Gaia DR2 in 6D: Searching for the fastest stars in the Galaxy

We search for the fastest stars in the subset of stars with radial velocity measurements of the second data release (DR2) of the European Space Agency mission Gaia. Starting from the observed positions, parallaxes, proper motions, and radial velocities, we construct the distance and total velocity distribution of more than $7$ million stars in our Milky Way, deriving the full 6D phase space information in Galactocentric coordinates. These information are shared in a catalogue, publicly available at this http URL To search for unbound stars, we then focus on stars with a median total velocity in the Galactic rest frame $> 450$ km/s. This cut results in a clean sample of $165$ sources with reliable astrometric parameters and radial velocities. Of these, $28$ stars have probabilities greater than 50 $\%$ of being unbound from the Galaxy. On this latter sub-sample, we perform orbit integration to characterize the stars' orbital parameter distributions. We find $2$ to $5$ hypervelocity star candidates, stars that are moving on orbits consistent with coming from the Galactic Centre, and $9$ hyper-runaway star candidates, coming from the Galactic disk. Surprisingly, the remaining unbound stars cannot be traced back to the Galaxy, including our two fastest stars (above $700$ km/s). These may constitute the tip of the iceberg of a large extragalactic population or the extreme velocity tail of stellar streams.