4 Line profiles

4.1 Line shapes

  Within the limitations of the S/N-ratio most of the line profiles lie in the range of the expected, i.e., between a rectangular (spatially unresolved, optically thin emission) and a parabolic (spatially unresolved, optically thick emission) line shape. Nevertheless, there is a relatively high fraction of lines showing various kinds of asymmetry. In a few cases the line shapes clearly suggest the presence of at least two winds with different velocities.

4.1.1 Asymmetry

We have calculated a simple line asymmetry factor, $I_{\rm r/b}$, for the lines with the highest S/N-ratios, see Tables A3-A8. It gives the ratio of the integrated intensities on the red- and blue-shifted sides of the central velocity (determined by a fit, see Sect. 2.3). The results are given in Fig. 5. It is clear that the lines are on average stronger on the red-shifted side, but the asymmetry decreases with increasing excitation requirements for the transition (note the markedly lower number of high-quality 1-0 spectra due to the relative weakness of this line). The mean (median) values for the 1-0, 2-1, and 3-2 lines are 1.13 (1.16), 1.10 (1.09), and 1.03 (1.03), respectively. A straightforward explanation to the asymmetry is self-absorption in an envelope with a negative radial temperature gradient (as first observed in IRC+10216 by Olofsson et al. 1982, and modelled by Huggins & Glassgold 1986). The trend with J-level probably reflects the fact that the higher-J lines come from regions closer to the star where self-absorption is less important.

  

Figure 5: Distribution of the asymmetry parameter $I_{\rm r/b}$ for the CO(J=1-0, 2-1, and 3-2) lines

4.1.2 Multi-component line profiles

Among our detected stars there are four that clearly show multi-component line profiles: EP Aqr, RV Boo, X Her, and SV Psc (all are SRbs). Typically a very narrow feature with a full width less than $\sim$5kms^-1 is centered, within the uncertainties, on a much broader line $\sim$18kms^-1), see Table 3. The broad component is close to being parabolic. SV Psc and EP Aqr are maybe the most extreme examples of this phenomenon. The central peaks are very narrow, and, if interpreted as arising from expanding envelopes, they imply expansion velocities of $\sim 2$kms^-1. In RV Boo, the only one of these stars for which we have high-quality data in two lines, the narrow component becomes much stronger (relative to the broad component) for the higher-frequency transition. Knapp et al. (1998) recently presented and discussed similar data for nine stars.

One possible interpretation of these observations is outlined in Kahane & Jura (1996) where they reported on a bipolar outflow around the nearby XHer. They were able to spatially resolve the blue- and red-shifted lobes of a (weakly collimated) bipolar outflow, while the low-velocity emission, i.e., the narrow component, appears to outline a symmetric envelope. In the case of RVBoo we have obtained data with the OVRO mm-wave interferometer, which partly resolved the CO(2-1) emission from this more distant object. The data suggest that in this case it is rather the narrow component that originates from a bipolar outflow, while the higher-velocity gas comes from a symmetric envelope. However, a final interpretation has to await a more detailed analysis. Knapp et al. (1998), on the other hand, suggest a scenario where episodic mass-loss plays a role.

A similar narrow spike in the middle of a broader line could also be interpreted in terms of emission from a long-lived disk as suggested by Jura et al. (1995) for the post-AGB object the Red Rectangle, and by Kahane et al. (1998) for the silicate carbon star BM Gem.

At this stage no definite conclusions can be drawn, except that it is very likely that these objects are far off the picture of a constant, spherically symmetric mass-loss.

