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Astron. Astrophys. 334, 1016-1027 (1998)

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3. Physical parameters and properties of our sample

Table 1 lists the observed sources compiled with their coordinates, IRAS fluxes, spectral type and variability type. Most of the stars are Mira type, but some semirregular, supergiants and OH-IR stars were also observed. The selection criterion for the sources was based on premise that the stars were known sources of o-H2 O (at 22 GHz) and SiO maser emission. Due to the short period of time in which the atmospheric transmission at the critical frequency of 183 GHz was high enough to allow the observations, some stars known for emitting intense masers at 22 GHz and SiO could not be observed (e.g. the supergiant VY CMa). Nonetheless, the sample of sources is representative of O-rich evolved stars though, more evolved objects, such as (proto)planetary nebulas and detached envelopes, were not observed.

Table 2 lists the mass loss rates ([FORMULA]), distances (D), terminal velocities ([FORMULA]) and envelopes radii inferred from CO observations ([FORMULA]). Uncertainties in these quantities are high in some cases, and present the major obstacle for the analysis and interpretation of carried out observations. The best known, among the parameters listed in Table 2, is [FORMULA], which is determined directly from the line width of the CO [FORMULA] emission or from the velocity of the OH masers. The values of [FORMULA] specific to some stars have been borrowed from literature and not from the CO [FORMULA] emission, due to the fact that in this line the self-absorption in the blue-shifted emission, evident in some objects, could lead to an underestimation of its true value. The CO [FORMULA] transition is optically thinner and the effect described above is less important.


Table 2. Mass loss rate ([FORMULA]), distance (D), terminal velocity of the envelope ([FORMULA], units of km s-1), envelope radius ([FORMULA], units of [FORMULA] cm), reference for [FORMULA] (R) and number of lines observed in the sources (N).
References: 1, Loup et al. (1993); 2, Bowers et al. (1983); 3, Kastner (1990); 4, this paper

There are several ways to estimate the distance D from Earth to the stars. A first approach -and the most commonly used- is to assume a certain star luminosity (normally [FORMULA] [FORMULA] for Miras and [FORMULA] [FORMULA] for supergiants) and then calculate the distance from the bolometric flux. Uncertainty in [FORMULA] amounts approximately to a factor of 3 and arises fundamentally from the luminosity as assumed for the stars. This is the method used by Knapp & Morris (1985) and Loup et al. (1993). On the other hand, the mass loss rate from the star, [FORMULA], is normally inferred from the emission of the CO [FORMULA] line according to the models developed by Knapp & Morris (1985). The various estimates which can be found in the literature differ occasionally by almost one order of magnitude. The two most important causes for this lack of agreement are, in the first place, that [FORMULA] depends approximately on [FORMULA] and, secondly, that [FORMULA] depends on the supposed envelope's radius, [FORMULA], calculated from CO photodissociation models. Uncertainty in [FORMULA] amounts in some individual cases to a factor of 5-10. Nevertheless, we shall associate a global uncertainty of 3 to [FORMULA], which derives from the dependence of [FORMULA] on [FORMULA].

In the following section, plots of the type [FORMULA] versus [FORMULA] ([FORMULA]) are discussed, where Y represents the main beam temperature ([FORMULA]) or the integrated line intensity (W). In order to obtain the least distorted correlations of the plots stemming from systematic errors in [FORMULA] and [FORMULA], it is advisable to consider a set of values based on a unique criterion and model for those variables. If the systematic error in [FORMULA] is similar for all the objects, it will produce a global shift of points through the ordinates axis. Similarly, for the [FORMULA] [FORMULA] relation, global systematic errors will result in a global shift of points by the same amount through the abscissa. These shifts will not modify the slope of fitted lines. Furthermore, if the slope is similar to 1, the shift will not affect the Y intersection of the fitted line. Similarly, systematic errors in [FORMULA] will not affect the slope of the fitted straight lines in the plots of type [FORMULA] versus [FORMULA] ([FORMULA]), yet they will affect the Y intersection of the fitted line.

It would be advisable, then, to have the systematic errors related to distance determinations similar for various objects. For that reason, we have always tried, whenever possible, to take the values D and [FORMULA] from the compilation of Loup et al. (1993). In most cases, [FORMULA] has been inferred from the CO [FORMULA] line intensity. But in the case of T Cep, the value of [FORMULA] in Loup et al. (1993) is inferred from the CO [FORMULA] line. And since this result is less reliable than the one determined from the CO [FORMULA] line, we have used the Kastner (1990) values. For Y Cas and S Per, however, no CO [FORMULA] data has been found in the literature, and henceforth, we have calculated the mass loss rate for these stars from our CO [FORMULA] data following the same approach as Loup et al. Finally, we were unable to find in the literature any reliable value of D for µ Cep. Likewise, for RS Vir no CO data was available. Consequently, these two stars have been excluded from our analysis.

Fig. 3 represents [FORMULA] versus the IRAS flux ratio [FORMULA] for the observed sources. R is sensitive to [FORMULA]: the higher [FORMULA] is, the thicker is the envelope in the continuum, thus the grains become globally cooler and the stellar radiation is reemitted by the dust at higher wavelengths. Fig. 3 shows a correlation between [FORMULA] and R ([FORMULA]) which cannot be explained in terms of the uncertainties in [FORMULA] ([FORMULA]). This distribution is obviously an artifact of sensitivity. Since R and [FORMULA] are correlated, Fig. 3 indicates a correlation between [FORMULA] and [FORMULA]. Loup et al. (1993) also found a similar correlation between D and R for a much greater number of O-rich stars (more than 150 sources), as well as between [FORMULA] and R.

[FIGURE] Fig. 3. Logarithmic plot of the square of the distances to the stars versus the 25 µm to the 12 µm IRAS flux ratio for the stars in the sample. The correlation coefficient is [FORMULA]

Fig. 4 shows that the terminal velocity of the gas in the envelope ([FORMULA]) increases globally with [FORMULA] (see Loup et al., 1993). The dispersion of the data is, however, very high. The least square fitting of a straight line gives a dispersion of [FORMULA] and the correlation coefficient is [FORMULA].

[FIGURE] Fig. 4. Logarithmic plot of the terminal velocity of the envelope versus the mass loss rate. The fitted line has a dispersion of [FORMULA] and the correlation coefficient is [FORMULA]

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© European Southern Observatory (ESO) 1998

Online publication: June 2, 1998