The observations presented in this paper show that a phase lag between metallic lines is present during the pulsation of RRLyr. It is small (between 1 and 2%) but, due to the high quality of our observations, it is clearly established. Thus, this observational result, reveals for the first time that the pulsation motion of the atmospheric layers localised just above the photosphere have the form of a running wave. Its amplitude is certainly appreciable, since for instance, the distance between two metallic layers is strongly variable and increases during the contraction.
Some effects associated with the three main shock waves detected in nonlinear pulsating models (Fokin & Gillet 1997), are observed within our new data. This confirms that the deep atmosphere of RR Lyrae, and certainly more generaly of RR Lyrae stars, is strongly affected by the nonlinear behaviour of the pulsation. In particular, the so-called ``early shock'', first theoreticaly discovered by Hill (1972), is indirectly detected by our observations.
This type of high quality observation provide us with a new opportunity to investigate the atmospheric structure of pulsating atmospheres of relatively large amplitude but also to give a new quantitative tool to check theoretical results of nonlinear models.
The authors would like to express their sincere thanks to Drs. A.B. Fokin and P. Mathias for valuable discussions on some aspects of this paper and for their constructive help. The work of MC has been done during the first year of a CNRS-post-doc fellowship (Centre National de la Recherche Scientifique, France).