  To derive space velocities of stars along the line of sight from wavelength
shifts in stellar spectra requires accounting for a number of second-order
effects. For most stars, gravitational redshifts, convective blueshifts, and
transverse stellar motion are the dominant contributors. We provide theoretical
corrections for the net velocity shifts due to convection expected for the
measurements from the Gaia Radial Velocity Spectrometer (RVS). We used a set of
three-dimensional time-dependent simulations of stellar surface convection
computed with CO5BOLD to calculate spectra of late-type stars in the Gaia RVS
range and to infer the net velocity offset that convective motions will induce
in radial velocities derived by cross-correlation. The net velocity shifts
derived by cross-correlation depend both on the wavelength range and spectral
resolution of the observations. Convective shifts for Gaia RVS observations are
less than 0.1 km/s for late-K-type stars, and they increase with stellar mass,
reaching about 0.3 km/s or more for early F-type dwarfs. This tendency is the
result of an increase with effective temperature in both temperature and
velocity fluctuations in the line-forming region. Our simulations also indicate
that the net RVS convective shifts can be positive (i.e. redshifts) in some
cases. Overall, the blueshifts weaken slightly with increasing surface gravity,
and are enhanced at low metallicity. Gravitational redshifts amount up to 0.7
km/s and dominate convective blueshifts for dwarfs, but become much weaker for
giants.
