Galactic Cepheids in the vicinity of the Sun have a residual line-of-sight velocity, or gamma-velocity, which shows a systematic blueshift of about 2 km/s compared to an axisymmetric rotation model of the Milky Way. This term is either related to the space motion of the star and, consequently, to the kinematic structure of our Galaxy, or it is the result of the dynamical structure of the Cepheids atmosphere. We aim to show that these residual gamma-velocities are an intrinsic property of Cepheids. We observed nine galactic Cepheids with the HARPS spectroscope, focusing specifically on 17 spectral lines. For each spectral line of each star, we computed the gamma-velocity (resp. gamma-asymmetry) as an average value of the interpolated radial velocity (resp. line asymmetry) curve. For each Cepheid in our sample, a linear relation is found between the gamma-velocities of the various spectral lines and their corresponding gamma-asymmetries, showing that residual gamma-velocities stem from the intrinsic properties of Cepheids. We also provide a physical reference to the stellar gamma-velocity: it should be zero when the gamma-asymmetry is zero. Following this definition, we provide very precise and physically calibrated estimates of the gamma-velocities for all stars of our sample. To understand this very subtle gamma-asymmetry effect, further numerical studies are needed. Cepheids atmosphere are strongly affected by pulsational dynamics, convective flows, nonlinear physics, and complex radiative transport. Hence, all of these effects have to be incorporated simultaneously and consistently into the numerical models to reproduce the observed line profiles in detail.
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