The ratio of pulsation to radial velocity (the projection factor) is currently limiting the accuracy of the interferometric Baade-Wesselink method. This work aims at establishing a link between the line asymmetry evolution over the Cepheids pulsation cycles and their projection factor, with the final objective to improve the accuracy of the Baade-Wesselink method for distance determinations. We present HARPS high spectral resolution observations of nine galactic Cepheids having a good period sampling. We fit spectral line profiles by an asymmetric bi-Gaussian to derive radial velocity, Full-Width at Half-Maximum in the line (FWHM) and line asymmetry for all stars. We then extract correlations curves between radial velocity and asymmetry. A geometric model providing synthetic spectral lines, including limb-darkening, a constant FWHM (hereafter sigma_c) and the rotation velocity is used to interpret these correlations curves. For all stars, comparison between observations and modelling is satisfactory, and we were able to determine the projected rotation velocities and sigma_c for all stars. We also find a correlation between the rotation velocity (Vrot sin i) and the period of the star: Vrot sin i = (11.5 +- 0.9) log(P) + (19.8 +- 1.0) [km/s]. Moreover, we observe a systematic shift in observational asymmetry curves (noted gamma_O), related to the period of the star, which is not explained by our static model: gamma_O = (10.7+-0.1) log(P) + (9.7+-0.2) [in %] . For long-period Cepheids, in which velocity gradients, compression or shock waves seem to be large compared to short- or medium period Cepheids we observe indeed a greater systematic shift in asymmetry curves. (abridged)
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