Envelope tomography of long-period variable stars - I. The Schwarzschild mechanism and the Balmer emission lines

This paper is the first one in a series devoted to the study of the dynamic s of the atmospheres of long-period variable (LPV) stars. Results from a tw o-month-long monitoring of the Mira variables RT Cyg and X Oph around maxim um light with the ELODIE spectrograph at the Haute-Provence Observatory are presented, The monitoring covers phases 0.80 to 1.16 for RT Cyg and phases 0.83 to 1.04 for X Oph. The cross-correlation profile of the spectrum of R T Cyg with a KO III mask confirms that the absorption lines of RT Cyg in th e optical domain appear double around maximum light. No line doubling was f ound in the optical spectrum of X Oph around maximum light, indicating that this feature is not common to all LPVs. This paper also presents the application to RT Cyg of a new tomographic(1) technique deriving the velocity field across the atmosphere by cross-correl ating the optical spectrum with numerical masks constructed from synthetic spectra and probing lavers of increasing depths. This technique reveals tha t both the temporal evolution of the line doubling, and its variation with depth in the atmosphere of RT Cyg, are consistent with the 'Schwarzschild s cenario'. This scenario relates the temporal evolution of the red and blue peaks of the double absorption lines to the progression of a shock wave in the atmosphere. The temporal evolution of the Balmer H alpha, H beta, H gamma and H delta e mission lines around maximum light is also presented for RT Cyg and X Oph. The velocity variations of H alpha and of the absorption lines are discusse d in the framework of two competing models for the formation of Balmer emis sion lines in LPV stars.