Envelope tomography of long-period variable stars - III. Line-doubling frequency among Mira stars

This paper presents statistics of the line-doubling phenomenon in a sample of 81 long-period variable (LPV) stars of various periods, spectral types a nd brightness ranges. The set of observations consists of 315 high-resoluti on optical spectra collected with the spectrograph ELODIE at the Haute-Prov ence Observatory, during 27 observing nights at one-month intervals and spa nning two years. When correlated with a mask mimicking a K0III spectrum, 54 % of the sample stars clearly showed a double-peaked cross-correlation prof ile around maximum light, reflecting double absorption lines. Several piece s of evidence are presented that point towards the double absorption lines as being caused by the propagation of a shock wave through the photosphere. The observation of the Balmer lines appearing in emission around maximum l ight in these stars corroborates the presence of a shock wave. The observed velocity discontinuities, ranging between 10 and 25 km s(-1), are not corr elated with the brightness ranges. A comparison with the center-of-mass (CO M) velocity obtained from submm CO lines originating in the circumstellar e nvelope reveals that the median velocity between the red and blue peaks is blueshifted with respect to the COM velocity, as expected if the shock move s upwards. The LPVs clearly exhibiting line-doubling around maximum light w ith the K0III mask appear to be the most compact ones, the stellar radius b eing estimated from their effective temperatures (via the spectral type) an d luminosities (via the period-luminosity relationship). It is not entirely clear whether or not this segregation between compact and extended LPVs is an artefact of the use of the K0III mask. Warmer masks (F0V and G2V) appli ed to the most extended and coolest LPVs yield asymmetric cross-correlation functions which suggest that line doubling is occurring in those stars as well. Although a firm conclusion on this point is hampered by the large cor relation noise present in the CCFs of cool LPVs obtained with warm masks, t he occurrence of line doubling in those stars is confirmed by the double CO Deltav = 3 lines observed around 1.6 mum by Hinkle et al. (1984, ApJS, 56, 1). 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, alt hough with a somewhat narrower profile. This is an indication that the shoc k is weaker in extended than in compact LPVs, which may also contribute to the difficulty of detecting line doubling in cool, extended LPVs.