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 (), distances (D), terminal velocities () and envelopes radii inferred from CO observations (). 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 , which is determined directly from the line width of the CO emission or from the velocity of the OH masers. The values of specific to some stars have been borrowed from literature and not from the CO 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 transition is optically thinner and the effect described above is less important.
Table 2. Mass loss rate (), distance (D), terminal velocity of the envelope (, units of km s-1), envelope radius (, units of cm), reference for (R) and number of lines observed in the sources (N).
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 for Miras and for supergiants) and then calculate the distance from the bolometric flux. Uncertainty in 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, , is normally inferred from the emission of the CO 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 depends approximately on and, secondly, that depends on the supposed envelope's radius, , calculated from CO photodissociation models. Uncertainty in amounts in some individual cases to a factor of 5-10. Nevertheless, we shall associate a global uncertainty of 3 to , which derives from the dependence of on .
In the following section, plots of the type versus () are discussed, where Y represents the main beam temperature () or the integrated line intensity (W). In order to obtain the least distorted correlations of the plots stemming from systematic errors in and , it is advisable to consider a set of values based on a unique criterion and model for those variables. If the systematic error in is similar for all the objects, it will produce a global shift of points through the ordinates axis. Similarly, for the 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 will not affect the slope of the fitted straight lines in the plots of type versus (), 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 from the compilation of Loup et al. (1993). In most cases, has been inferred from the CO line intensity. But in the case of T Cep, the value of in Loup et al. (1993) is inferred from the CO line. And since this result is less reliable than the one determined from the CO line, we have used the Kastner (1990) values. For Y Cas and S Per, however, no CO data has been found in the literature, and henceforth, we have calculated the mass loss rate for these stars from our CO 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 versus the IRAS flux ratio for the observed sources. R is sensitive to : the higher 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 and R () which cannot be explained in terms of the uncertainties in (). This distribution is obviously an artifact of sensitivity. Since R and are correlated, Fig. 3 indicates a correlation between and . 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 and R.
Fig. 4 shows that the terminal velocity of the gas in the envelope () increases globally with (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 and the correlation coefficient is .
© European Southern Observatory (ESO) 1998
Online publication: June 2, 1998