Gaia DR3 high radial velocity stars: Genuine fast-moving objects or outliers?

The third Gaia data release includes 33.8 million radial velocity measurements, extending to a magnitude of G_RVS = 14. To reach this magnitude limit, spectra were processed down to a signal-to-noise ratio (S/N) of 2. In this very low S/N regime, noise-induced peaks in the cross-correlation function can result in spurious radial velocity determinations. Quality filters were applied to the dataset to mitigate such artefacts as much as possible prior to publication. Nevertheless, the high radial velocity (HRV) stars -- defined here as those with radial velocities below -500 or above +500 km/s -- are so sparsely populated that even a few hundred spurious measurements can lead to significant contamination. The objectives of the present study are as follows: (i) to confirm or refute the radial velocity values of the order of one hundred Gaia DR3 HRV stars, (ii) to evaluate the rate of spurious radial velocities in the Gaia DR3 catalogue as a function of S/N and radial velocity, and (iii) to examine the properties of the genuine HRV stars. A total of 134 Gaia DR3 HRV stars were observed using the SOPHIE and UVES spectrographs. (abridged) Ground-based measurements confirm the Gaia DR3 radial velocities of 104 out of our 134 targets, and they refute those of the remaining 30. The combination of these data with the spectroscopic surveys mentioned above enabled an assessment of the rate of spurious measurements as a function of S/N and across three intervals of absolute value of the radial velocity. (abridged) The majority of these stars follow retrograde orbits. Their location in the energy-vertical component of the angular momentum diagram coincides with the region where several structures associated with past merging events have been identified: Sequoia, Arjuna and I'itoi, Antaeus, ED-2, and ED-3. It is likely that most of these HRV stars were accreted.