Abstract

In this third paper we determine the maximum possible turbulent motion for a Cepheid with an extended stellar atmosphere and a large pulsational amplitude, where we can expect to detect strong nonlinear phenomena (shocks, etc. ). Thus, we observed high resolution spectra of the classical Cepheid star X Cygni at two different spectral domains, one including Hot and the other one including the sodium D lines. In contrast to other classical cepheid stars (e.g. δ Cephei, ∊ Aquilae and S Sagittae), X Cygni shows that its pulsation has already the form of a progressive wave, looking at the photosphere (Fe I lines) and the higher level where the Na I (D) lines are formed. The main result of this paper is to point out that the amplification of the turbulence strongly depends on the initial turbulent state of the gas. Indeed, we have shown that the turbulence has increased greatly during the first (smaller) photo spheric acceleration while it practically has not changed during the following main acceleration. In addition this study shows that the amplification of the turbulence increases with the pulsation amplitude.