The IRAS LRS database has revealed a large variety in the mid-infrared
spectra, particularly in the 10 
m region,
of M-type Mira variable stars
(Cheeseman et al. 1989;
Little-Marenin & Little 1988, 1990;
Simpson 1991).
Stencel et al. (1990) discussed the diversity in terms of
the time evolution of the dust shell, while Sloan & Price (1995,
1998) proposed a classification
scheme of the mid-infrared spectra with the silicate index following
the classification by Little-Marenin & Little (1988, 1990).
Onaka et al. (1989a) and Miyata et al.
(2000) have shown that the dust shell spectra can be
decomposed at least into two components,
silicate and aluminum oxide. Speck et al. (2000) have
studied the diversity in more detail by
recent ground-based observations of a large number of AGB stars.
The variety in the observed
dust features suggests a complex dust formation process
in oxygen-rich Mira variable stars (cf. Ferrarotti & Gail
2001).
Dust grains are formed in the mass-loss outflow which is accelerated by the radiation pressure on the grains. The pulsation has been suggested to play an important role in the mass loss and dust formation process (Vardya et al. 1986). Theoretical investigations indicate complicated interactions between dust formation and mass-loss processes in pulsating stars (Winters et al. 1994, 2000; Höfner & Dorfi 1997; Höfner et al. 1998; Simis et al. 2001). The light variation affects the incident energy on the circumstellar dust shell, while dust formation may be modulated by the variability. Thus the study of the variability in the infrared spectrum of the dust shell gives insight into the mass loss and dust formation process as well as the optical properties of circumstellar dust grains.
Past studies of the infrared variability in oxygen-rich Mira variables based
on the IRAS LRS database suggested
an enhancement of the silicate emission around the visual maximum
for a few Mira variable stars (Hron & Aringer
1994; Little-Marenin et al. 1996). Ground-based
photometric
observations indicated a similar trend (Le Betre 1993).
However, the IRAS observations were
not well suited for periodic monitoring of variable stars and
hampered as they were by limited
temporal coverage. Creech-Eakman et al. (1997) have suggested
variations
in the 10 m silicate feature of several long-period variable (LPV) stars
by comparing
ground-based observations with the IRAS LRS spectra. After decomposing
the 10 m region spectra
of 18 oxygen-rich Mira variables into two components,
Miyata (1998) has
suggested that only the silicate component shows a clear variation with the
visual variability based on
the comparison between ground-based observations and the IRAS LRS spectra.
Possible long-term variations, however, make
it difficult to directly compare the data taken at nearly a decade apart
(Monnier et al. 1999). With the recent development of
mid-infrared instruments for
ground-based telescopes Monnier et al. (1998) have clearly
shown by ground-based spectroscopy that there are different
variability types of LPVs in the 10 m region, and indicated that a class
of stars show an enhancement in the 10 m silicate emission feature
around the visual maximum. Model calculations by
Lobel et al. (2000) have indicated that the variation seen
in the 10 m band can be caused by the modulation of the mass-loss
rate due to the luminosity change of the central star.
While the accessible spectral range in the mid-infrared from the ground is
limited, a wide spectral coverage
in the 10 to 20 m
region is crucial for the study of dust shell properties as
demonstrated by IRAS LRS studies (e.g., Bedijn 1987;
Volk & Kwok 1988; Onaka et al. 1989a; Simpson 1991).
We have carried out periodic observations of infrared variability in two
M-type Mira variable stars with the
Short-Wavelength Spectrometer (SWS; de Graauw et al. 1996) on
board the Infrared Space Observatory
(ISO; Kessler et al. 1996) to
investigate the time variability of their infrared spectra free from the
terrestrial
atmospheric disturbance (Onaka et al. 1999, TONAKA.TIMVAR
and VARSPC).
In this paper we present the results of observations and analysis
of the infrared variability
in one of the target stars, Z Cyg.
In a preliminary study Onaka et al. (1999) have shown that all of the Z Cyg spectra taken at different variability phases were fitted fairly well by simple models of optically thin dust shell with the same dust emissivity with different inner dust shell temperatures and densities. While the variation in the inner dust shell temperatures may be interpreted in terms of the central star luminosity variation, the variation in the density is difficult to account for since it requires changes in the amount of dust in the entire dust shell.
The derived mass-loss rate is a function of the inner dust shell temperature,
which is then a function of the adopted dust optical properties.
In the previous work by Onaka et al. (1999), the optical
properties
were derived from the observed spectrum at maximum by assuming
rather arbitrarily that the inner dust shell temperature was set as 800 K
and that the dust temperature was given by a power law of the distance from
the
star. A key parameter to determine the dust temperature from the observed
spectra is the ratio of the
18 m to 10 m bands in the dust emissivity.
Several optical properties have been proposed and investigated
for silicate grains (Draine & Lee 1984;
Bedijn 1987; Volk & Kwok 1988;
Simpson 1991;
David & Papoular 1990;
David & Pégourié 1995), among which this ratio
ranges from 0.28 to 0.50 (see Ossenkopf et al.
1992) for
more detailed discussion of each data set).
The dust emissivity in the circumstellar shell can be
derived in a statistical way based on a large sample of stars,
such as the IRAS LRS database, but either the inner dust shell temperature
(Volk & Kwok 1988), the 18 m to 10 m
band ratio (Simpson 1991), or the inner shell radius
(Marengo et al. 1997) still has to be assumed in the derivation.
The inner dust shell temperature has, in fact, been one of the important issues in the dust shell studies and should be a crucial parameter in the investigation of the dust formation process. Chemical equilibrium calculations indicate a condensation temperature around 1200 K for silicate grains (Salpeter 1977), while the classical nucleation theory suggests that the condensation occurs around 1000 K (Draine 1981; Kozasa et al. 1984). Condensation around oxygen-rich stars may involve complicated chemistry because no simple monomers of the silicate composition are expected to exist in the gas phase. A recent more sophisticated model of heterogeneous condensation around M-type stars suggests that most dust is condensed in the region of T = 800-1000 K for a large mass-loss case (Gail & Sedlmayr 1999). Some of the observational studies of the dust shell have indicated much lower inner dust shell temperatures (<700 K) than these theoretical predictions, particularly for thin dust shells (Rowan-Robinson & Harris 1982, 1983; Onaka et al. 1989a). However, it cannot be ruled out that the uncertainties in the adopted optical properties may result in the low temperatures. Recent interferometric observations have suggested that the inner dust shell is located at the region with temperatures around 1000 K for o Cet and 850 K to 1170 K for R Aqr although the infrared spectrum from the fitted models did not show a satisfactory agreement with the observed spectra (Danchi et al. 1994; Tuthill et al. 2000). Episodic mass loss in AGB stars has been suggested by several observations (Izumiura et al. 1997; Hashimoto et al. 1998) and it could also lead to low inner dust shell temperatures.
It is difficult to fix the inner dust shell temperature either from observations or theories with accuracy at present stage and the determination of the dust properties has to be made in a different way. In this paper we propose a method to derive the optical properties that consistently explain the variabilities both in the dust temperature and the dust shell flux and apply it for the observations of Z Cyg. We investigate whether the observed variation can be interpreted in terms of the light variation of the central star and whether there is any evidence indicating the dust formation in the variability seen in the SWS spectrum. In Sect. 2, we present the observational results and describe the method of analysis in Sect. 3. Comparison with previous studies and implications on the dust formation are discussed in Sect. 4.
Copyright ESO 2002