Hypervelocity stars (HVSs) unbound to the Galaxy can
be formed with extreme stellar interactions, for example close encounters
with supermassive black holes or in massive star clusters, supernova
explosions in binary systems, or the stripping of dwarf galaxies.
Observational evidence comes from measurements of radial velocities (RVs)
of objects crossing the outer Galactic halo and of tangential
velocities based on high proper motions (HPMs) and distances
of relatively nearby stars. I searched for new nearby HVS candidates and reviewed
known objects using their Gaia astrometric measurements. Candidates were selected with significant Gaia parallaxes
of $>$0.1\,mas, proper motions of $>$20\,mas/yr, and computed galactocentric tangential velocities $vtan\_g$$>$500\,km/s. The DR2 and DR3 samples of several thousand HVS candidates were studied with respect to their proper motions, sky distribution, number of observations, location in crowded fields, colour-magnitude diagrams, selection effects with magnitude, and RVs in DR3. The 72 most extreme ($vtan\_g$$>$700\,km/s) and nearest (within 4\,kpc) DR3 HVS candidates were investigated with respect to detected close neighbours, flags, and astrometric quality parameters of objects of similar magnitudes in DR3. The quality checks involved HPM objects in a global comparison and all objects in the vicinity of each target. Spurious HPMs in the Galactic centre region led to false HVS
interpretations in Gaia DR2 and are still present in DR3,
although to a lesser extent. Otherwise there is good agreement between
the HPMs of HVS candidates in DR2 and DR3.
However, HVS candidates selected from DR2 tend to have larger
parallaxes, and hence lower tangential velocities in DR3. Most DR3
RVs are much lower than the tangential
velocities, indicating that the DR3 HVS candidates are still
affected by underestimated parallaxes.
None of the 72 extreme nearby DR3 HVS candidates,
including three D$^6$ stars, passed all the quality checks.
Their tangential velocities may turn out to be lower,
but at least some of them still appear unbound to the Galaxy.