High resolution spectroscopy for Cepheids distance determination. V.
  Impact of the cross-correlation method on the p-factor and the
  gamma-velocities
  The cross correlation method (hereafter CC) is widely used to derive the
radial velocity curve of Cepheids when the signal to noise of the spectra is
low. However, if it is used with the wrong projection factor, it might
introduce some biases in the Baade-Wesselink (hereafter 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. 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 misunderstood previous
calculation of the K-term of Cepheids. We observed eight galactic Cepheids with
the HARPS 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 derived in Nardetto et al. (2007). Their average value (or
gamma-velocity) are also compared to the center-of-mass velocities derived in
Nardetto et al. (2008). 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 gamma-velocity derived from the CC method is systematically
blue-shifted by about 1.0 +- 0.2km/s compared to the center-of-mass velocity of
the star. An additional blue-shift of 1.0km/s is thus needed to totally explain
the previous calculation of the K-term of Cepheids (around 2km/s). The new Pp
relation we derived is a solid tool for the distance scale calibration
(abridged).
