Astron. Astrophys. 336, 654-661 (1998)

## 4. Gas mass-loss rate deduced from CO data

In accordance with SRIV we derive gas mass-loss rates using Kastner's (1992) self-consistent model calculations for circumstellar CO emission (in fact, they apply only to C-rich envelopes where CO is the dominant coolant). He solved the energy balance equation for the expanding circumstellar gas simultaneously with the radiative transfer for the CO line emission. One of the results was a formula for estimating the stellar gas mass-loss rate from the CO (J=1-0) antenna temperature, (in K), and the expansion velocity, (in kms), of an envelope with unresolved emission,

where d (in m) is the diameter of the telescope, D (in pc) is the distance to the source, and is the abundance of CO with respect to H2. A value of was adopted for the latter (Smith & Lambert 1985). An of 0.5 was used for our low mass-loss rate sample (see below). We used the same formula for the CO (J=2-1) and CO (J=3-2) data, except that the -values were divided by 5 and 15, respectively (see next section for a short discussion of line intensity ratios).

In order to estimate distances a luminosity L= was adopted following the work of Jura & Kleinmann (1992). The values for the individual objects were obtained by integrating the energy distributions ranging from visual data over the near infrared to the IRAS-range. Table 2 lists the estimated distances, D (in pc), for all objects having the information required to derive the bolometric magnitudes. The values are rounded to multiples of 10.

Table 2. Estimated mass-loss rates

We are aware that Eq. 1may lead to considerable systematic errors in the mass-loss rate estimates (see e.g., SRIV), but we believe that it contains the proper dependences of the mass-loss rate on the observed intensity, expansion velocity, and distance. In this way it can be used to reliably study the relative differences in the mass-loss rates within, as well as between, the different variablity groups.

In Table 2 the derived values of are given for all stars and all transitions. A code gives the origin (as in Table 1) of the CO data and the observed transition (10, 21, 32). Taken at their face values, it is clear that, as expected, all of our sources are low mass-loss rate objects, i.e., . Figure 6 shows the distribution of the gas mass-loss rates of our new IRV-sample in comparison with the SRVs taken from SRIV and the new material in Kerschbaum & Olofsson (in preparation). It is clear that we are not covering the whole range with our small IRV-sample, but it seems that they populate a similar mass-loss regime to the SRVs.

 Fig. 6. Distribution of gas mass-loss rates

© European Southern Observatory (ESO) 1998

Online publication: July 20, 1998