High resolution spectroscopy for Cepheids distance determination ⋆ III. A relation between γ-velocities and γ-asymmetries

Context. Galactic Cepheids in the vicinity of the Sun have a residual line-of-sight velocity, or γ -velocity, which shows a systematic blueshift of about 2 km s -1  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. Aims. We aim to show that these residual γ -velocities are an intrinsic property of Cepheids. Methods. We observed eight galactic Cepheids with the HARPS (High Accuracy Radial velocity Planetary Search project developed by the European Southern Observatory.) spectroscope, focusing specifically on 17 spectral lines. For each spectral line of each star, we computed the γ -velocity (resp. γ -asymmetry) as an average value of the interpolated radial velocity (resp. line asymmetry) curve. Results. For each Cepheid in our sample, a linear relation is found between the γ -velocities of the various spectral lines and their corresponding γ -asymmetries, showing that residual γ -velocities stem from the intrinsic properties of Cepheids. We also provide a physical reference to the stellar γ -velocity: it should be zero when the γ -asymmetry is zero. Following this definition, we provide very precise and physically calibrated estimates of the γ -velocities for all stars of our sample [ in km s -1 ] : -11.3 ± 0.3 [R TrA], -3.5 ± 0.4 [S Cru], -1.5 ± 0.2 [Y Sgr], 9.8 ± 0.1 [ β  Dor] , 7.1 ± 0.1 [ ζ  Gem] , 24.6 ± 0.4 [RZ Vel], 4.4 ± 0.1 [ $\ell$ Car] , 25.7 ± 0.2 [RS Pup]. Finally, we investigated several physical explanations for these γ -asymmetries like velocity gradients or the relative motion of the line-forming region compared to the corresponding mass elements. However, none of these hypotheses seems to be entirely satisfactory to explain the observations. Conclusions. To understand this very subtle γ -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.