation synchronizes fairly well with the visual light variation. Previous investigations of oxygen-rich Mira variables have suggested a similar enhancement in the 10 $\mu$m silicate band around visual maximum in several stars (Hron & Aringer 1994; Little-Marenin et al. 1996; Creech-Eakman et al. 1997; Miyata 1998; Monnier et al. 1998). Creech-Eakman et al. (1997) have suggested a change in the dust emissivity at maximum and attributed it to a change in the dust size distribution. Based on the ground-based observations, Monnier et al. (1998) have indicated that some M-type AGB stars show an enhancement in the 10 $\mu$m band and suggested an associated sharpening of the band at maximum. The present observations were made over one variability period more frequently than previous studies owing to the good visibility of the ISO mission. The general trend seen for Z Cyg is in agreement with previous work, indicating that the present results may be representative for the variation in the infrared spectrum of this class of variables. In contrast to Creech-Eakman et al. (1997) and Monnier et al. (1998), however, the present analysis suggests that the silicate band profile does not change appreciably with variability phase and that the same dust emissivity can reproduce the observed spectra taken at different phases reasonably well. Based on detailed radiative-transfer model calculations, Lobel et al. (2000) have suggested that the observations of o Cet by Monnier et al. (1998) can be interpreted in terms of the luminosity variation of the central star without any variation in the dust properties, in agreement with the present results.

Figure 7: The dust feature spectra of Z Cyg, in which the stellar continuum has been subtraced in the same way as in Monnier et al. (1998). The denotations of each spectrum are shown in the figure.

Figure 7 shows a plot similar to that by Monnier et al. (1998). The stellar continuum has been subtracted in the same manner: the stellar continuum is assumed to be a 2500 K blackbody and the intensity is fitted at 8  $\mu$m. The intensity at the band peak is enhanced more at maximum than that at 12 $\mu$m, a result similar to Monnier et al. (1998). Figure 7 also confirms that the spectral profile varies systematically with phase. The apparent sharpening of the feature in Fig. 7 is interpreted in terms of the change in the dust temperature in the present analysis. Lobel et al. (2000) suggested that the observed sharpening results from the variation in the dust shell opacity due to the modulation in the mass-loss rate. Based on the silicate and aluminum oxide two-component model, Miyata (1998) has suggested that only the silicate component varies with the visual variation, but the aluminum oxide component does not. The variations seen in the 10 $\mu$m band profile in the sample of Monnier et al. (1998) may result from the variation in the silicate component if the dust consists of more than one components. Then the present results suggest that the silicate component does not change its profile appreciably with the visual variation.

Although the general shape of the spectra is reproduced by the same dust emissivity quite well, there are some deviations in individual spectra (Fig. 1). There is an excess feature around 13 $\mu$m at $\phi = 0.79$. A similar excess is also seen at $\phi = 1.63$ and thus this seems to be a real feature around minimum. This feature may be related to the 13 $\mu$m feature seen in other oxygen-rich Mira variables (Sloan et al. 1996). The feature in Z Cyg seems to be broader than the 13 $\mu$m feature but the low signal-to-noise ratio together with the strong underlying continuum makes a precise comparison difficult. The 13 $\mu$m feature has been proposed to originate from a high temperature condensate of aluminum oxide (Kozasa & Sogawa 1997; Begemann et al. 1997), titanium oxide, spinel grains (Posch et al. 1999; Fabian et al. 2001), silicon dioxide or highly polymerized silicates (Speck et al. 2000). All of these materials should have additional weak features at $\lambda > 15$ $\mu$m. Those are not visible in the present spectra, but may be masked by the strong 18 $\mu$m silicate band. If the presence of the 13 $\mu$m feature in Z Cyg at minimum is confirmed, the present results suggest that the grains responsible for the 13 $\mu$m feature behave differently with variability and therefore must be a separate component.

Some deviations can also be seen around the peak of the 10 $\mu$m band at $\phi = 0.79$ and 1.63. The peak in the model spectra is somewhat sharper than in the observed spectra. Hron et al. (1997) have suggested that there should be variations in the 10 $\mu$m region due to the molecular absorption in the outer atmosphere of Mira variables. Part of the observed variations in Z Cyg could be attributed to variations in the underlying continuum of the photosphere or of the outer atmosphere of the star. The spectrum at $\phi = 0.55$ indicates a depression in the range 16-18 $\mu$m relative to the model spectrum. This may also be attributable to variations in the underlying outer atmosphere emission. A similar depression is not clearly seen at other phases. There are some deviations seen in the 20 $\mu$m band ( $\phi = 1.42$and 1.63) and also in the region longward of 30 $\mu$m, but the low signal-to-noise ratio prevents further analysis.

