Radial velocity follow-up of \textit{Gaia} astrometric substellar companions: six confirmed brown dwarfs and 13 impostor binaries
With microarcsecond precision, \textit{Gaia} has made the astrometric discovery of substellar companions feasible. However, follow-up observations are needed to check on orbital solutions and rule out astrophysical false positives. We validate and characterise a sample of 20 \textit{Gaia} Data Release 3 (DR3) astrometric candidates for substellar companions, with the dual goal of identifying false positives and deriving robust physical parameters for genuine companions. We performed high-resolution spectroscopy using FIES, NIRPS, and NEID at the Nordic Optical Telescope, the ESO 3.6m telescope, and the WIYN Telescope, respectively. Double-lined spectroscopic binaries were identified as false positives, and surviving systems were characterised through joint \textit{Gaia} astrometry and radial velocity modelling. Thirteen of the candidates proved to be near-twin binary stars for which the astrometric motion of the center of light is small enough to mimic that of a single star in response to a substellar companion. We confirm that six companions are brown dwarfs with masses in the range ${\sim}26$--$68\,M_\mathrm{Jup}$, two of them for the first time. In contrast to earlier studies of lower-mass \textit{Gaia} candidates, we find that the astrometric orbital solutions are generally reliable to within the stated uncertainties.