A. B. Fokin

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 and brightness ranges. The set of observations consists of 315 high- resolution optical spectra collected with the spectrograph ELODIE at the Haute-Provence Observatory, during 27 observing nights at one-month intervals and spanning two years. When correlated with a mask mimicking a K0III spectrum, 54% of the sample stars clearly showed a double-peaked cross-correlation prole around maximum light, reflecting double absorption lines. Several pieces 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 light in these stars corroborates the presence of a shock wave. The observed velocity discontinuities, ranging between 10 and 25 km s 1 , are not correlated with the brightness ranges. 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. The LPVs clearly exhibiting line-doubling around maximum light with the K0III mask appear to be the most compact ones, the stellar radius being estimated from their eective temperatures (via the spectral type) and 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) applied 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 rm 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 conrmed by the double CO v = 3 lines observed around 1.6 m by Hinkle et al. (1984, ApJS, 56, 1). Moreover, the H 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 prole. This is an indication that the shock is weaker in extended than in compact LPVs, which may also contribute to the diculty of detecting line doubling in cool, extended LPVs.

Envelope tomography of long-period variable stars - II. Method

A tomographic method is described that makes it possible to follow the propagation of shock waves across the photosphere of long-period variable stars. The method relies on the correlation of the observed spectrum with numerical masks probing layers of dierent atmospheric depths. The formation depth of spectral lines is derived from synthetic spectra of non-variable red giant stars. When applied to Mira stars around maximum light, the tomographic masks reveal that the deepest photospheric layers are generally characterized by blueshifted absorption lines (attesting to their upward motion), whereas the uppermost layers generally exhibit redshifted absorption lines (indicating their infalling motion). Double absorption lines are found in intermediate layers, where the shock front is located. At later phases, the shock front is seen moving towards upper layers, until it leaves the photosphere.

Tomography of the Atmosphere of Long-Period Variable Stars

This paper presents a new tomographic technique to derive the velocity feld across the atmosphere of long-period variable (LPV) stars. The method crosscorrelates the optical spectrum with numerical masks constructed from synthetic spectra and probing layers of increasing depths. This technique reveals that the line doubling often observed in LPV stars around maximum light is the signature of the shock wave propagating in the atmosphere of these pulsating stars.

Tomography of the atmosphere of the Mira variable Z Oph

Abstract. The new tomographic technique devised by Alvarez et al. (2000) to explore the velocity field across the atmosphere of long-period variable stars (LPVs) is applied to the Mira variable Z Oph. The method cross-correlates the optical spectrum with numerical masks constructed from synthetic spectra and probing layers of increasing depths. This technique reveals that the line doubling often observed in LPVs around maximum light is the signature of the shock wave propagating in the atmosphere of these pulsating stars.

Stellar Parameters of the Post-AGB Star HD 56126

We discuss the stellar parameters ( M, L, T eff ) of a post-AGB star, HD 56126, deduced from observations and non-linear radiative pulsation models. We show that pure radiative pulsation models are in contrast with stellar evolution.