Near-infrared observations indicate that a typical variation amplitude in the bolometric luminosity of Mira variables is in the range of a factor of 3-5 (Catchpole et al. 1979). The observed variation in the integrated infrared flux of Z Cyg has an amplitude of a factor of 3.3 (Fig. 5), suggesting that the luminosity variation of the central star can account for the variation in the infrared flux. The variation in the dust temperature results from the luminosity variation. However, there exists an apparent discrepancy between the first two observations. The observed spectra indicate an increase in the temperature from $\phi = 0.55$ to 0.79, but the flux level does not change accordingly. The discrepancy may still be within the range of the flux uncertainties because a comparison with the PHT data suggests that the SWS flux at $\phi = 0.55$ may be overestimated by approximately 10% relative to the other phases (see Appendix A). On the other hand, this could also be the result of dust formation. If new dust grains are formed at $\phi = 0.79$ we can expect more grains of high temperature near the inner shell radius at this epoch and the dust emission could become hotter.

To investigate the effects of possible dust formation on the emergent spectrum, we make a simple calculation. We assume that the dust grains are formed only near minimum and their amount is equal to that integrated over one variability cycle. Then the emission from the newly-formed dust grains $F_{\rm new}(\lambda)$ can be given by

$$F_{\rm new}(\lambda) = 4\pi~n_{\rm i} ~ v_{\rm i} ~ r_{\rm i}^2 ~ P ~ \sigma(\lambda) B_\lambda(T_{\rm f})/D^2,$$ (7)

where P is the period of the variability (264 days), $v_{\rm i}$ is the dust flow velocity at the inner boundary of the dust shell, and $T_{\rm f}$is the dust temperature at formation. We use the fit parameters at $\phi = 0.97$ for $(n_{\rm i}/D^2)$ and $(r_{\rm i}/r_*)$, and assume $v_{\rm i} = 5$ km s^-1, $r_* = 3 \times 10^{13}$ cm, and $T_{\rm f} = 700$ K. Then $F_{\rm new}(\lambda)$ is added to the model of $\phi = 0.55$. The result is shown in Fig. 8. The effect is not large, though not negligible. The increase in the intergrated flux between 5-45 $\mu$m is only $9 \times 10^{-13}$ W m^-2 and will not affect the estimate of the dust shell luminosity. However, the increase in the 10 $\mu$m flux relative to 20 $\mu$m is obvious and the best fitted $T_{\rm i}$ changes from 421 K to 462 K for Q₇ and becomes close to $T_{\rm i}$ of $\phi = 0.79$ (477 K). Thus this may account for part of the increase in $T_{\rm i}$ at $\phi = 0.79$. A similar deviation does not seem to be observed around the second minimum so that a repetition of this phenomenon could not be confirmed. The density in the inner part of the dust shell could also be affected by the shock propagation. While Fig. 8 suggests that the effects of local variations in the density profile on the dust shell emission are not very significant, further studies of detailed modeling taking account of the dynamical motion and of dust formation (cf., Winters et al. 2000; Simis et al. 2001) as well as observations around minimum would be quite interesting to investigate possible dust formation process and effects of the shock in detail. Interferometric observations will also be valuable to study dust formation in the circumstellar region (Onaka et al. 2001).

Figure 8: Effects of possible dust formation. The dotted line indicates the "best fit'' spectrum at $\phi = 0.55$ with Q7 and the solid line represents the spectrum in which the emission from newly-formed dust grains is added (see text).

In the present analysis the absorption properties of dust grains in the near infrared are fixed. Also the photospheric emission is approximated by a simple function and the stellar temperature is assumed rather arbitrarily. However, since we use the infrared integrated flux rather than the stellar luminosity to estimate the incident radiation variation, these assumptions have little effect on the derived results. The integrated infrared flux simply represents the radiation absorbed by the dust grains and it is directly related to the dust temperature. The change in the absorptivity or the stellar emission will change the absolute value of the distance from the star for a given dust temperature, but the emergent spectrum will not be much affected because the dust shell is optically thin.

Laboratory experiments indicate that the silicate emissivity changes with temperature (Day 1976). Henning & Mutschke (1997), however, suggest that the temperature effects are relatively weak for silicates (less than 10% from 300 K to 10 K). While it is difficult to completely rule out the possibility, the variation of the emissivity with temperature might result in a different band profile. The fact that all observed spectra can be fitted by the same dust emissivity suggests that the temperature effect does not play a dominant role in the observed variations.

Figure 9: Comparison of various dust emissivities with the present results. All the emissivities are normalized at their peak. The thick solid line indicates Q7 and thin solid lines Q6 and Q8 derived for y0=0.1 in the present analysis (see text). The dotted line indicates those of circumstellar dust (set 1) of Ossenkopf et al. (1992) and the dot-dashed line those of "astronomical silicate'' by Draine & Lee (1984). The dashed line show the emissivity of MgFeSiO4 grains (Dorschner et al. 1995).

