3. Discussion and conclusions
As it can be seen in Table 1 the values of the distances evaluated with our method are in substantial agreement with those found by other authors for the same carbon stars. For a quantitative summary of such comparison we can actually group the results in two categories:
In addition to the stellar distances, starting from the corrected values of the star radius, we have also evaluated again for each source the mass-loss rate, finding results in agreement, within a factor of 2, with those reported in Paper I. In this way it has been possible to reconsider in the new framework the relation between the band strength of the SiC feature and the mass-loss rate of carbon stars. In Fig. 1 we report the data found with our method for all the 55 sources considered both here and in Paper I. It is worthwhile to recall that the quantity plotted in ordinate can be written as:
where the star distance d is calculated as described in the previous section, represents the ratio of the power radiated in the SiC band to that of the underlying continuum at 11.4 µm, while F(12 µm) is the color corrected Band 1 flux. We have evaluated the last two quantities taking the data from the IRAS-LRS catalog (IRAS Science Team 1986) and from the IRAS Point Sources Catalog (Gezary et al. 1987). Since the IRAS flux at 12 µm is obtained with a broad bandpass filter, we have calculated for all sources the color correction factor in order to obtain the flux values at the effective wavelength of the filter. This factor has been derived by interpolation of the data listed in Table VI.C.6 of the IRAS catalog and Atlas Explanatory Supplement (Beichman et al. 1988).
The very clear and extremely good correlation (r=0.92) obtained in Fig. 1 confirm again the results already reported in Paper I as well as those found by SW for a lower number of sources (27 carbon stars). This means that the mass-loss rate can be linked with the band strength of the SiC band by the relation:
where is in W m-2 Hz, while is in yr-1. We note that, while the exponent of is in perfect agreement with that obtained by SW, the coefficient of the correlation obtained in our case is a factor of 2.8 higher. The relation given in Eq. (6) is certainly more accurate than the corresponding law reported by SW and the reason is that in our case it has been obtained using a homogeneous sample of star distances; SW, instead, use values reported by different authors and obtained with various methods. Moreover, as already mentioned, the number of stars taken into consideration in our case is almost double that by SW (55 versus 28).
In conclusion we have shown how, using some best-fit parameters coming from a radiative transfer model, it is possible to evaluate the distances and the mass-loss rates of the carbon stars showing the 11.3 µm emission feature. Using such data for all the 55 stars of our sample, we have shown that the correlation between the absolute band strength of the SiC feature and the mass-loss rates not only confirms what already found by SW with an independent method, but it is statistically strengthened by the increased number of stars taken into consideration. This correlation provide an easy method to derive the distance and/or the mass-loss rate of other carbon stars not included in our sample.
We plan in the near future to apply the results obtained here and in Paper I to the ISO spectra of many other carbon stars. This will allow us to provide the scientific community of a set of physical parameters which will be useful for the study of dust formation processes, the evolutionary sequence and the galactic distribution of the same type of objects.
© European Southern Observatory (ESO) 2000
Online publication: June 5, 2000