  

Table 3: Multi-component line profiles^a

4.2 Gas expansion velocities

In this section we compare the circumstellar gas expansion velocities obtained from our data on the SRVs and IRVs with results taken from the literature for O-rich Mira variables (L93; Y95). The two sources for the Mira data differ significantly in their selection criteria. Whereas L93 contains a very inhomogeneous collection from many different surveys, Y95 is a distance limited survey of visually bright Miras, i.e., an approach that is quite similar to ours. However, since only visually classified Miras (GCVS4) were taken from L93, also this data set provides us with stars of comparable properties. Finally, we note here that one expects only small systematic errors in the gas expansion velocity estimates between different studies, as opposed to the case for the mass-loss rate. If, for an individual object, more than one independent measurement of $v_{\rm e}$ are available the best was chosen, or, if they are of comparable quality, they were averaged. The resulting gas expansion velocity distributions are shown in Fig. 6.

The mean (median) velocities for the three sub-samples are 7.7 (7.9)kms^-1 (IRV), 8.8 (8.3)kms^-1 (SRV), and 10.0 (8.6)kms^-1 (Mira). The main difference between the groups is the existence of a tail towards high expansion velocities among the Miras. These are all longer-period Miras as can be seen in Fig. 7. Of particular interest for mass-loss mechanism discussions is the high number of stars, in all three groups, with very low expansion velocities,  km s^-1. We here just mention a few clear examples from our data: the IRVs V584 Aql, BI Car, and AZ UMa; the SRVs T Ari, RX Lep, L² Pup, Y Tel, and BK Vir. The median values obtained for this sample of O-rich IRVs and SRVs are clearly lower than the corresponding values obtained by Olofsson et al. (1993) for a sample of optically bright carbon stars, 10.5 km s^-1 and 10.8kms^-1, respectively, and in the latter sample (68 objects) there are only two objects with expansion velocity estimates below 5kms^-1.

  

Figure 6: Distribution of circumstellar gas expansion velocities

In Fig. 7 we have plotted the gas expansion velocity as a function of the pulsation period for our SRV sample and the Miras. For SRVs below periods of about 200 days there appears to be no trend in the expansion velocity. For longer periods (, i.e., in the classical Mira regime) it seems that the expansion velocity increases with period in the way suggested by Wood (1990, dotted line in Fig. 7), although there is a considerable scatter. It is clear that from this point of view the SRVs cannot be a short-period extension of the Miras. Hence, it seems that the pulsation mode does not have a drastic influence on the gas expansion velocity.

  

Figure 7: Gas expansion velocity versus the pulsation period. The symbols denote the variability class

4.3 Line intensity ratios

Line intensity ratios can be deduced, since we have observed more than one transition per star for a number of objects. We have used only high-quality spectra and no upper limits. The results for the 2-1/1-0-ratio are on average 4.2 at SEST (15 objects) and 3.0 at IRAM (2 objects). For the 3-2/2-1- and 4-3/3-2-ratios the results are 1.8 (9 objects) and 1.1 (7 objects), respectively, at JCMT. One may conclude from this that up to the 3-2 line the intensity increases significantly with increasing J-levels. However, the exact increase with J-level is uncertain, since we find an intensity ratio in the 2-1 line between SEST and JCMT of 0.7 (4 objects), possibly indicating a discrepancy in the absolute calibration of this line at either or both telescopes. We find that there is a considerable spread in the intensity ratios (within each group), by more than a factor of three. Parts of this is certainly due to uncertainties in the calibrations (incl. pointing problems, etc.), but the different natures of the sources probably also add significantly to this.

For optically thin emission with equal beam filling one would expect values of 4, 2.3, and 1.8 for the 2-1/1-0, 3-2/2-1, and 4-3/3-1 line intensity ratios. Thus, our results indicate optically thin emission for the lower J-lines, whereas the higher ones start to saturate. It appears therefore that we observe a very different behaviour than in the case of Mira variables with optically thick envelopes, where a ratio of 2 is typical for the 2-1/1-0-ratio (Groenewegen et al. 1995). Groenewegen et al. also found large ratios for their sample of short period ($P<400^{\rm d}$), O-rich Miras. They argued that the CO excitation in thin shells is different, and that possibly radiative excitation could be more important than the one by collisions.