Figure 9 shows a comparison of the dust emissivity derived in the present study with previous work. All emissivities are normalized at their peak. The emissivities Q₇ (thick solid line) as well as Q₆ and Q₈ (thin solid lines) are plotted to indicate the range of the most likely dust emissivity around Z Cyg. The absorption efficiency factor Q₇ and the dielectric constants derived from Eqs. (5) and (6) are listed in Appendix B. In Fig. 9 the emissivity of astronomical silicate (Draine & Lee 1984) is plotted by a dot-dashed line. The emissivity of circumstellar silicate grains (set 1) of Ossenkopf et al. (1992) is shown by a dotted line. The emissivity of Z Cyg dust has a peak at a slightly longer wavelength, but the profile is quite similar to "astronomical silicate'' in the 10 $\mu$m region. The optical properties of astronomical silicate have been derived from the interstellar dust emission while the peak wavelength of the interstellar dust is known to be slightly shorter than that of the circumstellar dust (Ossenkopf et al. 1992). The peak of the circumstellar dust emissivity in the 10 $\mu$m region of Ossenkopf et al. (1992) seems to be shifted to longer wavelengths relative to the Z Cyg dust. There is also a clear difference in the 20-30 $\mu$m region. The Z Cyg dust has a broad hump around 20-25 $\mu$m in addition to the peak around 18 $\mu$m. The presence of this feature seems to be secure since all the observed spectra require this component. A similar broad feature has been suggested in young stars and attributed to FeO (Molster et al. 1999; Demyk et al. 1999; van den Ancker et al. 2000). Arendt et al. (1999) have indicated the presence of a broad 22 $\mu$m feature in the Cas A supernova remnant and attributed it to Mg protosilicate. Chan & Onaka (2000) have suggested a similar feature around 22 $\mu$m to be present in the dust in H II regions and external galaxies. Since this feature in the Z Cyg dust is merged to the strong silicate feature, it is difficult to make a precise comparison with the interstellar feature. Further investigations are definitely needed to understand the origin of the 22 $\mu$m feature.

Taking account of the possible range of the derived emissivities (Q₆-Q₈), we obtain the ratio Q(18 $\mu$m)/ Q(10 $\mu$m) to be $0.51 \pm 0.08$. This value is located in the higher end of the range of proposed emissivities (Ossenkopf et al. 1992). However, laboratory measurements suggest that the band ratio around 0.5 is not unusual for amorphous or glassy silicates (Koike & Hasegawa 1987; Henning & Mutschke 1997). Henning et al. (1995) also suggested that the mixture of silicates with metal oxides increases the ratio. Dorschner et al. (1995) have shown that olivine glass (Mg$_{\rm 2y}$Fe $_{\rm 2-2y}$SiO₄) has a ratio as large as 0.7. For comparison, the emissivity of MgFeSiO₄ grains is also plotted in Fig. 9. It has a 20 $\mu$m peak at shorter wavelengths than the Z Cyg dust. Greenberg & Li (1996) have suggested that the polarization spectrum of the Becklin-Neugebauer object in the mid-infrared region is best fitted by core-mantle grains whose silicate core has a large 20 $\mu$m to 10 $\mu$m band ratio, like MgFeSiO₄ grains. The present results indicate that the silicate grains formed around Mira variables may provide a core for such grains.

Figure 10: Examples of the model fit with the Z Cyg dust emissivity for the SWS spectra of RR Aql (a) and o Cet (b). Thin solid lines indicate the model spectra

Figure 10 shows the results of fitting models using the Z Cyg dust to two other AGB stars, o Ceti and RR Aql. Both spectra were taken from the ISO data archive and reduced in a similar way. The fitted model for the RR Aql spectrum clearly shows a discrepancy in the 12-16 $\mu$m region, but reproduces the rest of the observed spectrum relatively well, particularly in the 20 $\mu$m region. The emission around 12-16 $\mu$m may come from other kinds of dust. Potential carriers of small and broad dust emission bands in the trough between the two silicate features are Mg-Al-oxides, Ca-Al-oxides, or solid TiO₂. The contribution from CO₂ molecules may also be significant in this spectral range. The spectrum of o Cet is obviously different from that calculated with the Z Cyg dust. It does not show the 22 $\mu$m hump, and the 10 $\mu$m peak seems to be shifted to longer wavelengths. There is excess emission for $\lambda > 30$ $\mu$m in both stars, possibly due to a different dust component. It is clear that the Z Cyg dust cannot reproduce silicate features around all AGB stars with silicate emission. It is highly desirable to carry out similar investigations on a larger sample and see whether the Z Cyg dust is able to reproduce the circumstellar silicate dust emission in the majority of Mira variables or not. The observations of the other target star of the present program, T Cep, show a quite different variation in its infrared spectrum (Onaka et al. 1999; Yamamura et al. 1999a), indicating that the variation of Z Cyg indeed does not represent that of all Mira variables. Further observations of a larger sample of stars are definitely needed to better understand the general characteristics of the variation in the infrared spectrum of Mira variables.