  The Rossiter-McLaughlin (hereafter RM) effect is a key tool for measuring the
projected spin-orbit angle between stellar spin axes and orbits of transiting
planets. However, the measured radial velocity (RV) anomalies produced by this
effect are not intrinsic and depend on both instrumental resolution and data
reduction routines. Using inappropriate formulas to model the RM effect
introduces biases, at least in the projected velocity Vsin(i) compared to the
spectroscopic value. Currently, only the iodine cell technique has been
modeled, which corresponds to observations done by, e.g., the HIRES
spectrograph of the Keck telescope. In this paper, we provide a simple
expression of the RM effect specially designed to model observations done by
the Gaussian fit of a cross-correlation function (CCF) as in the routines
performed by the HARPS team. We derived also a new analytical formulation of
the RV anomaly associated to the iodine cell technique. For both formulas, we
modeled the subplanet mean velocity v_p and dispersion beta_p accurately taking
the rotational broadening on the subplanet profile into account. We compare our
formulas adapted to the CCF technique with simulated data generated with the
numerical software SOAP-T and find good agreement up to Vsin(i) < 20 km/s. In
contrast, the analytical models simulating the two different observation
techniques can disagree by about 10 sigma in Vsin(i) for large spin-orbit
misalignments. It is thus important to apply the adapted model when fitting
data.
