5 Summary

The most striking result relative to the statistics of occurrence of the line-doubling phenomenon in a sample of 81 LPVs of various periods, spectral types and brightness ranges is the fact that the compact LPVs are more prone to exhibit the line-doubling phenomenon than large-size LPVs (at least when comparing their K0III CCFs). The possibility that this segregation is an artefact of the use of the K0III template may not be totally excluded, since warmer masks (F0V and G2V) applied to the most extended and coolest LPVs yield asymmetric cross-correlation functions. This suggests that line doubling is occurring in those stars as well. Although a firm conclusion on this point is hampered by the large correlation noise present in the CCFs of cool LPVs obtained with warm masks, the occurrence of line doubling in those stars is confirmed by the double CO $\Delta v = 3$ lines observed around 1.6 $\mu$m by Hinkle et al. (1984). Moreover, the H$\delta$ line in emission, which is another signature of the presence of shocks, is observed as well in the most extended stars, although with a somewhat narrower profile. This is an indication that the shock is weaker in extended than in compact LPVs, which may also contribute to the difficulty of detecting line doubling in cool, extended LPVs.

Stars with double absorption lines around maximun light exhibit S-shaped radial-velocity curves similar to the one observed for infrared lines.

A comparison with the center-of-mass (COM) velocity obtained from submm CO lines originating in the circumstellar envelope reveals that the median velocity between the red and blue peaks is blueshifted with respect to the COM velocity, as expected if the shock moves upwards.

Acknowledgements

RA benefits of a TMR "Marie Curie'' Fellowship at ULB. A.J. is Research Associate from the Fonds National de la Recherche Scientifique (Belgium). We thank J. Mattei for providing data from the AAVSO database. This program would not have been possible without the generous allocation of telescope time at the Observatoire de Haute-Provence (operated by CNRS, France). We tank S. Udry for providing us with F0V and G2V templates.