Not Gone with the Wind: Planet Occurrence is Independent of Stellar Galactocentric Velocity

We demonstrate that planet occurrence does not depend on stellar galactocentric velocity in the Solar neighborhood. Using Gaia DR2 astrometry and radial velocity data, we calculate 3D galactocentric velocities for 197,090 Kepler field stars, 1647 of which are confirmed planet hosts. When we compare the galactocentric velocities of planet hosts to those of the entire field star sample, we observe a statistically significant (KS p-value = $10^{-70}$) distinction, with planet hosts being apparently slower than field stars by $\sim$40 km/s. We explore some potential explanations for this difference and conclude that it is not a consequence of the planet-metallicity relation or distinctions in the samples' thin/thick disk membership, but rather an artefact of Kepler's selection function. Non Kepler-host stars that have nearly identical distances, temperatures, surface gravities, and Kepler magnitudes to the confirmed planet hosts also have nearly identical velocity distributions. Using one of these identical non-host samples, we consider that the probability of a star with velocity $v_{\mathrm{tot}}$ hosting a planet can be described by an exponential function proportional to $e^{(-v_{\mathrm{tot}}/v_0)}$. Using a Markov Chain Monte Carlo sampler, we determine that $v_0 > $976 km/s to 99% confidence, which implies that planets in the Solar neighborhood are just as likely to form around fast stars as they are around slow stars. Our work highlights the subtle ways in which selection biases can create strong correlations without physical underpinnings.