Convective line shifts for the

Context. 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. Aims. We provide theoretical corrections for the net velocity shifts due to convection expected for the measurements from the Gaia Radial Velocity Spectrometer (RVS). Methods. 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. Results. 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-1 for late-K-type stars, and they increase with stellar mass, reaching about 0.3 km s-1 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 to 0.7 km s-1 and dominate convective blueshifts for dwarfs, but become much weaker for giants