High-resolution spectroscopy for Cepheids distance determination V. Impact of the cross-correlation method on the p-factor and the γ-velocities

Context. The cross correlation method (hereafter CC) is widely used to derive the radial velocity curve of Cepheids when the signal to noise ratio of the spectra is low. However, if it is used with an inaccurate projection factor, it might introduce some biases in the Baade-Wesselink (BW) methods of determining the distance of Cepheids. In addition, it might affect the average value of the radial velocity curve (or gamma-velocity) important for Galactic structure studies. Aims. We aim to derive a period-projection factor relation (hereafter Pp) appropriate to be used together with the CC method. Moreover, we investigate whether the CC method can explain the previous estimates of the K-term of Cepheids. Methods. We observed eight galactic Cepheids with the HARPS(star star star) spectrograph. For each star, we derive an interpolated CC radial velocity curve using the HARPS pipeline. The amplitudes of these curves are used to determine the correction to be applied to the semi-theoretical projection factor. Their average value (or gamma-velocity) are also compared to the center-of-mass velocities derived in previous works. Results. The correction in amplitudes allows us to derive a new Pp relation: p = [-0.08 +/- 0.05] log P + [1.31 +/- 0.06]. We also find a negligible wavelength dependence (over the optical range) of the Pp relation. We finally show that the.-velocity derived from the CC method is systematically blue-shifted by about 1.0 +/- 0.2 km s(-1) compared to the center-of-mass velocity of the star. An additional blue-shift of 1.0 km s(-1) is thus needed to totally explain the previous calculation of the K-term of Cepheids (around 2 km s(-1)). Conclusions. The new Pp relation we derived is a reliable tool for distance scale calibration, and especially to derive the distance of LMC Cepheids with the infrared surface brightness technique. Further studies should be devoted to determining the impact of the signal to noise ratio, the spectral resolution, and the metallicity on the Pp relation.